Proceedings of the. 3rd International Conference on Innovation in High Performance Sailing Yachts. Cité de la Voile Eric Tabarly Lorient - France

Transcription

1 Proceedings of the 3rd International Conference on Innovation in High Performance Sailing Yachts Cité de la Voile Eric Tabarly Lorient - France Website:

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3 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France FOREWORD On behalf of the organizing committee, it is my great pleasure to welcome you all to the third edition of the conference INNOV SAIL. The close cooperation between the Cité de la Voile Eric Tabarly, Eurolarge Innovation and the French Naval Academy Research Institute made this conference exist and develop. This time again, INNOV SAIL has attracted a great interest worldwide, with a wide range of high quality papers and a large participation. We are glad to welcome both new and returning delegates, and I am particularly happy to see the participation of many students, proving that the topic is attractive. The event is now well established, and we are very glad to announce that we have concluded an agreement with the organizing committees of the two other famous conferences, High Performance Yacht Design Conference in Auckland and the Chesapeake Sailing Yacht Symposium in Annapolis to coordinate and alternate over the years the organization of our three conferences. We believe that cooperating and joining our forces will help develop and amplify the community working in yacht engineering and research and help fruitful collaborations. This goal to coordinate activities in the community and help networking has also driven the will to create the International Association of Yacht Engineering, to be announced during the conference. I believe that the field of high performance sailing is developing, and as the industry is growing and the racing competitiveness is increasing, it gives rise to more and more research activities. Actually, architects, boat builders, sail makers and the whole industry around sailing require more and more studies and optimising tools to gain performance, and I think that there are good opportunities for challenging research activities, because the problems issued from sailing are quite difficult to cope with and to model. Hence, some really advanced research is done in this field which does not often get the visibility and the acknowledgement it deserves in the scientific community. Aiming at increasing the visibility of the high quality research achieved on yachts, we agreed with the high impact peer-reviewed scientific journal Ocean Engineering to edit a special issue on yacht research with a selection of high scientific quality papers presented at the conference. With the huge amount of work needed to organize and run the conference, I would like to warmly thank all the organizing committee for their fantastic work, and all members of the scientific committee for their great and necessary help in reviewing the papers, increasing the conference quality and releasing information about the conference in their own country. Finally, I would like to warmly thank Lorient Agglomeration, Region Bretagne, Conseil General du Morbihan, and GIP Ecole Navale for their very much appreciated support which made the conference possible, as well as our sponsors, North Sails France, 727 Sailbags and AFM. I hope you will all have a very informative and interesting conference, as enjoyable as the previous ones. Patrick Bot Conference Chair

4 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France MANY THANKS TO OUR SPONSORS

5 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France Organizing Committee - Jean-Marc Beaumier, Cité de la Voile Eric Tabarly - Patrick Bot, Naval Academy Research Institute, France - Marie Coz, Naval Academy Research Institute, France - Yann Dollo, Eurolarge Innovation - Cécile Ezanno, Cité de la Voile Eric Tabarly - Christelle Marécaille, Eurolarge Innovation - Katia Meigney, Cité de la Voile Eric Tabarly - Sabrina Millien, Eurolarge Innovation Scientific Committee - Prof. Christophe Baley, Université Bretagne Sud, France - Prof. Dario Boote, University of Genova, Italy - Patrick Bot 1, Naval Academy Research Institute, France - Prof. Richard Flay 1, Yacht Research Unit, University of Auckland, New Zealand - Prof. Fabio Fossati 1, Politecnico di Milano, Italy - Prof. Kaï Graf, Yacht Research Unit, University of Applied Sciences, Kiel, Germany - Len Imas, Stevens Institute of Technology, USA - J.A. Keuning, Delft University of Technology, The Netherlands - Prof. Lars Larsson, Chalmers University of Technology, Sweden - William Lasher, Pennsylvania State University, USA - Prof. Yutaka Masuyama, Kanazawa Institute of Technology, Japan - Prof. Marc Rabaud, Université Paris Sud, France - Ignazio Viola, University of Newcastle, UK - Prof. Michel Visonneau, Ecole Centrale de Nantes, France - Sandy Wright, Wolfson Unit MTIA, UK 1 Editors of the special issue in Ocean Engineering

6 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France Session 1: Hydrodynamics TABLE OF CONTENTS Dagger-Board Evaluation for an IMOCA60 Yacht p. 1 I. Campbell, M. Owen and G. Provinciali Advancements in Free Surface RANSE Simulations for Sailing Yacht Applications p. 11 C. Böhm, K. Graf Database Building and Statistical Methods to Predict Sailing Yachts Hydrodynamics p. 23 L. Huetz, P.E. Guillerm A Simplified Method to Assess Acceleration Loads on Sailing Yacht Masts p. 35 A. Combourieu, F. Faloci, D. Boote, T. Pais Session 2: Hydrodynamics Numerical Study of Asymmetric Keel Hydrodynamic Performance through Advanced CFD p. 45 D. Mylonas, S. Turkmen, M. Khorasanchi Narrow Ship Wakes and Wave Drag for Planing Hulls p. 57 M. Rabaud, F. Moisy Session 3: Aerodynamics Conceptual Ideas on a Double Surface Sail Inflated by Dynamic Pressure p. 63 S. Brüns, H. Hansen, K. Hochkirch Comparison of Full 3D-RANSE Simulations with 2D-RANSE / Lifting Line Method Calculations for the Flow Analysis of Rigid Wings for High Performance Multihulls p. 71 K. Graf, A.V. Hoeve, S. Watin A Comparison of Downwind Sail Coefficients from Tests in Different Wind Tunnels p. 85 I. Campbell Session 4: Structure / Materials Smart Materials Application on High Performance Sailing Yachts for Energy Harvesting p. 99 S. Turkmen, D. Mylonas, M. Khorasanchi Long Term Immersion in Natural Seawater of Flax / Biocomposite p. 109 A. Le Duigou, A. Bourmaud, C. Baley, P. Davies Session 5: Aerodynamics Wind-Tunnel Pressure Measurements on Rigid Model-Scale Downwind Sails p. 119 Bot P., Viola I.M., Flay R.G.J., Brett J.S. Delayed Detached Eddy Simulation of Sailing Yacht Sails p. 129 I.M. Viola, S. Bartesaghi, T. Van. Renterghem, R. Ponzini

7 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France An Experimental Investigation of Asymmetric Spinnaker Aerodynamics Using Pressure and Sail Shape Measurements p. 145 D. Motta, R.G.J. Flay, P. Richards, D. Le Pelley Session 6: Fluid Structure Interaction - Aero-elasticity Numerical Study of a Fexible Sail Plan: Effect of Pitching Decomposition and Adjustments p. 155 B. Augier, F. Hauville, P. Bot, J. Deparday, M. Durand FSI Investigation on Stability of Downwind Sails with an Automatic Dynamic Trimming p. 165 M. Durand, C. Lothode, F. Hauville, A. Leroyer, M. Visonneau, R. Floch, L. Guillaume Development of Computational Fluid-Structure Interaction Method for Yacht Sails p. 173 F. Bergsma, N. Moerke, S. Zaaijer, H.W.M. Hoeijmakers Session 7: Fluid Structure Interaction - Hydro-elasticity Flutter of Racing Yacht Keels and Appendages p. 183 R. Balze and H. Devaux Dynamic Fluid Structure Interaction of a Foil p. 191 C. Lothodé, M. Durand, Y. Roux, A. Leroyer, M. Visonneau, L. Dorez An Unsteady FSI Investigation into the Cause of the Dismasting of the Volvo 70 Groupama 4 p. 197 W. Menotti, M. Durand, D. Gross, Y. Roux, D. Glehen, L. Dorez The Work Achieved with the Sail Dynamometer Boat Fujin, and the Role of Full Scale Tests as the Bridge between Model Tests and CFD p. 205 Y. Masuyama Estimating a Yacht s Hull-Sailplan Balance and Sailing Performance using Experimental Results and VPP Methods p. 215 M.P. Prince, A.R. Claughton Session 8: Tactics - Meteo - Simulator Sailing Site Investigation through CFD Modelling of Micrometeorology p. 223 M. Le Guellec, Y. Amice Optimal Yacht Routing Tactics p. 231 F. Tagliaferri, A. Philpott, I.M. Viola, R.G.J. Flay Development of an America s Cup 45 Tacking Simulator p. 239 A.K. Lidtke, L. Marimon Giovannetti, L.-M Breshan, A. Sampson, M. Vitti, D.J. Taunton

8 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France Posters Coupled Open Navigation and Augmented Reality Systems for Skippers p. 249 J.C. Morgere, R. Douguet, J.P. Diguet, J. Laurent. Lecco Innovation Hub Sailing Yacht Lab Project. A Sailing Research Infrastructure p. 255 F. Fossati, S. Muggiasca, I. Bayati, C. Bertorello. Study of the Influence of Singularities Created by Automated Fiber Placement on the Performance of Composite Materials for Naval Structures p. 261 M. Lan, D. Cartié, P. Davies,C. Baley. Tag Sheperd: a Low-Cost and Non-Intrusive Man Overboard Detection System p. 267 N. Le Griguer, J. Laurent, J.P. Diguet. Kite and Classical Rig Sailing Performance Comparison on a One Design Keel Boat p. 273 R. Leloup, K. Roncin, G. Blès, J.-B. Leroux, C. Jochum, Y. Parlier. Advanced Structural Analysis Method for Aeroelastic Simulations of Sails p. 281 S. Malpede, F. D Angeli, R. Bouzaid. Fluid-Structure Interaction Modelling on a Sail p. 289 K. Suresh, A.K. Sahoo, A. Tripathi.

9 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France AUTHOR INDEX Y. Amice B. Augier C. Baley , 261 R. Balze S. Bartesaghi I. Bayati F. Bergsma C. Bertorello G. Blès C. Böhm D. Boote P. Bot , 155 A. Bourmaud R. Bouzaid L.-M. Breshan J.S. Brett S. Brüns I. Campbell... 1, 85 D. Cartié A.R. Claughton A. Combourieu F. D Angeli P. Davies , 261 J. Deparday H. Devaux J.P. Diguet , 297 L. Dorez , 197 R. Douguet M. Durand , 165, 191, 197 F. Faloci R.G.J. Flay , 145, 231 R. Floch F. Fossati D. Glehen K. Graf... 11, 71 D. Gross L. Guillaume P.E. Guillerm H. Hansen F. Hauville , 165 K. Hochkirch H.W.M. Hoeijmakers A.V. Hoeve L. Huetz C. Jochum M. Khorasanchi... 45, 99 M. Lan J. Laurent , 267 A. Le Duigou N. Le Griguer M. Le Guellec R. Leloup D. Le Pelley J.-B. Leroux A. Leroyer ,191 A.K. Lidtke C. Lothode , 191 S. Malpede L. Marimon Giovannetti Y. Masuyama W. Menotti F. Moisy N. Moerke J.C. Morgere D. Motta S. Muggiasca D. Mylonas... 45, 99 M. Owen... 1 T. Pais Y. Parlier A. Philpott R. Ponzini M.P. Prince G. Provinciali... 1 M. Rabaud T. Van Renterghem P. Richards K. Roncin Y. Roux , 197 A.K. Sahoo A. Sampson K. Suresh F. Tagliaferri D.J. Taunton A. Tripathi S. Turkmen... 45, 99 I.M. Viola , 129, 231 M. Visonneau , 191 M. Vitti S. Watin S. Zaaijer

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11 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France DAGGER-BOARD EVALUATION FOR AN IMOCA60 YACHT Ian Campbell 1, Merfyn Owen 2, Giorgio Provinciali, Abstract. The IMOCA 60 Class has a complicated set of appendages: with canted and tilted keels, cambered daggerboards that can be designed to be fitted to the hull in different orientations along with toed-in and twin rudders that can also be configured in different orientations. Curved dagger-boards and straight boards with positive lift inducing dihedral angles have been used in number of recent IMOCA 60 designs and in other classes, principally multi-hulls. These were considered an option by the client for their new Open 60 design and so a research and development programme was instigated by Owen Clarke Design to compare new curved designs with conventional straight daggerboards optimised for upwind conditions. It was felt that the modelling of the trim of the yacht was very important to the calculation and sharing of loads between all of the appendages, and so our group chose to use a combination of one third scale high speed towing tanks tests and computational fluid dynamics (CFD), rather than CFD alone to investigate the relative performance between these dagger-board types. NOMENCLATURE, Leeway angle (degrees) TWA, True wind angle (degrees) TWS, True wind speed (knots) 1. INTRODUCTION There has been a good deal of discussion in recent years regarding the pros and cons of curved verses straight dagger-boards in the IMOCA 60 class. It was natural then that as part of the design package for Owen Clarke s latest Open 60 that a proportion of budget and time should be set aside to evaluate the relative performances of straight verses curves boards and to build on the previous test and CFD work that had already been undertaken by the group on various board configurations, angles and placement. This evaluation was undertaken as part of a wider study into Open 60 performance looking at the sharing of loads, affects of trim and various appendage designs and built on the one third scale testing undertaken for Ecover 3 in Before concentrating on dagger-board selection it s important to have an overview of the factors affecting the appendage design, the forces involved and why the experimental methods used were selected. Owen Clarke s current IMOCA60 design Acciona started with the known performance of their seven previous designs, including Gamesa (ex Ecover 3), compared to that of more recent Open 60 s from other designers. One of the parameters that had changed in recent IMOCA60 designs, including Ecover 3 and her sister-ship Aviva, is increasing fore and aft inclination of the canting keel pivot axis to DWL, or as it is sometimes described; keel tilt. The interaction between the multiple appendages on these craft has always been complex and the introduction of tilt has added a further factor. Tilt refers to the fact that at the hull/keel intersection the forward pivot bearing is placed higher than the aft. The result is that when the keel is canted the fin takes on a positive angle of attack, inducing lift, reducing righting moment, altering hull trim, rudder loading and changes the proportion of load sharing with the dagger-board when it is deployed. This was subject to the previous paper by the authors [2]. This change of trim induced by the keel foil can itself be altered by varying the size, angles and placement of the dagger-boards as well as by boat speed and sail selection. Sail selection and reefing has a significant effect on the sail force trimming moment, which itself has the affect of driving the bow down and increasing rudder load/drag. If this were not complicated enough, Open 60 s are able (depending on true wind speed/true wind angle and sail selection) to adjust their fore and aft trim using up to between 5,000 and 6,000kg of water per side and they alter the selected balance not just based on wind, but also sail selection and sea state. In addition, when reefed, lower sail centers of effort and the addition of water ballast increase the side force required to be developed by the appendages and we will show why this is important in dagger-board selection and their angles to the yacht s centerline and DWL. There are therefore a considerable number of interrelated factors that contribute to a matrix of experimental conditions one may look to investigate. Deriving accurately the change in trim of the yacht caused by these factors and therefore the actual attack angles/lift and drag forces on each of the foils and then squaring the circle so that the resulting correct trim is 1 Emeritus Fellow, Wolfson Unit MTIA 2 Owen Clarke Design - 1 -

12 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France derived for each equilibrium condition is a highly complex, crucial problem to solve. While as a group we have great confidence in the ability of CFD to derive foil loadings we felt that a combination of the use of CFD and scale model testing was likely to provide the best overall understanding of the problem. Using CFD in parallel with model testing would also provide us with data that we could compare and so we would not be reliant wholly on one source of information that might lead us up a blind alley and/or to false conclusions. The design team required greater confidence in any analysis than it was felt reliance on a single methodology (especially one without a long history of use in this boat type) could provide. The crux of the matter being that this was not an academic exercise, their recommendations would be acted upon by the client; months of work would be undertaken, many millions of Euros spent and ultimately one sailor would have to deal with the results. There was already anecdotal information from some of Owen Clarke s competitor s yachts that indicated; whilst increasing keel tilt improved reaching performance at say 16 knots, excessive tilt could lead to control problems when sailing downwind at higher speeds and while there was a requirement to improve performance this was not come at the cost of control or sea-keeping in difficult conditions. 1. DAGGER-BOARD SAILING CONDITIONS The dagger-boards are used to generate sideforce efficiently with low induced drag. It will be seen later that the tank tests reveal the cross-over speed is somewhere above 13 knots, where it becomes effective to raise the dagger-boards because the hull and canting keel can produce sideforce with a net drag saving by eliminating the profile drag of the dagger-boards. In the Vendee Globe race average speeds are: 11.4 knots with a Vendee record of 11.7 knots in the Atlantic heading south with the wind predominantly aft the beam. 11 knots in the Atlantic heading north with the wind predominantly forward of the beam knots in a straight line in the Southern Ocean with the Vendee record of 12.7 knots for the Pacific but actually a little below 15 knots over the ground. with curved daggerboards deployed, in order to test this hypothesis. For an Open 60, any vertical force generated by the canting keel or by a curved dagger-board has to benefit the yacht by reducing the drag of the hull in relatively slow conditions and not where light displacements yachts such as the AC72 catamarans or International Moth dinghies can become fully foil borne. 2. DESIGN TOOLS VPP calculations, based on hydrodynamic data from previous tank tests, were performed and some adjustments made to match the performance to that of Ecover 3. This tricky job was performed using the WinDesign VPP with customised features to match the canting keel effects on stability and different flotations to match the various water ballast configurations for the boat. Detailed output from the VPP was used to provide input to the tank tests and CFD calculation. While not directly relevant to the dagger-board design itself and prior to the appendage development phase, 1:7 scale model testing was undertaken over a two week period on the most promising candidate designs based on a range of representative hull forms from other designers working in the Volvo/IMOCA circuit. The 1:7 scale tank tests were conducted up to a scale speed range of 7 to 20 knots using only the canting keel without dagger-boards to simplify the test setup whilst enabling differences in hull hydrodynamics to be evaluated. The test programme also included variations in keel tilt, which helped establish its benefits. Of the six models tested, three were short-listed and the final winning model (a development of the OCD genre) was then used both to build the 1:3 scale model and the parallel CFD studies. The problem of load sharing when sailing upwind between the canting keel, dagger-board, rudder and hull is complex, as illustrated in Figure 1. Whilst the lift from the canting keel produces a smaller side force compared to the straight dagger-board, it produces a vertical force that offsets some of the boat s displacement. This can be considerable at higher speeds when the dagger-board is raised. Previous experience: computer modelling, tank testing and on the water in two boat testing had shown that the speeds of interest for dagger-board development are in the displacement and semi-displacement speed range for the yacht of 9 to 13 knots (Froude numbers of 0.35 to 0.50). In the higher speeds of 15 knots, sailing down the Atlantic and in the Southern Ocean, the daggerboards tend to be raised. However, to be sure of this we would include in our test Matrix runs at higher speeds - 2 -

13 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France Model tests were performed at 1:3 scale using a hull selected from the 1:7 scale tests and fitted with a canting keel and dagger-boards with an arrangement that allowed different keel tilt and board toe-in and board tilt angles to be set. These tests were conducted over a 3 week period and were aimed at running the model in its sailing equilibrium condition, with the correct running trim, sailing side force, sail force trimming moment and associated leeway for the water ballast configurations appropriate to each speed, ranging from 9 to 28 knots. Finally the scaled data from the tank tests was used to refine the hydrodynamic model in the VPP for use when conducting the sailing trials on the new boat. Figure 1 Side force contributions Setting the ratio of the side force developed by the dagger-board to that by the keel is a crucial factor in optimising the performance of the boat in any mode when the dagger-board is in use. Introducing curvature into the dagger-board results in it also producing some vertical force to complement that from the keel at lower speeds. The load sharing and associated variations in induced drag was investigated using a CFD panel code, which had the advantage over RANS codes that it enabled calculations to be performed for a large number of configurations in a cost effective and timely manner. The calculations over an extensive test matrix were simplified by performing them at fixed speed and trim. 3. VPP CALCULATIONS The normal VPP output is a polar diagram of boat speeds for a range of true wind speeds (TWS) and angles (TWA), as illustrated in Table 1, but underlying these speeds are the associated equilibrium hydrodynamic and aerodynamic forces and moments together with the optimised sail configurations. Important data for setting up tank tests or CFD calculations derive from the sail combinations, including masthead or fractional headsails and reef or twist settings that affect the centre of effort height. The water ballast condition affects the stability and combined with the associated sail combinations enable the sailing side force to be calculated. This is used in the tank tests to determine the equilibrium leeway angle. The CFD work undertaken over several months resulted in a selection of appendages which were then narrowed down to a select number which were then built for the 1:3 scale tests. As importantly using the results from this stage of the work we were able to narrow down the test matrix somewhat, discounting some areas and thereby saving time in the tank that could be dedicated to other work. The canting keel has to be a symmetrical section to operate on both tacks but the dagger-boards are asymmetric so can be a cambered section to minimise their viscous drag. The two dimensional code MSES was used to develop the dagger-board sections used throughout the work. The sections used early on in the preparatory work were developments of those already used on Ecover 3 and Aviva. At the point where candidate boards had been developed for the 1:3 scale testing Giorgio Provinciali developed sections that were optimised around the predicted lift forces which we were expecting the boards to produce, based on the predicted load sharing with the keel. Using MSES, a small adjustment to the final section used on Acciona was made, post scale model testing, once the final load sharing and board type selection had been made. Table 1 Boat speeds for different wind conditions Models were towed in the tank tests from close to the waterline (DWL) whereas the actual boat is driven by sails with a centre of effort approximately 40% of the sail height above DWL. This difference is compensated in the tank by applying trim moment using a ballast shift in the model to simulate the bow down trim from the thrust of the sails. The hydrodynamic drag increases significantly between upwind speeds of 11 knots and running speeds of 28 knots the resulting in large trim moments and it is important to simulate these correctly - 3 -

14 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France to ensure that the running trim of the model matches how the boat will actually sail, particularly when reefed downwind and/or flying masthead or fractional gennaker. It can also be seen from the VPP calculations that the sailing conditions where dagger-boards will be deployed, at boat speeds of less than 15 knots, are with true wind angles below 90 degrees and true wind speeds up to 16 knots. 4. CFD CALCULATIONS To investigate the upwind performance of a tilted keel with dagger-boards and as a precursor to further tank tests a CFD model was set up. This was created from a 3D Iges file of the hull and appendages, which included straight and curved dagger-boards. Prior to the 1:7 scale hull model testing, all CFD was carried out using straight boards with differing dihedral angles and angles to the centreline in order to develop an initial understanding of the relative trade off between the vertical lift force and induced drag. The dihedral angles ranged either side of vertical, as shown in Figure 2, with the positive angle boards acting in the same manner and creating vertical lift equivalent to those of curved boards. Figure 3 CFD model with curved dagger-board The raw data obtained from the panel code at the three different sinkages, with fixed trim, were interpolated to find the results at the desired displacements. The results were then further interpolated for three set values of total side force appropriate for the upwind sailing condition, with the force applied at a distance from the bow to represent the balance with the rig forces, i.e. at a fixed value for the yaw Moment. Variation of resistance with siderforce 2 Vs = 10 knots, tilt 4deg, toe-in 0deg 4.0 Figure 2 CFD model with straight dagger-board Resistance - kn All dagger-boards were cambered and so were asymmetric with handed port and starboard boards. Thus the dagger-boards would produce side force with the hull operating at zero leeway and without any toe-in angle Sideforce 2 - kn 2 The computed drag differences at sailing sideforce were generally less than 1% for an increase in vertical force of up to 3% of the displacement of the yacht. These variations due to dihedral were small enough to tank test the straight dagger-board at just one dihedral angle for comparison with the curved dagger-board. For later work, creating the foils to be used in 1:3 scale testing, curved boards were developed, as represented in Figure 3, that would more closely model the pressure field between the hull and foil. This was considered to be an advantage that the curved foil has compared to a straight foil with a large positive dihedral angle. Figure 4 Resistance from CFD calculations Resistance values from the set side force for one appendage configuration are shown plotted in Figure 4 against the square of side force. It can be seen that, just as with the tank data shown in Figure 11, this produces a linear trend. Force and moment values for each individual appendage and the hull were tabulated for variations in keel tilt and dagger-board toe-in angles at two different displacements. Also calculated were the leeway angle associated with the side force and drag, an example is shown in Figure

15 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France Leeway - deg Variation of leeway with dagger-board angle Vs = 10 knots Tilt 2 deg 3.0 Tilt 4 deg Tilt 6 deg deg deg 6 deg Dagger-board angle - deg Figure 5 Variation of leeway with toe in angle It can be seen that the leeway angle decreased as the toe-in angle of the dagger-board was increased and became negative at higher toe-in angles. Increasing the keel tilt also reduced the leeway angle and caused it to become negative. In effect the angle of attack of the flow over the keel and dagger-board was determined by the fixed side force value that was required and this set the hull leeway. The interesting data related to performance was the variation in resistance with keel tilt and dagger-board toe-in and an example is shown in Figure 6. The resistance ratios are compared to a base condition of 2 degrees keel tilts with 0 degrees dagger-board toe-in angle. It can be seen that increasing the dagger-board toe-in deduced the drag for all keel tilt angles but was required particularly for the highest keel tilt of 6 degrees. Drag ratio Variation of drag with dagger-board angle Vs = 10 knots Tilt 2 deg 1.06 Tilt 4 deg 1.05 Tilt 6 deg deg deg deg Dagger-board angle - deg Figure 6 Variation of drag with toe-in angle The upwind resistance variations due to keel tilt with the dagger-board were considerably smaller than those due to keel tilt obtained from the 1:7 scale tank tests without the dagger-board for the reaching condition. Care, however, needed to be exercised because the CFD calculations were run with fixed trim whereas the tank tests were conducted free to trim and the trim changes with keel tilt were significant at 16 knots and will have affected the resistance. CFD calculations gave the contributions of the individual appendages to the total forces and an example of the side force components with the keel tilt angle at 2 degrees is shown in Figure 7. It can be seen that approximately 80% of the side force was produced by the dagger-board and when the dagger-board toe-in angle was increased to 4 degrees the keel and rudder produced negative side force in order to achieve the required total equilibrium side force. This is considered to be a bad setting because the appendages are working in opposition rather than load sharing. The hull and bulb contributed approximately 8% of the side force and this only varied slightly with dagger-board angles. Sideforce - % Variation of sideforce with dagger angle Vs = 10 knots, keel tilt 2 deg Dagger-board angle - deg Rudder Keel Dagger-board Hull and bulb Figure 7 Variation of side force components with toe-in The CFD results also provided the vertical force produced by each appendage. An example is shown in Figure 8, with the vertical force expressed as a percentage of the displacement of the yacht. This illustrates two features: i) The vertical forces increase linearly with sideforce. This is because both are related to the pressure distribution over the appendages. The sailing sideforce is, however, determined by the stability of the yacht and, as is shown in Table 2, this was 12kN for the upwind sailing condition where dagger-boards would be deployed

16 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France ii) The keel produced a small vertical force at the sailing sideforce and the curved dagger-board significantly more but only approximately 5% of the yacht s displacement. The horizontal projected area of the keel was considerably greater than that of the dagger-board and the ratio of vertical to sideforce was approximately 1.4 from the keel but only 0.5 from the dagger-board. The higher vertical force produced by the dagger-board is attributed to its greater share of the overall sideforce. Verical force % Displacement Variation of vertical force with siderforce Vs = 10 knots, tilt 4deg, toe-in 0deg Keel Dagger-board Sideforce - kn Figure 8 Variation of vertical force with sideforce The CFD results confirmed sailing experience of the benefit of increasing the dagger-board toe-in angle, particularly with the higher keel tilt angle and provided the basis for setting the matrix of test configurations for the 1:3 scale tank tests. There were also small variations in the heeling moment associated with the dagger-board toe in and keel tilt which were included in the performance analysis. Figure 9 - Model with dynamometer The tank length enabled tests to be conducted at three upwind speeds or two reaching speeds within one run but the high speed running condition require the full length of the tank. This enabled good productivity from the tests Tests were conducted with the model in three conditions: Table 2 - Model test conditions Tests were conducted at two or three different leeway angles to enable the resistance to be interpolated at the sailing side force and the resistance data was plotted as shown in Figure 10. This figure contains data from upwind configurations with the same curved daggerboard set with 3 degrees keel tilt and tested with three different toe-in angles of 0, 2 and 4 degrees. 5. 1:3 TANK TESTS The tests were conducted in the CEHIPAR Calm Water Towing Tank at El Pardo Madrid. This tank is 320 m long, 12.5 m wide, and 6.5 m deep and the towing carriage operated at speeds up to 10 m/s. The model was mounted from the carriage using the Wolfson Unit s 3post dynamometer as shown in Figure 9. This had previously been used for testing 1:3 scale America s Cup Class yacht models of 24t displacement but was light enough to enable the light 9t sailing displacement of an IMOCA 60 hull to be towed and had suitable load ranges for the high speed runs

17 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France Variation of resistance with sideforce 2 curved dagger-boards with different toe-in Variation of resistance with sideforce 2 with straight and curved dagger-boards Resistance - kn kts 2 deg toe-in 11kts 2 deg toe-in 13kts 2 deg toe-in 0 deg toe-in 0 deg toe-in 0 deg toe-in 4 deg toe-in 4 deg toe-in 4 deg toe-in Linear (0 deg toe-in) Linear (0 deg toe-in) Linear (0 deg toe-in) Sideforce 2 - kn 2 3deg keel tilt Figure 10 Variation of resistance for different toein angles The speed was stepped up in the run down the tank enabling three speeds of 9, 11 and 13 knots to be tested at a fixed leeway. This resulted in the increase in side force with speed and associated increased values of resistance. Whilst it is an efficient means of testing it results in a group of data at lower side force values for the lower speeds and a higher group of values for the higher speeds, however the resistance values can be interpolated from both groups of data for the sailing side force, which is constant for all speeds, as given in Table 2. The change in toe-in angle produced relatively small differences in resistance, which was consistent with the CFD results. The resistance at the sailing sideforce was interpolated from the tests at different leeway angles to determine the best toe-in angle. Resistance - kn St DB 9kts St DB 11kts St DB 13kts "Cu DB 9kts" Cu DB 11kts Cu DB 13kts Sideforce 2 - kn 2 2 deg toe-in Figure 11 Comparison between straight and curved dagger-boards The cross-over boat speed where the curved daggerboards can be raised was investigated by testing at 14 and 15 knots with and without the dagger-board with the results shown in Figure 12. The increased wetted area of the dagger-board added form drag, represented by an increase in drag at zero side force but reduced the induced drag, represented by a lower slope in the linear fit through the data. The crossover between the bold lines without the daggerboards and the feint lines with represents equal drag but occurred at higher side force values with increasing speed. When the cross-over side force was greater than the sailing side force the performance would benefit from the lower drag without the dagger-board. The effect of toe-in angle on the resistance of straight dagger-boards was less than on curved boards. Comparisons were made between the straight and curved dagger-boards, as shown in Figure 11. These were made across the speed range and for two different heel angles of 15 and 22.5 degrees

18 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France Resistance - kn Variation of resistance with sideforce 2 with and without dagger-board K5 14 kts K5 15 kts No DB 14 kts No DB 15 kts No DB 16 kts Sideforce 2 - kn 2 Figure 12 Variation of resistance with side force Results are also included in Figure 12 from tests at 16 knots without the dagger-board. The resistance is significantly higher than at 15 knots but this is partly due to the higher displacement from the ballast condition shown in Table 2. The slope of the linear fit through the data is however significantly lower than at 15 knots, which represents the reduced induced drag at higher speeds. This can be partly attributed to the lower lift coefficient on the keel to produce the required side force. The yacht is also operating in a semidisplacement mode at 16 knots, with an associated Froude number of 0.61, and its trim angle increased by approximately 1 degree and it s heeled asymmetric waterplane also contributed to the side force, although with the tilted keel angle the sailing side force was produced with close to zero leeway, similar to the result from the 1:7 scale tank tests. The curved dagger-boards could also be tilted, in a similar manner to the canting keel. This tends to load the curved tip of the dagger-board, increasing its vertical lift in relation to its sideforce. An example of results from these tests is shown in Figure 13 and it can be seen that increasing the tilt increased the resistance. Resistance - kn Variation of resistance with sideforce 2 curved dagger-boards with different toe-in deg toe-in 0 deg tilt 14 knots 0 deg toe-in 0 deg tilt 15knots 4 deg toe-in 4 deg tilt Sideforce 2 - kn 2 3deg keel tilt Figure 13 Variation of resistance with side force for the curved dagger-boards with tilt The relative loading on the keel and dagger-board was also monitored during the tank tests using strain gauges to measure the bending moments and typical results are shown in Figure 14. Bending moment - Nm Variation of bending with sideforce With and without dagger-board Sideforce - N K5 bend K5bend DB K5 DB bend K5 bend 16 kts Figure 14 Variation of keel bending moment with side force The model scale bending moments from tests at 14, 15 and 16 knots are shown plotted against side force and linear trend lines have been fitted to the data. It can be seen that the data for 14 and 15 knots is distributed about a common line, although the leeway angles associated leeway angles differ. It can also be seen that - 8 -

19 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France the bending moment in the keel without the daggerboard is similar to the bending moment from the dagger-board with the keel, indicating that the keel generates the side force in the absence of a daggerboard. There were negative bending moments in the keel at lower values of side force with the dagger-board installed, which was similar to the CFD results shown in Figure UPWIND OPTIMISED STRAIGHT, VERSES CURVED BOARDS The previous sections describe the background necessary for an understanding of how we undertook the tests and how these led to the results related directly to the comparison of straight upwind optimised, verses curved boards. Having established from Figure 12 that the additional drag of the curved dagger-board being used for lifting the hull for a given required side force was substantially greater than that of a hull with daggerboard raised at 14, 15 and 16 knots, testing was then undertaken with an upwind optimised straight board at 9, 11 and 13 knots. The results are highlighted in Figure 11. The difference in vertical lift between the straight and curved dagger-boards was obtained from model scale heave measurements made in the tank and an example is shown in Figure 15. It can be seen that the heave change from static is negative, indicating that the hull has sunk as a result of its wave pattern. The heave becomes less negative with increasing sideforce due to the associated increase in vertical force and it can be seen that the curved dagger-board reduced the sinkage of the model by approximately 5mm. Heave - mm Variation of heave with sideforce with straight and curved dagger-boards St DB 9kts St DB 11kts St DB 13kts Cu DB 9kts Cu DB 11kts Cu DB 13kts Linear 30 (St 40 DB 11kts) Sideforce - kn 2 deg toe-in Figure 15 Variation of heave with side force between straight and curved dagger-boards At nine knots of boat speed which would be a very low speed, associated with 8 knots of true wind as shown in Table 1, for a dagger-board to be deployed there was little difference between the drag at equivalent side force and leeway of a curved and upwind optimised straight dagger-board. The difference was more pronounced at higher speeds. Testing was also undertaken at side loads greater than those capable of being developed by an Open 60 at any reef or ballast condition. In Figure 16, which contains data from the higher stability condition of 22.5 degrees heel, it can be seen only at a sideforces greater than 25 kn or sideforce squared of 625, did the curved daggerboard show signs of less induced drag. This could be attributed to the vertical lift from the board causing a reduction in the resistance of the hull sufficient to overcome the increased induced drag of the foil and so be more efficient. Resistance - kn Variation of resistance with sideforce 2 with straight and curved dagger-boards 22.5 deg heel St DB 9kts St DB 11kts St DB 13kts Cu DB 9kts Cu DB 11kts Cu DB 13kts Sideforce 2 - kn 2 Figure 16 Variation of resistance with side force between straight and curved dagger-boards at 22.5 degrees heel Although the differences in total resistance are small, the conclusion was that the straight board, optimised to develop side force upwind over all wind angles and wind speeds, was more efficient over a curved board or a straight board with an equivalent dihedral angle. This result has also assumed that boards are of equivalent weight and so given the requirement that the IMOCA rule requires boards to be in the raised position when measured, result in the same bulb weight. This is not the case however. The curved or heavily angled dihedral board needs to be longer to generate the same side force. The increase in board weight related to length is negligible however compared to the increased weight of board (and internal structure of the yacht) - 9 -

20 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France required to allow a board to be used at higher reaching boat speeds. For example; engineering a board at stall, at a boat speed of sixteen knots as opposed to a speed of thirteen knots would require a 50% increase in design load. There are significant drivers therefore, discounting potential damping effects of curved boards in waves,to keep dagger-boards in IMOCA 60 s as light as the their required performance envelope will allow. 7. CONCLUSIONS The combination of tank tests and CFD panel codes enabled a wide range of appendage test configurations to be investigated across a wide range of speeds. The 1:7 scale tank tests were used to compare hulls but also provided information on the beneficial reduction in resistance at semi-displacement speeds due to tilting the fore and aft axis of the canting keel. The CFD panel code calculations provided information on the relative loading of the keel and dagger-board for the upwind sailing condition with variations of toe-in angles and keel tilt, albeit at fixed trim. The results of which were used to develop appendages and a test matrix for 1:3 scale model testing, cross-check/verify results during testing and refine dagger-board design post testing. The 1:3 scale tank tests produced similar results to the CFD calculations for the upwind keel and dagger-board combinations, mitigated risk in decision taking and provide substantial confidence in the decision taken regarding the dagger-board selection and the keel tilt angle for the Open 60, Acciona. Although in ORMA 60 s, where lift producing devices clearly work well, in IMOCA 60s one is operating at considerably lower side forces (proportional to righting moment) and at higher displacements. The relationship therefore between additional induced drag from a lifting foil and the reduction in displacement of the hull are quite different. We were able to show in Figure 16 that only at an unrealistic value of side force were we able to produce a situation whereby an IMOCA 60 would benefit in reaching conditions in flat water from utilising lift inducing dagger-boards. That being said, from a practical point of view, the percentage deltas/differences between dagger-boards that are designed to provide lift as opposed to boards optimised for upwind use are not so significant that they would detract significantly from the performance of a yacht in a range of conditions. The final conclusion for the Acciona team was that there appeared to be no likely performance driven reason to select a heavier more expensive dagger-board type. development and acknowledgement is given for their permission to publish. Thanks are also given to the staff at CEHIPAR and ACCIONA for their assistance in conducting the 1:3 scale tests References 1. Ward B. & Cochran C., Development of the Volvo Ocean 65, 21 st Chesapeake Sailing Yacht Symposium, Annopolis MD USA, March Campbell, I., Owen M. & Provinciali G., Tuning of appendages for an IMOCA60 yacht, 4 th High Performance Yacht Design Conference, Auckland NZ Claughton. A R & Oliver C (2004), Design considerations for canting keel yachts, 18th International HISWA Symposium on Yacht Design and Yacht Construction, Amsterdam, Campbell, I., Robinson, J. & Brown, M (2002), The accuracy and repeatability of tank testing from experience of ACC yacht development, High Performance Yacht Design Conference, Auckland, New Zealand, RINA, December G. Delhommeau (1993) Wave resistance code REVA, Cours de la 19th WEGEMT School, Ecole Centrale de Nantes, Septembre G. Delhommeau (2002), La simulation mécanique en hydrodynamique : application en ingénierie navale", Chapitre 9, pp , "CAO et simulation en mécanique", Editions Hermès, Lavoisier, 2002, ISBN Maes F. (2006), An experimental study of the hydrodynamics of a yacht with a canting keel and forward rudder, 19th International HISWA Symposium on Yacht Design and Yacht Construction, Amsterdam, Acknowledgements The work in this paper was commissioned by Owen Clarke Design as part of their ongoing research and development programme into IMOCA60 design

21 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France ADVANCEMENTS IN FREE SURFACE RANSE SIMULATIONS FOR SAILING YACHT APPLICATIONS Christoph Böhm, Delft University of Technology, NL / Yacht Research Unit Kiel, GER, christoph.boehm@yru-kiel.de Kai Graf, University of Applied Sciences Kiel, GER / Yacht Research Unit Kiel, GER, kai.graf@fh-kiel.de The analysis of yacht hulls performance using RANSE based free surface simulations has become an accepted approach over the last decade. Access to this technology has been eased by the development of user-friendly software and by the increase of computational power. Results are widely accepted as superior to previous non-viscous approaches and have to compete with towing tank results in terms of accuracy. However, many practical applications suffer from a numerical smearing of the free surface interface between air and water which can be described as numerical ventilation. This problem occurs when the intersection between bow and calm water surface form an acute angle and is further pronounced if the stem is rounded or blunt. It is therefore especially linked to sailing yacht applications. The problem manifests itself as a non-physical suction of the air-water mixture under the yacht hull, causing a significant underprediction of viscous resistance. While this is the easily observable appearance of the problem, a second issue is its effect on wave resistance. It can be shown that wave damping is significantly increased, causing a prediction of wave resistance which is also too low. The paper provides a review of the Volumeof-Fluid method. It discusses the resultant implications for practical applications. A remedy to circumvent the problem is described and its impact on the accuracy of the result is shown. Simulations on an identical appended hull with and without interface smearing are compared. Effects on free surface visualization and numerical accuracy are shown. The paper finishes with a thorough verification and validation of a fully appended yacht in accordance with ITTC standards. NOMENCLATURE (1 + k) Form factor (-) CFL Courant number (-) C D Drag coefficient (-) C L Lift coefficient (-) C T Total resistance coefficient (-) C k Correction factor (-) E Comparison error (-) Fn Froude number (-) P k Order of accuracy (-) R k Convergence ratio (-) Rn Reynolds number (-) S Simulation results (-) T Truth (-) U SN Numerical uncertainty (-) U P Parameter uncertainty (e.g. iteration (-) number I, grid size G, time step T ) V Volume (m 3 ) α i Volume fraction of fluid i within a (-) cell δk error estimate with sign and magnitude of kth parameter (-) δ p Parameter error (e.g. iteration number (-) I, grid size G, time step T ) δ S Simulation error (-) δ SM Simulation modeling error (-) δ SN Simulation numerical error (-) ɛ ijk Solution change (-) λ Scale factor (-) S Surface vector (m 2 ) n Surface normal vector (-) v velocity vector (m.s 1 ) v b grid velocity vector (m.s 1 ) φ C normalized value of central node (-) w.r.t. face f φ C normalized face value (-) r k refinement ratio of parameter k (-) Subscripts f Cell face Corrected error or uncertainty C 1 Introduction During the last decade RANSE based viscous free surface simulations around ship hulls have gained a certain degree of maturity. Their capability to produce reliable data which

22 can compete with towing tank experiments has been proved, e.g. by the Gothenburg 2010 Workshop on Ship Hydrodynamics [5]. The rapidly developing availability of computational power has increased the popularity of this kind of CFD technology and the access to it has been eased by software packages which guide the user through the pre-processing procedure. The once time-consuming procedure of creating a computational grid has been improved by new meshing techniques which can reliably handle complex geometries and allow to tailor the mesh such that it meets the special needs of ship hydrodynamics. These advances in computational power and numerical techniques have changed the challenge in CFD towards achieving results that are within an expected uncertainty. As mentioned above, verifications and validations for ship hydrodynamics can be found in literature and benchmark cases including geometries are available. Unfortunately the same does not hold true for yacht hydrodynamics were validations are rare and usually non-public. This might change in the future since results and geometries of the Delft Systematic Yacht Hull Series (DSYHS) have recently become publicly available. 2 Motivation An attempt of the authors to validate RANSE CFD against towing tank results of an America s Cup Class Version 5 boat (ACCV5) [1] showed good results at time of publication. Resistance in non-lifting conditions was resolved to -6.2% of the Experimental Fluid Data (EFD), whilst lifting condition proved to be a problem with drag and lift deltas of -2.5% and 19% respective. With the above mentioned advancements in RANSE CFD these simulations have been repeated including more recent free surface modeling and body motion techniques and a larger and apparently better suited computational grid. However, the results did not reflect the expected improvements, indeed they were even worse than before with differences between CFD and EFD resistance curves of approximately -8%. This obviously led to the question why these behavior occurred. In general, single phase RANSE simulations tend to over-predict drag values if grid resolution is not sufficiently small. This behavior is not absolutely transferable to free surface ship flows, were a insufficient resolution of the wave pattern might also lead to an under-prediction of drag. Nonetheless, under-prediction of drag hints to look at modeling errors. Figure 1 illustrates the volume fraction of water values on the hull. Normally one would expect that these values are zero in the air region, one in the submerged area of the hull and between zero and one in a small region around the free surface interface. In the vicinity of a sharp in- Figure 1: VOF terface, this region should not significantly extend over more than three cells. Figure 1 clearly shows that this not the case. Instead volume fractions are smeared over the complete hull, expect around the appendages and in their wake. This clearly indicates a behavior which is sometimes referred to as numerical ventilation but can be shown to be a smeared free surface interface. Due to the nature of the treatment of physical properties of flow phase within the VOF (Volume-of-Fluid) model, this will lead to smaller resistance values. It has to be highlighted that the interface smearing as described above has only been encountered for specific floating bodies. These bodies have in common that they share a rather blunt bow which forms a small, acute entrance angle with the waterline. For conventional vessel which normally have sharp bow with a right angle at the water line, this problem does not occur. It is therefore kind of yacht-specific. 3 Volume-of-Fluid method The Volume-of-Fluid (VOF) method was introduced by Hirts and Nicols [3]. It is an Interface Capturing Methods without reconstruction and thus does not treat the free surface as a sharp boundary. Instead the calculation is performed on a fixed grid, and free surface interface orientation and shape is calculated as function of the volume part of the respective fluid within a control volume (CV). The VOF method employs the concept of a equivalent fluid. This approach assumes that the (two) fluid phases share the same velocity and pressure fields allowing to solve the same set of governing equations describing momentum and mass transport as in a single phase flow. The Volume fraction α i describes to which level the cell is filled with the respective fluid. The free surface is then defined as the isosurface at which the volume fractions take the value of 0.5. It is important to note, that this location is not at the control volume center but rather interpolated to the geometrical value. To simulate wave dynamics, one has to solve an equation for the filled fraction of each CV additionally to the conservation equations for mass and momentum. Assuming incompressible flow, the transport equation of volume fractions α i is described by the following conservation equation: α i dv + α i (v v b ) nds =0 (1) t V S The physical properties of the equivalent fluid within a control volume are then calculated as functions of the physical properties of the phases and their volume fractions. Strict conservation of mass is crucial, but this is easily obtained within this method as long as the sum of all volume-fractions per cell is 1. The critical issue for this kind of methods is the discretization of the convective term. Low-order terms like for instance 1st order upwind are known to smear the interface and introduce an artificial mixing of the two fluids. Therefore higher order schemes are preferred. The goal is to derive schemes which are able to keep the interface sharp and produce a monotone profile across it. Development of differencing schemes has been the pinnacle of research in the fields VOF methods for many years. Consequently a large

23 number of schemes is available and successfully used in different codes. The vast majority of these schemes is based on the Normalized Variable Diagram (NVD) and the Convection Boundedness Criterion (CBC) introduced by Leonard [6]. 3.1 HRIC Scheme The HRIC scheme (High Resolution Interface Capturing Scheme) is one of the most popular advection schemes and widely used in many CFD codes. It has been developed by Muzaferija and Peric [8, 10, 9]. Like most other schemes, it is based on a blending of bounded upwind and downwind schemes. The aim is to combine the compressive properties of the downwind differencing scheme with the stability of the upwind scheme. The bounded downwind scheme is formulated as: φ C if φ C < 0 2 φ f = φ C if 0 φ C if 0.5 φ (2) C 1 φ C if 1 φ C Since the amount of one fluid convected through a cell face shall be less or equal to the amount available in the donor cell, the calculated value of φ f is corrected with respect to the local Courant number (CFL).The CFL is calculated by employing the the velocity at the cell face v f, the surface vector S f, the respective cell volume V f and the local time step size dt as follows: CFL = v f S f dt (3) V f The correction takes the form of (4) and effectively controls the blending between HRIC and UD scheme with two limiting Courant numbers C L and C U which normally takes values of 0.5 and 1.0 respective 0.3 and 0.7. φ f ( if CFL < 0 φ f = φ C + φf φ ) CU CFL C C U C L if C L CFL < C U φ C if C U CFL (4) Effectively this correction implies that the HRIC scheme is used for a CFL smaller than the lower CFL limiter and UD scheme for CFL equal or greater than the upper CFL limiter. Between those values a blending of both schemes is used. This correction is applied to improve robustness and stability when large time variation of the free surface shape is preset and the time step is too big to resolve it. After this correction φ f experiences a final modification based on the interface angle, which is the angle θ between between the normal of the free surface interface n and the cell surface vector S f. This final modification reads: φ f = φ f (cos θ) C θ + φ C (1 cos θ) C θ (5) Here C θ = represents an angle exponent. Its default value according to [9] is The final cell face value is calculated as: φ HRIC f = φ f (φ D φ U )+φ U (6) As a consequence of the modifications due to interface angle and local Courant number, the NVD can take different forms. For the three different blending states depending on local CFL, Figure 2 illustrates the possible forms of the HRIC scheme with respect to the interface angle θ. The areas shaded in red represent the possible forms the scheme can take depending on the angle factor for the respective local Courant number. This kind of blending strategy is more or less the same for all interface capturing schemes, so care has to be taken when modeling free surface flows to avoid unwanted switching to a lower resolution which is often accompanied with interface smearing. Figure 2: (HRIC) NVD of High Resolution Capturing Scheme 4 Theoretical Test Case The theoretical review of the HRIC revealed that the encountered interface smearing is most probably related to the use of high Courant numbers. A modifier was found which implies that the HRIC scheme is used for a CFL smaller than the lower CFL limiter and UD scheme for CFL equal or greater than the upper CFL limiter. Between those values a blending of both schemes is used. From a theoretical point of view, the sole purpose of the correction of the HRIC scheme for local CFL is to improve robustness. If unsteady phenomena like slamming and or seakeeping are of interest, local Courant Figure 3: Sketch of test case setup

24 Number should be inherently lower than 0.5 anyway. If robustness is not problematic then this switch should be of no interest for calculation which seek a steady state solution. Since simulations mimicking towing tank procedures seek such a steady state solution, the HRIC scheme is modified such that the switch is effectively removed. If this assumption is true, this would remove the necessity to keep Courant number below 0.5 for even the smallest cell. The impact of this on practical applications is vast because it has the potential to significantly reduce computational effort by allowing larger time step sizes. To control the validity of this assumption a test case has been constructed. Aim of the test case is to produce a worst case scenario which makes it possible to judge if the modified differencing scheme can cope with the situation. From a theoretical point of view, the case which would produce the highest amount of numerical diffusion and thus the highest amount of interface smearing is a flow through a quadratic grid cell at an angle of 45. Therefore a 2D Cartesian grid has been build which consists of 128 x 128 grid cells with edge length of 0.5m. Total edge length of the domain is 64m. Initial volume fraction distribution is such that the lighter fluid (air) occupies the upper left triangle of the domain (blue) whilst the heavier fluid (water) is found in the lower right side (red). Inflow conditions for volume fraction have been set such that this state should remain within the simulation. Outlet has been set to Neumann conditions. A sketch of the setup is depicted in Figure 3. Depending on the local Courant number, the HRIC scheme switches between: 1. A pure HRIC scheme if CFL < A linear between HRIC and UD scheme if 0.5 CFL A pure UD scheme if CFL > 1.0 The influence of these different states on the sharpness of the interface is tested by varying flow speed and time step size such that the relevant criteria is fulfilled. First, CFL is set to 0.3 resulting in a pure HRIC scheme (Figure 4a). Even though the flow direction with respect to cell faces is unfavorable, the HRIC scheme is able to resolve the sharpest interface possible within the VOF method (1 cell). Next the CFL is increased to 0.75, resulting in 50% blend between HRIC and UD (Figure 4b). This blend is also still sufficient to retain the sharp interface and therefore gives a valid solution. An explanation for this behavior can be found in the blending strategy depending on interface angle. As depicted in Figure 2, the difference between the pure HRIC and the blended HRIC is reasonably small for a cell flow angle of 45 which explains the similar results. Finally, flow speed and time step size of the unsteady simulation are set to values such that the Courant Number in the entire domain is 3.0. This leads to switching to a pure Upwind Differencing Scheme within the HRIC scheme. As a result the interface between air and water becomes severely smeared and is forming a cone-like shape starting from inlet towards outlet (Figure 4c). Now the HRIC scheme is modified by removing the CFL dependency. The Courant number is kept at 3.0 and the simulation repeated. Figure 4d illustrates the result which clearly shows that this modification al- Figure 4: Impact of HRIC modes on free surface resolution lows using higher CFL numbers whilst a sharp interface is retained. This allows the conclusion that the modification of the HRIC scheme is well suited to simulate free surface flows at higher Courant numbers, allowing to converge faster towards a steady state solution. 5 Validation & Verification against Towing Tank data In most cases validations are conducted by comparing simulation results with trusted towing tank data. Deviations from experimental data are corrected by grid refinements until a acceptable agreement between EFD and CFD is found. However, this approach can lead to false confidence in the results if modeling or grid errors are present. Therefore, validation & verification are conducted here with a formal approach which allows to draw additional conclusions with respect to error types and error sources. First at all a short definition of the terms verification and validation is necessary: Verification includes the assessment of numerical uncertainty, magnitude and sign of numerical error (if possible) and uncertainty in error estimation. Validation is the assessment of uncertainty of the simulation model by means of experimental data plus the assessment of the modeling error itself. The verification & validation procedure will be carried out in accordance with recommendations of the ITTC regarding Uncertainty Analysis in CFD [4]. For a detailed description see also Stern et al. [11, 12]. The simulation error δ S is defined as the difference between simulation result S and reality

25 or truth T. It consists of the modeling error δ SM and the numerical error δ SN. Unfortunately δs can never be determined exactly since instead of T only experimental results are available which also contain a certain level of uncertainty. δ S = S T = δ SM + δ SN (7) For some cases magnitude and sign of the numerical error can be estimated, leading to corrected numerical uncertainty U SC N. For the uncorrected case only the numerical uncertainty U SN is assessed. Therefore the numerical error δ SN is decomposed into contributions from iteration number δ I, grid size δ G, time step δ T and other parameters δ P. With uncertainty U as described above this gives the following expression: U 2 SN = U 2 I + U 2 G + U 2 T + U 2 P (8) For validation purpose the comparison error E between the benchmark experimental data D and the simulation result S is determined in order to asses modeling uncertainty U SM. E = D S = δ D (δ SM + δ SN ) (9) To determine if validation of a value has been achieved, comparison error E is compared with the validation uncertainty U V. U 2 V = U 2 D + U 2 SN (10) If E < U V, than the combination of all errors in both simulation and experimental data is smaller than the validation uncertainty. Then validation has been achieved for this validation uncertainty level. In the case that U V << E, the modeling error δ SM can be used to achieve modeling improvements. 5.1 Verification Procedure In the course of the verification process a grid convergence study has to be conducted. In order to do this it is necessary to use a minimum of three grids which have been uniformly refined with an increment Δx k such that constant refinement ratio r k exits. r k = Δx k 2 Δx k1 = Δx k 2 Δx k2 = Δx k m Δx km 1 (11) ITTC Guidelines recommend refinement ratio r k between 2 and 2. Throughout this work ratios of 1.5 and 2 have been used. Next a convergence ratio R k is defined to give information about convergence respective divergence of a solution. It is defined as follows: ɛ 21k = S k2 S k1 ɛ 32k = S k3 S k2 (12) R k = ɛ 21k /ɛ 32k with ɛ ijk as the solution changes for the input parameter k between three solutions ranging from fine S k1 to coarse S k3. According to the ITTC guidelines [4], three different cases are distinguished: (i) Monotonic convergence: 0 <R k < 1 (ii) Oscillatory convergence: R k < 0 i (iii) Divergence: R k > 1 (13) In the case of (i) the Generalized Richardson Extrapolation is used to assess the uncertainty U k or the error estimate δ k and the corrected uncertainty U kc. For oscillatory convergence (case (ii)) the uncertainty U k is estimated by determining the error between minimum and maximum of the oscillation. In the case of divergence (iii) it is not possible to estimate errors or uncertainties Generalized Richardson Extrapolation As stated above, in case of monotonic convergence generalized RE is used to determine the error δk with respect to refinement ratio r k and order-of-accuracy P k. Usually δk is estimated for the finest solution of the input parameter m =1 only. With number of available solutions m = 3 only the leading-order term of the error may be evaluated. This gives the following equations for δk andp k. δ k 1 = δ RE k1 = ɛ 21 k r p k k 1 (14) p k = ln (ɛ 32 k /ɛ 21k ) ln (r k ) (15) Unless the solution is in the asymptotic range, equation (15) only gives a poor estimation of the order-of-accuracy. Therefore a correction factor C k is used to include the effect of higher-order terms priory neglected. C k is defined as follows: C k = rp k 1 r P (16) kest 1 The corrected error δk 1 is defined by combining equations (14) and (16) ( ) δk 1 = C k δre ɛ21k k1 = C k r p k k 1 (17) Depending how close the corrected error δk 1 is to the asymptotic range (how close C k is to 1) the expression to assess the uncertainties take different forms. If C k is sufficiently greater than one and lacking confidence only U k is estimated by the following formula: U k = C k δre (1 k1 + Ck ) δre k1 (18) For C k being sufficiently smaller than one the ITTC recommends to use expression (19) to assess U k. U k = δre (1 k1 +2 Ck ) δre k1 (19) If C k is sufficiently close to 1, the error δk can be estimated. This allows to determine a corrected solution S C and a thus a corrected uncertainty U kc. U kc = (1 C k ) δre k1 (20)

26 5.2 Validation Procedure As stated in section 5, validation is defined as a process to the model uncertainty U SM and, if possible, sign and magnitude of the modeling error δ SM itself. This is done by using experimental data to compare the simulation results with. Thus the error in the experimental data has to be considered, making it easier to validate simulations if the experimental error is large. It must thus be noted that the level of validation is strongly depended on the quality of the comparison data. The validation procedure is based on the relation between validation uncertainty U V, predefined programmatic validation requirement U reqd and comparison error E. These three variables may form the following six combinations: E <U V <U reqd E <U reqd <U V U reqd < E <U V U V < E <U reqd U V <U reqd < E U reqd <U V < E (21) In cases 1-3 of(21) the results are validated. Validation is achieved at the level of validation uncertainty U V. This means that the comparison error is below the noise level resulting in an impossibility to estimate error due to modeling assumption δ SMA. In the case of 1, the validation level is also below U reqd which makes the validation successful from a programmatic point of view. For case 4-6 the comparison error is above the noise level. Sign and magnitude of E can be used to estimate δ SMA. In the fourth case the validation is achieved at E level with respect to the used software. 5.3 Grid Convergence Studies on ACCV5 boat for nonlifting cases Verification and validation is performed on the geometry of Americas Cup Class Version 5 boat (ACCV5) for which experimental towing tank data is available. These boats have a rather complex geometry which besides hull, keel fin and rudder also includes a trim tab for the keel and a ballast bulb with wings. Since model scale λ=3, which is rather close to full scale compared with tank models for conventional vessels, it was decided that it is possible to do the validation in full scale. Therefore experimental data have been transformed to full scale by employing a modified version of the ITTC procedures. The modifications applied mainly consist of own friction coefficients and form factor (1+k) values for yacht appendages. The conditions of the calculations are a Froude number Fnof and normalized Reynolds number Rn of The boat is allowed to sink dynamically, but not to pitch. The pitch angle is prescribed at ψ =0.46 bow down trim. STAR-CCM is used as flow code to solve the Reynolds-Average-Navier-Stokes equations for the flow field around the yacht. The simulation is conducted at fully turbulent conditions and the k ω based Shear Stress Transport (SST) model has been used to model turbulence Computational Grids Grid Convergence studies have been conducted using 3 different combinations of refinement parameters to study their impact on grid densities and computational results. The computational grid has been modeled such that it depends on one base number. This way it can be ensured that a constant grid refinement ratio r k is used. Two exceptions from this modeling paradigm exist. First the prism layer used to resolve the boundary layer around hull and appendages is excluded from refinement because this would lead to large changes in dimensionless wall-scale Y +. Most likely this would lead to changes in near-wall treatment like using a low-reynolds approach for one simulations and wall functions for the other. This would render the simulations incomparable. Therefore the total thickness of the prism layer, the thickness of the wall nearest node and the number of prism layers are kept constant throughout this verification & validation. The second exception concerns the resolution of the free surface. Since free surface resolution is very important for correct resolution of ship drag, it has been given its own base number. This way it is possible to evaluate the influence of different refinement ways on both computational grid and solution. The refinement ways investigated within this work are: 1. Global refinement; were only the global grid base number is refined. 2. Free Surface refinement; were only free surface parameters are refined by their base number. Free surface refinements consists of a vertical refinement in the whole domain at the expected level of the wave pattern and a second refinement in both longitudinal and traversal direction in the vicinity of the Kelvin pattern. 3. Overall refinement; were both global and free surface base number are modified as a function of the refinement ratio r k. For all three cases four grids with constant refinement ratio r k =2have been constructed. Resulting grid sizes varied from cells for the coarsest grid to for the finest Verification and Validation of Resistance The verification of resistance has been performed with respect to grid convergence. Iterative convergence has been taken into account, but since it was in the order of 0.05% C T it was considered neglectable. The results of the studies have been summarized in table 1 and 2. Table 1 illustrates the C T values for the different grids as well as the solution change ɛ from a coarser to a finer solution between adjacent grids. Here ɛ is defined as: ɛ = (S i S i+1 ) (22) S i+1 The results show that the changes of C T between the different solutions are largest in the case were free surface parameters variations are involved (Case 2-3). Verification results are illustrated in table 2. Here convergence ratio R G indicates

27 Table ( 1: Grid convergence study for total resistance C ) T 10 3 for ACCV5 Grid Number Nr. Var EFD 1) C T ɛ -2.0% -0.6% -0.2% 2) C T ɛ 2.6% 2.7% 1.5% 3) C T ɛ -0.1% 3.1% 0.6% %S G Table 2: ( Verification of total resistance C ) T 10 3 for ACCV5 Nr. Grid R G U G δg S C 1) % 0.07% -0.07% % 0.20% 0.01% 2) % -0.50% 0.5% ) % -0.20% 0.2% %S G monotonic grid convergence of solutions for grids 1-3 for all three case (R G < 1). For the coarser grid sequence (grids 2-4) only case 1 (Global refinement) shows monotonic convergence. For the coarser grid sequence of the free surface refinement study (case 2) R G indicates divergence whilst for the same grid sequence of the global refinement study (case 3) the solution appears to be of oscillatory nature. However, the later indicator seems to be misleading, so results for case 3.b are also treated as divergent. It is therefore not possibly to estimate error or uncertainty for case 2.b and 3.b. Where appropriate Generalized Richardson Extrapolation is used to estimate sign and magnitude of the grid error δg and a corrected uncertainty U GC as well as a corrected solution S C (equations (14) - (20)). The thus gained corrected solution can be compared to the solution S G. This gives an estimation of the level of verification of the simulation. In all cases were an estimation of the numerical uncertainties was possible, the corrected solution does not differ much from the originally calculated with differences in the range of to 0.5%S G. It can thus be concluded that in all those cases the level of verification is rather good and the results can be considered verified. Validation of the simulation results is performed with respect to the results of the towing tank tests. Therefore the comparison error is calculated according to equation (9) taking into account the simulation result S and the experimental data D. In order to conduct the validation as defined in (21), the validation uncertainty U V has to be calculated (10). The corrected comparison error E C is defined as in (9) but using S C instead of S. Table 3 summarizes comparison error E, Table 3: ( Validation of total resistance C ) T 10 3 for ACCV5 Nr Grid E% U V % U D % U SN % 1) 1-3 E E C E E C ) 1-3 E E C E E C ) 1-3 E E C %D 2-4 E E C validation uncertainty U V, experimental uncertainty U D and simulation uncertainty U SN as percentage of D for both corrected and uncorrected approaches. It has to be noted that data uncertainty U D has not been specified in the experimental towing tank data. Details regarding experimental uncertainties of large towing tank facilities are rarly found in literature. Longo and March [7] give values between 0.6% - 1.5% for a systematic investigation of the surface combatant DTMB 5415 model with respect to experimental errors whilst Yan et al. [13] give values of 2.8% for the same ship. Similar data for yacht investigation have not been available. The only source found for uncertainties of yacht investigation has been a presentation given by Frank DeBord at Stevens Institute [2]. The data given in this presentation show the long term repeatability of towing tank tests to be approximately 3%. Also this overview of towing tank uncertainties is by no means complete, it can be concluded that the data uncertainty normally should not exceed 3%. It was therefore decided that it is feasible to take into account a experimental uncertainty U D of 2% for validation purpose. By comparing E and U V of table 3 one can easily see that for all cases in which the comparison error could be calculated, E<U V is true. Therefore results have been validated for all cases except case b (grids 2-4) of both free surface and overall refinement studies. This coincides with the findings of the verification study and allows the conclusion that both verification & validation has been achieved for all refinement studies except the two cases stated above. The formal validation and verification procedure as conducted above only allows to draw conclusion regarding the finest grid in the study, in this case grid 1 respective grid 2. Whilst not giving the same level of certainty a plot of results deltas over grid cells is a feasible approach to judge the sensitivity of the solution to grid changes. Figure 5 illustrates resistance coefficient ΔC T over grid points. It is interesting to note that with ongoing refinement cases including free surface grid parameters show an increasing drag whilst for the general refinement case the opposite holds true. The later one coincides with the

28 widely held doctrine that with ongoing refinement a RANSE solution gives smaller forces until grid invariance of results is reached. This investigations suggest that while this certainly holds true for single phase investigation of deeply submerged bodies, it is not applicable to free surface flows around floating bodies. The rationale behind this behavior probably is that a too coarse resolution of free surface leads to increased wave damping thus altering the pressure fluctuations on the hull such that a lower wave resistance is predicted. However, to be sure this theorem would have to be proofed. The distribution of results also illustrates the high impact of free surface refinement parameters on overall grid density and result accuracy. It can be concluded that special attention has to be devoted to these parameters in order to achieve reliable results. Figure 5: ΔC T over Grip Points w.r.t to Experimental Data Since the correct determination of wave resistance is crucial for reliable results on total resistance of ships, a refinement study for free surface flows also has to take into account its influence on generated wave patterns. Figure 6 compares wave resolution from initial studies (top) with results gained with the modified HRIC scheme.the top picture shows that the computational domain is too short and the wave patterns is diffuse and damped. Especially the later suggests an insufficient resolution of the free surface. The bottom of figure 6 shows the finest grid of the investigation. Obviously there are large differences between the two simulations, the later one showing a sharp resolution of primary and secondary wave trains. Here wave damping seems to be largely reduced. One of the goal of this investigation was to reduce numerical ventilation caused by the smearing of the free surface interface. Figure 7 shows the volume fractions of water at the yacht surface for the old approach with Courant number dependency whilst figure 8 illustrates the same for the new approach without. Comparing the two cases one can clearly see from the profile view that the new approach gives a much sharper interface between air (blue) and water (red). The differences are most distinctive at the bow wave which takes an entirely different shape. The bow wave of the old approach (figure 7) has a large region over which the interface is smeared and this smearing is transported significantly down- Figure 6: wave contours from initial studies (top) and from Grid Convergence studies (bottom, grid 1 - finest grid) stream. For the new approach (figure8) the bow wave is much more distinctive and the free surface interface is usually captured over 3-4 cells. This clearly shows an advantage of modified approach over the old. However, plan view reveals that the volume fraction achieved with the new approach still is not perfect. Whilst the improvements between old approach and new approach are obvious and pleasant, plan view still reveals some remaining interface smearing. Still the improvement is large since the volume fraction for the old approach ranges between 0.4 and 1.0, whilst for the new approach the range is between 0.85 and 1.0. It seems that within the VOF method achieving perfect results without smeared interfaces for this rather blunt bows is still very hard if not impossible. Nonetheless from an engineering point of view the simulation is absolutely applicable since with respect to the verification & validation results the error in total resistance is small. Figure 7: Numerical Ventilation with Courant Number dependency

29 trim moments and vertical forces exist as input values. These values have been used as input data for the CFD simulation instead of dynamic calculation of these values, which would also have been possible Computational Grids Figure 8: Numerical Ventilation without Courant Number dependency 5.4 Grid Convergence Studies including Lift After the successful verification & validation of the point variable C T for the sailing yacht in upright conditions reported in section 5.3, a further study has been conducted in order to proof the feasibility of the approach for heeled conditions of the yacht. Heeled conditions include the generation of hydrodynamic lift by the yacht and its appendages. Therefore a validation & verification for these conditions cannot be restricted to the evaluation of total resistance C T. Instead it has to include the lifting component to consider the complete state of the yacht. Therefore the two point values total drag coefficient C D and total lift coefficient C L are evaluated together. The correct evaluation of this forces within towing tank experiments or CFD simulations requires the modeling of aerodynamic forces which a sailing yacht encounters. In order to correctly simulate the influence of the aerodynamic force generated by the sails, one has to introduce an additional dynamic sail trimming moment around the y-axis of the yacht which is equal to hydrodynamic drag D times the vertical center of efforts of the sails VCE aero. M Ydyn = D VCE aero (23) Additionally, the generation of lift by the yacht hull and appendages introduces a vertical force pointing up. Similar to the trimming moment explicated above, this force has to be countered by a collinear aerodynamic vector of equal length and different sign. This sail force has to be modeled during testing as a additional dynamic sink force F Zdyn. It is modeled as heeling force F H times the sine of the heeling angle φ. F Zdyn = F H sinφ (24) Contrary to the upright resistance grid convergence study, this study has been conducted in model scale. This approach not only allows easier comparison between results but also makes the appliance of the various additional input parameters easier. Whilst for the non-lifting test cases validated in section 5.3 trim was kept fixed and only sinkage was dynamically calculated, the present case sets both state variables free. This is a major change since it makes it necessary to account for similar trim and sinkage forces in order to compare simulation and experiment. For the towing tank experiment prescribed The grid convergence study has also been conducted according to ITTC standards as explicated in section 5.3. The principal design of the grids is identical to the one used in section 5.3. It includes refinement of the free surface in vertical direction and additionally in horizontal dimensions in the vicinity of the kelvin angle around the boat. The results of the non-lifting verification & validation study clearly showed that the major factor towards a grid independent solution is the refinement of the free surface. Figure 5 illustrates that surface grid refinement is already sufficient. Therefore only free surface refinement has been varied for the present grid convergence study. Grid parameters have been systematically varied according to table 4. In contrast to the grid convergence study for the non-lifting case in section 5.3 the constant grid refinement factor has been decreased from 2 to 1.5. This has been done to get a more uniform refinement in terms cell sizes which enhances the comparability of the results. The Table 4: Grid Parameter for Grid Invariance Study Ref. Interface Spacing Factor dz dx & dy Grid Size (-) (mm) (m) (-) differences of lift and drag coefficient to the experimental data derived from the grid convergence study is shown in figure 9. The figure illustrates that the drag coefficient C D is always underestimated, whilst for the lift coefficient C L the contrary holds true. However, differences to EFD are rather low for both coefficients and in the same order of magnitude. Generally both coefficients converge quite satisfactorily, giving the first indication of a high quality solution. Table 5 gives the numerical values of the convergence of drag, lift and lift/dragratio. The solution change from a coarser to a finer solution ɛ, as defined in (22), decreases continuously. The results of the verification procedure (table 6) show that the convergence ratio R G < 1 is true for all cases, allowing the conclusion that the decrease is monotonic for all values. The biggest uncertainty of the computational grid U G is 0.52% for the liftto-drag ratio C L /C D which is already very low. Since the convergence is monotonic, it is possible to use Generalized Richardson Extrapolation in order to apply a correction for numerical error. In particular, it is possible to calculate a correct grid uncertainty U GC and a corrected solution S C. With a maximum derivation of 0.14%, these corrected values are even closer to the experimental values. It can be generally said that from a numerical point of view the results of the grid convergence study show a docile behavior and steadily

30 Figure 9: ΔC i over Grid Points Table 5: Grid Convergence of drag and lift for ACCV5 Grid 3 Grid 2 Grid 1 EF Data C D ɛ - 0.7% 0.1% C L ɛ % -0.4% C L /C D ɛ % -0.5% %S G converge towards the experimental values with increasing refinement. This allows the conclusion that the simulation is verified. Table 7 gives an overview of the values necessary for Table 6: Verification of drag and lift for ACCV5 Variable R G U G δ G U GC C D % -0.12% 0.08% C L % 0.30% 0.14% C L /C D % 0.41% 0.11% %S G the validation procedure. Data uncertainty U D and numerical simulation uncertainty U SN are combined to the validation uncertainty U V. U V is then compared to the comparison error E C which is defined as data D minus simulation result S as per equation 9. The table list all values both for the uncorrected solution and the solution corrected by means of Generalized Richardson Extrapolation. Per definition, a simulation is validated if the comparison error is less or equal the validation uncertainty. This clearly the case for all six comparison cases. The simulation can therefore be considered validated at validation uncertainty level. It can be summarized that verification & validation for lifting conditions was highly successful. Achieved results are not Table 7: Validation of drag and lift for ACCV5 Variable E% U V % U D % U SN % C D E 0.4% 2.0% 2.0% 0.19% E C 0.3% 2.0% 2.0% 0.08% C L E -0.9% 2.0% 2.0% 0.44% E C -0.6% 2.0% 2.0% 0.15% C L /C D E -1.3% 2.1% 2.0% 0.53% E C -0.9% 2.0% 2.0% 0.11% %D only considerably below validation uncertainty level but also very close to experimental data. Although this formally does not decrease the uncertainty of the results, it still increase the confidence in the applied methods. It also shows again that the assumptions regarding free surface interface smearing made in the previous sections are correct. 6 Summary The motivation for this investigation has been a failed first attempt to correctly determine total resistance of free surface flow around an ACCV5 hull. A review of the first simulations led to the assumption that the problem could be traced back to the occurrence of extensive interface smearing at the yacht hull. This led to a thorough review of the theory behind the interface capturing model in section 3. This review showed that the problems encountered most likely were situated in the use of Courant numbers exceeding 0.5, thus causing the switch to a 1st order upwind differencing scheme. Since reducing the overall time step size such that it would allow the maximum Courant number to be lower than 0.5 would lead to undesirable long simulation times an alternative approach was sought to allow the use of higher order schemes like e.g. the HRIC scheme within acceptable time step size. It was concluded that it might be possible to modify the VOF model such that it does not switch to upwind differencing even if the local Courant number would be larger than 0.5. This approach seems feasible as long as only a steady state solution is sought-after. Section 4 shows a numerical test case which allows the conclusion that this approach is feasible. Therefore, the modified scheme was applied to the simulation of the total resistance of the ACCV5 yacht. Verification and Validation according to the ITTC guidelines was then conducted against experimental data for lifting and non-lifting test cases. Extensive grid studies have been carried out, thus also allowing to judge the sensitivity of the results to the change of various grid parameters. The results showed a much sharper capturing of the free surface interface with the new approach. It was also shown that the initial differences in overall resistance were mainly caused by the poor free surface resolution caused by the interface smearing. This interface smearing caused a numerical damping of the waves resulting in a wave resistance which was too small. The grid convergence studies clearly showed that the free surface simulations for yachts are more sensible to free surface resolution and thus to wave resistance

31 than they are to yacht surface resolution (friction and pressure forces). Overall it can be concluded that the use of the higher order scheme which was made possible by the modification of the existing implementation led to large improvements and a successful verification & validation. It has to be stressed that the new approach with the modified scheme is only valid if one is interested in a steady solution. It was also shown that the simulation still suffers from a small amount of interface smearing, however the overall effect on the results may be considered as small. Generally, the error in verification & validation was satisfying small. REFERENCES [1] C. Böhm and K. Graf. Validation of ranse simulations of a fully appended accv5 design using towing tank data. In International Conference on Innovation in High Performance Sailing Yachts, Lorient, France, April [2] Frank DeBord. Hydrodynamic performance prediction for grand prix sailing yachts. Presentation at Stevens Institute. [3] C Hirt and B Nichols. Volume of fluid (vof) method for the dynamics of free boundaries1. Journal of Computational Physics, 39(1): , [4] ITTC. ITTC Recommended Procedures and Guidelines; Uncertainty Analysis in CFD; Verification and Validation. International Towing Tank Conference, [5] Lars Larsson, Frederick Stern, and Michel Visonneau. Gothenburg 2010, A Workshop on Numerical Ship Hydrodynamics. Chalmers University of Technology, [11] Fred Stern, Robert Wilson, and Jun Shao. Quantitative v&v of cfd simulations and certification of cfd codes. International Journal for Numerical Methods in Fluids, 50(11): , [12] Fred Stern, Robert V. Wilson, Hugh W. Coleman, and Eric G. Paterson. Comprehensive approach to verification and validation of cfd simulations part 1: Methodology and procedures. Journal of Fluids Engineering, 123(4): , [13] Kai Yan, Feng Zhao, Cheng sheng Wu, and Lei Yang. Numerical and experimental uncertainty analysis for the prediction of resistance and wave profile of a surface ship model. In 8th International Conference on Hydrodynamics, AUTHORS BIOGRAPHY Christoph Böhm holds a diploma degree in naval architecture from the University of Applied Sciences Kiel. He is currently working as a flow scientist at the Yacht Research Unit Kiel. He is specialized on RANSE simulations of sailing yacht appendages and hulls as well as subsequent VPP integration. He is currently working towards his PhD thesis at TU Delft. Kai Graf is professor for ship hydrodynamics at the University of Applied Sciences Kiel and senior scientist of the Yacht Research Unit Kiel. Kai is working on sailing yacht aero- and hydrodynamics since 1998, being specialized on numerical simulation methods. [6] B. P. Leonard. Simple high-accuracy resolution program for convective modelling of discontinuities. International Journal for Numerical Methods in Fluids, 8(10): , [7] Joe Longo and Fred Stern. Uncertainty assessment for towing tank tests with example for surface combatant dtmb model Journal of Ship Research, 49, No.1:55 68, March [8] S. Muzaferija and M. Peric. Computation of freesurface flows using the finite-volume-method and moving grids. Numerical Heat Transfer, Part B: Fundamentals, 32(4): , [9] S. Muzaferija and M. Peric. Computation of free surface flows using interface-tracking and interface-capturing methods, chapter 2, pages Computational mechanics publications. WIT Press, Southampton,, nonlinear water wave interaction edition, [10] S. Muzaferija, M. Peric, P. Sames, and T. Schellin. A two-fluid navier-stokes solver to simulate water entry. In Twenty-Second Symposium on Naval Hydrodynamics, Washington D.C:, 1999.

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33 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France DATABASE BUILDING AND STATISTICAL METHODS TO PREDICT SAILING YACHTS HYDRODYNAMICS Lionel Huetz, Marc Lombard Yacht Design Group, France, Pierre Emmanuel Guillerm, Ecole Centrale de Nantes, France, Abstract. The model characterizing the hydrodynamic forces acting on a sailing yacht hull can be built using extensive tank testing or CFD computations carried out on the studied hull shape. Unfortunately, in most cases involving sailing yachts, time and money are limited and testing each hull at the required speeds and attitudes is impossible. The idea is then to rely on a hydrodynamic model gathering results on various hulls; able to describe the evolution of the hydrodynamic forces depending on the hull shape through geometrical variables. The building and calibration of this type of model requires numerous computations but once the model is built, this approach is very fast. Furthermore, these models can provide a better understanding of the trends than tests on isolated hull shapes since they contain the results on a whole database of hulls. This type of approach using metamodels can be used in various fields to produce lots of results in a very short time and a better understanding of the phenomena involved. This paper presents a methodology to produce the database, select the relevant explanatory variables and build the formulations in the context of sailing yachts hydrodynamics. The regressions allowing the prediction of the running attitude and forces are presented. NOMENCLATURE ALA Apparent leeway angle ( ) A HL Lateral area of immersed part of the hull (m 2 ) A X Maximum section surface (m 2 ) BEI Bow entry incidence ( ) B WL Waterline beam (m) C B Block coefficient CBR Relative camber C f Friction coefficient C flot Flotation coefficient C P Prismatic coefficient C Pfront C P of the hull in front of maximum section C X Maximum section coefficient F Non dimensional form of F (N) Fn Froude number L WL Waterline length (m) L T Longitudinal position maximum draft (m) L X Longitudinal position maximum section (m) L CB Longitudinal position centre of buoyancy (m) L CG Longitudinal position centre of gravity (m) R Rocker angle ( ) Roy Running trim angle ( ) S C Static wetted surface of the bare hull (m 2 ) T Draft (m) Trz Running sinkage (m) T T Immersion of transom (m) 1. INTRODUCTION Is it fast? is certainly the most common question that arises when observing a sailing yacht at the dock or ship lines in a design office. Sailing yachts find their energy in the relative motion between air and water. Their behaviour is governed by the equilibrium between aerodynamic forces one side and hydrodynamic forces on the other side. The combined simulation of these forces is a challenge and finding the three dimensional attitude, tuning and speed of the yacht fulfilling the equilibrium condition between all the forces is even more complex; so complex that computational time is very far from matching designer s needs. Furthermore, a fully coupled simulation would be very hard to interpret in a design perspective since very various physical phenomena are interacting and mixed in the simulation. As a result, the aerodynamics and the hydrodynamics are always treated separately. Velocity prediction programs (VPPs) gather the results of each model to find the equilibrium of the yacht and finally predict its speed and attitude. In the present work, we are dealing with the characterization of the hydrodynamic model. 1.1 CONTEXT Various approaches can be used to define the hydrodynamic model of a yacht. Indeed, the model may characterize directly the behaviour of the appended hull or deal with the bare hull and its appendages separately. Then, the hydrodynamic forces decomposition and their coupling with the attitude of the yacht can be dealt with in various ways. Finally, a choice has to be made between a steady or unsteady approach. The level of decomposition is one of the main issues ruling the equilibrium between accuracy, computational time and versatility; the higher the level, the faster the computations and versatility but the more restricting the hypothesis on the physical effects involved. In fact, each time a problem is split into simpler problems, hypothesis on the coupling between the latter are made. This may lead to a loss of accuracy but also to a better understanding of the different separated physical phenomena and an enlarged field of application. Finding the right balance between a direct approach of complex phenomena and a reductionist approach dividing complex problems into simpler ones is a recurrent problem in applied science. Choices have to be made, based on expertise and practice. Several TH 28 TH June, 2013

34 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France preliminary designs and yacht performance studies as well as numerical simulations and analysis of the existing state of the art predictions led to the following conclusions: Significant improvements can be made while remaining in a quasi static VPP approach based on the coupling of three separated mathematical models (hull model, appendage model and aerodynamic model). Quasi static refers to the fact that dynamic effects are not directly included. Some attitude variables (leeway, running trim and sinkage) have to be added to the models and the VPP to improve the overall accuracy by improving the coupling between the different models. In this context, the accuracy of the prediction relies mainly on the accuracy of the three models characterizing separately the hydrodynamic behaviour of the bare hull (without appendages), of its appendages and the aerodynamic behaviour of the yacht. The appendages are relatively well described by the lifting line theory implemented in most of the VPPs, especially for high aspect ratio foils used on most of the modern yachts. The bare hull behaviour is much more complex to predict. There are two main ways of characterizing the hydrodynamic properties of a hull. The first one is to carry out some tests on the studied hull shape for different values of speed and attitude variables such as heel and leeway angles. The results of these tests are stored in a matrix giving the relation between these input variables on one side and the forces and running attitude of the boat (output variables) on the other side. The tests can be carried out on scaled models in towing tank facilities or using computational fluid dynamic (CFD) tools. These two methods have their advantages and drawbacks, but they share one main drawback, they are so expensive and time consuming that their use is extremely restricted. The other method is to use a mathematical model that is able to approximate the matrix described before; each term depending on geometrical parameters describing the shape of the hull. Different methods can be followed to build this type of mathematical models. Since the flow around a yacht hull is very complex, they are all based on empirical or semi empirical approaches, using experimental results databases or real scale measurements on various hull shapes. In some cases, specific experimental campaigns called systematic series are set in order to build mathematical models describing the behaviour of ship hulls. Despite a lower accuracy, the approach based on mathematical models presents many advantages. Once it is built, its use is very fast and cheap, facilitating the comparison of very various hulls during the design phase. Furthermore, the mathematical analysis of a large database can provide a better understanding of the phenomena involved than isolated tank tests or numerical simulations since they contain the results on various hulls. The most famous formulations able to predict the hydrodynamics of sailing yacht hulls are based on the Delft Systematic Yacht Hull Series [1], [2]. The limitations of these formulations have been discussed in a previous paper [3]. These articles showed that a more detailed characterization was needed to improve the performance prediction, especially the influence of heel, leeway and trim. 1.2 MOTIVATIONS The goal of the present study is to produce valuable information for the naval architects involved in the design of sailing yachts. This encompasses an improved accuracy and sensitivity of the velocity prediction but also the understanding of the physics involved. Our goal is to make this work as intelligible as possible for the designer, to stimulate the intuition and creativity instead of trying to replace them. In other words, turn the question is it fast? into why is it fast? This led to the following conclusions: Build a computational loop that will be as versatile as possible to generate large databases of numerical experiments such as systematic series. Define a methodology and statistical tools to identify the relevant geometrical variables and build new formulations to predict the hydrodynamic forces and running attitude of yacht hulls. Develop a specific VPP to implement the developed formulations with their additional variables, especially the running attitude of the yacht. The previous paper [4] presented the first results of this work and we will present here a more detailed description of the key issues of the methodology, much more extended formulations and the first results of the developed VPP. 2. TOOLS The building of a numerical database involves various types of computations, realized by several modules. The different tools that are used in the loop are presented hereafter. 2.1 LOOP MONITORING Figure 1 describes the modules involved in the loop used to build the database. DOE stands for design of experiments and will be discussed in the next section. Figure 1: Chart of the loop TH 28 TH June, 2013

35 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France Input variables are: The parameters of the deformation used in the CAD module. The attitude variables (speed, yaw) Outputs variables are: The hydrostatic coefficients. The hydrodynamic forces. 2.2 MORPHING TOOL A morphing tool is used to generate various hulls and the associated volume meshes by deforming an initial hull and mesh. It is based on the hull modeller developed by HydrOcean as a plug in of Rhinoceros. This approach allows large changes in hull shapes without degrading the properties of the initial structured volume mesh. Figure 2 presents a zoom on the boundary layer meshing of the initial hull in blue and a deformed hull in red Adaptation of classical measurements As we are dealing with asymmetrical wetted shapes, even the classical measurements have to be redefined. Once the hydrostatic equilibrium is achieved in the flow referential R0, i.e. L CB =L CG and weight=displacement, the apparent leeway angle ALA is computed. This angle is quoted in green in Figure 4 and defined in the next section. Once ALA is computed, a new referential R1 is defined as a rotation of R0 around Z0 axis. The rotation value is ALA, so that the wetted shape is aligned with the X1 axis. All the measurements such as waterline beam and length, master section area, prismatic coefficient and so on are then carried out in the R1 referential. BEI Y0 Y1 ALA Figure 2: Initial and deformed meshes Each deformation is defined by its volume of action and spatial functions. Three spatial functions define the displacement of the hull control points, depending on their x, y, z position. These functions are defined using 1 to 5th order Splines. Each transformation is monitored by the amplitude of the spatial functions, its volume of action remaining unchanged. Figure 3 shows a function which modifies the front sections fullness. The original section in the middle is black, negative amplitude leads to a narrower V shaped section in blue, positive amplitude creates a wider U shaped section in red. More details about this tool can be found in [5]. f(x) 1 0 Loa x Boa/2 g(y) 1 0 h(z) 1 Boa/2 y zmin zmax Figure 3: Definition and visualization of a transformation z X0 = FLOW DIRECTION Figure 4: Measurements of asymmetrical wetted shapes Parameters quantifying the asymmetry Three measurements depicted on figure 4 were defined in order to characterize the asymmetry. The apparent leeway angle, ALA. The points A and B are defined as the centre of the sections situated respectively at 5% and 95% L WL. ALA is the angle between (AB) and the direction of the incoming flow. The bow entry incidence, BEI defined as the angle between the bisectrix of the water plane entry and the direction of the incoming flow. The relative camber, defined by the deviation of the mean line of the water plane divided by LWL Additional hydrostatic parameters The pressure field and the hydrodynamic drag of the tested hulls present a high sensitivity to the longitudinal shape of the hull. Some measurements such as the rocker angle R were defined as shown in Figure 5 to characterize the keel line. Regardless the heel value, these angles and immersions are always measured in the vertical plane (X1, Z0) in which the hull has the larger lateral area. X1 2.3 HYDROSTATIC MODULE A hydrostatic module has been developed specifically for this study. In fact, the characterization of the wetted shape of sail boat hulls under various hydrostatic equilibriums is the key of the chosen approach. In fact, as highlighted in [4], the measurements of the wetted shape under heel allow significant improvements in the accuracy of the prediction. Transom immersion 10% LwL 10% LwL 5% LwL LwL Rocker Forward Rocker Point 1 Point 2 Figure 5: Measurements of the keel line Stem immersion TH 28 TH June, 2013

36 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France 2.4. RANSE SOLVER ICARE [6] is a RANSE (Reynolds Average Navier- Stokes Equations) free-surface solver initially codeveloped by Ecole Centrale Nantes under French Ministry of Defence support, and by Hydrocean. It uses the k- turbulence model developed by Wilcox [7]. The free surface is described by an interface tracking method. General schemes are based on second order (in space and time) implicit finite differences. Discrete unknowns are distributed on a hexahedral structured curvilinear grid fitted to the hull and the free surface. The interface tracking approach allows a very a good precision/time ratio and is also very suitable for the construction of a systematic series. The drawback of this mesh deformation approach is its inability to describe breaking waves. This reduces the maximum Froude number to about 0.6 to 1.0, depending on the hull shape. A satisfying validation of the ICARE code on sailing yacht hulls has been performed. As part of collaboration with the Delft Ship Hydromechanics Laboratory, J.A. Keuning and his team made available the detailed tank test results of three different models of the DSYHS. The length to displacement ratios vary from 5 for model 23 to 7 for Model 28. Results on bare hull but also on appended hulls were available. ICARE computations on both bare and appended hull were performed. The computations were carried out at model scale, with semi captive method. On the three models, the agreement between the tank tests and the RANS solver was good, within the 5% range concerning drag and showing the same behaviour concerning the heave and trim over the whole speed range. The results concerning Model 25 are presented in Figure 6. Error bars have been represented with a 0.5 N measurement uncertainty plus a 5% margin to help the reading of the discrepancies. Drag (N) Tank tests ICARE Froude number Figure 6 : ICARE solver validation - DSYHS Model 25 Satisfying results were also obtained and published in [8] concerning validation of the ICARE solver on an IMOCA 60 hull. 3. DATABASE AND REGRESSION BUILDING In the field of statistics and data mining, a lot of the knowledge and tools were developed to process real life data, such as demographical, economical or medical figures. Here, we have the luck to control most of the data we will process in the end. In fact, a database made of numerical simulations is in a way the exact opposite of a real life database. Not only we control most of the explanatory variables value of our experiments as in a laboratory, but we have a 100 % repeatability of the experiments. This does not mean that the result is perfect, but from a statistical point of view, it is very different from real life experiments. It is luck, but it is also additional work. The data does not exist, we need to build it and find a satisfying way of building it. 3.1 DATABASE BUILDING DESIGN OF EXPERIMENTS Once the extreme values of the inputs variables are defined, there are many ways to design the experiments, i.e. define the number of points needed in the database and their spacing with respect to the sensitivity of the response (outputs) is a complex problem. The aim is to extract as much of the physics as possible with a minimum number of experiments. In our case, the input variables are the magnitude of the transformations applied to the parent hull and the computational parameters such as speed, weight and LC G. Once a range and a step of variation have been defined for each input variable, the straight forward approach is to follow a full factorial design of experiments. In our case, we have at least 10 input variables. If we want to explore at least three different values for each variable, this leads to 3 10 = computations, which is not realistic in our context. Several methodologies have been developed to reduce the number of experiments needed before the beginning of the experiments and the building of the model. We can quote the following methods: Reduced Factorial,, Box- Behnken, Latin Square, Taguchi Matrix. The general idea is to assume some properties in the data and use them to reduce the number of experiments. Some methods assume linear or quadratic response in the data; others neglect the interaction between the explanatory variables, etc. A very good overview of the quoted methods and their applications can be found in [9], dealing with most of the classical statistical methods. Another interesting paper by Astrid Jourdan [10] deals more specifically with the design of experiments applied to numerical simulations with approaches allowing more flexible responses such as the Kriging technique. In our case, the design of experiments can be adapted as the database grows. We do not need to follow a plan defined a priori. In fact, the automated post treatment of the solver s solution makes the results of each experiment immediately available in the database. It is worth to exploit the information collected about the response in order to figure if there are portions of the experimental region which could require a denser sampling than others. The design of experiments is realized in two steps. The first step can be described as exploration and the second one is the refining of the database Exploratory design Sobol sequence Several methodologies have been developed to optimize the exploration phase. The goal is to provide a first TH 28 TH June, 2013

37 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France response surface that will be the starting point of the refining phase. The response surface has to be defined on its whole range of variation and the points have to be distributed as evenly as possible. A specific structure in the repartition of the variables values may lead to a false interpretation of the response. A random sequence could be used but it tends to generate concentration of points in the same region, leaving other regions empty. Figure 8 shows how the Sobol sequence improves the repartitions of the variables values compared with a random sequence on a simple two dimensional case. Figure 8: 1000 points generated with a random sequence on the left and a Sobol sequence on the right The Sobol sequence has been chosen as initial design of experiments in this study. This sequence is widely used in the exploration phase, to initiate an optimization process for example. In the present work, the goal is not only to find the optimum of the response surface but to characterize it as well as possible in a given time lapse Database enhancement Lipschitz sampling One of the most promising approaches to refine a response surface is called Lipschitz sampling [11]. Once a first response surface has been defined, the algorithm computes a scalar called Lipschitz constant quantifying the local complexity the surface. This constant is regularly recomputed on the whole surface to readjust the choice of the next experiments and the high gradient zones become more and more well defined as the database is built. Figure 9 shows a typical case of application. X and Y represent two explanatory variables and Z is the response variable. From a initial response surface, the algorithm has refined around the break line to allow a very satisfying modelling of the response. The Y vs. X graph on the left of figure 9 illustrates the behaviour of the algorithm. The original average density of points was 5 points per unit in the X direction and 4 points per unit in the Y direction. This density has been increased by the algorithm in both directions up to 20 points per unit in the break region. Figure 9: Example of a 3D response surface refined using Lipschitz sampling (Y vs. X graph on the left) This algorithm highlights one of the main advantages of a completely numerical approach to build a systematic series: the ability of following an adaptable design of experiments, which is more and more relevant as the database grows. The experiments have no longer to be designed a priori, assuming properties in an unknown data base REGRESSION BUILDING VARIABLE SELECTION In this section, the goal is to identify the relevant relations between the predictive variables on one side (the attitude variables and geometrical measurements computed by the hydrostatic module) and the dependant variables on the other side (the hydrodynamic forces and running attitude). What is a relevant relation? The literature on naval hydrodynamics shows that the purposes motivating regression analysis may differ largely; the qualities sought after in the regressions will vary accordingly. The regression analysis can be used to build a very simple model, with focus on the reduction of required predictors and a low constraint on accuracy, in order to reduce the number of required measurements to predict a given quantity. In our case, unlike twenty years ago, the hydrostatic computations and measurements are quasi instantaneous, the number of predictive variables will therefore not be reduced to avoid fastidious measurements. This number will be a compromise between accuracy and robustness. Too few predictive variables will lead to a lack of sensitivity and therefore to obsolete regressions. If too many variables are to be introduced, the regression parameterization will be unstable; mainly due to multi collinearity between the predictors. Multi collinearity is a linear relationship between two or more predictive variables. In the presence of multi collinearity, the value of the coefficient estimates a i associated to the collinear predictors may change erratically in response to small changes in the model or the data. A small change in the sample will cause a large variation of a i, which is to be avoided as the a i value should give relevant information on the effect of the associated predictor. The choice of the relevant predictors is therefore one of the keys of this study. The multi collinearity has to be avoided above all. The correlation between the predictors has to be kept as low as possible. Each independent variable should have a non-zero correlation coefficient at a high significance level (low p-value). It should not be possible to significantly improve the accuracy of the regression by introducing extra independent variables. It should not be possible to exclude a predictor without significantly reducing the accuracy of the regression. Several statistical tools have been tested in order to build multivariate regressions and avoid multi collinearity as far as possible. A simple and satisfying approach is the forward selection algorithm TH 28 TH June, 2013

38 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France Forward selection algorithm This algorithm will produce a multiple linear regression to explain a dependent variable based on independent variables that will be selected during an iterative process. The selection methodology is based on partial correlation computations. It starts with the best linear fit using the most correlated variable. Then the partial correlation of the remaining predictors is computed (i.e. their correlation to the residuals of the first regression). The variable showing the highest partial correlation is selected. This new variable is added in the regression and the residuals recomputed. This is repeated until the p-value of the test of significance of remaining variables is below a specified significance level. A more detailed description of the variable selection methodology is available in [5]. 4. PROPOSED FORMULATIONS In order to provide a representative but synthetic example of the proposed methodology, a specific database has been created around the Volvo 70 rule. 4.1 GENERATION OF THE DATABASE Description of the geometries From a parent design, two initial hull shapes are extracted. The first one is the upright hull; the second one is derived from the wetted shape of the heeled hull (20 degrees heel angle). Figure 10 shows four random hulls in the series, two symmetrical hulls on the left and two asymmetrical hulls on the right. Figure 10: Four random hulls of the Volvo 70 series These hulls and the corresponding meshes are generated using the presented morphing tool. Eight different geometrical transformations are defined and applied at various magnitudes to generate 250 different hulls. These transformations must generate realistic hull shapes but also maximize the changes in the physics of the flow to give as much information as possible on the design space. The choice of the transformations is guided by the experience of designing hulls by hand and by the literature which highlighted some relevant hydrostatic parameters to be varied. In fact, the computer has to reproduce what is carried out by hand during a typical preliminary design phase, producing a wide range of realistic hull shapes in order to understand as well as possible the design trade offs of the project. The volume of action of the six deformations includes the whole hull. Two deformations concern the shape of the fore sections of the hull, two other the stern sections. Those transformations are modifying the beam, draft and fullness of the sections. The longitudinal repartition of each transformation is smoothed using Bezier functions. Every transformation is carried out under hydrostatic constraints. For example, when the beam of the fore sections is increased, their draft is automatically reduced to keep the same longitudinal volume repartition. The two last transformations concern solely the asymmetrical hull shapes. They change the leeway and the longitudinal curvature of the immersed part of the hull in the transverse direction. This allows various combinations of ALA, BEI and relative camber to be generated. More details about those transformations can be found in [5]. Figure 11 gives the range of variation and the distribution of some of the main hydrostatic parameters used in the regressions. Sample size min max min max ALA ( ) R ( ) BEI ( ) FR ( ) ie ( ) X T/L WL C P L WL/ L OA C B I S/T C flot S T/S MS C M B/L L CB B/T C P Sample size Figure 11: Range of variation of some geometrical measurements (top) and distribution of Cp (bottom left) and Rocker angle (bottom right) A Gaussian fit is represented in red on the histograms to illustrate the gap between the distribution of the considered explanatory variable and a normal distribution. It allows a synthetic overview of the distribution of the variables. In the present case, the geometrical transformations cover a wide range of Cp and Rocker values with a satisfying distribution Testing conditions The geometries are tested at three different speeds, 10, 14 and 18 knots. The computations are carried out at real scale, with boats of 21.5 m overall length. The boats are free to heave and trim. The sail centre of effort is situated 13.5 m above the water plane. The longitudinal position of the centre of gravity of the boat is varied among three different values: 11.2, 11.8 and 12.4 m (i.e. L CB /L OA =0.52, 0.55 and 0.58). The transition of the boundary layer is forced at the bow of the boat, so that the flow is fully turbulent. All the forces are expressed in R TH 28 TH June, 2013

