THE 20 th CHESAPEAKE SAILING YACHT SYMPOSIUM ANNAPOLIS, MARYLAND, MARCH 2011

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1 THE 20 th CHESAPEAKE SAILING YACHT SYMPOSIUM ANNAPOLIS, MARYLAND, MARCH 2011 Effective Wind Tunnel Testing of Yacht Sails Using a Real-Time Velocity Prediction Program David Le Pelley, University of Auckland, Auckland, New Zealand Peter Richards, University of Auckland, Auckland, New Zealand ABSTRACT Wind tunnel testing to determine yacht performance has been carried out for at least the last 50 years. A common perception is that experimental methods do not improve significantly over time. This paper shows how modern wind tunnel testing is still the only realistic way of providing a complete picture of aerodynamic performance over a full range of conditions in a rapid and cost-effective manner. The use of a Real-Time VPP and a sail shape recognition system combine to enhance the accuracy and repeatability of testing. The influence of examining boat speed instead of driving force is investigated. NOTATION A Area AWA Apparent wind angle CFx.A Drive force area coefficient Cl.A Lift force area coefficient CMx.V Roll moment volume coefficient Cl Lift coefficient Fx Drive force Fy Side Force Mx Roll moment Mz Yaw moment TWS True wind speed VMG Velocity made good Vs Boat speed 1. INTRODUCTION Wind tunnel testing of sails at model scale offers a costeffective method of accurately predicting yacht performance at an early stage. This paper looks at how recent advances in wind tunnel modelling combine the sail trimmer s experience with a Real-Time Velocity Prediction Program (RT-VPP), allowing not just the sails but the yacht s performance as a whole to be evaluated. Wind tunnel testing allows both trimmers and designers to see the candidate sails flying at an early stage. From a purely visual perspective, this is a very powerful tool that provides useful information. The sail is then tested over its full range of conditions. Traditionally, the data is then post-processed and made into curves of lift and drag coefficients and centre of effort locations. These are then run through a standard VPP to determine the sail s performance. One of the main problems with this method is that, by the time the results are produced, the test session has finished and there is no opportunity to recut or rebuild sails based on the lessons learnt. Computational Fluid Dynamics (CFD) simulation of sails has increased rapidly over the last few years. Whilst Vortex Lattice Methods can accurately model upwind sail behaviour in an efficient and accurate manner, offwind sail CFD is still in its infancy. To avoid the use of turbulence models completely (ie. direct numerical simulation) a model with the order of 30 billion cells must be used even for a scaled yacht in a wind tunnel [Viola and Ponzini, 2008]. Whilst simulations have been achieved with 1 billion cells, no iteration on sail shape has been performed and computation times are in the region of 170hrs on 512 CPUs. If the number of cells is reduced to a sensible size to allow iterations with a membrane code in a realistic time frame for non-academic use, some degree of turbulence modelling must be used. Various studies [Viola 2009, Wright et al., 2010] have shown the limitations of turbulence models and the difficulty of achieving a similar result using different methods. With the assumption of computer power doubling every two years, in the not too distant future it will be possible to carry out accurate downwind CFD. However, at the present time it remains the domain of the wind tunnel. The approach detailed in this paper represents a more holistic way of wind tunnel testing. When all of the systems available are used together in a cohesive way, the results are all produced in real time, and the clients are able to walk away with the final results immediately after the final test. 93

2 2. WHY USE A REAL-TIME VPP? 2.1 Historical testing Offwind sail testing has changed significantly in the last 10 years. This is demonstrated dramatically by the Volvo Round the World yachts. The VO60s, prior to the race, used asymmetric and symmetric spinnakers set on poles, and much of the flying sail performance was centred around optimum downwind Velocity Made Good (VMG) at Apparent Wind Angles (AWA) of º. Heel angles were generally small. Today s much more powerful VO70 yachts have asymmetric spinnakers with huge overlaps flown from a bowsprit, with canting keels to increase stability. This leads to higher boat speeds which bring the AWA forward, and increased heel angles. The limiting state for reaching is now often not lack of stability but lack of lift from the keel or rudder combined with seaway limitations. This evolution is also epitomised by the previously proposed America s Cup AC33 monohull which would have had achieved optimum downwind VMG at an AWA of less than 40 degrees in light airs. Historically, offwind sail testing has been carried out either upright or at a fixed heel angle depending on the AWA being tested [Claughton and Campbell, 