Date Author Mdress October, 2007 Keuning, J.A., M. Katgert and A Mohnhaupt Deift University of Technology Ship Hydromechanlcs Laboratory Mekelweg 2, 26282 CD Deift TU Deift DelftUnlversltyof Technology The use of a maneuvering model for the optimization of the tacking procedure of an IACC sailing yacht by l.a. Keuning, M. Katgert and A. Mohnhaupt Report No. 1550-P 2007 Presented at the International Conference The Modern Yacht, 11-12 October 2007, Southampton, UK. Organized by the RINA, ISBN: 978-905040-39-1 Page lof 1/1
INTERNATIONAL CONFERENCE THE MODERN YACHT 11-12 October 2007, Southampton, UK PAPERS THE ROYAL INSTITUTION OF NAVAL ARCHITECTS lo UPPER BELGRAVE STREET, LONDON., SW1X 8BQ Telephone: +44 (0)20 7235 4622
RINA THE MODERN YACHT 11-12 October2007 2007: The Royal InstitutiOn of Naval Architects The Institution is not, as a body, responsible for the opinions expressed by the individua1-authorsor speakers THE ROYAL INSTITUTION OF NAVAL ARCHITECTS 10 Upper Beigrave Street London SW1X 8BQ Telephone: 020 7235 4622 Fax: 020 7259 5912 ISBN No: 978-l-905040-39-1
CONTENTS What Rules and Regulations Should You Apply to the Construction of Mega Yachts Over 3000 GT? J. Strachan, Burness Corlett - Three Quays, UK B. Mclligott, Lloyd's Register of Shipping, UK United Kingdom Regulation of Yachts. 15 W. Ralph, Maritime and C'oastguard Agency, UK. New Rulés For New Designs.. 23 Thiberge, B. Collier and M Pachot, Bureau Ventas, France. Development and Implementation of Heideck Requirements for Yachts. 31 I. Lardner, Maritime and C'oastgzard Agency, UK. RCD Scantling Assessment Process - A UK Notified Body Evaluator's 37 Perspective. R. Loscombe Southampton Soient University /RYA. scantling evaluator, UK Multi Faceted Inspection of Composite Marine Structures. 47 R. Gregory, Composite Inspection Ltd, UK New RINA Approach for Structural Scantlings in GRP Yachts. * L. ScarpatiandF. Cartti, R[NA, Italy. Impact on Marine Laminates. 53 L. & Sutherland and C Guedes Soares, Technical University of Lisbon, Instituto Superior Técnico, Portugal Custom Composite Structural Design of Components For The Modern 63 Superyacht. A. Shimell, and M Eaglen, J. Anderson, High Modulus, New Zealand Project Gemini - Design Development and Engineering of The World's Largest 71 Saffing Catamaran. i Lawless, J. Roy and J. Bonafoux, BMTNigel Gee Ltd. UK M Maurios, Van Peteghem - Launiot Prévost. France. "Into The 21st Century" - The Shape of Superyachts To Come?. R. Harvey, Ray Harvey Design / Southampton Soient University, UK 79 Noise and Vibration Considerations in Mega Yachts. 91 M Insel, Istanbul Technical University and Turkish Loyd, Turkey YUnsan, Istanbul Technical University, Turkey ASTTan g, Hong Kong Institute of Vocational Education, Hong Kong SAR, China The Voller Energy Concept Fuel Cell Yacht. 101 R. Olingschlager, Voller Energy, UK 2007: The Royal Institution of Naval Architects
Aerodynamic of Modern Square Head Sails : A Comparative Study Between 107 Wind-Tunnel Experiments and RANS Simulations A. B. G. Quérard, University of Southampton, UK P. A. Wilson, University of Southampton, UK Measürement of Accelerations and Keel Loads on Canting Keel Race Yachts 115 M Hobbs And P. Manganelli, SP, UK (* SP is The Marine Business of Gurit Are Daggerboards and Trimtabs Necessary When Sailing Upwind With.A 123 Canting Keel? G. S. Barkley, Southampton Soient University, UK D.A. Hudson and S.R. Turnock University of Southampton, UK. D.R.B. Spinney, BMT Defence Services Ltd, UK The Use of a Maneuvering Model for The Optimization of The Tacking 135 Procedure of an IACC Sailing Yacht. J. A Keuning and M Katgert, Delfi Shiphydromechanics Laboratory, The Nether1ands A. Mohnhaupt, United Internet Team, Germany. Including Human Performance En The Dynamic Model of A Sailing Yacht: 143 A Matlab -Simulink Based Tool M Scarponi, and P. Gonti, University of Perugia, Italy. R. A. Shenoi and S R. Turnock, University of Southampton, UK Hydro-Impact and Fljiid Structure Interaction of Racing Yacht. 157 F.J. Lee andp.a. Wilson, University of Southampton, UK Authors' Contact Details 165 * Unavailable at the time of publishing. 2007. The Royal Institution of Naval Architects