39 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France R 0. The moments are computed with respect to the centre of gravity. This database is made of 2250 computations (250 shapes x 3 L CG x 3 speeds). 4.2 FORMULATIONS The formulations are speed dependent; meaning that each speed has its associated set of estimates (or regression coefficients). All the forces and attitudes are expressed in R0. The trim angle is indeed computed in the water referential, y0 axis being perpendicular to the incoming water flow and normal to the water surface. As described before, we use generalized linear regressions to approximate the quantities. This means that each quantity is expressed as the weighted sum of explanatory variables or the weighted sum of combination of explanatory variables. Once one of the response variables is formulated, it is a combination of explanatory variables and thus might be used in the formulation of second response variable. On the bright side, this encapsulation might enhance the formulation of the second response variable and also facilitate the understanding of the physics. On the dark side, this decreases the stability of the formulation, by summing the errors. At this stage, it was felt that a trial and error approach would be valuable, in order to have an overview of the potential gain in accuracy allowed by the different encapsulation orders compared with no encapsulation at all. The forward selection algorithm was run several times for each response variables leaving access to other response variables or not. The resulting chosen order is presented hereafter. The numerical values of formula s coefficients are regrouped in figure 13. A much more detailed analysis and interpretation of the following formulations is available in [5] Side force generation The following expression gives a good approximation of the side force production: Where: 3 = Fy a ALA a ALA a BEI a CBR Fy = A HL Fy 1. ρ. V Pressure drag Numerical codes compute total resistance as the sum of the pressure drag (normal forces) and frictional drag (tangential forces); it seems therefore natural to use this decomposition to build the formulations. Fx = Fpx+ Ffx As the displacement variations of the hulls in the considered database are relatively small, a simple non dimensional form has been used: Fpx L WL Fpx =. 1 Fz 3 2 The pressure drag is one of the hardest quantities to model on a sailing yacht. Several physical effects are involved and their contribution to the total drag is highly dependant on the Froude number and the Reynolds number. This explains why numerous variables are used in the following expressions; however Figure 13 shows that some variables are not used at every speed, the corresponding coefficient being null. LWL Fy 2 2 L L CX CX Fpx = b0 + b1... Fy + b 1 2. ALA + b3. CP + b4. CP + b5. + b6. 3 Fz LWL LWL 2 LT LT T b7. + b8. + b9. + b10. CPfront + b11. CPfront + b12. CX + b13. CX + b14. R L L L WL WL WL It is interesting to plot contribution of the C P terms for different values of C P at the three speeds. The contribution is the value of the sum (b 3.C P + b 4.C P 2 ), this sum changes the value of the pressure drag depending on the C P value. Contribution Speed = 10 knots Cp Contribution Contribution Speed = 18 knots Cp Speed = 14 knots Figure 12: Contribution of Cp to Fpx depending on the Cp value at 10 kts (top left), 14 kts (topright) and 18 kts (bottom) Figure 12 shows a very consistent behaviour of the pressure drag formulation, being in the trend of what can be read in the literature on naval hydrodynamics. At 10 knots, or Fn=0.35, the optimum C P lies around At 14 knots, or Fn=0.5, the optimum C P lies around 0.61.At 18 knots, or Fn=0.65, the optimum C P lies around As for C P, most of the expressions are quadratic with a positive value of the estimates of the squared term. This allows an optimisation process without ending in the corners Running trim The running trim is defined as the change in trim angle between the hydrostatic position at the considered heel angle and the trim angle reached at the considered Froude number. Fpx LT LBWL LCB TT Roy = c0 + c1. + c2. + c3. + c4. + c5. + c6. R Fz LWL LWL LWP T This approximation of the running trim is very promising. It allows the coupling with an appendage model, providing the proper angles of incidence of the lifting devices fitted on the hull. Cp TH 28 TH June, 2013

40 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France Running sinkage The running sinkage is defined as the change in sinkage of the centre of gravity between the hydrostatic position at the considered heel angle and the sinkage reached at the considered Froude number. LBWL 2 Trz = d0 + d1. CB + d2. CWP + d3. + d4. ALA LWL Where Trz = Trz T Frictional drag Ffx = e + e. Trz + e. Roy + e. C + e. C + e. ALA WP 4 Pfront 5 With Ffx Ffx = 1 2 Cf.. ρ. V. SC 2 C f is determined using the ITTC 57 extrapolation line; based on the hydrostatic waterline length. As S C is the static wetted surface of the hull, Ffx contains the variations of wetted surface due to the dynamic position of the boat and the free surface deformations. A fraction of the form coefficient is also contained in Ffx, leaving the other fraction in the pressure drag Yaw moment The yaw moment is computed in R 0, with respect to the centre of gravity. This moment can be split into two components: A component coming from the drag force, multiplied by the lever between the centre of gravity and the centre of effort of the drag. A component coming from the side force, multiplied by the lever between the centre of gravity and the centre of effort of the drag. On most of the mono hulls, the component coming from the drag forces is very small compared with the component coming from the side force, except when the side force is very small. In this case, the yaw moment is also very small and its approximation is useless. The sample used to approximate the yaw moment has been selected using the following criteria: Fy 5% Fpx The following expression has been used to determine the longitudinal position of the side force centre of effort with respect to the centre of gravity, often called centre of lateral resistance (CLR). Mz LCLR = Fy The following expression gives a good approximation of the scaled centre of effort position. Trz 2 LCX BWL LCLR = f0 + f1. + f2. BEI + f3. BEI + f4. CB + f5. + f6. L L L WL WL WL With LCOE LCLR = L WL Fn Speed (kts) a1.10^3 a2.10^6 a3.10^3 a4.10^3 R Fn Speed (kts) b0 b1 b2.10^3 b3 b4 b5 b6 b Fn Speed (kts) b8 b9 b10 b11 b12 b13 b14 R Fn Speed (kts) c0 c1 c2 c3 c4 c5 c6 R Fn Speed (kts) d0.10^3 d1 d2 d3 d4.10^3 R Fn Speed (kts) e0 e1 e2.10^3 e3 e4 e5.10^3 R Fn Speed (kts) f0 f1 f2.10^3 f3.10^3 f4 f5 f6 R Figure 13: Estimates of the presented formulations A detailed evaluation of the accuracy of these formulations is available in [5]. 4. FORMULATIONS BENCHMARK In order to evaluate the sensitivity and accuracy of the presented formulations, a candidate hull which wasn t part of the systematic series has been characterized with different tools at two speeds, 3 heel and 4 leeway angles. Four tools are compared: The RANS code ICARE. The RANS code Star CCM+. The DSYHS formulations as implemented in WinDesign VPP of the Wolfson unit [12]. The presented formulations. Due to the limited length of the paper, only two graphs are presented on figure 14. They present the changes in side force production and pressure drag of the bare hull with respect to changes of heel angle with zero leeway and 14 knots of boat speed. A more extended validation study is available in [4]. The forces are expressed in Newton and the angles in degrees. In the chosen referential, a positive side force is a force to windward TH 28 TH June, 2013

41 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France Figure 14: Side force and pressure drag predictions at 14 knots for different heel angles and no leeway. With the exception of the side force at 14 knots, where the discrepancy reaches 25 %, the overall agreement between the two solvers is very good, despite very different computational methods; finite differences against finite volumes; interface tracking against interface capturing, etc. The discrepancy on side force at 14 knots might be related to bow wave effects. In fact, the bow region has a large contribution to side force and the bow wave is the most intense at this pre-planing speed. The DSYHS show a 45 % overestimation of the upright pressure drag which means a 23% discrepancy on total drag. These figures confirm the results published in [8], where the DSHYS are compared with tank tests on an IMOCA 60 and show around 19 % overestimation of total drag at Fn=0.6. The influence of heel on side force production is not taken into account by the DSYS since the asymmetry of the heeled hull is not explicitly measured. The pressure drag sensitivity to heel is in the right trend, even though overestimated on this hull. The presented regressions give very satisfying results, showing the appropriate trends on side force and pressure drag between the different heel and leeway angles. The absolute values given by the regressions are good, often under 5% and a maximum of 15 % discrepancy compared to ICARE computations. Further work includes new series and associated formulations to tackle more various hull shapes, including larger displacement to length ratios. This will be a step towards more versatile formulations, which will be compared with the DSYHS on some of the models of the Delft series. 5. INTEGRATION IN A VPP FIRST RESULTS The current ongoing work concerns the development of a VPP able to take advantage of the presented formulations. Two separated models are used in addition to the presented formulations for bare hulls: an appendage model based on the lifting line theory [13] and an aerodynamic model based on the Offshore Racing Committee model [12]. This VPP finds the equilibrium between the forces computed by three models on the six degrees of freedom of the boat. It solves the equilibrium equations to find the heel, speed, leeway, running trim and rudder angle fulfilling the best equilibrium between all the forces. The best equilibrium is found when the boat speed is maximum in a given true wind speed and wind angle. An apparent weight of the boat carried by the hull is also computed, accounting for the appendages and sails contributions on the vertical axis z0. This VPP allows a very fast evaluation or optimization of fine tunings such as dagger-boards toe-in or keel tilt angle. The keel tilt is defined as the angle between the rotation axis of a canting keel and the horizontal axis when the boat is in its hydrostatic equilibrium upright. This tilt angle introduces a coupling between the cant angle and the keel angle of incidence. A positive tilt (forward bearing moved upwards) tends to generate lift on the keel fin (positive side force and upwards lift), modifying the running trim and sinkage of the hull as well as the leeway angle and the yaw equilibrium, see figure 15. Z0 Z0 Y0 Y0 Positive vertical force Positive side force Figure 15: No keel tilt (left), positive keel tilt (right) In order to test the sensitivity of the recently developed VPP, the influence of the keel tilt on the equilibrium of a Volvo 70 is investigated. The keel is canted 40 degrees to windward, the leeward rudder 15 degrees to leeward and the dagger boards are lifted out of the water. This typical broad reaching configuration is studied with full mainsail and a fractional headsail from true wind angle of 110 to 140 degrees. Figure 16 presents the boat speed, displacement carried by the hull, running trim and leeway angle for 3 different keel tilt angles in 12 knots of true wind speed. On the presented configuration, the keel fin centre of surface is placed 1.15 m in front of the yacht centre of gravity. Boat speed [KTS] Leeway [>0 to leeward] Keel Tilt = 0 Keel Tilt = 2 Keel Tilt = VB Δ var True Wind Angle 6 1 Keel Tilt = 0 Keel Tilt = 2 4 Keel Tilt = Leeway Trim True Wind Angle Figure 16: Speed, weight reduction (top), running trim and leeway angles (bottom) for 3 different keel tilts Weight reduction [kg] Running Trim [>0 bow up] TH 28 TH June, 2013

42 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France The results show a very satisfying sensitivity to the change in keel tilt, showing large changes in the vertical and horizontal forces generated by the appendages. The trends are good, high values of keel tilt leading to significantly reduced apparent weight and leeway angles. The apparent weight carried by the hull is reduced by 500 kg with a keel tilt of 4 degrees compared with no keel tilt. The leeway angle is reduced by almost 2 degrees. The resulting changes in maximum boat speed are not negligible, up to 0.5 knots. The boat speed and true wind angle are expressed with respect to the course of the yacht (water flow referential), not its longitudinal axis (boat referential). The presented coupling between hull and appendage models neglects their hydrodynamic interaction. In fact, the flow around the hull is indeed modified by the presence of the appendage and the hull changes the behaviour of the appendages. The model might therefore be enhanced by introducing corrective terms to take this interaction into account, based on appended computations or tank tests. It is part of the ongoing work. As this interaction is highly dependant on the distance between the appendage root and the free surface, the running trim and running sinkage formulations presented in this report will be used to compute the free surface proximity. It must be mentioned that this interaction phenomenon is much weaker on modern yachts than in the past mainly due to the high aspect ratio of the appendages. Modern appendages present much smaller volume close to the hull and therefore weaker interaction with hull and the free surface. 6. CONCLUSION A complete methodology to study the hydrodynamic behaviour of yacht hulls was presented. First step is the database building: choice of the experiments, generation and measurement of the geometries, meshing and finally computation using a RANSE code; second step is the statistical methodology to treat the database. An effort is made in this article to detail this methodology to allow its application to other fields. New formulations for the approximation of the forces production and attitudes of bare hulls in calm seas have been presented. A specific VPP has been developed to use these formulations and the first results of the coupling with the appendage and aerodynamic models are very promising. ACKNOWLEDGEMENTS Gianluca Guelfi from the University of Genoa is gratefully acknowledged for his work on the VPP, implementing lifting line theory, aerodynamic model and optimization algorithms. Hydrocean is also to be acknowledged concerning the development of the morphing tool used in the database building loop. Finally, the authors would like to thank all the members of Marc Lombard Yacht Design Group for their support and the funding of this research program. AUTHOR BIOGRAPHY L. Huetz currently works at Marc Lombard Yacht Design Group. He is responsible for performance studies, hull design and optimization. He obtained his PhD. at Ecole Centrale de Nantes in REFERENCES 1. JA. Keuning, U.B. Sonnenberg, Approximation of the hydrodynamic forces on a sailing yacht based on the Delft Systematic Yacht Hull Series. The International HISWA Symposium on Yacht Design and Yacht Construction, JA. Keuning, M Katgaert, The bare hull resistance of the delft systematic yacht hull series at high speeds. Proceedings of the 1 st Innovsail Conference, Lorient, L. Huetz, B.Alessandrini, Systematic study of the hydrodynamic forces acting on a sailing yacht hull using parametric design and CFD, Proceedings of OMAE,, Rotterdam, The Netherlands, L. Huetz, Y. Andrillon, P.E. Guillerm, B. Alessandrini, Systematic study of the hydrodynamic forces on a Volvo 70 yacht using parametric design CFD and variable selection, 4th High Performance Yacht Design Conference, Auckland, New Zealand, L. Huetz, Systematic study of the hydrodynamic behaviour of sailing yachts hulls. PhD. Thesis. Ecole Centrale de Nantes, B. Alessandrini, G. Delhommeau, Simulation of three-dimensional unsteady viscous free surface flow around a ship model. International Journal for Numerical Methods in Fluids, vol 19, pp , D. C. Wilcox, November, Multiscale model for turbulent flows. AIAA Journal Vol 26, pp , J. Raymond, Performance estimation of planing yachts. PhD Thesis, Ecole Centrale de Nantes, NIST/SEMATECH, E-Handbook of Statistical Methods, itl.nist.gov/div898/handbook, A. Jourdan, Planification d expériences numériques. Revue MODULAD, A. Lovison, Lipschitz Sampling for Improving Metamodels in modefrontier. Technical report, ESTECO, ORC VPP Documentation J. Katz, A. Plotkin, Low speed aerodynamics. McGraw Hill, TH 28 TH June, 2013

43 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France A SIMPLIFIED METHOD TO ASSESS ACCELERATION LOADS ON SAILING YACHT MASTS A. Combourieu, Engineer in hydrodynamics, France, adrien.combourieu@innosea.fr F. Faloci, RINA Services SpA (Italian Classification Society), Italy, flavio.faloci@rina.org D. Boote and T. Pais, University of Genoa, Italy, dario.boote@unige.it, tatianapais@hotmail.it The behaviour of sailing boats in open sea is strictly related to their hydro and aerodynamic performances and to the wide range of loads acting on the hull and rigging system. Their evaluation could be done only by a careful seakeeping analysis with particular attention to the acceleration loads caused by hull motions which can create severe problems to mast and rigging up to extreme consequences such as dismasting. The main reasons of dismasting are related both to human errors and to the lack of load knowledge; as a matter of fact Classification Societies' Rules are quite poor about this subject and the structural design if often committed to the designer experience. The aim of this work is to investigate on the hull dynamic responses which mainly influence the mast and rigging loads with particular attention focused on the pitching behaviour of the vessel. With this goal in mind the seakeeping behaviour of a number of sailing yachts, different each other in sizes and typology, has been investigated. Despite the small size of the database, the achieved results allowed to formulate a preliminary simplified method to estimate the pitch Ratio Amplitude Operator (RAO), based only on the boat length. From the pitch RAO knowledge a very rough and quick formulation to evaluate the longitudinal acceleration in the mast centre of gravity has been obtained. NOMENCLATURE a Amplitude of wave (m) B Breadth (m) B wl Waterline breadth (m) Angle of heading (degrees) Peakness factor D Draught (m) Displacement (Kg) Wave slop (m) f Frequency (Hz) g Gravity acceleration (m/s 2 ) H Wave height (m) k yy Gyration radius (m) Wavelength (m) 0 Wavelength for which the RAO is equal to 0,05 in terms of pitch/wave slope(m) 1 Wavelength for which the RAO is equal to 0,95 in terms of pitch/wave slope(m) L ao Overall length (m) L wl Waterline length (m) p max Pitch RAO maximum RAO Ratio Amplitude Operator S Spectrum (m 2 /s) T Period (s) t Time (s) U Forward speed (m/s 2 ) Phase (degrees) Wave pulsation (rad/s) 1 INTRODUCTION With regard to sailing yachts, dismasting is considered an impressive and extreme event, very dangerous for crew and for the vessel. Nowadays some Classification Societies have a section in their Rules specifically dedicated to mast and rigging scantling [1] - [6]. In particular, the Italian Classification Society RINA, recently published a draft of its new Rules in which a specific section for sailing yacht design has been introduced [7]. Nevertheless the last word about mast and rigging design is often left to designers and mast builders and the first step of this activity should be the full understanding of acting loads. Two kinds of loads can be individuated: aerodynamic loads due to wind action on sails and inertial loads due to the yacht motion in waves; a complete review of all loads to be considered in yacht design can be found in [8]. In this paper attention has been focused on sea loads and, after a first investigation, performed also on references made available in literature, such as [9], [10], [11] and [12], the main hull response leading to important acceleration loads on mast has been individuated on pitching motion. A comprehensive study on the pitching behaviour of sailing yachts at sea has then been carried out by means of the well known seakeeping software HydroStar [13]. This is a linear potential flow solver using panel methods in frequency domain and developed by Bureau Veritas. When nothing is explicitly specified, RAO calculations

44 are carried out with no heel, no forward speed and in pure head sea. The analysis has been carried out on a database of seven modern sailing yacht hulls of different lengths and typology, from 8 to 30 meters in length.. Basic hull descriptions have been derived from commercial leaflet or shipyard web site, where only few information are available. In most cases, main dimensions (such as length, beam, displacement, ballast weight) and only top and longitudinal views are given. A synthesis of the considered boats is presented in Table 1. Starting from these information CAO models have been created using the open software FreeShip [14]. Only the canoe hull bodies are modelled, assuming that with regard to pitch motion, the keel effect is negligible. Table 1: Main dimensions of the seven hulls considered. Figure 1: Pitch RAO from HydroStar compared with experimental results of [10] (red dots). 2.1 WATERLINE LENGTH L wl The seven hulls collected in our database are different in sizes but quite similar in shape. Therefore, the reference parameter assumed in this study is the waterline length L wl. By using potential methods, only the underwater parts of the hulls are taken into account. The seven pitch RAOs obtained by HydroStar calculations are displayed in Figure 2. The waterline length is obviously the most critical parameter driving pitch motion. 2 IMPORTANT YACHT HULL PARAMETERS The influence on pitch RAO of different hull parameters has been deeply analysed in this study. Some of them have been proven to have a significant impact on the pitching behaviour of a sailing hull at sea, whereas others have been found to have a negligible impact. The most critical parameters are listed and discussed in the following subsections. Before any other activity a comparative analysis has been carried out in order to set up the various HydroStar parameters. The study has been performed on the yacht called AME004 on which huge real scale measurements of ship motions have been performed at sea and published in [10]. The AME004 hull has been modelled by FreeShip software and the results obtained by HydroStar calculations have then been compared with experimental ones. The comparison of pitch RAO results are plotted in Figure 1 and they show a good agreement. Figure 2: Pitch RAOs of the seven yachts obtained by HydroStar calculations. 2.2 PITCH GYRATION RADIUS Typically, for modern sailing boats, the pitch radius of gyration k yy is in the range [0.25 L wl L wl ]. For the considered boats, they have been found to be between 0.27 L wl and 0.30 L wl. As a consequence, the impact of pitch gyration radius varying in this range has been studied. It can be expected that gyration radius will change the maximum value of the pitch RAO and the value of the resonance frequency as well. Making the analogy with a simple spring, it can be expected that with bigger gyration radius (i.e. bigger inertia) the resonance

45 frequency should decrease (as it is related to the stiffness over inertia ratio). On the other hand, the peak at resonance should be bigger. Let us define some value that will describe the simplified RAO: - 1 : the wave length (m) from which the boat starts to simply follow the wave and f 1 the corresponding wave frequency. It can be defined as the wave length for which the RAO is equal to 0.95 in terms of pitch/wave slope; - 0 : the wave length (m) up to which the boat does not respond to the wave and f 0 the corresponding wave frequency. It can be defined as the wave length for which the RAO is equal to 0.05 in terms of pitch/wave slope. Figure 5: Influence of the pitch gyration radius k yy on Swan 66 pitch RAO plotted as a function of wavelength. 2.3 FORWARD SPEED Figure 3 : three regions of interest on SW pitch RAO plotted as pitch/wave slope against wave length. Figure 4 shows the pitch RAOs of the Swan 66 for different pitch gyration radius. The resonance does not seem to change significantly in this range of kyy. Figure 5 shows the same results but plotting the RAOs in term of pitch over wave slope as a function of wave length. It can be noticed that the motion in the range of interest between 0 and 1 is quite sensitive to k yy. On the other hand, out of this range, results are quite similar. The estimation of the RAO in the range 0-1 might thus be refined in the future, using the value of k yy in some way. Up to now, calculations have been carried out with no forward speed for sake of convenience and simplicity. In practice, of course, the yacht has a forward speed. The best case is to have the polar diagram of the yacht to be studied to perform a detailed computation at a given speed and heading. Anyway, the effect of forward speed is double: - first it changes the equations to be solved by changing the boundary conditions of the potential problem; - secondly it determines the encounter frequency. - Indeed, if the wave has a frequency "f" the boat experiences and responds at the frequency "f e " where: - is the heading angle (head sea=180 ) - U is the forward speed in m/s - g is the acceleration of gravity m/s² Figure 4: Influence of the pitch gyration radius k yy on Swan 66 pitch RAO. The effect of increasing forward speed in head sea for the yacht SW is shown in Figures 6 and 7 respectively for pitch RAO and longitudinal acceleration at middle height of the mast. The forward speed effect on pitch is quite big (+28% around 10 knots) whereas it is huge for acceleration in the mast (4.3 times bigger at 10 knots than 0 knot). It seems logical if thought that, in a way, for a given wave, the yacht has to make the same pitch but quicker at 10 knots rather than at 0 knot.

46 Figure 6: Influence of forward speed on SW pitch RAO. Figure 7: Influence of forward speed on SW mast acceleration RAO. Figure 8: Influence of heading on Swan 66 pitch RAO. 2.5 STERN SHAPE With regard to pitch motion, the shape of bow and stern is critical. Modern sailing hulls tend to have a flat and large stern along with a straight bow. This minimizes the pitch for several reasons. First, it maximizes the waterline length which decreases pitch motion. Then, large and wide stern increases the wave damping effect which, again, reduces pitch motion. On the contrary, older sailing yacht hulls are narrower and sharper. In that case, the keel is part of the hull and to neglect it in the seakeeping calculations may be wrong. Figure 10 shows the example of the Centurion 32 with original hull and enlarged stern. Predicted pitch motion is surprisingly big but, as expected, results to be reduced by assuming an enlarged stern. 2.4 HEADING Till now, only motion in pure head sea (180 heading) has been considered. This approach is justified by the fact that the maximum pitch happens when going up sea (which is generally also upwind). The pure head sea is not necessarily the worst case in term of pitching, as shown in Figure 8. Nevertheless, around 180 degrees, RAOs are quite close to each other and they really decrease at around 90 degrees (side sea). Depending on cases, pitch can be bigger around degrees. Figure 9: Mesh of the original Centurion 32 (left) and with enlarged stern (right) For a sake of simplicity, in the following pitch motion is thus studied in pure head sea by default. Figure 10: Comparison of pitch RAOs of original Centurion 32 and enlarged stern model.

47 Among the tested parameters, the following ones has proven to be of great influence on pitch motion: - waterline length; - pitch gyration radius; - forward speed; - heading; - stern shape. Other parameters have been investigated without showing important impact on pitch motion, such as: - heel angle; - keel shape; - water depth; - centre of gravity position; - beam-draft ratio; - draft-displacement ratio. The regression based on the yacht waterline highlights a linear correlation between L wl and both res and 0. Then, the approximated pitch RAO is obtained by: - the wave slope for f < f 1 ; - 0 for f > f 0 ; - simple triangulation using the point (f res, p max ) for f 0 < f < f 1. A comparison between pitch values calculated by HydroStar software and determined by the present simplified method (based on L wl ) has been carried out; the assumed case study is the sailing yacht "Kiboko" built by "Southern Wind Shipyard" and not belonging to the seven yachts database. 3 SIMPLIFIED METHOD FOR QUICK PITCH MOTION AND ACCELERATION ASSESSMENT In this section, a very simple method is proposed to quickly estimate pitch motion and induced acceleration on the mast. The driving idea is to provide a fast method to assess these values by simple formulas, without using any software. From considerations given in part 2, the method herein proposed is only based on yacht waterline length. In addition it can be valid only in case of head sea and with no forward speed. 3.1 SIMPLIFIED PITCH RAO Figure 11: "Kiboko" sailing yacht during launching and the corresponding CAO model prepared by FreeShip. Results can be seen in the following Figure 12. The starting point of this method is to consider the pitch RAO plotted in a different way. Usually, the pitch amplitude for a 1 m wave is plotted against wave frequency or pulsation. In this approach, the pitch amplitude divided by wave slope (or steepness) has been plotted versus the wave length. Indeed, linear wave theory in infinite water gives a unique relation between wave period and wave length, through the dispersion equation: =1.56 T 2 = 1.56/f 2 Then, the wave slope is given by: It s clear that for long waves, the boat just follows the wave and its maximum pitch is equal to the wave slope. On the other hand, for very short waves, the boat almost does not respond. Now, let us define some values that will describe the simplified RAO: - res : the resonance wave length (m) and f res the pitch resonance frequency (Hz); - p max : the pitch for one meter wave at resonance frequency ( /m). Figure 12: "Kiboko" pitch RAO computed by HydroStar (green) and estimated by her waterline length (blue). Table 2: Comparison of computed and estimated pitch RAOs Calculated with HydroStar Pitch resonance frequency (Hz) Maximum pitch ( /m) Estimated with Lwl Pitch resonance frequency (Hz) Maximum pitch ( /m)

48 3.2 EXTENSION TO A ROUGH MAST ACCELERATION ESTIMATION A very important capability of HydroStar software is to provide accelerations at any point of the vessel, taking into account different motion coupling. Nevertheless, as the authors' aim is, it could be of interest to assess roughly and quickly the mast acceleration without the necessity of using any software. The idea here is to assume that the worst case, for what mast acceleration are concerned, occurs at pitch resonance. Moreover, let us assume that the total longitudinal acceleration can be approximated by the pitch acceleration only. Then, starting from the results exposed in part 3.1, the estimation of the mast acceleration can be derived in the following way: - evaluate pitch resonance frequency and pulsation ( res) and maximum of the pitch RAO (p max ); - evaluate the lever arm. For example in the mid mast, it can be roughly estimated as ; - evaluate peak acceleration value (for 1m wave amplitude) by deriving twice the motion value and multiplying by lever arm: Table 3 shows the estimated maximum acceleration for 1m wave compared to the one computed by HydroStar software. The estimation is made making reference only to L OA and L wl. Here, these values are obtained from the yachts used to build the model. Table 3: Comparison of computed and estimated longitudinal accelerations at mid mast. accxmast max computed accxmast max estimated Name Ratio m/s 2 /m m/s 2 /m SW Swan Oyster Swan Ref AME J elevation is decomposed in a sum of regular waves. The sea surface profile can be written, making reference to a fixed axis system, as: The dependence from space vanishes if we consider a boat with no speed. Waves are supposed to have random phases i. Then, as the problem is linear and solved for regular waves, the response for motion x i would be: The RAO used in this procedure is the one computed for the heading of interest. A fundamental issue of this time domain approach is how to define the sea state. The problem is thus commonly addressed in the frequency domain. The sea state is often described by a Jonswap spectrum. With = 0.07 if f < f p and = 0.09 if f >f p Such a spectrum is completely defined by three parameters: - the significant wave height H s. It is linked to the area under the curve of the spectrum. It is close to the height a human observer would give by watching the sea. Parameter is adjusted to fit H s ; - the peak period T p =1/f p. It is the period corresponding to the peak of the spectrum; - the peakness factor. It describes the width of the peak or how the peak is spread over frequencies. Typical values of are 1 (fully developed sea) and 3.3 (wind sea). Then, the spectrum of the motion of interest can be obtained: From the spectrum, the time series can be reconstructed by: 4 MOTION IN IRREGULAR SEA STATES 4.1 THEOEITICAL FORMULATION Previous results were obtained in regular or harmonic waves while, as a matter of fact, sea free surface is irregular. In the linear theory approach the sea surface With being the frequency step of discretization. Now, for a boat with forward speed U and a heading, the assumption of encounter frequency is made. The boat is supposed to stay at the origin of the axis but what is

49 changed is the frequency of the waves it sees. To a real wave frequency f it corresponds an encounter frequency f e : So, for an excitation at frequency f, the yacht response is no more at f but at f e : In that case, the RAO to be used is that computed with the heading of interest and at the forward speed of interest, computed in this work by HydroStar software. 4.2 COMPARISON WITH EXPERIMENTAL RESULTS Unfortunately a large amount of experimental data to be compared with this model doesn't exist. In [11], real scale on board measurements of pitch motion were performed. The yacht is a J80 sailing yacht. From personal communication with the authors of this paper, some information about the test conditions have been obtained: - boat was going upwind (40 degrees from wind) at mean speed around 5 knots; - wave height was visually evaluated to 0.3 m; - encounter period was deduced from measured pitch period to 1.3 s; - measurements have been performed in the bay of Brest, France, which is almost a closed basin. Experimental results are given as a plot of the pitch time series over 35 seconds (see Figure 13). It has been chosen to perform the computation with the following parameters: - in pure front waves (heading of 180 degrees); - with a speed of 5 knots; - in a sea state of H s = 0.3 m, T p = s (which corresponds to encounter period of 1.3 s) and with = 3.3 (as the basin is closed, the sea was probably not fully developed); - no heel angle. Figure 13: Comparison of pitch time series measured in [11] (in black) and computed (H s = 0.3 m, T p = 2.25s and = 3.3, in red). However, the longer a yacht stays on a given sea state, the more likely it is to meet a wave bigger than the average wave. A value that can be recorded is the maximum response staying a given time in a given sea state. As even this value will vary by repeating the same experiment, an average over several similar experiments can be done. This last value would be a bit more robust or less random. 4.3 IRREGULAR SEA STATE RAO As previously explained, the maximum value of yacht response at sea during a given duration can be recorded. A typical duration for a sea state to be considered constant is 3 hours. This duration is used in the following. Some computations showed that the influence of the peak enhancement factor value almost does not impact on the values of this maximum. On the other hand, the significant wave height and the peak period/frequency impact a lot on this value. Figure 14 shows, for a given peak frequency, the influence of the significant wave height on the maximum pitch response. Comparison of time series over 35 s can be seen in Figure 13. This comparison shows very good agreement in terms of amplitude and period between the model and the real measurements. It must not be forgotten that there is a random part (the phases) in the computation of these time series. Results will thus not be the same by running twice a computation with the same parameters. It means that the two curves in Figure 13 will never superimpose but what matters is the significant height and period of the response. Figure 14: Influence of significant wave height on pitch motion.

50 As a linear theory has been used, the maximum responses linearly depend on the (significant) wave height. The wave height can be considered to be H s = 2m (i.e. 1m amplitude). Then, as for regular waves, the results in term of maximum response in an irregular sea state can be plotted as a function of the peak frequency only. It is the definition of a RAO, but here in irregular sea state. Figure 15 and 16 show an example for the pitch and the acceleration at mid-mast. Figure 17: Irregular sea pitching results (H s =1m, =1) obtained by using the RAO computed by HydroStar ( in red) and the RAO estimated by the presented procedure (in blue) Figure 15: Irregular pitch RAOs. Maximum pitch for a 3 hours sailing in irregular head sea, with H s = 2 m, = 1 and no forward speed. Figure 16: RAOs of irregular sea acceleration in the mast centre of gravity. Maximum longitudinal acceleration at mid mast for a 3 hours sailing in irregular head sea, with H s = 2 m, = 1 and no forward speed. The results obtained for irregular sea RAOs are bigger than for RAOs in regular sea; this can be explained by the fact that in a sea state of 2 m significant wave height (1 m amplitude), the boat can experience to meet waves of bigger amplitude. Using this representation, the irregular pitch RAO of Kiboko yacht can be plotted using both the regular RAO computed by HydroStar and the estimated RAO obtained by the proposed method. This is depicted in Figure 17. The oscillations are due to the random part of the irregular wave generation. This diagram shows very good agreement in terms of real pitch motion in irregular sea. The results using computed and estimated RAOs are really similar. It can be again recalled that the blue curve is obtained without using any hydrodynamic software. 5 CONCLUSIONS The main objective of this work was to investigate on maximum accelerations acting on the mast and rigging system of yachts when sailing in severe sea states. In the preliminary phase of the study it has been verified that the parameter which mainly affects mast accelerations is represented by the pitch response of the vessel. In the second phase the influence of different variables on pitch motion has been deeply investigated. Key parameters of the pitching behaviour have been individuated to be: waterline length, pitch radius of gyration, stern shape, heading and forward speed. In order to have a wide and reliable set of results a number of sailing yachts has been collected in a data base ranging from 8 to 31 meters in length. The described calculations have then been carried out on all the yachts of the database. For seakeeping analyses the well known HydroStar software by Bureau Veritas, has been utilised. In the third phase of this work, starting from the gathered seakeeping results, a very quick and simple formulation has been proposed to estimate the pitch RAO of a modern sailing hull in head sea, with no forward speed. This formulation is only based on the hull waterline length and it represents a first, rough approach to estimate the order of magnitude of the acceleration in the mast. These estimations are irrelevant with forward speed. In the final phase, a state-of-the art process has been set to get seakeeping results in irregular seas. It has been successfully compared with real on board measurements performed on the sailing yacht "Kiboko". In case of no forward speed, pitch motion RAO in irregular sea seems to satisfactorily match those obtained by the proposed simplified method. This work is to be considered as a preliminary study of mast and rigging response to yacht motions at sea and

51 many further improvements appeared to be very interesting to the authors during the development of the performed investigations. In the following some possible hints are presented: - improve the simplified formulation proposed by taking into account the effect of other important parameters highlighted before, such as forward speed; - build a much bigger database, get results and perform a regressions using these key parameters to better estimate the pitching behaviour; - keep comparing results with incoming on board measurements on Kiboko and other sailing yachts; - investigate the relevance of results out of the range of the linear model (e.g. in breaking waves). ACKNOWLEDGEMENTS The authors want to thank the Italian Classification Society RINA for having made possible this research. Authors are thankful to Bureau Veritas for providing HydroStar software together with technical support. Mr Patrick Bot and Mr Benoit Augier are also acknowledged for the valuable data they shared with the authors about J80 measurements. Finally Southern Wind Shipyards are very much acknowledged as well for making very unique sea tests by their sailing yachts and making results available for this research. This work was developed as a master thesis in the University of Genoa in the frame of the European Master Course Erasmus Mundus "EMSHIP - Integrated Advanced Ship Design. REFERENCES 1. AMERICAN BUREAU OF SHIPPING, Guide for Building and Classing Offshore Racing Yachts, New York, USA, BUREAU VERITAS, Rules for the Classification and Certification of Yachts, Paris, France, DET NORSKE VERITAS, Rules for construction and certification of vessels less than 15 metres, Hovik, Norway, GERMANISCHER LLOYD, Design and Construction of Large Modern Yacht Rigs, Hamburg, Germany, GERMANISCHER LLOYD, Guidelines for the Type Approval of Carbon Strand and PBO Cable Rigging for Sailing Yachts, Hamburg, Germany, REGISTRO ITALIANO NAVALE (RINA) Regolamento per la Costruzione e la Classificazione delle Barche a Vela da Regata 12 m S.I. e 6 m S.I. (in Italian), Genoa, Italy, RINA, Rules for the Classification of Yachts Designed for Commercial Use, Part B, 8.4 Masts and Rigging, ISSC 2009 Report, V.8 Committee Sailing Yacht Design, Seoul, Korea, August FOSSATI, F., MUGGIASCA, S., Experimental investigation of sail aerodynamic behaviour in dynamic conditions, Journal of Sailboat Technology, McRAE, B., BINNS, J., KLAKA, K., DOVELL, A., Windward performance of the AME CRC systematic yacht series, RINA International Conference on the Modern Yacht, Portsmouth, UK, March AUGIER, B., BOT, P., HAUVILLE, F., DURAND, M., Experimental validation of unsteady models for fluid structure interaction: Application to yacht sails and rigs, Journal of Wind Engineering and Industrial Aerodynamic, pp , AUGIER, B., HAUVILLE, F., BOT, P., DURAND, M., Numerical investigation of the unsteady fluid structure interaction of a yacht sail plan, 4th High Performance Yacht Design Conference, Auckland, March BUREAU VERITAS, HydroStar for experts user manual, Paris, DELFTSHIP FREE, FreeShip Manual, Netherlands, AUTHORS BIOGRAPHY A. Combourieu holds the position of R&D engineer at Innosea, engineering office in offshore renewable energies. He is graduated from Telecom ParisTech and EMSHIP, European post-master in advanced ship design and hydrodynamics. His current research deals with waves energy converters (WEC). F. Faloci holds the position of Naval Architect at Italian Classification Society RINA. He is responsible for rule development of RINA Rig Guidelines. He graduated in Naval Architecture and Marine Engineering from the University of Trieste. After three years as ship designer at Maierform Engineering he joined RINA as branch office surveyor. His experience includes fifteen years of surveys and plan approval activity on all kind of boats and ships, ranging from rowing boats up to passengers ships. From 2004 he was assigned to RINA head office

52 in Genoa. He is an amateur yacht designer, as well a dinghy and keelboat instructor with more than 35 years of sailing experience. D. Boote holds the position of Ship Structure Professor at the Naval Architecture section of the Department of Electrical, Electronic, Telecommunications Engineering and Naval Architecture (DITEN) of the University of Genova. He is the Chairman of the Bachelor and Master Course in Yacht Design in La Spezia. His initial experiences include a long research activity in the field of Ship and Offshore Structures followed, since 2000, by an intense activity in the field of sailing and motor yachts. From 2006 to 2012 he has been Chairman of the V.8 ISSC Committees on "Sailing Yacht Design" and "Yacht Design". T. Pais holds the current position of PHD in the Naval Architecture section of the Department of Electrical, Electronic, Telecommunications Engineering and Naval Architecture (DITEN) of the University of Genova. Her research activity deals with the dynamic behaviour of hull structures and the analysis of seakeeping characteristics of ships and motor and sailing yachts.

53 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France NUMERICAL STUDY OF ASYMMETRIC KEEL HYDRODYNAMIC PERFORMANCE THROUGH ADVANCED CFD D. Mylonas, S. Turkmen and M. Khorasanchi, University of Strathclyde, Glasgow, UK The hydrodynamics of an asymmetric IACC yacht keel at angle of yaw are presented using simulations performed by advanced computational fluid dynamics using state-of-the-art software. The aim of the paper is to continue working on the improvement of numerical viscous flow predictions for high-performance yachts using Large Eddy Simulation and Detached Eddy Simulation on unstructured grids. Quantitative comparisons of global forces acting on the keel and wake survey are carried out. Qualitative comparisons include flow visualisation, unsteady and separated flow and other features. Star-CCM+ and the trimmed cell method give better forces and wake prediction compared to the unstructured mesh of ANSYS Fluent. Both solvers give good flow visualisation near and far field of the keel. 1 INTRODUCTION Recent shift and progress in numerical and computational methods based on Computational Fluid Dynamics (CFD) has focused on aerodynamic applications of sails performance, due to the prominent arrival of the state-of-the-art catamarans ready to compete in the forthcoming America s Cup. Free-surface hydrodynamics are also increasingly studied, partly due to the boost in computational resources and partly because of their importance in competitive sailing concerning flow interactions between appendages and hull in certain sailing conditions (e.g. Volvo Ocean Race). Below the waterline, another area where CFD simulations play a crucial role is the design and performance of the appendages. Keel hydrodynamics are studied to gain an understanding of effects and interactions occurring in the near and far field flow, depending on the sailing conditions. Keel, bulb, winglets and rudder should be developed accordingly in order to guarantee global optimal performances. The advantage of the numerical approach relies on the possibility to test several different configurations and to have a complete picture of the flow behaviour at every time instant. The viscous hydrodynamic flow around a keel is important for several reasons: The transition from laminar to turbulent flow is still a delicate topic in numerical simulation that requires continuous investigation. The unsteady & separated flow is also a critical aspect that researchers want to grasp to minimise losses and constraints during races. Modelling the flow at key locations such as rootjunction of keel, bulb and winglets helps predicting when they occur. The continuous need for validation of quantitative results for CFD codes is important for high Reynolds number flow. Additionally, qualitative data that can provide practical help to those involved in yachting is necessary. Information about local and global distribution of flow quantities (e.g. pressure, velocities, vorticity and turbulence) can be useful to improve the hydrodynamic performances of keels. Creating and computing the flow around the appendages can help understanding the formation of the main flow characteristics and their interaction with the boat components. In this context, CFD simulations of keel hydrodynamics have been carried out in various published studies using numerical methods based on potential flow codes and Navier-Stokes solvers with varying level of quantitative success but with useful qualitative applications. Ticono et al. [1] showed good agreement between wind tunnel tests of generic keels for the 1992 America s Cup campaign and potential flow/boundary layer computations validated against wind-tunnel data. Their findings concluded that the numerical method was suited for induced drag computations of the keel configurations, but lacked in accuracy in the predictions of the viscous resistance of the bulbs. Werner et al. [2, 3] validated a potential flow code (SHIPFLOW) coupled with a boundary layer code against the wind tunnel tests on an America s Cup keel. The errors in the potential flow code coupled to the boundary layer solution results were within the experimental uncertainty (2% error for both lift and drag), but given that the correct panelisation is used (in some cases, absolute error was as high as 18%). In addition, the same research group also performed RANS based calculations with comparisons in terms of lift, drag forces, and wake survey. The multi-block structured approach used grids ranging from 1 million to 2.6 millions cells; the finest mesh was adding up to 3.6 million. The errors of the RANS code (FLUENT) were found to be a little higher than the experimental uncertainty. The study reported that errors between the measured values and the RANS computations for a

54 wingless keel yielded differences of between 0.4% and 3% for lift, depending on the turbulence model, and between 0.3% and 12% for drag. For a winged-keel, the corresponding discrepancies were around 3% for both forces. Ambrogi et al. [4] performed a RANS simulation of the flow field around the same keel using a viscous code developed by INSEAN. The study showed differences in terms of pressure contours, velocity fields, vorticity and comparisons with experiments in terms of nondimensional global forces and axial velocity. An overgrid, structured mesh of 7 million cells was used. The authors reported quite large errors between numerical results and measured values, of the order of about 8% in drag and as much as 23% in lift, for both arrangements tested. The differences were put down as modelling errors. Thys [5] used Werner s geometry to test and evaluate the non-viscous, potential flow CFD code RAPID.One configuration was tested (winglets in aft position). Forces were found to be within the uncertainty region of the experimental measurements; drag was over predicted, lift was good for one case, but bad for the other. Out of the three lift-prediction methods used, (pressure integration, Trefftz-plane method and wing theory) the first was found to be the most accurate. Mylonas and Sayer [6] presented initial work based on the use of Large Eddy Simulation (LES) and Detached Eddy Simulation (DES) using a commercial CFD code with mixed success. Error in forces prediction was found to be high at times, depending on the model used and the mesh size, but qualitative observations were found to be useful and relevant to keel flow hydrodynamics. The main motivation behind this research is to continue on the improvement of previous numerical study on advanced CFD using a LES and DES approach of keel hydrodynamic prediction. is simulated. The fin and the winglets have a NACA 0012 profile. The bulb has a flat bottom and a beaver tail tip. This is known to produce minimum drag, by extending the effective span of the keel and ensuring that the wetted area is not increased excessively. The dimensions of the keel are given in Table 1. The tunnel blockage ratio between the model frontal area and the section area was found to be around 3%, and does not exceed the recommended 7.5% limit; hence, it is neglected in the study. Several configurations were tested and a selection of results is presented in the paper. Table 1: model keel dimensions in metres Bulb Chord Bulb Max Thickness Fin Mean Chord Fin Max Thickness, Mean Chord Fin Span Winglet Mean Chord Winglet Max Thickness, Mean Chord Winglet Span Winglet Dihedral (deg) 17 Winglet Pitch (deg) 0 The asymmetry of the case is represented by an angle of attack between the undisturbed inlet flow and the model. Constraints in the experimental wind tunnel setup of the keel led to a yaw angle fixed around 4 degrees. Moreover, it can be observed that the fin is not perfectly aligned with the bulb, causing a further gap (Figure 1). This incurs flow separation at the trailing edge of the fin keel and aft part of the bulb, which will be investigated. In addition, this means that any computational model will have to be meshed entirely, instead of using a half-model, which is common norm in CFD when dealing with symmetric bodies. In the present study, the hydrodynamics of an asymmetric IACC keel in idealised upwind conditions are simulated using advanced computational methods based on the LES and DES turbulence models inside a virtual wind tunnel. The problem is further defined in the next section, followed by an outline of the mathematical formulation and numerical solution. Finally, the results are presented and discussed, and include quantitative & qualitative comparisons between CFD models. 2 PROBLEM DESCRIPTION The wind tunnel experiments by Werner et al [2] are used as a validation case for the numerical study presented here. The fully appended IACC model keel is placed in the test section of the wind tunnel where flow Figure 1: front view of the keel with yaw angle

55 The experiments reported the global forces in the undisturbed flow direction along the x-axis and the z- axis, corresponding to total drag and total lift forces. In addition to the forces, the following values were provided in the experimental data and were measured at a plane located at 2.375m from the tunnel inlet zone: velocity magnitude, velocity components in x-, y- and z- direction, static and total pressure. The inlet flow conditions are summarised in Table 2. The Reynolds number based on the length of the bulb and the free stream inlet velocity is equal to 3.2 x 10 6, turbulent flow is expected around the keel. Table 2: inlet flow conditions for CFD simulations Atmospheric Pressure (kpa) Inlet Velocity U (m/s) Dynamic Viscosity μ (kg/ms) Turbulent Intensity (%) 0.1 Turbulent Length Scale (m) In addition to validating the numerical results against experimental data for forces and wake survey, we also present characteristics of the flow linked to the current case study, in terms of unsteady viscous and separated flow, investigation of the laminar-turbulent transition and observation of junction flow around intersections between the components of the keel. The commercial CFD codes ANSYS FLUENT 12.1 and STAR-CCM+ v7.02 are used in the study. 3 MATHEMATICAL MODEL 3.1 LARGE EDDY SIMULATION Large Eddy Simulation possesses good application prospect in research of flow fluctuation for its advantages in capturing instantaneous flow characteristics and unsteadiness compared to unsteady RANS. Using LES to study the instantaneous flow characteristics in engineering becomes more and more widespread, and continues to progress in reaching a level of maturity with the help in computational power increase Governing Equations The governing equations employed for LES are obtained by filtering the time-dependent Navier-Stokes equations and the continuity equation. The filtering process effectively filters out the eddies whose scales are smaller than the filter width or grid spacing used in the computations. The resulting equations thus govern the dynamics of large eddies. A filtered variable (denoted by an overbar) is defined by D ( x) ( x') G( x, x') dx ' (1) D is the fluid domain and G is the filter function that determines the scale of the resolved eddies. Filtering the equations in incompressible form, we obtain the following formulation: ( ui ) 0 x i and ui 1 p ( uu i j) t x x j ui u j ij ( ) Si xj xj xi xj i (2) (3) where the overbar represents the spatial filtering, called the grid-scale filter. u are the resolved velocity components, p is the resolved pressure, ρ is the density, ν is the kinematic viscosity, S i is the source term and ij is the subgrid-scale (SGS) stress tensor defined as: ij uu i j uiu j (4) Compared with the original Navier-Stokes governing equations, LES formulation has an additional SGS stress tensor ij. It is a second-order symmetric tensor, which includes six independent variables, and requires modelling with different SGS models Subgrid-Scale Modelling The subgrid-scale stresses resulting from the filtering operation are unknown, and require modelling. The SGS turbulence models employ the Boussinesq hypothesis (or eddy-viscosity assumption) as in the RANS models, computing subgrid-scale turbulent stresses from: 1 ij kkij 2t ij 3 S (5) here t is the SGS subgrid-scale stress turbulent viscosity, kk is the isotropic part of the subgrid-scale stresses added to the filtered static pressure term. S ij is the resolved strain rate tensor defined by: S ij 1 ui u j ( ) 2 x x j i (6)

56 In the Smagorinsky-Lilly model [7], the form of the SGS eddy-viscosity is modelled by 2 ( C ) S (7) t S with S 2Sij Sij defined as the magnitude of the resolved strain rate tensor, Δ is the filter length scale and C S is the non-dimensional Smagorinsky constant, which is taken equal to 0.1. In the Dynamic Smagorinsky-Lilly model, the constant C S is calculated dynamically at every time and position in the flow based on the Germano identity and the scale invariance assumption [8, 9]. The new filter width is equal to twice the grid filter width Δ. The dynamic procedure thus obviates the need for users to specify the model constant C S in advance. The Germano identity is defined as: L T (8) ij ij ij where T ij is the stress at a test filter scale, and L ij is the resolved stress tensor which can be computed by the resolved scales. Applying SM to model the SGS stress at a test filter scale, T ij can be expressed by: 1 T 2[ ( ) ] 2 ij Tkk ij CS S S ij (9) 3 Substituting (9) and (5) into (7), and considering the scale invariance assumption, we obtain: 1 L 2( ) 2 2( ) 2 ˆ ˆ ij L C S S C S S 3 kk ij S ij S ij (10) Assuming 2 ˆ ˆ 2 Mij SSij 2 2 SSij, (10) can be rewritten as: 1 Lij 3 ijlkk C S (11) M ij M ij The C S obtained using the dynamic Smagorinsky-Lilly model varies in time and space over a wide range. To avoid numerical instabilities, its value is clipped between zero and The upper bound limit aims at preventing the appearance of high C S values that, on one hand, are not physical and on the other can lead to high spatial variations of Cs and destabilize the solver. Finally, the third SGS model of interest is the Wall- Adapting Local Eddy-Viscosity model (WALE) of Nicoud and Ducros [10]. The WALE model is a Smagorinsky type model but with a modified dependence on the resolved strain field, which is supposed to provide improved near-wall behaviour. The difference with the previous models comes in the way the eddy viscosity is modelled (7): d d 3/2 ( S ) 2 ij Sij t ( Cw) ( ) 5/2 ( d d ) 5/4 SS ij ij SS ij ij where d Sij is a deviatoric part of rate-of-strain tensor. (12) The default value of the WALE constant, C w is and has been found to yield satisfactory results for a wide range of flow. The rest of the notation is the same as for the Smagorinsky-Lilly model. 3.2 DETACHED EDDY SIMULATION In the DES method, the unsteady RANS models are employed in the near-wall regions, while the filtered versions of the same models are used in the regions away from the near-wall. The LES region is normally associated with the core turbulent region where large turbulence scales play a dominant role. In this region, the DES models recover the respective subgrid models. In the near-wall region, the respective RANS models are recovered Realizable κ-ε Model This RANS model is similar to the well known realizable κ-ε model [11] with the exception of the dissipation term in the κ equation. In the DES model, the Realizable κ-ε RANS dissipation term is modified such that: 3/2 Y ldes (13) where: ldes min( lre, lles ) (12) 3/2 k lrke (13) l C (14) les des C des is a calibration constant used in the DES model and has a value of 0.61 and Δ is the maximum local grid spacing in x-, y- z- direction SST κ-ω Model The dissipation term of the turbulent kinetic energy from the standard κ-ω model [12] is modified for the DES turbulence model as described by Menter [13] such that: * Y F DES (15)

57 Lt where FDES max(,1), with C des and Δ as C above, and L t des. * STAR-CCM+ employs the following SGS models: SM and WALE for LES and SST κ-ω for DES. ANSYS FLUENT also offers the Dynamic Smagorinsky-Lilly and the Realizable κ-ε. In the present study, the different models are used and compared between the two solvers. non-structured grids incorporating a prism layer mesh around the keel and were generated in STAR-CCM+. The grids were based upon the medium-to-fine density (base size between 10-20) size control with additional anisotropic volumetric refinement in the relevant areas where the flow is expected to be important (boundary layer, wake, separated areas, winglets). This approach allows the grid resolution to be increased in the turbulent wake pattern region only around the keel if necessary. 4. COMPUTATIONAL AND NUMERICAL APPROACH 4.1 COMPUTATIONAL DOMAIN AND MESH The computational domain was reproduced as an exact copy of the experimental set-up; therefore, it is identified as a virtual wind tunnel. The complete test section was modelled from the inlet plane, where the wind tunnel contraction ends, to the outlet plane, where the expansion begins. The domain dimensions are Length (m) x Width (m) x Height (m): 2.5 x 1.8 x The coordinate system was defined at the inlet base of the tunnel, x-direction streamwise, y-direction upwards and z-direction transversally. As mentioned previously, blockage effects were neglected as they are not influencing the outcome of the simulation results. Two types of mesh were created for the purpose of the study. On one hand, the simulations were performed on a single-block adapted unstructured mesh consisting of prismatic cells in the boundary layer and vicinity of the keel, with tetrahedral cells in the outer part of the volume. Surface mesh on the keel comprised on triangular face elements. This type of grid was associated with the ANSYS FLUENT simulations and developed following the lessons learned and the finding of previous study [6]. A view of the mesh can be seen in Figure 2. The adapted unstructured approach is the most suitable for this solver, because of the complexity of the geometry and the flexibility it offers to the user. Figure 3: Computational domain, trimmed cells, meshed with STAR-CCM+ The near-wall boundary layers were extruded at a rate of 1.1 from the surface of the model, and depending on the configuration, comprised of between 5 and 20 inflation layers in total. The first cell height was kept to a minimum, of the order of 1-10 μm, resulting in a y + value of under 5. For the coarsest meshes, this value was increased and wall-function treatments were used near the model (in DES). The grid spacing, normalised by friction velocity and viscosity, at the wall was (Δx + ;Δy + ;Δz + ) (30-80;1-5;20) for unstructured mesh and (Δx + ;Δy + ;Δz + ) (12-110;0.3-1;15) for the cut-cell mesh. The simulation grids consisted of between 3 to 8 million elements. This resolution was reached based on the mesh specifications defined (near-wall resolution, refinement in specific areas ), the experience from previous study [6] and using the computational resources available for handling such large mesh sizes. 4.2 BOUNDARY CONDITIONS A constant velocity condition of m/s with 0.1% turbulence intensity was applied as a boundary condition at the inlet of the domain. They correspond to the values used in the experiments and defined in Table 2. At the outlet of the domain, zero static pressure is imposed. On the surface of the appendage, no-slip condition was employed. To ease computational time, the tunnel walls were defined as slipped surfaces. Figure 2: plane cut of mesh around the winglets, unstructured grid, ANSYS FLUENT On the other hand, the automated meshing approach offered by STAR-CCM+ was used. The meshes employed were predominantly hexahedral trimmed Since LES and DES are unsteady models, the velocity profile imposed at the inlet of the domain must be timedependent. To model the fluctuating velocity, several techniques exist to account for this. In the study, the Vortex Method was employed for both solvers [15, 16].

58 It consists of generating and transporting randomly in the inlet plane a given number (in this study 190) of 2D vortices whose intensity and size depend on the local value of κ, the turbulence dissipation rate or the turbulent intensity, for which profiles are prescribed based on the experiment. The advantage of this method is that it does not require additional simulation. 4.3 NUMERICAL SOLUTION An implicit, segregated solver was chosen as the solver algorithm. Second-order temporal discretization was used. The bounded central-differencing scheme is used to discretize the convection term in the filtered momentum equation in FLUENT. In STAR-CCM+, the pure central-differencing scheme is adopted. The flow velocities and pressures in the domain are calculated using the standard SIMPLE (STAR-CCM+) or SIMPLEC (FLUENT) pressure correction method. A second-order upwind differencing scheme was employed for the solution of the momentum and turbulence equations. An algebraic multigrid method is employed to accelerate solution convergence. The steady state computation was initially carried out with the solution of a preceding RANS calculation to have a convergence below 10-3 /10-4 depending on the case (forces, residuals, surface values were monitored). After, the unsteady simulation to model the fluctuating velocity is superimposed. The time-step value has been adapted for the computational grids (between seconds of order of magnitude). One flow-through time was equivalent to about 0.069s (T ft =L/U, where L is the domain s length). LES and DES were run for a sufficiently long flow-time to obtain stable statistic of flow and turbulence (35-45T ft ), and further to gather relevant data for the results (45T ft ). Simulation were performed on an Intel Xeon 2 CPUs with eight cores, 24 GB Ram capacity and of processing power equal to 3.2 GHz. The computations were run in parallel processing. 5 RESULTS AND DISCUSSION In this section, a selection of results will be presented and discussed, based on the CFD simulations performed for this study. The validation consisted of comparing the global loads on the keel, and the prediction of the velocity magnitude for the wake survey. Other results presented are relevant examples of the flow encountered in keel hydrodynamics and of the capabilities of LES and DES to capture the complexity of the flow. 5.1 GLOBAL FORCES ON KEEL The results obtained from the present CFD calculations are compared to the experimental values of Werner in terms of time-averaged Lift (L) and drag (D) forces. The later is measured longitudinally in the direction of the undisturbed flow and the former is taken perpendicular to the wind, along the z-axis. The exp uncertainty of the forces was 3.2% for the lift and 3.1% for the drag and is shown in the graphs in the form of error bars. For clarity sake, the figures have been refined near the measured force values, so that the differences between the turbulence models and the CFD solvers can be appreciated. Results shown here are for grids of around 3.5 million cells for the no wings configuration, and about 6 million for the winglets in forward position. Lift (N) Exps Fluent Star-Ccm+ LES SM LES WALE LES DSM DES κω DES Rκε Figure 4a: Comparison of lift force for CFD models, no-wing configuration Drag (N) Exps Fluent Star-Ccm+ LES SM LES WALE LES DSM DES κω DES Rκε Figure 4b: Comparison of drag force for CFD models, no-wing configuration Lift (N) Exps Fluent Star-Ccm+ LES SM LES WALE LES DSM DES k-w DES R ke Figure 5a: Comparison of lift force for CFD models, forward wings configuration

59 Drag (N) Exps Fluent Star-Ccm+ LES SM LES WALE LES DSM DES k-w DES R ke Figure 5b: Comparison of drag force for CFD models, forward wings configuration The results are in quite a good agreement with the experimental data and represent a much-improved performance compared to the previous data published with one of the numerical solver by the author [6], for both cases with and without winglets. Most of the turbulence models for both solvers are within the experimental uncertainty. Comparing case by case, STAR-CCM+ gives the most accurate results in the non-winged keel computations. The main differences are found for the drag prediction of the DES κω model, likely linked to the fact that a Delayed DES model was chosen in the simulation. The results with Fluent show a wider range of estimations depending on the model. The highest errors were found to be about 5.6%. For the forces computed in the other configuration, the discrepancies in the models are slightly larger than the previous case. The flow is more complex but the results are still within a range of validity. Again STAR-CCM+ outperforms Fluent on all common models, baring the drag prediction of the WALE model, where it is above the experimental uncertainty and above fluent. Differences in the two codes are likely down to the different mesh topology, since numerical formulation was almost identical for both codes; non-structured hexahedral trimmed cells look to be more accurate than the tetrahedral unstructured cells of the other solver. A thorough error and uncertainty analysis is required in the future though, particularly for advanced numerical models. 5.2 WAKE SURVEY To assess the accuracy of the methods in terms of velocity and vortex structure at the far field, a comparison of the wake at a given plane behind the keel has been carried. Results for the case without wings are presented. This type of assessment is instructive in cases when data such as surface pressure, velocity measurements on or near the body are not obtained from experiments. As the two solvers use different grid topology, observing the wake of the flow is important in evaluating the CFD simulations in terms of level of accuracy and turbulence models. The velocity magnitude was measured in a wake plane orthogonal to the undisturbed flow defined at x/l: 0.95 from the wind tunnel inlet. Numerical results are shown for grids of around 3.5 million cells. Figure 6 shows the comparison of the velocity magnitude contours for DES SST κω (averaged values) & for LES SM (instantaneous values taken at t =2s) in the turbulent wake. Areas of low velocity correspond to regions of high vorticity magnitude. Three main vortices can be identified [3]; they are in the clockwise direction (view is looking downstream, leeward side to the right) from top to bottom: the bulb-tip vortex, the bilge vortex and the fin junction vortex. The overall wake shape and position is in fair agreement with the experimental data. Vortex shape and intensity in the bulb wake can be considered satisfactory; there is some lack of resolution in the bottom part of the vortex for most but the overall trend is reasonable. The DES predictions of Star-CCM+ are in satisfactory agreement with the tunnel measurements. The velocity is slightly underpredicted as are the bilge and the junction vortices. General trend is good. If we link to the force results, then we can observe that refinement is needed in the longitudinal to resolve the vortices better (drag is under predicted). The results from Fluent results differ in magnitude and resolution of the vortices, and not corresponding to the higher value of drag reported in the force comparison. The instantaneous velocity contours show the unsteady nature of the flow in the wake, exhibiting a number of additional vortices on top of those reported. Depending on the grid topology, vortices are more developed, but main contours appear to be in the correct location. The range in Velocity magnitude is slightly underpredicted by both solvers, but within an acceptable range of validity and in agreement with the forces prediction. It can be seen from the results that κω SST is recommendable for both solvers and mesh type, with preference to hexahedral trimmed cells. Performance is matching that of experiments. For that specific case, the cell size in the wake region was too coarse. Prediction was found to be increasing in details with targeted refinement and cell size control. Another possible explanation may the Vortex Method set at the inlet boundary and the turbulent intensity, which seem to work better in one of the solvers.

60 Figure 6a: Contours of velocity magnitude at wake plane with STAR-CCM+. Top to bottom: Experiments, DES κω SST and LES SM models Figure 6b: Contours of velocity magnitude at wake plane with ANSYS Fluent. Top to bottom: Experiments, DES κω SST and LES SM models

61 5.3 UNSTEADY FLOW REGIME Vortices and junction flow comparison, both solvers predict the vortices and the separation and recirculation on the body. Flow past an appended keel is a challenging case for CFD because of the different flow regimes around the body; including the laminar boundary layer, transition region, turbulent boundary layer, separation point, and separation region as well as wake region. There were no other formal observations during the experiments of the flow to report as comparison, but physics of the flow can be reported. At the yaw angle of the measurements, separation is expected to occur at the trailing edge of the suction side of the model. Although it can be argued that there is no massive separation to justify the use of LES or DES (i.e. large angles of attack), the models nonetheless predict the flow unsteadiness in a characteristic manner. LES is particularly suitable to investigate the generation and evolution of coherent structures in turbulent flows. Figure 7 shows the instantaneous flow pathlines at the intersection close of the fin with the bulb. The vortical structures emanate from the junction towards the end of the trailing edge and from the bulb. The rotation in the flow carries on further down the length of the bulb and in the wake; these vortices, move towards the starboard side, as expected. Figure 7: Pathlines coloured by velocity magnitude near the fin/bulb junction Similarly, the surface streamlines on the keel show the presence of a horseshoe vortex when the undisturbed flow reaches the fin at the junction with the bulb; figure 8. On the trailing edge, reattachment occurs. The flow remains unsteady and turbulent in the aft part, inducing further separation down the keel. In the pressure side, the flow is less disturbed, due to the yaw angle, pressure transfers from the windward to the leeward side. The surface streamlines show that the numerical simulations capture the important features of the recirculation zone. Similar behaviour is reported for the flow near the winglets, but not as pronounced because the winglets pitch was zero degrees. In terms of code Figure 8: Surface streamlines on the appended keel Laminar and turbulent flow Turbulence is expected around the fin and the winglets over most part of the structures. Based on the inlet flow, their Reynolds number is equal to Re f = 5.04 x 10 5 and Re w = 1.80 x 10 5 respectively, which means transition will occur sooner than for the bulb. In computational terms, this means that further resolution may be necessary near the wall of these lifting surfaces to fully grasp the unsteadiness and the transition from laminar to turbulent flow. The flow around the bulb is laminar over a longer part, whereas the turbulence on the fin and the winglets is much more pronounced. As an example, figures 9 and 10 show the instantaneous velocity vectors in the boundary layer of the fin at the plane y = 0.61, over a part of the cross section near the intersection with the bulb. The top picture shows the trailing edge on the leeward side, and the bottom is the leading edge on the windward side. A vortex structure can be identified on the trailing edge, with separation and turbulence occurring on the viscous sublayer. The flow then reattaches after the vortex. On the pressure side, there is less relevant turbulent effect and the flow exhibits a laminar regime over a longer range. It appears more energized; as a result, the boundary layer thickness in the pressure side is much thinner than in the suction side. The regions of stagnation points, reattachment and separation on the suction side correspond to changes in the surface pressure of the fin, due to the flow unsteadiness. The streamlines show that the numerical solution captures the important features of the boundary layer including separation, recirculation zone and turbulent boundary layer. Further insight into these complex phenomena is required, with the investigation of parameters influencing the turbulence for LES and DES, such as intensity and turbulent viscosity at the inlet.

62 Figure 9: Velocity vectors in the boundary layer, on the leeward side (TE) Figure 10: Velocity vectors in the boundary layer, on the windward side (LE) 6 CONCLUSIONS In the present paper the hydrodynamic performance of and asymmetric keel at yaw angle is presented using advanced CFD based on the Large Eddy Simulation and Detached Eddy Simulation turbulence models. Two solvers were tested, with two different grid types. Results obtained were compared quantitatively against wind-tunnel forces and wake plane observation. The following observations and conclusions can be drawn from the results obtained in the current study: The forces prediction showed a significant improvement compared to previous study, with a maximum error of about 6%. The hexahedral non-structured grid offered a better prediction of forces and a more detailed account of the wake flow than tetrahedral unstructured mesh Characteristics of the flow such as separation, vortices, and wakes are correctly predicted and resolved qualitatively. Likely influence of some inlet parameters depending on the grid topology, the SGS model and the solver. Possible directions of future research and developments in this research topic will consist of the following: Introduce the laminar zones around part of the bulb and fin keel

63 Investigate the transition models of the solvers further. Study the influence of winglets pitch angles, likely to influence the separation and exhibit flow features Apply the cut cell method of ANSYS FLUENT 13.0 to compare with equivalent method used by STAR-CCM+. Investigate uncertainty and errors of CFD Modify and use different inlet boundary conditions (Spectral Synthesizer, turbulent intensity, viscosity ratio) ACKNOWLEDGEMENTS The authors would like to thank Sofia Werner for kindly providing with the geometry of the model keel as well as the experimental data from the wind-tunnel tests. The authors are also grateful to the Faculty of Engineering, University of Strathclyde, for accessing the HPC cluster facility for running and post-processing some of the simulations. REFERENCES 1. TINOCO, E. N., GENTRY, A. E., BOGATAJ, P., SEVIGNY, E. G., and CHANCE, B., IACC Appendage Studies, Proceedings of the 11 th Chesapeake Sailing Yacht Symposium, WERNER, S., LARSSON, L., and REGNSTROM, B., A CFD Validation Test Case - Wind Tunnel Tests of a Winglet Keel, 2 nd High Performance Yacht Design Conference, WERNER, S., PISTIDDA, A., LARSSON, L., REGNSTROM, B., Computational Fluid Dynamics Validation for a Fin/Bulb/Winglet Keel Configuration, Journal of Ship Research, Vol. 51, No. 4, AMBROGI, M.M., BROGLIA, R., DI MASCIO, A., Numerical Simulation of a flow around an America s Cup Class Keel, Proceedings of the 18th International Offshore and Polar Engineering Conference, THYS, M., Performance Evaluation of a Sailing Yacht with the Potential Code RAPID, ENSTA, France, MYLONAS, D., and SAYER, P., The hydrodynamic flow around a yacht keel based on LES and DES, Ocean Engineering 46: 18-32, SMAGORINSKY, J., General Circulation Experiments with the Primitive Equations. I the Basic Experiment, Monthly Weather Review, vol. 91, , GERMANO, M., PIOMELLI, U., MOIN, P., and CABOT, W.H., Dynamic Subgrid-Scale Eddy Viscosity Model, Summer Workshop, Center for Turbulence Research, Stanford, CA, LILLY, D.K., A Proposed Modification of the Germano Subgrid-Scale Closure Model, Physics of Fluids, 4: , NICOUD, F., and DUCROS, F., Subgrid-scale modelling based on the square of the velocity gradient tensor, Flow, Turbulence and Combustion, vol. 62, pp , SHIH, T. H., et al. A new κ-ε eddy viscosity model for high Reynolds number turbulent flows, Computers & Fluids 24 (3): , WILCOX, D. C., Turbulence Modeling for CFD, DCW Industries, Inc., MENTER, F.R., KUNTZ, M., and LANGTRY, R., Ten Years of Experience with the SST Turbulence Model, Turbulence, Heat and Mass Transfer 4, pages , ANSYS FLUENT, Fluent 12.1 User Manual, ANSYS Inc, SERGENT, E., Vers une méthodologie de couplage entre la Simulation des Grandes Echelles et les modèles statistiques., PhD thesis, L'Ecole Centrale de Lyon, MATHEY, F., COKLJAT, D., BERTOGLIO, J. P., SERGENT, E., Assessment of the vortex method for large eddy simulation inlet conditions, Progress in Computational Fluid Dynamics, An International Journal, 6(1), 58-67, CD-ADAPCO, STAR-CCM User Guide, CD-Adapco, AUTHORS BIOGRAPHY D. Mylonas has recently completed his PhD in the Department of Naval Architecture and Marine Engineering, University of Strathclyde, Glasgow and officially graduates in July His research topic focused on the application of LES and DES in yacht hydrodynamics. He also holds an M.Eng from the same department. Other interests include ship & marine hydrodynamics, smart materials, yacht design and CFD simulations on marine and aerodynamic applications. S. Turkmen is a PhD student in the Department of Naval Architecture and Marine Engineering, University of Strathclyde, Glasgow. He has been researching on the topic of smart material application to mitigate noise and vibration in ships. He is also investigating underwater-radiated noise due to the cavitating propellers.

64 M. Khorasanchi is a research fellow in the Department of Naval Architecture and Marine Engineering, University of Strathclyde, Glasgow. Dr Khorasanchi has carried out several studies on vortex-inducedvibration (VIV) of marine risers and VIV suppression devices. His current teaching and research interests centre on hydrodynamics and marine propulsion. He investigates the hydrodynamic performance of marine vessels through full-scale CFD simulation. He also works on retrofitting technologies to improve the performance of marine vessels and reduce the fuel consumption and carbon emission of shipping industry.

65 NARROW SHIP WAKES AND WAVE DRAG FOR PLANING HULLS M. Rabaud, Laboratory FAST, Université Paris-Sud, UPMC Université Paris 6, CNRS. Bât. 502, Campus universitaire, Orsay, France, F. Moisy, Laboratory FAST, Université Paris-Sud, UPMC Université Paris 6, CNRS. Bât. 502, Campus universitaire, Orsay, France, The angle formed by ship wakes is usually found equal to its Kelvin value, α =19.47 degrees. However we recently show that this angle can be significantly smaller at large Froude number [8]. We show how the limited range of wave numbers excited by the ship explains the observed decrease of the wake angle as 1/Fr for Fr > 0.5, where Fr = U/ gl is the Froude number based on the hull length L. At such large Froude numbers, sailing boats are in the planing regime, for which the wave drag becomes a decreasing function of the velocity. We discuss here the possible connection between the evolutions of the wake angle and wave drag at large Froude number. NOMENCLATURE Symbol Definition (unit) B Waterline beam (m) c ϕ Phase velocity (m s 1 ) c g Group velocity (m s 1 ) C W Wave-making coefficient D Static immersed volume (m 3 ) Fr Hull Froude number g Acceleration of gravity (m s 2 ) k Wave number (m 1 ) L Waterline length (m) P Pressure (N m 2 ) R W Wave-making resistance (N) U Boat velocity (m s 1 ) α Half-angle of the wake θ Angle (k, U) ρ Density of water (kg m 3 ) 1 INTRODUCTION A ship moving on calm water generates gravity waves with a characteristic V-shaped pattern. Lord Kelvin in 1887 [4] was the first to explain this phenomenon and to show that the wedge angle is constant, independent of the boat velocity. According to this classical analysis, only the wavelength and the amplitude of the waves change with the velocity and the halfangle of the wedge remains equal to degrees. In contrast to this result described in many textbooks, we have shown recently that the wake angle is no more constant at large velocity [8] and decreases as 1/U. We have shown that this decrease can be modeled by including the finite length of the boat in Kelvin s analysis. Some years before Kelvin s work, William Froude, by towing model boats, observed that the hydrodynamic drag increases rapidly with the boat speed U, and more precisely that the drag is a function of the hull Froude number Fr = U/ gl, where L is the waterline length. Following the pioneering works of Froude [4], Michell [7, 10] and Havelock [5], the computation of hydrodynamic drag still represents a challenge for naval architects. The wave drag or wave-making resistance R W is the part of this hydrodynamic drag that corresponds to the energy radiated by the waves generated by the hull translation. For a displacement hull sailing at large velocity (Froude number in the range 0.2 to 0.5) the major part of the hydrodynamic drag is given by the wave drag. In this paper we discuss the possible link between the decrease of the wake angle observed at large Froude number and the evolution of the wave drag for planing sailing boats. 2 WAVE PATTERN When a boat sails on calm water at constant velocity U, the waves present around and behind the hull are only those that are stationary in the frame of reference of the boat. For a given wave of wave number k propagating in the direction θ with respect to the boat course, this condition writes: U cos θ(k) =c ϕ (k) (1) where c ϕ (k) is the phase velocity of the considered wave (figure 1). Because of the dispersive nature of gravity waves, c ϕ is function of the wave number, c ϕ = g/k, implying that for a given propagation direction θ only one wavenumber is selected by Eq. 1: g k(θ) = U 2 cos 2 θ. (2) As a consequence, the smallest wave number (i.e. the largest wave length) compatible with the stationary condition is given by k g = g/u 2, and corresponds to waves propagating in the boat direction (θ =0). These so-called transverse waves are visible along the hull and following the boat.

66 M c g t c t k H g Ut Figure 1: Geometric construction of the wave pattern and angle definitions for a boat sailing at constant velocity U. Importantly, energy propagates at the group velocity and not at the phase velocity, and for gravity waves the group velocity is equal to half the phase velocity (c g = 1 2 c ϕ) [6]. It follows from this 1/2 factor that the angle α, where waves of a given wave number are observed (figure 1), is given by [8]: I α(k) =tan 1 ( k/kg 1 2k/k g 1 O ). (3) In this classical description the boat is considered as a point source, generating all the waves with a small constant amplitude (broad band flat spectrum). In reality all the points of the hull are sources and the detail of the amplitude of the wave depend of the exact shape, trim, sinkage of the hull and of the Froude number. For example, for a poorly streamlined hull at low Froude number, two V-shaped wakes are visible, one originating at the bow and the other at the stern. The waves generated by the boat are therefore characterized by a spectrum which cannot be considered as flat, and the resulting wake pattern may escape from the classical Kelvin s description. 3 WAVE ANGLE FOR RAPID BOATS We recently showed that the commonly admitted result of Kelvin of a constant wake angle equal to degrees is no longer true at large velocity for planing boats [8]. This is illustrated in figure 3, showing a wake angle significantly smaller than the Kelvin prediction. This evolution of the angle α with the wave number is shown in figure α(k) (degrees) Figure 3: Photograph of a fast planing motorboat exhibiting a narrow wave wake (source: k / k g Figure 2: Evolution of the angle α versus the wave number ratio k/k g (Eq. 3), where k g = g/u 2 is the gravity wave number. This plot shows that for any given angle α smaller than degrees there are two possible values of k that correspond to two directions θ (Eq. 2). One solution corresponds to transverses waves (smaller θ) and the other to divergent waves (larger θ). The angle α takes its maximum value α 0 =19.47 deg for k 0 /k g = 3/2, and no waves can be observed beyond this angle. This maximum wake angle corresponds to a cusp (a caustic) in the wave pattern, and also to the locus of maximum amplitude of the waves, since α/ k =0, which implies an accumulation of energy at k 0 /k g =3/2. These results correspond to the well known Kelvin angle [3]. Analyzing a set of airborne images from Google Earth c, we measured the wake angles and the Froude numbers for boats of various sizes and velocities. Using the scale provided on the images, we measured the overall length of the boat (assumed to be equal to the waterline length L) and the wavelength of the waves on the edge of the wake. From this wavelength the boat velocity U is determined using Eq. 2 and the Froude number is then computed. Our data clearly show a decrease of the wedge angle for Froude numbers larger than 0.5 (figure 2 of [8]). Values as small as 7 degrees are observed. Wake angles smaller than the Kelvin prediction can be explained as follows. The key argument is that, contrary to the Kelvin assumption, a moving boat does not excite all the wavelengths with the same energy. In particular it cannot excite surface waves significantly larger than its waterline length L. The energy radiated by the boat is therefore characterized by a spectrum which is truncated below the wavenumber k min 2π/L. At large boat velocity this wavenumber can be larger than the wave number k 0 which corresponds to the maximum Kelvin angle in figure 2. Thus only the wave numbers corresponding to divergent waves, i.e. rightmost part of

67 figure 2, are of significant amplitude, so the largest visible angle is given by Eq. 3 taken for k = k min 2π/L. This model predicts that the wake angle is given by the Kelvin prediction as long as the k 0 mode contains energy, i.e. up to Fr c = 3/4π = 0.49, and by a decreasing function α(k =2π/L) at larger Froude. For Fr Fr c the wake angle decreases as 1 α 2 2πFr. (4) This previously unnoticed Froude number dependence of the wake angle compares well with the wake angles observed from airplane images. This is also consistent with the fact that at Fr > 0.5 the transverse waves behind the boat (θ =0), which are visible for smaller Froude numbers, are no more visible (see figure 3), since they fall outside the wave spectrum excited by the boat. Equation 4 is also found to describe very well the wave patterns obtained by numerical simulations (figure 4). More details on the numerical simulation can be found in Ref. [8]. generates. We now know that this limit speed can be overcome with light and powerful boats as they reach the planing regime. In this regime of large Froude number, hydrodynamic lift becomes significant, decreasing the immersed volume of the hull. Because of the resulting smaller mass of fluid which needs to be pushed away, a decrease of the wave drag is observed. During this transition to planing, a significant acceleration of the boat can be observed. We discuss here the possible connection between this wave drag decrease during planing and the decrease of the visible wake angle described in the previous section. The wave drag R W is the part of the hydrodynamic drag due to the energy radiated by the waves generated by the boat. In order to compare boats of different forms and displacement a dimensionless wave drag coefficient C W is usually defined. Assuming hulls having all the same shape but not the same size, the wave drag will only depend of the boat velocity U, waterline length L, gravity g and water density ρ. One finds by dimensional analysis: R W ρu 2 L 2 = C W (Fr). (5) Figure 4: Perspective view of the wave pattern generated by an axisymmetric (Gaussian) pressure distribution at Fr =1. The measured wake angle is α =11degrees. 4 WAVE DRAG In order to describe the classical result of the increase of the wave drag for displacement navigation (Fr < 0.5) we come back to figure 1. We focus here on the transverse waves propagating in the boat direction (θ = 0). These waves are the stationary waves observed along the side of the hull and behind the boat. Their wavenumber is given by Eq. 2, k g = g/u 2, and their wavelength λ g =2π/k g can be written as λ g =2πL Fr 2. For increasing speed their wavelength increases, up to a particular velocity for which the wavelength is equal to the length of the boat. This velocity corresponds to Fr =1/ 2π 0.4. For this value the waves generated by the bow are in phase with the ones emitted at the stern and the draught or sinkage of the hull is maximum. This critical velocity is known as the hull limit speed, because around this Froude number the wave drag increases drastically and the trim of the boat starts to be strongly affected by the waves it In reality this coefficient C W also depends on the exact shape of the boat, and alternate definitions where L 2 is replaced by LB or B 2 (where B is the beam of the hull) are also found in the literature. Another possibility is to build a dimensionless drag coefficient by normalizing the wave drag force R W by the weight of the boat ρgd, where D is the static immersed volume of the hull. For displacement boat, the wave drag coefficient rapidly increases (at least as Fr 4 if defined by Eq. 5) and becomes the dominant part of the hydrodynamical drag at large Fr. Note that the power law C W Fr 4 can be recovered by scaling argument, assuming that the amplitude of the waves scales as U 2 (using Bernoulli relation) and that the wavelength observed along the Kelvin angle scales as U 2 (Eq. 2). In order to compute the wave drag, Havelock [5] has introduced a classical simplification which consists in replacing the boat by an imposed pressure field P (x, y) at the water surface. The resulting surface deformation ζ(x, y) can then be computed as a Fourier integral (see Eq. 2.17b of Ref. [9], or Eq. 11 of Ref. [1]). From this imposed pressure and calculated wave field, the wave drag is then computed by integrating the product of the local pressure by the slope of the interface in the direction of the motion: R W = P (x, y) ζ dxdy. (6) x On figure 4 we have simulated the wave pattern generated by a moving Gaussian pressure field, g(r) = (2πF 0 /L 2 )exp ( 2π 2 r 2 /L 2), where F 0 is a normalization force, which corresponds here to the weight of the boat (F 0 = ρgd). From this simulated surface height, we have computed the wave drag using Eq. 6 for various Froude numbers. The results, plotted in figure 5, are in perfect agreement with the exact result found by Benzaquen et al. [1] for a Gaussian

68 pressure field: ( ) 2 D 1 π/2 dθ C W = [ L 3 Fr 8 ( 2πFr ) 4 ] 0 cos 5 θ exp cos θ (7) C W (L 3 /D) Simulation (N=2048) Benzaquen et al. (2011) Fr Figure 5: Dimensionless wave drag calculated for a gaussian moving pressure field with our simulated wave field ( ) and comparison with Eq. 7 ( ). in our analysis, the prescribed pressure P (x, y) does not depend on the velocity, so it does not contain the physics of the dynamical lift on the hull. This suggests that the dynamics of the planing and the decrease of the immersed volume are not necessary ingredients for the decrease of the wave drag at large Froude number. Note that the decrease of the wave drag at large velocity is often partly hidden by the increase of the other sources of hydrodynamic drag, which increase as Fr 2. 5 CONCLUSIONS At large velocity many racing sailing boats are now planing under the action of the strong hydrodynamic lift. The fact that the dynamically immersed volume is smaller than in static condition provides a reasonable argument for the diminution of the wave drag. We propose here an alternative interpretation, in which the combined decrease of the wave drag and the wake angle both follow from the finite extent of the wave spectrum excited by the ship. This interpretation is based on our simulations of the wave pattern generated by an imposed pressure disturbance, suggesting that the narrow wake angles at large Froude number can be observed without lift and thus without planing regime. Further investigations are necessary to better describe the relative importance of trim and sinkage evolution of planing boat to better understand the relative importance of the finite size of the boat compared to dynamic lift. We note that the present description is by construction limited to stationary motion, i.e. boat translating on a flat sea surface. In real situations, when in planing conditions the wind and thus the wind waves are usually large, inducing a periodic motion of the boat at the wave encounter frequency. This non stationarity increases the hydrodynamic drag when sailing at close reach but can also decreases the drag when surfing on swell. REFERENCES Figure 6: Dimensionless wave drag for a parabolic strut (figure 1 of Ref. [11]. This wave drag coefficient is maximum for Fr 0.37, followed by a decrease as C W 1/Fr 4 at large Froude numbers. Interestingly, this maximum is very close to the critical Froude number Fr c 0.49 at which the wake angle starts decreasing. Both results are consequence of the finite extent of the wave spectrum excited by the disturbance: as the Froude number is increased, the surface deformation in the vicinity of the boat is no longer able to supply energy to the waves of wavelength λ g = 2πU 2 /g, resulting in a combined decrease of the wake angle (α 1/Fr) and of the wave drag (C W 1/Fr 4 ). The overall shape of C W computed by Eq. 7 is surprisingly similar to the experimental curve of Chapman [2] with computation by Tuck et al. [11] (figure 6). This curve is usually interpreted as the result of the lift of the hull and the resulting decrease of the immersed volume at Fr > 0.5. However, [1] M. Benzaquen, F. Chevy, and E. Raphaël. Wave resistance for capillary gravity waves: Finite-size effects. EPL (Europhysics Letters), 96(3):34003, [2] R. B. Chapman. Hydrodynamic drag of semisubmerged ships. Journal of Basic Engineering, 72: , [3] F. S. Crawford. Elementary derivation of the wake pattern of a boat. American Journal of Physics, 52: , [4] O. Darrigol. Worlds of Flow: A Hystory of Hydrodynamics from the Bernoullis to Prandtl. Oxford University, [5] T. H. Havelock. Wave resistance: Some cases of threedimensional fluid motion. Proceedings of the Royal Society of London, Series A, 95: , [6] J. Lighthill. Waves in fluids. Cambridge University Press, Cambridge, 1978.

69 [7] J. H. Michell. The wave resistance of a ship. Philosophical Magazine, Series 5, 45: , [8] M. Rabaud and F. Moisy. Ship wakes: Kelvin or mach angle? To appear in Phys. Rev. Letters, [9] E. Raphaël and P-G. De Gennes. Capillary gravity waves caused by a moving disturbance: wave resistance. Physical Review E, 53(4):3448, [10] E. O. Tuck. The wave resistance formula of jh michell (1898) and its significance to recent research in ship hydrodynamics. The Journal of the Australian Mathematical Society. Series B. Applied Mathematics, 30(04): , [11] E. O. Tuck, D. C. Scullen, and L. Lazauskas. Wave patterns and minimum wave resistance for high-speed vessels. In 24th Symposium on Naval Hydrodynamics. Fukuoka, JAPAN, 8-13 July 2002, AUTHORS BIOGRAPHY M. Rabaud holds the current position of professor at University of Paris-Sud. F. Moisy holds the current position of professor at University of Paris-Sud, and is member of the Institut Universitaire de France.

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71 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France CONCEPTUAL IDEAS ON A DOUBLE SURFACE SAIL INFLATED BY DYNAMIC PRESSURE S. Brüns, Technical University of Berlin, Germany, soerenbruens@hotmail.com H. Hansen, FutureShip GmbH, Germany, Heikki.Hansen@gl-group.com K. Hochkirch, FutureShip GmbH, Germany, Karsten.Hochkirch@gl-group.com This paper presents conceptual ideas on an unconventional sailing system. It is designed in principle and compared in terms of performance with two established sailing systems. The concept is a double surface sail, which is to be inflated by the dynamic pressure at the leading edge of the profile. The fundamental principle is the same as used by paragliders and kites, where openings at the leading edge of the wing allow the air to fill the profile to give it a beneficial aerodynamic shape. For the analysis of the structural mechanics of the sail system qualitative model tests in a wind tunnel are conducted. A profile segment is exposed to different angles of attack and the trim mechanism of mast rotation is varied. The resulting profile shapes and the profiles of the comparative sail types are then analysed to determine their characteristics by conducting 2D flow simulations. Also the effects of mast rotation to change the profile characteristics of camber and thickness are reviewed. The double surface sail showed a good-natured behaviour at a wide range of angles of attack and a competitive performance potential compared to conventional sail sections and a wing sail section. NOMENCLATURE α Angle of attack (effective) ( ) α nom Angle of attack (nominal) ( ) β Mast rotation angle ( ) c Chord length (m) C D Drag coefficient (-) C L Lift coefficient (-) Re Reynolds number (-) v Wind velocity ( m / s ) 2D Two dimensional 3D Three dimensional AoA Angle of attack Bft. Beaufort CFD Computational fluid dynamics DSS Double surface sail FSI Fluid structure interaction NACA National Advisory Committee for Aeronautics 1 INTRODUCTION Current developments in competitive yachting show more and more wing sails being used as they become allowed by class rules. That is because they have a greater performance potential compared to single surface sails. However, there are some disadvantages associated with the better performance; the handling is much more complicated and difficult. In most cases the sail cannot be hoisted nor pulled down on board by the crew. Reducing sail area is also not possible or complicated. Modern wing sails are usually split in two or three chordwise segments to create an adjustable asymmetric profile shape. The control mechanism of these flaps is complex and therefore maintenance intensive if breakdowns are to be avoided. It also raises the weight of the system. The thin covering of the wings is not very robust against physical impacts. In the past there have been some attempts to build a good aerodynamic profile from flexible materials, but so far none of them have been utilised by the sailing community. They were either too heavy or too complicated to use. Several concepts suggest using vertically arranged inflated battens between two sail surfaces [1] [2]. Other designs use inflated horizontal battens where the shape is controlled by varying the batten pressure. In a literature review on different kinds of double surface sails (DSS), only two designs utilise dynamic pressure to fill the sail with air [3] [4]. One is composed of two sail surfaces, which are attached to the port and starboard side of the mast. To set the sail to one tack the mast rotates a little, that way the leading edge moves towards the windward side and a special structure at the leech goes over, so that the high pressure side is shortened and the suction side is lengthened. This flap mechanism seems to be complex to realise and complicated to use. The other concept is more similar to the one presented here. The sail wraps around a rotatable cylindrical device, which is positioned behind the mast where the standard sail is normally hoisted. The leading edge is therefore located in the mast wake, which has a negative influence on the performance potential.