1994]. At each AWA, the sails are trimmed for maximum driving force and the point recorded. The sails are then progressively depowered by dropping the traveller and easing the sheet and several points recorded over this sweep. On completion of the testing, the data is then converted into lift and drag coefficients and centre of effort locations. Fair curves of these variables then need to be created for input into an offline VPP. Whilst this is relatively straightforward for upwind sails, it is much harder for offwind sails, especially if multiple heel angles have been investigated, to make these curves fair enough for VPP input such that one can be confident that the VPP will find the global maximum rather than just a local maximum. This is due to effects such as varying amounts of separation on the sails, non-linear effects such as interference with the water surface or the deck edge and also the trend for flying sail driving force to increase with small heel angles before dropping again. The original forces and moments usually conform to fair curves much better than the decomposed lift and drag. The data is then entered into the VPP for each sail. When run, the VPP converts all of the lift and drag data back to aerodynamic forces and moments to balance against the hydrodynamic data at each point of iteration. In its simplest form, the VPP is then free to chose suitable values of REEF, FLAT and TWIST to cope with the sail depowering. Ongoing improvements to these original techniques have been made. Several studies have shown the inability of REEF and FLAT to cope with depowering offwind sails and work has been done to develop improved depowering models [Hansen, 2006, Claughton et al., 2008, Ranzenbach and Teeters, 2002]. The process is also streamlined by modifying the VPP to read direct force and moment data from experimental testing instead of converting to lift and drag coefficients [Hansen et al., 2003]. Without running the data through a VPP, the trends are impossible to distinguish. Particular sails may produce more driving force but create too much heeling moment. Even using the method described by [Wright et al., 2010] of creating a nominal maximum heeling moment line to discard runs which would heel excessively, the effects of roll moment, side force and yaw moment with speed cannot be examined. Indeed, it is more likely for a modern offshore racer with canting keel to stall the keel or rudder before reaching a limiting stability condition at many points of sail, and at other times the sea state will be the limiting factor. 2.2 A holistic testing approach Wind tunnel sail testing falls very much into two categories: research work and commercial sail testing. Testing for research purposes and developing handicapping VPPs [Teeters et al., 2003, Claughton et al., 2008] still requires knowledge about the physics of the flow and needs to ensure that results are valid for a wide range of conditions. The existing approach outlined above still offers many advantages in this case. This paper deals almost exclusively with commercial sail development testing. Here, the aim is to produce the most accurate simulation possible whilst presenting the results clearly in a format which can be understood by sailors, owners and sail designers. Once either the wind tunnel or CFD starts introducing more questions than answers, clients will rapidly revert to rule of thumb design. It is also extremely important to produce the right results on the day. As many as 10 people may attend the testing session, and it s all too easy to take away the wrong impression by viewing a single result out of context, or having a visual impression without the matching performance. This is also often one of the few times that the sailors get to speak with the designers. To this end, the testing approach described here is aimed at not only measuring the performance in real time, but producing the final results instantly in an understandable format. 3. EXPERIMENTAL TESTING 3.1 Physical setup The Twisted Flow Wind Tunnel at the University of Auckland has been well documented before [Le Pelley and Hansen, 2003, Hansen, 2006]. A scale yacht model is positioned on a force balance on a rotating turntable in the 7m wide x 3.5m high open jet. Upstream, vanes and roughness elements are used to create the required twist and velocity profiles respectively. Figure 1 shows a picture of the model yacht installed in the wind tunnel. 94