TIlE USE OF A MANEUVERING MODEL FOR TIlE OPTIMIZATION OF TRE TACKING PROCEDURE OF AN IACC SAILING YACHT J A Keuning and M Katgert, Dem Shiphydromechanics Laboratoiy, The Netherlands A Mohnhaupt, United Internet Team, Germany SUMMARY Following previous papers on the formulation of a maneuvering model for sailing yachts by Deffi Shiphydromechanics Laboratory, further improvements have been made to a number of the generic expressions originally presented to determine the coefficients of this model. In particular the side force production by the keel and the rudder, also in each others presence, has been improved. New experimental results have been incorporated to account for the influence of downwash and heeling angle. In cooperation with the 2007 JACC team United Internet Team Germany the model has been used to get more insight in what is going on during a tack and if possible to find ways to optimize the tacking procedure. With the data available from both dedicated tests with the design in the wind tunnel and the towing tank the coefficients in the maneuvering model have been fine tuned to fit the German IACC contender. Subsequently the model has been used to analyze different rudder and trim tab operating procedures to find an "optimal" tackingprocedure. The results of this study are presented here. NOMENCLATURE CL CD CD+I Lifi coefficient Drag coefficient Drag + induced drag coefficient Leeway angle 13 cb Downwash angle Are Effective aspect ratio I. INTRODUCTION In 2004 and 2005 De Ridder, Keuning and Vermeulen [Ref 1] presented a mathematic model for the maneuvering of a sailing yacht. This model was based on a model presented earlier by Masuyama [Ref 2]. For the determination of the hydrodynamic coefficients of the maneuvering model Keuning and Vermeulen presented generic expressions by making use of the extensive results of the Dem Systematic Yacht Hull Series (DSYHS) and for some of the particular forces and moments in yaw they relied on expressions developed earlier in 2003 by Keuning and Vermeu.len and presented in [Ref 3]. For the determination of the aero forces and moments in the maneuvering model use was made of similar expressions as used in the Velocity Prediction Program (VPP) of the Lnternational Measurement System (ilvis). For a more detailed déscriptioti of the maneuvering mathematical model reference is made to these publications because such a description is outside the scope of the present paper. The simultaneous solution of all the coupled equations of motion of the maneuvering model in surge, sway, roll and yaw in the time domain yields a simulation type result. This enables all the variables to be plotted against the time during the maneuvers and so their mutual relations in the time can be viswli7ed. Also by imposing different-procedures onihe input signalssuch as forward speed, rudder and trim tab action, the rudder and trim tab procedure could be optimized for, as an example, minimal speed loss. It was exactly this kind of use that brought the United Internet Team Germany to contact the Dem University to investigate the possibility for a joint research in the possible application of the aforementioned model for an IACC type of boat tack optimization. From the onset of the project it was clear that not all the generic coefficients would yield accurate results for an IACC type of boat, because quite a few of the parameters describing the hull and appendage geometry are far out of the range covered by the DSYHS. Therefore the results of tank tests, wind tunnel tests and D calculations, carried out by the United Internet Team of Germany on their IACC design, were used to reformulate or replace the appropriate terms in the equations of motions. By doing so, a more "dedicated" version of the maneuvering model was generated for use in this specific project. It should be noted that the formulation of the set of overall equations in the dedicated model was kept the same as with the original maneuvering model, as presented in [Ref 1-]. Using the onboard measurement system of the IACC boat a series of full scale tests have been carried out to validate the results of the simulations using this now dedicated model. These comparisons were made with- the boat sailing on a straight and steady course as far as possible. If these results showed a good enough correlation between the simulations and the full scale measurements the next step was to use various rudder and trim tab procedures in the model and to find the best possible procedure. In the optimizing process special attention was paid to the variation in time during the cxccuted-taek-of-the-effcctjvc angle-of attack.ofthe_water 2007: The Royal Institution of Naval Architects 135