72 Besides some patent specification and general ideas, little supporting academic work or scientific studies in relation to maritime applications were found. In Marchaj s Aero- Hydrodynamics Of Sailing [5] so called lined sails are introduced where foam material layers are inserted between two cloth layers. However, wind tunnel tests showed less potential of these half rigid sails compared to single surface sails. Research on different types of glider wings by Princeton University showed promising results for the performance potential of the semi rigid double surface wings [6]. The results are compared to this work later in the paper. The common ban of DSS and wing sails in most class rules for professional yachting events in the past might be a reason for the very limited research and development activities. In aviation the idea of wings made from flexible material has developed well, as can be seen by modern parachutes and paragliders. Some kites also work with the same principles. The aim is therefore to develop a concept of a flexible DSS for sailing boats. This requires solutions to let the DSS be formed asymmetrically to both sides to enable sailing on both tacks. A concept has been developed, which tries to address some of the shortcomings of other systems; weight, complexity and usability. The complete device has the purpose to create a stable and favourable aerodynamic lift-generating airfoil to provide better performance than conventional single surface sails. At the same time the device should be light weight and storable to make it more practical than rigid wing sails. The working principles, qualitative wind tunnel test results of a two dimensional section and a comparison to other sail types sections based on 2D flow simulations are presented in this paper. 2 WORKING PRINCIPLES The beneficial aerodynamic profile is created in nearly the same way as done in paragliders and foil-kites, with the difference that the system is able to change the side of the camber. The double surface cloth or laminated sail wraps around the mast and is attached to the front of the mast. At the trailing edge the surfaces run together to form the leech. The mast can be rotated to regulate the camber and profile thickness of the sail. Mast and sail surfaces have superposed openings on both sides of the mast. The sail openings can be controlled by a special valve system. Fig. 1 shows the profile of the sail viewed from the top. In case of wind coming from the port side the mast is rotated clockwise. By that the openings on the port side of the mast and sail come towards the leading edge close to the forward stagnation point. The increased pressure in this region passes through the opening in mast and sail into the DSS. In this position the opposite openings on the suction side of the sail are closed by the value system. A special structure inside the DSS is conceived to prevent the two surfaces to separate too much from each other and form bloated shapes. This can be achieved by strings or membranes between the two surfaces. Membranes have the advantage of preventing span-wise flow inside the sail, but non-shear resistant material should be used to permit chord-wise movement between the two sail surfaces. Utilising strings allows this movement. Due to the increased pressure between the two sail surfaces and their spacial separation a comparatively stable and stiff structure is generated. Since this sail system needs no rigid components apart from the mast, it is possible to store and reef it. The only extra effort in terms of trimming the sail is controlling the mast rotation and the valve system for the sail openings. It is conceivable that the valves can be opened and closed automatically when tacking. Figure 1: Section structure of the DSS concept

73 Through the mast rotation it is possible to adjust the thickness of the profile. 3 ANALYSIS PROCEDURE A common way to analyse a sail system is to conduct model tests and measure the forces. When using computational fluid dynamics (CFD) to assess a sail, which is made from some kind of flexible material like cloth, a prediction of the distortion due the aerodynamic forces is needed to obtain realistic results. Nowadays a complete simulation of the fluid structure interaction (FSI) is typical for commonly used sail systems. For this new conceptual design a combination of wind tunnel tests and CFD simulations is chosen to assess the concept in a physical hands-on way. Qualitative model tests are conducted to proof the concept and obtain the sail shape. CFD simulations for the resulting sail shape are performed afterwards. In this study the analysis of the DDS system is conducted for a 2D section. A 3D investigation is regarded as too extensive for this conceptual work as many other factors would influence the performance comparison of the different sail types. It is therefore seen as most interesting and feasible to look at the sectional behaviour compared to other sail systems for this initial investigation into the concept. First a 2D section model is made and tested in a wind tunnel to assess the structural behaviour. Afterwards the achieved profile shapes are analysed by running a 2D flow simulation. Thereby only close-hauled courses are considered. To compare the predicted performance potential flow simulations of a rigid wing sail profile and a conventional single surface sail profile are also performed. 4 WIND TUNNEL TESTS FOR PROFILE SHAPE ANALYSIS 4.1 TESTING FACILITIES AND MODEL The deployed wind tunnel is part of the testing facilities of the institute for dynamics of maritime systems at Technical University of Berlin. The test section has a cross section of 0.5m x 0.3m and the maximal wind speed is v=6m/s. The focus of this investigation is the behaviour of the profile section. A 3D assessment and comparison to other sail types is seen as unrealistic as part of this conceptual project due to the resulting model complexity and accuracy. A quasi-endless 2D model is used in the wind tunnel (Fig. 2). It is assumed that the gap at the top and the bottom of the model is small enough to prevent significant loss of pressure inside the DSS. To account for scaling effects the model is constructed of very thin and light sailcloth so that the fold ratio shows comparable stiffness to full-scale sailcloth [7]. For the mast an aluminium pipe is used. The chord length is about c=340mm and the mast diameter is 20mm. The model is fixed to synchronously rotatable disks in the floor and ceiling of the testing section. They can be adjusted to ±40. The mast pivot passes through the tunnel ceiling and can be adjusted from the outside to any angle. Figure 2: Model in test section Additionally there are tell-tales along one circumference, so that separation effects can be detected. 4.2 TESTING PROCEDURE AND ANALYSIS The wind speed is set to v=3.25 m / s, which is equivalent to a Reynolds number of about Re= At that speed the model behaves consistently and the stiffness is still adequate at large angles of attack (AoA). At higher speeds the gaps between the model and the tunnel ceiling and floor increase due to sail cloth stretch, so that the two dimensionality of the flow and the pressure inside the DDS would not be maintained. The rotatable disks are set to nominal angles of attack of 3, 5, 7, 10, 15 and 25. The effective AoA is always about 2.5 lower since the trailing edge is not fully constrained against moving sideways. The test cases are labelled based on nominal AoA combined with the mast rotation (e.g.: nom =5, =30 05_30). The mast rotation is varied from β=0 to β=50 in increments of 10. Through the transparent ceiling of the test section photos are taken from above the centre of rotation, so that the profile shapes in the different combinations of AoA and mast rotation can be observed (Fig. 3). Altogether there are 36 tested combinations of AoA and mast rotation. For closer investigation six cases with different mast rotation angles at the same AoA and six modulations of AoA with fixed mast rotation are chosen. By that the influence of these two values can be assessed separately. The other combinations show trends, which

74 Figure 3: Profile section in wind tunnel with digitised shape, α nom =7, mast rotation angle β=30 can largely be explained by the two systematic variations. The photos of all reviewed cases were digitised in a computer aided design (CAD) programme by manually tracing the section shape. As an orientation aid the telltales along the circumference were used. Fig. 3 shows the digitised section profile in the photo (case 07_30). 4.3 QUALITATIVE MODEL TEST RESULTS The digitised shapes of the selected section profiles are shown in Fig. 4 and Fig. 5. In Fig. 4 one case (α nom =15 ; β=30 ) is shown where the windward surface shape is inverted. The pressure inside the DDS is higher than the pressure on the windward side so that this convex shape occurs. Presumably the openings in the sail at the leading edge are close to the stagnation point, which creates the high internal pressure. The same effect can be observed for the other five test cases at α nom =15 and six further combinations (03_50, 05_50, 07_50, 07_40, 25_20, 25_10). These shapes are not considered in the analysis since they are not suitable for lifting devices with a high C L /C D ratio. This behaviour could possibly be avoided with an inner structure to limit spacial separation of the two surfaces, which was omitted due to the small scale model, or by reducing the size of the leading edge openings to lower the internal pressure. Figure 4: Variation of AoA with fixed mast rotation angle of β=30 Figure 5: Variation of mast rotation angle with fixed AoA of α nom =10

75 The twelve pairs of equidistantly spaced tell-tales show first signs of separation near the trailing edge of the suction side for AoAs greater than α nom =10 and at every case with mast rotation angle of β=50. This observation can be explained by the fact that the suction side is highly curved at these large mast rotation angles. At an AoA of α nom =25 wide areas of separation are visible for all mast rotation angles. By closing all dynamic pressure openings on both sides the sail section model showed a different shape being flatter immediately behind the mast. Noticeable was the back winding and a less stable behaviour for small AoAs. profile for dimensioning the DDS. In order to obtain an asymmetric profile which can be utilised on both tacks, a flap is introduced at 50% of the chord length. To achieve the same camber as the DSS and sail emulation, the flap angle has to be The fluid simulation showed excessive separation effects with this profile configuration. Also it seems not to be practical. Therefore the flap angle was reduced to 10. At this setting no more separation effects are recognised. Hence efficiency lost is reduced. The thickness-to-length ratio is slightly larger than the DSS, which has to be remembered when comparing the results; the NACA profile drag is overrated. 5 AERODYNAMIC SIMULATIONS By conducting 2D flow simulations the aerodynamic characteristics of the different sail sections are assessed. The focus is set on the potential performance, expressed by the lift (C L ) and drag (C D ) coefficient at the different AoAs. These coefficients are the dimensionless values of the lift and drag force affecting the aerodynamic body in a flow. They are normalised with the dynamic pressure and chord length [8], which is set to c=1 for all simulations presented here. Furthermore a point of interest is the width of the AoA sector, in which good performance is achieved. This characteristic is beneficial to cope with apparent wind angle fluctuations. For the aerodynamic simulation the software XFLR5 1 is used, which is in essence XFOIL extended by a GUI. It uses a 2D panel code with boundary layer condition for calculation of the profile circulation [8]. 5.2 SIMULATION PROCEDURE To compare the effectiveness of the DSS with established sails and wings, profile shapes of these types are analysed as well. For every DSS shape at a tested AoA a sail shape is created. The most important factors influencing the drag of aerodynamic bodies are the thickness-to-length ratio, the position of the maximum thickness and the shape of the nose [5]. Considering this, the mean profile line of the corresponding DSS attached to a mast with the same dimension is chosen for the single surface sail (Fig. 6). Thereby camber is not changed and a good comparability is achieved. A mast pocket is constructed to emulate a possible application of a single surface sail on a dinghy. For the wing sail section the NACA 0016 profile is chosen [9]. It has the same nose radius as the DSS and the cloth sail emulation since it was used as the reference 1 Deperrois, A. XFLR5 v6.05 beta, 2011 Figure 6: Profiles for comparison (top: sail emulations, bottom: wing sail profile) In the flow simulation the effective angle of attack obtained from the photographs is used. Assuming an average wind speed of v=6 m / s ( 3-4Bft.) and a chord length of c=2m the Reynolds number is about Re= , which is used in the conducted simulation. These values are representative of high performance sailing dinghies like the moth class boats, on which prototyping such a sail system is conceivable and complies with the class rules. The openings at the suction side are omitted to simplify the simulation. It is supposed that they do not interfere with the flow significantly, when the sail is filled with the stagnation point pressure. Furthermore the flow inside the sail is not considered. It has yet to be determined what the exact effect will be, but it is supposed that the dynamic pressure is different at the head and the foot of the sail and therefore a flow inside the DSS is possible to appear. To avoid that kind of undesired flow horizontal divisions would be possible, but they could reduce the ability of the structure to produce the observed shapes. 5.3 SIMULATION RESULTS Analysis of variation of AoA For the performance comparison exemplarily the five profiles with the same mast rotation of β=30 and varied

76 AoA are taken. This way there are five data points each for the DSS and the sail emulation. Due to the immutable profile of the wing section, a finer resolution of AoAs is chosen (Fig. 7). Fig. 8 shows the lift to drag ratio of the three 2D profiles. However, it has to be remembered that the wing sail section is thicker than would typically be used and the flap position and angle is not necessarily set to an ideal value. The mast of an optimised single surface sail would be much thinner and may have an aerodynamic shape. Therefore the characteristics of both reference profiles are probably underrated. But even by considering these arguments the DSS shows a high performance potential. A fluid simulation of a thinner wing sail profile (NACA 0010) with 10 and 27 flap angle produced a maximal C L /C D ratio of 70, which is about the value the DSS achieves. An adjustment was also made for the single surface sail. The mast diameter was reduced by 40% for the case 10_30 (α nom =10, β=30 ) to approximate the rig proportions of an International Moth. The simulation shows a reduction in drag coefficient of about C D = The resulting maximum C L /C D ratio of about 43 still remains below the maximum of 69 for the DSS. Consequently the difference between the DSS and the sail emulation is about 40%. A study at the Princeton University on the aerodynamic characteristics of different glider wings showed comparable performance differences between a profile section with an elliptical nose and a single cloth surface, which resembles the sail emulation, and a profile section similar to the DSS. Wind tunnel tests were conducted at a Reynolds number of Re= with 3D wing models with an aspect ratio of 8.5. The tests showed an approximately 45% lower C L /C D ratio for the single surface type [6]. Figure 7: C L and C D comparison (2D sections) The 2D fluid simulation indicates potential of the DDS compared to a standard single surface sail and a wing sail. It can be seen that the lift coefficient of the DSS decreases and drag rises noticeably between α=4.16 and α=7.39, which can be explained by the observed separation effects. As discussed later less mast rotation angle could reduce or eliminate this behaviour. The flapped NACA profile has the smoothest curves and reaches the maximal lift to drag ratio at the largest AoA, because it has less mean camber and consists of symmetrical segments. The low drag of the NACA profile over a large range of AoAs is due to the general characteristic of the 4-digit series to have a wide sector of attached flow [9]. The single surface sail has the highest drag coefficient because of the presence of the mast. Generally aerodynamic profiles with a thickness are advantageous over cambered plates above a Reynolds number of Re= [5], which would represent a wind speed of about 2 Beaufort for a conventional sailing dinghy. Figure 8: C L /C D ratio over AoA (2D sections) Clearly visible in Fig. 8 is a narrow peak of maximal lift to drag ratio for the sail emulation. This characteristic is typical and one disadvantage of single cloth sails. The wing sail on the other hand shows the well-tempered behaviour followed by the DSS. The C L /C D ratio of the DSS remains nearly constant over a range of 3 in AoA. Not considered in the context of this project is the variation of the chord length (outhaul tension) to

77 optimise the profile shape. Although it is an important trim parameter to change camber, the effect on the single surface sail and the DSS is expected to be similar so that the relative performance should remain comparable Analysis of the mast rotation angle The DSS has an especial trim mechanisim by rotating the mast. In the tested condition a rotation of β=70 is sufficient to pull one side of the sail straight and by that to maximise the length of the opposite side. A longer adjustment of foot length would result in less mast rotation needed to create this effect. As described in section 4.2 the mast rotation is analysed in increments of 10 from β=0 to β=50. In the flow simulation six cases are exemplarily calculated whereby the AoA of α=7.3 is constant. It also has to be remembered that these effects depend on the Reynolds number and respectively the wind speed. In full-scale when all trim mechanisms can be used together camber and thickness can be adjusted separately from each other. This is supposed to be a great advantage over single surface sails and wing sails. None of which has the capability to change their profile thickness. 6 CONCLUSIONS The aims of the study were to draw up a conceptual design of a DSS and to analysis its viability in terms of structural behaviour and potential performance. Therefore qualitative wind tunnel tests with a quasi 2D profile section were conducted and the resulting shapes were analysed by a 2D fluid simulation. The qualitative wind tunnel tests showed a good-natured and stabile standing sail section. The principal functionality is assured and realisable. The presented sail system showed good aerodynamic characteristics in the 2D flow simulation and a high performance potential. Figure 9: C L and C D at different mast rotation angles The lift and drag coefficients at the different mast rotation angles in Fig. 9 show a decreasing performance with rising rotation angles. This is explained by Fig. 10. It can be seen that the thickness rises while the camber decreases. The increase of profile thickness is mainly responsible for the increase in drag, while the decreasing camber reduces the lift of an aerodynamic profile. [5]. It becomes apparent that the trim mechanism of mast rotation is an influential device by allowing the DSS to vary its profile thickness. That is a unique characteristic compared to conventional single surface sails and wing sails. Considering probable weight and cost no significant disadvantages compared to already applied sail systems are expected. The intended simple structure of the DSS should result in user-friendly handling. This study investigates the concept for a 2D section. Further CFD studies in 3D at different Reynolds numbers and model tests are needed to make reliable statements about the structural stability and performance. Thereby the optimal trim could be detected and a more practical comparison could be made. Moreover downwind conditions should also be investigated. 7 REFERENCES 1. Milidragovic, M., WING SAIL AND METHODE OF USE, United States Patent Nr: , Freistadt, W., Freistadt, O., PROFILSEGEL, Patentschrift Nr: , Trost, M. D., VARIABLE CAMBER INFATABLE AIRFOIL, United States Patent Nr: , 1997 Figure 10: Geometric variation by mast rotation angle 4. Lyngholm, T., WING PROFILE SAIL, United States Patent Nr: , Marchaj, C.A., AERO-HYDRODYNAMICS OF SAILING, Granada Publishing, 1979

78 6. Maughmer, M. D. and Princeton University, A COMPARISON OF THE AERODYNAMIC CHARACTERISTICS OF EIGHT SAILWING AIRFOIL SECTIONS, Technical report, Hansen, H., ENHANCED WIND TUNNEL TECHNIQUES AND AERODYNAMIC FORCE MODEL FOR YACHT SAILS, PhD thesis, The University of Auckland, Drela, M., Youngren, H., XFOIL 6.9 USER GUIDE, ( ), Abbott, I.H. and Doenhoff, A.E., THEORY OF WING SECTIONS, Dover Publications Inc., AUTHORS BIOGRAPHY S. Brüns holds a diploma degree in naval architecture from the Technical University of Berlin. He is currently working as assistant project engineer at FutureShip GmbH, where he wrote his diploma thesis on DEVELOPMENT OF A DOUBLE SURFACE SAIL SYSTEM; INFLATED BY DYNAMIC PRESSURE. H. Hansen is a team leader at FutureShip GmbH for aerodynamics, hydrodynamics and performance prediction of ships and sailing yachts. He has previously worked on performance prediction and sail development for America s Cup teams and on sports car aerodynamics. Heikki holds a Ph.D. in Mechanical Engineering from The University of Auckland and a B.Eng. in Yacht & Powercraft Design from Southampton Solent University. K. Hochkirch is Vice President at FutureShip GmbH, where his department offers naval architecture, software design and consultancy with focus on parametric modelling, fluid dynamic analysis and formal optimization for the shipping and yachting industry. He studied mechanical engineering and naval architecture at the Technical University of Berlin from which he received his doctoral degree in He realised and applied the complex measurement system DYNA - the TU Berlin's sailing yacht dynamometer. At TU Berlin he lectures aero- and hydrodynamics of sailing yachts.

79 COMPARISON OF FULL 3D-RANS SIMULATIONS WITH 2D-RANS / LIFTING LINE METHOD CALCULATIONS FOR THE FLOW ANALYSIS OF RIGID WINGS FOR HIGH PERFORMANCE MULTIHULLS K. Graf, Yacht Research Unit - Univ. Applied Sciences Kiel, Germany, kai.graf@fh-kiel.de A. v. Hoeve, Technical University Delft, The Netherlands, advanhoeve@gmail.com Simon Watin, VPLP Yacht Design, Vannes / France, watin@vannes.vplp.fr Abstract: This paper reports about a comparison of a 3D RANS investigation to calculate the flow around wing sails with a method based on 2D RANS calculations of flow around wing profiles in conjunction with a lifting line method to account for 3-dimensional flow phenomena. Both methods shown here are of general use for wing investigations, however in the context of this paper they are used for rigid wings with two elements: a main element with a hinged flap, as they are currently used on some performance multihulls. Wing sails can well be analyzed using conventional three dimensional RANS based flow investigation methods; however the computational costs for these investigations are quite high. In this paper, an alternative approach to 3D RANS investigations is introduced. It is based on planar flow 2D RANS profile investigations in conjunction with a lifting line method to account for 3-dimensional flow phenomena and induced drag. The lifting line method uses an iterative approach in order to make use of non-linear profile lift coefficients. This approach is so computational efficient that it can be combined with constrained optimization methods in order to optimize performance of the wing. The paper describes the motivation for the development, the lifting line theory and validation efforts. Some applications of the new method are shown, demonstrating the ability of the method to be used for wing sail design and operation optimization. NOMENCLATURE AoA Angle of Attack (-) AWS Apparent wind speed (m/s) AWA Apparent wind angle (rad if not defined otherwise) c Profile Length (m) c D Drag coeffient (-) c L Lift coefficient (-) L Lift (N) L L (N) r Vector from point to integrator ds (m) r r (m) s vector along filament (m) u Flow Velocity vector (m/s) v Induced wind speed (m/s) w FVF Lower free vortex filament weighting (-) x Longitudinal coordinate (m) y + Dimensionless wall distance (-) z Vertical span-wise coordinate (m) z fvf Vertical coordinate of free vortex filament (m) z C Vertical coordinate of the panel center (m) z 1, z 2 Coordinates of lower and upper bound of wake sheet (m) Aspect ratio of wing (-) Vorticity (m²/s) bound Stepwise change of bound vorticity (m²/s) bound Vorticity of bound vortex filament (m²/s) fvf Vorticity of free vortex filament (m²/s) 1, 2 Vorticity at lower and upper bounds of wake sheet (m²/s) Density (kg/m³) Relaxation factor (-) SI units only 1 INTRODUCTION With the decision to sail the next America's Cup on multihulls featuring multi-element rigid wings, these systems of wind propulsion came into the focus of designers, engineers and scientists involved in the design of the respective yachts. Compared to conventional soft sails, wing sails provide extraordinary performance, in particular very high lift to drag ratios, thus making them particularly interesting for high speed catamarans. Wing sails became popular with the Little America's Cup, where they are used since a while; however the America's Cup with its known high level of science and engineering has boosted the demand in accurate and efficient flow analysis methods applicable to wing performance prediction. Typical analysis methods for the three-dimensional flow around such wings are 3D-RANS flow simulations. They are well-suited for rigid wings, since they are able to take into account the viscous and turbulent flow phenomena that are crucial for the operation of these wings with small gaps between the elements. However an assessment of the performance of a wing requires the execution of a quite complex test matrix, being defined by the permutation of angles of attack, twist and flap angles to be investigated. With a single RANS simulation using finite volume discretization of about 10 to 30 million grid cells, the computational burden for the execution of a full test matrix for single wing geometry is very large. A remedy to this problem are flow analysis methods based on the combination of a lifting line method in conjunction with profile lift and drag data generated from 2D-RANS simulations. 2D-RANS simulations are dramatically less computational expensive than 3D- RANS simulations and can predict the complex flow pattern around a multi-element profile with gaps while lifting line methods take care of three dimensional flow phenomena, in particular induced drag. This method promises to be far less computational demanding than 3D-RANS investigations.

80 A rough estimate of the amount of computations necessary for a full wing analysis quantifies the motivation behind the work: for an assessment of the performance of a wing (for example by a VPP) a permutation of angles of attack, flap angles and twist has to be investigated. A small test matrix for a single wing geometry (neglecting Reynolds number changes) would consist of about 10 angles of attack, each combined with 2 to 4 base flap angles and let s say 2 to 4 twist angles to cover a minimum range of operational states covering non-linear effects due to separation. A 3D-RANS investigation would thus consist of more than 100 computational simulations of a grid of about 10 to 30 million grid cells as a minimum. In contrast to this a profile investigation will investigate a few 2- element profile shapes in order to account for profile variations with span, each shape investigated with a computational grid of about to grid cells. Each profile will be investigated at about 10 angles of attack and 2 to 4 flap angles. The effect of twist will be taken into account by the lifting line approach. Since the computational costs of the lifting line method itself is negligible compared to the computational load of even the smallest RANS investigation, the 2D-RANS lifting line approach theoretically reduces the computational burden for the investigation of a wing by the factor of 100. Even more, a variation of the planform of the wing would require redoing almost the entire test matrix of the 3D-RANS investigations, while in a first approximation no need for additional 2D- RANS simulation exists for the 2D-RANS lifting line method. Consequently the computational burden for the investigation of let s say 10 wing planforms for a variational study of planform can be reduced by the factor of Obviously the accuracy of the 2D-RANS lifting line method has to be proven and has to provide the same level of confidence as the 3D-RANS method. The description of the 2D-RANS lifting line method and the comparison with 3D-RANS results are the main foci of this paper. In addition some practical applications are shown, making use of the computational efficiency of the new method. This paper focusses on rigid wings and profiles of two elements: the symmetric main element which is assumed to be completely rigid and a hinged flap, which can be rotated around an axis, lying somewhere on the center line of the main element. The flap is divided in span-wise direction into a couple of panels, allowing changing the flap angle with height in order to twist the wing. Obviously the entire wing can be rotated around a vertical axis resting on a wing step on the catamaran platform. 2 THE LIFTING LINE METHOD The lifting line method is based on the following principal: A bound vortex filament of piecewise linear, optionally discontinuous, vorticity distribution along span is running from root to tip of the wing. Individual free vortex filaments and/or wake sheets (in any combination) are shedding from bound vortex filaments into infinity in the direction of incident flow. Discrete vorticities of the free vortex filaments and the distributed vorticity per length of the wake sheet are calculated conforming to Thompsons rule: (i) a linear change of vorticity of the bound filament generates a wake sheet of constant vorticity per span length and (ii) a discontinuity of vorticity of the bound vortex filament generates a discrete free vortex filament, its vorticity being the jump of vorticity of the bound filament at the location of the discontinuity. Induced wind is calculated from the free vortex filaments and the wake sheet using Biot Savart's law. The vector sum of induced wind and undisturbed incident flow gives an effective incident flow. The lift calculated from Kutta's law acts perpendicular to it. This effective lift can be decomposed into a flow force perpendicular to the undisturbed incident flow the nominal lift and an additional flow force in the direction of the undisturbed flow the induced drag. The discrete form of this method calculates the total drag as integration over span of the induced drag per span plus the viscous profile drag. In a similar manner the profile lift is integrated over span, taking into account the local effective incident flow. The standard inversed lifting line method assumes constant derivative of lift coefficient over angle of attack, see SCHLICHTING and TRUCKENBRODT [1]. It involves the inversion of a matrix in order to calculate the discrete spanwise vorticity distribution of the bound vortex filament for a given geometry. However to take into account nonlinear lift coefficients with respect to angle of attack, in particular lift coefficient changes due to flow separation, an iterative approach is employed here. It is based on an iterative correction of induced wind from the spanwise lift distribution which takes into account the induced wind as a correction of angle of attack. Vorticity of bound vortex filament bound vortex filament z x free vortex filament vortex sheet Figure 2-1: Bound and free vortex filaments on a wing

81 2.1 THEORY We are using the theorems of Kutta, Biot Savart and Thompson as follows: fvf v 4 z fvf 1 z C (2-6) Kutta's Law is used to calculate the lift generated by a vortex filament: L u ds span (2-1) where L is the generated lift, the density of flow, u the incident flow, the vorticity of filament and ds an integrator along the filament. Biot-Savart's Law is used to calculate the induced wind generated by a free vortex filament: 1 v 4 s r ds 3 r (2-2) where v is the induced velocity generated by the vortex filament of vorticity and r is a vector from the point, where v is generated to the integrator ds along the filament. Free vortex filaments are calculated by Thompsons rule, saying that a vortex filament may only end at a fixed wall or at infinity. Prandl s concept of horseshoe vortices is used, saying that any change of the bound vortex filament results in a free vortex filament. This results in: d fvf bound( z) dz z (2-3) For a stepwise change of the vorticity of the bound vortex filament bound, the vorticity of the free vortex filament at the position of the stepwise change calculates from: fvf = bound (2-4) A free vortex filament of constant vorticity fvf (from a stepwise change of bound as to (2-4)) starting at x=0, z=z fvf, running at constant z to x=, generates induced wind in P by (see Figure 2-2): fvf dx v ( zfvf zc ) 3 4 r x0 fvf x ( z z ) ( ) 4 ( ) This yields (with fvf C 2 x0 zfvf zc r x r 1for x / ): (2-5) A vortex filament sheet generated from a span-wise change of bound (z) starting at z 1 till z 2 induces wind according to (see Figure 2-2): 1 v 2 4 z z z 1 bound dz z z C (2-7) We assume bound changes linear between z 1 and z 2 from to 2: 2 1 bound( z) 1 ( z z1) (2-8) z z 2 1 Introducing the constant expression: z ( )/( z ) into (2-7) yields: bound/ z1 z dz v 4 z z zz z2 zc ln( ) 4 z z z z z z fvf z C z 2 z 1 P 1 z r C C free vortex filament ds (2-9) x Figure 2-2: Free vortex filament and wake sheet generating lift at arbitrary point P Profile lift per span length L=d L /dz is calculated from a lift coefficient c L, the dynamic pressure 0.u 2 (density flow speed u= u ) and the profile chord length c. c L depends nonlinear on angle of attack AoA of incident flow. For a profile of a wing of finite span the angle of attack is AoA reduced by induced wind: L AWS c c AoA v u (2-10) L( / ) The induced drag then calculates from D Lv/ AWS (2-11) i

82 The bound vorticity of the profile is calculated from the lift per span length due to (2-1) bound L AWS (2-12) Since vorticity of free vortex filament depends on vorticity of bound vortex filament, which in turn depends on lift, itself depending on free vortex filament vorticity due to induced wind, this procedure is iterative by nature. For a wing of finite span with varying lift distribution over span the iterative procedure is: 1. Assume v=0 2. Calculate profile lift per span from (2-10) for a given geometric angle of attack, flow speed and chord length 3. Calculate bound over span from profile lift from (2-12) 4. Calculate v from (2-6) and (2-9) 5. redo until v converges 6. calculate induced drag 7. calculate total drag by adding parasitic profile drag to induced drag 2.2 DISCRETIZATION The envelope of the wing is discretized with an arbitrary number of horizontal profiles, numbered i=0,1,,n. Each profile is described by its z-coordinate z i, a chord length c i along with leading and trailing edge x-coordinates, an individual incident flow speed AWS i, an incident (geometric) angle of attack AoA i, a lift coefficient c Li, a parasitic profile drag coefficient c DPPi and a moment coefficient c Mi with respect to a local origin, for example the leading edge. No profile geometry is needed since the property of the profile is entirely described by the lift coefficient. However additional parameters can be used to change the flow force coefficients, for example the angle of a hinged flap of the profile. The planform area of the wing is defined by trapezoidal panels, number i=1,2,,n between profiles i-1 and i. Due to the definition by neighboring profiles, panels can have varying incident speed and angle of attack and can twist. Flow force coefficients c L, c DPP and c M can be provided by tabulated data for given AoA and additional parameters like a flap angle. This approach allows taking into account profile properties from any source, being it linear or nonlinear, from inviscid or viscous calculation methods N N N-1 N-1 z x Figure 2-3: Discretization of wing We assume a bound vortex filament at x=0 aligned with the z-axis for incident flow aligned with the x-axis. The vorticity changes linear between profiles, generating a free vortex wake sheet. At bottom profile (root) and top profile (tip) discrete free vortex filaments are generated in order to satisfy zero bound vorticity for z<z 0 and z>z N. Consequently bound (z) and fvf root as well as fvf tip can be calculated from profile definition information: for 0 <= i <=N: vi i 0.5 AWS i ci cli ( AoAi ) (2-13) AWS for z i < z < z i+1 i 1 i bound( z) i ( z zi ) z z fvf root fvf tip 0 i1 FVF i i (2-14) w (2-15) (2-16) N Here w FVF is a factor taking into account to which degree the root free vortex filament is suppressed by a wall. If the root of the wing is fixed to a wall without a gap, w FVF =0. If no wall is present at all, w FVF =1. Induced wind is calculated in the vertical center of each panel j=1,2,,n by summing up the induced wind generated by any free vortex wake sheet and the discrete free vortex filaments at root and tip. v Cj for 1<=j<=N: 1 4 w FVF N i z 1 i z i C j ln( ) z z z z 0 1 N 1 4 z z 4 z z i1 i i1 i1 C j 0 Cj N Cj (2-17)

83 where z C j 0.5( z j z j1) is the z-coordinate of the panel center and v C j the induced wind at x=0, z=z C j. Linear interpolation is used to calculate induced wind v i at profile vertical location z i : v i.5( v v ) for 1<=i<=N-1 (2-18) 0 C i 1 C i At root and tip induced wind is calculated using linear extrapolation: v C 0 2v 1 v1 (2-19) v (2-20) N 2vC N 1 vn 1 An iterative procedure has to be used in order to calculate induced wind. We assume that for any profile i, the local height z i, the profile length c i, the local geometric angle of attack AoA i and the local wind speed AWS i is given. We also assume that lift coefficient can be calculated using the above values. Induced wind then is calculated iteratively starting with a zero guess: (1) Set v i =0 for any profile i=0,1,,n (2) Predict profile lift coefficient cli( AoAi vi / AWSi ) using tabular data from 2D RANS profile simulations (3) Calculate i for any profile using (2-13) (4) Calculate induced wind in panel center v Ci from (2-17) (5) Calculate induced wind at profile height from (2-18), (2-19) and (2-20) (6) Repeat (2) to (5) until convergence, if convergence achieved continue (7) Calculate lift per span for any profile using (2-10) (8) Calculate induced drag per span for any profile using (2-11) and add parasitic profile drag per span (9) calculate driving and side force per span from trigonometric relationship (10) Integrate over span by trapezoidal integration To achieve convergence, the iterative procedure needs under-relaxation. If k denotes the current iteration step, the induced wind is calculated as a weighted average of the result of the current and last iteration step: k k v v v 1 (1 ) (2-21) Ci Ci Ci Calculation of driving and side force is necessary if undisturbed incident wind angle of attack changes over height (wind twist). In this case no global lift and drag can be calculated. Some attention has to be paid to the angle of attack AoA, usually defined by the angle between incident wind and a reference line of the profile (for the profile of a symmetric main element this is its center line). The angle of incidence AoA is calculated from the apparent wind angle AWA and the local rotation of the profile, given by wing rotation and wing geometric twist with respect to the sailing yacht center line, which is the reference line of the apparent wind angle. This allows taking into account the sheeting of the wing, the twisting of the wing and a twist of the incident wind. 2.3 IMPLEMENTATION The method is implemented as a spreadsheet calculation using MS Excel. The iterative method to predict induced wind is implemented as an embedded Visual Basic application. Under-relaxation factors around 0.25 are used, which achieve convergence usually after 15 to 30 iteration cycles. The runtime on an average PC for a single prediction of flow forces of a two-element wing, discretized with 21 profiles, was about 1 to 3 sec. 3 RANS METHOD The commercial RANS solver StarCCM+ has been used for 2D- and 3D- flow simulations around profiles and wings. An introduction of RANS methods is not given here, for a general introduction refer to FERTIGER and PERIC [2]. An example of application of RANS methods to yacht flow investigations conducted by one of the authors is given in GRAF and BOEHM [3]. The method used here is based on the solution of mass and momentum equations for incompressible adiabatically flow. For external flow at low Mach number the assumption of incompressible flow can be accepted. A finite volume discretization based on Cartesian hexahedral cells in the far field and body fitted prism cells in the vicinity of the flow body are used. Turbulence is taken into account using eddy viscosity hypothesis and the SST turbulence model for the prediction of turbulence viscosity. For some profile investigations however a Reynolds stress model has been used, see details below. For 3D-investigations, logarithmic wall functions were employed for the sake of computational efficiency. For 2D-profile investigations, some cases have been investigated employing wall functions, while other resolved the boundary layer. All of the investigations shown here were executed on a Linux-based compute clusters. A maximum of 30 partitions/cores have been allocated to a particular 3Drun, while 2D-runs typically employed four to eight cores.

84 4 TEST CASES The method introduced here has been used for the design and optimization of a wing, developed within the Shared Design Package, conducted by the French yacht designer Van Peteghem Lauriot Prévost Yacht Design/Vannes and Yacht Research Unit Kiel/Germany on behalf of America's Cup Race Management. In addition it has been used within the Swiss Hydros campaign to develop the wing of a C-class catamaran to participate in the Little Cup The results from these studies, however, are not publicly available. In this paper it is reported about two additional test cases, using geometries which are not covered by nondisclosure agreements: A rectangular foil of aspect ratio 4.5 with a 4- digit NACA profile A two-element wing in accordance with the AC72 class rules, however with some simplifications and approximations on main element and flap profile shape in order to reduce the computational load. Both test cases have been investigated employing full 3D-RANS investigations and 2D-RANS profile investigations in combination with the lifting line method as described above. For the rectangular foil wind tunnel test results have been available for validation. Figure 4-1: Rectangular wing and computational domain 4.1 RECTANGULAR WING The rectangular wing has a span of 1.8 m and a constant symmetric profile of type NACA 0012 with a profile chord length of 0.4 m. The root of the wing is fixed to a flat plate; see Figure 4-1, showing the wing together with the computational domain as well as the wing in the wind tunnel. The wing as well as the profile are investigated at a Reynolds number of Rn=1.28e5. The turbulence intensity at the inlet of the computational domain has been set to 1%, the value known from CTA field measurements in the wind tunnel. Since the simulations are carried out assuming fully turbulent flow, the wind tunnel model was equipped with turbulence stimulators. A polyhedral grid of approximately 2.2 million grid cells is used for spatial discretization for the 3D test case, featuring a cascading refinement of the region around the wing and downstream of it, see Figure 4-2. Prism cells are used to resolve the boundary layer. Dimensionless wall distance of the cells contacting the wing is about 20<y + <100. The grid for the 2D-RANS investigation has been derived from the 3D-grid via a cut at the root of the wing. The respective 2D grid contains approximately grid cells, see Figure 4-3. Figure 4-2: Polyhedral grid for 3D RANS investigation of rectangular grid

85 2 1 cd cl( KPP) (1 k) (log Rn 2) 2 (4-2) Figure 4-3: Computational grid around NACA 0012 profile for 2D-RANS simulation Figure 4-4 shows lift and drag coefficients as the result of the 2D-RANS investigation. The diagram depicts the expected results for attached flow condition and beginning flow separation at an angle of attack of approximately 10. At larger angles of attack it is conspicuous that the lift coefficient recovers and increases again, a behavior that shows a well-known deficiency of common turbulence model to properly resolve flow separation. Lift Coefficient [-] Lift Drag Drag Coefficient [-] Angle of Attack [ ] Figure 4-4: Lift and drag coefficients of the rectangular wing profile The lifting line method uses 21 profiles, distributed evenly over span. The result of the 2D-RANS investigation is used to calculate lift and parasitic drag coefficients. where the frictional drag is calculated using the ITTC 57 friction line, (1+k)=1.22 is the form factor of the profile and KPP=0.02 accounts for the parasitic profile drag. These formulas are widely used as empirical function for the prediction of flow force of rectangular wings, see SCHLICHTING and TRUCKENBRODT [1] and HARVALD [6]. The diagram shows fairly well agreement of 3D-RANS flow force coefficients with wind tunnel results at lower angles of attack. Lift coefficients are slightly overpredicted by the lifting line method. The angle of attack of maximum lift coefficient agrees well for all methods. It is slightly postponed to larger angles compared to the 2D-RANS results, this certainly the effect of the induced wind, which reduces the effective angle of attack. Maximum lift coefficient of wind tunnel test result is lower than the respective value from simulations and flow separation is less pronounced. A possible explanation for this may be the turbulence intensity and length scale in the wind tunnel. Large turbulence intensity is known to have a blurring effect on the onset of separation. At higher angles of attack drag coefficients from the simulation are lower than those from wind tunnel tests. Again this may be assigned to a lack of existing turbulence models to properly resolve separated flow. In general it can be observed that the agreement of 3D- RANS simulations with the method based on 2D- RANS simulations in combination with the lifting line method is rather good. Comparison with 3D-RANS investigations and wind tunnel result: Figure 4-5 shows lift and drag coefficients for 3D- RANS investigation in comparison with the result of the lifting line method and wind tunnel results. In addition estimated lift and drag coefficients from empirical functions are plotted. Here the lift coefficient is calculated by: cl 2 AoA 2 (4-1) where 2 span / chordlength is the effective aspect ratio of the wing. The drag coefficient is calculated using:

86 Lift Coeffient [-] Soedings Estimate Lift 3D RANSE Lift Windtunnel Lift LLM Lift Soedings Estimate Drag 3D RANSE DRAG Windtunnel Drag Angle of Attack [ ] Figure 4-5: Comparison of 3D-RANS investigations with lifting line method and wind tunnel test results 0 Drag Coeffient [-] 4.2 AC72 TYPE TWO-ELEMENT WING The second test case is a two-element wing designed in accordance with but not strictly following the rules for the AC72 catamaran (see AC72 Class Rules[7]). The wing has a span of 38 m and a planform area of 260 m². Leech and luff is fixed within the bandwidth given by the AC 72 rules. Some simplifications are made for the profile in order to reduce the computational load for the 2D-RANS investigations: the profile of the main element is a NACA0020 while the second element profile is a NACA The chord ratio of main and second element is 1 over the entire span. This simplification allows analysing only a single profile geometry for the 2D-RANS simulations, if Reynolds number effects are neglected. At zero flap angle the gap between main and second element is 10mm. The center of rotation of the second element is located at 85% of the chord length of the main element. Some additional simplifications apply in order to reflect the vertical partitioning of the flap into four panels. The root of the entire wing is located 0.5 m above a flat plate This wing design, see Figure 4-6, by far does not suggest being an optimized one. The sole reason for this design is a simplification, which allows restricting 2D-RANS investigations to a single shape, assuming that changes of flow forces due to moderate changes of Reynolds number can be neglected. Figure 4-6: AC72 wing geometry and computational domain 4.3 COMPUTATIONAL GRID FOR 2D- AND 3D- RANS INVESTIGATIONS Intensive grid sensitivity studies have been carried out in order to get grid-invariant simulation results. Grids of 5 million to 18 million grid cells have been investigated. The final 3D grid uses about 10.2 million Cartesian grid cells in the far field with cascading refinements in the vicinity of the grid and additional local refinements at leading and trailing edge and at the gap between main and second element, see Figure 4-7. Figure 4-8 shows that this grid is a reasonable compromise between accuracy/grid independency of results versus computational costs. The 2D-grid has been even finer with about grid cells. For this grid the boundary layer has been fully resolved, y 1, see Figure 4-9

87 4.4 2D-RANS SIMULATION RESULTS 2D RANS investigations have been carried out executing the following test matrix: - 14 AoA with dense distribution of angles close to maximum lift - 5 flap angles ranging from 0 to 20 Some test calculations have been done using the SST turbulence model of MENTER [4]. The in-stationary RANS equation has been solved. Flow velocity has been set to a Reynolds number of about Rn=5e6 and turbulence intensity at inlet to 1%. Observations of the results however have shown conspicuous lift coefficients at higher angles of attack. In particular after reaching stalled conditions and the respective drop of lift coefficients the lift recovered and increased again with increasing angle of attack. This behavior cannot be found in experiments, suggesting the lack of the SST- and other 2-euqation turbulence models to properly resolve stalled flow conditions. Change in Lift or Drag [%] 104% 102% 100% Figure 4-7: Computational grid of 3D RANS simulations around wing sail 98% 5.0E E E E E E E+07 Number of cells [-] Figure 4-8: Result of Grid Sensitivity Study Lift Drag As a remedy the entire range of AoAs and flap angles has been re-investigated using the Reynolds Stress Model of GIBSON and LAUNDER [5]. For 2D-flow this does not increase the number of unknowns and consequently the computational workload is the same as for a 2-equation turbulence model. The conspicuous behavior of lift at higher angle has been avoided at least to an acceptable degree. The 2D-RANS-results shown here use this Reynolds stress model. Simulations have been conducted solving the instationary RANS equation with 1 st order time integration and a time step size of t=0.015s for 2D flow and t=0.15 s for 3D-flow. Figure 4-10 shows streamlines for angle of attack A0A=5 and a contour plot of velocity magnitude for AoA=15. While the flow pattern looks as expected for low AoA, the in-stationary vortex shedding at separated flow condition can clearly be depicted. The in-stationary vortex shedding obviously generated oscillating flow forces at stalled condition. For the calculation of lift and drag coefficients, some averaging over a larger number of time steps of the in-stationary calculation has been employed. Figure 4-11 and Figure 4-12 show lift coefficient over AoA and the drag over lift profile polar. Figure 4-9: Computational Grid for 2D RANS wing profile investigation The second diagram shows an unexpected bump of the drag with increasing lift. The rational for this could not be completely unveiled within this study, however it can be assumed that this behavior can be linked to the flow mechanics in the gap between main element and flap.

88 Earlier investigation of two-element profile clearly showed, that for each AoA there is exactly one flap angle for which the profile is working under optimum conditions with respect to lift-to-drag ratio. It can well be assumed that the very pronounced bump of the graph at flap angle of 20 is generated by a flow pattern where the gap has a positive impact on the boundary layer at the trailing edge of main element as well as the leading edge of the flap, preventing the boundary layer to separate there. Drag coefficient [-] beta=0 beta=5 beta=10 beta=15 beta= Lift coefficient [-] Figure 4-12: Drag over lift for 2D-RANS investigation Figure 4-10: Streamlines at AoA=14, Flap angle 10, velocity magnitude contour plot at AoA=20, Flap at 20 Lift coefficient [-] cl Beta=0 cl beta=10 cl beta=20 cl Beta=5 cl Beta= AoA [deg] Figure 4-11: Lift coefficient over AoA for 2D-RANS profiles at various flap angles 4.5 3D-RANS SIMULATION RESULTS AND COMPARISON WITH THE 2D-RANS LIFTING LINE METHOD Full 3D RANS investigation of the wing have been investigated for a test matrix of 13 angles of attack ranging from 0 < AoA < 22. These have been combined with flap angles of 0 < < 20. A single twist case has been studied, where the flap angle at the root of the wing was =20, reducing linearly to =0 at the tip. Flow velocity was set to 10m/s. SST turbulence model has been used and turbulence intensity at inlet was set to 1%. Figure 4-13 shows flow pattern at angle of attack of AoA=14 and a flap angle of 5. It shows beginning flow separation at the trailing edge of the main element.

89 for the entire test matrix. However an excerpt of the results is shown here only. Figure 4-14 to Figure 4-19 show lift and drag coefficients from 3D RANS simulations and the lifting line method over AoA for flap angles of 0, 10 and 20, while Figure 4-20 and Figure 4-21 show lift and drag coefficients for the twisted test case. Lift Coefficient [-] D RANSe LLT 0.0 Flap Angle Angle of attack [ ] Figure 4-14: Lift coefficient over AoA, Flap angle Drag coefficient [-] Flap Angle 0 3D RANSe LLT Angle of attack [ ] Figure 4-15: Drag coefficient over AoA, Flap angle 0 Figure 4-13: Flow pattern around wing The 2D-RANS Lifting line calculations are based on 21 horizontal profiles evenly distributed along span. A free vortex weighting factor of FVF has been used. Results of the 2D-RANS profile investigations have been integrated for the full range of the test matrix, including very large angles of attack with fully separated flow. Comparisons of the 3D-RANS results with those of lifting line method have been generated Lift Coefficient [-] D RANSe LLT Flap Angle Angle of Attack [ ] Figure 4-16:Lift coefficient over AoA, Flap angle 10

90 Drag coefficient [-] Angle of attack [deg] Figure 4-17: Drag coefficient over AoA, Flap angle 10 Lift Coefficient [-] Flap Angle 10 3D RANSe LLT Figure 4-18: Lift coefficient over AoA, Flap angle 20 Drag coefficient [-] 3D RANSe LLT Angle of Attack [ ] Flap Angle Angle of attack [ ] Figure 4-19: Drag coefficient over AoA, Flap angle 20 Lift Coefficien [ ] Flap Angle 20 3D RANSe LLT 3D RANSe LLT Flap Twist Angle of Attack [ ]l Figure 4-20: Lift coefficient over AoA, Flap angle 0 (root) to 20 (tip) Drag coefficient [-] Angle of attack [ ] Figure 4-21: Drag coefficient over AoA, Flap 0 (root) to 20 (tip) 4.6 ASSESSMENT OF THE RESULTS A comparison of the 3D RANS results and those of the lifting line method shows a twofold trend: 3D RANSe LLT Flap Twist For small AoAs where no flow separation can be detected the agreement of the two methods is very good. This holds for the lift as well as the drag, which in case of the lifting line method is calculated as a sum of the induced drag from the LLT and the viscous drag from 2D RANS profile simulations For larger angles of attack and small flap angles the maximum lift coefficient is lower for the 3D RANS simulations. The AoA of maximum lift is predicted lower for the 3D RANS simulations. Beyond the AoA of maximum lift coefficient the lift from LLT is generally too large For very large flap angles the lifting line method is not able to predict a result. Here the nonlinearity of the 2D lift coefficient is so pronounced that the iterative method of the LLT fails to converge. It remains to be concluded that the LLT method works well in the attached flow regime. For separated flow the results show some deviation. This can be traced back to the three-dimensional nature of flow separation. An analysis of the flow pattern of the separated flow for the 3D case depicts, that the vortex shedding at the trailing edge of the main element has a strong vertical orientation. This obviously cannot be modeled by the RANS profile investigations. 5 OPTIMIZATION OF TWIST AND ANGLE OF ATTACK Once the lifting line method has been implemented and the results of the profile investigation properly integrated, the computational runtime to investigate a single wing is almost negligible. LLT calculations can be carried out on a standard PC and take no more than a few seconds to calculate lift and drag as well as side

91 and driving forces and heeling moments for a particular planform and given settings for flow speed, angle of attack AoA and flap angle, which may vary with height in order to take into account wing twist. This opens the window for intensive optimizations studies of trim settings and planform within the preliminary design of a wing. In the following examples the lifting line method has been combined with a constraint optimization method based on conjugate gradient algorithms with penalty methods to account for constraints. This method is readily available within the Excel spreadsheet calculation program. base of the wing to a slightly negative value at the tip. The lift coefficient at the tip remains positive but small. For an even higher apparent wind speed of AWS=24m/s this effect of twisting the flap is even more pronounced. Figure 5-3 shows lift, lift coefficient and flap angle over span for this case. Here the flap angle has been reduced dramatically and the top of the wing shows inverted twist, generating some righting moment. The driving force is F xmax =11320N at a wing angle of Alpha=14.6. In the following example the wing angle with respect to centerline of the catamaran and the flap angle, able to change over span, have been predicted for maximum driving force at a heeling moment constraint of M Xmax =500kNm. The main element twist has been fixed to 10, apparent wind angle to 20. For an apparent wind speed of AWS=12m/s the optimizer found the maximum of driving force of F Xmax =7324 N, at a wing angle of =9.3. Figure 5-1 shows flap angle, lift and lift coefficient over span. Figure 5-2: Lift, cl and Flap Angle over span, AWS=18m/s Figure 5-1: Lift, cl and Flap Angle over span, AWS=12m/s Figure 5-2 shows the same calculation for AWS=18m/s. Here the result gives a driving force of F xmax =9335 N with a sheeting of the wing which is eased compared to the case of AWS=12m/s from =9.3 to =13.8. The diagram clearly indicates that the optimizer not only eased the main element but also twists the flap significantly from an angle =15 at the Figure 5-3: Lift, cl and Flap Angle over span, AWS=24m/s More results can be derived from the optimization calculations which may give hints for trimming the wing. The optimizer tries to minimize induced drag by maximizing effective span, however at higher wind

92 speeds effective span is traded in against low vertical center of effort with respect to side forces. Figure 5-4 depicts vertical center of effort VCE and effective span of the wing over apparent wind speed. The diagram shows that any reduction of VCE is costly with respect to induced drag. Effective Span [m], Vertical Center of Effort [m] Effective Span 5 Vertical Center of Effort Apparent wind speed AWS [m/s] Figure 5-4: Effective span and VCE for optimum trim 6 CONCLUSIONS The results from the two methods compared in the study presented here show a clear pattern: the lifting line method is well suitable to predict the performance of a two-element wing quite well in the attached flow regime. While the LLT method as implemented here principally can take flow separation into account, the flow force results generated in this regime diverge from those derived from 3D-RANS simulations. While generally the confidence to provide accurate results is greater for a full 3D RANS simulation than for the combination of lifting line method with 2D- RANS simulations, it has to be understood that the simulation of separated flow is still error-prone for the turbulence models available for practical engineering investigations. Consequently it cannot be claimed that the 3D-RANS simulations based on the turbulence models employed in this study are sufficiently accurate on an absolute scale and agree fully with the reality. It is left to speculation only if the 3D-RANS results are closer to reality than the lifting line method results. Only a rigorous validation and verification study with qualified experimental results may enlighten this in more detail. This has been beyond the scope of the current study. Where applicable, the lifting line method in combination with 2D-RANS simulation is of high value due to its computational efficiency. This holds obviously for the 2D-RANS simulations compared to those in 3D. In addition the principal of the employed lifting line method allows to be combined with constraint optimization methods. It can thus be used to find optimized trim settings of the wing for given wind conditions and hydrostatic constraints with very little effort. To do this based on 3D-RANS simulations; the computational load of such investigation easily can exceed any computational resources available to engineers. In addition 2D-RANS - lifting line method promises to be valuable for the investigation of wing design alternatives, such as a planform study, which once again can be conducted with very little effort using conventional tools like a spreadsheet calculation program. REFERENCES 1. Schlichting and Truckenbrodt: Aerodynamik des Tragflügels, Springer Verlag, Berlin, Ferziger, J.H. and Peric, M.: Computational Methods for Fluid Dynamics, Springer, New York Böhm, C. and Graf, K.: Validation of RANS simulations of a fully appended ACCV5 design using towing tank data, Proceedings of the INNOV'Sail08, Lorient, France, April Menter, F.R.: Two-equation eddy-viscosity turbulence modeling for engineering applications, AIAA Journal 32(8) pp , Gibson, M.M. and Launder, B.E.: Ground effects on pressure fluctuations in the atmospheric boundary layer, J. Fluid Mech., 86(3), pp , Harvald, S.A.: Resistance and Propulsion of Ships, Krieger Publication Company, Melbourne/USA, America's Cup Properties, Inc: AC 72 Class Rule, Version 1.0, Oct AUTHORS BIOGRAPHY K. Graf is a professor of ship hydrodynamics at the University of Applied Sciences Kiel in Germany and chief scientist of the university s Yacht Research Unit. He has been involved in several professional sail sport campaigns since more than 10 years. S. Watin is a R&D engineer at VPLP Yacht Design and responsible for flow and performance predictions. He has been involved in numerous design projects of VPLP, among them the AC 72 Shared Design Program and the Hydros C-Class Campaign. A.v. Hoeve is a Naval Architect of Delft Technical University who was working at YRU-Kiel as a flow analyst and CFD expert within a scientific exchange program.

93 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France A COMPARISON OF DOWNWIND SAIL COEFFICIENTS FROM TESTS IN DIFFERENT WIND TUNNELS I.M.C Campbell, Wolfson Unit MTIA, University of Southampton, UK, imc@soton.ac.uk Summary: This paper contains results from five different tests on model sailing yacht rigs and sails. The tests were conducted by the author in four different wind tunnels over a fifteen year period between 1991 and The tests were conducted as part of development programmes for Whitbread 60 and America s Cup Class yachts and for particular racing teams. They were originally subject commercial confidentiality so have not been published previously. Although the aim of the original tests was to compare sail designs and develop the performance of the individual yachts this aim of this study is somewhat different and uses the data to compare wind tunnels. The paper describes features of the wind tunnels that affect the results together with the test requirements for investigation of downwind sailing performance. A large number of individual results are presented from tests over a range of apparent wind angles and curves of maximum lift and drag coefficients from each tunnel are then compared. Although the original tests were not designed for benchmarking wind tunnels the sail coefficients from the different tests showed broad similarity within a tolerance band, which helps validate the technique of wind tunnel testing of sailing yacht rigs. Conclusions have been drawn from the results about the effect of lift on the drag of downwind sails and the overall accuracy of wind tunnel tests on rigs. 1. INTRODUCTION The Wolfson Unit MTIA s archives contain a large body of commercially confidential data from wind tunnel and other tests. The results presented in this paper have been abstracted from five different wind tunnel sail test projects, selected to enable results from different wind tunnels to be compared. Permission to publish the results was kindly given by the clients. Even though only one or two comparable sail configurations were selected from each of the five test programmes there remained a large amount of data to condense into this paper, which provides the basis for a reasonably rigorous evaluation of downwind sail wind tunnel testing. The tests were originally conducted to aid the development of the individual yachts and their sails and relative results between sails were consistent within each test. The aim of this paper was to examine consistency between different wind tunnel tests. The sail coefficients presented in this paper are the original values obtained at the time of each test, they have not been re-analysed or corrected to improve correlation as a result of the analysis performed for this paper. 2. WIND TUNNELS The four wind tunnels used together with the year of the test were: 1994, Volvo automotive tunnel, Gothenburg, Sweden [1] 1991, former Marchwood Engineering Laboratory (MEL) wind engineering tunnel, Southampton, UK [2] 1996 and 2003, University of Southampton (Soton) aeronautical tunnel, UK 2006, Politecnico di Milano wind engineering tunnel, Bovisa, Italy Table 1 Dimensions of the tunnel test sections Tunnel Volvo MEL Soton Milano Width m Height m Length m Model scale ACC W The principle features of the tunnels that could affect the sail tests are given in section TESTS Two of the five tests from which results have been abstracted were of Whitbread 60 yachts (W60), developed for Round the World races. The other three

94 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France tests were of America s Cup Class yachts of different versions; both IACC and ACC. The W60, IACC and ACC yachts were similar, being single masted sloop rigs with asymmetric gennakers set from spinnaker poles. There were differences: fractional and masthead sails were tested on the W60s and mainsails were developed during the period of the tests with increasing leech roach leading to squared headed sails. Results are presented from both W60 and IACC yachts tested in the Soton tunnel so the effect of these differences on the sail coefficients can be seen. Table 2 Summary of sails tested Tunnel name Yacht class Main Gennaker Area Code Area m 2 m 2 Volvo W G5 195 G-MH-1B 243 MEL IACCv1 197 CC1 423 Soton IACCv2 215 A1 453 Soton W ASY73B 300 FASY 215 Milano ACCv5 212 A DOWNWIND SAILING ANGLES The apparent wind angles for downwind sailing vary depending on the course, the size and performance of the yacht, its boat speed and the true wind speed. For windward/leeward courses, such as the America s Cup races in the IACC and ACC Classes the optimum true wind angles were βtw =150+/-10 degrees, with an associated mean gybe angle of 60 degrees. VPP calculations provide the optimum true wind angle (βtw) and associated apparent wind angles (βaw), however these are obtained from the simple solution of the wind triangle, as illustrated in Figure 1. Figure 1 Wind triangle for downwind sailing It can be seen that the apparent wind angle is dependent on the ratio of boat speed to true wind speed (Vs/Vtw) and varies between 60 and 120 degrees for ratios between 1.15 and The boat speed tends to be higher than true wind speed in light winds and lower in stronger wind speeds because of the non-linear relationship between hydrodynamic resistance and aerodynamic thrust. It is therefore necessary to test downwind sails through a wide range of apparent wind angles, although there may be different sails may be designed for different ranges of angles. Similar apparent wind angles can occur at lower true wind angles associated with reaching, although they tend towards 60 degrees and lower. Downwind sailing is, however, characterized by low heel angles, typically less than 5 degrees for the ACC yachts, whereas reaching performance can cause significant heeling. The maximum driving force is of primary interest for downwind sail testing, with the heeling moment having little effect on sailing performance. This is different to upwind and reaching where depowered sail settings are of importance for sailing in moderate and strong wind conditions. Downwind sailing at an apparent wind angle of 90 degrees is an interesting condition, which for Americas Cup Class yachts sailing arose in a true wind speed of 12 knots - the mid wind range for good sea breezes in Valencia. At this angle all the driving force was derived from aerodynamic lift and all the heeling force from drag so maximum driving force equated to maximum lift. At deeper apparent wind angles the lift force contributed to the righting moment as opposed to contributing to the heeling moment at closer or smaller apparent wind angles. The heeling moment tended to zero at an apparent wind angle of 135 degrees, where the righting moment from the lift force balanced the heeling moment from the drag force or in other terms where the resultant aerodynamic force was aligned with the boat axis. 5. DATA REDUCTION The measured forces can be expressed in various ways and although a yacht s performance depends principally on driving force and heeling moment in the body axis it is better to compare sail aerodynamics in conventional lift and drag coefficients in the wind axis. These are used in VPP calculations and show less variation with apparent wind angle than forces in the body axis. Cd = D Cdi = ACl Di = L ρvaw A 2 πhe ρvaw 2 2 He () 1 ( 2) 2 ()

95 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France The reduction of measured forces to aerodynamic coefficients depends on apparent wind speed (Vaw) or the associated dynamic pressure and sail area (A). Measurement accuracy of these is discussed in separate sections of this paper but the influence of any differences between the tunnels is discussed here. Relative results between sails tested in one tunnel remain unaffected by errors in the wind speed measurement, provided it is taken in a consistent manner. Scaling to the yacht s performance depends on the wind speed measurement for the yacht as well as that in the tunnel, which is also problematic since measurements for the yacht are generally obtained from a masthead anemometer that is particularly affected by masthead downwind sails and by the prevailing wind gradient. Both the lift and drag coefficients would appear to be affected similarly by differences in wind speed but this does not apply to the induced drag due to lift. It can be seen from equation 2 that the induced drag coefficient depends on the square of the lift coefficient and the aspect ratio, which has been expressed as He 2 /A where He is the effective rig height a distance related to the geometric rig height. The effective rig height is a useful parameter to derive because, as shown in equation 3, it is independent of sail area but its correct determination relies on the correct measurement of dynamic pressure. This can cause differences when comparing effective rig heights from tests in different wind tunnels. 6. SAIL AREAS Both the America s Cup Class Rule and the Whitbread 60 Class Rule had sail measurements designed to produce the surface area of the sails. There were differences in the details of the measurements but the differences between the actual and measured surface areas of the sails will have been relatively small, within a few per cent. Details of the measurements are given in the published class rules. The sail coefficients given in this paper are based on the Rule measurements of sail area and not the planform or projected areas that are sometimes used in the definition of lift and drag coefficients of other bodies in different applications. 7. WIND SPEED MEASUREMENTS The four tunnels had different wind circuits that affected the wind speed profiles and their measurements. Sail tests require relatively large working sections and low wind speeds compared to convention aeronautical testing. The working test section in conventional aeronautical wind tunnels is downstream of a larger section of the tunnel with a contraction, which improves the flow uniformity and reduces the turbulence intensity. But there were no contractions immediately upstream of any of the sections used for these tests because of the requirement for a large working section. The model in the Volvo wind tunnel [2] was approximately 25m downstream from the last corner and approximately 10m from the start of the slotted wall test section. The flow uniformity was very good with variations in pitot pressure of +/- 0.2%. The boundary layer thickness was approximately 80mm. The model in the low speed section of the University of Southampton wind tunnel was only approximately 2m from the last corner and its associated smoothing screens. An additional screen was fitted prior to the W60 tests with the aim of improving the flow uniformity. This had a static pressure drop of twice the dynamic pressure, which was suitable for use in wind tunnels. The flow, however, was not as uniform as the in the Volvo tunnel and there were consistent variations of dynamic pressure across the model s location with an rms value of 5%. The flow in the high speed section, which was downstream following a contraction with a 5:1 area ratio, was much more uniform and the reference speed for the tests was taken from this section. The boundary layer was within 150mm from the tunnel floor. The tunnels at the Marchwood Engineering Laboratory and the Politecnico di Milano were designed for wind engineering work so had long sections used to grow a stable boundary layer flow to model that of the atmosphere, albeit at a scales at least an order of magnitude smaller than those of sail test models. The MEL wind tunnel [1] was open circuit with a bell mouth intake that drew air from the outside environment into the enclosed working section. The inlet was fitted with screens to help isolate the flow in the test section from the external wind environment but some sensitivity remained. The air was drawn down the working section by a single 1MegaWatt centrifugal fan and exhausted back outside. The tunnel was reported to have suffered from a slow oscillation in its wind speed, likened to an organ pipe effect, but sail force measurements were averaged over a period of approximately 1 minute such that any oscillations did not affect the results, evidenced by good repeatability. The tunnel floor was covered with toy lego brick blocks to increase its roughness and create a boundary layer, which extended to a height of approximately 500mm. The flow speed remained consistent within the boundary layer and was measured from a pitot tube within the working section. The Politecnico di Milano wind tunnel had a closed circuit, with a bank of fourteen fans driving the air through the final bend into the low speed section. The tunnel floor was smooth and the boundary layer was approximately 300mm thick but there were consistent lateral and vertical variations in flow speed and across the location of the model. These were associated with the flow pattern from the individual fans and amounted to an rms variation in pitot pressure of approximately 5%. The tunnel had a high speed section on the return

96 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France circuit below the low speed section with a contraction ratio of approximately 3:1so, to avoid the problems with the flow variations, the mean flow speed was taken from measurements in this section. Height ratio Z/Z10m Apparent wind gradient and Tunnel boundary layer measurements ACC mast height Baw=90 1/20 power MEL 1:20 scale Milano 1:12.5 scale Soton 1:18 scale Speed ratio U/U10m Figure 2 Wind tunnel gradients at the time of the tests Examples of the flow measurements taken at the time of the wind tunnels test in way of the model are shown in Figure 2 together with the apparent wind gradient for the 1:12.5 scale ACC yacht model tested in the Politecnico di Milano tunnel. Unevenness in the wind profile can be seen in data from this and the Southampton tunnel but it should be noted that the mean test speed was derived from a grid of measurements taken across the test area not just those shown in Figure 2. Reduced wind speeds over the lower part of the model sails were most significant in the MEL tunnel. The wind speeds us for the downwind sail tests were approximately 5 m/s. This was within both the structural strength of the model and the power of the remotely operated sheet winches. It also matched the scale relationship between the wind pressure and sail cloth weight, ensuring reasonable modelling of the flown sail shapes. The test Reynolds numbers were consequentially less than full scale by the order of the model scale, i.e. a factor for at least 12.5 to 20 lower than full scale. This is an unavoidable feature of model testing. 8. WIND GRADIENT AND TWIST The apparent wind speed gradient and twist that is experienced by the yacht when sailing depends on the true wind gradient and the yacht s speed and heading. This involves solution of the wind triangle shown in Figure 1 with height. Tests with a twisted flow device [8] were conducted in the Milano tunnel for the America s Cup using a true wind gradient measured in Valencia for the prevailing sea breezes. The gradient was curve fitted by a power law of between 1/20 and 1/30, which was considerably lower than the conventional 1/7 or 1/10 curves. The associated apparent wind gradients and twist for a 1/20 true gradient are shown in Table 3 for different ratios of boat speed (Vs) to true wind speed (Vtw), which correspond to racing conditions for downwind sailing at a true wind angle of βtw = 150 degrees. Table 3 Calculated values for the apparent wind gradient Vs/ Vtw Vaw/ Vtw Baw Twist Vaw/Vaw10m 10m Boom Mast Boom Mast ratio ratio deg deg deg ratio ratio Considerable twist occurs below boom level, where it has little influence on the sails and its effect on modelling in the wind tunnel is on hull windage. It can be seen that the twist at the boom was only slightly greater than at the masthead. After some adjustments of the vanes in the wind tunnel, similar twist was achieved at the boom and mast of +/- 5 degrees. It can be seen from Table 3 that the actual apparent wind gradient at sea is relatively small at high boat speed ratios, which are associated with light winds. So these conditions are reasonably represented by the uniform wind speeds in the Soton and Volvo tunnels. The wind gradient in the Milano tunnel, shown in Figure 2, was representative of medium wind sailing conditions with apparent wind angles of 75 to 108 degrees. The deep boundary layer in the MEL tunnel was less representative of the downwind sailing conditions, which is not surprising as the tunnel was designed to model the true atmospheric wind gradient for building work not the apparent wind gradient produced by a moving yacht. 9. BLOCKAGE CORRECTIONS The most significant correction for downwind sail measurements made in closed jet test sections is the wake blockage correction. This corrects for the reduced pressure, i.e. higher suction, in the wake resulting from the tunnel wall constraints on the streamlines downstream of the model. The so called Maskell correction was applied to some of the tests using the method given in ESDU data sheet The correction is based on the drag due to separated flow, obtained by subtracting of the induced drag due to the measured lift

97 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France Although the wake blockage is calculated from the measured drag the correction is of the base pressure acting on the sails so is applied to both lift and drag forces. Wake blockage corrections were studied by the automotive industry in the 1980s, when manufacturers were vying to produce low drag coefficients for their cars and the Volvo tunnel was designed with slotted walls in an attempt to overcome the problem. The test section has similarities with an open jet tunnel, where blockage corrections are applied in the opposite sense due to less suction of the wake, but at the time of the tests blockage corrections were not applied to the sail test results from this tunnel. The MEL tunnel was relatively large compared to the Southampton tunnel so at the time an average estimate of the wake blockage correction was applied to all results. The analysis process was refined for subsequent tests such that corrections were calculated for individual test points. The maximum correction factors used for the tests in this paper are shown in Figure 3. Wake blockage correction Variation of blockage with apparent wind for tests in various tunnels Apparent wind angle - degrees blockage could also be retrospectively applied to the Volvo tests. 10.MEASUREMENT METHODS The results given in this paper were obtained using test methods that were evolved by the Wolfson Unit MTIA over a prolonged period and numerous projects. They were derived from the methods used by the Yacht Research Group at the University of Southampton in the 1960s, described by A J Marchaj in his classic book Sailing Theory and Practice, but differ considerably due to improved dynamometry, data acquisition, model sail construction, remote winch operation and test procedures [7]. Different dynamometers were used in the different tunnels but all were calibrated and corrected for interactions with an overall accuracy and repeatability of the order of +/- 1%. The models were isolated from the wind tunnel turntables to avoid problems with tare corrections on roll moments due to wake interactions. The measurements included the forces due to the hull, deck, mast, rigging and sails. The data acquisition system used for these tests displayed in real time the sail forces, measured on body axes. The sail sheeting and spinnaker pole adjustment were made remotely with the wind on, which enabled the sail settings to be optimised and the maximum forces to be sought. Individual test points were obtained by averaging force measurements over a period of time, of the order of 30 seconds, and each point represents the result of several minutes of sail adjustments using the real time display. ACC Milano IACC MEL Linear (ACC M ilano) IACC Soton Poly. (IACC Soton) Figure 3 Wake blockage corrections for different tunnels It can be seen that the wake blockage corrections in the Southampton tunnel were approximately twice those in the Milano tunnel, particularly at the wider apparent wind angles where the lift was lower and the drag due to separation was higher. In retrospect the wake blockage corrections applied to the MEL data are low compared to those applied to the Milano tunnel data. Some wake

98 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France Driving force coefficient Cx Variation of driving with heeling forces IACC in Southampton tunnel Heeling force coefficient Cy A1M3 50 A1M3 70 A1M3 90 A1M3 100 A1M3 120 A1M3 140 IACC fit Figure 4 Driving and heeling force coefficients Procedures for downwind sail testing, where heel angles are small, were developed to obtain the maximum driving force that the rig could produce, since this would cause the yacht to sail at its fastest speed downwind therefore real time VPP techniques are not required during downwind wind tunnel tests. Once the sail coefficients were derived the VPP was used to predict apparent wind angles for different true wind speeds, using the wind triangle shown in Figure 1. Typical results are shown in Figure 4 from measurements were made with a number of different sail settings at different apparent wind angles. The force data was plotted at the time of the tests and although tests were made at discrete apparent wind angles the forces were presumed to vary smoothly with apparent wind angle so low values could be identified and sails readjusted in the search for the maxima. It can be seen that the driving force coefficients are greatest at apparent wind angles between 90 and 120 degrees. The same force data can be transformed from body to wind axes to produce the lift and drag coefficients shown in Figures 8 and 9. In addition the centre of effort height can be obtained from the heeling moment measurements, as shown in Figure 13. Figure 5 Sails set at two apparent wind angles The sails are readjusted at each apparent wind angle and, as can be seen in Figure 5, the use of the spinnaker pole results in similar sail geometry relative to the apparent wind direction with quite different sheeting relative to the yacht. Although the maximum forces are of primary interest for downwind sailing, other useful information on the rig performance can be extracted from the lower force measurements by plotting the variation of drag coefficients with the square of lift, as shown in Figure 12. Linear trends in the data can be seen, particularly at the lower wind angles of 50 to 70 degrees and these are attributable to the variation of induced drag due to lift. The reduced lift conditions are achieved mainly by adjustment of the mainsail sheeting angle, with this sail acting like a flap to the highly cambered asymmetric sail and there is a range of settings where this flap causes relatively small changes to any flow separation so of the variations in drag are associated with invicid flow. The slope of the induced drag line can be used to derive and effective aspect ratio and height or span for the rig that can provide a useful comparison between the tests. 11.DISCUSSION OF RESULTS The curves summarising the maximum lift coefficients from all the tests are shown in Figure 6 and the associated drag coefficient curves in Figure 7. Given there were differences between the tunnels, wind, yacht design, models and sails over the 16 year test period, as discussed previously, it is remarkable that the

99 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France maximum lift coefficient curves are all similar within a 10% band. All the tests showed the maximum lift coefficient to occur at apparent wind angles between 50 to 70 degrees and to be slightly lower at 90 degrees. 1.2 Variation of Cd with apparent wind angle fits from tunnels Lift coefficient Cl Variation of Cl with apparent wind angle fit from all tunnels Apparent wind angle - degrees Drag coefficient Cd Apparent wind angle - degrees IACC Soton ACC Milano W60 Volvo W60 Soton Figure 7 Summary of maximum drag coefficients IACC Soton W60 Volvo ACC Milano W60 Soton Figure 6 Summary of maximum lift coefficients Maximum lift was sought at 90 degrees since this will have produced maximum driving force so there is probably something associated with the sail geometry and sail interaction that enabled higher lift to be achieved at the closer angles and also for the lift to reduce at wider angles. The side shrouds limit the boom sheeting angle to less than 90 degrees to the yacht s centreline, which may have restricted the lift at deeper apparent wind angles. The drag coefficient curves show greater variation than the lift curves of approximately 20% and with the opposite trend of drag increasing with apparent wind angle. The factors influencing these differences are considered further. Comparison of lift and drag from the two different tests in the Soton tunnel on the W60 and IACC models produced similar maximum lift and drag curves with slightly lower values from the W60. Both these tests included reduced lift settings, although conducted at slightly different apparent wind angles, and the variation of drag coefficient with the square of lift is shown in Figures 12 and 20. The effective rig heights from the slope of the induced drag lines were very similar, being 89% of the mast height above the water-line for the IACC rig and 90% for the W60 rig. These are lower than the effective rig heights used for upwind rigs, although these have some form of deck sealing. The intercept of the induced drag line at zero lift can be considered to be the base drag, including viscous drag, windage from the hull and rigging and any drag due to separation that does not vary due to lift. There was an apparent increase in base drag to increase with apparent wind angle, as can be seen from Figure 12 by the difference in the parallel lines from the IACC tests at apparent wind angles of 50 and 70 degrees. This may be caused by increased separated flow off the gennaker at higher apparent wind angles. The drag due to windage of the hull and rig was measured with the sails removed and is shown in Figures 9 and 12 and it can be seen that it is relatively small compared to both the total sail drag and the residual base drag after subtraction of the induced drag

100 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France The W60 fractional and masthead gennakers produced similar lift and drag coefficients but it can be seen from Figure 21 that their centre of effort heights were distinctly different. The centre of effort only varied with apparent wind angle by a few percent but it can be seen by comparing Figures 13 and 21 that the IACC tests produced slightly higher centres of effort. The IACC tests in the MEL tunnel produced only a few maximum lift points compared to the complete IACC tests conducted in the Soton tunnel so the results are shown plotted together in Figures 8,9,12 and 13. It can be seen that the lift was similar except at the apparent wind angle of 110 degrees and the drag approximately 10% lower. It is possible that the wake blockage was underestimated at the apparent wind angle of 110 degrees, as discussed previously, however whilst increasing the correction could improve correlation in lift it would reduce the drag. The centre was higher from the MEL tests, particularly at the problematic apparent wind angle of 110 degrees, and this may be attributed to the boundary layer shown in Figure 2. Data from the W60 tests in the Soton and Volvo tunnels are shown in adjacent Figures 16 to 23 for ease of comparison. Lift and drag coefficients were similar at an apparent wind angle of 90 degrees but were lower from the Volvo tunnel at lower apparent wind angles and higher at higher angles except for a single test point at an angle of 50 degrees. This point has both higher lift and drag than the curve fit though the data set but it can be seen from Figure 22 that the drag is consistent with the increase in induced drag due to lift. It is therefore possible that the sails were not set in the Volvo tests to produce the maximum lift, except at this single point. It can be seen from Figures 20 and 22 that the induced drag from the effective rig height obtained from the Soton tests at an apparent wind angle of 60 degrees also matched the Volvo test results at 40 and 50 degrees, albeit with lower base drag. It is possible that the absence of any blockage correction to the Volvo tunnel data influenced the higher lift and drag data at the apparent wind angle of 90 degrees. Two different sized gennakers were tested in the Volvo tunnel and slightly higher drag coefficients were measured from the smaller G5B. There centre of effort heights were similar, although the G5B was recorded to be a fractional gennaker, but the height tended to decrease with apparent wind angle, not remain constant as from the other tunnel tests. It is possible that there was a roll moment measurement problem. Data from the IACC tests in the Soton tunnel and the ACC tests in the Milano tunnel are shown in adjacent Figures 16 to 23 for ease of comparison. The Milano tests were the most recent and used the largest model in the biggest tunnel and were undertaken with great care as part of a comprehensive 14 week test programme. It can be seen that both the lift and drag were lower from the Milano tests and the centre of effort was slightly higher. It is possible that either the wind gradient or twist reduced the maximum lift coefficient from the Milano tunnel with, as discussed previously, an associated reduction in induced drag. Although different apparent wind angles were used in the Soton and Milano tests it can be seen from inspection of lift and drag data in Figures 12 and 14 that the Milano data matched the Soton data at comparable values of lift. The Milano tests were focused on achieving the maximum sail force in order to compare different gennaker shapes, so there were not many reduced lift points to use to compare induced drag and effective rig heights with those from the Soton tests. It is, however, notable from Figure 14 the concentration of lift and drag coefficients from tests over a wide range of apparent wind angles compared to the spread of driving and heeling forces shown in Figure 4. There is a similar concentration of data from the W60 Volvo tests shown in Figure 22, particularly at reduced values of lift. The effect of the apparent wind angle on the aerodynamic coefficients is secondary to its effect on the transformation of the aerodynamic force vector from wind axes to body axes. Finally, it is possible that higher lift coefficients were obtained from the Soton tunnel because of the fine scale turbulence induced into the flow by the smoothing screens immediately upstream of the model, which was a unique feature of this tunnel. It is also possible that full scale maximum lift coefficients could be higher than those measured in any of the wind tunnels but they should not be lower. 12.CONCLUSIONS Consistency has been found in the maximum lift coefficient obtained from the different wind tunnel tests on downwind sails within a band of 10% across the range of apparent wind angles associated with downwind sailing. Induced drag is associated with the lift produced by the downwind sails with an associated effective rig height of approximately 90% of the mast height above the waterline, which is lower than associated with upwind sails. This induced drag accounts for some of the 20% variation in the maximum drag coefficients obtained from the different wind tunnel tests. There were similar trends in the variation of lift and drag with apparent wind angle from each of the wind tunnels, indicating the validity of these trends. These trends showed a reduction in the maximum lift coefficient with apparent wind angle and an increase in the drag coefficient, with part of this increase associated with the base drag

101 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France There were variations in the centre of effort height that could be attributed to the different wind gradients in the tunnels. Lower maximum lift coefficients were obtained from the Milano tunnel, which may be attributed to the wind gradient and twist simulated in this tunnel or it is possible that fine scale turbulence in the Soton tunnel allowed higher maximum lift to be achieved. The applied wake blockage corrections appear to have aided the correlation of sail coefficients obtained from different wind tunnels. The effects of apparent wind angle on aerodynamic coefficients, defined in the wind axes, are smaller than those on the driving and heeling force coefficients, defined on the body axes. The general similarity in the sail coefficients obtained from the different tests in different wind tunnels helps validate the technique of wind tunnel testing of sailing yacht rigs. 13.WIND TUNNEL RESULTS The following figures contain results from each of the five different tests of lift and drag coefficients and centre of effort height

102 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France Variation of Cl with apparent wind angle IACC in Southampton tunnels Variation of Cl with apparent wind angle ACC in Milano tunnel Lift coefficient Cl Lift coefficient Cl Apparent wind angle - degrees MEL 70 MEL 90 MEL 110 Apparent wind angle - degrees A1M3 50 A1M3 70 A1M3 90 A1M3 100 A1M3 120 A1M3 140 IACC fit A2 60 A2 75 A2 90 A2 105 A2 120 ACC fit Figure 8 Figure Variation of Cd with apparent wind angle IACC in Southampton tunnels Variation of Cd with apparent wind angle ACC in Milano tunnel Drag coefficient Cd Drag coefficient Cd Apparent wind angle - degrees MEL 70 MEL 90 MEL Apparent wind angle - degrees A1M3 50 A1M3 70 A1M3 90 A1M3 100 A1M3 120 A1M3 140 IACC windage IACC fit A2 60 A2 75 A2 90 A2 105 A2 120 ACC fit Figure 9 Figure

103 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France Variation of drag with square of lift IACC in Southampton tunnels Variation of drag with square of lift ACC in Milano tunnel Drag coefficient Cd Drag coefficient Cd lift coefficient squared Cl 2 MEL 70 MEL 90 MEL 110 A1M3 50 A1M3 70 A1M3 90 A1M3 100 A1M3 120 A1M3 140 Windage IACC Cdi Cdi IACC fit Figure Lift coefficient squared Cl 2 A2 60 A2 75 A2 90 A2 105 A2 120 ACC fit Figure 14 Centre of effort height above DWL % Variation of Ceh with apparent wind angle IACC in Southampton tunnels Apparent wind angle - degrees Centre of effort above DWL - % Variation of Ceh with apparent wind angle ACC in Milano tunnel Apparent wind angle - degrees MEL 70 MEL 90 MEL 110 A1M3 50 A1M3 70 A1M3 90 A1M3 100 A1M3 120 A1M3 140 Figure 13 Figure 15 A2 60 A2 75 A2 90 A2 105 A

104 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France Lift coefficient Cl Variation of Cl with apparent wind W60 in Southampton tunnel Apparent wind angle - degrees Lift coefficient Cl Variation of Cl with apparent wind W60 in Volvo tunnel Apparent wind angle - degrees FASY 60 FASY 80 FASY 100 ASY73B 60 ASY73B 85 ASY73B 110 ASY73B 135 Soton W60 fit Figure 16 G-MH-1B 40 G-MH-1B 50 G-MH-1B 70 G-MH-1B 90 G-MH-1B 110 G5B 40 G5B 50 G5B 60 G5B 70 G5B 80 G5B 90 Volvo fit Figure Variation of Cd with apparent wind W60 in Southampton tunnel 1.2 Variation of Cd with apparent wind W60 in Volvo tunnel Drag coefficient Cd Drag coefficient Cd Apparent wind angle - degrees Apparent wind angle - degrees FASY 60 FASY 80 FASY 100 ASY73B 60 ASY73B 85 ASY73B 110 ASY73B 135 Soton W60 fit G-MH-1B 40 G-MH-1B 50 G-MH-1B 70 G-MH-1B 90 G-MH-1B 110 G5B 40 G5B 50 G5B 60 G5B 70 G5B 80 G5B 90 Volvo fit Figure 17 Figure

105 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France 1.2 Variation of drag with square of lift W60 in Southampton tunnel 1.2 Variation of drag with square of lift W60 in Volvo tunnel Drag coefficient Cd Drag coefficient Cd Square of lift coefficient Cl 2 Square of lift coefficient Cl 2 G-MH-1B 40 G-MH-1B 50 G-MH-1B 70 FASY 60 FASY 80 FASY 100 G-MH-1B 90 G-MH-1B 110 G5B 40 ASY73B 60 ASY73B 85 ASY73B 110 G5B 50 G5B 60 G5B 70 ASY73B 135 Soton W60 fit G5B 80 G5B 90 Volvo fit Figure 20 Figure 22 Centre of effort to DWL % Variation of centre of effort with apparent wind, W60 in Southampton tunnel Apparent wind angle - degrees FASY 60 FASY 80 FASY 100 ASY73B 60 ASY73B 85 ASY73B 110 ASY73B 135 Figure 21 Centre of effort to DWL - % Figure 23 Variation of Ceh with apparent wind W60 in Volvo tunnel Apparent wind angle - degrees G-MH-1B 40 G-MH-1B 50 G-MH-1B 70 G-MH-1B 90 G-MH-1B 110 G5B 40 G5B 50 G5B 60 G5B 70 G5B 80 G5B

106 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France 14.ACKNOWLEDGEMENTS It has only been possible to publish the previously confidential results due to the kind permission of Sir Michael Fay, Mr Bruce Farr, Mr Laurie Smith, Dr Peter Van Oossanen and Sig Patrizio Bertelli. The work was originally performed for the organisations they represented and were instrumental in creating, all with the common aim of winning prestigious yacht races. The original tests were conducted with the assistance from colleagues at the Wolfson Unit MTIA and the University of Southampton together with that of the staff from the organisations operating the different wind tunnels. 16.AUTHOR S BIOGRAPHY Ian Campbell is an Emeritus Fellow at the University of Southampton, having previously worked at the Wolfson Unit MTIA for 38 years. He has conducted numerous experiments and trials for the development of sailing yachts and power craft and was Senior Scientist for the Luna Rossa challenge for the America s Cup in The Wolfson Unit was awarded, as a group, the RINA Small Craft medal in 2013 in recognition of its services over many years to the small craft industry. Ian continues to cruise in his own yacht and race his dinghy. Thanks are also extended to the sailmakers associated with each project for designing and manufacturing the model sails. 15.REFERENCES 1. A. G. ROBINS, Plume dispersion from ground level sources in simulated atmospheric boundary layers, Atmospheric Environment Vol. 12, pp Pergamon Press Ltd L-U NILSSON AND A BERNDTSSON, The new Volvo multipurpose automotive wind tunnel, SAE International Congress and Exposition, Detroit Michigan, Feb TAHARA T, MASUYAMA Y, FUKASAWA AND KATORI M, CFD calculation of downwind sail performance using flying shape measured by wind tunnel test, HPYD4 Auckland IGNAZIO MARIA VIOLA, RICHARD G.J. FLAY, Sail pressures from full-scale, wind-tunnel and numerical investigations Ocean Engineering 38 (2011) WRIGHT, S., CLAUGHTON, A., PATON, J. AND LEWIS, R., Off-Wind Sail Performance Prediction and Optimisation, 2nd International Conference on Innovation in High Performance Sailing Yachts (INNOV SAIL), Lorient, France, June-July, TEETERS, J., RANZENBACH, R. AND PRINCE, M., Changes to Sail Aerodynamics in the IMS Rule, The 16th Chesapeake Sailing Yacht Symposium, March, CAMPBELL I.M.C., The Performance of Offwind Sails Obtained from Wind Tunnel Tests, R.I.N.A. International Conference on the Modern Yacht, March, ZASSO A., FOSSATI F., VIOLA I.M., Twisted Flow Wind Tunnel Design for Testing Yacht Sails, 4th European and African Conference on Wind Engineering (EACWE4), July 2005, Prague, Czech Republic

107 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France SMART MATERIALS APPLICATION ON HIGH PERFORMANCE SAILING YACHTS FOR ENERGY HARVESTING S. Turkmen, D. Mylonas and M. Khorasanchi, University of Strathclyde, Glasgow, UK Piezoelectric patches are bounded on a keel bulb in order to harvest vibration energy by converting electrical output. Unsteady computational fluid dynamics method is also used to find the structural boundary condition such as the hydrodynamic pressure fluctuation. Finite element analysis (FEM) is used to find structural and electrical responses. NOMENCLATURE T Transpose of a matrix (Italic) Sym Definition [ Unit] δ Variation operator The permittivity (IEEE std) F/m C/(m V) Permittivity of vacuum (8.854E- 12) Voltage, electrical potential V/m Frequency rad/s Surface, area m 2 The mass density kg/m 3 Surface charge density C/m 2 E Electric field V/m F P Point force N F V Body force N F Surface force N c Mechanical stiffness (IEEE std) N/m 2 [C] Structural damping matrix d Piezoelectric strain constants C/N D Electric displacement field C/m 2 H Total potential energy or electric enthalpy Joules K Kinetic energy Joules [M] Mass matrix kg P Power Watts Q Total electrical charge V/m 2 S Strain (IEEE std) m/m t 1,t 2 Time s Stress (IEEE std) N/m 2 {u} Displacement field vector m { } Velocity field vector m/s W Total virtual work Joules Z Impedance ohm Superscripts T Values taken at constant stress (T=0) s Values taken at constant strain (S = 0) E Values taken at constant electric field (E=0) or i,j Subscripts Strain or stress applied in the j-axis and the normal direction of the electrode is i-axis. 1. INTRODUCTION Piezoelectric (and pyroelectric) materials are types of smart material made from ferroelectric crystals. Curie brothers discovered the piezoelectric effect in Knowing that the electrification is generated by mechanical pressure, they investigated in what direction pressure should be applied and from which crystal classes the effect is to be expected. One of the early applications was made by Paul Langevin to detect submarines. He used quart-steel sandwich transducers, which are called the Langevin-type transducer in ultrasonic engineering [1]. Piezoelectricity is an electromechanical phenomenon that couples the elastic (dynamic coupling) and electric (static coupling) fields. In operation, this phenomenon can be observed when a piezoelectric material is adopted in a noise-vibration system or a mechanical force/pressure, cyclic electric field is excited. This is called the direct piezoelectric effect. Conversely, if an electric charge or field is applied to the material then it is called converse piezoelectric effect [2]. This dual action of the material has become a tool for vibration control and energy sources for many applications, for instance sensors and actuators, frequency filters, or high-frequency ultrasonic transducers. If this electric energy is consumed via a suitable resistor as Joule heat, mechanical noise vibration is significantly suppressed; that is, it acts as a passive damper. Power generation ability has been studied in the past years [3, 4]. Operating wireless electronic devices without a wired power source has become an issue so researchers mainly focus on output power, piezoelectric properties, complexity of the system and cost efficiency [5-8]. Studies show that smart materials or intelligent system concepts modify the structural properties without additional materials or mechanisms [9]. Lead Zirconate

108 Titane (PZT) is one of the piezoelectric materials that are used in both actuators and sensors. It is bonded to the surface of the base structure as a thin film or laminated [10, 11] Applications of smart materials in sailing yachts are limited. Murayama et al. [12] and Shimada et al. [13] studied the structural health monitoring and damage detection of IACC yacht hull and keel through fiberoptic strain sensors. Shenoi et al. [14] give a review and status of smart materials use in the marine environment, and their potential for application in various fields. In this study, the piezoelectric material PZT-5H is used to harvest the energy of the flow-induced vibration in a yacht keel. Two numerical approaches are used: computational fluid dynamics (CFD) to calculate the input excitation forces, and finite element analysis (FEM) to find structural and electrical responses. FFT analysis is done to find vortex shedding frequency (as a dominant frequency) over the keel. Estimate of output power is calculated when the piezoelectric plate is excited by a time-harmonic surface normal stress. Piezoelectricity may be explained as a linear interaction between electrical and mechanical systems. One of the differences in piezoelectric materials, which make them smart materials, is that material properties are not constant. Their values change with external mechanical loads (stress), electric field strength and temperature. Linear interaction between mechanical and electrical systems is presented in Figure 1. It is assumed the ambient temperature does not vary significantly so thermal properties are ignored in this study. The diagram helps to understand how mechanical and electrical properties are mediated by the different material constants [1, 15]. This shows the constitutive relationships and coupling coefficients in a linearly coupled system. Electromechanical coupling between the elastic and the electric fields is demonstrated. In this figure, the rectangles indicate the intensive variables such as forces and the circles show the extensive variables such as displacements. Thus, the piezoelectric material characteristics are the elastic, dielectric, and piezoelectric tensor components [15]. 2. INTERACTION BETWEEN ELECTRICAL AND MECHANICAL SYSTEMS Figure 1 Piezoelectric effect In Figure 1, mechanical quantities are {σ} is the stress; {S} is the strain; [c] is the elastic stiffness matrix (forth-order tensor of elasticity coefficients); and electrical quantities are {E} is the electric field; {D} is the electric flux density vector; e is the piezoelectric tensor; [ε] is the dielectric matrix at constant mechanical strain, d is the piezoelectric strain constant matrix. The piezoelectric strain constants d ij describe how much of the electric charge flows through short circuit when the force generating strain is applied to the piezoelectric material. In the other words, it is the ratio of charge density to applied mechanical strain: 1

109 Where, k ij is the electromechanical coupling factor. It is a material constant which shows effectiveness of energy conversion between mechanical and electrical energy. There are three different factors depend on the actuation mode: 1. Thickness mode k In-plane mode k 31 =k Shear mode k 15 =k 24 Then dielectric matrix can be given by substituting those electromechanical coupling factors which are: Where, is the stress tensor; S is strain tensor; E is the electrical field vector and D is the electric displacement or induction vector. The total virtual work W done by the external mechanical and electrical forces on the domain boundary is: Where T i is the surface traction (=σ ij n i ); is the surface electrical charge (=D i n i ) on the domain boundary and Φ is the electrical potential. The linear piezoelectric enthalpy function is written as [2]: GOVERNING EQUATIONS AND FINITE ELEMENT FORMULATION Very often the solutions to these mathematical problems are complicated. The behaviours of the system cannot be seen explicitly and directly from the solutions; and numerical calculations have to be made for further examination of the system. Hamilton s principle is used for theoretical derivations of the piezoelectric material governing equations of motion [2]. Here, K is the kinetic energy and H is the total potential energy. Kinetic energy and electric enthalpy function are called Lagrangian work L. W is the virtual work; δ denotes the variation; t 2 and t 1 are starting and finishing time, respectively. The total kinetic energy K for volume V of the piezoelectric material is [16]: 6 Where, is the velocity field vector and is the mass density. The potential energy H includes mechanical strain and electrical potential energies. It is also called the electric enthalpy: 5 Here, [c] is the elasticity coefficients matrix measured at a constant electric field; [e] is the piezoelectric constant matrix; [ε] is the dielectric constant matrix measured at a constant strain. It is assumed that isothermal process, thermo-mechanical coupling and pyroelectric effects are negligible. The piezoelectric constitutive equations for the stress and the electric displacement D are derived from the enthalpy function. These equations were standardized in 1988 by IEEE association [17]. The linear piezoelectric relation of a piezoelectric continuum at a constant temperature and independent variable S and E is given as: The stress tensor has two effects, mechanical and electrical. The first equation above denotes the converse piezoelectric effect and the second is the direct piezoelectric effect. In the linear piezoelectric constitutive equations, electrical field vector E is related to the electric potential field Φ given as: 12 The strain tensor S kl is given as: 13

110 An alternate formulation of the linear piezoelectric constitutive equations can be obtained when different independent variables, i.e. σ and E, are chosen such as: The virtual work W done by external mechanical and electrical loads is then given as [2]: Where,, and are the body, surface and the point load vectors, respectively. is the electrical potential; is the surface charge density; Q is the total charge on the surfaces. is the external mechanical loading surface, and is the external electrical loading surface. By taking the constitutive equations into account and substituting the other parameters, Hamilton s principle yields the governing equations of motion in variational form [18]: The mechanical displacement and electric potential field are unknown functions. Hence, Finite element method is used to calculate these variables. To define finite element formulation the displacement is related to corresponding node values by the mean of the shape function. Similarly, the strain field and the electrical field are related to nodal displacements and potential by shape functions derivatives. The elementary matrix form of governing equations can be obtained by substituting the nodal values into the above equations Here, [M] is the mass matrix; [C u ] is the mechanical damping matrix; [K u ] is the mechanical stiffness ;{u} is the displacement vector; {F} is the external force vector. [K Z ] is the piezoelectric coupling matrix which contains piezoelectric constants in either [d] form (strain/electric field) or [e] form (stress/electric field); [K V ] is the dielectric permittivity matrix; V is the electric voltage vector; and {Q} is the externally applied charge vector. 3. BOUNDARY CONDITION DEFINITION An America s Cup Keel developed by Werner et al under the version 5 of the IACC rules is used for the numerical study [12, 19]. Mylonas and Sayer presented the forces acting on the keel model [20]. A good accuracy has been found between CFD results and the experimental results. Different keel bulb configurations were used such as with winglets in different location on the bulb and no winglet in their study. In this study, no winglet configuration was chosen. Pressure fluctuations on the surface are due to the vortices being shed from the body. They may excite the structure to vibrate and generate acoustic sound [21]. The frequency of excitation force is equal to the vortex shedding frequency, which depends on the shape and size of the body, the velocity of the flow, the surface roughness and the turbulence of the flow. The relation between vortex shedding frequency (f s ) and flow speed (U) is identified by the Strouhal number (St). where c is a characteristic length. The commercial CFD package STAR-CCM+ was used to calculate the pressure distribution on the structure. A spectral analysis was performed on the results to find the vortex-shedding frequency. The frequency of pressure fluctuations was found in the range of Hz. The corresponding Strouhal Number is in the range of (Figure 2). This result is reasonable when compared with open literature [22, 23]

111 Figure 2 Sound Pressure Level derived from lifting force vs. Strouhal Number Figure 3 Sound Pressure Level derived from lifting force vs. Frequency 4. ENERGY HARVESTING FROM FLOW- INDUCED VIBRATION OF KEEL The piezoelectric materials (PZT-5H plate element) are bounded on the port side and starboard side surfaces of the fin (Figure 4). The thickness h is 1 mm; the top and the bottom surface dimensions are 80x80mm. It is considered the PZT, poled in thickness direction (z or x 33 axis), is excited by harmonic pressure (p). The finite element model is shown in Figure 4.The thickness of the fin is very thin compared with the base structure. Top and bottom surfaces are electrodes and are connected by a simple electrical circuit. Although pressure that on the surface is imposing in thickness direction of surfaces total force is bending the structure. The piezoelectric material data should be set up by respect to actuation mode. The elastic compliance matrix s; the piezoelectric constant d; and the permittivity matrix ε are given for the PZT poled in the Z (or x 33 ) direction [24]:

112 ; 4.2 MODAL ANALYSIS Maximum benefit of the piezoelectric material can be obtained by installation at correct location with maximum strain. Therefore, the deformation due to pressure fluctuations of the surface is investigated before piezoelectric patch is added. It is expected to achieve higher output voltage at the natural frequency of the structure. A modal analysis was carried out to estimate the natural frequencies of the structure without and with piezoelectric patch. Short circuit electrical boundary conditions are added for PZT bounded structure. In other words, top and bottom surfaces of piezoelectric materials are grounded (V=0 Volt). The results are given in Table 1. Here; s 66 =2 (s 11 -s 12 ); and the superscript T is matrix transpose. is permittivity of free space. is the mass density. Figure 5 Finite element model of keel bulb bounded by the piezoelectric patch Figure 4 Physical model of the keel bulb bounded by the piezoelectric patches 4.1 STATIC ANALYSIS At the beginning, a static analysis is performed to determine the static capacitance C o. This value will be used to determinate the static impedance. Boundary conditions are determined as the top electrodes of the piezoelectric patch are applied 1V and bottom electrodes are grounded (V=0 volt). As motion is time-harmonic, output power depends on the real part of impedance. The value is used to calculate impedance Z: 20 Here, is the rotational frequency (1/sec). The major surfaces of the piezoelectric patch are electroded and a circuit with impedance Z (at timeharmonic motion) connects the electrodes. Table 1 Comparison between the natural frequencies for the keel Bulb vs. the keel Bulb bounded piezoelectric material Mode No Frequency (Hz) Frequency with PZT (Hz) The mode shape gives preliminary idea about the location that piezoelectric material should be laminated on the structure. The result in Table 1 shows the natural frequency can be shifted when electrical load on the piezoelectric structure is controlled.

113 Figure 6 Mode Shapes of the keel bulb 4.3 HARMONIC ANALYSIS A harmonic analysis was performed to find the charge on the electrodes of piezoelectric patch at a frequency around the range of vortex shedding frequency. The structure is excited by the flow and the response is in the form of electrical output. It is expected to find higher output at the natural frequency of the structure. As motion is time-harmonic, output power depends on the real part of impedance. The average output electrical power per unit plate area over a period is [25]: 21 The result of output voltage is given in Figure 7. Although dominant frequency due to the vortex shedding is around 35 Hz, it is clear that the material develop higher voltage at structure s natural frequencies. Mechanical input power (P 1 ) can be calculated by using velocity 3 which is in the z (x 33 ) axis and at the surfaces: 22 The asterisk represents a complex conjugate. The efficiency of the piezoelectric harvester is the ratio of output power and input power. 23 The efficiency of the system at different frequency is shown in Figure 8. The efficiency is proportional to excitation frequency. An abnormal behaviour is observed in the plot. It might be due to static definition of impedance in a dynamic problem.

114 Figure 7 Output voltage versus frequency Figure 8 Efficiency of generating power 5. CONCLUSIONS The present study proposed a new concept into the sailing and marine industry to save energy by harvesting unused (waste) vibration energy due to the flow around the structure. It can be also called a technology transfer as this concept has been successfully applied for aerospace structures. A piezoelectric patch was installed on the keel of a yacht. A CFD analysis was carried out to find the excitation force and the predominant frequency. Next, a finite element study was performed to investigate the response of the structure and the generated electricity by piezoelectric patch. It was observed that the output power is dependent on real part of impedance which is resistance of piezoelectric material. It is expected that piezoelectric system is more efficient at higher frequencies. Piezoelectric effect occurs under stress and the direction of the stress. Flow pressure generates load in the thickness direction, however total pressure deforms the structure. The type of forces on the piezoelectric patch is important for correct selection of piezoelectric material. If the dominant forces are imposed in the thickness direction then piezoelectric patch operates with thickness-stretch mode and the corresponding piezoelectric constant d ij is the important property. Flow causes bending motions on the structure so piezoelectric material operates with thickness-shear modes. In this case the parameter d 31 plays the significant role and must be considered. It is also interesting to investigate this concept study applied to a mast and rigging structure (due to the bluff body nature of the mast), and even on sails in certain sailing conditions as it is expected the influence of the flow-induced vortex vibration to be more significant.

115 Future work will follow and will consist of experimentally investigating the piezoelectric effect of PZT bonded on a fin (Figure 9) or flat plate in a towing tank, with measurements of vibration, damping and electrical output, seconded by further numerical validation at full scale. A closed electric circuit will be attached to piezoelectric patch (called piezoelectric shunt damping system) in order to reduce vibration. Figure 9 A piezoelectric patch on a test fin 6. ACKNOWLEDGEMENTS The authors would like to thank Prof. O. Turan for bringing the idea and opportunity to study this topic, and Prof. S. Day for giving access to test facilities and equipment. The authors also acknowledge the experience and discussion shared with Mr. P. Zoet, CEO of PZDynamics. Finally, the authors are grateful to the faculty of engineering of Strathclyde University for providing access to HPC facilities. 7. REFERENCES 1. IKEDA, T., Fundamentals of piezoelectricity. Oxford ; New York : Oxford University Press, TZOU, H.S., Piezoelectric shells- Distributed sensing and control of continua. Dordrecht, Netherlands: Kluwer Academic Publishers (Solid Mechanics and Its Applications) 19, JIASHI, Y., HONGGANG, Z., and YUAMTAI, H., Performance of a Piezoelectric Harvester in Thickness--stretch Mode of a Plate. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 52(10): p , KONG, N., et al., Resistive impedance matching circuit for piezoelectric energy harvesting. Journal of Intelligent Material Systems and Structures, 21(13): p , BADEL, A., et al., Single crystals and nonlinear process for outstanding vibrationpowered electrical generators. IEEE transactions on ultrasonics, ferroelectrics, and frequency control, 53(4): p , JI, H., et al., Semi-active vibration control of a composite beam by adaptive synchronized switching on voltage sources based on LMS algorithm. Journal of Intelligent Material Systems and Structures, 20(8): p , RAKBAMRUNG, P., et al., Performance comparison of PZT and PMN PT piezoceramics for vibration energy harvesting using standard or nonlinear approach. Sensors and Actuators A: Physical, 163(2): p , BADEL, A., et al., Piezoelectric vibration control by synchronized switching on adaptive voltage sources: Towards wideband semiactive damping. The Journal of the Acoustical Society of America, 119: p. 2815, SCHMIT, L.A. and FARSHI, B., Optimum laminate design for strength and stiffness. International Journal for Numerical Methods in Engineering, 7(4): p , HWANG, W.-S. and PARK, H.C., Finite element modeling of piezoelectric sensors and actuators. AIAA journal, 31(5): p , KUMAR, N. and SINGH, S.P., Vibration control of curved panel using smart damping. Mechanical Systems and Signal Processing, 30: p , WERNER, S., Computational hydrodynamics applied to an America's Cup class keel-best practice and validation of methods. Chalmers University of Technology, SHIMADA, A., et al., Damage Detection for International America's Cup Class Yachts Using a Fiber Optic Distributed Strain Sensor. IEICE transactions on electronics, 86(2): p , SHENOI, A., WADDAMS, A., and SINHA, A., Smart Materials in the Marine Environment a State of the Art Review, A.W. Ajit Shenoi, Ashutosh Sinha, Editor, Materials Knowledge Transfer Network (KTN), HEYWANG, W., LUBITZ, K., and WERSING, W., Piezoelectricity: Evolution and Future of a Technology. Vol. 114, Springer Verlag, TZOU, H. and TSENG, C., Distributed vibration control and identification of coupled elastic/piezoelectric systems: finite element formulation and applications. Mechanical Systems and Signal Processing, 5(3): p , MEITZLER, A., et al., IEEE standard on piezoelectricity. IEEE, New York, PIEFORT, V., Finite element modelling of piezoelectric active structures, Université Libre de Bruxelles, WERNER, S., et al., Computational fluid dynamics validation for a fin/bulb/winglet keel

116 configuration. Journal of Ship Research, 51(4): p , MYLONAS, D. and SAYER, P., The hydrodynamic flow around a yacht keel based on LES and DES. Ocean Engineering, 46(0): p , BLEVINS, R.D., Flow-induced vibration. Van Nostrand Reinhold Co., Inc, New York, KRYLOV, V.V. and PORTEOUS, E., Wavelike aquatic propulsion of mono-hull marine vessels. Ocean Engineering, 37(4): p , TAYLOR, G.K., NUDDS, R.L., and THOMAS, A.L.R., Flying and swimming animals cruise at a Strouhal number tuned for high power efficiency. Nature, 425(6959): p , XIE, J., et al., A piezoelectric energy harvester based on flow-induced flexural vibration of a circular cylinder. Journal of Intelligent Material Systems and Structures, 23(2): p , YANG, J., Analysis of piezoelectric devices. World Scientific, AUTHORS BIOGRAPHY S. Turkmen is a PhD student in the Department of Naval Architecture and Marine Engineering, University of Strathclyde, Glasgow. He has been researching on the topic of smart material application to mitigate noise and vibration in ships. He is also investigating underwater-radiated noise due to the cavitating propellers. D. Mylonas has recently completed his PhD in the Department of Naval Architecture and Marine Engineering, University of Strathclyde, Glasgow. His research topic focused on the application of LES and DES in yacht hydrodynamics. He also holds an M.Eng from the same department. Other interests include ship & marine hydrodynamics, smart materials, yacht design and CFD simulations on marine and aerodynamic applications. M. Khorasanchi is a research fellow in the Department of Naval Architecture and Marine Engineering, University of Strathclyde, Glasgow. Dr Khorasanchi has carried out several studies on vortex-inducedvibration (VIV) of marine risers and VIV suppression devices. His current teaching and research interests centre on hydrodynamics and marine propulsion. He investigates the hydrodynamic performance of marine vessels through full-scale CFD simulation. He also works on retrofitting technologies to improve the performance of marine vessels and reduce the fuel consumption and carbon emission of shipping industry.