3 Figure 1 - Model installed in the wind tunnel showing twisting vanes upstream The trough, which the model sits in, is filled with water, to represent the full scale condition by eliminating air flow and pressure leakage beneath the hull, whilst not transferring any force from the yacht to the ground. Tests [Hansen et al., 2005] have shown that even the smallest gap, as must be left if sealing the gap with solid board, produces a significant difference to the pressure distribution on the hull and therefore the final yacht forces. Improvements to the physical setup for the RT-VPP include a heel driver linked directly to the force balance. The initial design took the form of a small servo motor attached to the yacht s frame, with an accelerometer to provide angle feedback. However, this has recently been replaced with a linear actuator with inbuilt potentiometer, which offers greater accuracy, repeatability and speed. Heel rotations of 30degs can be achieved in about 5s, with custom ramping to minimise inertial forces. To cope with the significant changes in buoyancy and rotating weight of the model, a simple calibration is done before testing to remove the heeled tare forces. The model with sails present but no wind blowing is heeled in increments of 5degs and the voltage values of each of the transducers is recorded at each angle. A fair polynomial is then fitted through each balance channel, which can be checked and altered by the user. When the tests are later run, the program stores the angle at which the model is zeroed (eg. 15degs) and then interpolates along each polynomial in real-time to remove the static heeled forces. Unpublished work has led to an improved understanding of the effects of twist and velocity profile on sail performance, and as such the twist is now varied depending on both performance and AWA in a premeasured, repeatable fashion. The velocity gradient is also modified, depending on the AWA, between upwind, closereaching and deep-reaching scenarios. This is done by adjusting the vertical distribution of a set of horizontal bars which span the upstream section of the wind tunnel (seen upstream of the twisting vanes in Figure 1). All of these changes are made in a matter of seconds between runs. The model has remote-controlled electric winches which allow the sail trimmers to adjust the sails exactly as they would do at full scale. A range of both numerical and visual feedback systems is available to enable the trimmers to find the optimum sail performance for each test condition. The camera-based sail and rig shape system VSPARS [Le Pelley and Modral, 2008] is used in the wind tunnel as an important tool to help the retrimming and also to provide real-time shape recognition. Miniature cameras mounted on the yacht automatically detect coloured stripes on the sails. One camera with a fisheye lens is used to capture the headsails and one camera with a conventional wide angle lens is used for the mainsail and rig deflection. The stripe images are converted to three dimensional sail shapes in real time by knowing information about the lens distortion, the position of the cameras and the length of the stripes. The output variables from the RT-VPP are streamed to the VSPARS computer so that acquired sail shapes have the run number, AWA, boat speed, etc stored with the results, which can be used subsequently in the VSPARS filterable database. Knowledge of the sail shape both allows trimmers to accurately repeat previous sail trims and also allows sail designers to assess the impact of quick changes to sail geometry for retesting. For static offboat pictures, cameras are mounted overhead and on arms which rotate with the turntable. A typical VPSARS output, with a target shape for depowered trimming, is shown in Figure 2. Figure 2 -Comparison of fully powered and depowered sail shapes viewed from above in VSPARS software 3.2 First principles RT-VPP This has been detailed by Hansen et al. [2003]. This system consists of the main data acquisition program SailView, developed by the University of Auckland, interfacing with the standalone FS Equlibrium VPP from FutureShip. The force and moment data is converted to lift and drag coefficients and centre of effort locations and sent via shared memory to the VPP. A switch in the VPP results in 95

4 this data being used instead of the conventional offline rig module, otherwise the VPP runs as normal. Each solution is then sent back to SailView and displayed. A yacht is defined through use of hull offsets and appendage displacement information for calculation of the hydrostatics. The hydrodynamics can then either be defined from first principles or by loading experimental or CFD data. A first principles approach defines the hydrodynamic characteristics of the hull and appendages in a conventional manner, using effective drafts and lift curve slopes. If precalculated hydrodynamic data is used, the user must manually fit the response surfaces to each variable. This approach offers a way of systematically looking at the aerodynamic influence of design. The parameters of the VPP, the number of degrees of freedom and the activation of different modules can all be adjusted whilst running. However, significant effort is involved with acquiring and formatting the data. 3.3 Simple RT-VPP Whilst the first-principles VPP offers a way of testing the effects of fundamental geometry changes in real time, it runs the risk of producing a different set of answers for a client due to it being a different VPP and possibly handling the balancing equations in a different manner. The vast majority of yachts tested in the wind tunnel have already been through