117 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France LONG TERM IMMERSION IN NATURAL SEAWATER OF FLAX/BIOCOMPOSITE A. Le Duigou, A. Bourmaud and C. Baley LIMATB- University of South Brittany, Lorient-France, P. Davies IFREMER- Material & Structure group, Plouzané-France, The present article gives information on 2 years seawater aging effect on injected flax/pla biocomposite. Biocomposite suffer from relatively high moisture absorption which is controlled by vegetal fibre. Simple rule of mixture allows for flax fibre the determination of a weight gain at saturation around 12% which is close to already published values. Bundles of fibres and especially middle lamellae influence water uptake. Water alters biocomposites, and flax fibres since their mechanical properties are reduced (Young modulus and tensile strength) with aging. Linear relationship is observed between water uptake and loss of mechanical properties. Load-unload cycles highlight damage occuring earlier as biocomposite undergo aging. These damages can be induced by fibre degradation and washing out of soluble components especially the fibre bundles cement, by debonding of fibre bundles linked to their swelling. LIST OF SYMBOLS : ΔW : Water uptake at saturation D : Fickian diffusion coefficient Dc : Fickian corrected diffusion coefficient E fl : Longitudinal fibre Young modulus E ft : Transverse fibre Young modulus E F : Longitudinal composite Young modulus E T: Transverse composite Young modulus 1 INTRODUCTION Plant fibre reinforced composite materials are increasingly being studied last years. Indeed environmental concerns dealing with composite materials are clearly identified and appears at each step of their life cycle. Development of marine industry and yachting have accompanied with wide spread of composite material such as Glass/polyester and nowadays Glass/Polypropylene composites. Biocomposites (plant fibre embedded in biopolymer matrix) possess large number of advantages to substitute convention composites materials. First, they come from renewable ressources, have high specific mechanical properties [1-5] to be used for marine application (pulleys ). Then they make possible waste management by recycling [6] or composting [7]. Overall, biocomposites (natural fibre embedded in biopolymer matrix) such as Flax/Polylactide use induces environmental footprint reduction compared to Glass/Polyester [8]. However Le Duigou et al. [9] have highlighted that lifetime span of Flax/PLA biocomposites has an influence on environmental impact. The more the lifetime is close to usetime, the more the impact is reduced. Therefore increasing use of biocomposite for outdoor applications depends in how the degradation mechanism is understood and handled. Marine environment is known to be aggressive as UV rays degradation is coupled with humidity, temperature and biological degradation [10]. Basically two kind of degradation appears during immersion in aqueous media : Physical degradation with plasticizing effect and swelling and chemical degradation induced by matrix hydrolysis and fibre degradation [10, 11]. These mechanism for natural fibre composites are deeply reviewed in work of Azwa et al. [12]. It is now established that vegetal fibres have affinity with water molecules due to their chemical composition (hemicellulose) and their porous structure [13]. In addition to conventional diffusion mechanism through the matrix, water can diffuse along the fibre/matrix interface thanks to capillary mechanism and through the fibre [14, 15]. Water will be able to establish intermolecular interactions (hydrogen) with fibre surface reducing practical adhesion between fibre and matrix [15]. Water sorption generally may provoke swelling of fibre especially when free volume is available [16]. Many authors claim that differential swelling between fibre and matrix generate high level of swelling stress involving cracking and delaminating [12, 17]. However no information is available in the literature for flax or hemp swelling under constraint which require care for interpretation. Then, some components located on fibre surface are washed out of the sample which lead to interfacial debonding and interfacial area altering [15, 17, 18]. Some authors [19] claim that enzymatic degradation occur for long term immersion even if no specific study have carried out. All these phenomena induce a loss of the mechanical properties and by consequence a reduction of the lifetime span of vegetal fibre reinforced composites. L ife expectancy is most of time evaluated by accelerated aging tests as performed on Hemp/PLA [20], on Flax/epoxy [21] and flax/pla [22]. Although these experiments permit time saving, comparison with natural aging is necessary

118 The present article proposes to study the effect 2 years natural seawater aging on Flax/PLA biocomposites. Weight gain measurements are performed associated with static mechanical characterization and SEM observation. Inverse estimation of fibre properties will be possible by using micromechanical modeling. Then, cyclic tensile tests are conducted in order to identify damage parameter d and its growing kinetic due to aging [23]. Mechanical characterization will be done on wet and dried samples to separate reversible from irreversible damage. 2 MATERIALS AND METHODS 2.1 Materials Flax fibres, harvested in France have been dew retted before being scutched. No chemical treatment has been added. Poly(L-lactide) (PLLA) supplied by Biomer is used as matrix. Initial molecular weight is g/mol. Mechanical, thermal properties and ageing behaviour have been studied previously [24]. 2.2 Biocomposite manufacturing Flax fibres have been cut (2 mm) before being blended with polymer during extrusion step. Fibre weight content is around 20% which corresponds to 16% by volume. PLLA pellets were dried under vacuum at 60 C for 48 h prior to extrusion. They were then extruded with flax fibres 20% in weight. Compounding was achieved in a single screw extruder at 20 rpm and with the following temperature profile: 175/180/185 and 185 C in the nozzle. Compounded pellets were also dried under vacuum at 60 C for 48 h. Injection moulding was then carried out on a Battenfeld 210/80 machine. Temperature profile was kept as follows: 165/170/175/180 and 180 C in the nozzle. Materials were injected in a mould designed to produce normalized specimens. The mould temperature was maintained at 50 C. 2.3 Aging conditions Samples are 5 m depth immersed in natural seawater during 2 years in Kernevel harbor (Lorient-France) where water temperature typically varies from 8 to 19 C. Samples are periodically removed to be weighted and characterized. Weight gain is determined as a percentage of initial weight using equation 1 : Wt - W0 Δ W = x100 (1) W0 The Fickian diffusion coefficient D is determined from Eq. (2) in the range where the values of W(%) are less than 60% of the equilibrium value W(): where is the slope of the linear part of the plot of weight gain versus square root of immersion time divided by sample thickness. However, a correction factor is needed to account for the finite width w and length h of the sample compared to its thickness, Eq.(3): 2 d d D = D1 + + (3) c h w where D c is the corrected diffusion coefficient. The use of a Fickian diffusion model to describe diffusion in a heterophasic medium such as a biocomposite with very substantial differences in D for the two phases is questionable, and the water profiles within the composite are clearly very complex. Biological activity (algae, microorganisms ) appearing on the sample surface (Figure 1) is systematically removed and water desionised rinsed before weighting. Figure 1 Biological development on the surface of Flax/PLA biocomposite To get additional gravimetric data, samples are placed in a 20L metallic bucket where seawater is renewed each week. Good correlation is observed between both set of samples. 2.4 Cyclic tensile behaviour : Damage analysis Injected Flax/PLA biocomposites have anisotropic reinforcement which can be considered as random inplane dispersed. Analysis of stress-strain tensile curves allows rough evaluation of damage threshold (loss of linearity) corresponding to crack initiation. In the area where reinforcement are transversally oriented compared to load direction [25]. To perform accurate evaluation of damage threshold as well as damage kinetic, load-unload cycles are applied to our samples. First loading cycle represent 5% of maximal load observed for static characterization. Following cycle increase by steps of 100N (Figure 1A). 2 dθ D = π 4 ( ) (2) ΔW

119 Stress (MPa) A Time (second) The purpose of this characterization method is to evaluate residual strain due to load-unload cycles and damage appearance (Figure 1B). Similarly, Davies et al. [23] have used for glass/polyester seawater aging a damage criterion d = 1-E/E 0 corresponding the evolution of Young modulus as a function of load-unload cycles. This approach will be applied to follow damage kinetic of seawater aging of Flax/PLA biocomposites. 2-5 Scanning Electron Microscopy (SEM) The fracture surfaces were analyzed by scanning electron microscopy (SEM). The samples were sputter-coated with a thin layer of gold in an Edwards Sputter Coater, and observed with a Jeol JSM 6460LV scanning electron microscope. 3 RESULTS AND DISCUSSION 3.1 Water uptake Time (s) Figure 2 A- Example of load-unload cycles- B Example strain evolution as a function of load-unload cycles Figure 3 shows the water uptake of the pure and 20%-wt flax fibre reinforced PLA. The diffusive behaviour is close to a Fickian one with a water uptake at saturation after an immersion time around one month and half. Water uptake (%) PLA Biocomposite Fibre (estimated) Strain (%) B after 2 months, of 3.3% and mm²/s, respectively. These values are higher than those obtained on infused polyester/glass composites [27] immersed in filtered seawater at 4 and 20 C, but strongly lower than those obtained on unprotected wood (around 20%) [28]. By knowing the incorporated fibre weight into the biocomposite, as well as the matrix and biocomposite weight uptake, it is possible to estimate the fibre weight uptake and diffusion coefficient, thanks to an additivity rule. For that, we suppose that the composite porosity rate is negligible. ΔW composite = Δw fibre x fibre content + Δw matrix x (1- fibre content) (4) Where ΔW is the water uptake. D c biocomposite = D c fibre x fibre content + D c x (1- fibre content) (5) Where D c is the corrected diffusion coefficient. The saturation water uptake and coefficient of diffusion values, for the matrix, the biocomposite and the flax fibres are resumed in Table 1. ΔW () D (%) (mm²/s) D c (mm 2 /s) PLA Biocomposite Fibre (estimated) Table 1. Equilibrium water uptake, apparent diffusion coefficients D and corrected coefficients D c. In this case, the saturation weight value is around 12% for the flax fibre which is clearly superior to the biocomposite or matrix ones. These values are close to those obtained by Dynamic Vapour Sorption (DVS) [13, 29] or gravimetric methods [30]. This important weight uptake could be explained by the chemical constitution and the surface properties of flax fibre. Indeed, the flax fibre exhibit a complex multilayer structure [31] as evidenced on Figure Time 1/2 (Hours) Figure 3. Water uptake behaviour of pure PLA, biocomposite and fibre (estimated) The PLA weight uptake is quite low (0.77%) when its coefficient is mm²/s. Nevertheless, these results are well correlated with the literature ones [26].The incorporation of flax fibres into the PLA matrix leads clearly to an increase into the water uptake and the water diffusion coefficient D c ; they reach some plateau values, Figure 4. SEM micrograph of two elementary flax fibres

120 The fibre surface could be assimilated to the external layer constituted by the primary cell wall. This first layer is around 200 nm thick and its main function is to be flexible enough to enable the fibre growing [32]. The main components of this primary wall are pectins (rhamnogalacturonan I, homogalacturonan, arabinan [33]), hemicelluloses (xyloglucans), low crystalline cellulose [34] and waxes [32]. The hydrophilic character of this wall is due to the hydroxyl groups of these various components [35]. In this way, the methylesterification degree of the pectins, the chains size and the hemicelluloses polymerization rate, as well as the cellulose crystallinity rate, influence the water accessibility [34, 36, 37]. Some authors [13, 29] underline the influence of micro capillarities or lumen into the water diffusion and particularly when the residual water rate is high. Thus, the water uptake by sorption could be done also by the amorphous polysaccharides accessible hydroxyl groups located inside the walls. Moreover, this water could be take place into the lumen. The estimation of the fibre diffusion coefficient from those of the matrix and the composite enables to obtain a coefficient around mm²/s. This value is higher than those obtained by DVS by Gouanvé et al. [38] ( mm²/s at 25 C). This result shows that the diffusion mechanisms inside the plant fibres composites are complex and could be governed by capillary progression phenomenons located at the fibre-matrix interfaces [15] or by capillarity inside the lumen. Indeed, the incorporation of rather hydrophilic vegetal fibres into a quite hydrophobic matrix [39] could induce an original water diffusion mechanism. Wang et al. [14] announced the notion of percolation phenomenon linked to the vegetal fibre loading. In this case, the plant fibres play the rule of bridge, making the water diffusion easier. 3.2 Mechanical properties and tensile behaviour after immersion Figure 5 shows the evolution of the tensile mechanical behavior of the wet (A) and dried (B) composites as a function of the immersion time. We can notice an initial brittle behaviour which becomes more and more ductile with the immersion time; the elastic-linear area, where the damages are irreversible, reduces as a function of the water ageing. The dissipated energy until the breakage, obtained from the under curve area, increases with the water uptake. The Young s modulus is calculated from the linear part of the stressstrain curve. This stiffness is generally evaluated from the tangent method between 0.05 and 0.25% [40]. Some authors, on UD composites, calculate the stiffness between 0,025 and 0.1% [41] or 0.05 and 0.1% [42]. Stress (MPa) Stress (MPa) Strain (%) Strain (%) Figure 5. Stress-strain curve for biocomposite as a function of immersion time- A Wet state, B Dry state In the order to visualize this linearity loss, the Young(s modulus is drawn according to different deformation ranges for each immersion time (Figure 6). Figure 6 shows a decrease into the composites stiffness after a 0.1% deformation, corresponding to the first biocomposites damages. Young modulus (MPa) Young modulus (MPa) Figure 6. Young modulus vs strain curve for different strain boundary: % (A); % (B) and (C) B strain (%) Strain (%) Young modulus (MPa) C Strain (%) A A B

121 The rigidity calculation can t be done on this entire range. Between and 0.1%, the Young s modulus seems to increase on most of the immersed samples and especially until 0.5%. This phenomenon could be due to the fibre stiffness increase as evidenced by Placet et al. [43] or to a water desorption during the tensile experiment. A plateau could be observed between 0.05 and 0.1%. The Young s modulus will be determined in this area. The drying of the specimen shows the reversible way of the water ageing (plasticization) as shown on Figure 5.B. We can notice a partial reversibility of the mechanical behaviour especially high as the immersion time is short. This reversibility indicates that matrix, composite and fibre plasticization phenomena occur during the water immersion. Nevertheless, from an immersion time of 15 days, the dried specimens have a different behaviour of the native ones, showing irreversible damaging mechanisms. They exhibit a more tenacious behaviour, gradually confirmed with the immersion time and the water uptake are increasing. Figure 7 shows the properties variation (stiffness and strength at break) according to the immersion time for dried and wet specimens. The properties values are indicated in Table 2. % property retention Wet Modulus Dried Modulus Wet stength Dried strength Time (days) Figure 7. % property change as a function of immersion time- Wet modulus (black symbol); wet strength (red symbol; dried modulus (empty black symbol); dried strength (empty red symbol). We can notice a drastic decrease of the Young s modulus and the strength at break (-40%) followed by a stabilization around 200 immersion days corresponding to the biocomposites saturation time observed by using gravimetric method (Figure 3). After stabilization, the Young s modulus and the strength at break are 4000 MPa and 32 MPa, respectively (Table 2). The PLA/flax 30%-wt samples, immersed during 18 months in filtered natural water exhibit a similar stiffness but a lower tensile strength (around 20 MPa). By comparison, some polyester/glass composites, immersed during 2 years in natural marine environment, exhibit a tensile stiffness and strength at break flexure decrease of around 10% and 20%, respectively [10]. An exposition at the marine air at 20 C during 30 years induces a flexure strength at break decrease of 20% on glass/polyester composites [44]. Table 2. Mechanical properties of the wet and dried composites Figure 8 shows the evolution of the mechanical properties change according to the weight uptake. The obtained values are compared with those of PLA/flax 30%-wt immersed in filtered sea water at 20 C and 40 C [22]. Property retention (%) Wet Young modulus (MPa) Dried Young modulus (MPa) Wet tensile strength (MPa) Dried tensile strength (MPa) Immersion time ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 1.3 Modulus Strength Modulus BC-30% Strength BC 30% 4102 ± ± ± ± Water uptake (%) 4003 ± ± ± ± 2.1 Figure 8. Property change (Young modulus and strength) as a function of water uptake. The evolution of the Young s modulus and the strength at break in natural environment for the 20%-wt composite exhibits the same trend than those of the 30%- wt immersed biocomposite; nevertheless, the ageing of the 30%-wt seems to be reduced. The fibre loading increases the water uptake of the biocomposite and in the same time, we can notice that the mechanical properties decrease as a function of the water uptake is more pronounced for the 20%-wt composites. The specimens drying highlight the ageing reversibility; thus, for immersion time lower than 60 days, the stiffness degradation is reversible. The strength at break is more sensible to irreversible degradations seeing that from 15

122 days, the properties degradation is not reversible (Figure 6). Indeed, the composite stiffness is strongly linked to the components properties and therefore, to their evolution in the case of ageing process; moreover, the Young s modulus is obtained at the beginning of the solicitation where the damages are lower. The strength at break also depends of the breakage properties of each component and especially of the interactions between each other, of the reinforcement s dispersion and also of the damages accumulation induced by the ageing. 3.3 Estimation of the fibre properties evolution into the composite It is possible to estimate the biocomposite Young s modulus from the components properties and the reinforcement morphology by using an analytical model as described by Halpin-Tsai [6]. The following data have been used to estimate the composite stiffness : E fl = 53.8 ± 14.3 GPa [45] and E ft = 7 ± 2 GPa [46], the anisotropy ratio is The longitudinal modulus E L and the transverse modulus E T for a ply reinforced by short unidirectional fibres is given by equations (6) and (7): M M m η = 1+ V = f 1 V f M f M M n f M m + ξ (6) 1 (7) where M=E L or E T, Mf = E fl or E ft and m, f and l correspond to matrix, fibre, longitudinal and transversal. V f is the fibre volume fraction and ξ the form factor. For the longitudinal modulus, ξ = 2 L/d where L/d is the fibre aspect ratio. For the transverse modulus E t, satisfactory results have been obtained with ξ = 2 [47]. The modulus of a ply reinforced by randomly dispersed fibres is given by the following expression [47]: E mat 3 5 = EL + E (8) T 8 8 where E L is the longitudinal modulus and E T the transverse modulus of the unidirectional ply. The estimated stiffness of the biocomposite is 6105 MPa against 6395 ± 175 MPa which could be considered as a correct estimation with an error around 5%. From the evolution of the biocomposite Young s modulus with the immersion time, it is possible to estimate the evolution of the transverse and longitudinal flax fibre moduli. The evolution of the PLA Young modulus is assumed to be negligible after immersion [24] as well as the anisotropy ratio. Moreover, the fibre matrix adherence is supposed to be constant during the immersion time. Figure 9 shows the evolution of the fibre transverse and longitudinal moduli with the biocomposites immersion time. Modulus (MPa) Wet Longitudinal modulus Wet Transverse modulus Dried Longitudinal modulus Dried Transverse modulus Time (Days) Figure 9. Evolution of the fibre longitudinal and transverse moduli estimated by using the Halpin Tsai equations. The Halpin-Tsai simulations indicate an important decrease of the longitudinal and transverse fibre properties with the immersion time and stabilization around 200 days. After drying, the biocomposite recover its initial properties until around 90 days, showing a plasticizing effect of the cell walls. The phenomenon has been previously showed on wood fibres mixed with a PLA matrix [48]. This tendency could explain the mechanical results obtained on immersed specimens. The definitive loss of the properties is certainly due to the washing of soluble components ensuring the mechanical integrity of the fibres. Some authors evidenced a slight decrease of the flax fibre Young s modulus with the relative humidity (between 30 and 70% RH) representing 0.39 GPa/% RH [37]. These observations are moderated by other results; for example, Placet et al. [29, 43] showed an improvement of the hemp fibre Young s modulus between 10% and 80% of humidity due to a realignment of the cellulose micro fibrils with the solicitation axis. The tensile properties seem to present an optimal value around a humidity rate of 70%. In our case, the immersion time play a major rule on the fibre ageing due to its action into the washing and the degradation phenomena induced by micro organisms [29]. 3.3 Evolution of the biocomposite damage process Figure 10.A shows the evolution of the cycling biocomposite behaviour before and after a 710 days marine environment immersion. From the curves and imposed cycles, it is possible to draw the evolution of a damage criterion d as a function of the immersion time (Figure 10.B). The damage criterion increase more and more with the deformation and the immersion time. We observe an increase of the damage criterion from a 0.3% deformation for the 60 days immersed samples against 0.6% for the virgin biocomposites. For the 180 to 710 days immersed samples, the d increase appears at the

123 very low deformations evidencing an early damage threshold. Stress (MPa) d A B Strain (%) Figure 10. Cycling behavior of virgin and 710 days immersed specimens (A) and evolution of the damage criterion as a function of the deformation for several immersion times (B). Next, the damage criterion d increases more quickly on the low immersed samples evidencing a most important damage kinetic. When the strain increases, a linearity loss between d and the strain appears, probably due to the desorption phenomenon, especially for long immersion times (between 180 and 710 days). On this kind of specimens with randomly dispersed fibres, the first irreversible damages occur in the transverse solicited areas. Figure 11 shows SEM images of the fracture surface of non-immersed biocomposites strain(%) present between the matrix and the transverse orientated fibre bundles (y-x plane). These fibres bundles could be considered as favoured breakage areas due to the heterogeneity of the surrounding stress [46]. Finally, some flow oriented fibres breakages could be noticed with low debonding length, evidencing important interface interactions between the flax and the PLA matrix [49]. Moreover, cohesive breakages could be observed (red arrow on the right). After an immersion of 2 years, the breakage behaviour of the matrix changes. In addition to the fibres plasticizing, the PLA breakage becomes ductile as highlighted by Figure 12.A. these phenomena could explain the mechanical behaviour of the immersed biocomposites (Figure 5.A). After ageing, some fibres breakages are still present with important debonding lengths, compared to non-immersed samples. Nevertheless, as shown on Figure 12.A, some fibre breakages with low debonding (red arrows) could be identified, showing the efficiency of the interfacial stress transfer; moreover, fibre peeling are remaining (Figure 12.B). The presence of water induces a fibre bundles division (Figure 12.C), inducing a decrease of the stress transfer and then an early damage of the biocomposite as shown on Figure 10.B. Indeed, Bourmaud et al. [50] shown that a 72h soft water treatment could facilitate the elementary flax fibre extraction by degrading the middle lamella pectins. According to Figure 3, the water uptake of the flax fibre after immersion is around 12%; this phenomenon should conduce to a swelling of the cell walls. The flax fibre swelling is isotropic with an axial and transverse component around 0.05% and 20-25%, respectively [51]. Little information is available on the bundle structure influence and on the rule of the matrix on the fibre properties (residual stresses). x z y x z y Figure 11. SEM micrographs of virgin biocomposites The non-immersed biocomposites exhibit complex damages after tensile test. First, we notice a brittle break of the matrix well correlated with the Figure 5 observations. Then, the interfacial breaks (red arrow) are Figure 12. SEM micrographs of the 710 days immersed biocomposites fractures. From literature papers summarized by Azwa et al. [12], the fibre swelling induces cracking and overstress in the surrounding matrix. Nevertheless, the SEM observation on elementary fibres doesn t enable to clearly identify these kinds of damages. In the same way as for wood

124 [52], the flax fibre under stress swelling could induce a stress swelling reduction due to a relaxation phenomenon. Some holes are mainly observed around the fibre bundles, explaining the non reversibility of the damages. As underlined by Almgrem et al. [53], the plant fibre composites swelling is depending of the consolidation and of the available free volume fraction. Thus, the lack of cohesion and the swelling should be favoured by the presence of fibre bundles (Figure 12.D). Moreover, the surface components dissolution could influence the interfacial decohesions. 4 CONCLUSION The present article has given information on 2 years seawater aging effect on injected flax/pla biocomposite. Biocomposite suffer from relatively high moisture absorption which is controlled by vegetal fibre. Simple rule of mixture allows for flax fibre the determination of a weight gain at saturation around 12% which is close to already published values.. Bundles of fibres and especially middle lamellae influence water uptake. Water alters biocomposites, and flax fibres since their mechanical properties are reduced (Young modulus and tensile strength) with aging. Linear relationship is observed between water uptake and loss of mechanical properties. Load-unload cycles highlight damage occuring earlier as biocomposite undergo aging. These damages can be induced by fibre degradation and washing out of soluble components especially the fibre bundles cement, by debonding of fibre bundles linked to their swelling. ACKNOWLEDGEMENTS Authors wish to acknowledge ADEME (French Environment and Energy Management agency) for financial support. REFERENCES 1. Bodros, E., I. Pillin, N. Montrelay, and C. Baley, Could biopolymers reinforced by randomly scattered flax fibre be used in structural applications? Composites Science and Technology, (3-4): p Le Duigou, A., P. Davies, and C. Baley, Macroscopic analysis of interfacial properties of flax/plla biocomposites. Composites Science and Technology, (11): p Oksman, K., M. Skrifvars, and J.-F. Selin, Natural fibres as reinforcement in polylactic acid (PLA) composites. Composites Science and Technology, (9): p Plackett, D., L. AT., B. PW., and L. Nielsen, Biodegradable composites based on polylactide and jute fibres. Composites Science and Technology, (9): p Roussière, F., C. Baley, G. Godart, and D. Burr, Compressive and Tensile Behaviours of PLLA Matrix Composites Reinforced with Randomly Dispersed Flax Fibres. Applied composite Material, 2011: p Le Duigou, A., I. Pillin, A. Bourmaud, P. Davies, and C. Baley, Effect of recycling on mechanical behaviour of biocompostable flax/poly(l-lactide) composites. Composite Part A, (9): p Kumar, R., M.K. Yakubu, and R.D. Anandjiwala, Biodegradation of flax fiber reinforced poly lactic acid. express Polymer Letters, (7): p Le Duigou, A., P. Davies, and C. Baley, Environmental impact analysis of the production of flax fibres to be used as composite material reinforcement. J. biobased. mater.bioenerg., : p Le Duigou, A., P. Davies, and C. Baley, Replacement of glass/unsaturated polyester composites by flax/plla biocomposites : Is it justified? Journal of biobased materials and bioenergy, Accepted. 10. Davies, P. and D. Choqueuse, Ageing of composite in marine vessels, in Ageing of composites, R. Martin, Editor Gautier, L., B. Mortaigne, and V. Bellenger, Interface damage study of hydrothermally aged glass-fibre-reinforced polyester composites. Comp. Sci. Technol., (16): p Azwa, Z.N., B.F. Yousif, A.C. Manalo, and W. Karunasena, A review on the degradability of polymeric composites based on natural fibres. Materials & Design, (0): p Hill, C., A. Norton, and G. Newman, The water vapor sorption behavior of natural fbers. Journal of Applied Polymer Science, : p Wang, W., M. Sain, and P.A. Coope, Study of moisture absorption in natural fiber plastic composites. Composites Science and Technology, : p Le Duigou, A., P. Davies, and C. Baley, Exploring durability of interfaces in flax fibre/epoxy micro-composites. Composites Part A: Applied Science and Manufacturing, 2013(0). 16. Clair, B., Etude des propriéts mécaniques et propriéts au séchage du bois à l'échelle de la paroi cellulaire: Essai de compréhension du comportement macroscopique paradoxale du

125 bois de tension à couche gélatineuse. Report thesis- ENGREF, Dhakal, H.N., Z.Y. Zhang, and M.O.W. Richardson, Effect of water absorption on the mechanical properties of hemp fibre reinforced unsaturated polyester composites. Comp. Sci. Technol., (7-8): p Joseph, P.V., M.S. Rabello, L.H.C. Mattoso, K. Joseph, and S. Thomas, Environmental effects on the degradation behaviour of sisal fibre reinforced polypropylene composites. Comp. Sci Technol., (10-11): p Chen, H., M. Miao, and X. Ding, Influence of moisture absorption on the interfacial strength of bamboo/vinyl ester composites. Composites Part A: Applied Science and Manufacturing, (12): p Islam, M.S., K.L. Pickering, and N.J. Foreman, Influence of accelerated ageing on the physicomechanical properties of alkali-treated industrial hemp fibre reinforced poly(lactic acid) (PLA) composites. Polym Degrad and Stab, (1): p Scida, D., M. Assarar, C. Poilâne, and R. Ayad, Influence of hygrothermal ageing on the damage mechanisms of flax-fibre reinforced epoxy composite. Composites Part B: Engineering, (0): p Le Duigou, A., P. Davies, and C. Baley, Seawater aging of Flax/PLLA biocomposite. Polymer Degradation and Stability, : p Davies, P., F. Mazeas, and P. Casari, Sea Water Aging of Glass Reinforced Composites:Shear Behaviour and Damage Modelling. J Compos Mater, Le Duigou, A., P. Davies, and C. Baley, Seawater ageing of Flax/PLLA biocomposites. Polym Degrad and Stab, ( ). 25. Gibson, R., Principle of composite materials mechanics. 1994, New york: McGraw-Hill International Editions. 26. Yew, G.H., A.M. Mohd Yusof, Z.A. Mohd Ishak, and U.S. Ishiaku, Water absorption and enzymatic degradation of poly(lactic acid)/rice starch composites. Polym Degrad and Stab, (3): p Boisseau, A., Etude de la tenue à long terme de matériaux composites immergés pour structures de récupération d énergies marines. Thesis report (In french), Glass, S. and S. Zelinka, Moisture Relations and Physical Properties of Wood- General Technical Report FPL- GTR. Chapter Stamboulis, A., C.A. Baillie, and T. Peijs, Effects of environmental conditions on mechanical and physical properties of flax fibers. Composites Part A: Applied Science and Manufacturing, (8): p Celinot, A., S. Fréour, F. Jacquemin, and P. Casari, Characterization and Modeling of the Moisture Diffusion Behavior of Natural Fibers. Journal of Applied Polymer Science, DOI: /APP Hearle, J., The fine structure of fibers and crystalline polymers. III. Interpretation of the mechanical properties of fibers. J. App Polym. Sci., : p Bos, H.L., The potential of flax fibres as reinforcement for composite materials-thesis report. Eindhoven, Cosgrove, D., Growth of the plant cell wall. Nature reviews- Molecular cell biology, : p Zykwinska, A., J.-F. Thibault, and M.-C. Ralet, Competitive binding of pectin and xyloglucan with primary cell wall cellulose. Carbohydrate Polymers, (4): p Zafeiropoulos, N.E., P. Vickers, C. Baillie, and J. Watts, An experimental investigation of modified and unmodified flax fibres with XPS, ToF-SIMS ans ATR-FTIR. Joural of Materials Science, : p Morvan, C., C. Andème-Onzighi, R. Girault, D.S. Himmelsbach, A. Driouich, and D.E. Akin, Building flax fibres: more than one brick in the walls. Plant Physiology and Biochemistry, (11-12): p Davies, G.C. and D.M. Bruce, Effect of Environmental Relative Humidity and Damage on the Tensile Properties of Flax and Nettle Fibers. Textile Research Journal, (9): p Gouanvé, F., S. Marais, A. Bessadok, D. Langevin, and M. Métayer, Kinetics of water sorption in flax and PET fibers. European Polymer Journal, (2): p Bourmaud, A., J. Riviere, A. Le Duigou, G. Raj, and C. Baley, Investigations of the use of a mussel-inspired compatibilizer to improve the matrix-fiber adhesion of a biocomposite. Polymer Testing, 2009(1-5). 40. British Standard, B.E.I., Plastics Determination of Tensile Properties Part 4: Test Conditions for Isotropic and Orthotropic Fibre-Reinforced Plastic Composites. British Standards Institution, London (1997) Shah, D.U., P.J. Schubel, M.J. Clifford, and P. Licence, The tensile behavior of off-axis loaded plant fiber composites: An insight on the nonlinear stress strain response. Polymer Composites, (9): p Baets, J., D. Plastria, J. Ivens, and I. Verpoest, Determination of the optimal flax fibre preparation for use in UD-Epoxy composites.

126 18 TH International Conference on Composite Materials, Placet, V., O. Cissé, and M. Boubakar, Influence of environmental relative humidity on the tensile and rotational behaviour of hemp fibres. Journal of Material Science, ( ). 44. GUTIERREZ, J., F. LELAY, and P. HOARAU, A study of ageing of glass fibre-resin composites in a marine environment. Proceedings of the International Conference on Nautical Construction with Composite Materials, Paris, IFREMER, p. 338., Bourmaud, A., G. Ausias, G. Lebrun, M.L. Tachon, and C. Baley, Observation of the structure of a composite polypropylene/flax and damage mechanisms under stress. Industrial Crops and Products, (0): p Baley, C., Y. Perrot, F. Busnel, H. Guezenoc, and P. Davies, Transverse tensile behaviour of unidirectional plies reinforced with flax fibres. Materials Letters, (24): p Gibson, R., Principles of composite material mechanics. New-York McGraw-Hill, Almgrem, K., Wood-fibre composites: Stress transfer and hygroexpansion. Thesis report- KTH Fibre and Polymer Technology School of Chemical Sciences and Engineering Royal Institute of Technology - SE Stockholm Sweden, le Duigou, A., A. Bourmaud, E. Balnois, P. Davies, and C. Baley, Improving the interfacial properties between flax fibres and PLLA by a water fibre treatment and drying cycle. Industrial Crops and Products, (0): p Bourmaud, A., C. Morvan, and C. Baley, Importance of fiber preparation to optimize the surface and mechanical properties of unitary flax fiber. Industrial Crops and Products, (3): p Mussig, J., H. Fisher, N. Graupner, and A. FDrieling, Testing methods for measuring physical and mechancial fibre properties (plant and animal fibres). Industrial application of natural fibres : Strcture, properties and technical application- Chichester, United Kingdom, John Wiley & Sons, 2010: p Virtaa, J., S. Koponenb, and I. Absetza, Measurement of swelling stresses in spruce (Picea abies) samples. Building and Environment : p Almgren, K., E.K. Gamstedt, F. Berthold, and M. Lindström, Moisture uptake and hygroexpansion of wood fiber composite materials with polylactide and polypropylene matrix materials. Polymer Composites, (12): p AUTHORS BIOGRAPHY A. Le Duigou obtained a Master degree in EcoDesign of Polymer and Composites in University of South Brittany (Lorient) in He holds PhD thesis entitled contribution à l étude des biocomposites in IFREMER (Brest) and LIMATB. Now he is associate professor in the LIMATB laboratory of the South Brittany University. His major research topic deals with biocomposites systems from durability to interfacial properties characterization. A. Bourmaud is Research Engineer in Material Engineering Laboratory of Brittany (LIMATB) in Lorient, France. His main research topics are the knowledge of mechanical behaviour of flax or hemp fibers, the recycling and processing of plant fibers composites and the nanoindentation. P. Davies is a researcher in the Materials & Structures group at IFREMER, the French Ocean Research Institute, in Brest. He has been working on fibres, polymers and composites for marine applications for over 25 years. C. Baley is currently Professor in the University of South Brittany. His main research topics are the reinforcement mechanisms of polymer natural fibers composites, the knowledge of the vegetal cell walls and the study of the plant fiber/polymer interfaces.

127 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France WIND-TUNNEL PRESSURE MEASUREMENTS ON MODEL-SCALE RIGID DOWNWIND SAILS Patrick Bot, Naval Academy Research Institute, France, Ignazio Maria Viola, Yacht and Superyacht Research Group, School of Marine Science and Technology, Newcastle University, UK, Richard G.J. Flay, Yacht Research Unit, University of Auckland, New Zealand, Jean-Sebastien Brett, Naval Academy Research Institute, France, This paper describes an experiment that was carried out in the Twisted Flow Wind Tunnel at The University of Auckland to measure a detailed set of pressure distributions on a rigid 1/15 th scale model of a modern asymmetric spinnaker. It was observed that the pressures varied considerably up the height of the spinnaker. The fine resolution of pressure taps allowed the extent of leading edge separation bubbles, pressure recovery region, and effect of sail curvature to be observed quite clearly. It was found that the shape of the pressure distributions could be understood in terms of conventional aerodynamic theory. The sail performed best at an apparent wind angle of about 55, which is its design angle, and the effect of heel was more pronounced near the head than the foot. NOMENCLATURE AWA Apparent Wind Angle Effective Apparent Wind Angle c Sail section chord (m) c av Average sail chord (m) Pressure coefficient (-) f Frequency (Hz) h Yacht model height (m) Sail surface pressure (Pa) Reference static pressure (Pa) Reference dynamic pressure (Pa) Re Reynolds number (-) Strouhal number (-) Reference velocity x chord-wise coordinate (m) 1 INTRODUCTION Modern yacht sails are aerodynamically very efficient but the flow field around sails is largely unknown. Knowledge of the flow features that make sails aerodynamically efficient will allow the performance of sails and also the aerodynamic efficiency of sail-like airfoils for other applications to be enhanced further. The aerodynamics of sails has mainly been investigated with force measurements [1-5] in wind tunnels [6-8], while only a few authors have recently measured sail pressure distributions [9-11]. The flow field around sails has been examined primarily through numerical simulations and, therefore, it is very important to validate such simulations with accurate measurements of local quantities such as surface pressure distributions, instead of only comparing them to global quantities such as forces Sail pressure distributions can be measured in modelscale from wind tunnel tests and in full scale [11]. The state-of-the-art experimental technique is based on flexible sails including semi-flexible single-skin fibreglass sails used by Richards and Lasher [9], and common spinnaker sailcloth used by Viola & Flay [10,12] - where pressure taps are attached to one side of the sail and pressures are measured on the other side of the sail through holes in the sailcloth. This technique allows realistic sail trims in different sailing conditions to be modelled, but is limited by (i) the unknown blockage effect due to the tubes and pressure taps, (ii) the alteration of both the static sail shape and the dynamic behaviour of the sails by the mass and stiffness of the tubes and pressure taps, (iii) the low accuracy in the reconstruction of the sail flying shape. The observed differences between the pressure distributions measured with this technique in the wind tunnel, and those measured in full-scale or computed numerically are expected to be partially due to the presence of tubes and pressure taps. A novel technique is presented in this paper, where the effect of the pressure taps is eliminated and the effect of the tubes on the flow field is minimised. Also, the sail is rigid allowing the flying shape to be detected with highaccuracy. This paper describes pressure distributions measured on the rigid asymmetric spinnaker in a wind tunnel, which are discussed and compared to pressures measured on soft flexible sails, and also to numerical simulation results. The pressure profiles along the sail chord on the leeward side enable interesting flow characteristics to be determined, such as leading edge separation bubble (sharp suction peak), sail curvature suction, and trailing

128 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France edge flow separation (pressure plateau). Helpful insights into sail aerodynamics are obtained from this investigation, which are explained using conventional aerodynamic and aeronautical knowledge of the aerodynamics of thin wings. Further details are given in the subsequent sections. a 2 EXPERIMENTAL ARRANGEMENT A rigid 1/15 th scale model of an AC33-class spinnaker has been tested at the University of Auckland Yacht Research Unit (YRU) Twisted Flow Wind Tunnel which has an open jet with a test section 7m wide and 3.5m high. The tests were performed in uniform flow (without twisting vanes) with a turbulence intensity of around 3%. The reference wind speed was approximately giving a Reynolds number based on the average spinnaker chord c av equal to. The solid spinnaker and mainsail were mounted on a yacht model (rig and hull), which was mounted on a turntable to adjust the apparent wind angle (AWA). The model was mounted on fore and aft bearings to enable the heel angle to be varied. Figure 1 shows two photographs of the model during the tests. In particular, Figure 1(b) shows the tubes carrying the pressures from the sail leech to the transducers in the cockpit; note also that the rig was reinforced by a deck spreader to windward due to the heavy spinnaker model, and the actuator used to adjust heel angle on the left hand side. The solid model spinnaker was built as part of a master s research project at the YRU by Brett [13], with the flying shape recorded from a sailcloth model spinnaker previously studied at the YRU [10]. The selected shape was recorded for a trim giving the maximum driving force with a non-flapping sail at an AWA of 55 and 10 of heel. The geometric parameters of the sail shape are given in Table 1. Unfortunately the shapes of the rigid asymmetric spinnaker and the soft sail were not perfectly identical, and this has implications on the pressure comparisons discussed in Section 4. The solid sail is a 5mm thick epoxy fibreglass sandwich where the core is a corrugated plastic material featuring a high density of individual pressure-tight flutes, which provide the pneumatic tubes to carry the pressure signal from the measurement location to the sail leech. Thin plastic tubes are connected to each flute on the sail leech to carry the pressure to the pressure transducers in the model cockpit. One-millimetre holes were drilled through the sail and tape was used to close one side in order to measure the pressures on the other side. A sketch of a pressure tap in section of the solid spinnaker model is shown in Figure 2. The rigid sail had a mass of about 10kg, and it was observed that its shape could distort due to self-weight. The implications of this are addressed later in the paper when the results are discussed. b Figure 1: Photographs of the rigid spinnaker setup in the wind tunnel; (a) general view from downstream; (b) close-up view from behind the yacht model. Figure 2: Sketch of a pressure tap in section of the solid spinnaker model, and definition of aerodynamic profile parameters Measurement system and experimental procedure All transducers were pneumatically connected to a reference static pressure measured with a Pitot-static probe located 10m upstream of the model, 0.5m below the wind tunnel roof. A total of 175 pressure taps were arranged along five horizontal sections located at fractions 1/8, 1/4, 1/2, 3/4 and 7/8 of the mitre height, which is the line equidistant from the leading and trailing edges of the sail. The distance between consecutive pressure taps ranges from around 10mm near the leading edge up to around 100mm in the middle of the chord 120

129 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France where the pressure gradient is expected to be lower. There are from 31 to 38 taps per section. The reference dynamic pressure was measured by the same sensor as described in the preceding paragraph. Two other Pitot-static probes were positioned 0.8m above the wind tunnel floor (corresponding to a full scale height of 12m) to check the air speed at these locations too. the trailing edge separated area. The high spatial resolution achieved due to the numerous pressure taps enables the very sharp gradients occurring near the leading edge to be resolved, which has not usually been possible in previously published work on sail pressure distributions. Notice that due to different chord lengths for the different sections, suction maxima at the same reduced coordinate x/c are not superimposed in reality. The piezoresistive pressure sensors used are Honeywell XSCL04DC transducers, and a calibration was made before each experimental run with a precision (+/ Pa) Druck-DPI 615LP pressure calibrator. The accuracy of the pressure measurements is of order 0.5 Pa. Pressures were measured on the 175 pressure taps on each side of the sail, for different AWA and heel angles. For the mean pressure distribution, pressures were recorded over 100s at a sampling frequency of 100Hz. Only the pressure distribution on the sail s suction side is shown for clarity. On the pressure side, the pressure was observed to be nearly constant with a pressure coefficient Cp ranging between 0.5 and 0.8 depending on the AWA. Table 1: Parameters of the aerodynamic profile on each section (see definition in Fig. 2) Section 1/8 1/4 1/2 3/4 7/8 Curve [mm] Chord [mm] Twist [ ] Camber [mm] Camber [%] Draft [%] Entry Angle [ ] Exit Angle [ ] MEAN PRESSURE DISTRIBUTIONS Figure 3 shows the mean pressure distributions recorded on the five sections of the spinnaker for an AWA of 55 and 10 heel. The three lower sections show similar behaviour with the following characteristics. A high suction peak at the leading edge is followed by a sharp pressure recovery with a minimum suction located around 2% of the chord length. The flow separates at the leading edge producing a strong leading edge separation bubble giving the strong suction, and the pressure recovery is associated with reattachment. On upwind sails [14] and on flat plates [15], the maximum pressure recovery occurs just downstream of the point of reattachment. Downstream of this point, the pressure decreases again due to the sail curvature and thus the associated flow curvature, with a maximum suction at around 20%-30% of the chord length. After the pressure recovery in the region where the sail shape becomes less curved, the pressure is nearly constant in Figure 3: Cp on the 5 sections of the spinnaker for 55 AWA and 10 heel. On the highest section, there is a very high suction (Cp = -3) at the leading edge and then a rapid pressure recovery with the minimum suction located at 10% of the chord followed by a relatively uniform pressure over the remaining chord. This pressure distribution suggests that there is a tight leading edge separation bubble (or vortex) at this location. Note that since this section is near the head of the sail, the flow will be very three-dimensional. There is a very flat maximum suction visible around x/c= On section 3/4, downstream of the high suction at the leading edge, the pressure recovery is smooth and essentially monotonic. The pressure distributions on the five sections are shown in Figure 4 for AWAs from 51 to 59. It should be noted that the rigid spinnaker shape corresponds (approximately) to the flying shape of the equivalent soft sail recorded at 55 AWA. This frozen shape is expected to perform well over a fairly narrow range of AWAs. Again, the three lower sections show similar behaviour to that described above. When the AWA is increased, the pressure recovery at the re-attachment location is reduced a little and the trailing edge separation point moves upstream. The pressure distribution on the lowest section is the least sensitive to AWA, whereas conversely, the pressure distribution on the highest section is the most sensitive to AWA. It may also be noticed that the pressure plateau in the trailing edge separated area for section 1/8 is more pronounced and with a higher suction (Cp around -0.8) for the highest AWA. The higher sections are mostly separated and totally stalled for the highest AWA. 121

130 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France Figure 4: Cp for AWA=51, 53, 55, 57 and 59 on the 5 sail sections. Note that the Cp scale is larger for sections 3/4 and 7/8. Figure 5: Cp for heel=5, 10 and 14 on the 5 sail sections, for AWA=55. Note that the Cp scale is larger for sections 3/4 and 7/8. 122

131 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France Figure 5 shows the pressure distributions on the five sections for heel angles of 5, 10 and 14, for an AWA of 55. On the three lower sections, the pressure is affected only slightly by heel angle, with the trailing edge separation slightly earlier for the highest heel angle. On the top two sections, where the flow is mainly separated, the effect of heel is stronger and the higher the heel angle, the more stalled the profile. In Figure 6, it is noticeable that the pressures on the top two sections at 5 heel for 55 AWA are nearly identical to pressures at 10 heel for 53 AWA, and that the pressures at 10 heel for 57 AWA are nearly identical to pressures at14 heel for 55 AWA, so that aerodynamically, additional heeling corresponds to increasing the angle of attack. In particular, the trailing edge separation point seems to move upstream when the heel angle increases. Figure 6 : Cp on sections 7/8 and 3/4 for AWA=55 and heel angles of 5, 10 and 14, and for heel angle = 10 and AWAs of 53, 55 and COMPARISON WITH OTHER PUBLICATIONS Figure 7 shows the present results and those achieved with recent numerical simulations made on the same geometry at 55 AWA using Delayed Detached Eddy Simulation [16], and those achieved experimentally on the equivalent soft sail [12]. Also shown on the figure are results of the present study obtained during another Figure 7: Cp measured on the solid spinnaker (present study) for AWA=53 and 55 (measurements from two distinct experimental runs are shown to assess the repeatability), measured on a soft sail [12] and computed with DDES [16]. 123

132 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France experimental run, which show the reasonable repeatability of the measurements. On the three lowest sections, the simulated and experimental results are similar. The general behaviour is well reproduced and a good quantitative agreement is found. In some cases, the simulation result is closer to the pressure recorded for a slightly lower AWA of 53 (see sections 1/8 and 1/4 for x/c<0.2 and section 1/2 for x/c<0.4). The pressure plateau associated with the trailing edge separation is found to be a little further downstream in the simulation than in the experiment. On the top two sections, the numerical pressures are similar to the experimental result for a lower AWA (53 ). The results obtained on the soft sail in a different experiment show general behaviour that is more or less compatible with the present results, but the discrepancies are important. In particular, the peak suction values and locations are rather different. It can be observed that the lower number of pressure taps on the soft sail did not allow the sharp gradients to be resolved. The differences between the soft and rigid sail results are also likely to be due to the differences in shape between them. In fact they are also slightly different in size. Another reason for the differences observed between the present results and the simulation results may result from an alteration of the shape of the solid sail. As the solid sail is quite heavy (around 10kg) compared to the aerodynamic force, and not perfectly rigid, it was observed after the tests that the model s weight altered the general sail shape by dropping the clew which would have increased the sail curvature and decreased the sail twist resulting in higher angle of attack on the highest sections, which could explain the stall of the top of the sail. In order to understand this point better, a subsequent research project is underway to measure both the spinnaker and mainsail pressures, with additional support of the solid spinnaker using wires to fix the distances between the head, tack and clew to the required values. 5 PRESSURE TIME SERIES For the particular analysis of pressure time histories, some tests were done with only 58 pressure taps located on sections 1/4, 1/2 and 3/4, and with shorter pressure tubes, recorded over 300s at a sampling frequency of 200Hz. The signals were then filtered with a moving average of span 20 data points to reduce the frequency to 20 Hz. Each tube length was adjusted to the length of each flute inside the sandwich sail in order to have an identical total cavity length equal to 2.15m. Such long tubes would have provided significant damping to the recorded pressure time histories. However, even though the sensor plus tube transfer function is not known with precision, the recorded pressures show quite different behaviours depending on their positions, and hence according to the region of the local flow, and some interesting features of the separation were detected. Figure 8 shows the time series of Cp variations (instantaneous Cp time averaged Cp) on section 1/2 from four characteristic locations along the chord: near the leading edge just downstream of the reattachment (x/c=0.0428), near the maximum of the curvature suction peak (x/c=0.240), in the separation region (x/c=0.617) and in the separated area near the trailing edge (x/c=0.889). In the two first locations, the fluctuation results from the turbulence of the flow. It is noticeable that the pressure amplitudes are much higher in the separated area and that the maximum amplitudes are observed where the separation occurs. The separation location is known to be oscillatory in time and the back and forth motion of the separation point associated with its high pressure gradient gives rise to these high pressure fluctuations. Moreover, as can be seen in the enlargement in Figure 8, the pressure fluctuations at x/c=0.617 undergo rather coherent oscillations at a frequency significantly lower than the pressure fluctuations at other locations. This low frequency ranges between 0.3Hz to 1Hz, which corresponds to a Strouhal number range. Such a Strouhal number range suggests that these fluctuations are associated with the large scale vortex shedding in the flow separation. Figure 8: Time series of the Cp variations on section 1/2, at x/c=0.0428, 0.240, and 0.889, enlargement: detail for x/c=0.617 and t from 100 to 150s. 6 DISCUSSION AND CONCLUSIONS The paper presents results from novel rigid sails, manufactured in a sandwich structure made of pressuretight flutes, which allows the pressure distributions on model-scale yacht sails to be measured. This model was used to measure the pressure distributions on an asymmetric spinnaker at different AWA and heel angles, and the results were compared with numerical results and another experimental method. The measurements confirmed the general pressure distributions and trends observed by other authors with flexible sails [10,12] and numerical simulations [16]. In particular, in the optimum trim condition, the pressure gently decreases from the leading edge to the trailing edge on the whole windward side of the sail. On the 124

133 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France leeward side (Figure 3), the pressure shows a suction peak due to the leading edge separation followed by a partial pressure recovery associated with the turbulent reattachment. Further downstream the pressure shows a second smoother suction peak associated with the sail and flow curvature, and then a pressure plateau extended to the trailing edge when separation occurs. On the highest sections, the second suction peak does not occur due to the tip vortex at the head of the sail. When the AWA increases (Figure 4), the leading edge suction peak increases while the trailing edge separation point moves upstream leading to a lower curvaturerelated suction peak. When the AWA is increased further, the flow fails to reattach and the pressure gradient decreases until a constant pressure is measured on the entire sail section. Increasing the heel angle has a similar effect to increasing the AWA (Fig. 6). This is expected to happen only in a limited range of heel angles, such as those measured in the present paper. In fact, it was noted by several authors (for instance Le Pelley et al. [2]) that downwind sails may allow larger aerodynamic forces when the yacht is slightly heeled than when upright. However, when the heel angle increases, the effective angle of attack in a plane perpendicular to the mast decreases according to Equation (1). Therefore, it is expected that heeling the yacht to high angles would modify the pressure distribution in a similar fashion to when the AWA decreases. Conversely, for low angles of heel, the reduction of with the heel is small. For instance, if the heel angle increases from 5 to 10, and from 10 to 14, decreases by 0.3 and 0.4, respectively. Therefore, in the tested range of heel angles (5-14 ), the reduction is negligible while other phenomena, which remain to be understood, may prevail. The effect of heel on the aerodynamic force produced by a spinnaker will also depend on whether or not it is re-trimmed. This novel model sail pressure investigation allowed progress beyond the current state-of-the-art method based on flexible sails [10,11,12] in several areas. In particular: Rigid sails allow better control of the sail geometry (particularly camber and draft) than flexible sails, though the control on the twist of the sails is still unsatisfactory. For instance, the comparison with the pressures computed numerically by Viola et al. [16] suggests that the sail was under-twisted by about on the highest sections during the experiments (Fig. 7). This undesirable sail deflection was probably caused by its own weight. On flexible sails the pressure tubes cannot be bundled together at the trailing edge and thus the tubes have a greater blockage effect than with rigid sails. For instance, when pressures on the leeward side are measured with flexible sails, the tubes on the windward side deflect the incoming streamlines, resulting in an increased angle of attack. This can be seen in Fig. 7, where higher suction peaks were measured with flexible sails than with rigid sails. On flexible sails, the weight of the pressure taps and tubes affect the sail shape leading to local flow accelerations and pressure changes, while rigid sails allow a much smoother surface. For instance, on the lowest section in Fig. 7, the pressure around 3/4 th of the chord decreases locally due to a kink (wrinkle) on the sail. Rigid sails also allow the pressure transducers to be placed very close to the pressure tap, minimising the displacement of the volume of air between the tap and the transducer that affects the frequency content of the pressure time series due to the filtering effect of long tubes. The study of frequencies and phases of the pressure time series may reveal very interesting information on the flow field. For instance, it may allow the detection of the location of laminar to turbulent transition, if the positions of separation and reattachment points are stationary, while correlations between signals from taps located in different places may allow the convection of coherent flow structures to be detected. The paper presents a preliminary attempt to analyse pressure time histories at four different locations (Fig. 8). For the first time it is shown that the position of the trailing edge separation point is not steady but oscillates with a frequency corresponding to. Future work in this area is expected to include the use of shorter pressure tubes, or pressure transducers embedded into the sail structure, as is commonly done in experimental aeronautical research investigations. In conclusion, the novel experimental methods discussed in the paper are very promising although further enhancements are needed to increase their accuracy. Firstly, the flying shape must be controlled more precisely and, secondly, it is desirable that the blockage due to the bundle of tubes at the trailing edge is decreased further. ACKNOWLEDGEMENTS The authors warmly acknowledge the help from the Centre for Advanced Composite Materials (CACM) at The University of Auckland to build the solid spinnaker model. The support from the YRU and especially David Le Pelley is gratefully acknowledged, as well as the help from research students Dario Motta, Francesca Tagliaferri and Novella Saccenti to carry out the tests. This research has been performed within the SAILING FLUIDS project, which is funded by the European Commission under the 7 th Framework Programme 125

134 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France through the Marie Curie Actions, People, International Research Staff Exchange Scheme. REFERENCES [1] Richards, P.J., Johnson, A. and Stanton A., 2001, America s Cup downwind sails - vertical wings or horizontal parachutes?, Journal of Wind Engineering and Industrial Aerodynamics, Vol. 89, Issues 14 15, pp [2] Le Pelley, D.J., Ekblom, P., Flay, R.G.J., 2002, Wind tunnel testing of downwind sails, In Proceedings of the 1st High Performance Yacht Design Conference, pp , Auckland, New Zealand. [3] Fossati, F., Muggiasca, S., Viola, I.M. and Zasso, A., 2006, Wind tunnel techniques for investigation and optimization of sailing yachts aerodynamics, In Proceedings of the 2nd High Performance Yacht Design Conference, Auckland, New Zealand. [4] Hansen, H., Richards, P.J. and Jackson, P.S., 2006, An investigation of aerodynamic force modelling for yacht sails using wind tunnel techniques, In Proceedings of the 2nd High Performance Yacht Design Conference, Auckland, New Zealand. [5] Fossati, F., Muggiasca, S. and Viola, I.M., 2006, An investigation of aerodynamic force modelling for IMS Rule using wind tunnel techniques, In Proceedings of the 19th International HISWA Symposium on Yacht Design and Yacht Construction, Amsterdam, The Netherlands. [11] Viola, I.M., Flay, R.G.J., 2011, Sail pressures from full-scale, wind-tunnel and numerical investigations, Ocean Engineering, 38(16), [12] Viola, I.M., Flay, R.G.J., 2010, Pressure distribution on modern asymmetric spinnakers, Transactions of the Royal Institution of Naval Architects Part B: International Journal of Small Craft Technology, 1512(1), [13] Brett, J.S, 2012, Downwind Sail Aerodynamics: A pressure distribution and an Aerodynamic Forces database for the validation of numerical code, Master Research in Naval Environment, Research Institute of the Naval Academy, IRENav, Arts et Métiers ParisTech, France. Research project undertaken at the Yacht Research Unit, University of Auckland. [14] Viola, I.M., Bot, P., Riotte, M., 2013, Upwind Sail Aerodynamics: a RANS Numerical Investigation Validated with Wind Tunnel Pressure Measurements, International Journal of Heat and Fluid Flow, Vol. 39, pp , DOI: /j.ijheatfluidflow [15] Crompton, M.J., Barret, R.V., 2000, Investigation of the separation bubble formed behind the sharp leading edge of a flat plate at incidence. In Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 214(3), [16] Viola, I.M., Bartesaghi, S, Van-Renterghem, T., Ponzini, R., 2013, Delayed Detached Eddy Simulation of sailing yacht sails. In Proceedings of the 3 rd International Conference on Innovation in High Performance Sailing Yachts, INNOV SAIL, Lorient, France (present volume). [6] Flay, R.G.J., Jackson, P.S., 1992, Flow simulations for wind-tunnel studies of sail aerodynamics. Journal of Wind Engineering and Industrial Aerodynamics, Vol. 44, Issues 1 3, pp [7] Flay R.G.J., 1996, A twisted flow wind tunnel for testing yacht sails, Journal of Wind Engineering and Industrial Aerodynamics, Volume 63, Number 1, pp [8] Le Pelley, D.J., Benzie, D., Flay, R.G.J., 2001, Correct simulation of the profiles of apparent wind speed and twist for testing yacht sails, In Proceedings of the 9 th Australasian Wind Engineering Workshop (AWES). Townsville, Australia. [9] Richard, P., Lasher, W., 2008, Wind Tunnel and CFD Modelling of Pressures on Downwind Sails, In Proceedings of Bluff Bodies Aerodynamics & Applications, Milano, Italy. [10] Viola, I.M., Flay, R.G.J. (2009). Force and pressure investigation of modern asymmetric spinnakers, Transactions of the Royal Institution of Naval Architects Part B: International Journal of Small Craft Technology, 151(2), AUTHORS BIOGRAPHY Patrick Bot, PhD, is associate Professor of Fluid Mechanics at the Naval Academy Research Institute in fluid mechanics and energy engineering. His research interests include yacht dynamics, sail aerodynamics and fluid structure interaction. His previous experience includes hydrodynamic instabilities and transition to turbulence. Ignazio Maria Viola, PhD, is Lecturer in Naval Architecture at the School of Marine Science and Technology of Newcastle University, UK. He has a background in applied fluid dynamics and a specialist expertise in yacht engineering. His previous experience includes a Post Doctoral Fellowship at the Yacht Research Unit (University of Auckland), which formerly was the Scientific Advisor of the America s Cup team Emirates Team New Zealand, and a PhD (Politecnico di Milano) on experimental and numerical modelling of the aerodynamics of sailing yachts, sponsored by the America s Cup team Luna Rossa. Ignazio is Coordinator of the SAILING FLUIDS project.

135 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France Richard G.J. Flay, PhD, is Professor of Mechanical Engineering and Director of the Yacht Research Unit in the Department of Mechanical Engineering at the University of Auckland. He has had a longstanding research interest in the wind and sailing. His PhD degree was awarded for a study of wind structure using field measurements. His Postdoctoral research as a National Research Council Visiting Fellow in Canada was focused on wind tunnel studies in a boundary layer wind tunnel. He then spent four years as an Aerodynamic Design Engineer in an Engineering Consultancy in Toronto where he worked on the design of several wind tunnels and environmental test facilities. Since 1984 he has worked at the University of Auckland, and in 1994 he designed the World s first Twisted Flow Wind Tunnel. He has been a member of the YRU since its inception in

136

137 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France DELAYED DETACHED EDDY SIMULATION OF SAILING YACHT SAILS IM Viola, Yacht and Superyacht Research Group, School of Marine Science and Technology, Newcastle University, UK, (corresponding author) S Bartesaghi, Mechanical Department, Politecnico di Milano, Italy. T Van-Renterghem, Yacht and Superyacht Research Group, School of Marine Science and Technology, Newcastle University, UK. R Ponzini, CINECA, SuperComputing Applications and Innovation Department (SCAI), Italy. Wind tunnel experiments on a 1:15 th model-scale AC33-class yacht were modelled with Reynoldsaverage Navier-Stokes simulations (RANS) and Delayed Detached Eddy Simulations (DDES). Numerical simulations were performed with two different grids, where the node distance was halved from the coarser to the finer grid, and with three different time steps, where the smallest one was 1/4 th of the largest one. High-grid-resolution DDES allowed drawing the topology of the turbulent structures in the sail wake and discovering new flow features, which were hardly detectable with lowgrid-resolution DDES and, particularly, with RANS. It was found that the span-wise twist of the spinnaker leads to a mid-span helicoidal vortex, which has a horizontal axis almost parallel to the apparent wind and rotates in the same direction of the tip vortex generated from the head of the sail. Vortical span-wise tubes are released from the trailing edges of the mainsail and the spinnaker and, while convecting downstream, these structures roll around the tip and mid-span vortices of the spinnaker. Vortical tubes are also detached intermittently from the sails feet and these break down into smaller and smaller structures while convecting downstream. 1 INTRODUCTION Sailing yacht sails are efficient aerodynamic fins, which operate at low Reynolds numbers (Re). In particular, fullscale sails operates at Re of the order of (based on the aerodynamic sail chords) but sails are commonly tested and optimised at Re of the order of using model-scale wind tunnel tests. Traditionally, low-re aerodynamics ( has received somewhat less attention than high-speed aerodynamics (, though today there is an unmet need for fluid-dynamic efficiency in emerging applications where fins operate at low Re, such as autonomous underwater vehicles, micro aerial vehicles and small renewable energy converters. These applications could benefit from the research on sail aerodynamics and, particularly, on the analysis of some characteristic flow features of highly cambered twisted sails leading to good aerodynamic performance. On conventional thick airfoils at high Re the laminar-toturbulent transition occurs near the leading edge. Therefore, the boundary layer is mostly turbulent allowing large entraining momentum from the outer layer and making it able to tolerate adverse pressure gradients due to the airfoil curvature. Conversely, on the suction side of airfoils at Re between roughly and [1], a laminar boundary layer develops from the leading edge until separation occurs due to the adverse pressure gradient; then the unstable separated shear layer triggers the laminar-to-turbulent transition and reattachment occurs, leading to the laminar separation bubble and to a turbulent boundary layer downstream the bubble. At low Re, the performance of conventional thick airfoils designed for high Re is poor and thinner airfoils may allow much higher maximum lift and lift/drag ratio than thick airfoils [2,3]. Sails are very thin airfoils and the flow separates at the leading edge due to the sharpness of the edge, leading to a high suction peak [4] (Figure 1). The laminar-to-turbulent transition occurs in the separated shear layer, leading to reattachment and then to the development of a turbulent boundary layer. Further downstream along the chord, the sail curvature leads to a second suction peak. Highly cambered sails show significant trailing edge separation due to the adverse pressure gradient correlated with the sail curvature, but allow a very high driving force. The sharp leading edge and the second suction peak due to the sail curvature are typical of sails and unusual on airfoils. Figure 1 shows the typical flow and pressure fields when the complementary angle between the true wind velocity and the boat velocity is larger than, leading the boat to experience a wind coming between roughly and from her bow. In these conditions, modern sailing yachts use a highly cambered foresail, namely the spinnaker, and flatter and smaller aft sail, namely the mainsail. Spinnaker (foresail) and mainsail (aftsail) can be compared with the two superimposed wings used by biplanes. The chord and span of the fins of an aircraft and a yacht are of the same order of magnitude but the thickness and the Re of yacht fins are more than one order of magnitude smaller than those of aircrafts. Differently from aircraft wings, sails are significantly twisted and cambered both chord-wise and span-wise. For instance, the spinnaker analysed in this paper has an aspect ratio (span/mean-chord) of, a span-wise twist angle (horizontal angle between the lowest and highest chords) of more than, TH 28 TH June, 2013

138 The Third International Conference on Innovation in High Performance Sailingg Yachts, Lorient, France a chord-wise camber of of the chord, and a spantwist wise camber of of the span. The sail moderates the increase of angle of attack due to thee twist of the onset flow experienced by a sailing yacht, namely the apparent wind. In fact, the apparent wind is the vectorial difference between the true wind and thee boat velocity, and it increases and rotates from thee bow towards the stern of the boat with thee height (Figure 2). The bi-cambered (chord-wise and span-wise) twisted geometry of the sails leads to a characteristic wake Cp 0 +1 Pressure AsymmetricSpinn coefficient naker Leadingedge bubble WIND Trailingedge separa on Spinnaker Leadingedge bubble Mast Mainsail Figure 1: Typical flow and pressure distributions onn sails never beer attempted. a However, forces [5-9] and pressures [10-16] were measured in full scale, though the non-controllable and unmeasured atmospheric boundary layer profile limited the measurement accuracy. Model scale sails are normally tested in wind tunnels, where flexible sails with w low thickness/chord ratio can be used (for instance,, [17]). However, PIV and LDV measurements are difficult in wind tunnels due to the need for inseminations and only unpublished smoke observations were performed. Flow visualisation is easier in water tunnels, where unfortunately thin models are used with difficulty due to the very highh hydrodynamic loads. A sensible way to study sail wakes is using numerical simulations. Potential flow codes cannot model viscous effects, which are dominant in the wake and, therefore, Navier-Stokes solvers must be used. The relatively high Re and the complex 3D geometry make Direct Numerical Simulations (DNS) unfeasible and turbulence must be modelled with turbulence models or subgrid models. Reynolds-averaged Navier-Stokes simulations (RANS) have been performed since 1996 on downwind sails [18] and, since then the agreement between numerical and experimental forces has increased in parallel withh the growth of computational resources. The number of grid cells increased by about one order of magnitude every three years: Hedges et al. [18] used a number of gridd cells of thee order 10 3, three years later Miyata and Lee [19] used a number of grid cells of the order 10 4, and ten t years laterr Viola [20] used a number of grid cells of the order Richards and Lasher [21] and Viola and Flay [15] compared pressure distributions computed with RANS to those measured in i wind tunnels. They found good numerical-experimental agreement on the mid sections of the sails but larger differences on the highest sail sections, wheree the suction peak near the leading edge was under-predicted by CFD. As far as known by the authors, the present paper presents the first published investigation on sail aerodynamics performed with Detached Eddy Simulations (DES). However, it must be noted that Braun and Imas [22] statedd that DES was used in the design process of an ACC-V5-class though no results were presented; and Wright et al. [23][ presentedd few resultss achieved with DES but no details were provided to verify the validity of yacht for the 32 nd America s Cup, the simulation. In the present paper, the wind tunnel test on a spinnaker with both RANS and DES, using different grids and time steps, are presented. Figure 2: Twist of the apparent wind experiencedd by a sailing yacht The study of sails wake can be performed experimentally or numerically. Full-scale experiments are very complicated for wake measurements andd have The paper is structured as follows: in the Method section, the experimental tests are introduced and the numerical simulations modelling the experiments are described, ncluding details of the equations solved, the boundary conditions, the grids and the time steps tested, and the hardware usedd to run the simulations. The procedure used to assess the numerical uncertainty in the computation off forces and pressures is also presented. In the Results section, the general flow field computed with the numerical simulations s is s presented, and details of the TH 282 TH June, 2013

139 The Third International Conference on Innovation in High Performance Sailingg Yachts, Lorient, France near-wall region and of the sail wake are discussed. Forces and pressures computed with the different simulationss are compared with the experimental data. In the Conclusions section, the key findings of the research are summarised. 2 METHOD 2.1 WIND TUNNEL TESTS WITH FLEXIBLE SAILS A 1:15 th model-scale AC33-class yacht equippedd with flexible sails was tested at the Auckland Universityy wind tunnel. Figure 3 (left) shows the model during thee wind tunnel test. The tunnel has a 3.5-m-high and 7-m-wide open jet section, wheree the floor and the roof extend downstream for 5.1m and 4.8m, respectively. The 2.3-m- 2.7m high model was placed on the wind tunnel floor att downstream from the open jet section. A flexible spinnaker and mainsail were mounted on a modell scale yacht, which included the hull and the t rigging, at apparent wind angle and heel angle. Viola andd Flay reported the force [24] and pressure [25][ measurements. Forces were measured using a 6-component balance placed underneath the wind tunnel floor, and sail surface pressures were measured using pressure taps attached to the sails. Pressure taps were 20-mm long, 10-mmm wide and 4-mm height, attached to the sail on the opposite side to that under investigation, and a 1-mm-diameterr hole was made in the sail to allow pressure transmission to the tap. PVC tubes with a 1-mm internal diameter, suspended from the sail to the boatt mast, carried the pressures from the tap to the pressure transducers located on the boat deck. Pressure taps were placed on 5 horizontal sections at heights of 1/8, 1/4, 1/2, 3/4 and 7/8 of the mitre, which is the line on the sail surface equally far from the leech and the luff. The far-field static pressure was computed by the difference of thee total and dynamic pressures measured by a Pitot static probe located approximately 10 m upstream at the top-mast height. The pressure transducers measured the difference between the sail surface pressure and at 100 Hz. Pressure coefficients,, were computed dividing this difference by the dynamic pressure,, which was time- averaged over a period of 70 s and was about 7.5 Pa. Forces were measured m at 200 Hz and averaged over the same period of 70 s. Uncertainties in the measurement of were estimated to be about and for the leewardd and windward sides, respectively. Several photographs were taken during the tests and were used to detect the flying shapes of the two flexible sails in order to make a mathematical model, whichh was used to perform CFD simulations and, successively, to build rigid sails for further tests WIND TUNNEL TESTS WITH RIGID SAILS The mathematical model of the flying shapes was used to build a CAD/CAM woodenn mould, which, in turn, was used to build rigid r sails with fibreglass and a a sandwich structure [26]. The sails were less than 4-mm thick, mainly due to the t thickness of the core, with the external fibreglass layer of negligible thickness. The thickness/chordd ratio was less than 1%.. The core was made of extruded polypropylene, resulting in parallel square tubes. These T were used to carry the pressure from 1-mm-diameterr holes on the sail surfacee to the trailing edge, where 1-mm internal-diameterr PVC tubes, gathered together along the trailing edge towards the sail foot, carried thet pressure to the pressure transducers located on thee boat deck. Figure 3 (right) shows the model during the wind tunnel tests. The same testing setup as the one adopted with flexible sails was used: pressures were measured at the same sail sections, forces and pressuress were measured with the same instrumentation, at the same frequency and averaged over 70 seconds. Uncertainties in the measurement of were estimated to be the same as for flexible sails. Figure 3: Wind tunnel tests performed with flexible sails (left) and rigid sails (right) TH 282 TH June, 2013

140 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France 2.3 COMPUTATIONAL DOMAIN AND BOUNDARY CONDITIONS The detected flying shapes of the sails were used to perform the numerical simulations. Sails, mast, boom (horizontal mast at the mainsail foot) and hull were modelled with non-slip condition. A prismatic computational domain 3-m high, 6.2-m wide and 18.4-m long was used to model the wind tunnel (Figure 4). The domain length is equivalent to eight times the boat height m). A smaller test section than the physical one was modelled (3x6.2 m instead of 3.5x7 m) in order to avoid solving the sidewall and roof boundary layers. Slip condition was used on these boundaries from the inlet to the open jet section, while pressure outlet was used downstream from the open jet section. The experimental blockage is almost negligible and mostly due to the wind tunnel sidewalls which decrease the deflection of the streamlines upstream the model. This effect is taken into account using slip conditions, though it has an almost negligible effect being the open jet section wider than and more than h upstream from the model. The onset vertical velocity profile measured in the wind tunnel experiment was used as inlet condition. The wind direction was uniform on the test section (un-twisted flow), while the wind speed presented a boundary layer profile on the floor. Therefore, non-slip condition was used on the floor boundary, which extend downstream from the model. The mean velocity of the onset flow was, the turbulent intensity was set to, as measured in the wind tunnel, while the turbulent length scale was assumed to be. The computational domain extended downstream further than the end of the physical roof and floor, therefore pressure outlet conditions were used on these boundaries. 2.4 GRIDS Two non-structured hexahedra grids were build with Pointwise version R1. The coarse grid was made of four million cells (4M). Figures 5 shows the surface grid on the spinnaker (left) and a grid section at 1/2 of the spinnaker s mitre height (right). The 4M-cell grid allowed modelling the spinnaker with about 60 cells chord-wise and about 64 cells span-wise, with y + ranging from 0.01 to 10. A finer grid was achieved using the hanging node function of Ansys Fluent version , which split every cell in eight cells leading to a 32- million-cells grid (32M). Table 1 shows the maximum and minimum y + computed by the different simulations on the suction side of the spinnaker. 2.5 REYNOLDS-AVERAGED NAVIER-STOKES The incompressible steady RANS equations for Newtonian fluids were solved with the finite-volume pressure-based solver of Ansys Fluent version The Spalart-Allmaras turbulence model was used to model the turbulence. This one-equation model was preferred to more accurate two-equations models in order to decrease the computational time. The production term of the modified turbulent viscosity was computed with a vorticity-based approach, and at the inlet it was set as follows:. A SIMPLEC scheme was used to couple velocity and pressure. A secondorder- accurate centred discretization algorithm was used for the pressure, while second-order-accurate upwind algorithms were used for momentum and modified turbulent viscosity. Figure 4: Computational domain and boundary conditions. Table 1: y + for the two grids computed with RANS and DDES Min Max 4M RANS M DDES M DDES DELAYED DETACHED EDDY SIMULATION The transient Navier-Stokes equations were solved with a DES approach. A Spalart-Allmaras turbulence model, with a vorticity-based production term, was used to model the turbulence in the RANS region. In order to preserve the RANS model throughout the whole boundary layer, the DES length scale was modified as suggested by Spalart et al. [27] for the Delayed Detached Eddy Simulation approach. A SIMPLEC scheme was used to couple velocity and pressure. Second order accuracy discretization algorithm was used for the pressure, while second order central difference algorithms were used for momentum and modified turbulent viscosity. The fluctuating velocity components at the inlet were computed by synthesizing a divergencefree velocity-vector field from the summation of 100 Fourier harmonics. More details on the numerics can be found in the User Manual of Ansys Fluent [28]. 2.7 TEST MATRIX A RANS simulation was performed on the 4M-cell grid, while DDES simulations were performed on both the 4M-cell grid and the 32M-cell grid. On the coarser grid, TH 28 TH June, 2013

141 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France three different time steps were tested, s, s and s, in order to estimate the uncertainty due to the time discretisation, while the maximum number of iterations per time step was kept constant to 20, allowing convergence at each time step. All these time steps allowed Courant numbers in the sails wake lower than one. For instance, with a time step of s and the 4Mcells grid, the Courant number ranged from to. On the 32M-cell grid, only the intermediate time step (0.001 s) was used with 20 iterations per time step. Table 2 summarises the numerical simulations performed. All the numerical simulations ran until convergence was achieved for the aerodynamic forces. In particular, lift, drag and heeling moment were monitored. Forces, pressure and velocity fields computed with DDES were averaged over a period of 10 s. For example, Figure 6 (left) shows the convergence of the drag coefficient of the two sails (hull and rigging excluded) for the DDES simulations performed with high grid resolution. Table 2: Test matrix of the numerical simulations Space Time Method discretisation discretisation RANS 4M-cell grid Steady DDES 4M-cell grid s DDES 4M-cell grid s DDES 4M-cell grid s DDES 32M-cell grid s 2.8 HARDWARE All simulations were performed in double precision on a 64-bit Hewlett-Packard Linux cluster made of 336 nodes HP 2x220 2xIntel Exa-cores GHz 24Gb RAM per node interconnected with Infiniband QDR and a node HP DL980 8 CPU Intel E GB RAM for postprocessing and results visualization. In order to take advantage of the High Performance Computing system, a preliminary scalability test using the smallest grid was performed. According to the scalability results the calculations on the different grid sizes have been performed using up to 256 computational cores. 2.9 VERIFICATION Different time and grid resolutions allowed estimating the numerical uncertainty for forces and pressures with DDES. This estimate is only approximate; in fact DDES does not necessarily show asymptotic convergence with increasing resolution [29]. The uncertainty at 95% confidence level was computed following the guidelines of Viola et al. [30]. For example, the uncertainty due to the time step for the C D were estimated using Equations (1): where and are the maximum and the minimum C D, respectively, between those computed with time steps s, s and s. The uncertainty due to the grid for the C D were estimated using Equations (2): where and are the maximum and the minimum C D, respectively, between those computed with the 4M-cells grid and the 32M-cells grid, respectively. The convergence uncertainty was estimated as two times the standard deviation of the time history of each quantity. For instance, Figure 6 (right) shows the mean (dotted line) and the uncertainty (error bar) of the drag coefficient: The convergence uncertainties for C D and C L were and, respectively. The numerical uncertainty was then computed as the L2- norm of the uncertainties due to the time step and due to the grid, plus the convergence uncertainty, which is not under the square root because it is not independent from the other two uncertainties (Equation 3): The resulting uncertainties for the aerodynamic forces were and ; while the largest numerical uncertainty for the pressure coefficient was TH 28 TH June, 2013

142 The Third International Conference on Innovation in High Performance Sailingg Yachts, Lorient, France Figure 5: Side view of the spinnaker s grid and plann view on a section at the spinnaker s midd height. Figure 6: Convergence of 3. RESULTS for the DDES 32M simulation (left) and examplee of convergence uncertainty (right) 3..1 GENERAL FLOW FIELD The DES approach allowed the identification off flow structures that have never been solved with a RANS approach so far. The key findings of this t research are the identification of these structures, and the t analysis of their effect on the sails mean pressures. In the nextt sub- flow field, then we show where the flow separates and sections, firstly we provide an overview of the general reattaches along the spinnaker surface, and then we discuss the different flow structures in the sail wake. We then discuss similarities and differences between the forces and the pressure distributions computedd with RANS, DES and measured experimentally. Figure 7 shows the general flow field around the yacht computed withh RANS usingg the 4M-celll grid. Pathlines are coloured byy flow velocity. The two sails behave like tandem wings where the spinnaker is larger and more cambered than the mainsail. The grey scale s shows the pressure difference across the sail surface. The larger delta pressures on the spinnaker than on the t mainsail are due to the favourable upwash of the mainsail, while the mainsail experiences the unfavourable downwash of the spinnaker. The flow is attached on the leeward (suction) side of the spinnaker near the leading edge, while near the trailing TH 282 TH June, 2013

143 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France edge separation occurs. Streamlines from the leading edge converge towards two vortical structures: the tip vortex at the head of the sails and a parallel vortex at mid-span height. As far as is known by the present authors, this mid-span vortex, which will be discussed in sub-sections, has never been identified before. It is due to the span-wise camber, which leads to convergence of streamlines toward mid-span. Most of the separated flow, downstream of the trailing edge separation, is convected into this vortex. On the windward (pressure) side, the flow is attached and the streamlines, which are not showed in Figure 7, are slightly deflected upwards. This is due to the trailing edge being somewhat higher than the leading edge. In fact, the lower corner of the trailing edge, namely the clew (Figure 5), is higher than the lower corner of the leading edge, namely the tack. Only those streamlines which are near the sail foot are attracted by the suction on the leeward side and are thus deflected downward convecting into the separated flow region downstream the sail foot. 3.2 NEAR-WALL REGION Figure 8 shows skin friction lines on the leeward surface of the spinnaker computed with the 4M-cells-grid RANS (left), the 4M-cells-grid DDES (centre), and the 32Mcells-grid DDES (right). Results for the two DDES simulations are achieved with a time step of s and we showed the instantaneous solution at 30 s. Mean skin friction lines for DDES were not computed within the timeframe of this research project. Representative skin friction lines, highlighted with a solid red line, show that the flow is mainly attached in the region near the leading edge, while trailing edge separation occurs (dash-dotted line) somewhere on the second half of the chord. As a reference, several fractions of the spinnaker mitre (the line equidistant from the leading and trailing edge) are showed on the right-end side of Figure 8. Between ½ and ¾ of the mitre, the flow is mostly horizontal before trailing edge separation occurs. Conversely, below ½ of the mitre, the attached boundary layer is deflected upwards. In the separated region downstream of the trailing edge separation, the flow from the lower region moves upwards and converges towards the trailing edge separation line (dash-dotted line) between ½ and ¾ of the mitre. It is interesting to note that the flow field near the spinnaker s clew is computed differently with low and high-grid resolution. Only DDES with high grid resolution predicts a clear trailing-edge separation from ¾ of the mitre to the sail foot, while RANS and DDES computed with low grid resolution do not show a continuous trailing-edge separation line. Near the sail foot, the flow from the leading edge is deflected downwards due to the low pressure associated with the highly curved streamlines coming from the windward side and rolling over the sail foot. Near the leading edge, a laminar-separation bubble occurs. In sail aerodynamics the separation is associated with the sharp leading edge and it is continuous along all the leading edge from the head to the foot. In conventional wings, such as those used in aeronautics, the laminar separation bubble occurs only in the middle of the wing and not near the root and the tip. For this reason it is called laminar-separation bubble. Therefore, in sail aerodynamics, it may be more appropriate to use laminar-separation tube. The laminar-separation tube (LST) is smaller near the sail foot and becomes progressively larger towards the sail s head. The flow within the LST has a strong vertical component, as observed also by Viola et al [15], transferring kinetic energy from the lower sections to the tip vortex. The 32M-DDES results are in very good agreement with the visual observations performed in the wind tunnel with rigid sails. In particular, the position of separation and reattachment lines were qualitatively confirmed using a stick with a wool tail. However, the vertical flow component of the flow in the region around mid-chord at 1 / 8 of the mitre height seemed over predicted. 3.3 WAKE Figure 9 shows iso-surfaces of Q-criterion [31] equal to 500. The higher the Q-criterion, the more the flow rotation dominates the strain and the shear of the flow, therefore it can be interpreted as an index of the coherency of the flow structure. Iso-surfaces are coloured by the sign of the helicity, red being positive and blue negative. Helicity is computed with reference to the right-handed (positive) Cartesian coordinate system, where the x, y, z axes are the longitudinal, transverse and vertical axes of the wind tunnel, positive towards the inlet, towards leeward and upwards, respectively. On the left in Figure 9 the results for the 4M-cell grid solved with a RANS approach are presented. The leeward side of the spinnaker is mostly covered by an iso-surface with negative helicity. The negative helicity is due to the negative span-wise vorticity of the boundary layer. Near the trailing edge, separation occurs leading to less coherent flow structures and lower values of the Q- criterion. The tip vortex from the spinnaker s head is the larger visible flow structure. It convects along an axis which is almost aligned with the wind direction. A similar vortex develops from the spinnaker s clew (lower corner of the trailing edge), and rotates in the opposite direction than the head vortex. Interestingly, the midspan vortex is not visible, meaning that its coherency is weaker than those of the visualised structures. In the centre of Figure 9, the same grid is solved with a DDES approach. Despite the low grid resolution (4Mcells), LES allows solving these flow structures with a much greater extent than RANS. In particular, we found that the tip vortex generated from the head of the TH 28 TH June, 2013

144 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France mainsail rolls around the spinnaker s tip vortex. Also, small flow structures, which become more visible with the 32M-cells-grid DDES (right in Figure 9), appear near the sail foot. These are chord-wise-stretched vortices generated from the spinnaker s foot and convected downstream intermittently, breaking down into smaller and smaller structures. Span-wise-stretched vortices are generated from the trailing edge with a significantly lower frequency than those from the sail foot. The few periods computed with the simulations did not allowed an accurate measurement of these frequencies. Decreasing the Q-criterion from 500 to 100, it is possible to see that these vortices do not break down as quickly as those from the foot but, conversely, are stretched between the tip vortex and the mid-span vortex. Figure 10 shows the same comparison between different simulations as Figure 9 but with a different prospective view and decreasing the Q-criterion to 100. In order to allow the spinnaker to be visible, the iso-surface of Q-criterion is hidden in a near-wall region. While the mid-span vortex is hardly visible for the RANS simulation, it appears clearly in the two DDES simulations. In particular, with low grid resolution (centre in Figure 10), the mid-span vortex is showed by a continuous vortical tube while its complicated structure is revealed using higher grid resolution. Figure 11 shows four views of the Q-criterion isosurfaces computed with the 32M-cells-grid DDES. In the four different views, only the flow structures upstream of section A, B, C and D (Figure 10), respectively, are shown. This sequence allows the visualisation of the correlation between the various flow structures in the sail wake. The vertically stretched trailing edge vortex rolls around the tip and the mid-span vortices, which both have horizontal axes and rotate clock-wise. Therefore, the trailing edge vortex, which is a tube parallel to the trailing edge when detached form the sail, assumes an S shape while convecting downstream. The S shape is schematically showed with a solid yellow line in Figure 12 (right), while dotted lines show the two axes of the tip and mid-span vortices. The weaker trailing edge vortex of the mainsail also rolls around the tip and mid-span vortices, but due to its windward position with respect to the mid-span vortex, it is broken down into two vortices schematically showed by two white solid lines in Figure 12 (right). Figure 12 shows the differences between 4M-RANS, 4M-DDES and 32M-DDES in modelling the evolution of the spinnaker and mainsail trailing edge vortices. In particular, the same view as Figure 11(C) is used in Figure 12. The axes of the tip and mid-span vortices computed with high grid resolution are superimposed for comparison on the low grid-resolution RANS and DES, revealing that the lower grid resolution leads also to different directions of the axes. Videos of the simulations, which are available on the webpage of the first author [ show that the directions of these axes are stationary but different for the two DDES simulations. High Vel High p Low Vel Low p Figure 7: Pathlines computed with RANS on the 4M-cell grid TH 28 TH June, 2013

145 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France 7/8 3/4 1/2 1/4 1/8 4M RANS 4M DDES 32M DDES Figure 8: Skin friction lines on the leeward side of the spinnaker computed by RANS and DDES with the 4M-cell and the 32M-cell grids. 4M RANS 4M DDES 32M DDES Figure 9: Iso-surfaces of Q-criterion 500 coloured by helicity computed by RANS and DDES with the 4M-cell and the 32M-cell grids C C D C B A 4M RANS 4M DDES 32M DDES Figure 10: Iso-surfaces of Q-criterion 100 coloured by helicity computed by RANS and DDES with the 4M-cell and the 32M-cell grids TH 28 TH June, 2013

146 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France A B C D 32M DDES 32M DDES 32M DDES 32M DDES Figure 11: Iso-surfaces of Q-criterion 100 coloured by helicity computed by DDES with the 32M-cell grid viewed from four different positions downstream the yacht model. C C C 4M RANS 4M DDES 32M DDES Figure 12: Iso-surfaces of Q-criterion 100 coloured by helicity computed by RANS and DDES with the 4M-cell and the 32M-cell grids viewed from position C. 3.4 FORCES The forces measured with the two experiments showed significant differences and the numerical results of the different simulations are mostly in between the experimental ranges. Figure 13 show the drag and lift coefficients (C D and C L, respectively) experimentally measured and numerically computed. Coefficients are defined as the total aerodynamic force acting on the sails, rigging and hull, divided by the far field dynamic pressure and the sail surface. The experimental C D ranges between 0.52 for the rigid sails to 0.64 for the flexible sails, while the C D computed with the different DDES simulations ranges between 0.52 and Similarly, experimental C L ranges between 1.31 for rigid sails to 1.51 for flexible sails, while C L computed with the different DDES simulations ranges between 1.43 and C D and C L computed with RANS show the maximum differences with the experimental data. In particular, while C D is between the maximum and minimum experimental C D, while C L is 1% higher than the largest experimental C L (flexible sails). C D and C L computed with DDES are lower than those computed with RANS, though their trends are to increase with the time and the space resolution. However, different resolutions lead to small differences. In particular, differences are smaller than 1% and 3% for C D and C L, respectively. Interestingly, RANS and DDES with the same grid resolution show larger differences than two DDES simulations where the grid resolution is doubled. Figure 14 shows the breakdown of the aerodynamic coefficients for the spinnaker, the mainsail and the two sails combined but without hull and rigging. For the three cases, the coefficients were computed using only the sail area of the spinnaker, mainsail and the two sails together, respectively. These broken-down coefficients, which are achieved with difficulty with experimental tests, show that the spinnaker is significantly more efficient than the mainsail, having higher C L and lower C D, despite its aspect ratio is about half the one of the mainsail. This is largely due to the upwash and downwash experienced by spinnaker and mainsail, respectively TH 28 TH June, 2013

147 The Third International Conference on Innovation in High Performance Sailingg Yachts, Lorient, France Figure 13: C D (left) and C L (right) for the whole model computed with the numerical simulations and measured with the two experimental tests. above the ideal one, a veryy sharp leading edge suction peak occurs, which w is clearly visible on the lowest sections of the sail. On the highest section of the sail, the angle of attack is higher, leading to a larger leading-edge suction peak but also to a wider pressure plateau near the trailing edge due d to trailing edge separation. On the highest sections, where thee LST fails to t reattach, the suction peak iss very close to the leading edge and does not show the t suction peak due to the sail curvature. Figure 14: C D and C L of the two sails computed by DDES with the 32M-celll grid PRESSURES Figure 15 shows the pressure distributions on five sail sections of the spinnaker: 7/8, 3/4, 1/2, 1/4 and 1/8 of the mitre respectively. The pressure coefficient is defined as, where is the pressures measured on the sail surface. on both the windward and leeward pressure sides are presented versus the non-dimensional chord-wise coordinate. On the left in Figure 15, computed with RANS, 4M-DDES and 32M-DDES are presented. The two DDES simulations are performed with a time step of s. Also, measured experimentally with both flexible and a rigid sails are presented for comparison. Error barss for the 32M-cells grid show the estimated numerical uncertainties. On the right in Figure 15, computed with 4M-DDESS and three different time stepss of s,, s and s, respectively, are presented. The pressure distributions show that sails operatee very close to the ideal angle of attack, meaning that thee flow at the leading edge is parallel to the local sail surface. In this condition, on the leeward sidee of the sail, the pressure decreases gradually from the leading edge to the point of maximum sail curvature. At angles a of attack just The larger differences between the numerical and experimental are near thee leading edgee on the highest section. In this region, the differences between numerical simulations performed with different grid and time-step resolutions showed large differences. Therefore, it seems that the spatial and time resolution used to t model the tip vortex is critical to the correct computation of the sail surface pressures. The different trends of on the 7/8 section are reflected on the 3/4 section, while differences are small on the t lowest sections. The computed base pressure of the pressure plateau near the trailing edge is also quite different from the one measured experimentally. Both the differences noted on the highest sections and those near the trailing edge suggest that flow separation was under-predicted by the numerical simulations. As a confirmation of the trends showed by the forces in Figure 13, computed with RANS and DDES show larger differences than computed with different resolutions. Particularly, larger differences occur near the head and foot of o the sail, while on the mid section of the spinnaker differences are smaller. On the lowest sections, RANS predicts a later trailing edge separation s than DDES and thus a larger suction peak correlated with the sail curvature. On the highest section, where the LST fails to reattach, the suctionn on the leeward side of the sail is quite sensitive to thee different time steps tested with DDES, leading to higher numerical uncertainty and thus to larger error bars. Using differentt time and grid resolutions, thee same pressure trend is computed near the trailing edge and on the windward side of the sail TH 282 TH June, 2013

148 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France The experimental tests presented in this paper are the first of their kind and the large differences between measured with flexible and rigid sails show that the level of accuracy of these tests is still quite poor. The differences between the two measurements are probably due to differences in the sail shapes used during the two experiments. In fact, on one hand the shape of flexible sails is measured with difficulty, and on the other hand rigid sails may experience deformations due to their own weight, being suspended only from the head and tack corners. The numerical simulations are based on the flexible-sail flying shapes, which were also used to build the mould for the rigid sails. Further investigations are in progress in order to establish if the main source of inaccuracy is the photogrammetric reconstruction of the flexible sails or the deformation of the rigid sails. In the first case, the geometry modelled numerically would be more similar to the rigid sails, while in the second case it would be more similar to the flexible sails. 4 CONCLUSIONS In the present work, wind tunnel experiments on a 1:15 th model-scale sailing yacht were modelled with RANS (Reynolds-average Navier-Stokes simulations) and DDES (Delayed Detached Eddy Simulations), allowing new insights on the aerodynamics of sails. In particular, sails are efficient aerodynamic fins, which operate at low Reynolds numbers. The tested configuration foresaw two sails in tandem where the spinnaker (foresail) had larger sail area, low aspect ratio and high camber, while the mainsail (aftsail) had smaller sail area, higher aspect ratio and less camber. Most of the aerodynamic load was carried by the spinnaker, which experienced the upwash of the mainsail. Experiments were performed with both flexible and rigid sails, and both global aerodynamic forces and pressure distributions on sails were measured. Numerical simulations were performed with two different grids, where the node distance was halved from the coarser to the finer grid, and with three different time steps, where the smallest one was 1/4 of the largest one. The high grid and space resolution allowed modelling the flow near the sails with high accuracy. An attached boundary layer was found on the windward side (pressure side) of the sails while the flow separates on the leeward side (suction side) along all the leading edge of the spinnaker. Laminar to turbulent transition occurs on the separated shear layer and the flow reattaches on most of the sail but not on the highest region, creating a span-wise-axis laminar separation tube. The reattached turbulent boundary layer grows along the sail chord for more than half chord, when trailing edge separation occurs. High-grid-resolution DDES allowed drawing the topology of the sail s wake and discovering new flow features, which were barely detectable with low-gridresolution DDES and, particularly, with RANS. A helicoidal tip vortex is generated from the head of the spinnaker and convects downstream in the direction of the far field velocity. The tip vortex from the head of the mainsail rolls around the former one. The span-wise twist of the spinnaker also leads to a mid-span helicoidal vortex having a horizontal axis and rotating in the same direction of the tip vortex. It should be noted that the mid-span vortex has never been reported by previous authors, and its role on the aerodynamic performance of the sail should be further explored. Vortical span-wise tubes are released from the trailing edges of the mainsail and the spinnaker and, while convecting downstream, these structures roll around the tip and mid-span vortices of the spinnaker. Vortical tubes are also detached intermittently from the sails feet and these break down into smaller and smaller structures while convecting downstream. The comparison between the different numerical models showed that DDES allow a step change in the understanding of the sails wake topology. Importantly, the more resolved sail wake led to differences on the pressure distributions on the sails and thus on the global aerodynamic performances. Forces and surface pressures computed with DDES were in better agreement with the experimental data than those computed with RANS, though significant differences between the measurements performed with flexible and rigid sails did not allow a proper verification of the numerical simulations. DDES with different time and space resolutions led to similar forces and pressure distributions, while RANS led to significantly different pressure distributions and, particularly to higher suction on the leeward side on the lowest sections of the spinnaker, leading to larger global aerodynamic forces. While the forces predicted by DDES were between the maximum and the minimum forces measured with flexible and rigid sails, RANS predicted a lift force 1% and 17% larger than the those measured with flexible and rigid sails, respectively. Therefore DDES seems to be able to predict sail performance more accurately than RANS. Forces and pressures were almost independent from the time and space resolutions tested in the present work. The largest differences were observed on the suction side of the spinnaker in the region of separated flow: on the highest sections near the leading edge and downstream from the trailing edge separation. 5 ACKNOWLEDGEMENTS This research was supported in part by CILEA Interuniversity Consortium (Italy), CFD Technologies (UK) and ANSYS (Italy), who kindly provided HPC resources, licences of Pointwise and Fluent, respectively TH 28 TH June, 2013

149 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France Model and grid-resolution effect C p -5 C p -5 Section 7/ Time step effect Section 7/ Section 3/ Section 3/ Section 1/ Section 1/ Section 1/ Section 1/ Section 1/8-2 Section 1/ x/c x/c Figure 15: C p versus x/c on five horizontal sail sections computed with different simulations and measured with the two experimental tests TH 28 TH June, 2013

150 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France 6 REFERENCES 1. Hain, R., Kahler, C.J., Radespiel, R., Dynamics of Laminar Separation Bubbles at low-reynolds-number Aerofoils, J. Fluid Mech., 630, Hoerner, S.F., Borst, H.V., Fluid-dynamic Lift. Information on Lift and its Derivatives, in air and in Water. Bakersfield, CA, Hoerner Fluid Dynamics. 3. Shyy, W., Lian, Y., Tang, J., Viieru, D., Liu, H., Aerodynamics of Low Reynolds Number Flyers, Cambridge University Press. ISBN: Viola, I.M., Flay, R.G.J., Sail Aerodynamics: Understanding Pressure Distributions on Upwind Sails, Experimental Thermal and Fluid Science, 35 (8), Milgram, J.H., Peters, D.B., Eckhouse, D.N., Modeling IACC Sail Forces by Combining Measurements with CFD, Proc. 11 th Chesapeake Sailing Yacht Symposium, January 29 th -30 th, Annapolis, MD, Masuyama, Y., Fukasawa, T., Full-Scale Measurements of Sail force and Validation of Numerical Calculation Method, Proc. 13 th Chesapeake Sailing Yacht Symposium, January 25 th, Annapolis, MD, Hochkirch, K., Brandt, H., Full-Scale Hydrodynamic Force Measurement on the Berlin Sailing Dynamometer, Proc. 14 th Chesapeake Sailing Yacht Symposium, January 30 th, Annapolis, MD, Masuyama, Y., Tahara, Y., Fukasawa, T., Maeda, N., Database of Sail Shapes versus Sail Performance and Validation of Numerical Calculations for the Upwind condition, J. Mar. Sci. Tech., 14, Hansen, H., Jackson, P.S., Hochkirch, K., Comparison of Wind Tunnel and Full-Scale Aerodynamic Sail Force Measurements, Int. J. of Small Craft Tech., RINA Trans., 145(B1), Warner, E.P., Ober, S., The aerodynamics of Yacht Sails, Proc. 3 rd General Meeting of the Society of Naval Architects and Marine Engineers, November 12 th - 13 th, New York, NY. 11. Flay, R.G.J., Millar, S., Experimental Consideration Concerning Measurements in Sails: Wind Tunnel and Full Scale, Proc. 2 nd High Performance Yacht Design Conference, February 14 th -16 th, Auckland, New Zealand. 12. Gaves, W., Barbera, T., Braun, J.B., Imas, L., Measurements and Simulation of Pressure Distribution on Full size scales, Proc. 3 rd High Performance Yacht Design Conference, December 2 nd -4 th, Auckland, New Zealand. 13. Puddu, P., Erriu, N., Nurzia, F., Pistidda, A., Mura, A., Full Scale Investigation of One-Design Class Catamaran Sails, Proc. 2 nd High Performance Yacht Design Conference, February 14 th -16 th, Auckland, New Zealand. 14. Viola, I.M., Flay, R.G.J., Fullscale Pressure Measurements on a Sparkman & Stephens 24-foot Sailing Yacht, Journal of Wind Engineering and Industrial Aerodynamics, 98, Viola, I.M., Flay, R.G.J., Sail Pressures from Full-Scale, Wind-Tunnel and Numerical Investigations, Ocean Engineering, 38, Viola, I.M., Flay, R.G.J., Sail Aerodynamics: On Water Pressure Measurements on a Downwind Sail, Journal of Ship Research (SNAME), 56 (4), Claughton, A.R., Wellicome, J.F., Shenoi, R.A., Sailing Yacht Design: Theory, 2 nd revised edition. University of Southampton, Computing Service, Southampton, UK. ISBN-10: Hedges, K.L., Richards, P.J., Mallison, G.D., Computer Modelling of Downwind Sails, J. of Wind Eng. and Ind. Aerody., 63, Miyata, H., Lee, Y.W., Application of CFD Simulation to the Design of Sails, J. Marine Science & Tech, 4, Viola, I.M., Downwind Sail Aerodynamics: a CFD Investigation with High Grid Resolution, Ocean Engineering, 36 (12-13), Richards, P., Lasher, W., Wind Tunnel and CFD Modelling of Pressures on Downwind Sails, Proc. BBAA VI International Colloquium on Bluff Bodies Aerodynamics and Applications, July 20 th -24 th, Milan, Italy. 22. Braun, J.B, Imas, L., High Fidelity CFD Simulations in Racing Yacht Aerodynamic Analysis, Proc. 3 rd High Performance Yacht Design Conference, December 2 nd -4 th, Auckland, New Zealand. 23. Wright, A.M., Claughton, A.R., Paton, J., Lewins, R., Off-Wind Sail Performance Prediction and Optimisation, Proc. 2 nd International Conference on Innovations in High Performance Sailing Yachts, June 30 th July 1 st, Lorient, France. 24. Viola I.M., Flay R.G.J., Force and Pressure Investigation of Modern Asymmetric Spinnakers, International Journal of Small Craft Technology, Trans TH 28 TH June, 2013

151 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France RINA, 151 (B2), 3140, 2009 (Discussion in Trans. RINA, 152 (B1), 51 53, 2010). 25. Viola I.M., Flay R.G.J., Pressure Distribution on Modern Asymmetric Spinnakers, International Journal of Small Craft Technology, Trans. RINA, 152 (B1) 4150, Bot, P., Viola, I.M., Flay, R.G.J., Wind-Tunnel Pressure Measurements on Model-Scale Rigid Downwind Sails. Proc. 3 rd International Conference on Innovations in High Performance Sailing Yachts, June 26 th 29 th, Lorient, France. 27. Spalart, P.R., Deck, S., Shur, M.L., Squires, K.D., Strelets, M.K., Travin, A., A new version of detached-eddy simulation, resistant to ambiguous grid densities. Theoretical and Computational Fluid Dynamics, 20, ANSYS FLUENT 12.0/12.1 Documentation, ANSYS Inc., Canonsburg, PA. 29. Spalart, P.R., Detached Eddy Simulation, Ann. Rev. Fluid Mech., 41, Viola I.M., Bot P., Riotte M., 2013 (in press). On the Uncertainty of CFD in Sail Aerodynamics, International Journal for Numerical Methods in Fluids. DOI: /fld Hunt, J.C.R., Wray, A.A., Moin, P., Eddies, stream, and convergence zones in turbulent flows. Center for Turbulence Research Report, CTR-S88, AUTHORS BIOGRAPHY Ignazio Maria Viola, PhD, is Lecturer in Naval Architecture at the School of Marine Science and Technology of Newcastle University, UK. He has a background in applied fluid dynamics and a specialist expertise in yacht engineering. His previous experience includes a Post Doctoral Fellowship at the Yacht Research Unit (University of Auckland), which was Scientific Advisor of the America s Cup team Emirates Team New Zealand, and a PhD (Politecnico di Milano) on experimental and numerical modelling of the aerodynamics of sailing yachts, sponsored by the America s Cup team Luna Rossa. Ignazio is Group Leader of the Yacht and Superyacht Research Group at Newcastle University, he serves in several international committees including the CFD Specialist Committee of the ITTC, he is Member of the Editorial Board of the Journal of Small Craft Technology, Reviewer for more than ten international journals and has written more than 50 peer-reviewed publications since Simone Bartesaghi, PhD, is a former PhD student of the Politecnico di Milano (Italy) who joined the Yacht and Superyacht Research Group for an internship of six months under the supervision of Dr Viola. Simone has a research interest on Computational Fluid Dynamics and, particularly, on its applications to yacht engineering. His previous experience includes Master in Yacht Design (110/110) at Politecnico di Milano and Università degli Studi di Genova. Other projects include consultancies for the small craft industry and yacht designers. In close collaboration with PortoRicerca snc, he was in the design team as CFD RANS analyst for the new design VOR70 s CAMPER/Emirates Team New Zealand Volvo Ocean Race campaign, 2 nd overall and 24h-speed record. Thomas Van-Renteghem is a former student of the engineering school Arts et Métiers Paris Tech, who joined the Yacht and Superyacht Research Group for an internship of nine months under the supervision of Dr Viola. Simone has a research interest on fluid dynamics and, particularly, on its applications to yacht engineering and aeronautics. Thomas is currently employed by Airbus (Toulouse). Raffaele Ponzini, PhD, is a member of the Super- Computing Applications and Innovation Department of CINECA, which is the largest Italian supercomputer centre. Raffaele, who was awarded a PhD in Bioengineering at the Politecnico di Milano in 2007, has a specialist expertise in High Performance Computing and Computational Fluid Dynamics. His research interests also include multiscale models in hemodynamics, and scientific visualization TH 28 TH June, 2013

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153 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France An Experimental Investigation of Asymmetric Spinnaker Aerodynamics Using Pressure and Sail Shape Measurements D. Motta, Yacht Research Unit, University of Auckland, New Zealand, R.G.J. Flay, Yacht Research Unit, University of Auckland, New Zealand, P.J. Richards, Yacht Research Unit, University of Auckland, New Zealand, D.J. Le Pelley, Yacht Research Unit, University of Auckland, New Zealand, A method for determining the aerodynamic forces and moments produced by sails at full-scale is investigated in this work. It combines simultaneous on-water pressure and sail shape measurements. The system has been given the acronym FEPV (Force Evaluation via Pressures and VSPARS). The experimental pressure and sail shape data were obtained from on-water tests conducted on a Stewart 34 Class yacht equipped with an asymmetric spinnaker. Data were recorded for a range of apparent wind angles in light winds, in order to check the reliability, accuracy and repeatability of the system. The flow around the sails is studied qualitatively by analysing the pressure distributions and sail shape. It was found that the results showed similar trends to the published literature, in spite of the low wind speeds during the tests. The accuracy of the system was investigated by wind tunnel tests, with particular reference to the determination of the entire sail shape from the stripe images and the VSPARS outputs, and was found to be relatively good, even for the foot shape which is outside the camera viewing region. NOMENCLATURE FEPV Force Evaluation via Pressures and VSPARS AWA Apparent wind angle (deg) CFx Driving Force Coefficient ( ) CMx Heeling Moment Coefficient ( ) Fx Driving Force (N) Mx Heeling Moment (N.m) TWS True Wind Speed (m/s) AWS Apparent Wind Speed (m/s) Vs Boat Speed (m/s) 1 INTRODUCTION Sail aerodynamics is commonly investigated by using wind tunnel testing [1, 2] and numerical methods [3-5]. However, both methods have various drawbacks [6]. Full-scale testing is usually required to validate results from these methods. Moreover, full-scale testing allows the investigation of yacht performance in real sailing conditions, quantification of the actual forces at work [7-9] and, for example, studies of the effects of the rigging on yacht performance [9, 10]. Several full-scale sail pressure measurements have been carried out in recent years [8, 11-14]. Difficulties in carrying out pressure measurements include the interference of the taps on the sails, the effects of long tubing to connect the taps to the transducers, the recording of an undisturbed static reference pressure, and zeroing of the pressure transducers [14, 15]. Capturing sail shape at full scale is now commonplace on many racing yachts. Many investigators have developed their own systems for determining sail shape [8, 9, 16]. Various full-scale techniques for the assessment of aerodynamic loads have been developed to date for sailing applications. The use of sail boat dynamometers [17-19] has been significant in improving performance prediction. Strain gauging the rigging and sails [9] has provided useful information on wind/rig/sail interaction. However, the determination of aerodynamic forces by combining pressure and sail shape measurements at fullscale enables useful insights into steady and unsteady sail aerodynamics to be obtained [7, 8, 10] by providing considerable detail on how and where the forces are developed. This paper reports on research on sail aerodynamics which is a continuation of previous work at the University of Auckland aimed at developing reliable and accurate methods for carrying out full-scale experiments on sailing yachts [7, 10, 20]. The system has been named FEPV (Force Evaluation via Pressures and VSPARS, where VSPARS stands for Visual Sail Position and Rig Shape ). The recording method combines pressure and sail shape measurements to obtain the aerodynamic forces and moments produced by sails at full scale. Le Pelley et al. [7] presented the results of the first fullscale test carried out using the FEPV system and a validation of the full system through wind tunnel testing for upwind sailing. Bergsma et al. [10, 20] describe an application of the FEPV system to upwind sailing, where the effects of shroud tension on upwind sailing performance were investigated. The present study extends the previous research from upwind to downwind sailing. The results from full scale testing in very light winds are presented, and an assessment of the accuracy of the sail shape interpolation procedure was carried out in the wind tunnel. On the day

154 of the scheduled testing the wind strength was lower than ideal, but testing could not be changed to another day due to the considerable setup and people commitments. The accuracy of the sail shape interpolation procedure was determined by comparing sail shape predictions from VSPARS data, with physical measurements. 2 COMPONENTS OF FEPV SYSTEM 2.1 VSPARS AND SAIL SHAPE MEASUREMENT The VSPARS system was developed in the Yacht Research Unit (YRU) at the University of Auckland by Le Pelley and Modral [16]. It is designed to capture sail shape both in the wind tunnel and whilst sailing. It uses deck-mounted cameras that look up at several coloured stripes on the sails. The camera lens distortion and the perspective effects are taken into account by the software, which then produces the global coordinates of each stripe relative to a fixed datum position on the yacht, as illustrated in figure 1. yacht racing syndicates to improve their knowledge of sail design. Therefore a self-imposed limit of 24 sensors for the mainsail and 44 for the gennaker was used. The mainsail is equipped with 3 rows of 8 sensors placed at ¼, ½ and ¾ sail heights, while the gennaker is equipped with 3 stripes of 12 sensors plus a 4 th stripe of 8 sensors placed at 7/8 of the height. The additional stripe at 7/8 height was used because previous studies in the wind tunnel have shown that the chord-wise pressure distribution on a gennaker can change dramatically between ¾ and 7/8 heights. Therefore it was felt that a simple interpolation up to the head using the ¾ stipe data would not be sufficiently accurate. The sampling frequency for the pressures was 60 Hz, but they were averaged over 30 measurements to filter out higher frequency fluctuations and resulted in an effective sampling rate of 2 Hz. Further details describing the pressure system can be found in Morris [21]. 2a 2b Figure 1: Global coordinates of VSPARS stripes for a mainsail and jib. 2.2 PRESSURE MEASUREMENT SYSTEM In order to avoid the issues associated with the use of long tubing and the recording of a reliable static reference pressure [15], in the present measurements the differential pressures across the sails were measured directly by using double-sided pressure sensors with transducers placed at the measuring locations as shown in figures 2a and 2b. The transducers were connected directly across the suction and pressure sides of the sail. In order to reduce the interference with the flow, sensors on the mainsail were covered with sail-cloth patches, and sensors on the gennaker were placed into pockets created by the overlap of adjacent sail panels. Although the use of a very large number of pressure sensors can lead to a highly accurate interpolated pressure distribution, the FEPV system is intended to be a cost- and time-effective system that could be used by Figure 2: VSPARS images of a) gennaker and b) mainsail, during full scale testing. 2.3 FEPV DATA ANALYSIS The FEPV analysis was coded in Matlab, and uses the output files from VSPARS and the pressure system to obtain the aerodynamic forces.

155 The whole sail surface is created from the known stripe shapes and the known tack position. The position of the head is estimated by extrapolating a spline curve passing through the known tack point and each stripe luff point. The head is assumed to be flat with no camber and to have a small finite length. Similarly, a spline curve joining the leech points of the known stripes is extrapolated upwards to the known head height position and also downwards by the known leech length of the sail, to give the head and foot twists respectively, together with the first estimate of the clew position. mainsheet and traveller, whilst the jib was left in a standard trim position. Secondly, the jib was swept from hard sheeted to fully eased using the jib sheet, whilst the main remained at a standard trim. Finally, both sails were eased together over 8 settings. The trends shown by the FEPV calculations compared well with the force balance results. The driving force and rolling moment predicted by the FEPV method were respectively 10% and 5% less than measured by the force balance. This underestimation is thought to be due to the additional windage from the mast, rigging etc., which is not measured by sail pressure integrations. Unfortunately the foot shape cannot be captured by the camera as it is out of the viewing area. Therefore an initial foot shape is estimated by fitting a spline curve through the known tack and clew positions together with a 3 rd point given by an estimated foot depth and draft position, obtained by extrapolating the depth and draft position of the known stripes. This foot shape is then scaled in both the longitudinal and transverse directions to match the known foot length. Starting from the low resolution sail shape defined by the VSPARS stripes and the foot and head positions, a fine quadrilateral mesh is then interpolated over the sail surface. The sail pressure distributions are obtained from the discrete pressure values recorded by the pressure system which are interpolated linearly, firstly in the chord-wise direction, and then secondly in the span-wise direction towards the head and the foot. The pressures are interpolated to the centre of each geometrical cell in order to obtain a pressure map distribution over both entire sails, as shown in figure 3. The VSPARS stripes and pressure tap locations are also shown in the figure. The choice of linear interpolation in the chord-wise direction allows the leading edge suction peaks and separation bubbles to be captured [7]. Forces in specified directions are computed by integrating the known pressures acting over the cell areas taking into account their surface normal directions. Moment contributions from each cell are calculated about the specified yacht moment reference centre. 3 FEPV SYSTEM VALIDATION In an earlier study [7] the FEPV system was validated for upwind sailing through wind tunnel testing. Results from the FEPV system were compared in terms of forces and moments to measurements from the wind tunnel force balance, and good agreement was found. The tests for the upwind validation were conducted at an apparent wind angle (AWA) of 25 and a heel of 20. Three types of trim change were investigated. Firstly, the main was swept through 8 trim settings from hard sheeted to fully eased using a combination of both Figure 3: Pressure map distribution over the entire surfaces of the two sails. The pressure system used for the present full scale downwind testing is the same as that used for the upwind sailing tests, and so it was felt that no further pressure system validation was required. However, a validation of the sail shape generation for downwind sail shapes was necessary because of the much more highly curved shape of gennakers compared with upwind sails. Indeed, particular attention was needed to assess the accuracy of the foot shape and the determination of the clew position, as these positions are obtained from extrapolations rather than from direct VSPARS measurements. Wind tunnel tests were carried out on a model scale VO70 yacht to obtain data for this assessment, as shown in figure 4. Two different gennakers were tested at AWAs varying from 60 to 120 in order to cover the full range of AWAs of interest at full scale. The clew, foot depth, and draft positions were measured physically during each test, and the sail stripe positions were also recorded by VSPARS, and used by the FEPV software to determine the sail shape. The results of this

156 comparision are shown in Table 1. The moment reference centre is located at the base of the mast, with x positive forward, y positive towards port and z positive upwards. Differences in clew positions in the x, y and z directions are given in Table 1. Foot depth and draft position are expressed as a percentage of the chord length. Average chord lengths of 1400 mm and 1100 mm for sails 1 and 2 respectively can be used for reference. The results show that the FEPV system can predict the clew position with an accuracy of better than ±70 mm (but usually much less). Fairly good agreement in foot shape is obtained as well, with errors within 5% of the chord length. As a general pattern, the present FEPV analysis software overestimates the foot depth and underestimates the draft position. It was observed during these FEPV validation tests that the foot of the sail was constantly moving, probably due to shedding of the foot vortex, which is a common characteristic of downwind sailing. Therefore the physical location of the sail could not be determined to better than a few cm (3-5 cm) during the tests, and so this is the validation accuracy. 4 DOWNWIND FULL-SCALE TESTING 4.1 TEST SETUP A Stewart 34 Class yacht was used for the full-scale testing. It was decided to equip the yacht with an available gennaker, which unfortunately was sized to fit a smaller boat, namely an International Platu25, which is about 7.5 m long. The gennaker was hoisted from a pole held against the forestay. Although this setup was not ideal, the gennaker flew in a reasonable manner, as can be seen in figure 2a. Figure 4: VO70 model scale yacht used for FEPV wind tunnel validation comparison of calculated sail postions with physical measurements. Table 1: Comparison of clew coordinates and foot shape between FEPV and physical measurements. Sail 1 Sail 2 60 AWA 80 AWA 100 AWA 120 AWA Coordinate difference [mm] between FEPV and Exp measure x_clew y_clew z_clew Sail 1 60 AWA 80 AWA [%chord] Experimental FEPV Experimental FEPV foot depth foot draft Sail AWA 120 AWA [%chord] Experimental FEPV Experimental FEPV foot depth foot draft Both the mainsail and gennaker were equipped with VSPARS stripes and differential pressure transducers (figure 2a and 2b). A GPS unit, sampling at a rate of 2.5 Hz, was used to record the speed over ground and boat location, while the boat instruments logged boat speed, wind speed and direction at 1 Hz. An Inertial Measurement Unit (IMU) was placed in the yacht cabin and logged the boat motion at 10 Hz. The VSPARS stripe recording system uses a sampling frequency of about 0.3 Hz which enabled several images to be averaged to obtain the shapes of the stripes for the FEPV calculations. A custom-made data acquisition unit recorded all these data, each one at its own sampling rate, and so the data were all time stamped to enable subsequent synchronous processing of the data streams. The measurements were performed in the Hauraki Gulf, Auckland, NZ, in a fairly constant but very light breeze between 6 and 8 knots with almost flat water, in an area with insignificant tidal flow. In this light breeze the sails were just able to fly. Such low wind speeds made it difficult to accurately measure the pressures across the sails, which varied from 0 to 30 Pa for the gennaker and from 0 to 15 Pa for the mainsail, due to the sensitivity of the pressure transducers.. More wind would have been preferred, but the tests were planned for a certain day and could not be rescheduled, and the wind was light on the day.

157 Nevertheless, the system proved to be effective and provided repeatable results, as discussed in section 4.2 The aim of the tests was to check the reliability and accuracy of the FEPV system, the repeatability of the tests, and to qualitatively study the flow around the sails by analysing the pressure distributions and the sail shape. The yacht was sailed at its optimum trim on starboard tack for AWAs varying from 65 to 115. A total of 24 runs were carried out, each about 60 s long. Sail trim (optimal sail trim with gennaker on the verge of luffing) was kept constant for each run and the boat heading was kept as straight as possible to enable the results to be averaged over the run time (45 60 s). Measurements from the instruments on board (including the pressures and sail shapes) were averaged over the run time, and the FEPV code used the average values for the computations. curvature is very small. This can be confirmed by the small values of pressure differences, which range between 10 and 30 Pa. The bottom row (1/4) has similar chord-wise distributions, with even smaller suctions generated by sail curvature, and only for the lowest AWAs. There is something interesting happening at 25% of the chord, where the suctions are lowest, but the reason for this is unknown possibly a transducer issue. Increased AWAs over 100 drastically flatten the pressure distributions in the proximity of the leading edge. 5 RESULTS In 2009, Viola and Flay [2] carried out wind tunnel tests on asymmetric spinnakers. Their results show that on the leeward side of the spinnaker the pressure has a negative peak at the leading edge, followed by a slow pressure recovery up to the trailing edge in stalled flow. In attached flow the suction peak at the leading edge is followed by a quick pressure recovery at around 10% of the curve length followed by a second suction peak due to the section curvature. Downstream of the second suction peak, that occurs between 10% and 40% of the curve length, the pressure becomes less negative, and then constant due to the trailing edge separation. Figures 5 and 6 show typical full-scale pressure distributions for the gennaker and mainsail respectively at different AWAs plotted against the sail chord percentage. The suctions are generally higher over the entire surface for lower AWAs. This trend is confirmed in terms of driving force determined by integration, which is higher for the lower AWAs. In all the figures showing pressure and force coefficients, the dynamic pressure was calculated based on the apparent wind speed (AWS), and the pressure differences are leewardwindward, thus giving negative values. The pressure coefficient plots have the negative direction upwards, as is common in showing pressure distributions on wings. The flow around the gennaker top stripe is stalled for all AWAs, as can be seen from the lack of pressure recovery after the leading edge peak, which occurs at around 5% of the chord length. The rows at ¾ and ½ of the height show similar behaviour; the leading edge suction peak, occurring at 5 to 10% of the chord length is followed by a pressure recovery (perhaps due to an intermittent leading edge separation bubble reattachment), a suction increase due to the sail curvature, and then a reduction in suction as the trailing edge is approached. However the sail is not able to generate much suction, probably due to the very light winds, and therefore the suction due to Figure 5: Gennaker pressure distributions for AWAs of 72, 89, 105 and 112 It is worth noting the consistency of the pressure distributions obtained in such light airs. When testing at full-scale, zeroing of the pressure sensors is not an easy task because the wind cannot be turned off, and because of the sensitivity of the transducers to their orientation if

158 the sail and sensors are put into a bag to obtain a uniform pressure. The pressure differences on the mainsail are even lower than on the gennaker, having maximum values of only 15 Pa. on shore (before and after the tests) and at sea during the measurements. Taking into account the sensors drift with time and temperature, the sensitivity of the transducers to their orientation and the noise during the measurements, the estimated accuracy of the pressure measurements for the current test is of about ±2.5 Pa, and thus ±0.3 in terms of pressure coefficients for the actual wind conditions. The variation of the driving force coefficient (CFx) with AWA is shown in figure 7. As discussed above, it was difficult to achieve significant suction over the sails due to the light winds. This has given values of CFx that are quite small (in the authors experience) for the whole range of AWAs investigated. Figure 6: Mainsail pressure distributions for AWAs of 72, 89, 105 and 112. The flow on mainsails is affected by the presence of the mast [22] which usually produces a separation bubble behind it with a low recirculation flow velocity and a low pressure core on the front part of the mainsail. This helps explain the suction peak at 7 to 15% of the chord exhibited in figure 6, followed by pressure recovery where the flow reattaches. Figure 6 shows 2 further suction peaks at all heights and for all AWAs. The reasons for these are not clear, but might be due to the sail curvature not being very fair due to the lack of pressure, thus resulting in a wavy sail surface. This will be the object of future investigations by the YRU. Another atypical behaviour is the presence of positive values of differential pressures before and after the leading edge suction peak. Again, this might be due to some reverse flow in the separated area. This behaviour is not likely to be caused by incorrect zeroing of the pressure transducers, as they were zeroed several times Figure 7: Drive force coefficient vs. apparent wind angle. Upper graph gennaker and mainsail coefficients, lower graph sum of gennaker and mainsail coefficients. The results in figure 8 also show that the yacht performance varies quite significantly in the range of true wind speeds (TWS) encountered during the tests (3 to 5 m/s). Figure 8 shows CFx plotted against TWS for runs carried out at similar apparent wind angles. The results generally show that an increase in TWS results in an increase in CFx, whereas repeated runs carried out at a similar TWS result in similar values of CFx. Hence it appears that the sails become more efficient as the TWS increases; perhaps they are less prone to separation. For all AWAs the mainsail contributes only a very small amount to the driving force compared to the gennaker (see the upper graph in figure 8). Indeed, the CFx values vary between 0.45 and 0.85 for the gennaker and between 0 and 0.11 for the mainsail. This is as-expected,

159 but note that the presence of the mainsail increases the loading on the gennaker due to the upwash it generates. figure 11). The boat speed is generally higher for low AWAs (giving a higher AWS), and this is associated with a small increment in heel angle. This is as-expected since the lower AWAs gave the higher thrust. Figure 8: Drive force coefficient vs. true wind speed. The heeling moment coefficient (CMx) generally decreases with increase in the AWA, as shown in figure 9 (note that the reference length for CMx is the mast length). The scatter in the results might be due to the different behaviour of the boat at lower and higher wind speeds. The values of heel angle are generally low (figure 10) and increase in an approximately linear manner with increase in the heeling moment (and thus decrease with increase in AWA). Figure 11: Drive force vs. apparent wind angle. Figure 12: Boat speed vs. apparent wind angle. 6 CONCLUSIONS Figure 9: Heeling moment coefficient vs. AWA. A method for determining the aerodynamic forces and moments produced by a yacht s sails at full scale is investigated in this work. It combines simultaneous onwater pressure and sail shape measurements. The sail shape measurement component of the system has been investigated through wind tunnel testing, and shown to be accurate. The system has been used for downwind sailing in low wind speeds at full scale and proved to work well, and provided reasonably accurate and repeatable aerodynamic performance measurements. Figure 10: Heel angle vs. heeling moment. Figures 11 and 12 show the overall drive force (Fx) and boat speed (Vs) plotted against the AWA. In this case a clear trend of increasing Fx for low AWA can be identified, as well as the expected increase in Fx for the runs performed in slightly stronger winds (red symbols in The next steps in this project are to use the FEPV system to investigate unsteady sail aerodynamics at full scale for both upwind and downwind sailing. The pressure distributions showed similar behaviour to other published results. The mainsail contributed only a small amount to the driving force compared to the gennaker.

160 The thrust, Fx and the boat speed, Vs, both decreased as the AWA increased. REFERENCES [1] Le Pelley, D.J., P.J. Richards, Effective Wind Tunnel Testing of Yacht Sails Using a Real-Time Velocity Prediction Program, 20 th Chesapeake Sailing Yacht Symposium, SNAME, Annapolis, 2011 [2] Viola, I.M., R.G.J. Flay, Force and Pressure Investigation on Modern Asymmetric Spinnakers, International Journal of Small Craft Technology, 2009, pp [3] P.J. Richards, W. Lasher, Wind Tunnel and CFD Modelling of Pressures on Downwind Sails, BBAA VI International Colloquium on Bluff Bodies Aerodynamics & Applications, Milano, Italy 2008 [4] Viola, I.M., Downwind Sail Aerodynamics: a CFD Investigation with High Grid Resolution, Ocean Engineering, 36 (12-13), , 2009 [5] Lasher, W.C., J.R. Sonnenmeier, An Analysis of Practical RANS simulations for spinnaker aerodynamics, Journal of Wind Engineering and industrial Aerodynamics, 96 (2008) [6] Wright, A.M., A.R. Claughton, J. Paton, R. Lewis, Off-Wind Sail Performance Prediction And Optimisation, The Second International Conference on Innovation in High Performance Sailing Yachts 2010, Lorient, France [7] Le Pelley, D.J., Morris, D. & Richards, P.J., Aerodynamic force deduction on yacht sails using pressure and shape measurement in real time, 4th High Performance Yacht Design Conference: Auckland, New Zealand, 2012 [8] Lozej, M., D. Golob, B. Vrtic, D. Bokal, Pressure Distribution on Sail Surfaces In Real Sailing Conditions. 4th High Performance Yacht Design Conference. Auckland, New Zealand, 2012 [9] Augier, B., P. Bot, F. Hauville, M. Durand, "Experimental validation of unsteady models for fluid structure interaction: Application to yacht sails and rigs." Journal of Wind Engineering and Industrial Aerodynamics 101(0): [10] Bergsma, F., D. Motta, D.J. Le Pelley, P.J. Richards, R.G.J. Flay, Investigation of sailing yacht aerodynamics using real time pressure and sail shape measurements at full scale, 18 th Australasian Fluid Mechanics Conference, Launceston, Australia, 2012 [11] Viola, I.M. and R.G.J. Flay, "Full-scale pressure measurements on a Sparkman and Stephens 24-foot sailing yacht." Journal of Wind Engineering and Industrial Aerodynamics 98(12): [12] Viola, I.M. and R.G.J. Flay, "Sail pressures from full-scale, wind-tunnel and numerical investigations." Journal of Ocean Engineering 38(16): [13] Graves, W., T. Barbera, J.B. Braun, L. Imas, Measurement and Simulation of Pressure Distribution on Full Size Sails, 3rd High Performance Yacht Design Conference. Auckland, New Zealand, 2008 [14] Puddu P., F. Nurzia, A. Pistidda, A. Mura, Full Scale Investigation of One-Design Class Catamaran Sails. 2nd High Performance Yacht Design Conference. Auckland, New Zealand, 2006 [15] Flay, R.G.J., S. Millar, Experimental Considerations Concerning Pressure Measurements on Sails: Wind Tunnel and Full-Scale, 2nd High Performance Yacht Design Conference, Auckland, New Zealand, 2006 [16] Le Pelley, D.J., O. Modral, VSPARS: A combined sail and rig shape recognition system using imaging techniques, 3rd High performance Yacht Design Conference, Auckland, New Zealand, 2008 [17] Herman, J.S., A Sail Force Dynamometer: Design, Implementation and Data Handling, Massachusetts Institute of technology, Cambridge, 1988 [18] Masuyama, Y., T. Fukasawa, Database of sail shapes versus sail performance and validation of numerical calculations for the upwind condition, Journal of Marine technologies, 2009 [19] Hochkirch, K., Design and Construction of a Full- Scale Measurement System for the Analysis of Sailing Performance, Technical University of Berlin, 2000 [20] Bergsma, F., D. Motta, D.J. Le Pelley, P.J. Richards, R.G.J. Flay, Investigation of shroud tension on sailing yacht aerodynamics using full-scale real-time pressure and sail shape measurements, 22 nd International HISWA Symposium on Yacht Design and Yacht Construction, Amsterdam [21] Morris, D., Derivation of Forces on a Sail using Pressure and Shape Measurements at Full-Scale, ME Thesis, Chalmers University Of Technology, 2011 [22] Viola, I.M., R.G.J. Flay, Pressure Measurements on Full-Scale and Model Scale Upwind Sails, 17 th Australasian Fluid Mechanics Conference, Auckland, 2010

161 AUTHORS BIOGRAPHY Dario Motta is a PhD student in the Yacht Research Unit at the University of Auckland. His research topic is the investigation of sail pressures and shapes to understand how they produce forces at full scale. Richard G.J. Flay, PhD, is Professor of Mechanical Engineering and Director of the Yacht Research Unit in the Department of Mechanical Engineering at the University of Auckland. He has had a longstanding research interest in the wind and sailing. His PhD degree was awarded for a study of wind structure based on full scale wind data. His Postdoctoral research as a National Research Council Visiting Fellow in Canada was focused on carrying out wind tunnel studies in a boundary layer wind tunnel. He then spent four years as an Aerodynamic Design Engineer in an Engineering Consultancy in Toronto where he worked on the design of several wind tunnels and environmental test facilities. Since 1984 he has worked at the University of Auckland, and in 1994 he designed the World s first Twisted Flow Wind Tunnel. Peter Richards has research interests in wind engineering, wind energy and yacht aerodynamics. He has been involved with the Yacht Research Unit at the University of Auckland for about 20 years and has published research papers on CFD, wind-tunnel and fullscale studies of sail aerodynamics. He is an author of over 70 journal papers and numerous conference papers. David Le Pelley is the manager of the Yacht Research Unit and a director of VSPARS Ltd. Current research interests include comparison of wind tunnel and full scale yacht performance.

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163 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France NUMERICAL STUDY OF A FLEXIBLE SAIL PLAN: EFFECT OF PITCHING DECOMPOSITION AND ADJUSTMENTS B. Augier, Naval academy Research Institute, France, benoit.augier@ecole-navale.fr F. Hauville, Naval academy Research Institute, France, frederic.hauville@ecole-navale.fr P. Bot, Naval academy Research Institute, France, patrick.bot@ecole-navale.fr J. Deparday, Naval academy Research Institute, France, julien.deparday@ecole-navale.fr M. Durand, K-EPSILON company, France, mathieu@k-epsilon.com Abstract A numerical investigation of the dynamic Fluid Structure Interaction (FSI) of a yacht sail plan submitted to harmonic pitching is presented to analyse the effects of motion simplifications and rigging adjustments on aerodynamic forces. It is shown that the dynamic behaviour of a sail plan subject to yacht motion clearly deviates from the quasi-steady theory. The aerodynamic forces presented as a function of the instantaneous apparent wind angle show hysteresis loops. These hysteresis phenomena do not result from a simple phase shift between forces and motion. Plotting the hysteresis loops in the appropriate coordinate system enables the associated energy to be determined. This amount of exchanged energy is shown to increase almost linearly with the pitching reduced frequency and to increase almost quadratically with the pitching amplitude in the investigated ranges. The effect of reducing the real pitching motion to a simpler surge motion is investigated. Results show significant discrepancies on the aerodynamic forces amplitude and the hysteresis phenomenon between pitching and surge motion. However, the superposition assumption consisting in a decomposition of the surge into two translations normal and collinear to the apparent wind is verified. Then, simulations with different dock tunes and backstay loads highlight the importance of rig adjustments on the aerodynamic forces and the dynamic behaviour of a sail plan. NOMENCLATURE A deg pitching oscillation amplitude C m sail plan chord at z a (from head-sail leading edge to mainsail trailing edge) C x driving force coefficient C x mean value of C x C y heeling force coefficient dx displacement along x axis at z a f r flow reduced frequency S m 2 total sail area T s pitching oscillation period V AW m.s 1 apparent wind speed V TW m.s 1 true wind speed V r flow reduced velocity W work associated to hysteresis loop area z a m height of the centre of aero. forces β AW deg apparent wind angle β eff deg effective wind angle β TW deg true wind angle φ deg heel angle θ deg trim angle α deg heading angle ρ kg.m 3 fluid density τ s phase shift 1 INTRODUCTION When analysing the behaviour of yacht sails, an important difficulty comes from the Fluid Structure Interaction (FSI) of the air flow and the sails and rig [19, 14, 9]. Yacht sails are soft structures whose shapes change according to the aerodynamic loading. The resulting modified shape affects the air flow and thus, the aerodynamic loading applied to the structure. This Fluid Structure Interaction is strong and non-linear, because sails are soft and light membranes which experience large displacements and accelerations, even for small stresses. As a consequence, the actual sail s shape while sailing the socalled flying shape is different from the design shape defined by the sail maker and is generally not known. Recently, several authors have focused on the Fluid Structure Interaction (FSI) problem to address the issue of the impact of the structural deformation on the flow and hence the aerodynamic forces generated [5, 22]. Another challenging task in modelling racing yachts is to consider the yacht behaviour in a realistic environment [6, 19, 14, 9]. Traditional Velocity Prediction Programs (VPPs) used by yacht designers consider a static equilibrium between hydrodynamic and aerodynamic forces. Hence, the force models classically used are estimated in a steady state. However, in realistic sailing conditions, the flow around the sails is most often largely unsteady because of wind variations, actions of the crew and more importantly because of yacht motion due to waves. To account for this dynamic behaviour, several Dynamic Velocity Prediction Programs (DVPPs) have been developed, e.g. by Masuyama et al.[21, 20], Richardt et al. [23], Keuning et al.[18] which need models of dynamic aerodynamic and hydrodynamic forces. While the dynamic effects on hydrodynamic forces have been largely studied, the unsteady aerodynamic behaviour of the sails has received much less attention. Shoop et al.[26] first developed an unsteady aeroelastic model in potential flow dedicated to flexible mem-

164 branes but neglected the inertia. In a quasi-static approach, a first step is to add the velocity induced by the yacht s motion to the steady apparent wind to build an instantaneous apparent wind (see [23, 18]) and to consider the aerodynamic forces corresponding to this instantaneous apparent wind using force models obtained in the steady state. In a recent study, Gerhardt et al. [15] developed an analytical model to predict the unsteady aerodynamics of interacting yacht sails in 2D potential flow and performed 2D wind tunnel oscillation tests with a motion range typical of a 90-foot (26m) racing yacht (International America s Cup Class 33). Recently, Fossati et al. [10, 11, 12] studied the aerodynamics of model-scale rigid sails in a wind tunnel, and showed that a pitching motion has a strong and non-trivial effect on aerodynamic forces. They showed that the relationship between instantaneous forces and apparent wind deviates phase shifts, hysteresis from the equivalent relationship obtained in a steady state, which one could have thought to apply in a quasi-static approach. They also investigated soft sails in the same conditions to highlight the effects of the structural deformation [13]. In a previous work [4], the aero-elastic behaviour of the sail plan subjected to a simple harmonic pitching was numerically investigated. This study has shown hysteresis phenomena between the aerodynamic forces and instantaneous apparent wind angle, which were more pronounced in the FSI case on a realistic soft structure than on a rigid structure. However, in this first work [4], the question of genuine hysteresis phenomenon versus simple phase shift between both oscillating signals was not clearly elucidated. Moreover, the energy associated to the hysteresis phenomenon was not determined. Hence, the first aim of the present work is to investigate further this hysteresis phenomenon to elucidate the hysteresis versus phase shift issue and to determine the associated energy. Most of studies about the unsteady effect due to yacht pitching have considered a 2D simplified problem and thus approximated the pitching motion by a translational oscillation aligned with the yacht centreline [7, 15]. Then, the usual procedure is to decompose this motion in oscillations perpendicular to and along the direction of the incident flow, which result in oscillations of apparent wind angle and speed respectively (Fig.7). The second aim of this work is to investigate the effects of such simplifications in the yacht motion considered by comparing the results obtained with the sail plan subjected to different types of motion. The third aim of this work is to address the effect of various rig and sail trims and adjustments on the unsteady aeroelastic behaviour of the sail plan subjected to pitching. This is investigated by comparisons of results obtained for realistic docktunes and backstay tensions used while racing a 28-foot (8m, J80 class) cruiser-racer. An unsteady FSI model has been developed and validated with experiments in real sailing conditions [1, 2, 3]. Calculations are made on a J80 class yacht numerical model with her standard rigging and sails designed by the sail maker DeltaVoiles. The FSI model is briefly presented in section 2. The methodology of the dynamic investigation is given in section 3. In the continuity of a previous work [4], section 4 gives further precisions on the dynamic behaviour. The analysis of pitching motion decomposition in simple translation is given in section 5 and the effects of various dock tunes and backstay loads are presented in sections 6.1 and 6.2. In the last section, some conclusions of this study are given, with ideas for future work. 2 NUMERICAL MODEL To numerically investigate aero-elastic problems which can be found with sails, the company K-Epsilon and the Naval Academy Research Institute have developed the unsteady fluid-structure model ARAVANTI made by coupling the inviscid flow solver AVANTI with the structural solver ARA. The ARAVANTI code is able to model a complete sail boat rig in order to predict forces, tensile and shape of sails according to the loading in dynamic conditions. For more details, the reader is referred to [25] for the fluid solver AVANTI and to [16] and [24] for the structural solver ARA and the FSI coupling method. ARAVANTI model has been validated. Numerical and experimental comparisons with the model ARAVANTI are based on measurements at full scale on an instrumented 28- foot yacht (J80 class, 8m). The time-resolved sails flying shape, loads in the rig, yacht s motion and apparent wind have been measured in both sailing conditions of flat sea and moderate head waves and compared to the simulation. The code has shown its ability to simulate the rig s response to yacht motion forcing, and to correctly estimate the loads. Thereby, ARAVANTI is a reliable tool to study the dynamic behaviour of a sail plan subject to pitching motion. For a detailed description of the experimental system and the numerical and experimental comparison, see [1, 2, 3]. 3 SIMULATION PROCEDURE The yacht motion in waves induces unsteady effects in the sails aerodynamics. In this paper we will study separately one degree of freedom, by applying simple harmonic pitching. The reference frame and the coordinate system attached to the yacht are illustrated in Figure Reference steady case First, the reference steady case is computed with the following parameters: true wind speed at 10m height V TW =6.7 m.s 1 (a logarithmic vertical wind profile is imposed with a roughness length of 0.2mm [8]), true wind angle β TW =40, boat speed V BS =2.6 m.s 1, heel angle φ=20 and trim angle θ=0. This first computation yields the converged steady flow, the rig and sails flying shape, and enables the steady state aerodynamic forces and centre of effort to be determined. This converged steady state is used as the initial condition for the computations with pitching forcing. The height z a =6.26m of the centre of aerodynamic forces is used to define the flow characteristic quantities: apparent wind speed V AW =8.81 m.s 1, apparent wind angle β AW =29.19 and sail plan chord C=6.22m defined as the distance from the head-sail

165 Figure 1: Coordinate, angle and motion references for the yacht. Z axis is attached to the earth vertical. Figure 2: Dynamic effect of pitching on the wind triangle (top view). V is the wind velocity, BS is the boat speed, z is the height of the aerodynamic centre of effort, θ is the pitching velocity, β is the apparent wind angle, subscripts TW and AW stand for True and Apparent wind leading edge to the main sail trailing edge at z a. Corrections of the apparent wind angle β AW due to constant heel φ (first introduced by [19]) and trim θ are considered through the use of the effective apparent wind angle β eff (see [17] for heel effect, and [12] for pitch effect): ( tan β eff =tan 1 βaw cos θ β eff =27.79 in the steady state. 3.2 Harmonic pitching ) cos φ The unsteady computations consist of a 20s run, with forced harmonic pitching being imposed on the rig, characterised by the oscillation amplitude A and period T (equation 2), other (1) Figure 3: Time dependent apparent wind speed V AW (a); apparent wind angle β AW and effective wind angle β eff (b) resulting from pitching oscillation at z a with period T=3s and amplitude A=5. parameters being constant and equal to those of the reference state. ( ) 2π θ = A cos T t To avoid discontinuities in the accelerations, the beginning of motion is gradually imposed by applying a ramp which increases smoothly from 0 to 1 during the first 3s of imposed motion (see first period in Figure 3). The investigation has been made with variables in the range A=3 to 6, and T=1.5 to 6s, corresponding to the typical environmental conditions encountered, as shown in the experiment of [3]. The unsteady nature of a flow is characterised by a dimensionless parameter defined by the ratio of the motion period T to the fluid advection time along the total sail plan chord C. Similarly to the closely related literature [13, 15], this parameter is called the flow reduced velocity V r (or the inverse: the reduced frequency f r ) defined by: V r = V AW T C (2) = f 1 r (3) The case V r 1 (f r 1) corresponds to quasi-steady aerodynamic conditions. The pitching period values investigated correspond to a reduced velocity V r from 2 to 8.5 (reduced frequency f r from 0.12 to 0.47), which positions this numerical study in a similar dynamic range to the experiments

166 of [12] where V r was from 2.3 to 56 (reduced frequency f r from 0.02 to 0.43) corresponding to typical conditions encountered by a 48-foot yacht (14.6m). The computed cases are summarised in Table 1. When the yacht is subjected to pitching motion, the apparent wind is periodically modified as the rotation adds a new component of apparent wind which varies with height. Following the analysis of [12], the apparent wind and pitchinduced velocity are considered at the centre of aerodynamic force height z a. This centre of effort is actually moving due to pitch oscillation, but variations are small enough to be ignored, and the reference height computed in the steady state is used. This yields time dependent apparent wind speed and angle, given by: V AW (t) = ( (V TW sin β TW ) 2 +(V TW cos β TW + V BS + z a θ(t)) 2 ) 1 2 β AW (t) =sin 1 ( VTW sin β TW V AW (t) And hence the time-dependent effective wind angle: ) β eff (t) =tan 1 ( tan βaw (t) cos θ(t) ) cos φ Figure 2 illustrates the dynamic vector composition for pitching velocities θ= θ max, 0 and θ min, and Figure 3 shows the resulting dynamic apparent wind velocity and angle computed with equations 4 and 5. As shown in Figure 3, the apparent wind angle variations are in phase opposition with the apparent wind speed. 3.3 Heeling and driving force coefficients Aerodynamic forces are calculated by the code at the sail plan s centre of effort. Forces are calculated in the boat frame and written in the inertial reference frame, in order to get F x and F y, the driving and the heeling forces. The transition matrix R T is defined by R T = R θ R φ R α with: R θ = cos φ 0 sinφ 0 cosθ sin θ, R φ = sinθ cos θ sin φ 0 cosφ cos α sin α 0 R α = sin α cos α Driving and heeling force coefficients are obtained by the normalisation with the product of the instantaneous apparent dynamic pressure and the total sail area S: F x C x (t) = 0.5ρVAW 2 (t)s (6) F y C y (t) = 0.5ρVAW 2 (t)s (7) In the steady state calculation, driving coefficient C x =0.379 and heeling coefficient C y = are obtained. (4) (5) 4 Dynamic behaviour Previous studies [13, 4] have shown that the dynamic behaviour of a yacht sail plan subjected to pitching clearly deviates from the quasi static approach. Particularly, the aerodynamic forces presented as a function of the instantaneous apparent wind angle show hysteresis loops as illustrated in figure 4. Different questions have been raised by this result. Is this a real hysteresis phenomenon or is this appearance in the Lissajous plot only a consequence of a simple phase shift between the signals? In the former case, can we determine the amount of energy corresponding to the hysteresis loop? Figure 4: Driving a) and heeling b) force coefficients versus effective wind angle β eff (t). 4.1 Phase shift τ The values of the phase shift τ between aerodynamic forces and instantaneous wind angle have been determined for each pitching period and amplitude by cross-correlation (Table 1). The phase delay increases (almost linearly in the investigated range) with the flow reduced velocity (with the motion period) but is not affected by the oscillation amplitude. When forces C x,y (t) are plotted versus the time shifted wind angle β eff (t+τ), the loop area is significantly decreased but does not vanish (see Fig. 5). Even for different values of the time delay that have been tested, the loop did not collapse into a single line. The best time delay corresponding to the lowest area is the one computed by cross correlation. This shows

167 T A V r f r τ 2πτ/T W s deg s rad e e e e-4 T A V r f r τ 2πτ/T W s deg s rad e e e-3 Table 1: Reduced velocity V r, reduced frequency f r, phase delay τ between C x and β eff determined by crosscorrelation, and non-dimensional energy W= T C xdx for different pitching amplitudes A and periods T Figure 6 shows the driving force coefficient as a function of the non-dimensional displacement dx for different pitching periods. The area of the hysteresis loop here corresponds to a work which is the amount of energy exchanged by the system. The values obtained for each case are given in Tab. 1. The energy increases (almost linearly in the investigated range) with the pitching reduced frequency and increases (almost quadratically in the investigated range) with the pitching amplitude. that there is a real hysteresis phenomenon and not only a phase shift between the signals. Figure 5: Driving force coefficient vs. instantaneous apparent wind angle β eff (t) (blue line with markers), and vs. the time shifted instantaneous apparent wind angle β eff (t+τ) (red line without marker), for a pitching period T=1.5s and amplitude A=5 Figure 6: Driving force coefficient vs. non-dimensional displacement dx for pitching periods T=1.5, 3, 5 and 6s. The loop area represents the work exchanged W. The aerodynamic behaviour is now clearly characterised: an hysteresis phenomenon is evidenced and the associated energy is computed. The next sections address the various influences of the yacht motion considered and of different rig trims. 5 PITCHING DECOMPOSITION Pitch Surge Decomposition 4.2 Energy exchanged The area contained in the hysteresis loop of Fig. 4 does not correspond to a work or energy as β eff is the effective apparent wind angle and its relationship to a displacement is not straightforward. To build an energy, the displacement of the centre of effort dx along the direction of the driving force is considered, and the non-dimensional work W of the driving force during one oscillation period is defined by: W = C x dx (8) dx = z a dθ cos(θ) (9) C VAW VAW x n VAW Figure 7: Different motions considered: pitching (rotation), surge (translation), surge decomposition into translations collinear to the apparent wind V c and normal to the apparent wind V n. The real pitching motion is modelled here by an angular n

168 oscillation around the y axis (Fig.7 Pitch), normal to the centreline with a rotation centre located at the mast step. Most of previous studies on the influence of pitching have considered a 2D simplified problem and thus approximated the pitching motion by a translational oscillation aligned with the yacht centreline (Fig.7 Surge). Then, the usual procedure is to decompose this motion in an oscillation parallel to the apparent wind, resulting in an oscillation of apparent wind speed, and an oscillation orthogonal to the apparent wind, resulting mainly in an oscillation of the apparent wind angle [15] (Fig.7 decomposition). Here, we want to test these two hypotheses by comparing the results of the dynamic simulation with AR- AVANTI obtained with different imposed motions, and investigate the effect on the specific dynamic features highlighted above. Motions are based on the standard pitching motion with amplitude A=5 and period T=5s (A5T5). Cx Cy Pitch 0.3 Surge quasisteady eff eff Figure 9: Driving and heeling force coefficients versus apparent wind angle for pitch and surge motion. The motion period and amplitude at the centre of effort are identical and correspond to a pitching amplitude A=5 and period T=5s. 5.2 Simple translations decomposition Figure 8: Time series of the driving and heeling force coefficients for FSI simulations of the various motions considered: pitching, surge, translations collinear and perpendicular to the apparent wind (see Fig.10), corresponding to a pitching amplitude A=5 and period T=5s. 5.1 Surge The first step is to compare the results with a real pitching motion (rotation) to the results with a translational surge motion with the amplitude of motion at the centre of effort height while pitching. As shown on Fig 8 the oscillation of aerodynamic forces is decreased by 25% and phase shifted (around T/10) when the pitching is reduced to a surge motion. This result gives the order of the error introduced by considering a surge motion instead of the pitching motion. Concerning the dynamic behaviour, it is interesting to notice that the case of surge does not show the same hysteresis phenomenon. Indeed, the aerodynamic behaviour in the case of surge is much closer to the quasi-steady theory than in the pitching case, as clearly shown on Fig 9. The loop of C x,y (β eff ) collapses and is superposed to the quasi-steady line. Figure 10: Wind triangle representation for the surge decomposition into 2 translations a) V c collinear to V AW and b) V n normal to V AW. The second step is to analyse separately the effects of translational oscillations parallel V c (Fig 10.a) and orthogonal V n (Fig 10.b) to the apparent wind direction. It is observed on Fig. 8 that the major contribution to the force oscillation is due to the orthogonal oscillation component, which is associated to the oscillation of apparent wind angle. When the variations due to both components of motion are added (not shown on Fig. 8 for clarity), the result is very similar to what is obtained with the surge motion (maximum of cross-correlation= 0.998), which justifies the linear superposition principle of

169 this approach. The effect of parallel oscillation variation of AWS(t) is small, but with an important phase shift (about T/3). Moreover, one can notice that the oscillation of forces is not symmetric the duration of increasing and decreasing phases are different for pitching, surge and parallel oscillation, but it is symmetric for the orthogonal oscillation. This can be explained in the following way. The orthogonal oscillation is associated to an oscillation of AWA(t), and the effect of angle of attack in a narrow range is almost linear on the aerodynamic lift. Contrarily, the parallel oscillation is associated with an oscillation of AWS(t), and the effect of wind speed is quadratic on aerodynamic forces. 6 INFLUENCE OF RIG ADJUSTMENTS In this section, the analysis of the effects of various dock tunes and backstay loads on the dynamic behaviour and the energy exchanged is presented. 6.1 Influence of dock tune The influence of various dock tunes on the sail plan dynamic behaviour is investigated. The same pitching motion (A=5 and T=5s) is simulated with three realistic dock tunes used while racing in different wind conditions. Dock tunes are defined as the number of screw turns applied to the shrouds turn-buckles. Tune 2 is the reference dock tune used for the considered sailing conditions. The three dock tunes are described bellow: tune 1 : -3 turns on V1 shrouds used in light wind tune 2 : reference dock tune tune 3 : +3 turns on V1 shrouds used in medium wind This three dock tunes not only modify the rigidity of the full rigging but have a significant influence on the camber and maximum camber height of the mast. The sails shape and more precisely their camber and twist are modified by the dock tune. Before the pitching simulation, the main sail and jib are trimmed in order to ensure that the chord at the centre of effort height has the same angle of attack for the different tunes. The centre of effort height z a is identical for the three dock tunes. Figure 11 illustrates the driving force coefficient evolution versus the non-dimensional displacement dx. The loops look similar, however, the exchanged energy computed as described in section 4 shows variations. Table 2 presents the relative evolution of the mean driving force and exchanged energy compared to the reference dock tune tune 2. The effect of various dock tunes on the mean driving force and energy inside the hysteresis loop is not very strong, but trends can nevertheless be noticed. For the same wind velocity and pitching amplitude and period, the energy associated to the driving force hysteresis is increased by 3% for the less tight dock-tune (tune 1 ) and reduced by 4% for the tightest dock-tune (tune 3 ), compared to the reference. The effect on mean driving force is only of order 1% in the same direction. Figure 11: Driving force coefficient vs. non-dimensional displacement dx for different dock tunes, for a pitching amplitude A=5 and period T=5s. The loop area represents the work exchanged. dock tune W W tune2 Cx C xtune2 Cy C y tune2 tune tune tune Table 2: Non-dimensional work W= T C xdx associated to hysteresis loop, mean driving force coefficient Cx and mean heeling force coefficient Cy for different dock tunes, relative to reference case (tune 2 ), for a pitching amplitude A=5 and period T=5s. 6.2 Influence of the backstay load The influence of a variation of the backstay tension on the dynamic behaviour is investigated. The same pitching motion (A=5 and T=5s) is simulated with four values of backstay load: 1000N, 1500N, 2000N and 2500N. The case 2000N is the reference backstay load used for the previous simulations. The sail trims are identical for the four backstay loads. Preliminary steady simulations with the four loads have shown the ability of ARAVANTI model to simulate the effect of the backstay: the main twist increases, the main camber decreases and moves backward when the backstay load increases. Figure 12 illustrates the driving force coefficient evolution versus the non-dimensional displacement dx. As expected, the mean driving and heeling forces are greatly affected by the backstay load, which changes the main sail camber and twist (see Tab. 3). The backstay load also has a great influence on the energy contained in the hysteresis loop (see Tab. 3). The computed work decreases when load in the backstay is increased. This interesting observation could be due to the great importance of the rig flexibility under pitching. The reduction of energy

170 Figure 12: Driving force coefficient vs. non-dimensional displacement dx for different backstay loads, for a pitching amplitude A=5 and period T=5s. The loop area represent the work exchanged W. Load W W 2000N Cx C x2000n Cy C y 2000N 1000N N N N Table 3: Non-dimensional work W= T C xdx, mean driving force coefficient Cx and mean heeling coefficient Cy for different backstay loads, relative to reference case (2000N), for a pitching amplitude A=5 and period T=5s. exchanged with the increase of load in the backstay seems to be due to higher longitudinal stresses on the rigging. With more stresses, the rig is getting closer to a rigid structure and comparison between FSI and rigid simulation [4] has shown that the hysteresis phenomenon is significantly lower in the rigid case. 7 CONCLUSIONS The unsteady fluid structure interaction of the sails and rig of a 28-foot (8m) yacht under harmonic pitching has been investigated in order to highlight the contributions of the rig adjustments and the consideration of a realistic pitching motion in the dynamic behaviour of a sail plan. The ARAVANTI model is based on an implicit unsteady coupling between a vortex lattice fluid model and a finite element structure model, and has been previously validated with full scale experiments in upwind real conditions [3]. Previous studies [13, 4] have shown that the aerodynamic coefficients plotted against the instantaneous apparent wind angle exhibit an hysteresis loop. These results confirm that the dynamic behaviour of a sail plan subject to yacht motion deviates from the quasi-steady theory. Oscillations of the aerodynamic forces exhibit phase shifts and hysteresis which increase with the motion reduced frequency and amplitude. In this article, it is shown that the loop area is not only due to the phase shift. After shifting by the phase delay τ, the hysteresis loop of C x,y = f(β eff (t + τ)) does not collapse into a single line. The energy contained in the hysteresis loop is determined by integration of the driving force along the back and forth motion due to pitching at the centre of effort height. The resulting work is shown to increase with the pitching frequency and amplitude. Further work is needed to better understand the energy transfer in the system, and to confirm the evolution of phase shift and amount of energy on a larger motion parameters range. Pure harmonic surge motion is compared to pitching motion in order to highlight the importance of a realistic 3D motion. Oscillations of the aerodynamic coefficients decrease by 25% in the case of surge motion compared to the pitching motion case. Moreover, in the case of the surge motion, the hysteresis phenomenon is almost cancelled, so that the dynamic behaviour is similar to the quasi-steady theory. When the surge motion is decomposed into two components, perpendicular to and along the apparent wind direction, it is shown that the major contribution to force oscillation is due to the orthogonal oscillation component, which is associated to the oscillation of apparent wind angle. Finally, a pitching motion of the structure with various shrouds dock tunes and backstay tension loads is simulated in order to study the influence of the rigging stresses on the dynamic behaviour. Both mean driving force and work inside the hysteresis loop are decreased when the stresses in the rig are increased. Acknowledgements The authors are grateful to K-Epsilon company for continuous collaboration. This work was supported by the French Naval Academy. References [1] B. Augier, P. Bot, F. Hauville, and M. Durand. Experimental validation of unsteady models for Wind / Sails / Rigging Fluid structure interaction. International Conference on Innovation in High Performance Sailing Yachts, Lorient, France, [2] B. Augier, P. Bot, F. Hauville, and M. Durand. Experimental full scale study on yacht sails and rig under unsteady sailing conditions and comparison to fluid structure interaction unsteady models. The 20th Chesapeake Sailing Yacht Symposium, Annapolis USA, [3] B. Augier, P. Bot, F. Hauville, and M. Durand. Experimental validation of unsteady models for fluid structure interaction: Application to yacht sails and rigs. Journal of Wind Engineering and Industrial Aerodynamics, 101(0):53 66, 2012.

171 [4] B. Augier, P. Bot, F. Hauville, and M. Durand. Dynamic Behaviour of a Flexible Yacht Sail Plan. Journal of Ocean Engineering, 66:32 43, [5] V. Chapin and P. Heppel. Performance optimization of interacting sails through fluid structure coupling. 2nd International Conference on Innovation in High Performance Sailing Yachts, Lorient, France, [6] T. Charvet, F. Hauville, and S. Huberson. Numerical simulation of the flow over sails in real sailing conditions. Journal of Wind Engineering and Industrial Aerodynamics, 63(1-3): , [7] A. D. Fitt and T. R. B. Lattimer. On the unsteady motion of two-dimentional sails. J. Appl. Maths, 65: , [8] R. G. J. Flay. A twisted flow wind tunnel for testing yacht sails. Journal of Wind Engineering and Industrial Aerodynamics, 63(13): , Special issue on sail aerodynamics. [9] F. Fossati. Aero-Hydrodynamics and the Performance of Sailing Yachts: The Science Behind Sailing Yachts and Their Design. Adlard Coles Nautical, [10] F. Fossati and S. Muggiasca. Sails Aerodynamic Behavior in dynamic condition. The 19th Chesapeake Sailing Yacht Symposium, Annapolis, USA, [11] F. Fossati and S. Muggiasca. Numerical modelling of sail aerodynamic behavior in dynamic conditions. 2nd International Conference on Innovation in High Performance Sailing Yachts, Lorient, France, [12] F. Fossati and S. Muggiasca. Experimental investigation of sail aerodynamic behavior in dynamic conditions. Journal of sailboat technology, (03), [13] F. Fossati and S. Muggiasca. An experimental investigation of unsteady sail aerodynamics including sail flexibility. 4th High Performance Yacht Design Conference Auckland, New Zeeland, [14] R. Garrett. The symmetry of sailing: the physics of sailing for yachtsmen. Sheridan House, Inc., [15] F. Gerhardt, Richard Go Jo Flay, and Patrick Jo Richards. Unsteady aerodynamics of two interacting yacht sails in two-dimensional potential flow. Journal of Fluid Mechanics, 668(1): , [16] F. Hauville, M. Durand, and Y. Roux. Aero elastic model applied to the deformation of a rig. European Journal of Environmental and Civil Engineering, 12(5): , [17] P.S. Jackson. An improved upwind sail model for vpps. The 15th Chesapeake Sailing Yacht Symposium, Annapolis, USA, [18] J.A. Keuning, K.J. Vermeulen, and E.J. de Ridder. A generic mathematical model for the manoeuvring and tacking of a sailing yacht. The 17th Chesapeake Sailing Yacht Symposium, Annapolis, USA, pages , [19] C.A. Marchaj. Sail performance: techniques to maximize sail power. International Marine/Ragged Mountain Press, [20] Y. Masuyama and T. Fukasawa. Full scale measurement of sail force and the validation of numerical calculation method. The 13th Chesapeake Sailing Yacht Symposium, Annapolis, USA, [21] Y. Masuyama, Y. Tahara, T. Fukasawa, and N. Maeda. Dynamic performance of sailing cruiser by a full scale sea reality. The 11th Chesapeake Sailing Yacht Symposium, Annapolis, USA, [22] H. Renzsh and K. Graf. Fluid Structure Interaction simulation of spinnakers - Getting closer to reality. 2nd International Conference on Innovation in High Performance Sailing Yachts, Lorient, France, [23] T. Richardt, S. Harries, and K. Hochkirch. Maneuvering simulations for ships and sailing yachts using friendship-equilibrium as an open modular workbench. International Euro-Conference on Computer Applications and Information Technology in the Maritime Industries, [24] Y. Roux, M. Durand, A. Leroyer, P. Queutey, M. Visonneau, J. Raymond, J.M. Finot, F. Hauville, and A. Purwanto. Strongly coupled VPP and CFD RANSE code for sailing yacht performance prediction. 3rd High Performance Yacht Design Conference Auckland, New Zeeland, [25] Y. Roux, S. Huberson, F. Hauville, J.P. Boin, M. Guilbaud, and M. Ba. Yacht performance prediction: Towards a numerical vpp. High Performance Yacht Design Conference, [26] H. Schoop and N. Bessert. Instationary aeroelastic computation of yacht sails. International Journal for Numerical Methods in Engineering, 52(8): , AUTHORS BIOGRAPHY Benoit Augier holds the current position of post doc fellow in Department of Structural Engineering at UCSD, San Diego, USA. He obtained his Ph.D. at the Naval Academy Research Institute, Brest, France in His research interests include Fluid Structure Interaction, Dynamic behaviour of a soft membrane, Full Scale Experiment and CFD Simulations. Frédéric Hauville holds the current position of Associate Professor at Naval academy Research Institute-IRENav. He is co-responsible of the Voil Enav project which concerns activities in the field of fluid dynamics applied to sailing yachts. His current research interests includes, both by

172 numerical and experimental approaches, problems of fluid structure interaction applied to the deformation of flexible surfaces and the hydrodynamic study of the forced moving foils applied to propulsion and marine current turbines. His previous experience includes a PhD in fluid dynamic in Patrick Bot holds the current position of associate professor at the Naval Academy Research Institute in fluid mechanics and energy engineering. His research interests include yacht dynamics, sail aerodynamics and fluid structure interaction. His previous experience includes hydrodynamic instabilities and transition to turbulence. Mathieu Durand holds the current position of R&D director at K-Epsilon company. He is responsible for FSI developments and sails simulations. His previous experience includes a PhD in fluid dynamic in 2012, but also sailing experience as match-racing skippers (#40 in world ranking in 2011). Julien Deparday is a Ph.D. student at the Naval Academy Research Institute. He is studying the Fluid Structure Interaction on soft surfaces applied to sails. He is in charge of the experimental work.

173 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France FSI Investigation on Stability of Downwind Sails with an Automatic Dynamic Trimming M. Durand, Company K-Epsilon, Sophia-Antipolis, France, C. Lothode, Company K-Epsilon, Sophia-Antipolis, France, F. Hauville, Research Institute of the French Naval Academy, France, A. Leroyer, Centrale Nantes/CNRS, France, M. Visonneau, Centrale Nantes/CNRS, France, R. Floch, Incidences-Sails, Brest, France, L. Guillaume, BSG-Développements, La Rochelle, France, Gennakers are lightweight and flexible sails, used for downwind sailing configurations. Qualities sought for this kind of sail are propulsive force and dynamic stability. To simulate accurately the flow around such a sail, several problems need to be solved. Firstly, the structural code has to take into account cloth behavior, orientation and reinforcements. Flexibility is obtained by modeling wrinkles. Secondly, the fluid code needs to reproduce the atmospheric boundary layer as an input boundary condition, and be able to simulate separation. Thirdly, fluid-structure interaction (FSI) is strong due to the lightness and the flexibility of the structure. The added mass is three orders of magnitude greater than the mass of the sail, and large structural displacement occurs, which makes the coupling between the two solvers difficult to achieve. Finally, the problem is unsteady, and dynamic trimming is important to the simulation of spinnakers [4]. The main objective is to use numerical simulations to model spinnakers, in order to predict both propulsive force and sail dynamic stability. Recent developments [2] are used to solve these problems, using a finite element program dedicated to sails and rig simulations coupled with a RANSE solver. The FSI coupling is done through a quasi-monolithic method. An ALE formulation is used, hence the fluid mesh follows the structural deformation while keeping the same topology. The fluid mesh deformation is carried out with a fast, robust and parallelized method based on the propagation of the deformation state of the sail boundary fluid faces [3]. Tests are realized on a complete production chain: a sail designer from Incidences has designed two different shapes of an IMOCA60 spinnaker with the SailPack software. An automatic procedure was developed to transfer data from Sailpack to a structure input file taking into account the orientation of sailcloth and reinforcements. The same automatic procedure is used for both spinnakers, in order to compare dynamic stability and propulsion forces. Then a new method is developed to quantify the stability of a downwind sail. 1 INTRODUCTION 1.1 UNSTEADY FSI ON DOWNWIND SAILS In recent years, CFD computations for sailing yachts and specifically for sails have increased considerably the performance of yachts sails. Most publications have concentrated on upwind sails. Downwind sails, due to their lightweight and instabilities are more frequently treated with experimental procedure (Renzsch [6]). A few publications try to simulate the complex flow and the response of the downwind structure [4] [7] [8]. To the author s knowledge, no published numerical unsteady FSI on downwind sails is available. 1.2 GOALS OF DOWNWIND SAILS Sail designers use specific software such as Sailpack to define the sail shape, called the moulded shape based on their experience to develop a flying shape. Sail designers try to optimize the parameters to maximize the propulsive force, while keeping the most stable flying spinnaker. Stability is essential for gennakers, particularly for single-handed boats. Stability can be defined by sailmakers as the capability of the sail to maintain its trimmed shape. The leading edge of a trimmed gennaker is very light and has a periodic behavior. When the sail is breaking (i.e. curling) on the luff, a stable gennaker does not need to have the trim adjusted: it is unfolding on its own. In the case of an unstable gennaker, a crew member

174 must adjust the trim or bear away to unfold the gennaker. Unfortunately, this behavior is very sensitive to wind variations, and to the boat motions. There is no physical quantity that directly measures the stability of a gennaker: it is only indicated by the sailor s feel. Stability as a dynamic behavior, requires the use of a dynamic FSI tool to simulate. We have also developed a trimming procedure, in order to quantify the stability of the gennakers. In this study, we investigate two real gennakers built, tested and used during the last Vendée Globe. Thus, the two spinnakers are really close in terms of their design, but have different performances. Those differences are small, but significant for both sailors and sailmakers. These two spinnakers have been digitized and then compared for one wind condition, taking into account the atmospheric boundary layer. 2 ARA WITH FINE TM /Marine: A COMPLETE UNSTEADY FSI SOFTWARE Figure 1 : quasi-monolithic algorithm for fluidstructure interaction, fluid algorithm in blue, FSI added procedure in red. for example, but sometimes also due to the unsteadiness of the flow itself (vortex shedding, unsteady separation location, etc). The problem for downwind sails is even more complex because the flow is often detached from the sails, and the sails are subject to large shape changes. IRENav, K-Epsilon and the DSPM team of LHEEA have jointly developed a coupled computational tool able to compute the fluid-structure interaction characterizing the dynamic behavior of sails in wind. This coupled simulation tool is composed of an original finite element code ARA [2] developed by K-Epsilon to simulate sails and the rig of sailing boats (mast, shrouds, sheets, etc). A wrinkle formulation is included to model the local deformations of sails without having to use too many elements. This code is coupled to the URANSE solver ISIS-CFD [1] (internationally distributed by NUMECA Int. as FINE /Marine) developed by the DSPM team of LHEEA. The fluid-structure interaction between sails and wind is a difficult problem because it is strongly coupled. As stated previously, the added mass on a spinnaker is typically three orders of magnitude larger than the mass of the structure. Adding the fact that the structure has almost no bending stiffness, this makes it a very difficult problem. The followed approach is based on the use of an improved strongly-coupled methodology. The stability of the multi-step procedure is ensured by the use of the Jacobian matrix characterizing the coupling between the structure and the fluid; this Jacobian is approximated with the help of a potential fluid solver AVANTI, developed by K-Epsilon. Although not monolithic, this algorithm is very stable, fast and parallelized. Figure 2 : Fluid mesh deformation around a main sail and gennaker, during an unsteady simulation. Modeling the wind, sail and rig interactions on a sailing yacht is a complex subject, because the quality of the simulation depends on the accuracy of both the structural and fluid simulations, which strongly interact. Moreover, the sails are subjected to highly unsteady oscillations due to waves, wind variations, course changes or trimming A new mesh deformation tool has also been developed to transmit the deformation of the sails to the fluid domain without having to rebuild a new grid from scratch. This method, based on the combination of an explicit advancing front method and smoothing is also

175 parallelized, fast, robust and used to compute the large deformations of the unstructured mesh around multiple bodies like a spinnaker and main sail interacting together. The code s accuracy was verified by an experimental comparison performed on a well-controlled test case with an original experiment developed by IRENav [2] [9], which consisted of a square of spinnaker fabric mounted on two carbon battens which were moved in a forced oscillation. Finally, applied application is made on an unsteady sailing spinnaker with an automatic trimming algorithm, interacting with a mainsail which was realized to illustrate the potential of the present fluid-structure coupling (show Figure 2 for an example, from [2]). 3 CHOICE AND DESIGN OF THE TWO GENNAKERS 3.1 CHOICE Shapes of gennakers are widely differing, depending of the type of boat, the range of wind and their use. In this paper, two very similar gennakers are compared, in order to estimate the capability of the process to distinguish the characteristics of closely related sails. These sails were designed and used during the Vendée Globe by two skippers. 3.2 DESIGN Once gennaker A was designed, Gennaker B was a small evolution with these differences: - the luff twist is 1% smaller and the luff roach is 0.4% smaller - the sail is 1% less twisted - the maximum sail camber is 0.7% deeper, and 1% further forward The sail areas are identical and the tack, head and clew points are in the same position for both spinnakers. Figure 3 : Top view of the two spinnakers as moulded: Gennaker A in red, and gennaker B in blue. On the top is the luff (leading edge), on the left is the leech (trailing edge). 3.3 TESTS IN REAL LIFE The two sails were tested by sailmakers during full-size sessions in real conditions. During tests, and without measurement, sailors feel that propulsive forces of the two gennakers were close. The goal of the modifications made on the second spinnaker was to get more stability. In fact, during test session, the luff of gennaker A was sometimes curling hard, and collapsing. The crew therefore had to modify the trim or bear away. This means that they change drastically the heading of the boat, in order to increase the incidence on the sail. These modifications of the trim or boat heading decreased the performance of the boat. The luff of gennaker B had a different behavior: The luff curled moderately, and most of the time, no actions were needed to uncurl the luff. 4 GENNAKERS DIGITALISATION Sails were designed by another sailmaker soft from the company Incidences. The real sails were digitized, using the software Sailpack developed by BSG Développements, in order to respect the initial shape of the mould. The design process is as follow: Design of the sail mould in 3D Definition of seam layouts Definition of patche layouts Definition of the cloth properties, the doubled or tripled layers and the orientation of the cloth for each panel. From this information, SailPack calculated the 2D panels that were used to build the real sail. Then a triangular mesh is generated for each 2D panel. The outline nodes of the meshes were connected to simulate the assembly of the sail. All the nodes were then moved to recompose the sail in 3D, keeping the 2D initial node distances. This way the resulting 3D mesh is based on the 2D panels that are used for the real assembly of the sail. Stiffness matrices were associated to each mesh element. The cloth, its orientation and the number of layers were taken into account (Figure 4). Additional reinforcements were made with undeformable patches of 20 cm radius around the three points. The structural model was composed of about 7000 membrane elements, with 1 wire element for the sheet. The stiffness matrices of each material used were provided from tests on each piece of cloth. To simplify the computation, the mainsail and all rigging were not meshed, and were not simulated.

176 Figure 4 : Left: View of the stiffness of the gennaker. Right: zoom on the tack point. Arrays symbolize the direction of maximal stiffness. for an air particle to travel from the luff to the leech was 3.5s at z= 15m. 5.4 UNSTEADY FSI The computations are realized on 2 dual-processor hexacore Xeon X5670 (24 cores). The computation was restarted from the converged structure and converged fluid of the initial computations. The computation was performed with unsteady RANSE, with the k-omega SST turbulence model. The simulation time is fixed at 25 seconds. Such a long time is necessary in order to obtain periodic results. 5 SIMULATION PROCESS The steps of a computation can be summarized: Structural computation Fluid meshing Fluid computation Unsteady FSI with trimming procedure 5.5 TRIMMING PROCEDURE The trimming algorithm (Figure 5) is defined in order to give an objective of zero pressure on the leading edge. This algorithm measures the pressure differential on the leading edge, and gives a trimming order such that the leading edge normal velocity is in opposition with the direction as the pressure force. A signal treatment with the leading edge velocity measurement is realized to obtain the sheet length. This procedure is dynamic: the length of the sheet is therefore always changing. Figure 5 : The trimming algorithm. 5.1 STRUCTURAL COMPUTATION In the first step, a structural computation is made with a uniform pressure on the sail. The length of the sheet is modified in order to orient the sail correctly according to the incoming flow. This first step permits the generation of the fluid domain. 5.2 FLUID MESHING In the second step, the meshing around the deformed sail is done through Hexpress TM, a fully hexahedral automated mesh generator based on the octree method. Boundaries are about 120m for the spinnaker in the two upwind directions, 240m in the two downwind directions, zmax is 120m and zmin is zero. Cells are refined close to z=0m to take into account the atmospheric boundary layer, and refined near the sail. The entire model is meshed with 1.8 millions cells. 5.3 FLUID COMPUTATION A fluid convergence is required before starting unsteady FSI simulation. Conditions on boundaries are made to simulate the atmospheric boundary layer. A boat speed of 5.92m/s is used in conjunction with a logarithmic boundary layer (Z0=0.002m); true wind speed measured at 30m is 7.72m/s, true wind angle is 150 degrees. The apparent wind speed at z= 15m is about 2.6m/s. The time Some tests were needed to adjust PID parameters: too violent of a trimming algorithm work like a pumping trimmer, some waves appears and move on the sail. With too slow of an algorithm, the luff collapses hard, and the computation could stop, due to limits of the mesh deformations. 6 RESULTS AND COMPARISONS BETWEEN THE TWO GENNAKERS Figure 2 shows the result of the trimming algorithm for the two gennakers. During the first five seconds, the large amplitude proved that the gennaker is in a bad trim position at the start. The length of the sheet then slowly becomes periodic, and after 17s of simulation, it has become fully periodic. Four periods of the periodic behavior of the two spinnaker are shown in Figure 6. The sheet lengths of the two gennakers are periodic, and very similar to the behavior of real life gennakers. Those sheet variations of gennaker A are much greater than those of gennaker B. Others results, reported in Table 1, Figure 9 and Figure 10, come from an averaging procedure of the two last

177 periods of the motion. Positions, as well as pressure and elongation have been averaged. Figure 7 : Top view and aft view of the averaged flying shape during computation. Figure 9 shows the delta pressure between pressure and suction faces of the sail. The trimming algorithm tries to obtain a zero pressure difference on the leading edge, this is accomplished for half of the luff: The upper half has a zero mean pressure difference. This is indicative of an attached flow on this part of the sail. In the lower part, where the luff is not curling, the low pressure on the leading edge indicates a detached flow. Global pressure values are quite similar between the two sails, but gennaker B has a larger difference pressure. Figure 6 : Result of trimming algorithm on the length of the two gennakers sheets (red line: gen. A, blue line: gen. B): variations showing the instability of the gennakers. From these results, we proposed a measurement of the stability, dependent of the triming algorithm, based on the height of the sail divide by the amplitude of the trimming: Stab = H / Amp Table 1 : Summary of the differences measured between the two gennakers. Gennaker A Gennaker B Difference Propulsive Force [N] % Side Force [N] % Vertical Force [N] % Stability %.

178 Figure 8 : Comparison of the behavvior of the luff for the two gennakers during 4 stepss of the period. Figure 10 : Front view off averaged deformation on gennaker A. Yellow represent 0.4% of deformation in the cloth. c Figure 9 : Two views of the averageed delta pressure (pressure - suction, [P]) during two period: p gennaker A on the left, gennaker B on the t right. Sailmakers are also interesteed in other results such as the deformation of the cloth: Figure F 10 shows the mean deformation in the cloth. Maaximum deformation of about 0.4% occurs near the lufff, on both sides, near the reinforcements. 7 CONCLUSIONS A complete procedure foor the comparison of two gennakers was described. Thhe procedure integrates CFD and FEA in a dynamic sim mulation with an automatic trimming procedure and is a powerful and advanced tool for the prediction of flyingg shape, as well as the sail forces and the stability off gennakers. A quantitative measure of the sail stabiliity has been presented and gennaker B has been show wn to be more stable with regards to this criteria. Further investigations with this tool will be made, such as modification of the turbulence models for the fluid part, investigation of the innfluence of the mainsail in terms of the gennaker desiggn and flying shapes. Other trimming procedures will be b tested with the help of sailmakers and professional sailors. Comparisons will be made with an instrumented gennakers. g

179 REFERENCES [1] B. Augier, P. Bot, F. Hauville, and M. Durand, Experimental validation of unsteady models for fluid structure interaction : Application to yacht sails and rigs, Journal of Wind Engineering and Industrial Aerodynamics 101 (2012), [2] M. Durand, Interaction fluide-structure souple et légère, applications aux voiliers, Ph.D. thesis, Ecole Centrale Nantes, [3] M. Durand, F. Hauville, P. Bot, B. Augier, Y. Roux, A. Leroyer, and M. Visonneau. Unsteady numerical simulations of downwind sails. In the second international conference on innovation in high performance sailing yachts (INNOV SAIL 2010) (2010), [4] K. Graf, H. Renzsch Investigations of Downwind Sails and integration into Sailing Yacht Design Processes 2nd High Performance Yacht Design Conference Auckland, February, 2006 [5] J. Wackers, B. Koren, HC Raven, A. van der Ploeg, AR Starke, GB Deng, P. Queutey, M. Visonneau, T. Hino, and K. Ohashi, Free-surface viscous flow solution methods for ship hydrodynamics, Archives of Computational Methods in Engineering 18 (2011), no. 1, [6] H. Renzsch and K. Graf. An experimental validation case for fluid-structure-interaction simulations of downwind sails, Proceedings of the 21th Chesapeake Sailing Yacht Symposium, March [7] D. Trimarchi, Analysis of downwind sail structures using non-linear shell finite elements, Ph.D. Thesis, University of Southampton, 2012 [8] M. Lombardi, Numerical simulation of a sailing boat: free surface, fluid-structure interaction and shape optimization, Ph.D. Thesis, Ecole polytechnique fédérale de Lausanne, 2012 [9] B. Augier, Experimental Studies of the Fluid Structure Interaction on Soft Surfaces: Application to Yacht Sails, Ph.D. Thesis, French Naval Academy Research Institute - IRENav, 2012 AUTHORS BIOGRAPHY M. Durand holds the current position of R&D director at K-Epsilon company. He is responsible for FSI developments and sails simulations. His previous experience includes a PhD in fluid dynamic in 2012, but also sailing experience as match-racing skippers (#40 in world ranking in 2011). C. Lothode holds the current position of R&D engineer at K-Epsilon company. He is responsible for FSI computations and development. His previous experience includes a M.Sc. in Applied Mathematics. F. Hauville holds the current position of Associate Professor at Naval academy Research Institute-IRENav. He is co-responsible of the Voil'Enav project which concerns activities in the field of fluid dynamics applied to sailing yachts. His current research interests includes, both by numerical and experimental approaches, problems of fluid structure interaction applied to the deformation of flexible surfaces and the hydrodynamic study of the forced moving foils applied to propulsion and marine current turbines. His previous experience includes a PhD in fluid dynamic in A. Leroyer holds the current position of Associate Professor at the LHEEA laboratory of Ecole Centrale Nantes. His research topics revolve around the numerical modelling of the incompressible isothemal flows around complex geometries and are more specifically focused on the methodologies to integrate new physical phenomena inside a Navier-Stokes solver, as the fluid-structure interaction and the numerical modelling of cavitation. He is part of the developer team of ISIS-CFD. His previous experience includes a PhD in fluid dynamics in M. Visonneau born in France in He obtained the Engineer's diploma in 1980 from Ecole Nationale Supérieure de Mécanique (now Centrale Nantes) and the diploma of Advanced Naval Architecture from ENSM in In 1985, he got a PhD of Fluid Dynamics and Heat Transfer of University of Nantes and entered the "Centre National de la Recherche Scientifique (CNRS)" as Research Scientist. He became the head of the CFD department of the Fluid Mechanics Laboratory (ECN) from 1995 to In 2001, he got the Research Habilitation Diploma and was promoted Research Director within CNRS in His main research topics are Computational Fluid Dynamics (CFD), Ship Hydrodynamics and Turbulence Modeling for high Re flows. In 1991, he got the 2nd Cray Prize for CFD and has been awarded 30th Georg Weinblum Memorial Lecturer ( ) in R. Floch holds the current position of Sail Designer at Incidence Brest. He is responsible of the R&D coordination, and the sails design of Figaro Class, M34, and Open 60. His previous experience includes two Olympics preparations with 470 boats. L. Guillaume holds the current position of R&D engineer at BSG Développements company. He is responsible for the development of SailPack sail design software and other sail analysis software. His previous experience includes the development of sail vision and analysis systems for different America s cup campaigns.

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181 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France DEVELOPMENT OF COMPUTATIONAL FLUID-STRUCTURE INTERACTION METHOD FOR YACHT SAILS F.M.J. Bergsma, N. Moerke and K.S. Zaaijer, Van Oossanen Naval Architects, Netherlands, H.W.M. Hoeijmakers, University of Twente, Netherlands, SUMMARY This paper presents a Fluid-Structure Interaction (FSI) method for sails. In this FSI method the pressure field around the sail is determined using the Computational Fluid Dynamics (CFD) package FINE/Marine using the ISIS solver. This computational method is based on the Reynolds-Averaged Navier-Stokes Equations (RANSE). The computed pressure field serves as input for a basic structural model implemented in the Nastran-based Finite Element Analyses (FEA) package Femap which determines the deformation of the sail subject to the aerodynamic load. In an iterative procedure the distribution of the surface pressure and the deformation of the sail attain a stable equilibrium. The aim of the FSI method is to determine the steady flying shape of the sail and to obtain the aerodynamic forces generated by the sail taking into account the deformation of the sail. A method is presented for 2D sail sections as well as a method for 3D upwind sails. These methods are capable of determining the steady deformation of the sail. The results of the method for 2D sail sections are compared with a set of experimental data. This comparison shows that the deformed shape of a 2D mast and sail section compares satisfactorily with measured data for various combinations of slackness and angles of attack. NOMENCLATURE sample point chord length (m) elasticity modulus (N m -2 ) gravitational acceleration (m s -2 ) turbulence kinetic energy (m 2 s -2 ) cloth length (m) outward bound normal vector (-) number of sample points in RBF (-) pressure field (N m -2 ) Reynolds number (-) control volume surface (m 2 ) rate of strain tensor (s -1 ) slackness (-) velocity field (m s -1 ) velocity of surface (m s -1 ) flow velocity fluctuation (m s -1 ) deformation (m) air speed (m s -1 ) control volume (m 3 ) weighting factor in RBF (-) interpolated point (m) dimensionless distance from wall (-) angle of attack ( ) excess cloth length (m) air dynamic viscosity (Pa s) turbulent viscosity (Pa s) Poisson ratio (-) density (kg m -3 ) stress tensor (N m -2 ) viscous stress tensor (N m -2 ) Reynolds stress tensor (N m -2 ) radial basis function (m) 1 INTRODUCTION Currently most procedures for sail design, i.e. providing planform, camber and cloth selection, are based on experience. Mostly crude analytical models and models based on a regression of previous wind tunnel tests are used to predict the lift and drag forces on sails. In the analysis of the aerodynamic performance of sail designs only a few designers use computational methods. These are usually based on potential flow methods for predetermined shapes. Since the deformation of the sail due to aerodynamic loads can be substantial, improvements in the prediction of the aerodynamic performance of sails can be achieved by using Fluid-Structure Interaction (FSI) analysis. FSI is the interaction between a deformable structure and the flow surrounding it. FSI is regarded as a frontier in numerical methods for sailing [1]. The flying shape is determined by the structural properties of the sail and the pressure distribution on the sail produced by the flow around the sail. A common approach is the so-called segregated or partitioned approach. This means that first the flow around a given shape of the sail and corresponding flow domain is solved using Computational Fluid Dynamics (CFD). This yields the pressure distribution on the sail. This pressure distribution is exported to a structural method (Finite Element Method), which solves for the deformed shape under the specified load.

182 The deformed shape is used to update the flow domain and the flow around the new geometry is calculated. This process repeats in an iterative manner until convergence of the sail shape and the flow is attained. The first efforts in fluid structure interaction were made by Schoop [2] [3] [4] and Fukasawa and Katori [5]. Vortex Lattice potential flow models were coupled with linear elastic models for the sails. The applicability of the used models can be questioned, but more computational power was required to introduce viscous flow models and non-linear elastic models for the structural behaviour of the sail [6]. From 2008 on, a new generation of FSI methods was introduced. These models are based on viscous flow CFD solvers, combined with more advanced models for the structural behaviour of the sail. In 2008 Renzsch, Muller and Graf presented a fluid structure interaction method for downwind sails [7]. A RANSE solver was combined with the self-developed code FlexSail for the structural behaviour of the sails. A wrinkling model was introduced to cope with compressional loads in the sails [8]. Paton Morvan and Heppel described the coupling between the RANS method CFX and a purpose-built code called RELAX for membrane structures aimed to model the structural behaviour of sails [9]. In 2011 the same structural model was weakly coupled to the RANSE solvers FLUENT and OpenFOAM [10]. Trimarchi et al. developed a weak coupling between the unsteady RANS solver OpenFOAM and a structural method that uses shell elements instead of the more common membrane elements. These shell elements are able to capture the wrinkling of the sail better [11]. A new approach to the coupling of the structural and the fluid model was applied recently by Lombardi, et al.. Instead of the commonly used weak coupling, the FSI problem is solved using a strongly coupled segregated approach. This is achieved by introducing a sub-iteration cycle for every iteration step. This is necessary to prevent numerical instability which occurs for large deformations [12]. Meanwhile, a strong coupling was established between the inviscid flow solver AVANTI with the structural model ARA which uses membrane elements. Validation was performed by comparing numerical results with the data from full scale tests. Comparison of the sail shape for the steady case showed good correspondence. [13] The aim of the work presented here is to develop and validate a method to predict the flying shape of the sail under steady conditions. Results of both 2D and 3D cases are presented. Numerical simulation for 3D FSI has been performed to investigate the capabilities of the FSI method, but crude methods are used for the prediction of the deformation. Three main topics are covered: the CFD method that is used to predict the pressure field around a sail; the structural method used to predict the deformation of a sail; and the computational procedure that handles the iterative process and the transfer of data between the structural method and the CFD method. 2 CFD METHOD In this section a description is given of the CFD method used to determine the flow. First the governing equations are given. This is followed by a description of the computational domain and the boundary conditions, and of the mesh. The geometry and flow conditions for the 2D and 3D case are given. 2.1 GOVERNING EQUATIONS The modelling of the viscous-flow is based on Reynolds Averaged Navier Stokes equations (RANSE) for the incompressible-unsteady turbulent flow. This is done using the ISIS solver from the FINE/Marine package [14]. The equation for mass conservation is given in integral conservation form by: The equation of conservation of momentum is given by: Closure of this set of equations is obtained by defining the stress tensor: Here is the Reynolds stress tensor and the viscous stress tensor. The viscous stress tensor is defined as: Here is the rate of strain tensor. The Reynolds stress tensor is defined as:

183 A closure of this term is required to solve the set of equations. Turbulence viscosity models are used for this closure. These models are based on the Boussinesq approximation. This commonly used approximation gives the Reynolds stress as follows: The SST-Menter turbulence model is used. This model is most suitable for both upwind and downwind sails [15]. 2.3 MESH Meshes have been generated using HEXPRESS v2.11: a top-down mesher for unstructured hexahedral meshes. For all cases the mesh near solid surfaces is sufficient to maintain a y + -value of around 1 in boundary layers. For the 2D case a mesh study has been performed using the NACA0012 wing section. This section is chosen since it has been used for experiments extensively, making it very suitable for validation purposes. A coarse but characteristic mesh for this geometry is shown in Figure DOMAIN AND BOUNDARY CONDITIONS The size of the domains used for 2D and 3D cases is tabulated in Table 1. For the 2D case the size of the domain in spanwise (up-down) direction is set to unity. For the 3D case the bottom of the domain is placed ½ chord length below the foot of the sail. This represents the water surface. The size of the computational domain followed from a study on the effect the size on the computed forces on the sail. Table 1 Computational domains in chord lengths c. Domain size (c) 2D 3D Upstream 50 8 Downstream Transverse 50 8 Up - 12 Down - ½ The boundary conditions are applied as tabulated in Table 2. The development of the earth s boundary layer is not incorporated. Instead, a symmetry (slip) boundary condition is applied, mimicking the presence of the water surface without generating a surface boundary layer at the bottom of the domain, which would complicate the numerical simulation. Table 2 Boundary conditions of computational domain. Boundary Condition type 2D 3D Inlet Far field velocity Far field velocity Outlet Zero pressure gradient Zero pressure gradient Transverse Far field Far field Top Mirror Far field Bottom Mirror Mirror Sail/foil No Slip No slip Figure 1 characteristic mesh for NACA0012 profile, generated with HEXPRESS v2.11. The number of elements along the chord was varied by increasing the number of refinements. Lift and drag coefficients were determined for various meshes. The results are shown in Table 3. Table 3 - Lift and drag coefficients for different number of chord-wise elements. NACA0012, Re = , =5, 19 viscous layers, y It shows that good convergence behavior occurs for the drag coefficient, which converges asymptotically to a value of for meshes with 256 chord-wise elements and more. The lift coefficient does not appear to converge monotonically. This is believed to be due to the unstructured meshing method, but for meshes finer than 512 elements along the chord, the variation of the lift is acceptably small (within 0.5%). This makes it possible to calculate the lift and drag of the section sufficiently accurate.

184 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France A mesh deformation algorithm that is included in the Fine/Marine package is used to adapt the meshes to the deformed sail shape. In FSI the flow needs to be solved for every iteration step taking into account a slightly deformed geometry. Being able to deform the mesh without loss of accuracy omits the need to re-mesh the computational domain every iteration. It was verified that using mesh deformation does not decrease the accuracy of the predicted lift and drag forces of the sail D GEOMETRY AND FLOW CONDITIONS The geometry used for 2D numerical simulations is based on the experimental setup by Yam, Karlin & Arieli [18]. The experimental setup is shown in Figure 3. In the figure the flow direction is from right to left. The chord of the sail is 138 mm and the span 350 mm. The cloth (white) is attached to the leading and trailing edge with two sleeves. At both ends of the wing endplates are mounted parallel to the flow (1) to reduce the 3D behaviour of the flow. The two endplates are connected by two circular rods (2) of 6mm diameter. One of them functions as the leading edge. This is used as pivoting point in order to vary the angle of attack. The trailing edge (3) consists of a 15 mm blade with a thickness of 1.5 mm that is connected to ball bearings that enable the plate to rotate freely around its longitudinal axis. Figure 2 Typical CFD surface mesh for a sail showing varying refinements along the height and additional refinements at the edges. For the 3D case a mesh has been generated with a varying number of refinements along the height of the sail. This is necessary because the geometry used has, roughly, a triangular shape. To maintain the specified number of cells along the chord, an increasing number of refinements is required with decreasing chord length of the sail. The sail of the experimental setup consists of a freely rotating trailing edge and a sleeve around the leading edge that is free to rotate around a rod. Accounting for these rotations in the numerical simulations is beyond the scope of the presented research and not relevant for the purpose of simulating the deformation of yacht sails. In the numerical simulations the leading and trailing edge are therefore considered rigid and fixed. Deformation of the cloth occurs between the two sleeves only. The shape and position of the leading and trailing edge are taken from the experimental data. This is visualized in Figure 4. The blue line shows the geometry as measured for the case of an angle of attack of 4.5 and a slackness of 1.5%. In addition, extra refinements along the edge of the sail are applied. Wilkinson [17] showed that these are the regions where flow separation due to high adverse pressure gradients can occur, which can be captured more accurately with the locally refined mesh. It was found that a mesh with 64 elements along the chord and edge refinements gives a good balance between accuracy and computational time. An example of a coarse surface mesh of this type is shown in Figure 2. Figure 3 - Test rig with a sail as used in the experimental setup [18].

185 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France The position and attitude of the plate of the trailing edge is taken from the measured data and used as input for the geometry of the numerical simulations. The geometry of the leading edge is constructed from the diameter of the mast and lines that are tangent to this mast corresponding to the cloth of the sleeve around the mast. In the numerical simulations this part of the geometry is fixed as well. The attitude of mast and trailing edge vary for each case and are therefore adjusted for each numerical simulation. The initial shape of the cloth (red) is constructed from the arc of a circle with a length equal to the length of the undeformed cloth between the sleeves in the experiment. Please note that this length is not necessarily equal to the length of the sail shape in the experiment, since the experimental data shows the deformed sail shape. This becomes clear in Figure 4 from the difference in arc length between the red line and the blue line. Figure 4 Deformed experimental result (blue dots) and the geometry used for numerical simulations: The deformable part in the simulation is shown in red (dashed). The fixed leading and trailing edge are shown in black (continuous). The flow conditions for the 2D case are tabulated in Table 4: Table 4 Flow conditions for 2D FSI simulations. Air dynamic viscosity (Pas) Air density (kg m -3 ) 1.2 Air speed (m s -1 ) 20 Reynolds number (-) D GEOMETRY AND FLOW CONDITIONS The geometry used for 3D numerical simulations has a span (height) of the sail of 10.5 m. The maximum chord is 4 m at the foot of the sail. The head of the sail is 0.2 m. the total surface area is m 2. The angle of attack is constant with height and has a value of 5. Commonly sails are designed with twist. However, since the CFD method does not account for a variation in wind speed and direction with height above the water surface, it was chosen to maintain a constant angle of attack by removing the twist in the sail. A mast is not incorporated in this geometry definition yet. This can be added to the geometry at a later stage. Flow conditions are tabulated below. The value for the Reynolds number is based on the maximum chord length. Table 5 Flow conditions for 3D FSI simulations. Air dynamic viscosity (Pas) Air density (kg m -3 ) 1.2 Air speed (m s -1 ) 8 Reynolds number (-) STRUCTURAL METHOD Sails are made of thin cloth with anisotropic material properties. These cloths are exposed to a laterally distributed load. This causes large deflections, i.e. deflections that are as large as multiples of the thickness of the cloth. This renders the structural problem nonlinear. The code used for the structural analysis is the Nastranbased Femap v10.0 package. The sail is discretized using plate elements. These elements have resistance against bending. Four-noded quadrilateral (CQUAD4) elements are used to discretize the geometry. From the mesh study it follows that for the 2D case a mesh with 100 elements along the chord of the sail is sufficient to obtain a mesh independent solution of the deformation. For the 3D case a mesh with 20x20 elements was used. This is a very coarse mesh. Literature recommends at least 15,000 elements in total [9]. Such a large mesh leads to time consuming interpolations of the pressure fields, therefore meshes of this size were not used for the actual FSI simulations in the present study. The mesh for the 3D sail should therefore be considered as crude and further development of the structural method is required. A nonlinear static analysis is performed to solve for the deformation of the plate under uniform lateral load. 75 increments or load steps are adopted with a maximum of 25 sub-iterations per load step. For the 2D case the cloth has a thickness of 62 μm. An isotropic linear elastic material model was adopted. The stiffness of the cloth was varied between E = N/m 2 and N/m 2 and the Poisson ratio was set to = 0.3. This is representative for the nylon spinnaker cloth used in the experiments by Yam et al. For the 3D case the sail has an -modulus of N/m 2 and a Poisson ratio of 0.3, representative for Dacron sail cloth. The thickness used is 5 mm, relatively thick compared to cloth used for sails. This was chosen in order to prevent large deformations that cannot be handled by the mesh deformation algorithm as currently implemented. 4 FSI COUPLING Fluid structure interaction covers the coupled system of fluid and structural mechanics. The behaviour in the fluid domain can influence the behavior in the structural domain and vice versa. The structure can move or deform due to flow phenomena on its turn. The structure influences the flow behaviour in its turn. The flying shape of the sail is determined by FSI. The flow field and the structural deformation balance each other. This balance can be both steady and unsteady.