the (experimental or numerical) towing tank, and their hydrostatic and hydrodynamic data is already well defined. In this case, the Simple RT-VPP uses this hydrodynamic data directly. This hydrodynamic data consists of the independent variables (speed, heel, leeway and rudder) and the dependent variables (Fx, Fy, Mx, Mz). For input into the software, this matrix needs to be squared out by ensuring that all combinations of the independent variables are present. Also, the dataset is extrapolated beyond the normal sailing conditions. This is to ensure that, during trimming, the VPP converges as frequently as possible even at infeasible sailing situations to avoid excessive iterations associated with failure and corresponding software lags. The hydrostatic righting moment curve is also provided in the input file, which again is invariably easily available at the design stage. The full process from measurement of forces in the wind tunnel through to equilibrium is described in Figure 3. As it can be seen, this is not a VPP in the true sense, rather a force balancing algorithm, hence the name Simple RT-VPP. Typically, an upper limit of 30 iterations is set using criteria that the drive force residual be less than 1%, the side force less than 2% and the yaw moment less than 5%. A failed solution (ie. 30 iterations) takes about 1s to process, whereas a converged solution takes approximately 0.2s to return a result. An added advantage of using the RT-VPP is that it allows a direct comparison with full scale performance. If boat speeds have been gathered whilst sailing on similar boats, they can be compared at run time in the wind tunnel to validate the simulation or detect problems in the setup. Measure raw forces, moments and dynamic pressure in wind tunnel Calculate force-area and moment-volume coefficients Calculate full scale forces and moments using AWS Balance aero and hydro Fx, Fy, Mz by iterating AWS converged? YES Move model to predicted heel angle Display speed, leeway, rudder, heel NO - iterate AWS Figure 3 Simple RT-VPP flow chart 4 EXAMPLE RESULTS servo changes heel 4.1 VO70 sail development A large number of tests on the Volvo Open 70 class have been carried out in order to optimise the sail development. Significant changes in the class rule for the race have seen the number of sails cut to 17 for the entire race, including restricting the number of masthead spinnakers to 2. Ironically, with fewer sails to be used more and more time and resources are spent ensuring that each sail performance is optimised and also that the performance of that sail is well known over all conditions, potentially saving valuable on-water testing time. The processes used in the wind tunnel are illustrated here with reference to tests performed in 2010 on a 1:14 scale model of a Volvo Open 70, for a wide variety of sails. A description of the sails typically tested is presented in Table 1. 96

5 Sail MH0 A3 A4 A6 J1 J4 Description Masthead code 0, tight luff, flat Masthead intermediate Masthead downwind, flying luff, deep Fractional heavy weather spinnaker Upwind fractional overlapping genoa Small non-overlapping genoa Table 1 Description of sails tested 4.2 Free v. fixed heel The testing process involves taking performance measurements of each sail over a surface of AWAs and True Wind Speeds (TWS). So for each AWA, a number of TWS values are simulated in the RT-VPP. One way of doing this is to pick say every 2kts TWS to test each sail at. Then for a genoa one might test at 8, 10, 12, 14, 16kts at 30awa. The model is allowed to dynamically free heel at each TWS until equilibrium is reached for a particular trim. This takes less than 10s to achieve. Whilst one advantage of this method is that all sails will be tested at identical increments of TWS, it is not ideal as different sails will respond differently to the increment in TWS. So a genoa may see a 5 degree change in heel angle for each TWS change of 2kts, whereas a deeper offwind sail may not change heel appreciably for this difference. Remembering that the only physical difference we are interested in is the change in performance with heel and trim, it is more sensible to ensure that a full range of heel angles are covered by the simulated TWS increments. The preferred method of testing to incorporate this, instead of using fixed TWS increments, uses fixed heel increments. For the initial measurement at each AWA, the model is constrained at 0 degrees heel. An initial TWS is set such that a heel angle of 0 is predicted. As there is a positive righting moment when unheeled even for noncanting keel yachts due to the crew weight, the resulting TWS will always be greater than 0. The trimmer then optimises the boat speed by modifying sail trim at this fixed TWS. When the trimmer is happy with the sail shape, the forces and moments are acquired over a longer period. At the end of this acquisition, the RT-VPP uses the acquired forces and moments to solve for the final equilibrium condition. However, because the sail was retrimmed since setting the TWS initially, the