186 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France 4.1 PRINCIPLE OF FSI COUPLING A steady staggered weak FSI coupling is established. This means that the deformation field on one hand and the pressure field on the other hand are solved independently, by specialized solvers. The main advantage of this approach is that readily available and optimized numerical methods can be used. For this approach an exchange of information at the interface between the domains is required. Iterations are performed until convergence is reached. 4.2 SCHEME A schematic representation of the FSI scheme is shown in Figure 5. This scheme consists of the following steps: 1. With the initial geometry and specification such as flow properties and structural properties two numerical simulations are set-up. A CFD computation is defined in FINE/Marine and a FEA computation in Femap. For both the application of the CFD method and the application of the FEM method a mesh is defined. All parts of the method that are identical for each iteration are defined in this step. 2. Using the initial mesh for the CFD method a CFD analysis is started for the initial geometry. This analysis leads to a pressure distribution on the surface of the sail. This part of the numerical procedure is written in Python. 3. The FEM method uses the pressure field from step 2 to define a load on the initial geometry and a numerical simulation is started. This leads to a deformation field. This part of the numerical procedure is written in VB.NET. 4. The deformation field is compared with the deformation field of the previous iteration. If the convergence criterion is met, convergence is achieved and the final (flying) shape of the sail is found. If convergence is not achieved the FSI cycle continues with step 5. For the first iteration no previous deformation field is available so the check on convergence is omitted. 5. The displacement field is only defined in terms of the coarse FEM grid. To define the deformed shape for the finer CFD grid an interpolation is required. This is performed using radial basis function interpolation This part of the numerical procedure is written in Matlab. 6. The FSI iteration number is increased by The geometry of the new iteration is written from the interpolated displacement field to a so called ITSfile. This is the geometry definition format for the input for the CFD method. 8. Using the definition of the deformed geometry step 2 is started again. The CFD method takes care of the mesh deformation. This step completes the cycle. This cycle is repeated until the convergence criterion is met. Figure 5 Schematic representation of developed FSI method. 4.3 INTERPOLATION The flow solver and the structural solver use different meshes. To be able to transport quantities (deformations/pressures) over the interface between the non-matching grids interpolation is required. Radial Basis Function (RBF) interpolation is used for the interpolation of the deformation to the flow domain. RBFs are functions whose value depends on the distance from a sample point: Sums of radial basis functions can approximate function values at random points: RBFs have been used for example by Lombardi et al. [12] for the interface between the fluid and structural domain. According to Smith, Hodges and Cesnik [19], RBF interpolation with thin plate splines (TPS) is the most accurate and robust method to transfer information between non-conforming meshes. This is confirmed by De Boer, Van Zuijlen & Bijl [20], who favor RBF with TPS over other methods because of the accuracy and the simple algorithm of such an approach.

187 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France The second interpolation is the interpolation of the pressure data to the structure. A function with which to do this is already present in the used code Femap used for the structural problem. Interpolation is performed via a Modified Inverse Distance Weighted Interpolation [21]. Locations at which pressures are known, are provided to the method and interpolated to a data surface with the pressure data in the FEA domain. 5 RESULTS The results of the first FSI calculations are presented in this chapter. An overview of the performed numerical simulations for the 2D test case is given and the simulation capabilities for 3D test cases are demonstrated D RESULTS Only a selection of experimental cases was steady enough to serve as test case for numerical simulations with the currently developed method. Numerical simulations have been performed for assessing the effect of three parameters: The slackness was varied in accordance with the experiments. The angle of attack was varied in a certain range. The E-modulus of the cloth of the sail. Since the material properties of the cloth are not available, a sensitivity study has been performed to assess the effect of the stiffness of the cloth on the flying shape of the sail. The used values of the E-modulus are based on values used for similar purposes as found in literature [11] [22]. An overview of the runs with their specifications is tabulated below. For each run the depth of the sail for the initial (unloaded) and final (loaded) geometry is given. The last column shows the maximum error between the numerically determined flying shape and the experimentally determined flying shape as a percentage of the chord length. Table 6 - Overview of numerical simulations of 2D sail. Re = ( ) (-) E-modulus (MPa) Depth (initial) Depth (final) Max error 1a % 3.56% 1.85% 1b % 4.35% 1.05% 1c % 5.45% 0.46% % 5.76% 0.48% % 5.74% 0.45% % 7.81% 0.78% % 9.87% 0.54% Cases 1a to 1c show the effect of the variation of the modulus of the cloth on the flying shape and on lift and drag. A clear dependence of the deformed shape on the stiffness of the sail is shown. From the three cases the flying shape with the lowest value of the E-modulus has the best correspondence with the experimentally observed flying shape. Therefore this stiffness was used for the remaining cases. Case 1c to 3 show the effect of the variation of the angle of attack on the flying shape and lift and drag. The angle of attack is increased by approximately 2 degrees in each run. There is no substantial variation in the deviation between experimental and numerically determined flying shape. This shows the good predicting qualities of the FSI method within the range of angles of attack considered. For larger and smaller angles of attack unsteady effects were present in the experimental setup which cannot be accounted for accurately by the present numerical FSI method. The method can be extended to cover unsteady simulations if needed. Cases 2, 4 and 5 show the influence of the variation in the slackness of the cloth on the flying shape and lift and drag. The increased slackness causes deformations to become larger. Generally this leads to a slightly lower accuracy in the numerical prediction of the flying shape but the results are still within acceptable accuracy (error less than 1%) D RESULTS Numerical simulation for 3D FSI has been performed to investigate the capabilities of the present FSI method. The FEA mesh of the 3D sail is very crude and requires further improvement to be capable of predicting the flying shape of a 3D sail more accurately. Since experimental data is not available for this case, a validation could not be performed. The deformation field of the sail is shown in Figure 6. In this figure the sail is given by coloured dots and the deformation field is represented by blue arrows. This is the deformed shape after 9 iterations. It can be observed that the leech of the sail stretches and bends away from the wind. This is the location where the largest deformation occurs. Along the luff or leading edge deformation to windward occurs indicating a too small angle of attack. The sail should be sheeted in more. The top and foot of the sail show large deformations. This can be due to tip vortices at each end of the foil/sail or due to the coarse FEM mesh.

188 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France Figure 7 - Ripples at leading edge near tack of deformed shape of 3D. 6 CONCLUSIONS The aim of this research was to develop a Fluid Structure Interaction method for yacht sails. This has resulted in a method that is capable of predicting flying shapes for sails for both 2D and 3D cases. Figure 6 Displacement vectors of deformed shape of 3D sail. Vectors are magnified for visibility. When the deformed shape is examined more closely near the tack of the sail ripples are observed. These are visualized in Figure 7. The grey sail is the original undeformed sail and the red sail is the deformed sail shape. These ripples are caused by the interpolation of the deformation data. This is an indication that more sample points (and thus a finer FEM mesh) are required for more accurate interpolation of the deformation. A steady segregated coupling is established to make optimal use of the available CFD and FEA packages. The flow field is determined by solving the RANS equations using FINE/Marine CFD package employing the SST-Menter turbulence model. A mesh study was presented for the 2D case. Mesh deformation is used to deform the mesh according to the deformed shape of the sail. The pressure distributions obtained for deformed meshes are validated with pressure distributions obtained for un-deformed meshes. Comparison of the results of the 2D case with experimental values shows good agreement in terms of deformation. It should be remarked that the application of a boundary layer method that includes a laminarturbulent transition model could improve the prediction of the drag coefficient. A coarse FEM mesh for computing the deformation of the sail under the aerodynamic load has been developed. The sail is discretized using four-noded quadrilateral elements. For the material properties linear isotropic homogenous material properties are chosen.

189 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France Interpolation of the deformation field across the nonconforming meshes of the fluid and structural domain is performed using Radial Basis Function interpolation. Errors in the interpolation can be reduced by using finer FEA meshes or increasing the number of sample points near the edges of the sail. FSI analysis of 2D geometries has been performed and has been compared with available experimental data. Several runs have been performed to tune the unknown material properties of the sail cloth. For several angles of attack and slackness of the sail cloth good agreement has been found with experimental data. Differences between experimentally and numerically determined flying shapes amount to 0.8% of the chord length. FSI analysis of a 3D geometry has also been performed, showing the capabilities of the FSI method to predict a flying shape for this specific geometry. The predicted deformation of the sail is in agreement with the expected flying shape, but experimentally obtained flying shapes are not available for validation. When assessing the flying shape it should be taken into account that a crude FEM mesh for the sail was used which should be improved to predict the flying shape more reliably. ACKNOWLEDGEMENTS The authors would like to thank Maor Yam for providing experimental data on their study to the deformation of 2D sails. The comparison of the results of the present method with experimental results would not have been possible without his experimental data. The Numeca support team and Benoit Mallol are thanked gratefully for their very quick response on support issues and for providing a pre-release with essential capabilities for meshing sails. Their enthusiastic reactions to our results were encouraging. REFERENCES 1. Fossati, F., Aero-Hydrodynamics and the Performance of Sailing Yachts. London : Adlard Coles Nautical, Schoop, H., Structural and Aerodynamic Theory for Sails. Eur. J. Mech. A/Solids 9(1), Schoop, H. & Hänsel, M. Structural and Aerodynamic Calculation of Sails as Flexible Membranes, Ship Technology, Vol. 44, Schoop, H., Bessert, N. & Taenzer, L., On the Elastic Membrane in Potential Flow, Int. J. For Numerical Methods in Engineering, Vol 41, Fukasawa, T. & Katori, M., Numerical approach to Aeroleastic Responses of tree-dimensional flexible sails, The 11th Chesapeake Sailing Yacht Symposium, Annapolis, Schoop, H. & Bessert, N., Instationary Aeroelastic Computation of Yacht Sails, Int. J. Numer. Meth. in Engineering, Vol 52, Renzsch, H., Muller, O. & Graf, K., FlexSail - A Fluid Structure Interaction Program for the Investigation of Spinnakers, Proc. Intl. Conference on Innovations in High Performance Sailing Yachts, Lorient, Renzsch, H. en Graf, K., Fluid Structure Interaction Simulation of Spinnakers - getting closer to reality, Proc. 2 nd. Intl. Conference on Innovations in High Performance Sailing Yachts, Paton, J., Morvan, H.P. & Heppel, P., Fluid Structure Interaction of Yacht Sails, Proc. Intl. Conference on Innovations in High Performance Sailing Yachts, Chapin, V.G., de Carlan, N. & Heppel, P., A Multidisciplinary Computational Framework for Sailing Yacht Rig Design & Optimization trough Viscous FSI, The 20th Chesapeake Sailing Yacht Symposium, Annapolis, Trimarchi, D., Turnock, R., & Taunton D.J., The Use Of Shell Elements To Capture Sail Wrinkles, And Their Influence On Aerodynamic Loads, Proc. 2 nd. Intl. Conference on Innovations in High Performance Sailing Yachts, Lorient, Lombardi, M., Cremonesi, M., Giampieri, A., Parolini, N. & Quarteroni, A., A strongly coupled Fluid- Structure Interaction model for wind-sail simulation, 4th High Performance Yacht Design Conference, Auckland, Augier, B., Bot, P., Hauville, F., Durand, M., Dynamic Behaviour of a Flexible Yacht Sail Plan, Ocean Engineering, 66:32 43, Numeca International, Theoretical Manual Fine/Marine v2.3., Collie, S.J., Gerritsen, M. & Jackson, P. A review of Turbulence Modelling for use in Sail flow Analysis, School of Engineering Report No Department of Engineering Sciences, University of Auckland, Abbott, I.H. & Von Doenhoff, A.E. Theory of Wing Sections, Mineola : Dover Publications, Inc., Wilkinson, S. Static Pressure Distribution over 2D Mast and Sails Geometry, Marine Technology, Vol. 26, Yam, M., Karlin, B.E. & Arieli, R., Estimation of Two-Dimensional Sail Shape from Single Camera Images., 52 nd Israel Anual Conference on Aerospace Sciences, Tel Aviv Haifa, Smith, M.J., Hodges, D. H. & Cesnik, C.E.S., An evaluation of computational algorithms to interface between CFD and CSD methodologies, AIAA paper , de Boer, A., van Zuijlen, A.H. & Bijl, H., Review of coupling methods for non-matching meshes, Computer methods in applied mechanics and engineering. 196, PLM, Siemens, Femap Commands version , Trimarchi, D. & Rizzo, C.M., A FEM-Matlab code for Fluid-Structure interaction coupling with application to sail aerodynamics of yachts, 13th Congress of Intl. Maritime Assoc. of Mediterranean, Istanbul, 2009.

190 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France AUTHORS BIOGRAPHY Friso Bergsma M.Sc. is CFD specialist at Van Oossanen Naval Architects. He is responsible for (hydrodynamic) optimization and various R&D projects. His previous experience includes full scale testing of sails at the University of Auckland. Niels Moerke M.Sc. B.Eng. is Director/Naval Architect at Van Oossanen Naval Architects. He is responsible for the CFD department and small craft design. His previous experience includes design and optimization of various award winning sailing yachts. Sebastiaan Zaaijer M.Sc. is CFD specialist/naval Architect at Van Oossanen Naval Architects. He is responsible for optimization and research projects. His research focuses on optimization methods for the shape of the hull and appendages of yachts. Prof. dr. ir. Harry Hoeijmakers is chairman of the research group Engineering Fluid Dynamics at the University of Twente. Among his research areas are fluid dynamics, aerodynamics of wind turbines, flow control for various applications and multi-phase flows for industrial applications.

191 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France FLUTTER OF RACING YACHT KEELS AND APPENDAGES R. Balze and H. Devaux, HDS BREST, France, In the field of aeroelasticity, flutter is a well-known instability phenomenon. Flutter is a synchronized vibration which takes place in a flexible structure moving through a fluid medium. It occurs when two regular, rhythmic motions coincide in such a way that one feeds the other, drawing additional energy from surrounding flow. A classic case of wing flutter might combine wing bending with either wing twisting. Flutter appeared for the first time on racing yacht keels with composite fins, so in water, in 2004, on both the IMOCA 60 POUJOULAT-ARMORLUX, which lost her keel, and SILL. Following these problems - particularly following the loss of the keel of Bernard STAMM sailboat, accident that could have dramatic consequences for the skipper - HDS company focused on the phenomenon. This paper will introduce the strategy of HDS faced to the problem and the analytical and numerical methods implemented to estimate the flutter critical speed. Our model is based on a truncated modal basis for the most energetic modes which are generally, for a bulb keel, the lateral bending predominant mode and the torsion predominant mode. One of our requirements was to make a simple model in order to integrate the calculation of the flutter critical speed in the first design loops of a composite or steel keel. Besides, an other requirement was to be able to calculate flutter critical speed on other type of appendages: hydrofoils, dagerfoils, dagerboards, rudders This model has worked well for the two cases of flutter appeared on IMOCA sailboat keels. Besides, to verify the quality of the model and to complete our analysis of flutter phenomenon on racing yacht keels, a 3 dimensional multiphysic simulation has been developed using the software ADINA. NOMENCLATURE Xb, Yb, Zb Boat axis system Xk, Yk, Zk Keel axis system x, y, z, t Space and time variables ux, uy, uz Translation degree of freedom x, y, z Rotation degree of freedom Ct Torsional center (neutral line position) F Lift center Keel sweep angle K Stiffness matrix M Mass matrix V Fluid velocity i Incidence angle A Slice area c Linear lift coefficient w Water density j Complex number j² = -1 i Damping terms i Damping rates i =2. i i Eigen frequencies in rad/s Fi Eigen frequencies in Hz Fiw Eigen frequencies in water in Hz i, i Real (imaginary) part of the roots i Global damping rates including flow Ma Added mass due to bending Ia Added inertia due to torsion Symbol used for a value close to zero ii Phase aii Amplitude 1 INTRODUCTION In September 2004 'Cheminées Poujoulat - Armor Lux' lost her composite keel in mid-atlantic. Her skipper Bernard Stamm recalls: 'I was going down below at the end of a surf at 27 knots when I felt the keel making horrendous thrashing vibrations, almost immediately the keel broke and the boat capsized. I just had time to call Mark Turner (race director) before water flooded in and the boat inverted.' Earlier that year Roland Jourdain on 'Sill et Veolia' had disturbing vibration problems in the composite keel when sailing at around 20 knots in calm sea. His experience raised concern for Jean Le Cam aboard 'Bonduelle' - an identical sistership to 'Sill et Veolia' - although she had never had such problems. Because of safety precautions, both pulled out of The Transat race even before it started. An increase of the torsional rigidity of the foil, by adding to the laminate permitted thereafter, on these two boats, to overcome the problem. But the composite keel flutter phenomenon remained an open question for yacht designers. Following the composite keel flutter problems, HDS tried to better understand what are the sailing conditions and the parameters of a keel design that could cause flutter. The main questions asked are 'Why are composite keels susceptible to flutter, and is it possible to predict and prevent this behaviour?', then 'Can a fair indication of the flutter critical speed be given at low cost and in the first design loops of a keel?'.

192 In this paper, we describe firstly the semi analytical model we implemented to predict keel flutter at an early stage of a keel design. Secondly, we present results obtained with a 3 dimensional multiphysic simulation on a keel flutter case and we compare it with the results obtained with our semi analytical model. Thus, the multiphysic simulation allows us to confirm some assumptions we take to build our model. Besides, it permits to have some estimation of some terms that are important in our semi analytical model to predict flutter phenomenon in the heavy fluid water is, especially fluid damping at zero flow velocity. 2 KEEL DESCRIPTION IMOCA 60 keels are vertical weighted wings, on the bottom of the hull. This wing is properly called keel fin and the weight on the bottom of it is called 'bulb' because of it shape. Anti-drift and stability functions are usually dissociated. Thus the keel fin is more a bulb support than an anti-drift profile (Daggerboards are actually the anti-drift profiles of the yacht). This allows to increase the maximum righting moment using canting keels (Figure 1), which means that we can change the keel s angle to the vertical axis. 3 HDS MODEL PRINCIPLE HDS model able to calculate flutter critical speeds is based on the equations introduced by R. MAZET in Mécanique vibratoire [1], applied to airplanes wings vibrations. In our case, hydrodynamic efforts are simplified and represented as distributed along the keel fin over two-dimensional slices. The systems dynamic is represented just by the first two eigenmodes. In fact, the first eigenmode will mainly represent bending behavior, and the second will represent torsional behavior. This explains why Mazet assumes that these two modes represent pure bending and pure torsion respectively. However, while dealing with IMOCA 60 keels, the presence of a solid bulb and the possible gap between its center of gravity to the main fiber of the keel fin, leads to important coupling between bending and torsion. HDS s model, takes this coupling into account for the calculation of bending and torsional displacements before projecting the equations on the truncated modal basis. Hydroelastic vibration s equations give us the movements damping rates for each speed. Flutter phenomenon appears when one of these rates becomes zero (self-maintained vibrations). 4 DEFINITIONS AND NOTES We will now only focus on the part of the keel under the hull. We use the axis system presented on Figure 2. Keel fin Hull Bulb Figure 1 : IMOCA 60 Keel description (left) and canting keel (right) The main features of an IMOCA 60 keel are the following one: keel length is about four meters (m), keel fin mass about five hundred kilograms (kg), bulb mass about three tons (T) and bulb inertia about one thousand two hundred kilograms square meters (kg.m²). Figure 2 : Useful notes and axis system used in the model (Profile view on the top, upper view on the bottom)

193 The keel axis system is defined by a rotation of an angle + around Yb axis. is the sweep angle and is generally between 0 and 15. In the following sections, we only present the case =0. 5 EIGENMODE CALCULATION The calculation of Eigenmodes is done by following the discretized finite elements method, using six degrees of freedom beam elements (one translation and two rotations by node, representing bending and torsion). The beam model element used is the bending-torsion beam model presented by G. BEZINE in La méthode des Eléments Finis en Calcul des Structures [2]. We can consider tow type of keel: Cantilever keel Canting keel: the keel is pinned at the upper edge and at the hull bearing, and unable to twist at the hull bearing. On the Figure 3, the point N represents the intersection between the main fiber of the fin neutral fiber and the bulb axis. The point G represents the bulb s center of gravity. We assume that the segment NG is infinitely stiff and that the bulb s weight and inertia are transported to the point N using Huygens theorem. (Segment NG is not represented in the beam FEA model). uy = 0 x y uy = 0 z = 0 z Figure 3 : The canting keel beam finite element model We have to solve the following classical system: MX + KX = 0 or G N 2 ( K ω M) X 0 = (1) This method of eigenmode calculation gives good results for keels, compared to eigenmodes experimentally obtained or calculated with a complete 3D composite finite element model, provided the composite material properties of the finite element beam model are properly input. To calculate the hydrodynamic lift force, we use the slice method. It s not possible to give a strictly accurate linearized expression of the resultant of water pressures on the slice except if the slice is motionless, animated with a uniform translation or animated with a sinusoidal vibration. However, an approximate expression of a lift force can be given, considering that we are in quasi-static regime. Thus, for a flow velocity V, this lift force is applied on the Lift Center F and can be decomposed into two forces: The first one is related to the incidence angle i between the slice and the flow s direction: 1 2 c ρ w A V i 2 (2) The second one is linked to translation speed of the lift center F, orthogonally to flow direction: 1 2 y F c ρw A V 2 V (3) The global lift force is the sum of the two previous expressions. The coefficient c is the linear lift coefficient, equal to 2. for a flat plane in linear theory without viscous effects ([3]). For a 3D wing profile with viscous effects, this coefficient, averaged on the height of the keel, is lower and depends on the wing aspect ratio. 7 RESULTS Applying the theorem of virtual works on both the two eigenmodes at each flow velocity, we obtain a system of two homogeneous second order equations and whose determinant must be zero. This determinant has four roots, two to two conjugated complexes: ε 1 ± j.ω 1 and ε 2 ± j.ω 2 (4) The following ratios represent the damping rates for a particular flow velocity V: 1 α1 = ε Ω 1 2 α 2 = ε and Ω2 Flutter phenomenon appears when one of these damping rates becomes zero. In fact, to find the critical speed, we will iterate on the speed until one of these damping rates becomes zero. On the Figure 4, 1 becomes zero at 18 knots flow velocity. (5) 6 LIFT FORCE

194 The time integration scheme for the structure is a Newmark one with the classical values =0.25 and =0.5 which permit to conserve energy, so to avoid numerical damping on the structure. 8.2 FLUID MODEL Fluid model dimensions are the following: L=7m, W=2m, H=4m. The 3D CFD mesh used and its close-up around the profile are shown on Figure 6. Figure 4 : Curves of the damping rates i versus flow velocity (knots) 8 MULTIPHYSIC SIMULATION MODEL To verify the quality of our semi analytical model and to have an estimation of some of its terms, we built some multiphysic simulations with the software ADINA. We present here one of these simulations. 8.1 SOLID MODEL We have modeled a cantilever keel as follows: Keel s fin with constant profile Upper section embedded Solid bulb concentrated on a single node (inertia matrix) The profile used is a typical keel fin profile and the keel height is 4m. Besides, the bulb mass is 3.1T and its inertia is 900 kg.m² as an IMOCA 60 keel bulb. The 3D keel model is presented on Figure 5. Most of the elements are hexahedral (8 nodes per elements, 3 degrees of freedom per node). The material model chosen is composite orthotropic one. Figure 6 : 3D CFD Mesh The fluid is modeled as a laminar incompressible Navier- Stokes fluid and is discretized using the ADINA FCBI-C ([4]) fluid elements. The time integration method is an Euler -method in which we make vary the parameter to evaluate the numerical damping. A priori the choice =0.5 allows to avoid numerical damping but causes convergence problems unless the velocity is extremely small. The fluid inlet velocity is a parameter that we make vary from 8 m/s to 12 m/s (Except for fluid damping analysis in that the inlet velocity is 0 m/s). The outlet is set to be traction free and the rest of the fluid boundaries are modeled as sliding wall boundary conditions. To generate a time response (damped for the stable regime or amplified for the unstable regime) of the keel, a small transverse perturbation load is applied on the bottom of the keel at the first time step. Figure 5 : Keel model We placed the bulb at two different positions for depending on each simulation: on the torsional center C t of the bottom section of the keel behind this torsional center (in the boat axis system) 9 ADDED MASS ESTIMATION To have an estimation of the added mass generated by the bending and torsion of the fin, we calculated eigenmodes in both cases with and without water around the keel. The following tables compare the frequencies obtained without and with the water for a bulb placed on

195 the torsional center of the bottom section of the keel (bending and torsion being decoupled): Without water : F1 (Hz) F2 (Hz) Therefore we can estimate separately the bending damping term 1 (Figure 7) and the torsion damping term 2 (Figure 8), each damping terms due to fluid model. 1.00E-01 Bending time response With water : F1 w (Hz) F2 w (Hz) F1 corresponds to the first eigen frequency (only bending here) and F2 corresponds to the second eigen frequency (only torsion here). The index w denotes a frequency in water. Transverse displacement of the bulb 8.00E E E E E E E E E E E E E E E E-02 Simulation results Analysis curve By comparing the frequencies obtained in presence and in absence of water, we can estimate the added mass terms generated by bending and torsion motion of the fin: M a (bending) (kg) I a (torsion) (kg.m²) E-01 time Figure 7 : Bending time response of the keel in water for Euler integration scheme parameter =1 and time step=0.01. The blue points are from simulation results, the pink curve is the analysis curve to estimate the bending damping rate. We can note that Ma is about the same order that the fin s own weight (240 kg in this simulation) and significantly less the bulb s own weight. Moreover, compared to bulb s inertia, Ia is negligible. 2.00E E E-02 Torsion time response For a bulb placed 0.160m behind C t (bending and torsion coupled): Rotation of the bulb 5.00E E E E E E E E E E-03 Simulation results Analysis curve Without water : F1 (Hz) F2 (Hz) With water : F1 w (Hz) F2 w (Hz) DAMPING ESTIMATION For any vibrating structure subjected to damping, time response signals to a load impulse can be decomposed on exponentials sums taking damping under consideration. If we focus on the two first eigenmodes of the structure, signal analysis allows to know the damping rates of each mode 10.1 FLUID DAMPING We analyze the time response of the keel after an impulse. There are two kinds of impulse, a transverse effort for a bending response of the keel and a torque for a torsion response of the keel, both applied on the bulb node. In order to turn the analysis easier, we decouple the eigenmodes by placing the bulb on the torsional center E E E-02 time Figure 8 : Torsion time response of the keel in water for Euler integration scheme parameter =1 and time step=0.01. The blue points are from simulation results, the pink curve is the analysis curve to estimate the torsion damping rate. Thanks to these time response, we can deduce the damping rates i (%) for each eigenmodes: η 1 = 10.6% and η 13.4% 2 = (6) These damping rates are not negligible but contain both fluid and numerical damping here linked to time step choice, Euler integration scheme parameter choice and mesh. We searched to evaluate the influence of time step (Figure 9) and Euler integration scheme parameter choice (Figure 10) on these damping rates.

196 40.00% 35.00% 30.00% Damping rates evolution according to the Time step estimated using the time response curves of the behavior of the keel after an impulse excitation. We note that these terms are strongly variable among the different keels; they particularly depend on the chosen materials and the construction method. Damping rates 25.00% 20.00% 15.00% Damping rates evolution for bending Damping rates evolution for torsion 11 CRITICAL SPEED COMPARISON 10.00% 5.00% 0.00% Time step Figure 9 : Damping rates evolution according to the time step with an Euler integration scheme parameter = % Damping rates evolution according to the parameter alpha In the following two paragraphs, the bulb is placed at 0.160m of the torsional center C t MULTIPHYSIC SIMULATION Figure 11 (resp. Figure 12) shows the bulb time response for a flow velocity of 9 m/s (resp. 10m/s). Blue curves represent the transverse displacement of the bulb, while pink ones represent the bulb rotation % 12.00% 3.00E-02 Bulb time response for a flow velocity of 9m/s Damping rates 10.00% 8.00% 6.00% Damping rates evolution for bending Damping rates evolution for torsion 2.00E E % Amplitude 0.00E TRANSVERSE DISPLACEMENT ROTATION 2.00% -1.00E % E-02 alpha Figure 10 : Damping rates evolution according to the Euler integration scheme parameter with time step= e-02 Time Figure 11 : Bulb time response for a flow velocity of 9m/s (=0.6 and time step=0.01). The evolution of damping rates according to time step and to Euler integration scheme parameter shows that fluid damping rates at zero flow velocity tend to the values: 6.00E E-02 Bulb time response for a flow velocity of 10m/s η 1 = 4.4% and η 0.2% 2 (7) These damping rates have to be taken into account in our semi analytical model to compare the estimated flutter critical speed given by both simulation model and semi analytical model. However, to avoid convergence problems in the multiphysic simulation model, we have to choose a parameter >0.5 which implies the unavoidable presence of a slight numerical damping. We choose the smallest parameter for convergence and low numerical damping and take into account this damping in our analytical model to allow proper comparison of results SOLID DAMPING This damping term is not taken into account in the multiphysic simulation model. However, thanks to keel eigenfrequencies measurement, recently imposed by the IMOCA 60 rules, structural damping term can be Amplitude 2.00E E E E E Time TRANSVERSE DISPLACEMENT ROTATION Figure 12 : Bulb time response for a flow velocity of 10m/s (=0.6 and time step=0.01). We note that for a flow velocity of 9m/s, the bulb oscillations are decreasing, while for a flow velocity of 10 m/s oscillation amplitude grows with time; there is flutter instability. Therefore, with this choice of time step and Euler parameter, Flutter critical speed is between 9 and 10 m/s. It s also interesting to note that the frequencies of transverse displacement and rotation of the bulb are almost mixed up, that is characteristic of the flutter

197 phenomenon, and that the phase between the two signals is about / SEMI ANALYTICAL MODEL Eigen frequencies calculated with our model are the following: F1 (Hz) F2 (Hz) With a linear lift coefficient of 2. and with, our model predicts a critical speed of 15.0 knots, corresponding to 7.7m/s. This result takes into consideration damping rates previously predicted by the multiphysic simulation model, but it considers added mass as negligible. If we consider the bending added mass (resp. torsional added inertia) previously computed into the mass (resp. inertia) of the bulb, we obtain the following eigenfrequencies: F1 (Hz) F2 (Hz) Therefore the critical speed becomes 15.3 knots, corresponding to 7.9m/s. In fact, if we consider the 3D effects (especially aspect ratio), the average linear lift coefficient will be smaller. For such a keel, the average lift coefficient is approximately 5.2. With this lift coefficient and taking into account the added mass, we find a critical speed of 16.9 knots, corresponding to 8.7m/s.All main headings should be in bold capitals. 12 CONCLUSION In this paper, we presented a rather simple semi analytical model which provides a good estimation of the flutter critical speed of a bulb keel at low cost. This model, based on some strong assumptions, especially concerning structure dynamic and calculation of hydrodynamic pressure loading, is confronted to a complete 3 dimensional multiphysic simulation and the comparison shows good agreements in terms of results. ACKNOWLEDGEMENTS The authors wish to thank Louis Jézéquel and the Laboratoire de Tibologie et de Dynamiques des Systèmes (LTDS) of the Ecole Centrale de Lyon, and Marc Le Boulluec and the hydrodynamic laboratory of the "Institut Français de Recherche pour l'exploitation de la MER" (IFREMER) in Brest, for their contributions to the success of this project. REFERENCES [1]. MAZET R., Mécanique Vibratoire, Dunod, 1966 [2]. BEZINE G., La méthode des Eléments Finis en Calcul des Structures, Notes De Cours, Ecole Nationale Supérieure de Mécanique et d Aérotechnique, 1998 [3]. ABHOTT I.H. and VON DOENHOFF A.E., Theory Of Wing Sections, Dover, 1958 [4]. BATHE K.J. and al, ADINA online manuels, AUTHORS BIOGRAPHY Rémy Balze is a Mechanical engineer in HDS Design in Brest since He recently finished his PhD in studying the field of hydroelastic phenomena especially composite keel flutter. Hervé Devaux is a Mechanical engineer Doctor and the CEO of HDS Design, in Brest. He has a background in structural dynamics. He can boast about a beautiful prize list in the world of racing yachts. Among HDS success stories, the Hydroptere (1 mile distance world speed record), Banque Populaire 5 (Jules Verne Trophy and 24 hours distance record), Groupama 4 winner of the Volvo Ocean Race, IMOCA 60 MACIF recent winner of the Vendée Globe and many others. He was involved in the last revolution of the America s Cup with multihulls and wingsails. With this semi analytical model, it is possible to calculate a good estimation of the flutter critical speed of a keel in about half a day contrary to the full multiphysics approach which takes several days. The damping terms fluid damping at zero flow velocity and solid damping are important parameters that must be well estimated for a good prediction of flutter. We give an estimation of fluid damping rates to use in the prediction of flutter critical speed for an IMOCA 60 keel. We also show that the added mass effects due to the fin deformation appear to be negligible in prediction of keel flutter but it s not the case for other appendages.

198 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France DYNAMIC FLUID STRUCTURE INTERACTION OF A FOIL C. Lothodé, K-Epsilon, France, corentin@k-epsilon.com M. Durand, K-Epsilon, France, mathieu@k-epsilon.com Y. Roux, K-Epsilon, France, yann@k-epsilon.com A. Leroyer, École Centrale de Nantes, France, alban.leroyer@ec-nantes.fr M. Visonneau, École Centrale de Nantes, France, michel.visonneau@ec-nantes.fr L. Dorez, Groupama Sailing Team, France, loic@groupamasailingteam.com In this paper, a dynamic computation of the Groupama 3 foil is performed. Foils are thin profiles, placed under the hull of a ship, allowing it to provide a lifting force. This study is placed in the context of the 2013 America s Cup, which will see the appearance of a new kind of high performance multihull. At high speeds, the foils are subject to intense hydrodynamic forces and to movement due to the sea state. The deformations are then sizable and there is a risk of ventilation, cavitation or vibration which could lead to a large modification of the hydrodynamic forces or to the destruction of the foil. The foil being light compared to the added mass effect, the interaction is a strongly coupled problem. In this paper, the problem is solved using a segregated approach. The main problems resulting of such a method are the numerical stability and remeshing. These problems are detailed and some results presented. As a first test case, the simulation of a vortex excited elastic plate proposed by Hubner is presented. This case is very demanding in terms of coupling stability and mesh deformation. Then, the foil of Groupama 3 is modelled in a simplified form without hull and free surface, and then in a more realistic conditions with free surface and waves. NOMENCLATURE μ Kinematic viscosity ( N.s.m 2 ) ρ Density of water (kg.m 3 ) P Pressure (N.m 2 ) F Force (N) M Moment (N.m) x, y, z Positions (m) t Time (s) 1 NUMERICAL METHOD The strategy used to solve the fluid structure interaction problem is a partitioned coupling between a fluid solver and a structural solver. The two solvers are described in the following as well as the coupling algorithm. 1.1 FLUID: ISIS-CFD The solver ISIS-CFD included in FINE/Marine TM is developed by the DSPM team of LHEEA laboratory. It solves the Reynolds-Averaged Navier-Stokes Equations in a strongly conservative way. It is based on the finite volume method and can work on structured or unstructured meshes with arbitrary polyhedrons [1]. The velocity field is obtained from the momentum conservation equations and the pressure field is extracted from the incompressibility constraint. The pressure-velocity coupling is achieved through a SIMPLE-like algorithm. All the variables are stored in a cell-centered manner. Volume and surface integrals are evaluated with second order discretization. The time integration is an implicit scheme of order two. At each time step, an internal loop is performed (called a nonlinear iteration) associated with a Picard linearization in order to solve the non-linearities of the Navier-Stokes equations. The equations are formulated according to the Arbitrary Lagrangian Eulerian paradigm and therefore can easily take into account mesh deformations. Several turbulence models are implemented in ISIS-CFD. In this study, we used the SSTk ω model [2]. 1.2 STRUCTURE: ARA The solver ARA was developed by the company K-Epsilon during the project VOILEnav [3]. The code was initially aimed at simulating the dynamic behaviour of sailboat rigs : sails, mast and cables. A non-linear finite element method with a large deformation formulation is implemented. At each time step, an equilibrium between external and internal forces is sought between all the elements and forces acting on them. The elements receive as an input the position, the speed and the acceleration of each of its nodes. It can contain internal variables in the case of elastic deformation, and the element computes the derivatives of forces according to those variables. These derivatives are assembled into a mass matrix [M] = F ẍ, damping matrix [D] = F F ẋ and stiffness matrix [K] = tx. Elements can be composed of different kind of finite elements

199 (cable, beam, shell, membrane). It is also possible to use elements with a penalization method such as contact or sliding elements. In the coupling algorithm, the fluid-structure interface itself is considered as an element. The time scheme used is the Newmark-Bossak scheme (second order accurate). This scheme has been chosen for its compromise between the necessary filtering of the high frequencies while maintaining the accuracy of the low frequencies. The scheme is conservative hence avoids numerical energy creation in case of large non-linearities. 1.3 ELEMENT USED While numerous element types have been implemented in the structural code, in the present study, only beam elements are used. These elements are Timoshenko elements, with the hypothesis of small deformations. We therefore have a constant stiffness matrix in the local frame. Each beam element is defined thanks to two points (for position) and two quaternions (for the tangent directions). More details on the non-linear algorithm used can be found in [4]. 1.4 COUPLING The fluid-structure coupling leads to four problems: the continuity of constraints at the interface ; the deformation of the interface ; the deformation of the fluid mesh ; the coupling algorithm Continuity of constraints The perfect continuity of constraints cannot be assured because of the difference between the fluid discretisation and the structural discretisation. Thus, a consistent method is used (see [4]). The method corresponds to an integration of the forces on the fluid faces : F M = (p n + τ n) dγ Γ and then a projection of those efforts on the degree of freedom of the closest beam element Interface deformation The fluid structure interface is entirely defined by the fluid faces. Each fluid node is projected onto the nearest beam elements in order to get a parameterized position of the projected point as well as a vector linked to the local frame of the beam. When the beam is deformed, the 3D deformation of the neutral axis is computed with the variation of the local frame from one end to the other end of the beam. The local frame evolves smoothly according to a cubic spline law. Therefore, the new fluid node position is computed from the new position of the neutral axis and its local frame (see Figure 1) MESH DEFORMATION Following the interface deformation, the whole mesh of the fluid domain needs to be deformed. This deformation occurs at each coupling iteration. The number of call to this procedure being non-negligible, the mesh deformation needs to be fast. To do this, a new method was developed that propagates the deformation state to the fluid mesh. The algorithm is described more thoroughly in [4]. The rigid displacement (translation and rotation) of each face of the interface is computed. This displacement is propagated to its neighbours and so on iteratively until the boundaries of the mesh are reached QUASI-MONOLITHIC ALGORITHM Time loop FSI loop Jacobian Matrix Computation Structural Computation Conv? no Fluid Computation Under-Relaxation no Conv? Figure 2: Dynamic coupling algorithm. In blue, the fluid solving scheme. In red, the added structural iteration with the Jacobian computation. yes (a) Fluid node projection (red) on the beam (blue segment) (b) Fluid node position is computed according to the neutral axis (cubic spline) and the local frame Figure 1: Fluid structure interface deformation. The global solution algorithm is based on a quasi-monolithic approach. This approach is an implicit coupling adapted to a partitioned solver while conserving the property of convergence and stability of the monolithic approach. To obtain such a result, the structural computation is performed at each non-linear iteration of the fluid (inner loop). The fluid algorithm is not modified. The non-linear iterations include a fluid subiteration and a structural convergence. The

200 y non-linear iterations are performed until convergence, therefore fluid-structure convergence is reached at each time step. Furthermore, an interface element is added to the structural solver. This element is computed from the Jacobian matrix of the interface. In the case of an exact Jacobian matrix, the algorithm is the same as a monolithic algorithm. With the same idea as the quasi-newton method where a simplified Hessian matrix is used, here a simplified Jacobian is computed. The Jacobian matrix is not necessary, even for strongly coupled problems. Nonetheless, its use permits the elimination of under-relaxation, implying a significant reduction in the number of coupling iterations required. With the present method, the ratio between the time of fluid structure interaction and fluid only computations is in between 1 and 2. According to the data, the Reynolds number is 200. The assumption of a laminar flow was used. The physical time of the computation is approximately 25 s and the time step is Δt = 0.001s. The fluid mesh was generated by HEXPRESS TM, the mesher of the software FINE/Marine TM. It has cells and vertices. The structural beam is made out of 100 beam elements. Fy 2e e-05 1e-05 5e e-06-1e e-05 y force Δy 2 TEST CASES -2e t (a) y force (N) t (b) y deflection (m) 2.1 HUBNER TEST To start, an academic test was studied [5]. This case is itself a modification of [6] by changing certain boundary condition and characteristics of the structure. With the case of Hubner, the structure is more bendable and the deformations are larger. The case is therefore harder to study. The parameters of Hubner were studied by Valds et Vázquez [7] and also by Guillaume De Nayer in 2008 [8]. The later modified the dimensions of the domain which he found to be too small. Those dimensions are used here (c.f. Figure 3a and TABLE 3b). Constant Velocity Figure 4: Evolution of forces and deformation The results obtained by Hubner show an amplitude of 6cm and correspond to the results obtained by the method presented here. Furthermore, the frequency (3.15 ± 0.05Hz) is also in the range obtained by Hubner and De Nayer (3.22Hz for De Nayer, 3.10Hz for Hubner). Figure 5 shows the results of the mesh deformation. The cell quality and orientation is preserved even with relatively large deformation. The tip oscillates in phase with the creation of vortices by the square block. We can see these vortices advected in the flow in Figure 5b. U x 0,0006m 0,01 m 0,04 m Constant Pressure 0,24 m 0,065 m y Constant Velocity x 0,21 m (a) Diagram of the simulation domain (a) u Fluid data Fluid density ρ f 1, 18 kg.m 3 Dynamic viscosity μ f 1, Pa.s Inlet velocity U x 0, 315 m.s 1 Structural data Square size a 0, 01 m Length of the tip L 0, 04 m Tip thickness d 0, 0006 m Young modulus E 0, 2 MPa Tip density ρ s 2000 kg.m 3 Poisson coefficient ν 0, 35 (b) Properties of the fluid and the structure Figure 3: Description of the benchmark (b) ω z Figure 5: Visualization of the mesh deformation and creation of vortices in established flow

201 2.2 DAGGERBOARD A daggerbpard is providing side force to counter the force produced by the sail. Recently on multihulls, it iss also use to provide lift force, either as a lift assist foil 1 or a fully flighting foil 2. Most of the time, the influence of the daggerboards can be modified by modifiying their orientation and position. The study is done on the foil of Groupama 3, trimaran of 105 feet (32 m) and 18 tons. The boat broke the Jules Vernes record (fastest circumnavigation around the world) in This boat represents a break through in the concept of oceanic racing yachts by being lighter and by including hydrofoils. The foil used by Groupama 3 is a C foil, which is the shape you can see by looking at it by the front side. It also has a winglet to reduce the induced drag. z zf e-05 Δz t (a) Convergence to the solution r 2 1e+08 1e+07 1e Niter Residual (b) Initial residual forces (before the structural computation is performed) Figure 7: Convergence The Figure 7 shows the quasi-static convergence. We notice that the deflection obtained is converged. The initial residual of the coupling (before computation of the structure) is decreasing by an order of magnitude at each coupling iteration. The solution is convergerd with only 6 quasi-static iterations. Figure 6: Groupama QUASI-STATIC CASE OF A FOIL ALONE In this case, a simplified version of the foil is used. The foil is simply an extrusion of a NACA 4512 profile, with a curvature radius of 3m, without the winglet. Furthermore, we do not take into account the free surface. The structural mesh is given by 14 beam elements, with the node at the highest elevation blockfixed in both position and rotation. The first step is a quasi-static computation to predict the equilibrium position of the foil. Fluid iterations are performed alone until convergence, then a structural convergence is performed. The mesh is updated and a new fluid convergence with the new deformed mesh is performed. The quasi-static loop is done until convergence of the geometry. This convergence is assured only if the problem is stable. The results obtained shows a deflection of 0.595m and a change in forces of N (for an initial F z force of N). Those results were obtained with an inlet velocity of 15m s 1. The gain in lift is big (+25%) whereas the drag is only augmented by a small factor (+3%). By adjusting correctly the neutral axis and the center of effort, this behaviour can be optimized. At this speed, for a deformed foil, the lift represent 50% of the weight of the boat. 1 to reduce the drag by reducing the immersed volume of the hull, which is the case of most sailing multihulls 2 hull out of the water, like the Hydroptre 2.3 VIBRATION STUDY : FLUTTER Starting from a quasi-static computation, it is possible to study vibratory behavior such as flutter. Flutter is a self-feeding and potencially destructive vibration. If the energy input by the hydrodynamic excitation in a cycle is larger than that dissipated by the damping in the system, the amplitude of vibration will increase, resulting in self-exciting oscillation. The prediction of such phenomenon is done through dynamic fluidstructure interaction computations. First, a quasi-static convergence is done on a configuration were the neutral axis is 35cm away from the leading edge (almost in the middle of the chord), with an added momentum at the tip of the foil and with an with an inlet velocity of 10m s 1. Then, the structure is released (no added momentum at the tip) and a dynamic computation is performed. The timestep used during the computation is 10 4 s. It is to be noted that only 13 non-linear iterations are required to reach convergence at each time step when 10 are required with the fluid only (no structure). In Figure 8a and 8c, it is possible to notice that the frequencies involved are not the same : about 200 Hz for the forces whereas the displacement shows a frequency of approxymatly 10 Hz. It is possible to notice that on this case, the vibration is not self-feeding and a damping occurs on the displacement.

202 Fy (N) z y (m) t (s) y force z force (a) y and z forces Fz (N) Fx frequency Fy frequency Fz frequency f (Hz) y position of the tip z position of the tip (b) FFT of y and z forces t (s) (c) y and z displacement of the tip Figure 8: Forces in time and frequency domain, and the displacement of the tip with respect to time FOIL WITH HULL AND WAVES In this section, the real geometry of the foil (including the winglet) is used and the hull is added. Unsteady fluid structure interaction computations were performed with the foil fixed at the interface of the hull. A free surface is imposed at z =0 as an initial condition. The hull is fixed and all of the nodes of the beam inside the hull are fixed in both translation and rotation. At t =0s, the speed of the boat is 0m s 1. The imposed motion is done according to a 1 4 sinusoidal law until 15m s 1. The waves are starting at t =0s, 45m in front of the foil and reach the foil at t = 6s. The waves are Stokes first order potential waves with 1m wave height and a period of 3s. Fz Force en z t (a) z force My Moment en y t (b) y moment z (m) Δz t (c) z deflection Figure 9: Forces and momentum acting on the foil with respect to time Figure 9a and Figure 9b show the variation of the lift forces and torsion moment in the foil local frame. The variation of r 2 1e+08 1e e Niter Rsidu initial Rsidu final (a) Start of the simulation r Niter Rsidu initial Rsidu final (b) End of the simulation Figure 10: Initial residual on the structure lift is 56 ± 12kN. The foil is very stiff and therefore does not bend very much. Nonetheless, the amplitude observed in waves is not negligible because it induces a vertical velocity that changes the incident flow, and thus the lift and drag. The Figure 10 permits us to conclude on the convergence of the coupling. It can be seen that the initial residual decreases quickly during the non-linear iterations until convergence. Furthermore, using the Jacobian matrix of the interface allows a convergence in 20 subiterations where a classic implicit coupling with under-relaxation would require about a hundred subiterations. A computation without fluid structure interaction needs about 10 iterations to reach convergence. 3 CONCLUSION The results of a partioned coupling between a viscous, incompressible fluid solver and a structural finite element analysis software are presented for strongly coupled problems. The Hubner case permitted the validation of the fluid-beam interaction. The quasi-static and dynamic results for the daggerboard of a high performance multihull were then presented. Furthermore, the design scope of this yacht was to do oceanic races and therefore it was designed to be both very reliable and safe. Thus, the foils used are smaller compared to what can be used for smaller, 60 foot (18 m) ORMA multihulls of the same generation. To use bigger foils on maxi trimaran, it will be necessary to predict the dynamic stability of the boat and also to dimension their structure. Vibratory phenomena such as flutter, which can lead to failure of the foil were investigated and the ability of the code to simulate such behavior proven. The boundary conditions for the structure play an important role in the determination of the structural deflections, hence it would be of interest to investigate a freely moving foil inside the hull with pinned connections at the lower and upper hull surfaces which corresponds more closely to what is happenning in reality. ACKNOWLEDGEMENTS We would like to thank PACAGrid and INRIA for providing the computational power required to undertake this study.

203 REFERENCES [1] J. Wackers, B. Koren, H. Raven, A. van der Ploeg, A. Starke, G. Deng, P. Queutey, M. Visonneau, T. Hino, and K. Ohashi, Free-surface viscous flow solution methods for ship hydrodynamics, Archives of Computational Methods in Engineering, vol. 18, no. 1, pp. 1 41, [2] F. Menter, M. Kuntz, and R. Langtry, Ten years of industrial experience with the sst turbulence model, Turbulence, heat and mass transfer, vol. 4, pp , [3] B. Augier, P. Bot, F. Hauville, and M. Durand, Experimental validation of unsteady models for fluid structure interaction: Application to yacht sails and rigs, Journal of Wind Engineering and Industrial Aerodynamics, vol. 101, pp , ISIS-CFD. His previous experience includes a PhD in fluid dynamics in M. Visonneau holds the current position of Research Scientist of the CNRS at the LHEEA laboratory of Ecole Centrale Nantes. His main research topics are Computational Fluid Dynamics (CFD), Ship Hydrodynamics and Turbulence Modeling for high Re flows. In 1991, he got the 2nd Cray Prize for CFD and has been awarded 30th Georg Weinblum Memorial Lecturer ( ) in His previous experience includes the head of the CFD department of the Fluid Mechanics Laboratory (ECN) from 1995 to L. Dorez holds the current position of head of the Groupama Sailing Team. [4] M. Durand, Interaction fluide-structure souple et legere, applications aux voiliers. PhD thesis, Ecole Centrale Nantes, [5] B. Hübner, E. Walhorn, and D. Dinkler, A monolithic approach to fluid structure interaction using space time finite elements, Computer methods in applied mechanics and engineering, vol. 193, no. 23, pp , [6] E. Ramm and W. Wall, Fluid-structure interaction based upon a stabilized (ale) finite element method, [7] J. Valds, J. Miquel, and E. Oate, Nonlinear finite element analysis of orthotropic and prestressed membrane structures, Finite Elements in Analysis and Design, vol. 45, no. 67, pp , [8] G. De Nayer, Interaction Fluide-Structure pour les corps lancs. PhD thesis, cole Centrale de Nantes, AUTHORS BIOGRAPHY C. Lothode holds the current position of R&D engineer at K-Epsilon. He is responsible for FSI computations and developpement. His previous experience includes a M.Sc. in Applied Mathematics. M. Durand holds the current position of R&D director at K- Epsilon. He is responsible for FSI developments and sails simulations. His previous experience includes a PhD in fluid dynamic in 2012, and is also a world ranker match racing skipper (#40 in world ranking in 2011). Y. Roux holds the current position of CEO of K-Epsilon. His previous experience includes a PhD in fluid mechanics. He did multiple study on victorious yacht such as Groupama 3 and 4. A. Leroyer holds the current position of Associate Professor at the LHEEA laboratory of Ecole Centrale Nantes. His research topics revolve around the numerical modelling of the incompressible isothemal flows around complex geometries and are more specifically focused on the methodologies to integrate new physical phenomena inside a Navier-Stokes solver, as the fluid-structure interaction and the numerical modelling of cavitation. He is part of the developer team of

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205 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France AN UNSTEADY FSI INVESTIGATION INTO THE CAUSE OF THE DISMASTING OF THE VOLVO 70 GROUPAMA 4 W. Menotti, Menotti Marine, France, wenceslas@menotti-marine.com M. Durand, D. Gross and Y. Roux, K-Epsilon, France, mathieu@k-epsilon.com, david@k-epsilon.com, yann@kepsilon.com D. Glehen, GSea Design, France, denis@gseadesign.com L. Dorez, Groupama Sailing Team, France, loic@groupamasailingteam.com This paper describes the use of an unsteady fluid-structure interaction (FSI) tool as an investigative tool into the cause of the dismasting of the VOR 70 Groupama 4. As more than one rig component failed during the dismasting, the cause of failure was not immediately apparent. The investigation therefore required isolating the cause of failure between two closely related rig components. The FSI coupling process and the determination of the initial rig loading based on a steady FSI computation and measured data will be described. The setup for two unsteady failure cases will be discussed and the results of those investigations will be examined. NOMENCLATURE Damping matrix (N.s.m -1 ) Stiffness matrix (N.m-1 ) Mass matrix (kg) R Residual force (N) u Position (m) Velocity (m.s -1 ) Acceleration (m.s -2 ) Incident flow velocity (m.s -1 ) Doublet induced velocity (m.s -1 ) Wake induced velocity (m.s -1 ) Vortex particle position (m) Vortex particle vorticity (s -1 ) 1 INTRODUCTION The edition of the Volvo Ocean Race was notable for the number of rig failures that occurred during the course of the race. The cause of the dismasting of Groupama 4 on the leg between Auckland and Itajai in calm seas and moderate breeze was not immediately apparent based on examination of the recovered pieces, as more than one secondary structural member had failed during the dismasting. In particular, it was necessary to determine if the mast failure was due to the port side D1 or the port side first spreader failing. The determination of the cause of the failure therefore necessitated that an investigative structural analysis be performed. To perform such an analysis would require that a detailed structural model of the rig and sails be utilized in conjunction with an accurate description of the static and aerodynamic structural loads. ARAVANTI, the tool utilized, is composed of ARA, an unsteady, finite element structural solver capable of being tightly coupled to AVANTI, an unsteady potential flow solver or ISIS- CFD, an unsteady RANS solver [1, 2]. In the present study, the need for a rapid determination of the cause of failure and the sailing angle at the time of failure justified the use of the unsteady potential solver for the determination of aerodynamic loads. The structural model of the rig utilized was developed as part of a prior study, and hence could rapidly be brought to bear on the problem. While failure analysis is most often performed utilizing normal finite element structural software, this approach has a number of drawbacks. Specifically, the aerodynamic loads at the time of failure must either be estimated by the structural engineer or determined from an aerodynamic solver separately and then inputted into the structural solver. Furthermore, as the sail shape will change during the course of the failure; a significant drawback of this approach is that it is unable to account for changes in the aerodynamic loads over the course of the rig failure. 2 FLUID SOLVER The flow code utilized in the present study, AVANTI is based on the assumptions that underpin potential flow; namely that the flow is incompressible, irrotational, and inviscid. The code combines a constant-strength, doublet surface representation of the bodies with a vortex particle method for the wake [3, 4]. The flow problem is thus broken down into two components: A lifting body problem based on a boundary integral; A wake problem in which vortex carrying particles in a Lagrangian framework are advected downstream in the wake. Hence, AVANTI represents the flow field as the sum of the contribution of three components: 1), the incident flow velocity; 2), the contribution induced due to the surface doublets; 3), the contribution due to the vortex particles. The vorticity of the individual particles must satisfy the Helmholtz equation. The equations for a particle i in the Lagrangian coordinate system, with the position of the

206 particle given as X i and the particle vorticity given by i, are therefore: The principle advantage of using a vortex particle method over a panel wake method is the avoidance of wake panels intersecting one another during unsteady computations. 3 STRUCTURAL SOLVER The unsteady finite element structural solver ARA, was developed by K-Epsilon as part of the project VOILE- NAV specifically with the aim of simulating the dynamic behaviour of sailboat rig [2, 5, 6]. To capture the unsteady behaviour in a time accurate manner, a Newmark-Bossak second-order accurate time scheme is used. The scheme is utilized because it provides the necessary filtering of non-physical high frequencies while maintaining an accurate description of the low frequencies. The scheme is conservative and hence avoids the generation of numerical energy in the case of very large nonlinearities. At each time step an equilibrium between the internal and external forces on all of the elements is required. To achieve this, the derivative of the forces with respect to the position, velocity, and acceleration of each element's nodes is found. The derivatives are then assembled into a mass matrix [M], damping matrix [D] and stiffness matrix [K]. The assembled matrix system of the form below is then solved utilizing the Newton-Raphson method after further rearrangement to be in a form suitable for the Newmark-Bossak scheme. region. The stiffness matrix of each element is thus able to account for the anisotropic material properties of competitive sail manufacturing techniques such as 3DI, 3DL, and D4 as well as local reinforcement patches. 4 FLUID-STRUCTURE COUPLING Sails, are light structures where the entrained added mass of the air is of comparable or greater size to the mass of the sails themselves. This poses a particularly difficult case for unsteady FSI coupling schemes. The strong coupling between the fluid and structure requires that the coupling scheme has a tight coupling between the structure and fluid solvers. The coupling scheme utilized is a quasi-monolithic approach. It is based on an implicit, partitioned solver approach, but maintains the convergence and stability of a fully monolithic approach. This is achieved by utilizing an additional interface element in the structural solver derived from the Jacobian matrix of the interface. In the case of an exact Jacobian matrix, the coupling matrix is identical to that of a monolithic approach. In the present approach, a simplified Jacobian is computed. The Jacobian matrix allows the elimination of the use of under-relaxation, yielding a significant reduction in the number of coupling iterations required. The coupling process is outlined in figure 1 below. At each time step an FSI loop is started by first updating the wake particle positions and then computing the Jacobian matrix. A structural computation is then performed to convergence and the motions are transferred to the fluid solver. This is then followed by a fluid computation, after which convergence of the coupling is checked. If convergence has not been achieved the fluid forces are transferred back across the interface and the structural computation is repeated. Hence, fluid-structure convergence is achieved at each time step. The rig and sails can be represented by membrane, shell, beam and cable elements. Sliding and contact elements are also implemented utilizing a penalization method. In the present study, membrane elements were utilized for the sails with beam elements for the mast, boom and spreaders. The beam elements utilized are sheardeformable Timoshenko beam elements. The membrane elements utilized are constant strain triangle (CST) elements suitable for large deformations. The stiffness matrix for the CST elements is found from the summation of the local stiffness properties of each ply used to fabricate the sail at that location. The local stiffness of each ply is determined from the density, orientation and stiffness of the fibres utilized in that Figure 1: ARAVANTI unsteady FSI loop

207 5 STEADY CASE SETUP AND RESULTS In order to perform the FSI computation, an accurate description of both the rig and the loads is required. As mentioned before, the structural properties and geometry of the rig and sails were developed before the current study as part of an earlier study. To replicate the structural loading at the time of failure, both the static and aerodynamic structural loads needed to be imposed. The static structural loads consisted primarily of the tensions applied to the shrouds. The initial tensions applied were taken from the measured dock tune tensions. The aerodynamic loading was generated by a steady FSI computation based on the measured yacht and wind conditions at the time of the failure. These conditions are given in table 1. Boat speed 12 knots True wind speed 21 knots Heel angle 22 Heading Close reach Table 1: Sailing conditions In order to obtain the correct aerodynamic loads, three criteria had to be met: 1) The sails had to be trimmed to a realistic setting for the given wind conditions and boat speed. 2) The forestay had to have a tension of 10 tons. 3) The heeling moment generated had to match the righting moment. To achieve these aims, the jib was first trimmed optimally. The main sail was then used to achieve the correct heeling moment. The resulting steady loads are given in table 2. Rig component Line/Port side tension (kn) Starboard side tension (kn) V V V D D D D Runner Forestay Main halyard Main sheet Jib halyard Jib sheet Table 2: Steady shroud, sheet and halyard tensions 6 UNSTEADY SETUP AND RESULTS The resulting sail flying shape and deformed shape of the rig from the steady computation was utilized for the initial shape and stresses of the unsteady computations. In order to model the sudden failure of a rig component, the member was made to no longer carry structural loads. This was accomplished for the D1 by changing the cable length to be very large such that it could no longer be under tension. The spreader failure was modelled by changing the element stiffness to 0, such that it no longer resisted applied loads. Failure of structural members was assessed based on the stress exceeding the ultimate strength of the member. As ARAVANTI does not have a built in capability to represent the effect of the failure of a structural element, if an element was determined to have failed, the computation was repeated with that element having its failure imposed at the time it exceeded its ultimate strength. The resulting time histories of the mast bending moments and deflections were then utilized to determine the mast failure point. Three unsteady computations were performed as part of the study : 1. A computation where the port side D1 is made to fail. 2. A computation where the port side first spreader is made to fail. 3. A computation where the port side first spreader is made to fail and after which the port side D1 is made to fail s later. The third computation was performed based on feedback from the structural engineer, who indicated a failure should occur then. For the present paper, the results of the first and third computations will be presented. It should be noted that the D1 case also leads to the eventual failure of the first spreader. However, a D1 computation with an imposed failure of the spreader was not performed as the conclusion as to the cause of failure had already been drawn and such a computation would have required a slight modification to the way ARAVANTI stores beam stiffness properties to accommodate such a case. For reasons of confidentiality, the correct failure case cannot be identified, but a number of results related to the two failure cases can be given. Both cases are given with the initial failure occurring at t= 0 s. 6.1 SHROUD TENSIONS The time histories of the tensions in the shrouds following the failure of the D1 are shown in figure 2. The loss of tension in the port D1 is visible at t= 0 s. The tensions undergo a rapid change immediately following the prescribed failure of the port D1, with an increase in tension on the starboard side and decrease in tension on the port side. The tensions then begin to gradually increase for the port side V1 and D2 while decreasing for all of the starboard side elements as the mast and spreaders continue to deflect. The port D3 and starboard D1 are rapidly unloaded until slack, with the starboard D2 following soon thereafter.

208 Figure 2: Time history of the shroud tensions, D1 case Similarly, the tensions for the spreader failure case in figure 3 exhibit an initial increase in tensionn on the starboard side and decreasee in tension on the port side. However, unlike the D1 failure case, the port D2 initially becomes completely slack before the tension begins to increasee again as the rig continues to deflect. The starboard D1 initially sees a rise in tension, but then slackens with further rig deflection. The port D3 remains under tension. The imposed failure of the port D1 is visible at s. Figure 4: Maximum spreader vertical bending curvature, D1 case Figure 3: Time history of the shroud tensions, spreader case 6.2 SPR READER DEF FLECTION Unlike the shroud tensions, there is no inflection in the time history of the spreader maximum vertical bending curvature, as shown for the D1 case in figure 4. The deflections increase gradually with time. Significant deflections occur for the first spreader and to a lesser extent the second spreader. In comparison to the D1 case, the spreader failure case curvature in figure 5 shows a much greater deflection of the second spreader. Figure 5: Maximum spreader vertical bending curvature, spreader case 6..3 MAS ST BENDING MOMENT AND DEF FLECTION The ability for a failure case to caus se a failure of the other suspected rig element was an important consideration in the assessment of the failure mod de. However, the mast failure location also needed to be correctly located. As mentioned before, ARAVANTI does not have a built in capability to represent component failure. Therefore, deter rmining when the mast first reaches its ultimate strength was necessary to determine where failu ure occurred. The time histories of the transverse bending moment for both failu ure cases are presented in figure 6. The bending moment is initially smalll from 0 to 0..1 seconds. The bending moment then begins to steadily increase both in magnitude and exte ent along the mast length. The bending moment is concentrated in the lower port tion of the mast; there is very little deflection in the upper portion of the mast. The bending moments are concentrated in two regions along the mast for both cases. The location of the two large bending moment regions is located further up the mast for the spreader case. The regions with large

209 bending moments are also more extensive and are of greater magnitude for the spreader case compared to the D1 case e. The location along the mast of the larg est bending moments does not change significantly over time. The growth rate of the bending moment is indicative of the rate by whic ch the mast is deforming. The two cases exh hibit noticeable differences in the growth of the bending moment. In particular, the lower region of the mast for the D1 case begins to have a bending moment greater than 50,000 N.m by 0.14 s, while the upper large bending moment region does not reach a comparable level until s. In contrast, the two large bending moment regions of the spre ader case achieve such a bending moment nearly simultaneously at 0.31 s. The curvature and bending deflection dynamic behaviours are therefore markedly different between the two cases. The diffe erence in the defo ormation behaviour is visible in the time lapse ima ages of the rig undergoing failure in figures 7 and 8. The lower region of curvature is more pronounced for the D1 case at s. By 0.25 s the defl ections of the spreader case have become larger relative to the D1 case. The difference in the location of the defl lections is clearly visib ble. For the D1 case the upper high curvature region is located close to the first spreader with the lower high h curvature regi on much closer to the foot of the mast. In contrast, for the spreader case the lower region of highh curvature is located close to the first spreader with the uppe er region located closer to the second spreader. the D1 case. The deflected shapes of the mast are significantly different with regards to wher re curvature occurs. The time histories of the mast bending moments for the D1 case exhibits higher bending mom ments sooner, near the base of the mast and then later further up the mast. In contrast the spreader case exhibits high her bending moments at both locations simultaneously. The time history of the rig tensions show a rapid drop in port side shroud tensions and incr rease in starboard tensions following both failures. This rapid change was then followed by a period of gradual change in the tensions with the starboard and som me of the port side shrouds elements decreasing in tension as the rig deflections increased. Deflections in the spreaders were found to increase grad dually with rig deflection. The numerical approach to the post-failure structural investigation of the Groupama 4 mast breaking has been described. The inve estigation was able to distinguish between the failure modes of two closely located rig components. The use of an unsteady FSI approach meant that the aerodynamic loads on the rig could be accurately modelled as the flying shape changed. The FSI tool ARAVANTI has been shown to be capable of solving cases with highly transient, large deformation structural responses, while maintaining the stability of the FSI coupling. This capability can thus be applied to numerous other high ly transient FSI problems such as sails undergoing wave e-induced motions. 8 REFERENCES 1. AUG GIER, B., BOT, P., HAU UVILLE, F., and DURAND M.., 'Experimental validation of unsteady models for fluid structure interaction', Application to yacht sails and rigs, Journal of Wind Engi neering and Industrial Aerodynamics 101, DURAND M., 'Interaction fluide-structure souple et légère, applications aux voiliers', Ph.D. thesis, Ecole Centrale Nantes, REH HBACH, C., 'Numerical calculation of three dimensional unsteady flows with vortex sheets', 16th Huntsville AIAAA Pape er , 1978 Figure 6: Time history of mast bending moments 7 CONCLUSIONS Results from the investigated cases showed the loss of either rig element leads to mas st failure, but only one of the two correctly locates the failure point. Both cases exhibit two regions of highh bending moments along the length of the mast, with the spreader case regions being located higher on the mast and of grea ater magnitude than 4. CHARVET, T., HAUVILLE, F., HUBERSON, S., 'Numerical simulation of the flow around sails in real sailing conditions', Journal of Wind Engineering and Industrial Aerodynamics 63, HAUVILLE, F., DURAND, M.., ROUX, Y., 'Modèle aèroélastique appliqué à la déformation d'un gréement', European Journal of Env vironmental and Civil Engineering 12-5, 2008

210 6. DURAND, M. HAUVILLE, P., BOT, P., AUGIER, B., ROUX, Y., LEROYER, A., VISONNEAU, M., 'Unsteady numerical simulation of downwind sails' The Second International Conference on Innovation in High Performance sail Yachts, AUTHORS' BIOGRAPHY W. Menotti holds the current position of owner at Menotti Marine. He was responsible for the computations around the sail and rig. His previous experience includes sail design on various racing boats, ranging from small dinghies to super yachts. M. Durand holds the current position of R&D director at K-Epsilon. He is responsible for FSI developments and sail simulations. His previous experience includes a PhD in fluid dynamics. He is also a world ranked match racing skipper (40th in world ranking for 2011). D. Gross holds the current position of CFD engineer and naval architect at K-Epsilon. He has an MSc in marine CFD from the University of Southampton, where he specialized in multihull appendage FSI. Y. Roux holds the current position of CEO of K-Epsilon, having, founded the company K-Epsilon in In partnership with laboratories, he and K-Epsilon develop numerical tools which are applied to unsteady aerodynamic, hydrodynamic and FSI studies. D. Glehen holds the current position of GSEA DESIGN owner. He is responsible for the mast design and has worked with numerous French racing teams for the last 16 years. His previous experience includes IMOCA, VOR70, and MAXI multihull mast design. He was involved with Groupama Sailing Team for the last VOR70 campaign. L. Dorez holds the current position of Head of Design at Groupama Sailing Team. In partnership with laboratories, structural design, hydrodynamic, and aerodynamic firms, he organizes the design and development of tools for Groupama Sailing Team.

211 Figure 7: Time lapse of the mast failure, D1 case Figure 8: Time lapse of the mast failure, Spreader case

212

213 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France THE WORK ACHIEVED WITH THE SAIL DYNAMOMETER BOAT FUJIN, AND THE ROLE OF FULL SCALE TESTS AS THE BRIDGE BETWEEN MODEL TESTS AND CFD Y. Masuyama, Kanazawa Institute of Technology, Japan, The work achieved with the sail dynamometer boat Fujin was reported. At first, the sail shapes and performance for upwind conditions were measured in steady sailing conditions. The results were compared with the numerical calculations. The database of three-dimensional coordinates of the sail shapes was also tabulated with the aerodynamic coefficients. The sail shape database provides a good benchmark for the validation of sail CFD in full scale level. Then, the aerodynamic force variation during tacking maneuvers was measured by Fujin, and a new simulation model of tacking maneuver was proposed. The simulated results showed good agreement with the measured data. Finally, the scale effect problem of wind tunnel tests was discussed. Wind Tunnel tests using model sails are performed at the region of critical Reynolds number. Therefore, the wind tunnel test had to be performed very carefully. On the other hand, the full scale tests using a sail dynamometer boat are free from scale effect problems and appear more promising. NOMENCLATURE C L, C D Lift force and drag force coefficients (-) C X, C Y Thrust force and side force coefficients (-) S A Sail area (m 2 ) U A Apparent wind speed (AWS) (m.s -1 ) V B Boat velocity (m.s -1 ) X, Y Force components along x and y-axis (N) K, N Moments around x and z-axis (N.m) γ A apparent wind angle (AWA) (deg) ρ Density of water (kg.m -3 ) ρ a Density of air (kg.m -3 ) φ Heel angle or roll angle (deg) ψ Heading angle (deg) 1 INTRODUCTION Because the recent advances in computational fluid dynamics (CFD) further motivate the application of numerical simulations to predict the sail performance, there is an ever increased need for reliable experimental data for validation. Wind tunnel tests can be performed relatively easily, but scale effects related both to flow and structural aspects, which yield inaccuracy in sail shape measurements, are always present. Full scale onboard measurements are free from scale effect problems and appear more promising, but the challenge becomes how to accurately measure the forces acting on the sail. Such studies on sail force measurements were performed by Milgram et al., Masuyama et al. and Hochkirch et al., who built full-scale boats with onboard sail dynamometer systems. Milgram [1] showed in his pioneering work that the sail dynamometer boat, Amphetrete, is quite capable. This measurement system consists of a 35-foot boat with an internal frame connected to the hull by six load cells, which were configured to measure all forces and moments acting on the sails. In his work, the sail shapes were also measured and used for CFD analyses; unfortunately, details of the sail shape and performance data were not presented. Hochkirch et al. [2] also built a 33-foot dynamometer boat DYNA. The aerodynamic forces acting on the sail were measured and compared with the results from wind tunnel tests [3]. The measured data were also used as input to the CFD calculation and a parametric survey was carried out [4]. However this work does not provide a database for the relation between sail shape and performance. Masuyama and Fukasawa [5, 6] were encouraged by Milgram s work, and built a sail dynamometer boat, Fujin. The Fujin is a 34-foot sailing cruiser, in which load cells, CCD cameras and sailing condition measurement system are installed to obtain the sail forces and shapes, and the boat attitude, simultaneously. In this report, the work achieved with the sail dynamometer boat Fujin is presented, and the role of full scale tests in the validation of CFD in full scale level is discussed. 2 SAIL DYNAMOMETER BOAT FUJIN 2.1 GENERAL ARRANGEMENT The Fujin was built in Fujin is a 10.3m-long ocean cruiser with a sail dynamometer system in the hull. Table 1 shows the principal dimensions of the boat and Figure 1 shows the sail plan of the Fujin. The sail dynamometer system is composed of a rigid aluminum frame and four load cells. The frame is separated structurally from the hull and connected to it by the load cells. The general arrangement of the dynamometer frame is given in Figure 2(a). The load cells are numbered in the figure. Two of these are 1-component load cells and the others are 2-component ones. The directions in which the loads were measured for each of

214 Table 1 Principal dimensions of Fujin HULL LOA [m] LWL [m] 8.80 BMAX [m] 3.37 BWL [m] 2.64 Disp [ton] 3.86 SAIL I [m] J [m] 3.61 P [m] E [m] 4.51 (a) (b) Figure 1 Schematic showing the sail plan of Fujin Figure 2 General arrangement of dynamometer frame and directions of measuring components of each load cell the load cells are shown in Figure 2(b). Hence, these load cells form a 6-component dynamometer system, and their outputs can be transformed to the forces and moments about the boat axes using a calibration matrix. All rig components such as the mast, chain plates, winches, lead blocks, etc. are attached to the aluminum frame through the deck holes. 2.2 MEASUREMENT SYSTEM Figure 3 Sea trial condition in light wind with 130% jib The sail shape was recorded using pairs of CCD cameras. The lower part of the mainsail was photographed using the CCD camera pair designated A in Figure 3. These were located at the mast top, 50 cm transversely from each side of the mast. The upper part of the mainsail was photographed using a portable video camera from below the boom. The lower part of the jib was photographed

215 using the camera pair designated B in Figure 3, which were located at the intersection point of the forestay and the mast, 10 cm transversely from each side of the mast. The upper part of the jib was photographed using a portable video camera from inside the bow hatch. The original data acquisition system consisted of a single PC which gathered all the data. However, the system was renewed later as a distributed system using three singlechip computers (Hitachi H8-2636) connected with the Control Area Network (CAN) bus. The CAN is a highspeed, serial bus developed for the automotive environment and has a high level of noise immunity. 3 STEADY SAIL PERFORMANCE FOR UPWIND CONDITION 3.1 TEST CONDITION AND ERROR ANALYSIS At first, the sail shapes and performance for upwind conditions were measured using mainsail and 130% jib in steady sailing conditions[6, 7]. Close-hauled tests were conducted over an apparent wind angle (AWA) range of 20 to 40 degrees, and an apparent wind speed (AWS) range of 5 to 11m/s. The effect of the AWA, and the draft and twist of the mainsail on the sail performance were measured. Data sampling was started when the sailing condition was considered to be in steady state. The sampling rate for the data acquisition system was set at 10Hz. Data sampling was continued for 90 seconds, and during this time the sail shapes were recorded using the CCD cameras. The boat was steered carefully during this time. However it was difficult to keep the variation in the AWA sufficiently small during the whole of the 90 seconds period. Therefore the steady state values for the aerodynamic coefficients were obtained by averaging the data over a 30 to 60 seconds period, in which the AWA was closer to the target value than during the whole 90 second period. For these tests if the range of deviation of AWA exceeded ±5 degrees, the results were discarded. All of the measured coefficients are plotted with error bars indicating the range of deviation over the averaging period. 3.2 NUMERICAL CALCULATION METHOD Numerical flow simulations were performed for the measured sail shapes and conditions. Two numerical methods were used: a vortex lattice method (VLM) and a Reynolds-Averaged Navier-Stokes (RANS)-based CFD method. A vortex lattice method using a step-by-step procedure developed by Fukasawa [8] was employed to compare with the results of a RANS-based CFD calculation. The code of the RANS-based CFD method was FLOWPACK developed by Tahara [9, 10]. The method has an automatic gridding scheme, and complete multiblock domain decomposition feature. 3.3 SAIL PERFORMANCE VARIATION WITH APPARENT WIND ANGLE Figure 4 shows the performance variation for the mainsail and 130% jib configuration as a function of AWA. Figures 4(a) and (b) show the variation of lift and drag force coefficients C L,C D, and thrust and side force coefficients C X,C Y, respectively. In the figure the solid symbols indicate the experimental results and the open symbols indicate the calculated results using the VLM and the RANS-based CFD. For the experimental results, both data from the starboard (Stbd) and port tack (Port) are shown. All of the measured coefficients are plotted with error bars indicating the range of deviation over the averaging period. There are some discrepancies between the data from each tack. During the experiments, efforts were made to remove this asymmetrical performance. However, the boat speed actually differed on each tack. It can be concluded that there was a slight asymmetry in the combination of the hull, keel, rudder and dynamometer frame. In this figure, AWA ranges from 20.3 degrees to 37.9 degrees for the port tack. The former is the closest angle to the wind that was achieved, and the latter is typical of a close reaching condition, where the sail is trimmed in the power down mode. There is some scatter in the experimental data because this is made up from measurements taken with the sails trimmed in slightly different ways. The experimental value of C L in Figure 4(a) varies with AWA from 0.91 to For the close reaching condition, unfortunately, the sails were not well trimmed to satisfy the power down mode. The calculated results for C L using the VLM show good agreement with the experiments at AWA angles less than about 35 degrees. Over about 35 degrees, the calculated results are lower than the measured ones. This shows that the calculated results strongly indicate the effect of incorrect sail trimming. The results for C L using the RANS-based CFD show the same trends with the experiments, but are slight higher than those from the experiments for AWA between 20 degrees to 30 degrees and lower for AWA greater than 30 degrees. In particular, the decrease in C L for AWA values greater than 30 degrees is considerably large. The calculated results for C D slightly over predict those from the experiments. Figure 4(c) shows the coordinates of the center of effort of the sails. The x and z coordinates of the geometric center of effort (x GCE and z GCE ) are 0.63m aft and 4.80m above the origin, which are indicated by alternate long and short dashed lines in the figure. It is seen that both the experimental and the calculated coordinates of x CE are near x GCE and move slightly forward with increasing AWA. Unfortunately, there is a wide scatter in the experimental values of z CE. This is thought to be because the measured Ks moment contains a large component from the mass of the dynamometer frame and rigging (659kg). This moment was subtracted from the measurement, taking into account the measured heel angle. If there is a slight error in the position of center of gravity of the dynamometer frame, or in the measured heel angle, the error in the calculated moment will be

216 C L, C D 2.0 (1) (2) Exp. (Port) Table 2 Sail shapes, measured experimental data and three-dimensional coordinates of the sails for the case of numbered point (1) in Figure 4 :C L :C D 1.5 (Stb d) C L :C L :C D 1.0 Cal. (Port) (VLM) :C L 0.5 :C D (RANS) C D :C L :C D A [deg] (a) CL and CD vs. AWA C X, C Y Exp. 2.0 (Port) C Y :C X :C Y (Stb d) :C X :C Y Cal. (Port) (VLM) :C X 0.5 :C Y (RANS) C X :C X :C Y A [deg] (b) CX and CY vs. AWA x CE, z CE [m] Exp. 7 (Port) z C E x C E Geometric zgce Geometric xgce A [deg] (c) xce and zce vs. AWA :x CE :zce (Stb d) :x CE :zce Cal. (Port) (VLM) :x CE :zce (RANS) :x CE :zce Figure 4 Performance variation as a function of apparent wind angle (AWA) for mainsail and 130% jib large. However, though there is a scatter in the measured data, it can be seen that z CE is decreasing as AWA increases. The trends in the movement of both x CE and z CE as functions of AWA might be caused by the decrement of force acting on the aft and upper parts of the sails due to the loosening of main and jib sheets with increasing AWA. The calculated results for z CE obtained using therans-based CFD show the same trend as the experiments. On the other hand, the calculated results using VLM are considerably higher than the experimental ones. This might be caused by over estimation of the force acting on the upper portion of the mainsail. In this area, since the jib is not overlapping, flow separation may occur easily. However, the VLM does not take flow separation into account. The shapes and three-dimensional coordinates of the sails are given in Table 2. This shows the case of numbered point (1) in Figure 4. The figure described above the

217 table shows the sail section profiles at 0, 20, 40, 60 and 80% of the sail height. The three-dimensional coordinates of each section are given in the table. The origin of the coordinate of sail dynamometer system is shown in Figure 1. In this table, the positive direction of the x coordinate is aft. The four lines at the top of the table are the measured values for the wind and sail trim conditions, the boat attitude and the sail performance coefficients. In reference [7], the same tables are shown which are measured at various sail trim conditions. These tabulated data may provide a good benchmark for the validation of upwind sail CFD in full scale level. 4 AERODYNAMIC FORCE VARIATION DURING TACKING MANEUVER AND TACKING SIMULATION 4.1 MEASUREMENTS OF AERODYNAMIC FORCE VARIATION DURING TACKING MANEUVERS Tacking of a sailing yacht is a quick maneuvering motion accompanied by large rolling angle changes in a short period of time. To analyze this type of large amplitude motion, a mathematical model for the simulation was proposed by Masuyama et al. [11,12]. The calculation method was applied to a 34-foot sailing cruiser and the simulated result showed good agreement with the measured data from full scale tests. However, in these research, the modeling of aerodynamic force variation during tacking was insufficient due to lack of information about the sail forces. In order to clarify the sail force variation during tacking maneuver, the measurements were conducted using Fujin [13, 14, 15]. Figure 5 shows two examples of the measured data in the time domain for X' Sd, Y' Sd, K' Sd and N' Sd during the tacking operation for 20 seconds, from five seconds before to 15 seconds after the start of tacking, where X' Sd and Y' Sd are the thrust and side force coefficients along the axes of sail dynamometer system, and K' Sd and N' Sd are the roll and yaw moment coefficients around the same axes. Figure 5(a) shows the case of tacking from starboard to port tack, and Figure 5(b) shows from port to starboard tack. The scattering of the data at the crossing points of the curves is caused by the crew action on the dynamometer frame in releasing and trimming the jib sheet during tacking. In the measured data, the inertia forces and moments due to the mass of the dynamometer frame are included. These effects clearly appear at the starting and finishing stage of the tacking maneuver, but are not so significant at the middle stage. Hence the measured data are indicated only subtracting the forces and moments due to the gravity force acting on the dynamometer frame using measured heel angle at every moment. Figure 6 shows the variation of sail force coefficients during tacking as a function of the heading angle of the boat ψ, where ψ = 0º means heading in the true wind direction. During tacking, the jib sheet was released just before the jib was backwinded on the new tack in order to minimize luffing of the jib and loss of wind power. The curves show the results of 10 tacking cases from starboard to port tack. It should be noted again that forces and moments are shown using the sail dynamometer coordinate system. The variations start from close hauled condition of starboard tack until the boat is on port tack, (i.e., from ψ = -45º to 45º). The corresponding AWA, from γ A = 30º to -30º, are also indicated in the second abscissa in the figure. Figure 6(a) shows the variation of X' Sd. When the boat heads directly into the wind, X' Sd becomes about -0.1, (i.e., drag force coefficient). Figures 6(b) to 6(d) show the forces and moments become zero not at ψ=0º, but around ψ=10º, which indicates a delay in the variation of forces and moments compared to the change of heading angle. This could be caused by the sail filling with wind due to the yawing motion from the former tack to ψ =10º on the new tack when the jib sheet was released. Inversely, for the case of port tack to starboard tack, the values of Y' Sd, K' Sd and N' Sd become zero at around ψ= -10º, and the variation of forces and moments are almost symmetrical to Figure 6. From this result, it can be considered that the bias of the zero crossing point of the forces and moments at the tacking maneuver is symmetrical. 4.2 MODEL OF SAIL FORCE VARIATION FOR TACKING SIMULATION Let us define the model of sail force variation for the tacking simulation as bold lines in Figure 7 referring to the measured data in Figure 6. Figure 7(a) shows the case of tacking from starboard to port tack. The abscissa indicates AWA (γ A ). In the model, the basic sail performance curves of X's 0 and Y's 0 are divided into three stages. Stage A is the range of γ A that is greater than 20º. In this region, the coefficients vary with γ A according to the basic curves. Stage B is the range of γ A = 20º to -10º. In this region, the coefficients are assumed to vary linearly along the lines determined from the results of Figures 6(a) and 6(b). Stage C is the range of γ A = -10º to -30º. In this region, the basic pattern of the coefficients is expressed as basic performance curves. However, it may take several seconds to recover to the basic curves due to the delay of trimming the sails for the new tack condition. Therefore, the coefficients are assumed to increase from the lowest values to the basic curve values with elapsed time. The recovery time was chosen from 5 to 10 seconds by taking the simulated heel angle corresponding to the measured one. Figure 7(b) shows the case of tacking from port to starboard tack. In this case the variation pattern proceeds in the opposite direction. The sail forces and moments expressed in equation (1) are used for the equations of motion in the following chapter. 4.3 EQUATIONS OF MOTION FOR TACKING SIMULATION In order to express the large amplitude motion such as a tacking maneuver of a sailing yacht, the authors

218 1.5 start of tacking 1.5 start of tacking X'Sd, Y'Sd, K'sd, N'sd X'Sd K'Sd N'Sd X'Sd, Y'Sd, K'Sd, N'Sd K'Sd X'Sd N'Sd Y'Sd Y'Sd elapsed time [sec] (a) Tacking from starboard tack to port tack elapsed time [sec] (b) Tacking from port tack to starboard tack Figure 5 Examples of measured sail force coefficients in the time domain during tacking operation P X'Sd 0.5 S P K'Sd S (a) X'Sd vs. and A A (c) K'Sd vs. and A A Y'Sd S P N'Sd 0.0 S P A A (b) Y'Sd vs. and A (d) N'Sd vs. and A Figure 6 Variation of sail force coefficients during tacking operation as a function of of boat (tacking from starboard to port tack) heading angle X'S0,Y'S0 2.0 Starboard tack A B 1.5 C 1.0 X'S0 Port tack Y'S0 Increasing with elapsed time Starboard tack X'S0 C X'S0,Y'S B 1.0 Port tack A Y'S0 0.5 X'S0 0.5 X'S A [deg] A Increasing with [deg] -0.5 elapsed time -1.0 Y'S0 Y'S0-1.5 =-45 =45 = (a) tacking from starboard to port tack -1.5 = (b) tacking from port to starboard tack Figure 7 Model of sail force variation during tacking maneuver for tacking simulation

219 employed equations of motion expressed by the horizontal body axis system introduced by Hamamoto et al. [16]. The origin of the coordinate system is on the C.G. of the boat which is shown in Figure 1. The x-axis lies along the centerline of the boat on the still water plane and is positive forward. The y-axis is positive to starboard in the still water plane. The z-axis is positive downwards. In this coordinate system, the maneuvering motion of the boat and aero/hydro-dynamic forces acting on it can be expressed in the horizontal plane even though the boat heels. Both added mass and added moment of inertia, which are referenced to the body axes fixed on the boat, can be obtained by the coordinate transformation. Then, the equations of motion expressed in the horizontal body axis system for the motions of surge, sway, roll and yaw are derived as follows. The left sides are forces and moments due to the mass and added masses of the boat, and the right sides are fluid dynamic forces and moments acting on the hull and sail with reference to the horizontal body axes. surge: m + mx U& 2 2 ( ) ( m + my cos ϕ + mz sin ϕ) Vψ& (1) = X + X H + X Vψ & Vψ& 0 + X R + X S sway: 2 2 ( m+ m cos ϕ + m sin ϕ) V& + ( m+ m ) Uψ& roll: ( I + J xx yaw: ( I y xx )&& ϕ = Y H z z + 2( m m )sinϕ cosϕ V & ϕ y + Y & ϕ + Y ψ& + Y & ϕ ψ& {( I + J ) ( I + J )} = K H yy yy + K & ϕ + K & ϕ zz R zz R x + Y S 2 sinϕ cosϕ ψ& + K mggm sinϕ 2 2 { yy + J yy )sin ϕ + ( I zz + J zz ) cos ϕ} + 2 {( I + J ) ( I + J )} sinϕ yy = N yy H zz zz + N ψ + N & ψ & R S + N S && ψ cosϕ ψ& & ϕ The derivation of these equations and calculation method of each term are described in detail in references [14, 15]. (2) (3) 4.4 COMPARISON BETWEEN MEASURED AND SIMULATED RESULTS The simulation method was applied to several boats and the results showed good agreement with the measured data. In this report, the cases of Fujin and Fair V are shown in the following sections. The Fair V is a 34-foot sailing cruiser, which was designed by the author and used for the first measurement of tacking maneuver. The Runge-Kutta method was employed to calculate the equations of motion. The rolling and yawing motions were calculated around the C.G. of the boat. Input data for the simulation is true wind velocity and the measured time history of rudder angle during tacking maneuver at increments of 0.1 seconds. (4) Results of Fujin Figure 8 shows the comparison between measured and simulated results of Fujin. Figure 8(1) shows tacking from starboard to port tack, and 8(2) shows tacking from port to starboard tack. The sail force variations in Figures 5(a) and 5(b) correspond to these cases, respectively. The indicated results were recorded for 35 seconds, beginning 5 seconds before the start of tacking. Figure 8(1)(a) shows the boat trajectories. Solid circles indicate the positions of measured C.G. of the boat at each second, while open circles indicate the simulated positions. The illustrations of the small boat symbol indicate the heading angle ψ every three seconds. The wind blows from the right side of the figure and the grid spacing is taken as 15 meters. Figure 8(1)(b) shows the time histories of rudder angle δ, heading angle ψ, heel angle φ and boat velocity V B. The solid lines are measured data and the dotted lines are simulated data. In Figures 8(1)(b) and 8(2)(b), the patterns of rudder angle variation can be considered as standard for tacking maneuvers. As shown, tacking with a yawing motion of 90 degrees is completed in 7 to 8 seconds. The boat velocity decreases about 30%, and the boat takes about 15 seconds to recover to the previous velocity after the yawing motion is completed. The measured time histories of ψ and φ indicate the delay of zero crossing point of φ compared with ψ. This might be caused by the sail filling with wind due to the yawing motion until around ψ= 10º on the opposite tack as shown in Figure 6. The simulated time histories show a slight delay when compared to the measured data. In particular, the delay of the simulated heel angle is relatively large. This might be caused by the over-estimation of the damping coefficient for rolling, K. For this point further investigation might φ & be necessary. However, the simulated results of velocity decrement show agreement with the measured results. This suggests that the model of sail force variation proposed in this report is adequate for the tacking simulation. In Figures 8(1)(a) and 8(2)(a), although the simulated trajectories show slightly larger turning radiuses than the measured trajectories, the simulated results show agreement with the measured values overall Results of Fair V Figure 9 shows the comparison between measured and simulated results of Fair V. The contents of these figures are identical to Figure 8. In these cases, the rudder angle variations in the first stage are relatively small. These cause the delay of yawing motion of the boat. Hence it takes more than 10 seconds to complete the tacking maneuver. On the other hand, the simulated results show a prompt response to the rudder angle variation. Therefore the simulated time histories vary slightly earlier compared with the measured histories. By the same reasoning, the simulated trajectories in Figures 9(1)(a) and 9(2)(a) show smaller turning radiuses than the measured trajectories.

220 measured simulated measured simulated U T=5.7m/s start of tacking U T=5.4m/s start of tacking WIND WIND WIND WIND 15m 15m [deg] start of tacking (a) Trajectory of boat [m/s] elapsed time [sec] (b) Boat attitude parameters V B VB [deg] start of tacking V B (a) Trajectory of boat elapsed time (b) Boat attitude parameters : HeadingAngle : Heel Angle : Rudder Angle V B: Boat Velocity (1) From starboard to port tack (2) From port to starboard tack Figure 8 Measured and simulated results of tacking maneuver of Fujin [m/s] [sec] VB measured simulated measured simulated UT=4.8m/s start of tacking U T=4.9m/s start of tacking WIND WIND WIND WIND 15m 15m [deg] start of tacking (a) Trajectory of boat [m/s] elapsed time [sec] (b) Boat attitude parameters VB VB [deg] V B start of tacking (a) Trajectory of boat elapsed time (b) Boat attitude parameters : Heading Angle : Heel Angle : Rudder Angle V B: Boat Velocity (1) From starboard to port tack (2) From port to starboard tack Figure 9 Measured and simulated results of tacking maneuver of Fair V [m/s] [sec] VB

221 Overall, although the timing of boat motion indicated in the simulated time histories shows a slight discrepancy, the tendency and amount of variation of the boat motion indicate good agreement with the measured data, including the decrement of boat velocity. 5 ROLE OF FULL SCALE TESTS AS THE BRIDGE BETWEEN MODEL TESTS AND CFD Wind Tunnel tests using model sails are commonly performed at the Reynolds number (Re) region of around 2x10 5 to 5x10 5. This region is referred to as the critical Reynolds number range, where the boundary layer flow turns from laminar to turbulent, causing the drag and lift coefficients change drastically. Hoerner [17] shows experimental results of wing sections in this region and indicates that the maximum lift coefficient varies as a function of the Reynolds number, camber ratio and noseradius ratio, and also can be very sensitive to the test conditions. From the author s experience of wind tunnel tests [18], the unexpected and unstable deviation on measured data occurred in particular in the case of downwind sail. Normally, a spinnaker has a large camber and a sharp leading edge which works at a high entrance angle. This causes the laminar-type separation at the suction side of the leading edge at the low Reynolds number region. When this separation area spreads over the surface of the suction side, the drag and lift coefficients change drastically. The author sometimes experienced that the slight shape change of a spinnaker by sheet trimming caused serious deviation on measured data. Therefore, it should be considered that the wind tunnel test in this Reynolds number region has to be performed very carefully. On the other hand, for the full scale boat, the sails work in the Reynolds number of almost greater than 1x10 6. In this region, although the effect of critical Reynolds number still remains, the effect on the measured data may be less than the case of wind tunnel tests. Recently, Viola et al. [19] measured the pressure distribution on the surface of full scale downwind sails during sea tests using a Platu25-class yacht. The results were compared with the measured data by wind tunnel tests, and showed very interesting differences in the pressure distributions near the leading edge. The author thinks this is the first report which points out the differences of pressure distribution on the downwind sails between full scale and scale model. It can be considered that this fact indicates the importance of full scale measurements for the developments of downwind sails. A sail dynamometer boat may provide more precise information not only about pressure distribution, but also aerodynamic forces and sail shapes simultaneously in full scale level. Investigation of effect on the sail aerodynamic forces by dynamic motion of the boat is another important research target of the full scale test using a sail dynamometer boat. The research of aerodynamic force variation during tacking maneuver should be broadened to investigate the best tacking procedure. The motions of pitching and rolling of a boat also have a serious effect on sail performance. For the research of these effects, a sail dynamometer boat will provide essential information. When the sail tests were performed using Fujin, it was difficult to measure the shape of sail such as balloon spinnaker simultaneously with aerodynamic forces. However, recently we can easily employ high performance digital cameras and 3-dimensional shape analyzing systems. Moreover, the developments of measurement systems such as small gyroscope, GPS sensor, electronics transmitter, etc. can also provide us good opportunities for carrying out sea tests easily. It is worth emphasizing that the tests using a sail dynamometer boat can provide the ultimate validation data for CFD in full scale level. Now, a new generation sail dynamometer boat is being prepared by Professor Fabio Fossati at Politecnico di Milano. We are looking forward to the results of this boat from tests at Lake Como in Italy. 6 CONCLUSIONS The work achieved with the sail dynamometer boat Fujin was reported. At first, the sail shapes and performance for upwind conditions were measured in steady sailing conditions. The results were compared with the numerical calculations using the measured sail shapes as the input data. The database of three-dimensional coordinates of the sail shapes was also tabulated with the aerodynamic coefficients. The sail shape database and the comparison with the numerical calculations indicated in this research provide a good benchmark for the validation of sail CFD in full scale level. Then, the aerodynamic force variation during tacking maneuvers was measured by Fujin, and a new simulation model of tacking maneuver was proposed. The simulated results showed good agreement with the measured data. Finally, the scale effect problem of wind tunnel tests was discussed. Wind tunnel tests using model sails are performed at the region of critical Reynolds number. Therefore, the wind tunnel test in this Reynolds number region had to be performed very carefully. On the other hand, the full scale tests using a sail dynamometer boat are free from scale effect problems and appear more promising. ACKNOWLEDGEMENTS The author wishes to thank Professor T. Fukasawa at Osaka Prefecture University and Dr. Y. Tahara at National Maritime Research Institute of Japan for their contributions as co-researchers. The author also would like to thank Mr. H. Mitsui, the former harbour master of the Anamizu Bay Seminar House of Kanazawa Institute of Technology, for his assistance with the sea trials. Help with the sea trials given by graduate and undergraduate students of the Kanazawa Institute of Technology is also acknowledged.

222 REFERENCES 1. MILGRAM, J. H., PETERS, D. B. and ECKHOUSE, D.N., N., Modeling IACC Sail Forces by Combining Measurements with CFD, 11th Chesapeake Sailing Yacht Symposium, SNAME, HOCHKIRCH, K. and BRANDT, H., Fullscale Hydrodynamic Force Measurement on the Berlin Sailing Dynamometer, 14th Chesapeake Sailing Yacht Symposium, SNAME, HANSEN, H., JACKSON, P. and HOCHKIRCH, K., Comparison of Wind Tunnel and Full-scale Aerodynamic Sail Force, International Journal of Small Craft Technology (IJSCT), Vol. 145 Part B1: 23-31, KREBBER, B. and HOCHKIRCH, K., Numerical Investigation on the Effects of Trim for a Yacht Rig, 2nd High Performance Yacht Design Conference, Auckland, New Zealand, MASUYAMA, Y. and FUKASAWA T., Full Scale Measurement of Sail Force and the Validation of Numerical Calculation Method, 13th Chesapeake Sailing Yacht Symposium, SNAME, MASUYAMA, Y., TAHARA, Y.,FUKASAWA, T. and MAEDA, N., Database of Sail Shapes vs. Sail Performance and Validation of Numerical Calculation for Upwind Condition, 18th Chesapeake Sailing Yacht Symposium, SNAME, 11-31, MASUYAMA, Y., TAHARA, Y.,FUKASAWA, T. and MAEDA, N., Database of Sail Shapes versus Sail Performance and Validation of Numerical Calculation for the Upwind Condition, Journal of Marine Science and Technology, JASNAOE, vol. 14, No. 2, , FUKASAWA, T., Aeroelastic Transient Response of 3-Dimensional Flexible Sail, Aero-Hydroelasticity, ICAHE'93, TAHARA Y., Evaluation of a RaNS Equation Method for Calculating Ship Boundary Layers and Wakes Including Wave Effects, J. Society of Naval Architects of Japan 180: 59-80, TAHARA, Y., HAYASHI, G., Flow Analyses around Downwind-Sail System of an IACC Sailing Boat by a Multi-Block NS/RaNS Method, J. Society of Naval Architects of Japan 194: 1-12, MASUYAMA, Y., NAKAMURA, I., TATANO, H. and TAKAGI, K., Dynamic Performance of Sailing Cruiser by Full-Scale Sea Tests, 11th Chesapeake Sailing Yacht Symposium, SNAME, , MASUYAMA, Y., FUKASAWA, T. and SASAGAWA, H., Tacking Simulation of Sailing Yachts-Numerical Integration of Equations of Motion and Application of Neural Network Technique, 12th Chesapeake Sailing Yacht Symposium, SNAME, , MASUYAMA, Y. and FUKASAWA, T., Tacking Simulation of Sailing Yachts with New Model of Aerodynamic Force Variation, 3rd High Performance Yacht Design Conference, Auckland, , MASUYAMA, Y. and FUKASAWA, T., Tacking Simulation of Sailing Yachts with New Model of Aerodynamic Force Variation During Tacking Maneuver, Journal of Sailboat Technology, SNAME, MASUYAMA, Y. and FUKASAWA, T., Tacking Simulation of Sailing Yachts with New Model of Aerodynamic Force Variation During Tacking Maneuver, Transactions, SNAME, Vol HAMAMOTO, M. and AKIYOSHI, T., Study on Ship Motions and Capsizing in Following Seas (1st Report), Journal of The Society of Naval Architects of Japan, No.147, , HOERNER, S. F., and BORST, H. V., Fluiddynamic Lift, Hoerner Fluid Dynamics, p.4-12, TAHARA, Y., MASUYAMA, Y., FUKASAWA, T. and KATORI, M., CFD Calculation of Downwind Sail Performance Using Flying Shape Measured by Wind Tunnel Tests, 4th High Performance Yacht Design Conference, Auckland, 38-47, VIOLA, I. M. and FLAY, R. G., Sail Aerodynamics: On-Water Pressure Measurements on a Downwind Sail, Journal of Ship Research, SNAME, Vol.56, No.4, , AUTHORS BIOGRAPHY Y. Masuyama is a Professor Emeritus and a Research Fellow at the Actual Seas Ship and Marine Research Laboratory, Kanazawa Institute of Technology, Japan. He graduated from the Department of Mechanical Engineering, Toyama University, and received a degree of Doctor of Engineering from Osaka University. He learned the yacht design process at the Kumazawa Craft Laboratory, yacht design office, and has been continuing research about sailing yachts at Kanazawa Institute of Technology. His research interests include sail performance, velocity prediction, maneuverability and stability of sailing yachts. He had been involved with the technical committee of the Japanese America s Cup challenge team Nippon Challenge. He was a chairman of the Sailing Yacht Research Association of Japan from 1993 to 2012.

223 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France ESTIMATING A YACHT S HULL-SAILPLAN BALANCE AND SAILING PERFORMANCE USING EXPERIMENTAL RESULTS AND VPP METHODS M. Prince and A.R. Claughton, Wolfson Unit M.T.I.A., University of Southampton, UK, wumtia@soton.ac.uk This paper describes an approach to calculate the longitudinal position of the hydrodynamic and aerodynamic force centres on a sailing yacht, and the resulting rudder angle required to hold a steady course across a complete range of sailing conditions. The paper discusses the effect on performance, in terms of boat speed, by means of experimental tank testing to derive the hydrodynamic data; wind tunnel testing to derive the aerodynamic data; and the use of a 4 plus degree of freedom (DOF) velocity prediction program (VPP). It highlights the data required to carry out such analysis and is summarised in a worked example. The main objective of this paper is to outline a process which is achievable within a design office environment and skill set, whereby a designer can use generic data derived from experimental or CFD and amalgamate it with theoretical and regression models for individual components to ensure that the balance question is satisfactorily addressed at a stage in the design and development process where meaningful changes can be made to geometry. 1 INTRODUCTION As sailing yachts are getting larger, 70 metre plus LOA is unexceptional, the achievement of good hull-sailplan balance across a complete range of sailing speed and heel conditions become more difficult. This is due to design features related to their size and operational constraints. Large sailing vessels often have shallow draft relative to their length, restricted draft and rudder(s) area and high induced drag characteristics leading to large leeway and high hydrodynamic drag angles. All of these effects make coinciding the aerodynamic and hydrodynamic lines of action more difficult, and the normal fixes to ameliorate the problem, such as altering mast rake and sail trim, or the sailing trim are not easy to apply on such large vessels. The long established rules of thumb to determine hull-sailplan balance or lead can no longer be relied upon, highlighted in [1] and [2]. This necessitates the use of alternative approaches to understand and determine the elements that contribute towards balancing the hull and sailplan. The majority of large superyachts have multimasted rigs to meet design and operational restrictions. These sailplans can have vastly different longitudinal centres of effort in comparison to sloop rigs with complex interactions between the cascade of sails and sheeting options. This makes the use of techniques such as wind tunnel testing or CFD invaluable as a means of determining the aerodynamic centre of effort and how it changes with apparent wind angle, sail flattening and easing. This paper breaks down this balance problem into three main stages: The estimation of the hydrodynamic forces including centres of lateral resistance; lift and drag values The estimation of the aerodynamic forces including centres of effort; lift and drag properties A solution phase, combining the above elements and other parameters including righting moment across a range of sailing conditions to predict steady state rudder angles and sailing performance. The budget often restricts the quantity of project specific experimental or computational data points that can be gathered. The designer can offset this restriction if he has the skills to use limited datasets, or data from similar vessels and casting these into a more complete summary of the yacht s performance, particularly in relation to helm balance effects. By incorporating other methods and sources of data more depth is added to the global yacht model and allows it to be extended beyond the limits of the original data and results in more complete and robust performance envelopes. This paper is aimed at the yacht designer, to show an approach that combines the use of different data sources to create a meaningful performance prediction tool that captures balance effects for large sailing yachts. Additionally the techniques described are relevant to the productive management of a mixed economy where data from physical experiments, CFD simulations and parametrically based force models can all be woven into the fabric of the design decision process.

224 2 TANK TESTING Sailing yacht tank testing is principally used as a means of estimating a vessel s resistance and sideforce generating properties, with limited attention paid to the impact of rudder use on resistance. This has typically been the case in race boat development where changes of longitudinal centre of lateral resistance (CLR) are reasonably well understood and easily predicted with deep keels and rudders taking large proportions of the lift generation. Large yachts often have comparatively shallow draft appendages which in turn leads to greater lift contributions from the relatively inefficient hull. This lift generation by the hull induces a Munk moment which can have a significant effect upon the centre of resistance. These effects must be incorporated within any analysis if it is to yield meaningful guidance for the designer. Standard semi captive model sailing yacht testing techniques adopted by the authors are described in [3] and [4]. Following the completion of an upright resistance curve (zero heel, zero yaw), at each test speed and heel test condition a sweep of leeway angles will be tested on both tacks with a rudder set to a plausible helm angle. Some judgement must be exercised here, it is clearly wrong to test at zero rudder because this means every test point has the wrong rudder angle. Therefore an angle of say 2 or 3 degrees may be chosen, although this will not be the correct angle it does at least mean that the test data has captured some of the effects of the pressure field around the rudder. A matrix of speed and heel combinations covering the expected vessel sailing range will be carried out. The major benefit of this style of testing is that it allows for good estimation of the different resistance components, robust scaling of the model scale results and provides a direct approach to assimilate the data for into a VPP. Figure 1 summarises the typical results for one speed/heel condition, on one tack. The labels show the leeway and rudder angle for each data point. The leeway variation sweep was carried out with the set rudder angle of 4, after which a rudder sweep was carried out at 5 of leeway. These results here can be used to determine: Heel drag (drag at zero sideforce) Drag at sailing sideforce Effective draft The effective draft is determined by applying a least square fit to the standard leeway speed data. This is appropriate for most vessels, however the linear assumption does not hold when significant lift is taken by the hull or low aspect ratio appendages operating at high leeway angles as is the case with many large yachts. In such cases a first order polynomial or similar is used to fit the data. Resistance ,4 5,8 5,6 5,4 5, Sideforce squared Figure 1: Typical tank testing resistance versus sideforce 2 plot The rudder effectiveness tests are carried at or close to the leeway setting coinciding with sailing side force (SSF) appropriate to that heeled condition, as can be seen in Figure 1 with the SSF line. Rudder angle changes are made over a range, i.e. 2, 4, 6, 8 degrees. These are then used to determine the relative change in CLR with rudder angle, which can be seen in Figure 2. This can then be undertaken across a range speed/heel conditions with the CLR change being expressed per degree of rudder angle for each condition. CLR (% LWL aft of FP) Leeway Variation Rudder Variation 2,4 Sailing Sideforce Figure 2: Typical longitudinal centre of lateral resistance (CLR) change with sideforce The complete set of data will eventually consist of 8-10 data sets like the one shown in Figure 1, and 3-4 rudder variation data sets like the one shown in Figure 2. These data are scaled to the full size and submitted to a fitting process which the VPP can interrogate across the entire range of boat speed, heel and sideforce to yield the following data: 7,4 Rudder variation at set leeway angle Sideforce 5,2 5,4 5,8 5,6 7,4

225 Resistance as a function of sideforce Vertical and Longitudinal centre of lateral resistance at standard rudder setting Sideforce versus leeway relationship Rudder angle relationship to CLR and resistance For direct input into a VPP this is summarised to a table input of: Boat speed Heel angle Leeway angle Rudder angle Resistance (Force along the vessel track) Sideforce (Force normal to the vessel track) Roll moment (Mx) Yaw moment (Mz) 3 SAIL AERODYNAMICS Large superyachts often have multi-masted sailplans due to mast height restrictions, ranging from ketches to 3 masted or more schooners. At the design stage, a number of questions are often being asked, such as what is the overall sail performance in terms of driving force, sideforce and achievable apparent wind angles. Are the masts in best location and are the separations suitable? Do the sails interact favourably? Do sheeting locations impact on the deck arrangement? The wind tunnel offers a perfect environment in which to address these questions. It often provokes a stimulating discussion between the stylists, sailmakers, Naval Architects, and designers. 3.1 WIND TUNNEL TESTING There are a number of practitioners of scale model experimental sail aerodynamics. Historically, these have focussed on driving force, sideforce and roll moment parameters [5], but in more recent times the importance of yaw measurement upon absolute yacht performance has received greater attention [6] and [7]. Sail testing techniques are discussed in a number of other sources. The authors adopt the following processes which enable robust analysis and scaling of the results to full scale and facilitates complete datasets for direct inclusion into VPPs. Bare hull and mast windage tests are carried out to assist in the understanding of the breakdown of forces. Whilst maintaining constant wind pressure, each sail combination at each tested apparent wind angle is optimised by sheeting all the sails to produce the maximum driving force. Having achieved this, other combinations of sheeting are used appropriate to depowered modes, i.e. maximum drive force (Df) at a specified limit of heeling moment (Hm) (optimising Df/Hm ratio). At this stage, the change of longitudinal centre of effort (CEA) with depowering and sheeting can be observed. This process indicates the range of potential movement of centre of effort. The data is analysed to apply the blockage corrections, and calculate the sail force and moment coefficients which are then used at full scale. The authors use an inhouse software WindCorrect to carry out this analysis and create aerodynamic data fit files for each tested sail set that can be read directly by the VPP. Figures 3,4,5 show typical results for one sail configuration and three apparent wind angles, Drag coefficient (C D ) versus Lift coefficient (C L ), nondimensional Driving force (Df) versus Heeling moment (Hm) and Centres of efforts versus Heeling force (Hf), respectively. The objective of the tests is to produce a set of data for each sailset (e.g. full sail, offwind and reefed configurations) that encompasses a range of apparent wind angles for input into a VPP. This uses an approach similar to that of the ORC [8] to model sail easing and flattening. In Figure 3, the line fit through the C D versus C 2 L data for the apparent wind angle ( a ) of 30 corresponds to the effective rig height and is used to derive the drag associated to the eased/flattened sail settings. This figure shows typical sail trimming effects, at 30apparent wind 2 angle the C D versus C L line is sensibly linear, the maximum C 2 L of 2.5 (2.5=1.58 C L ) is achieved by overtrimming the sail so that a little extra drag is incurred, then as the sail are eased the lift coefficient can be reduced to 1.0 before sail efficiency is lost. At the wider apparent wind angles it becomes increasingly difficult to efficiently de-power the sail. This is carried out on as many of the proposed sail plan options as is possible, covering upwind, reaching and downwind configurations as well as reefed settings. Figure 4 shows the VPP input file fit applied to the 30 a and the maximum Df values appropriate to each apparent wind angle. Drag Coefficient Cd Conf. A - 30 Conf. A - 36 Conf. A Lift Coefficient² Cl² Figure 3: Typical wind tunnel C D versus C L 2 plot Figure 5 shows forward and lower shift in centre of effort as the sailplan is eased. As with a majority of rig types, the most significant and efficient easing strategies result to sheeting out the aft most sail, with lesser easing moving forward through the sailplan.

226 ND Driving Force Conf. A - 30 Conf. A - 36 Conf. A - 45 extrapolating the effective rig height and the maximum lift coefficient with its associated drag coefficient across the apparent wind angle range. By adopting this physics based approach valid data can be derived for the full range of wind angles from a relatively sparse set of test data. All this data has been corrected to the upright condition, as the VPP will apply the appropriate heel manipulation ND Heeling Moment Figure 4: Typical wind tunnel driving force versus heeling moment plot Longitudinal Centre of E (% of LWL from FP) Vertical Centre of Effort (% mast height) Conf. A - 30 Conf. A - 36 Conf. A ND Heeling Force Figure 5: Typical wind tunnel CEH and CEA versus non dimensional heeling force plot It is important to maintain similar CEA characteristics as a sailplan is reefed to prevent large changes in rudder angle. This is the stage were alternative strategies can be tested to ensure this is the case and highlight reefed configurations that are not. 3.2 FITTING PROCESS From analysis of the scaled test data, the following data are determined for the range of apparent wind angles tested, this includes: C L C D CEH at maximum Df CEA at maximum Df Effective Rig Height (He) Function of change of CEH and CEA with C L This data set is then augmented by interpolating and extrapolating for other apparent angles that were not tested, to create a continuous set of data that can be used by the VPP. As with the hydrodynamic data fits the aerodynamic data are not simply faired surfaces through the test data points, they are derived by interpolating and This is a highly appropriate solution in the creation of a consistent and robust data set for direct inclusion into a VPP environment. Other test methods will answer specific questions, i.e. most appropriate sail settings for a specific wind condition, vessel stability and wind angle but will be of limited overall value in creating a systematic or complete dataset for inclusion in a mathematical fitting process such as a VPP. This analogous to the situation experienced in tank testing, where sailing dynamometer systems that generated data only at conditions where the roll moment equilibrium of the full scale boat was matched at each heel angle. This system gave instant gratification by capturing stability effects without the need for further analysis, but it generated data sets that lacked the heeling force degree of freedom, and in so doing provided data that was much less easily applied in the general case. 4 SOLUTION PHASE The velocity performance prediction program (VPP) has the ability to integrate the complete range of hydrodynamic and aerodynamic elements. 4.1 HYDRODYNAMIC COMPONENTS The drag and lift properties associated with hydrodynamic components include that of the: Keel Bulb Rudders Other appendages such as daggerboards The breakdown of hydrodynamic forces on each element includes: Viscous drag Lift and induced drag Wavemaking drag Interaction between the elements such as downwash angle and wake effects 4.2 AERODYNAMIC COMPONENTS The aerodynamic components include: Sails, various different types Mast and rigging including windage These are comprised of aerodynamic forces including: Viscous drag Lift and induced drag Drag due to separation Interaction effects such as bi-plane and blanketing

227 4.3 VPP The VPP used (WinDesign6) can incorporate different force models for each component, such as the Delft Systematic Yacht Hull Series for the canoe body, ORC aerodynamic sail coefficients and built in models based on theoretical and experimental regressed models. Sections 2 and 3 have briefly summarised the creation of models specific to a particular vessel which can be used directly within a VPP. Discussed here is a 4 DOF approach, whereby the VPP aims to resolve the force and balance equations: driving force resistance 0 heeling moment righting moment 0 hydro sideforce aero sideforce 0 Fx M x Fy M hydro yaw moment aero yaw moment 0 y The WinDesign 6 software uses a modified multidimensional Newton Raphson iteration scheme to resolve these equations. It must be borne in mind that each of the parameters listed above are functions of a number of variables. A breakdown of the simplified case of a 2 DOF VPP is detailed in [9]. For direct input of the externally derived hydrodynamic or aerodynamic data WinDesign 6 uses a thin plate spline (TPS) with radial basis function (RBF) which allows the program to apply reliable fits to multivariate, irregular data. In the majority of testing situations the authors endeavour to use systematic test programmes that allow the creation of well populated datasets covering as much of yachts sailing performance envelope in terms of speeds, heel, leeway and rudder angles as possible and ensure that the data is fair and extended to cover the entire condition range (as per section 2) prior to use within a VPP. It is often the case in a design environment that the data available to create a hydrodynamic or aerodynamic vessel specific fit is relatively sparse and the data points are not distributed regularly. This often results from limited results to base a fit upon which is often due to budget restraints as each data point comes with a cost implication or time constraints in the project plan, or computational constraints if using CFD. This is the case when using offwind sail data derived from Direct Eddy Simulations (DES) [10] where a comprehensive matrix of test results would be prohibitive. The RBF component of the spline fit allows the program to interpolate points and develop a smoothed surface across parameter space that is then used as a hydro or aerodynamic force component. For ease of understanding the aero/hydro balance problem parameters such as CLR and CEA have been used, whereas they each relate to a 3-D vector and as such this is what needs representing within the VPP modelling, and is defined in terms of boat axis Fx, Fy, Mx and Mz. 6 WORKED EXAMPLE A VPP is a primary tool in the design decision process, and therefore being able to use a mixed economy of input sources is very powerful. It is possible to use experimentally derived data and with minor adaptations to replace, or add new appendages. This can allow the user to build a complete hydrodynamic model around limited data, using built-in internal models and their own regressions. The worked example in this presentation aims to highlight the possibilities of changing and replacing rudder configurations. This has been focussed upon because the rudder arrangement is the primary longitudinal balancing control for a superyacht. Changing rudder angle can produce much larger changes in CLR than alterations to sail trim can make to the CEA. Also by controlling CEA with sail trim you inevitably lose driving force and efficiency. Sails are at their optimum at a single CEA position, whereas the hull resistance is less sensitive to change in CLR, as shown in Figures 1 & 2. Relative to rudder usage, sail sheeting and setting changes outside a reasonable restrictive range typically result in large losses in driving force. It is based on actual results derived from tank testing and wind tunnel sail testing and this scenario applies equally to CFD developed data, where a designer has commissioned various simulations. Following this programme of work particular features are modified which is not uncommon during a project. In the case of a luxury yacht project, various specifications may change. Therefore the previous derived yacht data will need to be modified to suit the new design requirements. A case study was undertaken using Windesign 6 using experimentally derived hydrodynamic and aerodynamic data for a very large multi masted schooner rigged superyacht. The tank testing was conducted with a single centreline semi-skeg rudder. The hydrostatic data such as GZ and displacement for each option is determined directly from geometry surface files of the hull and appendages, LCG and VCG definition and applied directly in the VPP. The design change simulated using the VPP was swapping the single rudder for a twin rudder arrangement. This example presents the results for both the single and twin rudder options and the resulting changes in rig/sailplan location in order to maintain acceptable helm angles and sailing performance. The original scaled and fitted tank data incorporates the combined effects of the canoe body, stub keel and single

228 centreline semi-skeg rudder, with limited rudder variation data. In order to build on this, it is manipulated to allow the VPP to use a virtual rudder that uses the internal rudder model (in terms of induced drag and lift) with a prediction of downwash and angle of attack effects. The force model components are shown in Table 1. Component Data Source Force Data Hull Keel Tank results Resistance, Rudder Virtual Rudder WD 6 internal model SF, Mx & Mz SF, CLRR and Induced Drag Table 1: Single Rudder Hydrodynamic Force Model Components Boat speed (knots) In this way the CLR relationships and a rudder volume contributionn effects in the original data are retained, but the virtual rudder angle can be varied by the e VPP solution algorithm to maintain the force and moment balance with the sails This is then run through the VPP using the experimental derived aerodynamic data. The predicted rudder angles across a comprehensive range of true wind speeds and angles are presented in Figure 6. This shows that the rudder angles for the standard single options are within a reasonable range across the matrix of true wind speeds and angles Figure 7: Polar performance plot in thee single rudder condition The predicted rudder r angles are presented in Figure 8. Figure 6: Rudder angles for single centreline rudder. It also leads to respectable sailing speeds as detailed on the polar plot of Figure 7. To model the twin rudder configuration the tank data was re-analysed to remove the viscous drag of the single centreline rudder and the force model componentss were adapted as shown in Table 2.. Component Hull Keel Rudder Dataa Source Re-analysed Tank Force Data Resistance, results SF, Mx & Mz Twin Virtual WD 6 internal SF, CLRR and Rudders model Induced Drag Table 2: Single Rudder Hydrodynamic Force Model Components Figure 8: Rudder angles for twin rudders and original sailplan Changing directly to the twin rudder option shifts the CLR 7% of the LWL aft leading to highly negative rudder angles in the light t upwind wind range. This results in part from the increased rudder effectiveness due to twin rudders having less influence from keel downwash, angle and wake that the single rudder experiences.

229 It must be borne in mind that thee negative rudders presented in Figure 8 are referenced to boat centreline and that the local angle of incidence will reflect the actual rudder loading which is a function of leeway and downwash effects. There is also a noticeable reduction in boat speed due to the hull and keel taking a greater proportion of the lift which is at the expense of greater induced drag. As can be seen in Table 3, where speed differences are significant, negative means that the twin rudder option is slower. This highlights the important of maintaining good hull sailplan balance. TrueWindAngle(deg) TrueWindSpeed(knots) Table 3: Reduction of boat speeds (knots) between single and twin rudders option The rudderr areas used are considered reasonable to maintain adequate manoeuvring qualities whilst under motor and sailing conditions. The remaining options to adjust balance are: to shift the CLR by moving the keel or longitudinal movement of the rigs and a sailplan. In light of the speed reduction with twin rudders a revised sailplan was modelled with the CEA shifted aft. This brings the rudder angles into a more acceptable range, slightly negativee at the lower upwind speeds moving to positive at the higher speeds as can be seen in Figure 9. viscous drag off the additional rudder overr that of induced drag differences. TrueWindAngle(deg) da TrueWindSpeed(knots) Table 4: Reduction of boat speeds (knots)) between single and twin rudders with aft shifted sailplan This process shows that if the twin rudderr option is taken then an aft shift of the entiree rig is necessary in order to maintain acceptable sailing rudder angles 6..1 DESIGN SOLUTION Experimental testing offers a very cost effective e way to generate accurate force and moment charactersitics for a sailing yacht hull, h capturingg the wavemaking effects of lifting surfacess and the Munk moment from the canoe body when yawed. The typee of analysis described shows how this data can be usedd as a baseline to simulate alternative configurations, using either the VPP internal models, or specific CFD tests on individual components. 7 CONCLUSIONS This paper has highlighted an integrated approach using experimentally derived hydrodynamic and aerodynamic data and a 4 plus DOF VPPP to evaluate the t yaw balance and predict steady state sailing rudder angles a and boat speed optimisation across a complete range of true wind speed and angles for sailing yachts. The benefits of this approach to aid the design process and additional versatility too existing data sources has been outlined. It also addresses particularr issues relating to the study of large sailing yachts. REFERENCE ES 1. Keuning, J.A., Vermeulen, K.J., On the balance of large sailing yachts, y 17 th HISWA Intl Symp on Yacht Design and Yacht Construction, Claughton, A.R. A et al., Hull-sailplan balance, Lead for the 21 st Century, 22 nd HISWA Intl Symp on Yacht Design and Yacht Construction, Figure 9: Rudder angles for twin rudders with sailplan aft As can be seen in Table 4 the rig and sailplann shift aftward results in significant less boat speed reduction when compared to the single rudder option. This speed difference is now primarily related to the additional 3. Campbell, I.M.C. Claughton, A.R.,, The interpretation of o results fromm tank tests on 12m yachts, 8 tht Chesapeakee Sailing Yacht Symp, Claughton, A.R., Wellicome, J.F., Shenoi, R.A.,, Sailing Yacht Design: Theory, 1998.

230 5. Claughton, A.R., Campbell, I.M.C., Wind tunnel testing of sailing yacht rigs, 13 th HISWA Intl Symp on Yacht Design and Yacht Construction, Campbell, I.MC., The performance of offwind sails obtained from wind tunnel tests, Intl Conf on The Modern Yacht, Le Pelley, D., Richards, P., Effective wind tunnel testing of yachts sails using a real-time velocity prediction program, 20 th Chesapeake Sailing Yacht Symp, Offshore Racing Congress VPP Documentation Oliver, J.C., Claughton, Development of a multifunctional velocity prediction program (VPP) for sailing yachts, RINA CADAP, Wright, A.M., Claughton, A.R., Paton, J., Lewis, R., Off-wind sail performance prediction and optimisation, Innovsail, AUTHORS BIOGRAPHY M. Prince holds the current position of Principal Research Engineer at Wolfson Unit M.T.I.A.. He is a consultant engineer/naval architect and his specialist areas of interest involve sailing yacht performance evaluation; this in part has involved conducting, analysing and managing a range of towing tank test and wind tunnel projects ranging from small cruising boats up to America s Cup R&D programmes. A.R. Claughton holds the current position of Director of Enterprise at Wolfson Unit M.T.I.A.. He is a consultant engineer/naval architect and his specialists areas include experimental aero and hydrodynamics of sailing vessels and racing yachts, and the development of velocity prediction software. His previous experience includes Technical Director of the 2007 Emirates Team New Zealand America s Cup Challenge and in 2008 he was awarded the Royal Institution of Naval Architects Small Craft Group Medal for contributions to yacht science. The Wolfson Unit was awarded the RINA Small Craft Medal in 2013 for its long standing service to the small craft industry.

231 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France SAILING SITE INVESTIGATION THROUGH CFD MODELLING OF MICROMETEOROLOGY M. Le Guellec, Fluidyn FRANCE, France, Y.Amice, Département Météorologie - Institut de Recherche de l École Navale, France, yann.amice@gmail.com; To have a prior accurate knowledge of the local wind currents on a water body is of crucial importance for the performance of the sailing team. In the recent years, Computational Fluid Dynamics (CFD) has proven itself a powerful tool in atmospheric modelling. By solving the Navier-Stokes equations and with correct description of the atmospheric boundary layer and turbulence at the domain boundaries, the local influences of the shore topography and the obstacles on the wind flows can be investigated in detail. Two examples of the use of CFD (Fluidyn PANWIND software) are presented here. The first one shows the coastal wind analysis of 2012 Olympic sailing site of Weymouth, UK. The local wind effects due to the harbour and hill have been determined and compared to observations of wind velocity and direction for several wind conditions. The second example required to model the wind over the training base of the French Sailing Team in Brest, France. This landlocked bay, surrounded by two steep hills and linked to the Atlantic Ocean by a strait, emphasizes the need for a CFD simulation of the wind which provided the patterns of wind around the racing area compared with empirical observations. NOMENCLATURE C 1 C 2 C S C E k-ε turbulence model constant k-ε turbulence model constant dimensionless turbulence production factor dimensionless turbulence viscosity constant for the k-ε model C p specific heat of air (J g -1 K -1 ) F g/p force due to: (g) gravitational acceleration, (p) interaction with droplets/particles (N m -2 ) g gravitational acceleration (9.8 m s -2 ) G turbulence production rate by shear = σ u (m 2 s -3 ) h m specific enthalpy of species m (J kg -1 ) I specific internal energy (J kg -1 ) J heat flux vector (W m -2 ) k turbulent kinetic energy per unit mass (m 2 s -2 ) k c thermal conductivity (W m -1 K -1 ) L Q h Monin-Obukhov turbulent length scale (m) rate of specific internal energy gain due to (h) surface energy budget (J kg -1 s -1 ) Richardson number, dimensionless time since the start of the release (s) temperature (K) Ri t T u fluid velocity (m s -1 ) u * surface friction velocity (m s -1 ) v wind speed (m s -1 ) W p z z 0 Turbulence production due to interaction with particles (m 2 s -3 ) height (m) ground roughness length (m) Greek letters density of air μ primary (shear) viscosity of fluid (kg m 1 s 1 ) λ secondary (bulk) viscosity of fluid (kg m 1 s 1 ) σ Newtonian viscous stress tensor (N m -2 ) ε dissipation of turbulent kinetic energy (m 2 s -3 ) ζ κ θ θ * σ h σ k σ ε Monin-Obukhov similarity variable = z/l, dimensionless Von Karman constant = 0.41, dimensionless potential temperature (K) temperature scale turbulent Prandtl number, dimensionless dimensionless turbulence model constant for the k equation dimensionless turbulence model constant for the ε equation Ψ 1/2 (ς) similarity profiles ν t turbulent viscosity (m 1 s 1 )

232 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France 1 INTRODUCTION Accurate wind field description (wind speed, wind direction and turbulence) plays an important role for sailing competitions. The proper wind speed range for sailing is between m/s. Traditional in-situ measurement data obtained are usually insufficient to characterise fully the flow, as data time series are too short, and only defined at a specific locations. Furthermore the interpolation wind flow models using mass consistent techniques which extrapolate the data from the point measurements (meteorological stations) do not provide the required accuracy over the entire area of interest. The atmospheric circulation in the lower layers is particularly dependent on local effects due to complex terrain. The topography, the transition zones between land and sea (estuaries, bays, ), the different roughness surface (urban areas, forests ), contribute to modify large scale flows and these influences have to be evaluated in details. The complex topography in coastal area emphasizes the need for a complete 3D CFD simulation of the wind. The wind flow modelling provides the patterns of wind speed and wind directions around the racing area. In many wind studies, the objective is to analyse the sea breeze effect based on the statistics of synoptic and local weather station measurements. This paper mainly focuses on the local wind characteristics with a predefined wind boundary condition assumed constant and considering topographical and roughness effect. Two different interesting areas have been studied in the frame of this project. Weymouth, a coastal city in Southern UK hosted the 2012 Olympic Sailing Events in August. The sailing competition spots are shown in Figure 1. Weymouth is a city surrounded by sea and hills. In the south of the city, i.e., in the south-east of the sailing area, there is a hilly island named Portland (130m). The topography is complex and consequently the local wind flow can be very difficult to comprehend. The second sailing area is located in the well-known roadstead (bay) of Brest, in Finistère department of France (see Figure 2). It is required to identify the characteristic of this water body into details to fully assess the impact of the surrounding topography. Indeed, it is a landlocked bay surrounded by two very steep hills (50 to 80 m) and linked to the Atlantic Ocean by a strait about 2 km wide with a 240 orientation. The wind modelling focuses here on two mains areas: the Quelern Peninsula (2 nd sub-domain) and the Cape of Armorique (3 rd sub-domain) Figure 1: Schematic map for sailing events in Weymouth Figure 2: Area of interests in Brest roadstead 2WIND FLOW MODELING 2.1 FLUIDYN-PANWIND Fluidyn-PANWIND is a module of fluidyn-panache family which allows a quick and accurate simulation of wind flows around buildings, hills at local or medium large scale by taking into account all kinds of obstacles, the topography, the influence of terrain and vegetation, the local meteorological conditions. The software solves the Navier-Stokes equations (Mass, energy and momentum conservation) with a finite volume method on structured or unstructured mesh. In this code the mass conservation equation for total fluid density is expressed as where is the gradient of the considered quantity. The momentum conservation equation for the fluid mixture is 224

233 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France where is Newtonian viscous stress tensor (= μ[ u+( u) T ]+λ( u)i, = first and second coefficients of viscosity, λ = -2/3μ; T = matrix transpose; i = unit dyadic - product of vectors). The energy conservation equation is: Where is the specific internal energy, is the heat flux = k c.t + ρ[h m (ρ m /ρ)], is the rate of specific internal energy gain due surface energy budget. 2.2 GEOMETRY AND MESH the sailing area is 25 m (see figure 3) resulting in a total of 2 million cells. Vertical mesh gets a 2m resolution from ground level to 12m of altitude. The vertical mesh is then coarser till until 200 m high. A large main domain of 43km by 32km was used for Brest s Roadstead case. A first nested domain of 30 km*28 km has been defined. Two smaller embedded domains with an area around 80 km² were used in order to evaluate accurately the wind flows as shown in figure 2.The topography was extracted from The NASA Shuttle Radar Topographic Mission (SRTM) who has provided digital elevation data (DEMs) for over 80% of the globe. The SRTM data is available as 3 arc second (approx. 90m resolution) Digital Elevation Model. The finest cell size of the unstructured mesh in the two nested domains is 30m and the averaged size dimension in the sailing area is 50m resulting in a 2.3 million cells. Vertical mesh gets a 3m resolution from ground level to 15m of altitude. The vertical mesh is then coarser until 200 m high. 2.3 TURBULENCE MODEL, BOUNDARY AND INITIAL CONDITIONS The standard k-ε model has been used throughout the simulations. The k-ε model is a two-equation linear eddy viscosity model. The PANACHE implementation of this model is derived from the standard high-re form with corrections for buoyancy and compressibility. It solves the transport equations for turbulent kinetic energy, k, and its dissipation rate, ε. The incompressible versions of the equations are: (a) k ν + ( ) = ν + t Uk l k + Pk + Pb ε t σ k ε ν t ε + ( Uε) = νl + ε + ε ( + ) ε ε σ C 1 Pk CbPb C 2 t ε k (b) Figure 3: Weymouth unstructured mesh at ground level ((a) full domain (b) nested domain) For Weymouth case, the topography of the site was collected from Landform Profile Plus data on a global domain of 24 km * 25 km. This data has a centimetre root mean square error (RMSE) accuracy and a grid resolution of 2 metres to 10 meters - sufficiently detailed to represent key terrain features. The harbour and jetties were modelled in finer details in an embedded domain of dimensions 5 km * 10 km. The finest cell size of the unstructured mesh in the harbour is 12 m and the averaged size dimension in where, P k =νγ&: t P b =νβ t U, the mechanical production rate of k gg T, the buoyancy production rate σ h of k σ k = Prandtl number for turbulent diffusion of k σ ε = Prandtl number for turbulent diffusion of ε μ t = turbulent eddy diffusivity C s1,c s2 =k-ε turbulence model dimensionless constants The eddy diffusivity is computed using: 225

234 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France Ambient mean wind speed and air temperature profiles are specified within the model domain and are represented by logarithmic functions, such that: Where θ * = temperature scale; and = similarity profile. The surface friction velocity,, the temperature scale θ *, and the Monin-Obukhov length, L are related by: L = u *2 T / (g κθ * )and θ * = Q h / (ρc p u * ). The micrometeorological parameters, θ *, and L are evaluated for different atmospheric stability classes. They have been evaluated for neutral conditions. In this study, the roughness length has been chosen equal to 0.001m (typical of water body). The roughness length for the land has been chosen equal to 0.4m. 2.4 SIMULATION AND SOLVER PARAMETERS In the frame of this study, the solver is a pressure-based fully implicit segregated method on unstructured meshes. It is well suited for flows that are steady or quasi-unsteady (slowly changing). It solves all governing equations separately. It uses an iterative procedure for both steady state and transient cases. SIMPLE scheme is used for pressure computation. It uses a formulation valid for flows at all speeds and for any thermodynamic model. 3 RESULTS Figure 4: The North Atlantic Oscillation (NAO) is a climatic phenomenon in the North Atlantic Ocean - L : Low pressure area in Iceland - H: High pressure area in Azores and Northern Africa Local effect of terrain on the wind flows The results of the modelling focus on the wind direction modification due to the topography around the sailing area. The wind directions are SW (225 ) and E (90 ) and the simulations were done for a wind speed of 10 m/s at a height of 10m for both directions. In Figure 5, the white colour arrows and the pink colour contours represent a deviation greater than +15 from the mean direction and the black colour arrows and the blue colour contours indicate a deviation greater than All the views are voluntarily schematic for an easy understanding of the wind fields in the area by nonspecialist people. 3.1 BREST ROADSTEAD CASE ANALYSIS Climatology The dominant flux in all seasons comes from west to west-southwest even if a few nuances exist depending on the season. The most significant factor is the south pathway of the low pressure zone. During winter, stronger west or southwest winds are usually observed and frequent disturbances which impact the Atlantic coast. During the summer, this scheme remains relevant but strengthening anti-cyclonic depression requires a more northern flow, which allows the Atlantic coast to sample light winds and a more conventional summer time. The North Atlantic Oscillation (NAO) is a climatic phenomenon in the North Atlantic Ocean of fluctuations in the difference of atmospheric pressure at sea level between the Icelandic low and the Azores high (see Figure 4). Through east-west oscillation motions of the Icelandic low and the Azores high, it controls the strength and direction of westerly winds across the North Atlantic. Figure 5: Wind deviation in case of SW conditions The wind flow is channelled through the axis of the strait, except where a little deviation is observed near the tip of Spanish peninsula Quernel. The flow is divided in a West-Southwest and a South-Southwest part when reaching the peninsula of Plougastel (see figure 6). 226

235 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France Figure 6: Wind direction contours for a wind condition m/s (Google Earth view) In blue color the negative deviation and in red color the positive deviation The results for the E condition (see Figures 7 and 8) show that the wind takes a North-East direction in the area between Brest and the peninsula of Plougastel. The effect of the tip of Armorique gives a southeast direction. In this area, the wind speed increases (see figure 9). In the strait, the wind takes a stable North-East direction. This is a classical phenomenon observed by the sailors in the area. Figure 8: Wind direction contours for a wind condition m/s on (Google Earth view) - In blue color the negative deviation and in red color the positive deviation Figure 9: Wind speed contours at surface level for m/s In red colour, the wind speed in higher then 10 m/s and in blue color, the wind speed in lower than 4 m/s 3.2. WEYMOUTH CASE ANALYSIS Figure 7: Wind deviation in case of E conditions The results of the modelling focus on the wind direction modification due to the topography around the sailing area. The wind directions are WSW (240 to 270 ). The wind keeps its initial direction (boundary conditions) in the middle of the harbour (zone 1 in figure 1) and in the middle of the bay (zone 6). The wind velocity for the WSW direction remains high in most of the zone 1. Nevertheless, the velocity fields show low wind speed in the North of the zone 1 if the wind direction is more than 260. In the zone 2 (figure 1), there is a predominant influence of coastal landforms. The sailing in 227

236 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France downwind area of hilly and disparate coast can be exposed to various effects within a few degrees of the wind direction. Although no quantitative results were yet available on these two sites, the qualitative assessment show a good agreement between the numerically predicted wind flows and the sailing team experience on the water. Further investigations will be carried out in order to compare measurements of the wind speed and direction. REFERENCES Figure 10: Wind deviation in case of WSW conditions Figure 11: Wind direction or a m/s wind condition (Google Earth view) - In blue color the negative deviation and in red color the positive deviation 6 CONCLUSIONS In order to demonstrate the usefulness of CFD modelling for the purpose of wind predictions for sailing teams, two examples of the use of CFD through Fluidyn PANWIND dedicated software have been presented here. The first one shows the coastal wind analysis of 2012 Olympic sailing site of Weymouth, UK. The local wind effects due to the harbour and hill have been determined and compared to observations of wind velocity and direction for several wind conditions. The second example modelled the wind over the training base of the French Sailing Team in Brest, France. This landlocked bay surrounded by two steep hills and linked to the Atlantic Ocean by a strait. emphasizes the need for a CFD simulation of the wind. This simulation provided the patterns of wind around the racing area which are compared with empirical observations. 1. GRYNING S.-E., BATCHVAROVA E., BRUMMER B., JØRGENSEN H., and LARSEN S., On the extension of the wind profile over homogeneous terrain beyond the surface layer, Boundary-Layer Meteorol., 124, pp , PEÑA A., Sensing the wind profile, Ph.D. Thesis, University of Copenhagen, March PEÑA A., GRYNING S.-E., Extending the wind profile much higher than the surface layer, European Wind Energy Conference and Exhibition (EWEC), Marseille, France March BURCHARD H., Applied Turbulence Modelling in marine Waters, Springer, BAUMERT H. Z. and PETERS H., Secondmoment closures and length scales for weakly stratified turbulent shear flows, J. Geophys. Res., 105 (C3), pp , HAN J., ARYA S.P., SHEN S., and LIN Y-L.: An Estimation of Turbulent Kinetic Energy and Energy Dissipation Rate Based on Atmospheric Boundary Layer Similarity Theory, NASA/CR , June PETERS H. and BAUMERT H. Z., Validating a turbulence closure against estuarine microstructure measurements, Ocean Modelling, 19, pp , DUYNKERKE P.G., Application of the k-ε turbulence closure model to the neutral and stable atmospheric boundary layer, J. Atmos. Sci., 45(5), pp , AUTHORS BIOGRAPHY M. Le Guellec holds the current position of Project Engineer at FLUIDYN FRANCE. He is responsible for environment impact studies and consequence assessment studies. His previous experience includes the wind field modelling at local scale in complex urban district for pedestrian comfort assessment and wind energy assessment in hilly region. Y. Amice holds the current position of Chief Petty Weather, seconded by the Navy with the French Sailing Federation. 228

237 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France OPTIMAL YACHT ROUTING TACTICS F. Tagliaferri, Yacht and Superyacht Research Group, School of Marine Science and Technology, Newcastle University, UK, (corresponding author) A.B. Philpott, Yacht Research Unit, The University of Auckland, Auckland, NZ, I.M. Viola, Yacht and Superyacht Research Group, School of Marine Science and Technology, Newcastle University, UK, R.G.J. Flay, Yacht Research Unit, The University of Auckland, Auckland, NZ, When the future wind direction is uncertain, the tactical decisions of a yacht skipper involve a stochastic routing problem. The objective of this problem is to maximise the probability of reaching the next mark ahead of all the other competitors. This paper describes a system that models this problem. The tidal current at any location is assumed to be predictable, while the wind forecast is based on current observations. Boat performance in different wind conditions is defined by the output of a velocity prediction program, and we assume a known speed loss for tacking and gybing. The resulting computer program can be used during a yacht race to choose the optimum course, or it can be used for design purposes to simulate yacht races between different design candidates. As an example of application, we compare strategies that minimise the average time to sail the leg, as opposed to those that maximise the probability of winning, and show how optimal routing strategies are different for leading and trailing boats. NOMENCLATURE Scalars Distance between two competitors Delay in finishing under strategy versus the perfect strategy Values that a discrete-time stochastic process can assume at the th time step Time to finish under the strategy Time to finish under the perfect strategy Discrete-time stochastic process, e.g. wind direction at the th time step th random variable uniform in (0,1) Matrices Policy matrix at the cross-section k on the tack, where is starboard or port Transition matrix Set of matrices Strategy, i.e. set of policy matrices Operators (A) Expected value of (A) (A B) Probability density function of A conditioned on B BS RMP SPP VMG Abbreviations Boat speed Race modelling program Shortest path problem Velocity made good 1. INTRODUCTION Finding a minimum cost route on a set of points is a shortest path problem (SPP) [1]. Specifically the aim is to find a path between two vertices of a graph such that the sum of its constituent edges, often representing a cost, is minimised. When cost depends on random quantities it becomes a stochastic problem, and the objective is to minimise expected costs (where costs include time) [2]. Many problems fall into the category of SPP and involve routing for emergency response (both civil [3] and military [4]) and applications in logistics [5] and transport [6]. When minimising expected costs there is always a risk factor that must be taken into account. Is the best route the one that allows the average shortest time with a small probability for a disaster or the one that has a higher average time but without the risk for disasters, or even the one with an even higher average time but with a positive (even if small) probability of a particularly high gain? Decisions taken by a sailor during a race can be seen as a stochastic SPP. The speed of a sailing boat depends on the wind speed and on the angle between boat heading and wind direction. It is usually expressed as a polar diagram like the one shown in Figure 1. The numbers around the semicircle represent different true wind angles, while the radial ones represent the boat speed. The red line correspond to the plot of boat speed corresponding for a particular true wind speed. While

238 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France no direct course is possible straight into the wind, it is possible to sail upwind with an angle between wind direction and sailed course which is usually between 30 and 50. Sailing closer to the wind direction (lower angle) makes the course shorter, but when sailing at higher angles a boat is faster. The compromise is given using the concept of velocity made good (VMG), which is the maximum velocity into the wind direction and is usually around (as in this example). behaving at another point, and to foresee how it will behave once that point is reached. Some sailors would prefer to be conservative and stay safely at the centre of the course, or in general close to the competitor, while others might prefer to take the risk and explore the corners hoping for a favourable wind shift. In a polar diagram like the one in Figure 1, it is possible to find the maximum VMG for a given wind speed by finding the intersection between the polar corresponding to the wind speed and the line perpendicular to the upwind direction. Figure 1. Example of a polar diagram (velocities in m/s and angles in deg). For this reason the common route towards an upwind mark, or in general towards the direction from which the wind blows, is a zigzag route. Such a route requires changes of direction which are called tacks. When manoeuvring for a tack, a boat points for a few seconds directly into the wind, therefore causing a temporarily decrease in boat speed. If the wind is constant during the race and all over the racing area, trying to do the minimum number of tacks is the best choice. Figure 1(a) shows two possible routes, and the one on the left is the faster because it involves just one tack. However, this situation is very unlikely, and wind can change in many different ways. Figure 2(b) shows a situation in which the wind shifts constantly towards the left. The best choice in this case is to go to the left of the course, and then tack and point towards the mark, while beginning a race going to the right, after what can seem an initial advantage, results in being the wrong choice. In real races the evolution of the wind can be much more complicated than this example, with temporary shifts or gusts that a sailor should take advantage of. While racing it can be difficult to know how the wind is Figure 2. Example of upwind routes with constant wind (a) and with a consistent left wind shift (b) One way to compute an exact solution to the problem of finding the optimum route between two points is an exhaustive search which is computationally impossible. In fact, even assuming that a boat travels always at its maximum VMG, there are 2 n possible routes, where n is the number of possible tacks. Considering that it is virtually possible to tack at every point of the race this is a continuum of possibilities, and for each one we have to compute the actual racing time. Dynamic Programming is a popular way of overcoming this problem. This technique divides the problem into

239 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France smaller sub-problems that are solved in stages. Moreover, instead of finding a solution for a single specific wind pattern, it allows computing a solution according to a certain probability distribution. We model the wind using a Markov process, where the state of the wind at a point depends on the state at the previous point. In addition to this, we want to include the attitude towards risk in order to consider more realistic behaviour of a sailor during a race. The risk that a skipper is willing to take is usually influenced by his position with respect to the opponent. A common behaviour pattern is to be conservative, or risk averse, when in a leading position, while being risk seeking when losing. When looking for a solution for our SPP, we want to also take the risk factor into account. We developed a race modelling program (RMP) for simulating races between two boats that can be used, for instance, to assess different designs, or as in our case, to compare different tactical decisions. The first RMP was developed in 1987 for the America s Cup syndicate Stars and Stripes and is described in [8]. Since then, RMP have been used mainly in America s Cup applications, and mostly to compare different designs. In our case as we are interested in comparing tactical choices, we model two identical boats (i.e. they have the same polar diagram). 2. METHOD 2.1 MARKOV MODEL FOR THE WIND AND SOLUTION METHOD A Markov process is a stochastic process used to describe the evolution of a dynamic system in which the state at the discrete time depends on the state of the system at time. For a system with a finite number of states the stochastic process is uniquely defined with an initial distribution for and a transition matrix. The matrix elements represent the probability that the system at time step is in state conditioned on the fact that it was in state at the previous time step : Interested readers can find more details on Markov processes in Norris [9]. For tactical purposes we are interested in changes in wind direction that significantly affect the racing time. We therefore define the state space to be, where represents the wind direction at which the upwind mark is set, and the other states represent shifts of from that direction. In order to obtain a realistic transition matrix we considered a time series of wind measurements from a weather station installed on the Newcastle University research vessel, and then built the matrix P using a maximum likelihood estimator. As we use for the model a grid with 15m resolution in the upwind direction and the decision of tacking is taken every time the boat crosses the grid line in the direction, the Markov model is built assuming a time step of three seconds. The wind direction signal was sampled every three seconds, and the corresponding wind directions were placed in bins of amplitude. The number of jumps from bin to bin divided by the total number of jumps out of bin corresponds to the value in the transition matrix. We consider an upwind leg of 6000m (corresponding to 3.24 nautical miles, which is a realistic length for the 2013 America s Cup course), divided by 400 lines perpendicular to the upwind direction. We refer to those lines as cross sections. Each one of those lines is divided in a linear grid of 19 segments. It should be noted that the resolution of for the wind shifts and for the racecourse can be increased by employing more powerful computational resources. Figure 3 shows a schematic diagram of the course with the axis orientation that is used throughout this paper. The solution method is based on the algorithms described by Philpott and Mason [7] and Philpott. [10]. It is implemented in a highly modular code written in Matlab with some specific subroutines in C. This program computes the policy that gives the minimum expected time for the completion of the leg of the race. The output of the algorithm is a policy, expressed as a set of 19x19 matrices, one for each of the cross sections on the course. The element represents the optimum angle at which the yacht should sail when it reaches the cross section, if it is on the sub-segment of the cross section, and observing a wind in state. The index can assume the value or, corresponding respectively to a port or starboard tack. If a boat is on a port tack it means that its windward side is the left side, while it is on a starboard tack if the windward side is on the right one

240 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France of equation determine the positions at which the decision is taken. y 6000m Wind patterns are generated according to the Markov model on states Using a standard procedure for simulating Markov processes we set. We then generate a series of random variables with uniform distribution in the interval using a random number generator. Given we set if both the following conditions are satisfied 15m Figure 3. Schematic representation of the course. The y axis is oriented in the upwind direction, and the course is divided into 400 stripes by lines at 15m spacing. The computation of the optimum angles begins from the top line and then proceeds iteratively with a backward procedure according to the description by Philpott and Mason [7]. 2.2 RISK MODELLING We modify the transition probabilities used to compute the solution in order to have conservative or risk seeking decisions. In a conservative case we want to model the behaviour of a boat skipper who is winning. She will try to behave safely, trying to stay ahead and to minimise her losses in bad wind outcomes. A probabilistic interpretation of this attitude is to assume that at the next step the wind will transition to a bad state with a higher probability than we have estimated from the data. In other words the skipper is pessimistic about the next transition. We implement this by adding a transformation in the solver, post multiplying the transition matrix by another matrix which redistributes the probabilities. The resulting matrix has to be normalised in order to represent again a probability distribution. Figure 4 shows a graphical representation of an example of transformation that can be applied to a transition matrix in order to obtain a more decentred distribution. With a notation that is used throughout this paper, we use a grey scale to represent values in the interval where white represents and black represents. The effect of this transformation on the transition matrix is to increase the volatility of the wind process. 2.3 RACE SIMULATIONS A race simulator based on a simple SPP was developed in order to compare different policies. The y-axis is oriented in the upwind direction, positive upwind. The starting position of a single boat is the origin. The lines The course of the sailing boat starts from the point (0,0), on a starboard tack. It follows a course corresponding to the angle, until the second cross section is reached. The time needed to go from a position to the next is computed according to a polar diagram like the one shown in Figure MODEL VALIDATION In order to assess the effectiveness of the model in finding an optimum solution, we use the algorithm to generate a policy by giving as input to the software the actual wind realisation. The expected values are then computed at each step by assigning a probability of one to the actual realisation. In this way we simulate the behaviour of the perfect tactician, who takes her decision knowing exactly how the wind is going to behave. In a real situation this is obviously not possible, but assuming that a very experienced sailor is able to fairly accurately predict what is going to happen in a race according to her experience, we want to show that our model still allows a good result against this ideal sailor. 3. SIMULATION RESULTS Figure 5 shows a graphical representation of the transition matrix for the Markov model obtained with the maximum likelihood estimator as described in the previous section. It can be noticed that the diagonal is dominant, meaning that, in general, if the wind is in state, the most probable state for the next step is to remain in state. Moreover, when the wind has deviated from the mean, the event of a shift back towards the mean value is more likely than one in the same direction. The wind for the simulations was generated as described in the previous section. When Markov chains are used, it is common practice to add a noise component to the generated output in order to avoid a step signal. However as in our case we are interested

241 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France only in wind shifts of at least, we clustered the measured wind in steps of, and we found that the behaviour of the simulated wind signal, achieved with no additional noise component, was fairly similar to the original one, as can be seen in Figure 6, with close values of mean and variance on different sub-intervals. A wind history of 400 values was generated for each of the 4000 simulated races. Figure 7 shows a histogram of the time needed by a yacht following the policy generated to minimise the expected time of arrival, according to the wind distribution previously modelled. The distribution is asymmetric, and this is due to the fact that even with a very favourable evolution of the wind there is a minimum time needed to complete the course. On the other hand, even with a policy which is effective in the majority of the cases, it is possible to be very unlucky and need a much higher time. This policy was generated according to the wind distribution pictured in Figure 4. This policy was then compared with another one, generated according to a new transition matrix obtained from a transformation of the previous one. As mentioned in the previous paragraph, in order to model the attitude of a sailor who is not in a winning position, we use a transformation aimed at giving a higher volatility to the wind process, therefore giving a higher probability to unlikely future wind directions. Simulations were carried out in order to verify the differences between a risk-neutral policy that minimises expected arrival time at the top mark, and a policy generated assuming a more volatile wind evolution. Results showed that following this second policy gives an overall worse performance with respect to the riskneutral one. The risk neutral policy led to a win in of the cases with an average difference of s. Those values were obtained by simulating races independently for each boat, but using the same wind patterns for all of them. These results confirmed the optimality of the policy previously computed. Figure 5. Representation of the transition matrix P obtained for the wind model. Wind deviation from mean [deg] Figure 6. Sixty-minute example of artificially generated wind and sixty-minute example of recorded wind. Number of races Time [min] Artificial wind Recorded wind Time (s) Figure 7. Distribution of time of arrival needed by a boat following the optimum policy. Figure 4. Example of a transformation used to modify the transition probability of the Markov model. Figure 8. Transition matrix P with increased volatility

242 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France Number of races Time differnce [s] Figure 9 Distribution of time of arrival differences between boats using the two different policies However, combining together the two strategies can lead to a significant improvement in the chances of winning. We simulated races between two boats that are denoted as boat A and boat B. Both boats start the race at the same time, on two different (random) points along the starting line. Boat A experiences the same wind as in the previously simulated races and always follows the optimum policy. Boat B experiences the same wind as A if their distance is less than, an independent wind if their distance is greater than, and a linear combination of the and wind if their distance is between and. At every spatial step, if B is more than 15s behind A, she uses the risk-seeking policy, while she uses the optimum risk-neutral policy otherwise. Results of those simulated races are shown in Figure 9. The -axis shows the arrival time of boat B minus the arrival time of boat A at the top mark. The average time difference is positive (actually s in this plot). This means that B arrives s later on average than A, as one would expect, since A is using the optimum policy to minimise the average time. However about of the race outcomes are to the left of the vertical axis, meaning that B wins of the time (always by a small margin). Of course sometimes B is hopelessly outclassed, losing by seconds (just around of the times, and those are extremely unfavourable events) but this is because B takes high risks when behind. If we consider win probability as a null hypothesis, then the probability of winning more than 57% of 4000 races by chance is the probability that a binomial random variable with mean and variance exceeds, which is about The standard error of the value 0.57 can be estimated using the central limit theorem to be approximately So we can be 97.5% confident that the hybrid policy will win at least 55.4% of the races (i.e. 2 standard errors less than 0.57). In order to quantify the tactical improvement on the policy we compare the results obtained by boat A and boat B with a third boat C that has perfect knowledge of the future behaviour of the wind. In this case we simulated 1000 races. Obviously the boat with perfect knowledge of the wind scenario always wins and the differences in arrival time are always positive. The sample average difference in time of arrival is 133s for boat A while for boat B the sample average difference is 114s. The difference is not significant because of high variance and low sample size. Indeed we show in the appendix that the expected time difference for boat A relative to C must be lower than the expected time difference for boat B relative to C. 4. CONCLUSIONS AND FUTURE WORK In this paper we have presented a method for approximating a solution of a stochastic shortest path problem with applications to yacht racing. We showed that with an adequate subdivision of the problem it is possible to find a solution that minimises the expected time needed to reach an upwind mark during a race. Moreover, we introduce for the first time a model of the risk attitude of the sailor. We showed that if a skipper of a trailing boat has a risk-seeking attitude it enhances the chance to win the race. An important result of the simulations run to simulate races was that aiming at minimising the expected time to finish is not always the best approach: being on average slower might allow a bigger probability of winning against an opponent following a fixed policy. The results presented in this paper underline that, when trying to optimise a policy in order to win a competition, looking at average values is rarely the best approach, and accounting for differing risk attitudes might give policies that perform significantly better. Further work is being carried out in order to validate the model with data registered during America s Cup races, and we are developing methodologies for learning risk parameters that yield maximum win probabilities. ACKNOWLEDGEMENTS This research has been performed within the SAILING FLUIDS project, which is funded by the European Commission under the 7 th Framework Programme through the Marie Curie Actions, People, International Research Staff Exchange Scheme. REFERENCES 1. Cherkassky, B.V., A.V. Goldberg, and T. Radzik, Shortest paths algorithms: Theory and experimental evaluation. Mathematical Programming, Series B, (2): p Bertsekas, D.P. and J.N. Tsitsikilis, An Analysis of Stochastic Shortest Path Problems

243 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France Mathematics of Operations Research, (3): p Yamada, T., A network flow approach to a city emergency evacuation planning. International Journal of Systems Science, (10): p Resch, C., et al. Path Planning for Mine Countermeasures. in SPIE - The International Society for Optical Engineering Orlando, FL. 5. Fleischmann, B., S. Gnutzmann, and E. Sandvoß, Dynamic vehicle routing based on online traffic information. Transportation Science, (4): p Li, S. Study on routing optimization problem of the logistics center. in World Automation Congress Puerto Vallarta, Mexico. 7. Philpott, A. and A. Mason, Optimising Yacht Routes Under Uncertainty, in Proc. of the 15th Chesapeake Sailing Yacht Symposium Letcher Jr, J.S., et al., STARS & STRIPES. Scientific American, (2): p Norris, J.R., Markov chains. 1st pbk. ed. Cambridge series on statistical and probabilistic mathematics1998, New York: Cambridge University Press. xvi, Philpott, A. Stochastic optimization in yacht racing, in Applications of Stochastic Programming, W. Ziemba and S. Wallace (ed.), SIAM, APPENDIX Proposition: Minimising the expected arrival time over all strategies will give a policy that is slower than a perfect skipper by the least amount on average. Proof: Suppose a perfect skipper sails races in wind that she predicts perfectly. Each race is a random sample of wind and so her time to finish is an independent identically distributed random variable. Suppose she now sails a strategy that is not clairvoyant in each of these same wind conditions. The time to finish under this strategy is an independent identically distributed random variable Now the delay in finishing under strategy versus the perfect strategy is also an independent identically distributed random variable. The expected delay from sailing is then AUTHORS BIOGRAPHY F Tagliaferri is a PhD student at Newcastle University and member of the Yacht and Superyacht Research Group. She holds a Masters degree with Honours in mathematics and her PhD project aims at developing navigation software for yacht races under uncertain weather conditions. AB Philpott, PhD, is a Professor in the Department of Engineering Science and Director of the Electric Power Optimization Centre at the University of Auckland, New Zealand. His research interests encompass optimisation under uncertainty and game theory with particular application to electricity markets. He has also applied these technologies to yacht routing and race modeling in several America s Cup campaigns. IM Viola, PhD, is Lecturer in Naval Architecture at the School of Marine Science and Technology of Newcastle University, UK. He has a background in applied fluid dynamics and a specialist expertise in yacht engineering. His previous experience includes a Post Doctoral Fellowship at the Yacht Research Unit (The University of Auckland), which is the Scientific Advisor of the America s Cup team Emirates Team New Zealand, and a PhD at the Politecnico di Milano, sponsored by the America s Cup team Luna Rossa, on experimental and numerical modelling of the aerodynamics of sailing yachts. RGJ Flay, PhD, is Professor of Mechanical Engineering and Director of the Yacht Research Unit in the Department of Mechanical Engineering at the University of Auckland. He has had a longstanding research interest in the wind and sailing. His PhD degree was awarded for a study of wind structure based on full scale wind data. His Postdoctoral research as a National Research Council Visiting Fellow in Canada was focused on carrying out wind tunnel studies over topographic models to compare with full-scale measurements, and for wind energy prospecting. He then spent four years as an Aerodynamic Design Engineer in a Consulting Engineering company in Toronto where he worked on the design of several wind tunnels and environmental test facilities. Since 1984 he has worked at the University of Auckland, and in 1994 designed the World s first Twisted Flow Wind Tunnel. To minimise this we should minimise as is a constant. So the strategy that minimises expected delay after a clairvoyant skipper is the one that minimises expected arrival time

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245 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France DEVELOPMENT OF AN AMERICA S CUP 45 TACKING SIMULATOR A.K. Lidtke, L. Marimon Giovannetti, L-M. Breschan, A. Sampson, M. Vitti and D. J. Taunton, University of Southampton, UK, akl1g09@soton.ac.uk, lmg2e09@soton.ac.uk, lb2e08@soton.ac.uk, ajs1g09@soton.ac.uk, mv4g09@soton.ac.uk, djt2@soton.ac.uk This paper describes the development of an AC45 simulator conducted as a student Master s project at the University of Southampton. The main aim was to be able to asses and improve the tacking skills of the helm and the crew through systematic training. The physical interface of the simulator replicates the seating position of the helmsman and the main trimmer and the graphical representation provides the users with visual cues of the simulated boat, boundaries and marks for a sample race course. The theoretical model uses hydrodynamic manoeuvring coefficients based on empirical formulae and experimental data. The aerodynamic forces are pre-calculated using a full-scale RANS CFD simulation. The accuracy of the model is verified against the AC45 racing tracking data to ensure that the speed loss during a tack, experienced by the users of the simulator, is as close to reality as possible. The ultimate aim of the project was to study the potential of the simulator to assess and train the crews, improving their skill in tacking the boat effectively. This has been done by examining the performance of two groups of users over a series of practice sessions. The simulator could be potentially used for training the helmsmen of the Youth America s Cup Red-Bull teams, which have limited budgets, training days and sailing experience compared to the professional AC sailors. 1 INTRODUCTION The design and construction of high speed sailing catamarans is going through a very innovative period. Since the last monohull America's cup, in 2007, a large number of them have been built. These boats have the power to attract media interest because of their speed and athletic skills required by the crew. Since 2007 one of the most prominent America's Cup teams, BMW Oracle, has developed the 90-foot trimaran that won the 2010 cup. Following that, the AC45 and the AC72 class boats have been designed and built. Approaching the next event (to be held in September 2013 in San Francisco Bay) it is important to acquire the expertise needed to sail the catamarans in the fastest way without damaging them. In order to compete at high level, a catamaran needs to tack in the most efficient manner. Such a manoeuvre involves a change in heading through the wind. During a tack, a catamaran loses a large part of its speed due to immersion of the flying hull and the associated increase in drag, the aerodynamic forces opposing its forward motion and inability to retain momentum due to lightweight construction. The present project aims to investigate, through the use of a dynamic velocity prediction program (VPP), the possibilities of a tacking manoeuvre training course for the helm and main sheet trimmer, focusing on an AC45 class boat. It was chosen over the AC72 because it is a monotype, meaning that all the catamarans sailing the America's Cup World Series are the same. This would make it viable for the simulator to be used by all the teams and youth squads alike. Another reason of having chosen the AC45 is that live tracking data is available to be downloaded from the ACWS (America's Cup World Series) web site, [1]. This data presents the race conditions and the boat speeds while racing, hence providing a useful validation tool. The most characteristic feature of the AC45 is its wingsails. This not only generates more lift while sailing, but also permits to sail closer to the wind, than a conventional sail. Wing sails have better trimming capability than standard soft sails, as the sheeting angle, camber and twist may be adjusted. In order to set the sail, the trimmer needs to adjust a series of sheets and control lines. Therefore, the crew can be trained with a simulator in order to practice the movements they need to perform and to regulate the sail accordingly to the boat state experienced. Nevertheless, the training of the helm in a simulator is more difficult, as the virtual environment should represent the actual race condition closely, taking into account the varying wind intensity, wave direction and height, cloud shapes and all other variables that may be encountered during a race. The real environment needs to be represented not only visually, but also through the physical interface to promote the user sensation of the boat motions. Sailing simulators have been used in previous works for the analysis of tacking [2, 3], the starting manoeuvre [4], match racing [5], handicap assessment [6, 7], and evaluation of elite athletes [8]. Most of the past work related to sailing simulators carried out at the University of Southampton has investigated the yachtcrew interaction and the possibility to improve the tactical steering and sail trim [9, 10]. One-design races stress the attention on the crew making the right decision at the correct time, so the abilities of the AC45 helm are the key of winning the races. Furthermore, flight [11], high speed craft [12] and F1 simulators [13] have been widely used to assess the performances of the users and to improve their skills where the expense and or danger are prohibitive to the using the real vehicle. This encourages the application of similar technology in sailing

246 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France 2 METHODOLOGY The project was split up into four main areas: interfacing with the user and modelling of the underlying physics which included the overall simulation framework development and an extensive CFD analysis of the boat s aerodynamics. These are discussed in the following section of this paper. The overview of the established simulator framework is presented as Figure USER INTERFACE One of the main deliverables of this project was a physical interface that would integrate effectively with the computational physics engine and the visual interface. This partnership was to increase the realism of the user experience and hence improve the training capability of the simulator. The aim of this part of the project was to facilitate positions for the helm and the main trimmer who would have to closely cooperate in the exercises carried out, much as on the real boat. The concept of creating a moving structure that would represent the motions of the boat was rejected due to time, budget and space limitations. A static main structure was hence designed and built. Substantial amount of care was taken to make use of anthropometric data to ensure that the users position would reflect what they would experience in real life, hence improving the realism greatly [8], [14, 15, 16]. It was decided that a hiking position, while using the physical interface, would be encouraged through designing a bench that simulates a heeled hull surface and by providing a set of toe straps. Information was gained on creating a suitable hiking configuration through analysis of the currently available hiking bench products. Due to space limitations the physical interface had to be dimensioned in such way as to make effective use of an average size room which was available for the testing. The main material used was aluminium, given its small density and the implied portability of the simulator. This was further encouraged by applying a modular design with no permanent connections. Two actuators were required, one to represent the tiller and one to act as the wing sail sheet. USB game controllers were used because of its advantages such as compatibility with MATLAB Simulink, minimal electrical engineering required and the low cost compared with creating an actuator from the ground up. It was aimed to enable the controllers to transmit force to the users and hence give them invaluable cues as to the state of the boat. For the rudder, the chosen game controller was the Microsoft Force Feedback 2 Joystick. Its setup required minimal effort in the conversion of the primary joystick axis to the tiller axis. Two motors controlling the x and y axes were connected to a PCB holding the processing unit in order to increase the magnitude of the generated torque. By default, each motor was fitted with a rotary potentiometer which was used to transmit the angular rudder displacement to the simulator. It has been discovered during the testing that mainly due to numerical reasons high-frequency oscillations would be fed to the users. These were commented on as very disturbing and blurring the actual response of the boat. A digital low-pass filter was therefore implemented. The main sheet actuator was made up of a Microsoft force feedback steering wheel. As the wheel is rotated it responds with a torque and creates tension in the mainsheet. As well as providing a force to resist the user sheeting in it also reels the main sheet back inside once the user force is removed. A set of mock-ups was built in the process and the input of a range of potential users was factorised into the design process. The finalised concept design is presented as Figure 2. Figure 1: Overview of the simulator framework. Figure 2: Final concept design of the actuators and seating positions for the crew

247 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France viscous drag [21]. Given the shallow draught of the boat the sideforce generated by the hull was neglected. It was decided to use the semi-empirical formulae presented by [22] to determine the forces acting on the appendages as they were thought to be easy to implement, robust and widely accepted for their accuracy. Torque on the rudder stock was also calculated in order to provide force feedback to the user, as discussed earlier in the paper. In order to determine the forces acting on the headsail the data presented by the ORC for implementation in steady-state VPP was used [23] as this has been widely recognised as a high-quality source. The most challenging part of describing the physics of an AC45 class boat was dealing with the forces generated by the wing sail. This was done based on an extensive CFD study described later in this paper. It is worth noting that wind speed and direction fluctuations are present in the real environment. In practice, this has a significant effect on the performance of the sails and requires constant attention of the crew in terms of trimming the sails for optimum performance. Multiple ways of describing this phenomenon mathematically exist, typically by employing a combined set of sinusoidal functions and by introducing an element of randomness. This was not implemented in the current simulator because of the possibility that the additional fluctuations will slow down the development of the force feedback effects and blur other phenomena taking place. At the initial development stage it has been discovered that the physics model is prone to oscillations in roll. This was believed to have originated from accounting for hydrodynamic damping components insufficiently (at that time the only damping terms present were provided by the varying inflow speeds and angles as a result of the roll motion which translated into a damping force). It has been suggested that an additional damping term would exist due to the fact that the windward hull penetrates the water surface when the heel angle varies. As a result, the GZ arm changes but also a moment proportional to the demihull heave damping force is imposed on the entire boat system. As the physics model was being refined at a later stage this component was accounted for by calculating the heave damping using strip theory based on the solution for Lewis sections. 2.3 WING SAIL CFD ANALYSIS The AC45 boats are characterised by a symmetric wing sail consisting of a main wing rotating about the mast and three rear flaps rotating at 90% of the chord of the forward wing, able to produce lift on both tacks. The approach was to obtain the aerodynamic forces and moments acting on the wing in an upwind sailing condition and then implement the results in the physics engine via interpolation. In order to accurately predict the boat speed during a tack, the available tracking data from the America's Cup series races were analysed. From this data it was possible to extract the sailing conditions of the catamarans (i.e. average wind speed, apparent wind angle and the corresponding boat speed). A test matrix for the CFD analysis was then completed by analysing five different parameters (i.e. apparent wind speed VA, apparent wind angle AWA, heel angle, wing sheeting angle, flap sheeting angles, and, where the subscripts 1, 2 and 3 represent the bottom. Middle and top flap respectively) and focusing on upwind sailing as only the tacking manoeuvre was analysed. The flow was modelled to be turbulent as the wing sail is affected by the presence of the free surface boundary layer and the relatively slow speed enhances the turbulence interactions between the wind and the sail. The surface roughness of the sea, constituting the bottom surface of the domain, was also modelled as it affects the wind shear profile. Multiple cases were solved using ANSYS CFX. However, some verification simulations were run in OpenFOAM using the North Sails software, previously used by the Wolfson Unit for Marine Technology and Industrial Aerodynamics (WUMTIA) to calculate the aerodynamic performance of the AC45 and AC72. The geometry of the wing sail was modelled to be placed at the centre of the domain, with the frame of reference at the free-surface below the centre of rotation of the forward wing. It was then necessary to assess the upwind sheeting angle variation. Based on consultations with Youth America s Cup sailors these were set as (forward wing camber), (rear wing camber with respect to the forward wing) and the twist angle. An unstructured mesh was created and a mesh refinement study was developed in order to prove the aerodynamic results to be independent of the mesh size. The region of the boundary layer was discretised with a structured mesh to better represent the flow properties. It was also necessary to avoid a large cell size difference between the inflated layers and the first unstructured elements around the body to retain sufficient accuracy. Finally, a mesh refinement in the vorticity region was applied to better capture the tip and root vortices. Due to its robustness and low computational cost, k- epsilon turbulence model, was chosen over the SST k- omega, as in upwind condition only small angles of attack were investigated and stall was not reached. The non-dimensionalised wall distance ( was set to be in the logarithmic region, so that fully turbulent flow was expected in the boundary layer, [24]. Due to the height of the mast, the wind shear profile, described by the log-layer law was added to the simulations, taking as reference height the weather stations of the AC45 committee boats, [25, 26]. The aerodynamic forces are a function of wind speed, direction, sheeting and heel angles. Dependency on the

248 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France To complement the physical actuators and provide the user with the necessary information about the boat condition a graphical user interface was included in the overall system. This was displayed and used via a 10 touchscreen monitor. One of the main purposes of this was to serve as an external control tool used by the main trimmer in order to control the twist in the wing, the flatness of the jib and the position of the daggerboards. Secondly, it would display the boat speed, the wind speed and direction, as well as a chart plotter with the boat position indicated with respect to ACWS race courses. This aimed to aid in the navigation and to allow full control over the boat to be executed. A sample of the interface window can be seen in Figure 3. STANAG 3869 AI aircraft ergonomics guideline and ISO standards (DIN EN ISO ) were followed in order to determine a suitable layout and formatting for the interface [17, 18]. Figure 3: Screen shot of the touschscreen user interface used for control of the boat and information transfer to the users. 2.2 PHYSICS MODELLING The principle idea behind a real-time simulation of a yacht revolves around constructing a set of equations of motion describing each of the degrees of freedom. For sailing yachts the model originally presented by Masuyama et. al. in 1995 is the most prevalent across the literature [2], [6], [9, 10], [14], [19]. It was used in this project given that it has been widely tested and became an industry standard of describing dynamic sailboat motions. The full set of equations of motion used can be written as: A substantial amount of consideration has been given to whether the pitch and heave motions should be ignored in the physics engine. Including these would allow pitch-poling to be examined, more realistic hydrodynamic drag values could also be calculated. However, the primary aim of the project was to simulate the upwind condition where pitch-poling is not an issue. Furthermore, the regattas are sailed in enclosed bays, where the waves encountered are relatively small. Also, the effort and amount of analysis required to introduce and validate a full six degree of freedom model were beyond the scope of this project. Hence it has been decided to exclude the heave and pitch motions from the simulation. The differential equations governing the motion can be integrated with respect to time twice, given a set of initial conditions, in order to yield the velocity and displacement in each of the degrees of freedom. The most commonly used numerical integration scheme adopted for sailing yacht simulation is a fixed-step Runge-Kutta 4 th order method which was used for the purpose of this project with a fixed time-step of 0.1 seconds. It has been found that reducing it does not yield any noticeable improvement in the quality of the solution obtained but may slow the simulation down significantly. An important task was to accurately estimate the mass and inertias of the boat. Some of these were calculated using the 3D model and mass properties of each of the AC45 principle elements. The added masses and inertias were calculated using potential flow, assuming the hull is a very high aspect-ratio ellipsoid. It is recommended, however, to use more detailed estimates as early as possible in the future if sufficient data is available. The flow speed experienced by the appendages and sails will be affected by the roll and yaw motions of the boat. The magnitude of this effect was estimated by calculating the local velocity due to turning motion a distance away from the axis of rotation and including it in the apparent wind or appendage inflow velocity computation in a vector form. For the adopted approach this was done at the centre of effort of each lifting element. In a dynamic VPP it is important to account for the unsteady effects, such as lift or drag coefficient changes. However, this was quite challenging for this application as it was never known a priori when the user will execute a manoeuvre and whether it will end in a tack or just a change of course and hence most known empirical formulae could not be adopted [20]. It was therefore decided to only account for the dynamic effects by considering the flow velocity variations. No towing tank data was available for the AC45 boat. For this reason an empirical formulation of the Southampton NPL series was used to calculate the wavemaking drag, which was complemented by the standard ITTC 57 friction line to account for the

249 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France latter was assessed and it was found that the following may be used to reduce the number of interpolation parameters: and to define lift and drag as function of heel. From the simulations the forces, moments, centres of effort, the lift and drag components were obtained. By analysing the results it was possible to identify a decrease in drag with increasing flow speed and a maximum lift coefficient occurring at a true wind speed of = 14 knots. Also, base drag of was estimated. Furthermore, a reduction of both lift and drag was found with increasing main sheeting angle. Applying twist to the wing resulted in a relatively small increase in lift coefficient and a consistent increase in drag. The latter values may be due to the high induced drag occurring at the gaps between rear wing elements. The centre of effort was found to be approximately at mid-span and was shown to reduce with increasing heel. Little variation in the centre of effort height due to twist was observed. As discussed in [27], the forward foil suppresses the peak pressure at the leading edge of the downstream foil (see Figure 4). This phenomenon, known as slot effect, permits the aft aerofoil to have a boundary layer with decelerated flux speed coming from the lee-side of the forward aerofoil rather than at the true angle of attack. Furthermore, the presence of the aft aerofoil creates a strong upwash in the streamlines of the forward foil; therefore increasing the net lift of the system. Figure 5 shows the streamlines with the tip and root vortices visible. Figure 5: Streamline distribution in the domain: and TWA= GRAPHICS ENGINE A detailed graphical model of the boat was created using the Rhinoceros 4.0 package. The boat was then exported and used with the VRML program integrated into the Simulink package (see Figure 6). To present a static frame of reference to the users, the buoys and laylines were placed in the race area so as to resemble an upwind leg of a race. Furthermore, a panoramic view of San Francisco was projected on a cylindrical boundary to give the users a sense of direction. One of the main objectives in developing the graphics was to create a sense of motion of the boat that would allow the users to estimate the boat speed over water without them having to make use of the provided dials, much as it is done in real life. Also, emphasis was put on representing the wind direction in the form of graphical cues. Figure 4: Pressure distribution along main wing and flaps: V T = 10 knots, TWA = 47, and. The pressure distribution is shown at three different heights along the wing, namely at polylines evaluated at mid-span of each rear flap, top 1, midlle 2 and bottom 3 positions respectively. The effects of both front and rear wings is shown. Figure 6: Screenshot from the simulator VRML environment showing the boat at the startline on a starboard tack. Note that the jib model was removed from the VRML visualisation due to lack of an appropriate modelling method. Two possible view configurations were incorporated in the graphical display: first with the camera located behind the boat and providing an overview of the entire catamaran and second with the viewport located on the windward demihull at the position where the helm would sit in the actual boat (the viewport changes

250 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France automatically after each tack). This setup allowed the degree of realism of the simulation to be more closely assessed and discussed with the participants. 2.5 VALIDATION Figure 7 shows the velocity plots over a tack compared with the data available from the AC45 GPS position tracking system [1]. Two clear differences can be seen: an overestimation of the maximum boat velocity by approx. 20% and too slow turning rate resulting in an extended tack time. There are two principle reasons for this. Firstly, the ratio of the drive-to-lift forces is approximately 35% larger than expected from the steady-state boat speed. This might originate from the hydrodynamic drag being underestimated by the less-than-ideal for this purpose NPL series, windage drag not being accounted for sufficiently well or the CFD analysis over predicting the aerodynamic drive force. Secondly, the rotary inertia in yaw (and partially in roll) is likely over estimated, hence leading to slower turning rates. Given the extremely light displacement of an AC45 boat even small discrepancies in this area will have a significant impact on the result obtained. Speed loss experienced through the tack was significant, however not as great as in the case of actual AC45 catamarans. This might indicate that the hydrodynamic resistance under estimation is a primary defect of the physics model. Also, substantial simplifications of the unsteady effects surely played an important role in this behaviour. Nonetheless, the overall physics and relative trends in the boat behaviour resembled reality quite closely. In an attempt to estimate the error magnitudes quoted above the inertias and net drive force were scaled by an arbitrary factor and the simulation runs were repeated with the recorded rudder and main sheet settings, yielding boat velocity also shown in Figure 7. It can be seen that a much closer convergence could be achieved by relatively small manipulations. The original setup was used in the human testing phase out of the fear that any arbitrary changes might influence the results to a greater extent than using the unmodified but less accurate version of the simulator. 3 TESTING 3.1 METHODOLOGY In order to test the simulator two groups of participants were evaluated: beginners (little to no sailing knowledge) and experts (over 10 years of sailing experience with at least part of it on catamaran boats). Both groups were formed of ten participants. Prior to the actual tests the participants were given a few acclimatisation runs to understand how the simulator works and each team member s responsibilities. Subsequently, the teams had to complete 5 runs of 5 tacks each in to travel as much upwind as possible. This was aimed to represent an upwind leg of a race. It was considered that from the crew training point of view this would be more quantitative than examining the speed loss through the tack as it formed a clearer objective for the participants. Records were held of the simulation parameters and all contestants were asked to fill in questionnaires regarding their experience. In order to correctly model an upwind leg of a race, a number of wind speeds and directions were chosen as characteristic values in upwind courses using the AC45 GPS data. 3.2 DISCUSSION OF THE RESULTS Almost all participants agreed that the physical interface was very ergonomic and comfortable as well as realistic. Frequently repeated comments appreciated the fitting of the toe straps, overall simulator layout and the use of the rudder and main sheet actuators. The key result obtained from the participant survey was that nearly everyone felt that they had improved their sailing and tactical skills over the simulated runs they took part in. Likewise, close to all participants thought that with a few improvements the simulator could be an essential and powerful training tool. A significant proportion of the users felt that the graphics used did not resemble the real world closely enough. Typical comments pointed out its limited ability to create an impression of the boat motion and lack of a sufficient amount of cues regarding the heading of the boat with respect to the wind direction. Moreover, it has been frequently said by the users that incorporating a moving platform instead of the stationary set of benches and frames would add greatly to the simulator. Also, the use of hardware push buttons over the touch screen monitor was suggested to have a possible effect on the realism of the simulation and handling of the virtual boat. Certain members of the expert group thought that presenting a velocity polar diagram would allow them to trim the boat to its full potential. A single but very important comment suggested that use of a realistic set of sound effects would benefit the simulation realism greatly. Figure7: Plot of the boat speed obtained from the AC45 GPS data, initial simulation runs and tests with the corrected inertia matrix and drive force magnitude

251 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France different (for instance in the case of a team who kept bearing away to a broad reach after each tack). Moreover, the testing was conducted over a period of two weeks and most of the test subjects were students from the same department and it is possible that there was an exchange of information on how to achieve best results in the simulation which could not have been prevented. Figure 8: An example of boat parameters for a series of tacks carried out using the simulator. In Figure 9 the mean speed of the boat and the standard deviation of the main sheet position can be seen for the two groups as a function of the number of test runs each team has accomplished. There is a clear difference between the average speed achieved by the novice and experienced sailors which indicates that there is an inherent level of realism in the simulation that causes the two groups to perform in a distinguishably different way. The speed achieved by the experts does not change significantly. However, there is a noticeable improvement in the velocity achieved by the novices. For the beginners the deviation in sheet position changed a lot more during the training session than it did for the experts. This suggests that the latter group have executed a much steadier control over the boat from the very beginning whereas the developed their skills by practice and experimentation. In all of the results it can be observed that the novice group s performance improved much more significantly whereas the experts scores were more stable but superior. This indicates that the simulator has the capability to teach and improve the users sailing skills. During the test sessions it could be clearly seen that the experienced sailors cooperated much more effectively than the novices. The latter group would often get confused and lose focus of the objective. While not necessarily clearly seen in the data, this very well resembled what can be observed on real boats in stressful situations. This indicated that the simulator has the potential not only to develop purely sailing skills, per se, but also improve the crew team work in much the same way as a practice session on the water would. Errors in the analysis might have arisen due to multiple reasons. There could have been issues associated with the accuracy of the physics model and input/output processing of the actuators. Despite clear instructions certain teams adopted a different techniques of sailing around the course and so some of the results had to be disregarded from the analysis due to being significantly 4 FUTURE WORK Based on the success of the current simulator it is planned to continue with further research and development in order to improve it. This will principally revolve around enhancing the physics model, probably by implementing more refined force estimation methods. An interesting research topic which has emerged is the development of a 6 degree of freedom manoeuvring model for a sailing catamaran which would allow a broad range of phenomena to be computationally studied. From the questionnaires it was concluded that the simulator might benefit from further development of the interface hardware so that it resembles the actual boat layout more closely. An example of this might be the addition of more realistic controls for the jib. Modern video games technology allows excellent graphics to be introduced and this will certainly see increased interest in further development stages to enhance the representation of the boat and the entire sailing environment. The budget allowed only a stationary physical interface design to be built. A substantially larger budget would have been required in order to build a physical interface capable of simulating motion in multiple degrees of freedom. Introducing this significant additional cost would also make it difficult for the Youth America s Cup teams and other interested sailing groups to access it. While a movable main platform would introduce an entire new level of realism and respond to the users feedback, it has been shown that good training results can be achieved with just a static one. For these reasons such a configuration is worth considering in the future but the current setup should not be discarded completely

252 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France Figure 9: Standard deviation in the wing sail sheeting angle versus the number of runs (linear fit presented for each series). 5 CONCLUSIONS The comparison of the boat speed variations obtained from the simulations with those provided by the America s Cup web site, as well as the comments and performance data gathered from the human testing of the simulator, have provided a solid basis for the future improvement and development of a virtual sailing environment to be used for the crew training purposes. It has been verified and demonstrated that even given limited means and time a successful sailing simulator can be created and used to develop the skills of the crew. The most important conclusion regarding this aspect is that a suitable balance has to be achieved between focusing on the accuracy of the simulation, be it the fidelity of the force model or the race environment, and ensuring suitable level of realistic experience. It has been stated multiple times by the participants that they paid much attention to issues such as details of graphics, minor features of the physical interface and less so to the actual boat physics. Based on the above it can be concluded that although a substantial amount of further investigation, research and development would be required in order to create a fully functional simulator that would suit the needs of training future America s Cup teams. Despite this fact at this stage it appears to be a perfectly feasible and potentially very beneficial solution. Figure 10: The final setup of the simulator with a participants crew executing a tack manoeuvre. REFERENCES 1. [Accessed ]. 2. Y. Masuyama, T. Fukusawa and H. Sasagawa, Tacking simulation of sailing yachts - numerical integration of equations of motion and application of neural network technique, B. Verwerft and J. Keuning, The modification and application of a time dependent performance prediction model on the dynamic behaviour of a sailing yacht, in International HISWA Symposium on Yacht Design and Yacht Construction, J. Binns, K. Hochkirch, F. de Bord and I. Burns, The development and use of sailing simulation for IACC starting manoeuvre training, in 3rd High Performance Yacht Design Conference, 2-4 December, Auckland, K. Rocin and J. Kobus, Dynamic Simulation of Two Sailing Boats in Match Racing, J. Keuning, K. Vermeulen and E. de Ridder, A generic Mathematical Model for the Manouevring and Tacking of a Sailing Yacht, Annapolis, A. Philpott and A. Mason, Advances in optimization in yacht performance analysis, High Performance Yacht Design Conference, Auckand 4-6 December, J. Mooney, N. Saunders, M. Habgood and J. Binns, Multiple applications of sailing simulation, in Simtec 2009, Adelaide, Australia, June M. Scarponi, R. Shenoi, S. Turnock and P. Conti, Interactions between yacht-crew systems and racing scenarios combining behavioural models with VPPs,

253 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France in 19th International HISWA Symposium on Yacht Design and Yacht Construction, Amsterdam, T. Spenkuch, S. Turnock, M. Scarponi and R. Shenoi, Development of a sailing simulator environment for assessing and improving crew performance, in Proceedings of 7th ISEA Conference, June 2-6, Biarritz, M. Shafer, In-Flight Simulation Studies at the NASA Dryden Flight Research Facility, J. Calver, W. Ellison, R. Langdon, L. Mirosevic, A. Parker and J. Tate, High Speed Craft Simulator - GDP Report, University of Southampton, [Accessed ]. 14. J. Binns, R. Bethwaite and N. Saunders, Development of a more realistic sailing simulator, in The 1st High Performance Yacht Design Conference, Auckland, W. Karwowski, M. Soares and N. Stanton, Human Ergonomics in Consumer Product Design,CRC Press, Humansizes.html. [Accessed ]. 17. R. Taylor and J. V. F. Berman, Aircraft keyboard ergonomics: a review, Butterworth Co. Ltd., C. Rudolf, Handbuch software-ergonomie (usability engineering), Unfallkasse, E. J. de Ridder, K. Vermeulen and J. Keuning, A mathematical model for the tacking maneuver of a sailing yacht, in The International HISWA Symposium on Yacht Design and Yacht Construction, Y. Masuyama and T. Fukusawa, Tacking simulation of sailing yachts with new model of aerodynamic force variation during tacking manoeuvre, Journal of Sailboat Technology, SNAME, no. 1, pp. 1-34, A. Molland, S. Turnock and D. Hudson, Ship Resistance and Propulsion, Cambridge: Cambridge University Press, A. Molland and S. Turnock, Chapter 5, in Marine Rudders and Control Surfaces, Oxfrod, Elsevier Ltd., 2007, pp ORC VPP Documentation J. Tu, G. Yeoh and C. Liu, Computational Fluid Dynamics: A Practical Approach, Butterworth- Heinemann, A. Meschini, Analisi Preliminare di Wingsail per Imbarcazioni di America's Cup, Politecnico di Milano, S. Hsu, Determining the Power-Law Profile Exponent Under Near Neutral Stability Conditions at Sea, Journal of Applied Meteorology, A. Gentry, The Application of Computational Fluid Dynamics to Sails, in Proceedings of the Symposium on Hydrodynamic Performance Enhancement for Marine Applications, November M. Young and C. Gorelli, AC 72 Class Rules, America's Cup Tech. Rep., AUTHORS BIOGRAPHIES A.K. Lidtke is a final year student at Ship Science department at the University of Southampton (Yacht and Small Craft). Following his graduation he will commence PhD studies at the same university in the field of numerical modelling of the influence of turbulence on propeller noise and cavitation. Up to now his undergraduate work focused on velocity prediction, design search & optimisation and hydrodynamics. L. Marimon Giovannetti is currently a Master student at the University of Southampton (Yacht and Small Craft). In the Fall of 2013 she is expected to start a PhD to research the passive adaption of curved foils such as the ones used in Nacra 17. Her undergraduate work focused mainly in Computational Fluid Dynamics. She is also an international sailor, representing Italy in the major World and European championships since L-M. Breschan currently studies Ship Science, with a specialisation in Naval Architecture at the University of Southampton. Previously she did an internship at RMK in Istanbul in the construction department and she worked at Seaway Group Slovenia. Earlier education included studying Industrial Design at a higher technical college in Ferlach, Austria. A. Sampson currently studies Ship Science, with a specialisation in Yacht and Small Craft at the University of Southampton. Previously he worked at Lloyds s Register as an intern, and will soon begin as a Naval Architect at the BMT Group. M. Vitti is a final year MEng student at the University of Southampton in Ship science, Yacht and Small Craft. His undergraduate work has focused on control systems, manoeuvring and testing. His main interest is in sailing yachts. D.J. Taunton is a lecturer at the Ship Science department at the University of Southampton. His research interests include experimental hydrodynamics of high speed craft, human factors and design methods. He received a Bachelor of Engineering with honours (Ship Science) from the University in Southampton in A Ph.D. in high speed craft seakeeping from the

254 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France University of Southampton in He has then worked on two research projects investigating the wash produced by high speed craft in shallow water. He worked for BMT SeaTech Ltd, a naval architecture consultancy company providing bespoke ship simulation products for two years before returning to Southampton University in

255 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France Coupled open navigation and augmented reality systems for skippers J.C. Morgere, Lab-STICC, UBS, France, R. Douguet, Lab-STICC, UBS, France, J.P. Diguet, Lab-STICC, CNRS, France, J. Laurent, Lab-STICC, UBS, France, This paper describes a new measurement and vision system for sailboat race. This system is composed of an open navigation processor and a see-through Augmented Reality (AR) glasses. This open navigation processor allows to plug most sensors in order to measure wind conditions, boat speed, dynamic motions and other parameters. Moreover, it is able to implement several wind correction algorithms in order to improve the true wind computation. On the other hand, the open navigation processor communicates with a see-through AR glasses through wireless network. The interest of this system is that it is flexible and can overlay any text, 2D or 3D objects on the true real world view, so the skipper is free to display the useful data. 1 INTRODUCTION In ocean racing, several domains such as materials, sails and yacht design are constantly evolved in order to improve the boat performance. In order to study the impacts of the proposed improvements, we need to acquire data from the system by using different kinds of sensors (strain gauges, speedometer,anemometer and so on). To achieve these measurements, most sailboats embed navigation processor that allows us to plug and to collect all the data from the sensors. Despite the use of navigation processor, some sensors cannot be plugged since they uses proprietary protocol or yet the navigation processor is too closed to allow plugging sensors that are not provided by the same firm. For instance is difficult to plug NKE sensor with B&G navigation processor. So in order to solve this problem we propose an open navigation processor that implements analogue to digital converters and several communication protocols as, RS232/485, CAN, Ethernet and so on in order to be able to plug most sensors (digital or/and analogue). Furthermore this platform allows the user to implement his own applications as for instance correction algorithms allowing to compute the true wind speed and angle. Another problem is the display of the information collected by the navigation processor to the crew because the displays do not provide the necessary data to analyze the boat performance. Indeed, due to the poor ergonomics and the few viewable data it is very difficult to analyze the boat performance without an embedded PC. The second problem is due to the fact that the crew needs to be able to view the information at different places of the boat. Today, the solution is to deploy several display screens on the boat but this leads cost increase. Furthermore, the weather conditions, as the solar glare or water, can affect the display reading so even the viewable data, provided by the navigation processor, could be unreadable. The solutions considered as the use of tablet is still not the best one because the tablet is not very convenient on boat and reduces the crew mobility since you must use one of your hands to hold it. So, we propose to solve these two problems by using mobile display system called wearable augmented reality system based on a see through device that allows the user to view the real world and also view objects superimposed. This kind of systems can display texts, 2D and 3D objects animated or not. The global solution is presented in Figure 1. Figure 1: System overview The first one presents the open navigation processor, the second the hardware display system and finally the last one an example of the graphical user interface (GUI). The rest of paper is organized as follows: Section 2 describes the open navigation processor. Section 3 and 4 presents the mobile augmented reality system and an application. Finally the Section 5 concludes the paper and presents the future works. 2 OPEN NAVIGATION PROCESSOR The open navigation processor is detailed in three parts: the hardware design (processor, peripherals, sensors), the soft-

256 ware design (Operating System, scheduling tasks) and the wind correction algorithm. 2.1 HARDWARE DESIGN The hardware is the core of the navigation processor. On the one hand, it must be able to receive, to store and to send all data provided by analog or digital sensors. On the other hand, it needs important computing capacities to implement complex algorithms in order to correct different measurements. Indeed, these algorithms require a lot of data processing to compute Kalman-like filters or other kinds of filters. Considering applications requirements a 10 Hz sampling rate is enough to process wind measurements. It also represents an opportunity to save power at the embedded system level. Actually, considering that during a race the fuel required to recharge batteries must be optimized, it is important to reduce the energy consumption. To meet these needs, we chose the STM32F407 microcontroller, which is based on ARM Cortex M4 Processor. This processor includes a floating point unit (to compute complex algorithms) and integrates several communication controllers (UART, SPI, ethernet, ADC...) and general purpose input output in order to plug analog or digital sensors. The hardware design diagram is shown in Figure 2. This hardware platform is also designed for other applications such as, for instance, a databuoy [1]. On the other hand, several peripherals are available to get real time access to data. Indeed, three serial bus are implemented to communicate with other devices. Two serial bus are directly used to send real time data to a computer and to standard displays. But as the STM32f4 microcontroller has not on-board wireless communication, one solution is to add a standard module to interface UART peripheral to wireless. In our case we chose the bluetooth module since it is a wireless networking widely used in smartphone environment for instance smartphone, tablet or computer. Moreover there are Bluetooth Low Energy (BLE) wireless modules which were designed for lowest possible power consumption. The Bluetooth module allows to communique between the navigation processor and the see through AR glasses. 2.2 SOFTWARE DESIGN The navigation processor software design is developed and is implemented through Keil uvision4 Integrated Development Environment (IDE). In order to facilitate a possible extension of this project we chose to divide this application in several tasks (or threads) by using a small footprint Operation System (OS). Indeed the navigation processor software is divided into 4 main tasks : acquisition task, computation task, storage task and communication task (cf. Figure 3). Other tasks runs in background to receive data through interrupts (cf. Figure 4). The selected OS is the FreeRTOS (Real Time Operating System). FreeRTOS is a real-time kernel which is designed for small embedded system. The interests of this OS are the size of kernel, which is limited to 5Kb in flash, it is portable on different supports and it is independent of Keil uvision4 IDE. It allows Cortex-M4 microcontroller applications to be organized as a collection of independent threads of execution by Figure 2: Hardware Design Diagram On this system, we are able to directly plug the standard sensors used on sailboats such as speedometer, anemometervan, Inertial Measurement Unit (IMU) and Global Positioning System (GPS). But many sensors, analog or digital, can be add to this platform since the microcontroller has still several available communication controllers. Indeed this microcontroller proposed up 15 communication interfaces : 3 I 2 C interfaces, 4 USARTs, 2 UARTs, 3 SPIs, 2 CAN interfaces and 1 SDIO interface. Moreover, this open navigation processor allows to record all data at 10 Hz on SD card memory through the SPI bus. Therefore, these data are available for post-processing in order that users can analyze boat performance. Figure 3: Flow chart of main tasks

257 and these measurements are disrupted by several phenomena, such as the boat motions, the drift, the upwash effect and the wind shear [2]. That s why, we have developed our own wind correction algorithm (cf. figure 5) that we implemented on the open navigation processor. So one advantage of this platform is to test differnet wind correction algorithms in order to improve the true wind computation. Figure 4: Flow chart of handler tasks using different tools such as mutexes, semaphores or queues to synchronize these threads Acquisition task This task converts the analog inputs and updates all data provided by the different peripherals. It is executed periodically with a frequency to be specified in the configuration file. This frequency is set to 10 Hz for navigation processor Computation task The computation task allows to calibrate, compute and filter all received data. Currently, it corrects and filters the wind measurement (cf. Section 2.6 for details). 2.3 Storage task This task allows to store all selected data in the file on the SD memory card. These data are logged in the CSV file in order to facilitate their analysis of Matlab, Excel or other softwares. 2.4 Communication task In the communication task, data are sent to several devices through three peripherals. The information sent via UARTs allow to communicate with a computer and with standard displays. Moreover, another UART coupled with a bluetooth module allows to send data to different devices such as smartphones, tablets and laptop and more specifically in our case to the see-through AR glasses. 2.5 Handler Tasks The handler tasks are synchronized by a semaphore with the interrupt functions. They allow to receive the data provided by sensors with serial communication. For example, when the processor receive a GPS packet, a semaphore is given in the GPS interrupt function and then the GPS task is unblock in order to parse the GPS packet. 2.6 WIND COMPUTATION Usually standard wind corrections are handled by navigation processors on sailboats where true wind is required. Indeed, the wind sensor is placed on the masthead most of the time Figure 5: Wind Correction Flow 3 MOBILE AUGMENTED REALITY 3.1 HARDWARE DESIGN The augmented reality device is composed of two parts, the first one is the display and the other is the embedded processor. The display is a see-through ski mask [3] which includes an electronic and optic system that diffuse frames in front of an eye (monocular system). In order to facilitate the reading information, the display system has the following features: The resolution of the mask is 800*600 pixels with a refresh rate at 60Hz The equivalent screen size is 97.5 inches at 2.7 meters so a large amount of data can be displayed and readable The light intensity is 5000 candela/m 2 in color mode (greater in monochrome mode) so the information displayed will be able to be visible even in outdoor.