predicted heel angle is unlikely to remain at 0 degrees. To fix this, the RT-VPP now iterates the TWS and re-solves until the predicted heel angle is 0. The model is then heeled to the next fixed angle (eg. 8 degrees) and the process repeated. The TWS is modified initially and the trimmer uses that to optimise the boat speed. On acquiring the forces, that TWS is modified to the final value for equilibrium. In this way, the RT-VPP solution is delivered in real time for exactly the TWS required to match the heel condition. This produces a number of surfaces for each sail of variables against AWA and TWS. If necessary, this surface can also be interpolated at fixed TWAs. The raw force and moment variables from the wind tunnel are not used, as they do not take into account small variations in the dynamic pressure which occur for each run. Instead, the forces and moments are divided by the dynamic pressure in the wind tunnel, to give force-area coefficients (e.g. CFx.A for drive force, Cl.A for lift force) and moment-volume coefficients (eg. CMx.V for roll moment). Each RT-VPP solution is saved in the main data file on a network drive. From here it is automatically loaded into a custom-made surface plotting software package. Immediately on completion of the run, the user can see the 3D surface plot of any variable (e.g. Vs, CFx.A, Cl.A in heeled plane, etc) and how this surface intersects with other sails. The best sail at any condition, and how much faster it is than the next best sail, can be instantly determined. Figure 4 shows an example surface plot for a typical IMS offshore racing yacht of drive force area coefficient. Figure 4 - Typical sail chart plotted in real time for IMS offshore racing yacht 4.3 Solving for varying hydrodynamic configurations The method outlined above predicts the performance for one particular condition of one particular boat. In reality, it is necessary to solve for different sailing conditions, (eg. varying amounts of daggerboard, crew weight) and also different candidate designs. Aerodynamically, what has been achieved up to this point is purely the matching of the correct sail trim to a particular heel angle. It is then possible to investigate different sailing conditions and boats by simply 97

6 recalculating the performance at each heel angle using the modified hydrodynamic and hydrostatic data, and recalculating the TWS required to make the predicted heel angle equal the physical heel angle. For example, Boat A is tested at 30AWA and 15 degs heel in the wind tunnel. The RT-VPP predicts that the TWS required to achieve this heel is 8.5kts and that the boat speed will be 6.8kts. The designer then wants to know how Boat B performs, which has slightly more righting moment than Boat A. The wind tunnel data is reprocessed using Boat B s hydrostatic and hydrodynamic data, and the RT- VPP predicts that the TWS required to achieve a heel angle of 15degs is now 8.7kts and the boat speed is 6.95kts. With a single point, it is difficult to deduce the faster boat as each has a predicted boat speed at a different TWS. However, when the whole depower curve, or the whole AWA surface, is reprocessed the faster boat becomes obvious. This approach can also be used in order to determine the optimum amount of daggerboard to be used at a particular condition. Care must be taken here as the method assumes that the behavior of performance with heel angle is similar for each candidate under consideration. If, for example, the daggerboard immersion is changed from 100% to 25% the effects of heel on the induced drag and resulting boat speed will probably be significant. For this reason, the best guess at daggerboard percentage is selected at run time by the operator for each condition, and the relevant hydrodynamic file is used in the RT-VPP. The wind tunnel results can then be reprocessed for changes in daggerboard immersion. The main reason for doing this is to ensure that the sail is being simulated in its optimum condition so that its crossovers with other sails is correctly determined. Running multiple hydrodynamic configurations like this can be done in real-time so that the optimum daggerboard immersion is predicted at runtime, but this adds unnecessary complexity and it is usually more suitable to post-process the acquired wind tunnel results in batches whilst other testing is occurring. An example of this is shown in Figures 5 and 6. Daggerboard immersions of 25%, 50%, 75% and 100% were simulated in the RT-VPP and the best performance in terms of boat speed is shown. In general, as the wind speed increases and the sails depower, less daggerboard is needed to maintain optimum speed. Figure 5. Best daggerboard configurations for MH0 (looking down on surfaces of boat speed) Figure 6. Best daggerboard configurations for A3 (looking down on surfaces of boat speed) 4.4 Whether to use drive force or boat speed? Whether using the free or fixed heeling methods described in Section 4.2, the TWS is constrained during the trimming period and it is therefore possible to use boat speed to optimise the sail shape. The limitations of using driving force as a performance indicator are perhaps well known, but have been examined in more detail here. Figure 7 shows a cut taken through the performance surface at 30AWA. At this stage, the RT-VPP has not been run so the TWS has not been calculated. The drive force area is therefore plotted against the rolling moment volume, which does not distinguish between the effects of changing the heel and physically changing the sail trim. The figure shows the A3, which is a deep sail with quite a loose luff, creating more driving force than the flatter MH0 until the rolling moment reduces by about 20%. In this case, that equates to the A3 producing the same driving force at 15degs heel as the MH0 does when upright. The most efficient sail 98

7 combination is shown to be the J1 with a reef in the mainsail. When the wind tunnel forces are processed by the RT-VPP, the drive force can then be plotted against the calculated TWS such as in Figure 8. Here we see a more a more useful trend, with the J1 outperforming the J1-reef until a TWS of about 12kts. The A3 produces more drive force than the MH0 up to about 7kts TWS. Finally, in Figure 9 the calculated boat speed from the RT-VPP has been plotted against the TWS. This shows a significant change in the ranking which is not otherwise obvious from the testing. Whilst the A3 produces more driving force, the extra roll moment, side force and yaw moment create increases in the leeway and rudder angle of 0.5degs and 3degs respectively compared to the MH0. This leads to a lower boat speed, and in fact the A3 is never chosen at this angle. The rest of the plot shows a logical progression of sail selection from MH0 to J1 to J1-reef to J4 to J4-reef. At this stage, a jib of intermediate size was still to be tested to fill the gap between the J1 and J4. Figures 10 and 11 show similar trends in the differences of examining driving force or boat speed. In general, the larger, fuller sails such as the A4 are less prevalent when examined using boat speed as the increase in driving force they produce comes at the cost of increased leeway or rudder angle. MH0 A3 J1 J1 reef J4 J4-reef TWS (kts) Figure 9 - Boat speed plotted against calculated VPP TWS at 30awa MH0 A3 J1 J1 reef J4 J4-reef Figure 10 - Selected sails plotted with best drive force area as the variable CMx.Vol Figure 7 - Drive force area plotted against roll moment volume comparison at 30awa MH0 A3 J1 J1 reef J4 J4-reef TWS (kts) Figure 8 - Drive force area plotted against calculated VPP TWS at 30awa Figure 11 - Selected sails plotted with best boat speed as the variable. 99

8 5. CONCLUSIONS A holistic approach to wind tunnel testing sails has been presented. Several systems have been linked to form a network that produces accurate results in real time. The importance of providing accurate and final results during and immediately at the end of a wind tunnel session has been demonstrated. Example results have shown that it is important to consider the yacht as a whole and that the driving force alone is not a good indicator of performance. The ability of the wind tunnel system to predict performance of different hydrodynamic designs has also been presented. Viola I.M., Ponzini R., Sailing yacht computational aerodynamics: An investigation in RANS capabilities with large computational resources, Presentation to International ModeFRONTIER, Mestre, Viola, I.M., Downwind sail aerodynamics: A CFD investigation with high grid resolution, Ocean Engineering, Elsevier, Vol 36 Iss , Wright A.M., Claughton A.R., Paton J., Lewis R. Offwind sail performance prediction and optimization, 2 nd InnovSail Conference, RINA, France, REFERENCES Claughton A.R., Campbell I.M.C., Wind tunnel testing of sailing yacht rigs, 13 th HISWA Symp., Netherlands, 1994 Claughton A., Fossati F., Battistin D., Muggiasca S., Changes and development to sail aerodynamics in the ORC international handicap rule, 20 th HISWA Symp., Netherlands, Hansen H., Jackson P.S. and Hochkirch K. Real-Time Velocity Prediction Program for Wind Tunnel Testing of Sailing Yachts, The Modern Yacht Conference, RINA, Southampton, Hansen H. Enhanced Wind Tunnel Techniques and Aerodynamic Force Models for Yacht Sails, PhD Thesis, The University of Auckland, Auckland, Hansen H., Richards P.J. and Hochkirch K. Advances in the Wind Tunnel Analysis of Yacht Sails, 26th Symposium on Yacht Design and Construction, Deutscher Boots- und Schiffbauer-Verband, Hamburg, Le Pelley, D.J. and Hansen, H. "An Investigation into the Effects of Heel on Downwind Sails", The Modern Yacht. RINA, Southampton, Le Pelley D.J., Modral O. Flying shape and rig position comparison and quantification using imaging techniques, 3 rd High Performance Yacht Design Conference, RINA, New Zealand, Ranzenbach R., Teeters J., Enhanced depowering model for offwind sails, 1 st High Performance Yacht Design Conference, RINA, Auckland, Teeters J., Ranzenbach R., Prince M., Changes to sail aerodynamics in the IMS rule, 16 th Chesapeake Sailing Yacht Symp.,