258 The second part of the system is the embedded processor. For the mobile augmented reality, this processor can be ARspecific embedded and reconfigurable systems [4]. This is a low consumption and small size architecture (due to the number of components needed) and it is dedicated to augmented reality systems with head tracking and using very small definition objects. Head tracking is employed to place objects in the user field of view, for this step MEMs are often used with correction algorithm to compute the system attitude. For better performance and consumption it would be necessary to produce and use Application-Specific Integrated Circuit (ASIC) but this technology is very expensive and not interesting for few units. But today this kind of solution is not usable since we need to offer to the user a large amount of objects that can be simple key arrow or text but also more complex objects like 3D texturing sailboats. So the AR-specific architecture performances are not sufficient this is the reason why we chose a classical SoC solution used for instance in commercial tablets or smartphones; the system architecture is shown in Figure 6. In our case, we use MEMs sensors: one magnetometer, one accelerometer and one gyroscope for the head tracking. Despite the use of these sensors, we must, in addition, execute a correction algorithm (usually an extended Kalman filter) in order to obtain a precise attitude. Some information, as GPS localization, are also required so in most case we will have to discuss with the navigation processor to obtain this data; this will be done by using a wireless communication (WiFi, Bluetooth). For low energy consumption criteria, we chose to use Bluetooth communications. To store the data, the applications and the OS we need memory capacities thus in our system we have emmc, DDR2 and SD-Card; emmc and SD-card are non volatile memories so applications and OS will be able to be implemented into one of these memories. Although the SD card is bigger than the emmc, this last would be used in order to increase the execution time, indeed the emmc is faster than the SD-card. Finally, as the embedded processor has to be connected to the ski mask, it s necessary to use a video connection in order to display the virtual objects on the mask. Today the ski mask uses an analog video stream (VGA) so as the SoC system generates a digital one (HDMI), we must convert the HDMI stream with a converter (will be change in future works). 3.2 SOFTWARE DESIGN Figure 6: Architecture SoC A9500 ST-Ericsson for Mobile Augmented Reality device This architecture is a System on Chip (SoC) designed for mobile applications running on embedded operating system (EOS) and composed of: General Purpose Processor (GPP) that executes the operating system (android in our case), Graphical Processor Unit (GPU) that allows us to generate and manipulate the graphical objects, Image Specific Processor (ISP) that manages the video stream (does not us in our case), Video that performs some decode step for compression/decompression algorithm, Peripherals that allows us to connect our system with others The GPP is composed of two ARM Cortex A9 whose the internal frequency can vary from 200 MHz up to 1.0GHz so it s very interesting for power/energy management. The GPU [5] can process about 1.1 Gpixels/s so these performances are sufficient for our target applications. However, to be able to place the virtual objects for the augmented reality system, we need sensors allowing to acquire 9 degrees of freedom (DoF). The software part of the system requires to manipulate different levels of abstraction from the physical level (sensors) to application level (3D objects for instance) so in order to facilitate the programming scheme, we implemented an EOS (Embedded Operating System) called Android. This EOS, thanks to the many APIs available like OpenGL ES 2.0 for GPU instructions, sensor manager for MEMs, location manager for GPS, and WiFi manager and Bluetooth adapter for wireless connectivity, allows us to rapidly develop our augmented reality application. Furthermore we can develop the application by using JAVA and/or C/C++ (for native applications) so in the same application, some parts can be realized in JAVA and communicate with others developed in C/C++. The software architecture is composed of four parts, a time service to read and control number of frames per second of the application, graphic service to send commands to the GPU, an input service to read sensor and wireless events and the last one is orientation service to compute position and orientation objects. Graphics service must read and load texture and shader objects, configure OpenGL ES parameters and send a draw command to the GPU. Input service is used to read and write data to the Bluetooth connection in a dedicated task whereas another task (looper task) is used to read sensor events and saves data. If head tracking added for geographic positioning, input service could add a special task for orientation computing with a filter (Gradient descent, Kalman, Extended Kalman filter and so on) to correct MEMs data and compute attitude. The orientation service updates orientations and positions of all objects, it can delete or add new objects (depends of the application) and can compute AIS data ( boat position, heading, and name) to collision detection.

259 TWS kt TWA deg BSP kt HDG deg Figure 7: Prototype 4 APPLICATION The aim of our application is to help crews during the ocean races or inshore. So the first application is dedicated to the skipper thus we display only text which gives him three kinds of data. The first one concerns the boat and gives the heading, speed, heel and drift. The second gives information about the wind; for both the apparent and true wind, we gives the speed and angle. Finally, we display various data come from GPS as the position, the time and so on. Each data are differentiated by a different color in order to respect the readability and ergonomic; this solution is shown in Figure 8, example A. application can display the boat polars so that everyone on the boat can have the boat performance to check and validate the sail choice and adjustment. Finally the last application (Figure 8 example D) can be dedicated to the tactician since during inshore it can be precious to be able to see the buoys and the positions of the other boats in order to take decisions. All the necessary data can come from the navigation processor (GPS and AIS data) via a wireless communication as Bluetooth for instance. With our open navigation processor this application is very easy to develop. 5 CONCLUSIONS In this paper, we present a new open solution to measure and visualize the sailboat performances. Our system has the advantage of flexibility since the navigation processor allows to plug most sensors and to easily implement new computations (by adding new tasks). On the other hand, the glasses display is totally flexible and allows to visualize all data or map navigation according to the skipper choices. Currently we have a prototype as illustrated in Figure 7. A box (Pelicase) contains the embedded system for the navigation processor and standard sensors such as anemometervan, speedometer, GPS and IMU can be directly plug it. All data are sent to the see-through AR glasses through a bluetooth link and we can visualize them in real-time. Figure 8: Examples of displays The second application allows us to provide for each crew members information in function of his job on the boat for instance for the wind presentation, we display a disc with sailing boat textured and arrow keys moving around it according to the wind angle; for the wind speed we use text form (Figure 8 example B). Another way to display the information can be the use of 3D boat in order to represent the heel, the trim and the heading and the use of key arrows for showing the apparent and true wind angle (Figure 8 example C). The second The next step of the project is to improve the see-through AR glasses by integrating all the embedded system (electronic board and battery) in this display device. This is, we study the energy consumption of this board to optimize power consumption in order to reduce the battery size and weight. REFERENCES [1] R. Douguet, J.P. Diguet, J. Laurent, Y. Riou Open Data Buoy to Analyze Weather and Sea Conditions for Sailing Regattas, OCEANS 13 MTS/IEEE, Bergen, NO, 2013.

260 [2] R. Douguet, J. P. Diguet, J. Laurent, Y. Riou A New Real-time Method for Sailboat Performance estimation based on Leeway Modeling, The 21 Chesapeake Sailing Yacht Symposium, Annapolis, MD, March [3] Laster Technologies, [4] J. P. Diguet, N. Bergmann, J. C Morgere, Embedded System Architecture for Mobile Augmented Reality (sailor case study), PECCS13, Barcelone, ES, [5] ARM, Mali-400 MP, arm.com/products/multimedia/ mali-graphics-hardware/mali-400-mp. php [6] A. Pons, D. Asiain, F. Quero, J. Cuevas, Racing Bravo. Un sistema de navigacion para alta competicion, Madrid Diseno de Yates 2004, Madrid, ES, AUTHORS BIOGRAPHY Jean-Christophe Morgère is a PhD student at Lab-STICC, Université de Bretagne Sud, he obtained his Master degree in Electronics. He is now working on design of a mobile augmented reality embedded system: multiple sensors, low consumption and prototype in marine domain. Ronan Douguet is a PhD student working between the Groupama Sailing Team and the Lab-STICC laboratory in Lorient, he obtained his Master degree in Electronics. His work concerns the sailboat performance analysis and more specifically the improvements in wind measurements. Jean-Philippe Diguet is a CNRS Research Director at Lab-STICC. He has multiple research activities which referred to modelling and electronic development in embedded platforms. His previous experience includes several thesis supervising in embedded systems and some marine specific topics about sailing performance or on-board mobile augmented reality. Johann Laurent works as an Associate Professor at Lab- STICC, Universite de Bretagne Sud. He is in charge of teaching in a Master degree in electronics and have research activities which deals mainly with the power energy consumption in embedded systems. He supervises several works around electronic research for sailing including thesis and internships with manufacturers and sailing teams.

261 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France LECCO INNOVATION HUB SAILING YACHT LAB PROJECT A Sailing Research Infrastructure F. Fossati, Politecnico di Milano, Italy, fabio.fossati@polimi.it S. Muggiasca, Politecnico di Milano, Italy I. Bayati, Politecnico di Milano, Italy C. Bertorello, University of Naples Federico II, Italy The present paper presents an overview of the Lecco Innovation Hub project and in particular of the Sailing Yacht Lab project which aims to be a full scale measurement device in the sailing yacht research field. A description of scientific frame, measurement capabilities as well as of the principal design, building process, project management and committing are provided. 1 INTRODUCTION The present paper presents an overview of the Lecco Innovation Hub project and in particular of the Sailing Yacht Lab project which aims to be a full scale measurement device in the sailing yacht research field. Lecco Innovation Hub (LIH) is a dedicated nautical research and training centre at the Lecco Campus of the Politecnico di Milano university. The project is part of a series of activities shared with the territory to relaunch the Lecco economy, and aims to encourage the transfer of technology to and from the nautical and related sectors. Lecco Innovation Hub consists of two basic entities: o o The Sailing Yacht Lab, a 10 m length sailing yacht fitted with instruments for acquiring data on the behavioural variables of the boat and its components at full scale to support a scientific approach to design and research activities related to sailing yachts design and their performance The S.Ma.R.T. (Sustainable Marine Research and Technology) laboratory designed to support nautical industry in meeting the increasing pressing demands for innovation and sustainability. Specific lines of research are the analysis and management of the entire life cycle (LCA) of nautical products, design for disassembling, experimentation with new materials for construction and fitting out, ergonomics, safety and comfort on board, interior lighting and the improvement of the quality of air. In addition to these are the research infrastructures present in other sites of the Milan Polytechnic, such as the Wind Tunnel Europe s largest on the Milan Bovisa campus [1]. This paper focuses on the Sailing Yacht Lab project: a brief summary of the origins and early evolution of the vessel s design will be given, along with a description of principal design and performance criteria. Scientific frame, measurement capabilities as well as the design, building process, project management and committing will be described in the following. 2 THE SAILING YACHT LAB PROJECT 2.1 THE SCIENTIFIC FRAME Nautical design, which originally used design methods coming from the naval sector and basically craft approaches to construction technologies, in recent years has undergone evolution drawing on the aeronautical, energy and automotive sectors and on applied fluid dynamics. Most of the research done by the scientific community in the nautical sector is currently orientated towards developing methods for defining the loads acting on the various structures of the boat, with a degree of accuracy higher than has so far been available. This implies significant spin-offs for construction and design methods, with a more appropriate use of innovative materials. Figure 1

262 The scientific data currently available to designers and builders derive from studies on scale models, prototypes or material samples analysed in artificial environments, such as wind tunnels, towing tanks or test benches (figure 1). The ambition of the Sailing Yacht Lab is to allow these data to be measured at full-scale and in real boat use conditions. The Sailing Yacht Lab project was strongly inspired and encouraged by the previous experiences (figure 2) developed at MIT [2], Kanazawa Institute of Technology [3] and Berlin TU [5]. Figure 2 The Sailing Yacht Lab (figure 3) is designed to function as a dynamometric balance that can acquire precious data on the aerodynamic and hydrodynamic loads acting on the main components of the yacht. The heart of the system is a framework inside the hull that allows the entire rig and sail plan to be connected to a system of load cells to measure the overall forces and moments transmitted by the sail plan to the boat when under sail. Figure 4 Another feature offered by the Yacht Lab, is the possibility of acquiring data on the geometric shape assumed by the sails when under way (flying shape), which differs considerably from the so-called design shape, the geometrical shape imagined by the sailmaker when designing and making the sail. The experience built up in this field by the Department of Mechanics at the Milan Polytechnic in several measurement programmes in the wind tunnel of the Milan Bovisa campus for some of the leading America s Cup syndicates over the past decade, has supplied the know-how needed to create a measurement system that can be used when under sail. In order to acquire sail shape data in dynamic situations a measurement system based on laser scanner technique which has great measurement accuracy and speed has been developed (figure 5). Figure 5 Figure 3 The added value of the Sailing Yacht Lab is thus the possibility of taking measurements in real scale and use conditions, taking account of trimming by the crew. The Yacht Lab also includes the installation of direct measurement systems on the various components of the rig (shrouds, winches and blocks) to obtain valuable information for their design). As an example figure 4 shows strain gages mounted on a conventional winch housing allowing for foresail sheet tensile measure. Sail shape data can be used in real time to compare sail trimming parameters with boat performance using in house developed algorithms and software. An important aspect of the project is the availability of systems for measuring the loads acting on the sails. The possibility of knowing the effective pressure distribution over the sailplan is of great interest for the aerodynamic and structural design of sails, and also for the selection and optimal use of materials and production techniques. Integral measurements alone may not be sufficient for an understanding of how to use a sailplan if it is not possible to determine the complex interactions they provoke. On the Sailing Yacht Lab, the distribution of pressure on the sails will be mapped using MEMS sensors (an excellent compromise between size, performance, costs and operational conditions) installed on the sails in horizontal lines so as to measure different sections of the sailplan. Wireless transmission of the pressure data will be a fundamental aspect given the characteristics of the work

263 environment. All the information acquired directly under sail, whether it be mechanical and structural or aerodynamic and hydrodynamic, will then be correlated with the dynamics of the boat to evaluate the incidence of the yacht motions on the measurements carried out. The dynamics of the boat are themselves an extremely interesting set of information for developing and validating numerical methods of performance prediction. This is why the Sailing Yacht Lab is equipped with a specially designed and optimised system for measuring the motions of the boat, integrated by a GPS system and a trim measurement system. lines from a well-known and widely tested production boat have been used. Hullform has to guarantee adequate sailing performance as well as a fair behaviour in term of form stability and seakeeping. While the choice to use lines from Comet 35 of COMAR YACHTS (figure 7) is related also to GRP bare hull shell availability the project has not suffered any constrain due to the use of an existing boat. 2.2 CONCEPT DESIGN The Sailing Yacht Lab project was entirely developed and managed by a team of researchers in the Mechanics Department of the Politecnico di Milano. Yacht design is a complex process in which the designer, starting from a certain amount of given information and available resources, deals with the problem of generating proposals able to meet specified functional requirements. The most common way of facing this problem has been, so far, to make use of an iterative approach in which the different design aspects as e.g. powering, strength, stability and seakeeping are considered in sequence as separate design moduli. This approach is quite intuitive and rather effective in most of cases, but requires much guess work to the designer when looking for the best compromise of counteracting features. Moreover the design moduli are not independent and have to be matched together by designer experience and skills. To get the best results from this conservative and subjective design approach the right choice of design moduli is of paramount importance; they have to be adequately detailed to cover any design feature but their number has to be reduced to allow quick iterations and easy result updating. 11-ON SHORE TEST SET UP 1-HULL 2-FRAME BACKUP Figure 7 10-RIG AND SAILS 9-DECK H/WARE SAILING YACHT LAB 3-DECK 4-HULL APPENDAGES Plating stiffeners, both transversal and longitudinal have been completely redesigned according to the identified load cells position (figs. 8-9). 8-ACCOM- MODATION 5-AUX PROPULSION 7- SYSTEM HW & SW 6- ELECTRICS Fig. 6 design moduli for Sailing Yacht Lab In figure 6 the design moduli for LIH Sailing Yacht Lab design are reported. Some of them are within standard yacht design procedure while 2, 7 and 11 are peculiar of the boat mission profile. In this project in order to avoid costs related to moulds building an already available mould was considered as a starting point: therefore hull has not be designed, but Figure 8

264 Figure 9 The light alloy frame has been designed to take loads from the standing and running rig and to transfer them to the hull through the six points where load cells are located assuring negligible deformations and misalignments. To this aim a 5083 H111 light alloy structure has been chosen and preferred to carbon fibre one for lower cost and easier load cell connections (figure 12). Although load cells and relative fittings assure a permanent rigid connection between hull and frame, a backup system to allow cell removing or to assure safety in case of cell structural failure has been provided. This system does not interfere during load acquisition but can be easily adjusted to lock any relative motion between hull and frame. Deck lines have been custom designed due to the strong interactions of deck lines with the light alloy frame and to the necessity of a very large open cockpit. The production boat deck layout was obviously very far from that. Deck, cockpit and doghouse have been laminated in a single piece of sandwich GRP using a one-off plywood mould Figure 12 Figure 10 A ballast keel case similar to that used on old AC monohull has been designed and fitted to the hull bottom allowing a very thin keel profile and most important a 200 mm keel longitudinal shift in case of different sail plan to be tested (figure 11). The last peculiar design feature of this project is related to the internal waters where the boat will be used. The Sailing Yacht Lab is a sustainable, non-invasive project that is compatible with the ecosystems in which it will operate. A zero emission electric auxiliary propulsion has been designed using standard production elements, to allow three hours range at five knots cruising speed in calm water (figure 13). The Sailing Yacht Lab will also be a testing ground for the further development of electrical propulsion in the nautical sector, especially as concerns the storage of electrical energy and the use of renewable sources. Figure 11 Figure 13

265 Also the construction has been entirely carried on by the Department of Mechanics staff (figure 14) within LIH facilities (figure 15). preferable for this project where almost no reference was available. The general policy of building process has been to manage separately the different subcontractors and to merge them according to identified steps in which partial results could be checked. This approach is very sound when the quality of the results is the primary target but will hardly comply with sharp deadlines. In the following Table 1 the most important prefabricated elements and the considered check points are reported. Figure 14 PURCHASING/PREBUILDING Hull shell purchasing Cradle construction Deck mould Deck laminating Frame components CNC cutting Frame welding Frame geometry check Engine-sail drive coupling Engine installation Hull transversal framing Load cells fittings Hull longitudinal stiffners Hull transversal framing Deck custom hardware Accommodation Battery installation Hw and Sw installation Deck mounting Outside decoration External- Internal-Finish Rudder shaft - Rudder blade Keel structure - Keel fairing Ballast model - Ballast cast Rig and Sails set up CHECK POINTS Hull aligned Deck completed Frame completed Engine installed Frame-cells-structures alignment check Frame mounting - cell alignment check Preliminary deck check- deck removed Genoa Boat Show Load cell system preliminary check with boat upright and heeled Table 1 Hull and deck completed Rudder and keel set Ready to sail Figure 15 The hull shell has been bolted to a dedicated cradle, (Fig. X) to get a permanent reference during the whole construction. 3 BUILDING PROCESS, PROJECT MANAGEMENT AND COMMITTING One off construction is very common in yachting. The most of large racing yachts are built this way. The options for a successful and effective building are basically two. The most common is to identify a main contractor that will take care and responsibility of the whole construction although allowing external contributes for specific yacht features. The second is to manage several contractors one for each yacht feature and merge these contributes together to get the final result. Although more risky and complex this last one is more flexible to design changes and has been considered Figure 16 The frame geometry and mass properties have been controlled before mounting it as well the load cell alignments with the relative hull structures (figure 17).

266 5. Hochkirch H., Brandt H. Y., Full Hydrodynamic Force Measurements on the Berlin Sailing Dynamometer, Proceedings of the 14 th Chesapeake Sailing Yacht Symposium, AUTHORS BIOGRAPHY Figure 17 The whole load acquisition system has been tested before deck mounting. 6 CONCLUSIONS In the present paper an overview of the Lecco Innovation Hub project has been provided with particular reference to the Sailing Yacht Lab project which aims to be a full scale measurement device in the sailing yacht research field. A description of scientific frame, measurement capabilities as well as of the principal design, building process, project management and committing has been provided. Sailing Yacht Lab us a very challenging project aimed at providing, together with Politecnico Wind Tunnel, an available tool for research, and design development in the yachting field. At the moment this paper is going to press Sailing Yacht Lab is ready to be launched. REFERENCES 1. Fossati F. et al., Wind Tunnel Techniques for Investigation and Optimization of Sailing Yachts Aerodynamics, 2 nd High Performance Yacht Design Conference Auckland, Feb Milgram J.H, Peters D.B., Eckhouse D.N., Modelling IACC Forces by Combining Measurements with CFD, 11 th Chesapeake Sailing Yacht Symposium, Masuyama Y., Full scale measurements of sail forces and the validation of the numerical calculation methods, Proceedings of the 13 th Chesapeake Sailing Yacht Symposium, Fabio Fossati Mechanical Engineer, PhD in Applied Mechanics and Full Professor of Applied Mechanics. He is scientific co-ordinator of wind tunnel testing of sailing yachts at the Wind Tunnel of the Milan Polytechnic. His research work is mainly concerned with numerical and experimental fluid dynamics applied to sailing yachts with special reference to sail plans aerodynamics and hull appendages. He was in charge of testing carried out in the Wind Tunnel for the PRADA Challenge America s Cup team in 2003, for the Luna Rossa team in 2007 and for the BMW ORACLE Racing America s Cup syndicate. He is currently Research Associate of the International Technical Committee of the Offshore Racing Congress deeply involved in the ORC International VPP development. Sara Muggiasca Mechanical Engineer, PhD in Applied Mechanics, holds the current position of researcher at Politecnico di Milano Department of Mechanics. Her researches are in wind engineering field with particular reference to aeroelasticity and sailing yacht testing Ilmas Bayati Mechanical Engineer, PhD candidate in Mechanical Engineering under the area of Dynamics and Vibration of Mechanical Systems and Vehicles. In particular he is a component of the Wind Engineering groupwork at the Wind Tunnel of the Milan Polytechnic. His research work is mainly concerned with numerical and experimental fluid dynamics. Carlo Bertorello Naval Architect, Ph. D., Researcher at University of Naples Federico II from 1999 where he is actually Professor of Ship Design. Professor of Naval Architecture and Marine Construction at Master Course of Yacht Design at Politecnico di Milano from Member of Italian Delegation at IMO SLF Sessions in 2000 and Author of scientific papers on: HSC hull forms and performance optimization, multihull ship stability, multiattribute design procedures, composite materials. At present involved in research programs concerning non-monohedral planing hull forms, experimental assessment and optimization of HSC seakeeping characteristics, aerodynamic resistance of HSC 4. Masuyama Y. et al. Dynamic performance of sailing cruiser by full scale sea tests, Proceedings of the 11 th Chesapeake Sailing Yacht Symposium, 1993.

267 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France STUDY OF THE INFLUENCE OF SINGULARITIES CREATED BY AUTOMATED FIBER PLACEMENT ON THE PERFORMANCE OF COMPOSITE MATERIALS FOR NAVAL STRUCTURES M. Lan, LIMATB, University of south Brittany, France, D. Cartié, Coriolis Composites Technologies SAS, France, P. Davies, IFREMER, France, C. Baley, LIMATB, University of south Brittany, France, The Automated Fiber Placement (AFP) process shows great potential for efficient production of large composite materials structures, in the construction of racing yachts. However, during the manufacturing of complex shapes, unavoidable singularities are induced on the entire structure manufactured. The lack of knowledge concerning the influence of these defects on the performance of composite materials led us to study the effects of two main singularities, the overlap and the gap. Ultrasound inspection and Scanning Electronic Microscopy have been performed to compare the microstructures of a plate without defects with plates containing these singularities. This study also compared the mechanical properties of a plate made by manual layup with those of a plate made by automated layup, by tensile tests on carbon / epoxy specimens. 1 INTRODUCTION Composite materials are widely used in the construction of racing yachts. Manufacturing is often by hand layup of pre-impregnated carbon/epoxy plies in a mould. The prepreg is a semi-finished product initially developed for aircraft parts. During the manufacture of boat hulls, and other structural elements, it is necessary to control the orientation of the fibers in the plies at all points and to obtain composites with a very low level of porosities. The aeronautical industry has the same constraints, and aircraft manufacturers are equipped with sophisticated means of production, in particular Automated Fiber Placement (AFP) machines. We are interested in the use of this technology to manufacture naval structures. the part. This is open to discussion, as it will depend on other parameters described below. However, above this value, the mechanical properties of the part can be significantly affected. Indeed, the interlaminar shear strength (ILSS) is very sensitive to the presence of these voids [1]. The porosity also affects the mechanical properties in tension, compression and in-plane shear but to a lesser extent [2]. Generally, an increase in porosity leads to a decrease in the mechanical properties of the material. In the aeronautical industry, a part with porosity greater than 2% should be scrapped. This value is still often far from those being achieved in the marine industry, where a porosity of around 4% is common with the methods currently used [3]. 2 POROSITIES OF COMPOSITE PARTS IN THE CONSTRUCTION OF RACING YACHTS Several methods of implementation are used to transform high performance composite parts in the field of shipbuilding, mainly for sailboats and racing vessels. Parts of larger sizes such as hulls and link arms are made of prepreg, and processed in a vacuum oven. The autoclave is used very little considering the dimensions of rooms and resources, with the exception of masts, and booms. Boat hulls can also be made by resin infusion. The assembly of the components is done in turn by stratification and/or wet processing. During the manufacture of parts with composite materials, various types of defects can affect the mechanical properties. The main defect is the appearance of porosity in the ply or between the plies of prepreg. Some examples of pores present in the hull of a racing yacht are illustrated in Figure 1. It is often considered that below a certain volume percentage such as 1%, the presence of porosity will not influence on the behavior of Figure 1: micrographs of porosity present in hulls made of pre-impregnated carbon /epoxy [3]

268 Specifying only the volume fraction of porosity is not enough to predict the mechanical behavior of a laminate. Indeed, not only the location of the voids in the thickness of the part, their dimensions and their shapes, but also their distribution can influence mechanical properties of the manufactured parts. The different process steps also play a role. Thus, in the case of composite parts made from prepreg, porosity may occur during the draping phase by trapping air between the plies but also during the curing phase that promotes the evaporation of steam and reagents trapped in the laminate. It is therefore essential to ensure that compaction is closely controlled and to adopt temperatures adapted to the material so that polymerization of the resin can proceed under the best conditions, in order to reduce the influence of these defects. 3 THE AUTOMATED FIBER PLACEMENT 3.1 PROCESS DESCRIPTION The AFP machine developed by the Coriolis Company consists of an automated robot arm, controlled by a computer, on which is fixed a placement head which makes it possible to drop off bands of pre-impregnated with precision onto a mould (Figure 2). The width of a band is 6.4 ± 0.25 mm. The robotic head allows the removal of 8-32 tapes simultaneously positioned next to each other respecting the orientation of plies and ensuring repeatability of parts manufactured during the layup. These parts are then placed in an autoclave to cure the resin and promote the consolidation of the plies to obtain high quality mechanical properties. This technology has the advantage of making parts of complex curvilinear forms, with single or double curvature, in order to optimize the composite structure. This technique has proven effective in improving the buckling load [4], reducing the effect of stress concentrations [5,6], and also decreasing the notch sensitivity of the part [7]. In the manufacture of parts with complex shapes or with varying thicknesses, misalignments may be induced at the edges of the tows. To remedy this problem, the AFP technology allows individual control of prepreg tape that is to say, their routing and cutting, according to the desired layup during the placement. However, the cuts are made perpendicular to the fibres which therefore introduces gaps or overlaps (Figure 3.a). The strategy chosen for draping is that fibers can be cut either before the limit of area, leading to the creation of a gap, that is to say, resin-rich areas, or after reaching the trajectory, creating a superposition of the fibres, either partial or complete which results in fiber-rich areas and promoting thickening of the ply. The appearance of these singularities, specific to the fiber placement process, will directly impact on the mechanical properties of the manufactured parts. Croft [7] has shown that the absence of such overlaps achieved the best structural configurations. A singularity of steering (Figure 3.b), which consists of depositing a tape on fibers on a curved path, can also be created during the draping of a composite part. The trajectories followed by the deposition head may have a small radius of curvature (by choice or due to geometrical constraint of the part) causing misalignments and fibre buckling can then occur due to the undulations of deposited fibers. Many studies on this singularity have defined models to reduce its impact on the mechanical properties of draped structures [8]. Another possible singularity is the formation of a towtwist that can appear when a tape prepreg turns accidentally when making a ply (Figure 3.c). This creates a misalignment and increased local thickness in the laminate. b) a) Figure 3: Illustration of singularities created during layup by AFP process: a) gap and overlap, b) steering, c) towtwist [9] c) Figure 2: Coriolis placement head 16 fibers 1/4'' 3.2 LIMITATIONS 4 MATERIALS The material used in this study is a pre-impregnated carbon fiber composite and epoxy matrix from Hexcel

269 and referenced under the name Hexply /8552/AS4. This material contained 57.4 % fiber content by volume, the size of the tows was 12K (12,000 carbon fibres per tow) and the laminate density is 1.58 g/cm 3. In the case of a hand layup, the prepreg is used directly in its original configuration as unidirectional bands. In the case of draping with the fiber placement process, the prepreg is presented as a fiber width 6.35 ± 0.25 mm from the mother band. These tows have been split to be implemented. Once the layup is finished, an autoclave cycle is applied with the presence of a backing mould, as generally used in the polymerization of aerospace parts. The cycle is as follows: the temperature increased to 110 C, this temperature is maintained for 60 minutes with an applied pressure of 7 bars. Then, the temperature is increased to 180 C and held for 120 min. The temperature then decreases with release of pressure at 60 C or less. All the plates produced in this study have been polymerized together in the same vacuum bag. 5 STUDY OF GAP AND OVERLAP SINGULARITIES 5.1 DRAPING PLATES To study the singularities created by the process of automated fiber placement, plates were draped with a robot at Coriolis Composites. The placement head can deposit 8 carbon fibers at the same time. To get the plates with the desired singularities, the draping program is modified to allow adding, deleting or overlaying deposited fibers. Each plate consists of 7 plies in the configuration [0 /90 /90 /90 /90 /90 /0 ]. This configuration was chosen to study the most critical situation and exaggerate the morphology of singularities, that are only positioned and superimposed in the plies oriented at 90. It is important to note that each of the plates has been draped with gaps between the bands based on the tolerances on the width of the fiber. Indeed, aircraft manufacturers impose a maximum shift of 0.5 mm, which is however not considered a defect, but as a rule of draping. Figure 4: Illustration of singularities configuration: a) without singularity, b) with gap, c) with overlap 5.2 ULTRASONIC INSPECTION All plates were inspected by ultrasound (C-scan) to determine the presence or absence of defects. The observations were made using a device equipped with a transmitting and receiving 10 MHz ultrasonic probe immersed in water. The comparison between the amplitude of the input signal and the output signal is used to locate defects. However, this method does not provide an indication on the distribution of these in the thickness of the plate or their morphologies. a) b) Three plates have been draped: - A first plate free of singularity; - A second plate draped with a gap the width of a fiber, 6.35 mm (this singularity is only located in the center of the plate in the 90 plies). This means the absence of a fiber equivalent to each of the plies at the same location (5 plies) corresponding to an extreme case; - A third plate draped with an overlap half the width of a fiber or mm (the singularity is only located in the center of the plate in the 90 plies). c) Figure 5: C-Scan Images of plates: a) plate free of singularity, b) plate with a gap-type singularity (6.35 mm), c) plate with an overlap-type singularity (3.175 mm)

270 The results obtained from this analysis are shown in the form of maps as illustrated in Fig.5. No defect is visible in the plate free of singularity since the reflected signal is uniform (except at the supports of the plate corresponding to the black spots on the map). In the case of the plate with a gap defect type, a line appears where the observed output signal is lower, which means the presence of large defect at the location area of the singularity created. In the case of the plate with an overlap defect, we also see a line in the center of the plate at the singularity, where the output signal is slightly weakened. 5.3 SEM ANALYSIS We focus now on the morphology of singularities in order to compare and observe the organization of plies. For this, we removed samples at the centre of each plate where defects were introduced. These samples were cut with a diamond disc and then polished to obtain clean surfaces. We then made observations in the Scanning Electron Microscope (Figure 6). a) In the case of a defect-free plate, it is difficult to make out the five central layers oriented at 90. Indeed, the presence of a backing mould during the autoclave cycle homogenized all layers. We further observe that there is no porosity across the sample. In the case of a plate with a gap, the presence of a backing mould favours the mixing between plies and helps to fill the defect. However, we still see the resin-rich areas and large porosities. The presence of the defect in the plate width of a fiber leads to a decrease fiber fraction relative to the previous plate which may explain this analysis. We also note that the thickness of the plate is less than that obtained for a plate draped without defects (respectively thickness of 1.18 mm and 1.30 mm). On the third plate, we see the same homogenization of plies as in previous plates. We also note that there is no presence of porosity. However, the thickness of the plate is slightly greater (thickness of 1.38 mm) than in the case of defect-free plate due to higher fiber density. To conclude this analysis, we can highlight that the presence of one backing mould during the autoclave cycle has achieved consistent plates, that is to say the central layers of the same orientation are mixed to create uniform plates. So there is a movement of the rovings during the polymerization of the resin. We note that the large gap (the width of a fiber) is thus filled despite the presence of resin-rich areas and large pores. In the case of an overlap-type defect, fiber concentration slightly favours an increase in the thickness of the sample. 6. COMPARATIVE STUDY OF HAND LAYUP AND LAYUP BY AFP 6.1 DRAPING PLATES For this study, we produced two plates (one hand layup and the other with AFP) consisting of 7 plies in a [0 /90 /0 /90 /0 /90 /0 ] configuration. The conditions of manufacture and the cycle in the autoclave are identical to those used in the previous study. 6.2 SEM ANALYSIS b) c) Figure 6: Micrographs of plates: a) plate free of singularity, b) plate with a gap (6.35 mm), c) plate with an overlap (3.175 mm) Before performing tensile tests, we are interested in the structure of the two types of layup. Samples were prepared for SEM micrographs as illustrated in Figure 7 below. When comparing the microstructures of a hand layup and an automated layup plate, we see very little difference. The impregnation of the plies is complete and the few pores visible have a diameter equivalent to a carbon fiber (micro-porosities) and are mainly located in the inter-ply region for both types of draping. We note, however, in the case of draping by AFP, a distinction between the tows (area slightly resin rich) due to the presence of a gap of 0.5 mm imposed by the aircraft manufacturers.

271 a) Ultimate strength (MPa) Number of sample Hand layup AFP layup / 2 / / 6 / / Mean value Standard deviation Tab. 1. Results of tensile tests with a break in the central part of the test for a hand layup and a layup by AFP Figure 7: Micrograph images of plates: a) hand layup plate, b) automated layup plate 6.3 TENSILE TESTS Method b) To perform tensile tests, rectangular specimens were cut from the plates in the direction of the plies oriented at 0 in accordance with the dimensions given in the ISO standard (dimensions of 25 x 250 x 1.30 mm) using a diamond disc. The specimen edges were then polished to remove traces of the cutting disc, thus reducing possible areas of damage. In order to avoid spurious constraints that may be caused by the clamping system of the tensile testing machine and avoid causing premature failure of the samples, glass-fiber/epoxy oriented +/-45 tabs of approximately 1 mm thickness were bonded to each end using a twocomponent epoxy adhesive. Tensile tests were performed on an Instron hydraulic tensile machine with a load cell of 50 kn. The tests were performed under displacement control at 2 mm / min Results The majority of the specimens broke in the central section, away from the end tabs. Results from specimens which failed in the tabs are excluded from the analysis. Table 1 presents the values of tensile strength determined during testing for the two sets of samples. Tab.1. shows that the mean stresses at break are almost identical for manually draped and AFP draped tensile specimens, with a slightly higher variability for the latter. The very small difference in tensile strengths may be due to the material used. Indeed, the AFP tape is a prepreg after a unidirectional sheet slitting operation. The material thus undergoes an additional processing step when cutting ribbons in the mother sheet. In contrast, for manually draping, the prepreg is directly used in its form of unidirectional sheet. This is an additional feature specific to the process of automated fiber placement. 7 CONCLUSIONS AND FUTURE WORK The process of fiber placement today has great potential for the manufacture of complex structures. However, there is still a lack of knowledge about the influence of the singularities specific to this process on the performance of composite materials. The objective of this study was to investigate the morphologies of the two main singularities, overlap and gap. We also compared the mechanical properties of an AFP plate to those of a hand draped plate. The analysis of micrographs of gap and overlap singularities has highlighted the important role of the backing mould during the autoclave curing of carbon/epoxy plates. Indeed, we found a reorganization of plies which took place before the polymerization of the resin, thereby reducing the size of singularities. Thus, even when a gap defect of width of a strand is present in the plate, the reorganization of plies can still fill the empty space created when draping. However, there are still some areas rich in resin and higher porosity compared to a plate without the gap defect. In the case of a plate with an overlap singularity of a half-fiber size, we also find a reorganization of plies with a slight thickening of the plate due to the increased density of fiber.

272 Regarding the comparison of the types of draping, we found that the mechanical properties of a laminate draped manually were virtually identical (within 2%) to those of a laminate draped by AFP. This suggests that for this type of tensile loading the additional slitting step required for AFP does not affect properties significantly. Further work is ongoing to examine these defects under other loadings (compression, shear). Engineering, Vol. 43, n 3, pp , April The use of AFP technology for the construction of racing yachts request to adapt the available robots for draping large hull. It will also require the development of prepreg tape with a feature specific of this industry and thus to lower that those of aviation costs. Another solution is to use this technology for the removal of powdered fibers for making preforms that are subsequently infused. REFERENCES 1. M.L. Costa, S.F. Müller de Almeida, M.C. Rezende, The influence of porosity on the ILSS of carbon/epoxy and carbon/bismaleimide fabric laminates, Composites Science and Technology, Vol. 61; pp ; L. Liu, B. Zhang, D. Wang, Void content in carbon/epoxy composites and its effects on flexural properties, 49th International Sampe Symposium and Exhibition, pp , R. Maurin, «Contribution à l étude des facteurs limitant l usage des matériaux composites pour la réalisation de bateaux de course», Thesis of LIMATB, University of South Britany, Z. Gürdal, B. Tatting, C.K. Wu «Variable-stiffness composite panels: Effects of stiffness variation on the in-plane and buckling response», Composites Part A: Applied Science and Manufacturing, Vol. 39, n. 5, pp , Mai C.S. Lopes, Z. Gürdal, P.P. Camanho «Tailoring for strength of composite steered-fiber panels with cutouts», Composites Part A: Applied Science and Manufacturing, Vol. 41, n. 12, pp , December L.E. Turoski, «Effect of manufacturing defects on the strength of toughened carbon/epoxy prepreg composites», Thesis of Montana State University, K. Croft, L. Lessard, D. Pasini, M. Hojjati, J. Chen, A. Yousefpour, «Experimental study of the effect of automated fiber placement induced defects on performance of composite laminates», Composites Part A: Applied Science and Manufacturing, Vol. 42, n. 5, pp , May A. Beakou, M. Cano, J.-B. Le Cam, V. Verney, «Modelling slit tape buckling during automated prepreg manufacturing: A local approach», Composites Structures, Vol. 93, pp , April D.H.-J.A. Lukaszewicz, C. Ward, K. Potter, «The engineering aspects of automated prepreg layup: History, present and future», Composites Part B:

273 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France TAG SHEPERD: A LOW-COST AND NON-INTRUSIVE MAN OVER- BOARD DETECTION SYSTEM Nicolas Le Griguer, Lab-STICC, Universite de Bretagne Sud, France Johann Laurent, Lab-STICC, Universite de Bretagne Sud, France Jean-Philippe Diguet, Lab-STICC, CNRS, France This paper presents a man overboard detection system based on the monitoring of a group of sailors. It introduces a set of existing solutions proposed to track and rescue a person falling into the water. Based on the state of the art, it describes our original solution which is low-cost and low footprint compared to the other ones. It was developed to be a plug-n-play system that can be generalized for every sailor to detect a man overboard. 1 INTRODUCTION Many fatal sea accidents still occur and most of them are overboard falls. For example, for the 2012 year, 15% of the rescue operations performed by the SNSM (the rescue team for the French coastline) was for a man overboard as we can see in figure 1 (just behind broken motors). The life expectancy of a sailor, who fell into the sea, is about 30 to 60 minutes for a 4 to 10 Celsius degrees water. The necessity to decrease the time to detect a man overboard is the key factor to save life. Furthermore, more the detection time is important and less is the chance to rescue an overboard sailor even if weather conditions are good. The rest of the paper is organised as follows: Section 2 presents the different existing solutions already available on the market. Section 3 describes our solution, including hardware details for the different parts. 2 EXISTING SOLUTIONS The improvement of the security on board is a real challenge for the manufacturers in the world of sailing, it s for this reason that many distributors sell different solutions. There are different levels of complexity which result in different price ranges. There are 3 main categories, from the most complex to the simplest one, resulting in different options and technologies, for instance the use of the AIS signal, the possibility to get the position of the Man OverBoard (MOB) or to connect the system to an automatic pilot for a rescue maneuver. The next section discusses AIS-based devices with GPS positioning of the person in danger. 2.1 AIS-based devices Figure 1: SNSM Statistics As we will see in the next section, some solutions already exist, as distress beacons integrated to a life-jacket; when the sailor falls overboard, the transceiver is powered on and alerts the other sailors on the boat. This solution supposes that everybody wears a life-jacket (the French SNSM statistics show that is rarely the case), and the boat must be fitted with bulky equipment that implies an expensive deployment cost. Others solutions exist but are not very suitable and so not used due to the size, cost or response time constraints. To offer the expected security with a reduced cost and a simple integration in the boat, we developed a low-cost and plug-n-play solution. The Automatic Identification System (AIS) is a communication protocol used to locate and identify ships on the sea but also some navigation elements like lighthouses or buoys. This protocol transmits many informations about the emitting vessel, like its position, course, speed, name and type for instance. This system is required to be fitted on board when the vessel tonnage is more than 300 tons but many lighter ships are equipped because of the security gain it offers. Indeed, it s used to perform many actions like: Collision Avoidance: by computing the different navigation data of each ship, it can alert about a collision. Check the vessel traffic: used in some maritime roads with a high traffic density to perform a regulation. Help for navigation: by giving some information about the traffic and the navigation assistance. (lighthouses and buoys for instance).

274 Search and rescue: used to coordinate the marine Search And Rescue (SAR) operations by giving position information of a damaged vessel that can be checked with another ship or an aircraft. It is this last usage, which is employed by some manufacturers to build some rescue beacons. When a sailor falls into the water, the device is switched on and an AIS-SART (Search And Rescue Transmitter) signal is broadcasted. In this case, the ship where the MOB comes from can rescue him, but the others vessels sailing near the MOB, lifeboats and rescue aircraft have also access to the signal. The illustration 2 shows the principle of an AIS-based MOB detection system. 2.2 RF-based devices Another way to detect a MOB is to put a RF transmitter on every sailor and check the signal with receiver positioned into the boat. When someone falls into the water, the RF link is broken and an alarm is switched on informing the danger. Generally, these products have a monitoring range which is about 10 to 30 meters, it means that when a beacon is far away of this range, the alarm is switched on. Some repeaters can be used to increase the monitoring range like in the Raymarine LifeTag MOB System [2]. Indeed, if the reception range of the base station is not enough compared to the size of the boat, some repeaters can provide a more important monitoring range. The figure 3 shows the functional scheme of this kind of solutions. Figure 2: AIS-based MOB detection These types of beacon have an integrated GPS chip to send the coordinates of the MOB, so it s possible to locate the person with a high precision and the signal is visible in a circle of around 4 nautical miles. The main problem of this type of equipment is its price, for example a Kannad R10 AIS emitter [1] is around 240e and a receiver (needed to get the signal from the boat) is approximately the same. So this kind of product is not intended to be used on a pleasure boat or in a small company due to its deployment cost. The main advantage of this kind of product is its good battery life, for example the Kannad R10 [1] distress beacon can emit the MOB position during 24 hours after that he falls overboard. It s because the system is powered on only when the people wearing it falls overboard, the rest of the time the beacon doesn t consume any power. At least, another problem of this solution is the portability of the device, this beacon must be fitted into a life-jacket to be activated with the inflation (or activated manually if it s not paired to a life-jacket). The observation of the sailors behaviour shows that people are rarely wearing life-jackets, it s true on the trade vessels, fishing boats and even pleasure boats. It is for this reason that another type of product was developed by others companies to detect a man overboard more easily, and to get a low-cost and hand-held device. Figure 3: Illustration of RF-based MOB detection This is a basic two-way radio based device that can be paired with the automatic pilot of the boat. Indeed, the automatic pilot can be used to stop the boat when the sailor is alone on board, or in the case of a sailing team, the navigation routing devices can give the direction to rescue the MOB. Each beacon emits continuously, it means that the battery is more stressed so the battery life will be altered. To give some examples, the systems based on the 2.4Ghz technology have a battery life about 200 operational hours (Raymarine Life- Tag MOB System [2]) to 2000 hours (MOB Dolphin 600 [3]). This type of device is smaller than the AIS-based one, indeed the Raymarine [2] and the Dolphin [3] beacon are approximately the same size, they can be carried on the arm but remains quite big with a size of 60x45x25mm. The price range of these devices is around 550e for the base station and 150e for each personal beacon. We can see that the price remains a problem to generalize a large adoption. Another device, similar to this one, is the MOBi from NASA Marine Instruments [5]. It s composed of a base station which is monitoring some beacons like in the others systems. Each signal delivered by the emitters is displayed on the screen of the base station and when beacon signal falls over a selected threshold, an alarm is activated to indicate the MOB. The most disadvantage of this solution is its size, each personal beacon measures 77x44mm. Since it needs to be powered with 3 AAA cells, its weight is also a problem and its

275 battery life does not exceed some weeks in a continuous usage. Finally, the price is about 350e for the base station and 50e per tag, which is the cheapest MOB detection system in the market usable with many beacons. 2.3 Water-detection based device This last kind of device is a simplified version of the previous one. It s a two-way radio principle very minimalist without options like the coupling to an autopilot. The most simple one is the HawkEye SA500SP [4], which is composed of a base station and an unique emitter. The alarm is activated when the beacon enters in contact with water, this detection is made through water sensor positioned on the surface. It means that this sensor must not be in contact with anything, the manufacturer says that this emitter is very sensitive and recommends to not place it in a pocket or in another place where the water sensor could be in contact with something. The main problem of this device is that it could be activated easily by anything with a contact even if there is no danger, but also with a water projection. On the other hand, the main advantage of this solution is its cost since the complete device cost is about 49$. It s the cheapest system available on the market, but currently it cannot be used to detect a man overboard in sailing conditions (wet environment and many actions making contact with the sensor) and with more than one sailor. 2.4 Conclusion Comparing these different solutions, we show that more the complexity is high, more the technical constraints are high and so the price too. On the contrary, a low-cost system is generally composed of some basic emitters and a monitoring base station, which waits for a missing signal, reducing the cost and improving the battery life even if it doesn t exceed some weeks in a continuous usage. The table below summarizes the different pros and cons of the different products. AIS-based devices RF-based devices Waterdetection based devices Cost Battery Life Size Table 1: Comparison between different types of MOB detection Considering this situation and the user requirements based on real-life behaviours, we worked to find a better compromise to reduce the size of the beacons, increase the battery life and reduce the cost of both the base station and the emitters. 3 OUR SOLUTION Starting from the constraints that we identified, we tried to design smaller and cheaper product based on the RF link between the sailors and the base station. A small device plugged into the boat (receiver), performs a continuous radio scan of the transmitters located in its field of action. These transmitters are based on longlife active RFID tag that are fitted into small package and can be carried as a key ring or putted into a pocket, a jacket or other clothing items. Each beacon emits its unique identifier with a given frequency (e.g. 1Hz) that can be tuned according a tradeoff between life time and reaction time. The receiver is configured to only monitor a set of selected beacons, when one of them is not emitting, it means that someone is out of a safe perimeter corresponding to the boat area. In this case an alarm notifies this event, and the crew can perform a rescue operation. In addition, this security central unit can be connected to a navigation processing unit to provide some useful information like the GPS positioning in order to guide the crew during the rescue maneuver. The maximum delay for considering the accident is about 4 seconds, with an optimal setting for the beacon emitting frequency, it garanties a one-year battery life; it is obviously much more efficient than a visual check by a busy crew. 3.1 Hardware Our solution is based on a simple link between some transmitters and a receiver. Each beacon worn by the sailors are transmitters and receiver checks the signal of each beacon, when some people falls overboard, the RF link is broken and the receiver puts an alarm on to forewarn the danger. The attention has been focused on the battery life of the beacons, their size and price but also on the small bulk for the base station in order to integrate the system easily in any boat Transmitter Each sailor is equipped with a personal distress beacon which is in fact a RF transmitter. The beacon is like an RFID active tag, each of them have a unique identifier which is broadcasted through a RF link. The frequency selected is MHz, it s a good tradeoff between emitting range and power consumption. Indeed, it consumes less power than a wireless solution using higher frequencies like we saw previously with the 2.4 GHz frequency. For example, an Xbee module transmitting a data consumes 50mA at 3.3V, it s two times more than our solution. An ultra low-power microcontroller is paired to an RF transmitter and periodically wake-up the system, broadcast its unique identifier and return into sleep mode. In that case, the power consumption is reduced to the minimum required to keep the system in the sleep mode and the peak of current consumption occurs only when the identifier of the beacon is sent. This power management offers the possibility to keep a beacon emitting at 1 Hz during one year and three months (this value was first estimated and validated with a prototype in real conditions). Depending of the conditions of usage, this period of emitting can be augmented to increase the battery life. For example a racing boat needs a shorter detection time than a pleasure boat sailing slowly. The maximum detection time is equal to two periods of emission, so depending of the boat speed and the response time needed, we can increase the

276 delay between two emissions, and so increase the battery life. Finally, we can tune the power amplifier of the RF device in order to increase the transmission range according to both the boat size and the perimeter of detection (larger is the transmission range, lower is the battery life). So, with these different settings and in function of the boat specifications and of the response time needed, the battery life can be increased up to several years. The figure 4 shows an example of battery life for a detection range up to 15 meters. The emitting period is computed in order to have a MOB alert before the distance between the boat and the MOB is higher than 15 meters. The figure below shows also the theoretical value of the battery life depending on the emitting period. the base station realizes a scan of the emitting beacons and put them into its list of monitoring. Then continuous scans are performed in its range of monitoring. When a signal is lost (corresponding to a falling into the water), an alarm is activated to prevent the rest of the crew. If the boat disposes of a set of beacons, and one of them is not used then it can be placed in a small box acting as a Faraday shield. In this way, when the captain will perform the detection of the emitting beacons available, the system will only see those worn by the sailors. Currently, the base station is just emitting a high acoustic signal and displays a flashing light, but it can also be connected to a navigation processor unit to keep the position when the man falls overboard and help during the rescue step. Our solution has been validated, including radio, hardware and software aspects. 3.2 Functional Diagram The figure 6 shows the system implemented in a boat with 3 sailors, we can see the receiver performing its scan of the different beacons. When there is a MOB event, the distress signal is emitted; in this figure we can also see an additional feature consisting of connecting the base station to the boat navigation processing unit. Figure 4: Battery life VS emitting period The size of the beacon is mainly determined by the battery size. Thus as shown before, several efforts are made in order to reduce the battery size while preserving a reasonable operating time. Currently, the transmitter prototype can be carried into a pocket or worn as key ring due to its small size (cf figure 5); this size still could be decreased by using a smaller battery. Figure 6: MOB detection system 3.3 About marketing Receiver Figure 5: Prototype picture The receiver, called base station, monitors a set of beacons selected by the user. When the user press the appropriate button, Each beacon is composed by one RF transmitter, one microcontroller and one battery. So as these devices are cheap, we estimate that beacon could be proposed twice cheaper than the MOBi from NASA MARINE INSTRUMENTS [5](price around 25e for a tag). The main station, which is also composed of the same type of components, could be also industrialized with a low-cost. In order to adapt the solution for different types of consumers, we have chosen to propose two alternatives for the product : Smart solution: Composed by the base station and a number of beacons needed by the client that can be connected to the boat just by powering it. It s a plug-n-play solution, ready for use without any other connection than the electric one. This solution, which is the cheapest one, is adapted for pleasure boating or small fishing boat.

277 Full solution: Same solution than the smart one but with the possibility to connect the board to a computer to check the different beacons and set the different options (receiving range of the base station, delay for alerting, setting of the monitored tags,...). This solution is more parametrizable, but also more expensive is made to be used in bigger boats than the previous one and could be deployed on big fishing vessels or race boats for instance. 4 CONCLUSION and PERSPECTIVES Assuming that the security is a real challenge in any type of sailing, we saw that many manufacturers propose solutions based on different technologies. In the objective of a mass deployment, we need a low-cost, small and easy pluggable system So we designed our solution to respect these considerations and finally we obtain a low power and size system that can be worn as a keyring or integrated in sailing clothes. In addition, the complete solution is low-cost, so it can be purchased by many pleasure sailors or small fishing companies, improving their security and the chances to rescue a MOB. The next development consists of connecting the base station to the main navigation system of the boat in order to take into account the GPS position of the boat to improve the rescue step. Another improvement would be the use of triangulation-based process to locate the sailors on board in order to improve the crew displacements on the boat (very useful for sailing teams). and software developments for the Groupama Sailing Team to prepare the Volvo Ocean Race and building prototypes for on board security based products for Lab-STICC projects. He s now in charge of electronic development for the Voilier du Futur project which aims to create a demonstrator cruising yacht which will incorporate eco-innovations in the areas of materials, energy, waste-water treatment, rigging components and fittings, ergonomics and safety. Johann Laurent works as an Associate Professor at Lab- STICC, Universite de Bretagne Sud. He is the head of the Master degree in electronics at the UBS. His research activities deals mainly with the power energy consumption in embedded systems. He supervises several works around electronic research for sailing including phd and internships with manufacturers and sailing teams. He is responsible for the electronic and safety part of the Voilier du Futur project with Jean-Philippe Diguet. Jean-Philippe Diguet is a CNRS Research Director at Lab-STICC. He had multiple research activities which referred to modelling and electronic development in embedded platforms. His previous experience includes several thesis supervising in embedded systems and some marine specific topics about sailing performance or on-board mobile augmented reality. REFERENCES [1] Kannad Safelink R10, kannadmarine.com/en/safelink-r10 [2] Raymarine LifeTag Man Overboard System, [3] Alltek Marine Dolphin, alltekmarine.com/products_detail. php?bgid=8&gid=21 [4] HawkEye SA500SP, hawkeyeelectronics.com/ SA500SP-water-sports-communication-system/ [5] Nasa Marine MOBi, com/proddetail.php?prod=mobi 5 AUTHORS BIOGRAPHY Nicolas Le Griguer holds the current position of Research Engineer at Lab-STICC, Universite de Bretagne Sud. He is responsible for developing prototypes and demonstrators for research projects. His previous experience includes electronic

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279 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France KITE AND CLASSICAL RIG SAILING PERFORMANCE COMPARISON ON A ONE DESIGN KEEL BOAT R. Leloup, K. Roncin, G. Blès, J.-B. Leroux, C. Jochum, LBMS (EA 4325), ENSTA - Bretagne, France, firstname.name@ensta-bretagne.fr Y. Parlier, OCEA, rue des Terres Neuves, BP 21, Bègles Cedex, yves.parlier@parlier.org, Abstract An implementation of a kite modelling approach into 6 degrees of freedom sailboat dynamic simulator is introduced. This enables an evaluation of kite performance in comparison with classical rig sailing. A zero-mass model was used to model kite forces. Influence of the wind gradient was properly taken into account which led to significant modifications in the calculation of the relative wind, both in magnitude and in orientation. The modelling is performed with real aerodynamic characteristics given by experimental data. An optimization is done to determine the best kite flight configuration in terms of performance. Validation steps of the sail yacht simulator are performed for a classical rig on the example of an 8 meter one design yacht. The experimental setup is described and validation results are discussed. An interpolation technique in space and time of the wind mesh was used, based on measurements made at four different locations of the navigation spot. Boat motions were recorded by high resolution GPS and inertial unit systems. Speed polar diagram results, reached by kite propulsion, were predicted versus true wind angle. At last a comparison is made for upwind and downwind legs in sea trials conditions, between simulations with the classical rig and the kite. It is shown that the boat towed by kite would achieve much better sailing performance. 1 INTRODUCTION Regarding world speed records, kite surfers demonstrated the performance efficiency of kites. In this context, taking advantage of wind using kites as propulsion systems for yachts can be an alternative to conventional sails. This study takes place within the project "Beyond the Sea " launched by Yves Parlier and is managed in partnership with the LBMS laboratory of ENSTA Bretagne and the French ministry of defense. A methodology for kite propulsion efficiency analysis regarding a classical rig sailing yacht is presented in this paper. The aim is to highlight and to explain differences between the two propulsion technologies applied to the same yacht. A modelling approach for a flying kite is presented in the first part of the study which takes into account the wind gradient linked to atmospheric boundary layer. Analytical expressions for apparent wind velocity seen by the kite and for kite velocity at each position within the wind window are presented. An optimization technique for best flight configuration is proposed. Especially, the optimization technique proposed differs from the literature [1] namely by the analysis of vertical 8 shaped trajectories which enable significant upwind benefits, as shown in the results section. The kite modelling approach was implemented into a Dynamic Velocity Prediction Program (DVPP) [2] for an 8 meters one design yacht, the Beneteau First Class 8. Validity of the DVPP was assessed by sea trials comparisons that are presented and discussed. Furthermore, to ensure the use of real validated data, kite aerodynamic parameters were taken from Dadd [3,4] experiments. A comparison between classical rig and kite propulsion is presented in the last section, based on velocity polar diagrams and on upwind and downwind legs. 2 MODELLING APPROACH OF A FLYING KITE This section presents the setting technique used to describe the kite within the flying window. This enables kite velocities descriptions which are the main input data for the velocity comparison strategy with a classical sailing rig presented in this study. 2.1 WIND WINDOW REFERENCE FRAMES An illustration of the kite within the half sphere wind window is shown in figure 1. In this figure O denotes the attachment point of the tethers to a reference point (ground or deck of a ship for instance)

280 Wind window edge 2.2 WIND GRADIENT DESCRIPTION y k0 x k0 K y x WR WR V V s z WR k y F x vk x F z k0 O vk z F Kite trajectory V WR Figure 1: Flying kite within the wind window. In case of a boat, the wind window is oriented by the relative wind velocity vector V WR at each point. Pay attention to the fact that relative wind is used to be called apparent wind for the sailing boat. The notation adopted here is the ITTC Standard notation [5] that allows, in the case of kite, to clearly distinguish the relative wind seen by the boat and the apparent wind seen by the kite. Figure 1 shows the kite in the wind window bounded by the wind window edge. The kite is represented by point K, which is located at the quarter chord in the symmetry plane of the kite. The reference frame R k0, which is attached to point K, is obtained by rotating about z WR by the azimuth angle, and then by the elevation angle (θ π/2) around y k0. Unit vector x vk is oriented along the direction of the kite velocity and is obtained by rotating vector x k0 about z k0 by angle χ vk. R b is the body reference frame, attached to the kite as presented in figure 2. The aerodynamic reference frame R a is oriented in accordance with the kite apparent wind velocity V a. Reference frame R F is fixed in relation to the flow so that x F axis is in the course direction along the ship velocity V s. F a - L α x b geom D (x k0,y k0 ) plane x a z V a a z b z k0 Figure 2: Aerodynamic forces vector decomposition in the kite symmetry plane. However, tethers length can usually be around several hundred meters to facilitate high wind capture. This makes sense to take wind gradients effects with altitude into account. The wind friction with the sea surface (or ground) leads to a zero wind velocity at sea level. Therefore the true wind velocity V WT decreases when altitude decreases. This phenomenon is called wind gradient and was introduced in the modelling instead of a constant wind velocity as a function of altitude. According to ITTC 2011 [5], the wind velocity as a function of altitude can be calculated using the formula: V WT = U 10 z 10 Where U 10 is the wind velocity at standard altitude 10 m (m.s -1 ) z is altitude above sea level(m) n is a coefficient which is equal to 1/7 for the sea surface according to ITTC 2011 [5] The wind velocity according to altitude is plotted in figure 3. One can see that the wind velocity increases when altitude increases. Therefore, it can be more favourable to use a kite which flies at high altitude where the wind velocity is higher. Figure 3: Wind velocity according to altitude. 2.3 KITE VELOCITY BASED ON THE ZERO MASS MODELLING APPROACH This section presents a review made on the common zero mass model [3,4,6] which was rewritten to enable an analytical and easy to use expression of the velocity of the kite. According to the Newton's laws applied to the kite at point K, assuming that the mass of the kite is neglected, equilibrium equation is as follows: n (1) T + F a = 0 (2) The aerodynamic resultant, F a, compensates the tethers tension, T, at any time and these two forces are aligned on the same axis that goes from attachment point O to the point K of the kite. The second equation which governs the kite motion is the apparent wind equation:

281 V a = V WR - V k (3) With V WR = V WT V s, where V s denotes the ship velocity. According to the definition of the aerodynamic resultant, we have: F a = L + D (4) The apparent wind velocity vector V a is assumed to remain in the symmetry plane of the kite. This leads in the plane (x a,z a ), to the configuration shown in figure 2. As demonstrated by Leloup [7,8] the projection of equation (3) onto the corresponding axes and by scalar product with z k0 : V a = - V WR x WR.z k0 (5) sin Moreover, using the scalar product properties equation (3) leads to: on the y F axis, we obtain the drift force. These forces are integrated with respect to time along the flight trajectory of the kite, in order to obtain their average values for a given trajectory. This enables comparison of the trajectories efficiency based on average propulsive force. x Wind WT β WT ywt window at a V s given U 10 β WR V WR altitude x WR x F O y WR y F Wind window at 10m V a 2 = V WR 2 + V k 2-2 V WR V k (x WR.x vk ) (6) Combined with equation (5), equation (6) can be seen as a second order equation of the velocity of the kite V k leading therefore to: V k = V WR x WR.x vk + (x WR.x vk ) 2 + x 2 WR.z k0-1 sin 2 (7) The velocity of the kite is real only if x WR.x vk 1 - ( (x WR.z k0 ) 2 ) sin 2 (8) Condition (8) shows that the existence of the velocity of the kite is only defined for a given flying area so-called "manoeuvrable area" below the red limit line shown in figure 1. In this area the kite can move in all directions. Above the red limit line, the kite cannot fly. It corresponds to the "wind window edge". 2.4 AERODYNAMIC CHARACTERISTICS A sail area of 35 m² was used during sea trials with a one design sailboat settled with a classical rig. To make a meaningful comparison the same area was taken for the kite. A typical tethers length of 100 m was considered in a first approach. Aerodynamic characteristics of the kite were taken from Dadd experiments done on a ram-air kite [3,4]. Thus, the lift coefficient C L and glide angle are and 9.55 respectively. 2.5 PROPULSIVE FORCE GENERATED BY THE KITE Once apparent wind velocity of the kite V a is known at each position within the wind window, the tethers tension resultant T, which is opposite to the aerodynamic resultant F a according to equation (2), can be expressed as follows: T = 1 2 C L ρ air A k V a z k0 (9) 2 cos The projection of the tethers tension on to the axis x F, directly gives the propulsive force generated by the kite. It depends on the relative wind angle β WR (relative to ship course) at kite altitude as presented in figure 4. Projecting Figure 4: Kite flying wind window 10 m above sea level and at a given altitude higher than 10m. As shown in figure 4, true wind velocity V WT variation with altitude modifies the relative wind angle β WR observed at 10m (ship level for instance). The orientation of the wind window is therefore varying with the altitude leading to a twist of the wind window edge as shown in figure 1. Especially, it is pointed out that the wind window orientation is modified with increasing altitude. The wind window is oriented by the relative wind angle WR at the altitude of the kite. As the kite altitude increases, the relative wind angle WR progressively increases as well, leading therefore to more efficient towing force in direction. This is a key point that has to be considered for kite propulsive force optimization strategy presented in next section. 2.6 MAXIMUM PROPULSIVE FORCE POLAR ALGORITHM For a given ship and wind velocity, the polar plot of the maximum propulsive force can be done according to the true wind angle β WT (relative to ship course). For each β WT value a kite flight optimization loop was developed testing, for a given elevation angle θ, both static and dynamic flight cases. In case of a static flight, which corresponds to a given elevation angle, the azimuth angle was computed in order to put the kite on the wind window edge which is the only location to keep the kite into a static position according to condition (8). The corresponding propulsive force given by equation (9) is then compared with the dynamic flight case. Note that azimuth angle, according to figure 1 can be expressed as follows: cos() = sin() (10) cos()

282 This leads to two solutions, one positive and the other negative, which only one can be remained as propulsive. On the other hand, the dynamic flight case was investigated for an horizontal and a vertical 8 shaped trajectory. At a given elevation, a variation of the azimuth angle of the trajectory was conducted in order to grasp the best average propulsive force obtained during one period of the flight. This loop is done up to the maximum elevation. Finally, identification of a maximum propulsive force is reached, which corresponds to a given trajectory within the wind window. Comparison between maximum static and dynamic propulsive forces is done. Corresponding ship transverse and vertical components of the tethers tension can be deduced. Company. All data feed the central unit to be synchronized and stored in memory. All data are transmitted in live to a base onshore by the mean of an Ultra High Frequency signal Wind measurements The wind was measured by ultra sonic wind vane CV3F by LCJ sensors. This kind of technology guarantees a good independence between wind measurement and platform motions. Four wind sensors were set around the sailing area on fixed KL15 catamarans. This enables a mesh of the wind field that covers all the sailing area as shown in figure 6. 3 YACHT DYNAMIC SIMULATIONS SET-UP The dynamic velocity prediction program set by Roncin [2] was used in this section which particularly highlights the experimental set-up and corresponding validation. The Boat is an 8 meter one design, the Beneteau First Class 8. Hydrodynamic forces were deduced from towing tank extensive tests studies performed with the design of experiment method principle. The aerodynamic model for the classical rig developed by Claughton [9] was considered. Claughton took also the waves into account and his formulation was used to calculate the added resistance in waves. 3.1 EXPERIMENTAL SET-UP The validation of the simulator was performed by sea trials conducted in collaboration with the Centrale Nantes (ECN) graduate school of engineering, the French national school of sailing (ENV) and the University for applied Technology on the Nantes campus [10] Yacht positioning data Figure 6: Example of KL 15 wind sensors platform location for wind field meshing. The wind at boat location was obtained from a simple linear interpolation in time and space. This technique takes advantage from a simple wind vane settled on the boat since it is far less disturbed by the air flow deviation around the sails or by the motions of the boat or the deformation of the mast and rig. Relative wind angle is deduced from the wind interpolation at boat location and from the boat speed given by the GPS measurements. Note that sea current was taken into account from public data provided by the SHOM, (French hydrography and oceanography service), and was interpolated in time. Wind interpolation was validated by comparison between measured wind and predicted wind done for one of the four sensors thanks to data provided by the three others. Results displayed in figure 7 are almost satisfying since they are mostly below sensors accuracy. 280 interpolation measurement Figure 5: Sea trials on the 8 meter one design yacht. The boat and the measurement system can be seen in figure 6. Speed and position were measured by a high resolution GPS DG16 from Thales, which give accuracy below the meter. Rudder angle was measured by a potentiometer. Attitude and rates in rotation are given by an inertial unit from Xsens provided by the Cadden Wind direction ( ) Time (s) Figure 7: Example of interpolated wind direction compared with experimental wind measure, for the same location.

283 The same interpolation technique was conducted for wind velocity. A relative gap of 13% was found between measurements and interpolation results which is reasonably satisfying at this stage. 3.2 DYNAMICS SIMULATIONS VALIDATION STEPS The leading idea of the validation step is to perform comparisons between simulations and measurements with the same initial conditions. Thus, initial location, attitude, angular rate and velocity measured by the high resolution GPS DG16 sensor and the inertial unit MT9 from Xsens were taken as input data for the dynamic simulation. triggered by the pull phenomenon of the rear side of the yacht at the beginning of the tack which accelerates the GPS sensor. As GPS sensor positioning was taken into account for the simulation, the pull phenomenon on velocity could be predicted. However, velocity loss predicted at tack exit is lower than what was observed. At this stage it is difficult to explain this difference by team motion effects, swell effects, manoeuvrability or aerodynamic models set into the simulation. Note that flapping of the sails is not modelled and virtual crew trim the sails instantly in the simulation Turning tests without sails The yacht without sails was towed at a given and constant velocity between 5 and 6 knots before towing release. Once released, rudder angle was set to 50 till end of the turning test. Turning results between simulation and yacht trajectory are shown in figure 8. Figure 9 : Yacht velocity prediction during a tack Sailing trajectory tests Turning and tack tests have demonstrated a rather satisfying prediction ability of the simulator, in agreement with the physics observed. The next and final validation step was to perform comparisons between simulation and data collected on a typical sailing trajectory. Figure 10 shows results obtained for a trajectory composed by classical upwind and downwind legs. Figure 8: Turning test results, without sail. Note that the yacht velocity decreases quickly once released and that the trajectory is strongly impacted by the current of the sea and the windage. These kinds of effects were taken into account by the simulation that exhibits a very satisfying prediction for the first 360 turn. However, prediction of the second loop is much less satisfying. This mismatch was unfortunately predictable in case of very slow velocities since the yacht can, in that case, easily be disturbed in a chaotic manner by the waves for instance. As these disruptions are random phenomenon they were not taken into account in the modelling Tack tests Simulation capability was checked on real tack tests. Same initial conditions as for the sea test were used for the simulation and the only governing parameter was the rudder angle. As shown in Figure 9, velocity predicted by the simulation appears to be in good agreement with the data. Especially, the increase of velocity at the beginning of the tack was almost well predicted. This increase is Figure 10 : Sailing Yacht trajectory prediction. The pilot of the simulated boat is only controlled by the measured relative wind angle at each time step. Trajectories for sailboat with a classical rig between the simulation and the measurements are in a very close agreement during the first upwind port leg and, after the first tack, during two thirds of the second upwind starboard leg. After that, the real boat suddenly loses speed for an unknown reason. Therefore, the simulated trajectory deviates significantly from the measured one. Indeed, since the simulated boat is controlled by the measured relative wind angle, the loss in velocity

284 necessarily results in an increase of the true wind angle to maintain the same relativewind angle. At the beginning of the third leg, a gap is observed and stays almost constant up to the end of the upwind leg. At the first, and at the last downwind leg, the simulated Yacht is faster than the real one. These phases correspond to the hoisting and the lowering of the spinnaker. Nevertheless one can reasonably consider that simulation results are in rather satisfying agreement with real sea trials. This enables therefore an acceptable validation of the simulator. Consequently, the simulator was extended to the case of kite propulsion and results are discussed in next chapter. 4 RESULTS 4.1 VELOCITY POLAR DIAGRAMS V S (β WT ) The performance of a boat towed by kite can be assessed by its velocity for each true wind angle. Consequently, a boat velocity is first postulated which enables the required tethers tension calculation. Corresponding flying configuration is searched thanks to the optimization loop. Especially, boat drag and lift norms are equal to the projection of tethers tension T on x F and y F respectively. At this stage, corresponding new boat velocity and drift angle are calculated. The velocity is injected at the beginning of the optimization loop until convergence. The polar curve of the boat towed by a kite was obtained for static, vertical and horizontal dynamic flights as presented in figure 11. The use of these polar diagrams enables the determination of the flight configuration that provides the best upwind and downwind Vmg with corresponding true wind angles. Two optimal flight trajectories correspond to these two angles: a vertical dynamic flight for the upwind case (shown in figure 1) and an horizontal dynamic flight for the downwind case as shown in figure 11. The upwind Vmg is equal to 1.62 m.s -1 with a true wind angle of 49 and a boat velocity of 2.47 m.s -1. The downwind Vmg is equal to 2.91 m.s -1 with a true wind angle of 170 and a boat velocity of 2.95 m.s -1. Only these two optimal configurations were calculated and the best was retained. This allows the plot of final velocities polar diagrams for the kite towed boat as displayed in figure 11. It can be seen in figure 11 that, excepted for very small true wind angles, the classical rig performed better than the kite static flight. This can be explained by the fact that the trim of a classical rig allows to reach more important forces by increasing the draft of the sails. The discontinuity observed on the classical rig plot is due to the use of a spinnaker for relative wind angles of more than 80 degrees (i.e. approximately 110 degrees in true wind angle). In this configuration the classical rig surface is about 70 m 2 while the kite surface remains 35 m 2. Figure 11: Velocity polar diagrams versus true wind angle with U 10 = 3 m.s -1. An additional explanation about performance differences between classical rig and kite static flight might be given by the lift coefficient that, according to IMS [9], can reach values of 1.5 to 1.7 for sails whereas a value of was measured by Dadd [3,4] on the kite. On the other hand the kite provides a better lift to drag ratio that allows to reach closer hauled true wind angles and probably a better upwind performance in stronger wind conditions. In addition an optimization on the trim angle of attack which is not achieved in the present study could be done to make better results in light wind condition or wider true wind angles. However, figure 11 clearly demonstrates that in case of a dynamic flight kite propulsion definitely performs much better than the classical rig, even with a spinnaker and a doubled total surface of 70 m². 4.2 COMPARISON BETWEEN CLASSIC RIG AND KITE PROPULSION The same configuration as for validation of the classical rig yacht simulation was used for the comparison between a kite towed boat and the same boat with a classical rig. The aerodynamic module for a classical rig boat developed by Claughton [9] was replaced by the module for propulsive force generated by the kite presented in the second chapter.

285 during sea trials). In a same manner, the analysis of the distance elapsed between 990 seconds and 1820 seconds shows that the downwind Vmg reached is 3.24 m.s -1 by kite instead of 2.02 m.s -1 by the classical rig (1.94 m.s -1 during sea trials). These results are consistent with figure 11 polar diagrams according to the fact that average wind speed during sea trials was 3.6 m.s CONCLUSION Figure 12: True Wind angle for kite and classical rig simulations. Relative wind angle β WR measured during sea trials appears to be not relevant to pilot a kite towed boat. Indeed, since boat velocities differ significantly, optimum working points have very different relative wind too. It was therefore chosen to pilot the kite towed boat according to true wind angle, in order to have similar trajectories. Manoeuvres were synchronized with sea trials ones. True wind angle orders given for the kite towed boat are shown in figure 12 and were deduced from velocity polar diagrams (figure 11) data for upwind and downwind Vmg. The dotted line exhibits sometimes some small gaps which are related to tack simulation. The green dotted line denotes the true wind angle seen by the classical rig boat. The rough shape observed is related to wind measurement dispersion. Furthermore, if upwind angle reached by the kite towed boat and the classical rig boat are close, it is absolutely not the case for downwind condition since kite propulsion enables a higher downwind efficiency thanks to the dynamic flight mode. Results have clearly demonstrated the significant benefit that would be provided by kite propulsion. As shown in figure 11, the most important benefit is provided by dynamic flight cases for the kite. In accordance with Dadd [3,4] initially proposed idea, this study demonstrated the advantage of vertical flight for upwind conditions. This interesting configuration seems to have been forgotten probably because of few kite towed ship studies existing in the literature in comparison with kite powered electricity supply studies [11]. This study has also highlighted the benefit of static flight case for small wind angles. Although this configuration does not match with an optimal working point for the sailing yacht investigated here, its benefit should be more visible for merchant vessels using kites as auxiliary propulsion device. The static flight case would also ensure benefits for reinforcing wind conditions and vessel stability issues. In such cases, the use of kite static flights should avoid issues related to kite size changes maneuvers which are weak points for kite towed systems. Although results were set on experimentally validated models, they are subjected to control command units that must be able to ensure reliable optimal flight trajectories. Required electrical supply for such control command units must still be estimated. Questions about woven fabrics durability and aerodynamic characteristics changes in tight turns remain open ended. ACKNOWLEDGEMENTS The authors of this paper are grateful to the French ministry of defense and Yves Parlier for their financial support. Figure 13: Classical rig and kite comparison. A trajectory comparison is shown in figure 13 where markers were put each 100 seconds to highlight time evolution of each boat. It is clearly demonstrated that kite propulsion enables a significant upwind performance benefit which is even higher in downwind condition. The analysis of the distance elapsed within 961 seconds shows that by kite propulsion the upwind Vmg reached is 1.86 m.s -1 instead of 1.57 m.s -1 by classical rig (1.54 m.s -1 REFERENCES 1. NAAIJEN, P & KOSTER, V. Performance of auxiliary wind propulsion for merchant ships using a kite. In : 2nd International Conference on Marine Research and Transportation, 2007, p RONCIN K., KOBUS J.-M., Dynamic simulation of two sailing boats in match-racing, Sports Engineering, 2004, Vol.7 no 3, p

286 3. DADD, G. M., HUDSON, D. A., SHENOI, R. A. Comparison of two kite force models with experiment, Journal of Aircraft, 2010, vol. 47, no 1, p DADD, G. M., HUDSON, D. A., SHENOI, R. A. Determination of kite forces using three-dimensional flight trajectories for ship propulsion. Renewable Energy, 2011, vol. 36, no 10, p ITTC Symbols and Terminology List International Towing Tank Conference, Version WELLICOME, J.F., WILKINSON S. Ship Propulsive kites an initial study. University of Southampton, Department of Ship Science, Faculty of Engineering and Applied Science, Tech. Rept. SSSU 19, LELOUP, R., RONCIN, K., BLÈS, G., LEROUX, J.- B., JOCHUM, C., PARLIER Y. Estimation of the effect of rotation on the drag angle by using the lifting line method: application to towing kites for auxiliary propulsion of vessels In: 13èmes Journées de l Hydrodynamique, Chatou, France, LELOUP, R., RONCIN, K., BLÈS, G., LEROUX, J.- B., JOCHUM, C., PARLIER, Y. Estimation of the lift-todrag ratio using the lifting line method: application to a Leading Edge Inflatable kite, Airborne Wind Energy, Springer, Ed. AHRENS, U., DIEHL, M., SCHMEHL, R., 2013, ch CLAUGHTON, A. Developments in the IMS VPP Formulations, In : Fourteenth Chesapeake sailing yacht symposium, Annapolis, Maryland, 1999, p RONCIN, K., KOBUS, J.-M., IACHKINE, P., & al. Méthodologie pour la validation du simulateur de voilier par des essais en mer, une première tentative, In : Workshop Science-Voile, 2005, p LOYD, M. L. Crosswind Kite Power (for large-scale wind power production), Journal of Energy, 1980, vol. 4, no 3, p AUTHORS BIOGRAPHY Richard Leloup is currently following a Ph.D. Degree at the graduate and post graduate school of engineering, Ecole Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne), Brest, Brittany, France. He graduated at ENSTA Bretagne in 2011 in naval architecture and offshore engineering. He is a member of the team which was launched in 2011 to work closely with the French sailor Yves Parlier on his Beyond the Sea project. His research focuses on modelling approaches and computational tools for kites sails kinematics and strengthening issues. Kostia Roncin is Associate Professor of Naval Hydrodynamics at the graduate and post graduate school of engineering, Ecole Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne), Brest, Brittany, France. He is currently the head of the Master of Science in Naval Hydrodynamics and gave during several years specialized lectures in naval construction and design. He received his Ph.D. degree (2000) with Honours from the University of Nantes, France. His research skills cover seakeeping, manoeuvrability and sail yacht dynamics. Guilhem Blès is Associate Professor of Mechanical Engineering and Materials Science at the graduate and post graduate school of engineering, Ecole Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne), Brest, Brittany, France. He is currently in charge of Naval and Offshore design courses. He received his Ph.D. degree (2002) with Honours from the University of Grenoble, France. His research skills cover woven fabrics and polymeric materials constitutive behaviours at large strain transformations. Jean-Baptiste Leroux is Associate Professor of Naval Hydrodynamics at the graduate and post graduate school of engineering, Ecole Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne), Brest, Brittany, France. He is currently in charge of fluid mechanics courses. He received his Ph.D. degree (2003) with Honours from the University of Nantes, France. His research skills mainly cover cavitation and hydrodynamics instabilities. Christian Jochum is Associate Professor of Mechanical Engineering and Materials Science at the graduate and post graduate school of engineering, Ecole Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne), Brest, Brittany, France. He worked several years in the Industry as head of the research department for a French supplier of track maintenance and construction equipment, involved in rigid body mechanics and structures design. He received his Ph.D. degree (1999) with Honours from the University of Metz, Lorraine, France. His research skills cover thermosetting composites from multiphysics couplings and internal stress issues to dynamical behaviour and strengthening. Yves Parlier has succeeded brilliantly in all the major nautical races and has strived throughout his life to promote respect for man and the environment. He has a graduate degree in composite materials and launched several innovations in sail yacht design. We remember the Vendée Globe 2000 when all alone, near an island off New Zealand, he successfully rebuilt and erected a new mast and finished his round the world voyage. Taking advantage of wind energy by using kites as auxiliary propulsion device is the aim of the Beyond the sea project launched by Yves Parlier.

287 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France ADVANCED STRUCTURAL ANALYSIS METHOD FOR AEROELASTIC SIMULATIONS OF SAILS S. Malpede, SMAR Azure Ltd, United Kingdom, F. D Angeli, SMAR Azure Ltd, United Kingdom, fabio@smar-azure.com R. Bouzaid, Doyle Sails, New Zealand, rbouzaid@doylesails.co.nz This paper presents an advanced method to predict the structural behaviour of modern fibermembrane sails and its validation by on-board sail photographic survey. The presented structural analysis method is an improvement of a direct stiffness method that shows good numerical stability and is able to treat nonlinearities with the same level of performance of a dynamic method, but less time consuming. In order to achieve this performance, a damping-like force has been added to the structural system. By tuning a damping factor, the behaviour of the structural analysis code can be switched from a classical static method to a dynamic-like one. Thus, this method allows running accurate analyses of fiber-membrane sails with battens by taking into account both the geometric nonlinearity and wrinkling behaviour of membrane structures in a timely manner. Furthermore, it is also very effective when sails are coupled with rigging elements, e.g. when the luff sag calculation is required. This advanced structural analysis method is coupled with a nonlinear vortex lattice method to enable a proper aeroelastic simulation of sails in upwind conditions, within the SMAR-Azure technology. The SMAR-Azure fully integrated aeroelastic analysis method has been extensively validated using on-board photographic survey. In this paper, the comparison between the calculated and the real flying sail shapes of the fiber-membrane sail plan of the 55ft race boat Living Doll is presented. NOMENCLATURE C Stiffness tensor (N.m -2 ) D Damping factor (N) F D Damping loads (N) F E External loads (N) F I Internal reaction loads (N) I Identity matrix ( ) K E Elastic stiffness matrix (N.m -1 ) K G Geometric stiffness matrix (N.m -1 ) Displacement (m) Strain vector ( ) 1 Principal Strain 1 ( ) W Wrinkling strain correction vector ( ) Stress vector (N.m -2 ) 1 Principal stress 1 (N.m -2 ) 2 Principal stress 2 (N.m -2 ) Wrinkling direction (rad) N Total Number of degrees of freedom NR Newton-Raphson FSI Fluid-Structure Interaction FEM Finite Element Model LOA Length Over All (m) LWL Waterline Length (m) AWA Apparent Wind Angle (deg) AWS Apparent Wind Speed (knots) TWA True Wind Angle (deg) TWS True Wind Speed (knots) BS Boat Speed (knots) 1 INTRODUCTION This paper presents an advanced structural analysis method used within the aeroelastic analysis tool developed by SMAR-Azure Ltd for the simulation of the structural behaviour of fibre-membrane sails. The structural simulation of sails is one of the challenging problems of the current marine engineering due to its strong nonlinearities. The aim of the work shown in this paper is the development of an accurate solution method that could be easily used in a timely manner in the everyday work of the sail designers. The paper describes the innovative theoretical approach to solve the finite element analysis for membrane sails and its validation via on-board photographic survey. The full fluid-structure interaction (FSI) solution turns out to be very robust and accurate. The code is able to solve even large sail-plan FSI problems in a reasonable time and is able to deliver the full optimization processes of sails on a simple Windows based personal computer. Specifically, Chapter 2 describes some of the main enhancements included in the SMAR-Azure structural code. The addition of a damping factor to the structural system increases the robustness of the code itself. The implementation of a robust wrinkling model increased the accuracy of the results. Furthermore, the possibility to include rig elements into the analysis make the SMAR-Azure analytical code able to take into account important aspects of the sail-rig system, like the influence of the forestay tension on the flying sail shape of headsails

288 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France Chapter 3 describes the experimental testing campaign carried out in conjunction with Doyle Sails New Zealand in order to validate and improve the code. 2 STRUCTURAL ANALYSIS METHOD 2.1 OVERVIEW The structural analysis code developed by SMAR- Azure Ltd to evaluate the flying sail shape of fibermembrane sails is a nonlinear finite element method. In particular, a direct stiffness method is used to solve the structural problem [1][2][3]. Since a nonlinear problem is solved, the Newton-Raphson s method is used to find the deformed equilibrium state of the structure. Geometric and wrinkling nonlinearities are taken into account. The stress-strain relation of the sailcloth material is considered as linear instead. Considering one step of the Newton-Raphson s (NR) algorithm, the structural system is linear and its behaviour is described by the equation: (K E + K G ) = F = F E - F I (1) The global stiffness matrices K E and K G are assembled adding the contribution of every finite element. CST (Constant Strain Triangular) membrane elements are used to model the sailcloth. The sailcloth can be modelled as made of an isotropic, orthotropic or anisotropic material. In case the real fiber layout has to be taken into account, a stacking procedure (classical lamination theory) is used to compute the anisotropic stiffness matrix of the laminate. Battens can also be included as beam elements. The wrinkling behaviour of the sailcloth is taken into account by a dedicated model that avoids compression stresses. The entire structural analysis can be coupled with a nonlinear vortex lattice method in order to obtain a proper fluid-structure interaction (FSI) simulation. F D = D (2) where D is a damping factor. Considering the i th row of the system of equations (1) and adding the damping force we obtain: N (K ij j ) = F i + D i (3) j=1 Extending the concept to the whole system, the equation (1) becomes: (K E + K G + D I ) = F (4) The addition of the damping diagonal matrix avoids the global stiffness matrix to become singular. Moreover, tuning the damping factor maintains the analysis stable. Indeed, increasing the damping factor D makes the analysis more robust but increases the number of Newton-Raphson iteration needed to get the equilibrium of the system. For that reason, it has been implemented an automatic adaptation of the damping factor during the analysis in order to get the best compromise between numerical stability and computational time. In Figure 1, the effect of the damping on the Newton-Raphson algorithm is explained. In that graph (Fig. 1), the slope of the tangent to the thick curve is proportional to the stiffness of the analysed structure. If that slope is almost horizontal, the system tends to be singular and the displacement would be unreasonably large. Adding the damping force increases that slope, avoiding the singularity of the linear system. 2.2 DAMPING-LIKE FACTOR One of the main issues of using a direct stiffness method with sail structures is its small robustness when the stiffness of the system becomes negligible. Indeed, the geometric stiffness K G is null at the beginning of the analysis because the sailcloth internal stresses are null. The elastic stiffness K E could have some zero-stiffness points as well because the out-of-plane stiffness of a membrane is negligible. For these reasons, the system of equations (1) could easily become singular and the solution diverges. In order to avoid diverging solution and improve the robustness of the code, a damping-like force has been added to the external loads. If we consider a step of the NR algorithm as a time-step, a damping force can be considered proportional to the incremental displacement of that particular step. Thus, for each FEM node, a damping force would be: Figure 1: Newton-Raphson algorithm with (red lines) and without (black lines) damping 282

289 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France In addition to the increased robustness of the code, this technique is also very effective when strong nonlinearities, like wrinkles, has to be taken into account. 2.3 WRINKLING MODEL points with the rig are applied on the rig finite element model. Once the rig analysis is performed, the displacements at the connection points are applied to the sail structure as imposed displacement constraint and the next NR iteration starts. A flowchart of the sail-rig coupling is shown in Figure 2. Since the stress-strain relation of a membrane element is linear, its stiffness under tension or compression is the same. This is not a realistic assumption because the sailcloth, having a negligible bending stiffness, cannot resist to a compressive load and it wrinkles. In order to predict that behaviour, a wrinkling model has been implemented [4]. At the end of each NR step, the strain state is evaluated for every membrane element and the related stress state is computed from the stress-strain relationship: = C (5) At that stage, a wrinkling state is evaluated according to a mixed stress-strain criterion: Taut: 2 > 0 Slack: 1 0 Wrinkled: 1 > 0 and 2 0 If a slack or wrinkled state is detected, a strain correction is computed and applied to the membrane element. Under wrinkling condition, the strain correction values satisfy the following relationship: [ 1 0 ] = C ( + w ) (6) 0 Indeed, when the sailcloth is wrinkled, only the stress along the wrinkling direction is positive ( 1 ). All the other components of the stress tensor have to be null. In order to make the convergence of the analysis easier, a relaxation factor is applied to the wrinkling strain correction. The wrinkling model works well with isotropic, orthotropic or anisotropic materials. In case of non-isotropic materials, equation (6) is solved upon the numerical computation of the wrinkling direction. 2.4 RIG COUPLING LUFF SAG Within the SMAR-Azure technology, the sail structure can also be coupled with the rig structures. An example of the coupled analysis features is the computation of the luff sag for headsails, which forestay bending has to be computed. When running rig-sail coupled analyses, the structural equilibrium for sail and rig are solved independently within each iteration. Two independent systems of equations are built and solved. From the sail analysis results, the reaction forces at the connection Figure 2: Sail-Rig coupling process Specifically, when computing the foresails luff, the forestay is modelled as a series of cable elements pinned at the ends. The internal tension of the forestay is considered constant during the whole analysis. The value of the sailing forestay tension is an input of the analysis. As a result, the converged forestay sag is not dependent on the mechanical properties of the forestay. 3 VALIDATION The SMAR-Azure has carried out a broad testing campaign in order to validate the structural and aeroelastic analysis code implemented for the solution of the sail-membrane structure as well as for the rig-sail structure. Specifically, the validation campaign has involved numerical simulations as well as experimental tests on-board. The present paper describes a specific experimental test carried out in collaboration with Mr. Richard Bouzaid, head designer of Doyle Sails New Zealand. The following sections describe the results of experimental tests carried out on a sailplan designed and optimised by Mr. Bouzaid using the SMAR-Azure technology for the boat Farr 55ft Living Doll (Fig. 3). The specifications of the boat Farr 55ft Living Doll are shown below. LOA = m LWL = m Beam = 4.57 m Draft = 3.50 m Displacement = 8980 kg It is important to say that one of the major problems of the testing campaign has been the retrieving of the flying sail shapes from the picture in known sailing conditions. 283

290 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France Figure 4: Flying shape of the Mainsail Figure 3: Photo of the Farr 55ft "Living Doll" Figure 5: Flying shape of the Jib ON-BOARD DATA The on-board photographic survey of the sail set Main+Jib2 (MJ2) is reported in this paragraph. Table 1 reports the wind condition of the sea trials. Table 2 reports the sails trimming conditions used in that wind condition. MJ2 TWS [Knots] 14 TWA [deg] 38 AWS [Knots] 21.4 AWA [deg] 23.7 BS [Knots] 8.6 HEEL [deg] 20 LEEWAY [deg] 4 Table 1: Wind data MJ2 Main [deg] 1 Jib [deg] 6.5 Table 2: Sails sheeting angles The forestay tension measured was N. During the sea trials, photos of the sails were taken. Figure 4 and 5 show the pictures of the Living Doll flying sails shapes used for the validation test described heretofore. The flying sail-shape was measured by evaluating the geometric characteristics of the sail sections at the draft stripes. The draft stripes are placed at 25%, 50% and 75% of the sail height. 3.2 NUMERICAL SOLUTIONS A full aeroelastic analysis of the sail plan and relative forestay interaction has been run. The sail plan FEM was built by 5143 membrane elements (3045 for the mainsail and 2098 for the jib), which was taking into account the real fiber layout, scrim and fill, as designed by Mr. Bouzaid. In order to carry the aerodynamic analysis out, wind data recorded on-board are used to define the boundary conditions (as from table 1). A logarithmic profile of the true wind speed is used to take into account the atmospheric boundary layer and the twist of the apparent wind direction. Sails were trimmed as in the sea trials (as from table 2), by moving the clew in the correct position. Some of the aeroelastic analysis results are described heretofore. In order to get the numerical solution of the flying sail shape, 8 aerodynamic and structural analysis iterations (FSI) were carried out. The resulting maximum displacement, which means the maximum difference between design and flying sailshape was 8.2cm for the mainsail and 15.4 cm for the jib. Figure 6 shows the aerodynamic pressure and the flying sail shapes compared with the design shape. From those two pictures, it is possible to note that the aeroelastic simulation is able to get a typical effect of the mainsailjib aerodynamic interaction: the jib makes the pressure on the luff of the mainsail to become negative (defined by the blue region in the pressure plot) and the cloth of the mainsail moves windward (defined by the green area in the flying sail shape plot). 284

291 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France Figure 7: Aeroelastic analysis results of the Mainsail. From left to right: principal stress 1 [Pa], principal stress 2 [Pa], principal strain 1 [%] Figure 6: Aerodynamic pressure (top) and deformed structural mesh (bottom) after the full aeroelastic analysis (or FSI) Figure 8: Aeroelastic analysis results of the Jib2. From left to right: principal stress 1 [Pa], principal stress 2 [Pa], principal strain 1 [%] Figure 7 and 8 show the principal stresses and strains on respectively the mainsail and the jib. The structural analysis takes into account the real fiber layout and finishing material of the sails thanks to the anisotropic formulation of the membrane elements. Thanks to the wrinkling model, the thermal plot of the principal stress 2 shows no negative stress in the sailcloth. Some wrinkled elements are shown in Figure 9, where direction and density of the lines plotted in each triangular element identify respectively the wrinkling direction and its amount. Figure 9: Wrinkled elements 285

292 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France The structural analysis of the jib has been coupled with the forestay, tensioned as measured during the sea trials. The resulting sag is shown in Figure 10. Figure 10: Forestay sag 3.3 COMPARISON The experimental validation test was carried out by comparing the flying sail-shape as evaluated by the SMAR-Azure aeroelastic code (FSI) with the one measured during the sea trials (see figure 4 and 5). Specifically, the main geometric data of the sail sections (camber, draft, twist) were extracted by analysing the draft stripes on the pictures taken during the sea trials. In order to compare the numerical flying sail shape with the one measured when sailing, it was necessary to extrapolate the same data from the numerical flying sail-shape (FEM mesh). Figure 11 shows the draft stripes on the numerical mesh and the draft stripes on the real sail shape. - the top section shapes are difficult to evaluate from the pictures, because of the smaller sail sections (they are actually flat) Figure 12 shows the comparison among the designed mainsail, the numerically calculated one and the real flying sail shape. From top to bottom, the camber, draft and twist measured at the draft stripes are plotted. Figure 13 shows similar comparisons for the jib 2. Considering the mainsail, it is possible to note that the SMAR-Azure code is able to evaluate the sail structural behaviour in a very accurate way. Indeed, both the numerical and the real flying sail shape indicate that the mainsail shape, when compared with the designed one, tends to be fuller (camber increases), the draft moves backward and the leech opens slightly in the middle and closes at the top (as shown from the twist graph). Considering the numerical and real mainsail flying shape, it is possible to note that camber and twist distribution along the sail vertical profile is accurately evaluated, while the draft shows a slightly higher discrepancy, which it is believed due to the difficulty to evaluate it using a graphical approach. As expected, the higher discrepancies are at the head section, because of the difficulty to measure it from the pictures. Figure 11: Mainsail qualitative comparison. It is important to say that discrepancies between the two measurements are expected for a number of reasons: - the computed flying sail shape is a discrete model formed by small flat triangular elements, although a fine granularity is used; - for the jib, the real luff sag is unknown Figure 12: Flying sail shape comparison of the Mainsail: from top to bottom, camber, draft and twist at the draft stripes. 286

293 The Third International Conference on Innovation in High Performance Sailing Yachts, Lorient, France Considering the Jib2, it is possible to note that both the numerical and the real flying sail shape indicate that the J2 shape, when compared with the designed one, tends to be fuller (camber increases), the draft moves backward and the leech opens. Looking at the flying sail-shape picture it is possible to note that the jib luff moves backwards (sags) causing an increase of the camber in the forward area. Considering the numerical and real mainsail flying shape, the results are very positive. Unfortunately, as the luff sag was not measured for the Jib2, it is difficult to appreciate the reasons for the higher discrepancy on the draft evaluation on it. Indeed, the twist and camber evaluated are almost identical. sailmakers and yacht designers. The extensive work of enhancement and validation carried out in conjunction with Doyle New Zealand led to excellent results. Further developments will concern the extension of the sail-rig coupling to the entire sailplan. Indeed, the whole rig could be included in the aeroelastic analysis and coupled with mainsail and headsails. It would allow taking into account the stiffness of the rig and the influence of the tuning of shrouds and stays. 5 ACKNOWLEDGEMENTS Special thanks to the technical team of SMAR-Azure Ltd, Dr. Donald W. MacVicar and Mr. Stephen Jordan, for their continuous and pro-active contribution to the development of the method and graphics presented in this paper. And thank you to Mr Michael Hyatt, owner of the Living Doll. 6 REFERENCES 1. MALPEDE, S, BARALDI, A, A fully integrated method for optimising fiber-membrane, Proceedings of the 3 rd High Performance Yacht Design Conference, MALPEDE, S., NASATO, F., A fully integrated sail-rig analysis method, Proceedings of the 2 nd InnovSail Conference, LEVY, R., SPILLERS, W.R., Analysis of Geometrically Nonlinear Structures, Springer, RENZSCH, H, GRAF, K, Fluid structure interaction simulation of spinnakers getting closer to reality, Proceedings of the 2 nd InnovSail Conference, AUTHORS BIOGRAPHY Figure 13: Flying sail shape comparison of the Jib 2: from top to bottom, camber, draft and twist at the draft stripes. 4 CONCLUSIONS A fully aeroelastic analysis tool (or FSI) for fibermembrane sails has been presented. The emphasis has been placed on the enhancement of the structural analysis code and its validation via on-board photographic survey. The increased robustness of the code due to the damping factor (section 2.2), the implementation of a robust wrinkling model (section 2.3) and the possibility to run sail-rig coupled analysis (section 2.4) made the SMAR Azure technology to become an effective and accurate analysis tool for Dr. Sabrina Malpede is the co-founder and Managing Director of SMAR Azure Ltd. Since 1997, she has been involved in developing a scientific approach for saildesign, firstly during her doctorate and then within SMAR Azure Ltd for the development of products and services required by the Industry. She is a graduate with honours in Aeronautical Engineering at the University of Naples (Italy), has a Ph.D. in Sail Design from the University of Glasgow (UK). Fabio D Angeli currently holds the position of Research and Development Engineer at SMAR-Azure Ltd. He is involved in the development of the aerodynamic and structural analysis methods of the SMAR-Azure Ltd technology. He graduated with honours in Nautical Engineering at the University of Genoa (Italy). 287