flow on the rudder, due to the changes in forward speed, the downwash of the keel and the rate of turn in yaw, and the effect of the resistance increase due to the turtiing of the boat. 2. MODIFICATIONS TO THE MATHEMATICAL MODEL Alter careful examination of the various force and moment components in the mathematical model and the data from which they were derived as well as considering the more specific data available for the IACC boat it was decided that the following modifications to the orginal model should be carried out: In the original model no provision was made for the presence of a trim tab on the keel. In the dedicated model this presence should therefore be accounted for. This resulted in a change (shift) of the lift curve slope with the angle of attack and a change in the drag coefficient, all these as function of the trim tab angle. The hydrodynalflic forces and moments generated by the rudder are derived using the generic method of the original model. An addition to the model was made by introducing the possible effects of stall on the rudder. In the model the effective angle of attack and the water velocity on the appendages is calculated making use of vector summation of all the velocity components involved at the rudder plane (i.e. due to roll, yaw, sway etc) at 43% of the span of the rudder and at the quarter chord point. Additional information is now required on the stall angle of the particular rudder (and if deemed necessary of the keel). This is determined using available inforrnaton in the open literature. Based on this angle and the dcl/dß of the rudder (and keel) the lift curve in a wide range of angles of attack may be constructed. An example of this is depicted in Figure 1. It should be noted that during all the simulations carried out in the context óf the present study the possibility of stalling either the keel or the rudder was avoided. In the original model no provision was made for the presence of a (large) bulb underneath the keel. In the dedicated model the drag of this bulb should be accounted for. Also its effects on the overall moments of inertia and the influence of the added mass should be taken into account. The trim tab angle should be brought into the simulation model as an independent and time dependent variable (i.e. as an input variable). 2.1 HYDRODYNAMIC MODIFICATIONS For the determination of the hydrodynamic forces and moments on the hull and appendages the following calculation methods were used: The mass moment of inertia of the boat in roll and yaw were calculated using the known weight calculation of the boat. The added mass of the hull, the fin and the rudder were calculated using the generic method as presented in the original model. This is in principle based on a two dimensional strip theory approach, as is quite common in ship motion calculations. The added mass moment of inertia for roll and yaw were taken from the generic model but now with the added mass of the bulb, as determined using known 2-D strip theory like methods, added. One important addition to the original method was made however. In this generic model, the sectional area coefficient in upright condition was used for the yaw calculations in both upright and heeled condition. To make this calculation more te. the sectional area coefficient under heel was also determined. -90-60 -30 0 30 60 90 Angle of Attack Figure 1: Example of the lift curve of the appendages including the effect of stall The dc1jd/3 of the keel is derived using the towing tank tests results, with addition of an extra input of the trim tab angle. The dc1/d/3 of the rudder comes from wing theory by Whicker and Febhier Ref 4]. The hydrodynamic resistance of the hull, i.e. the residuary resistance, is derived from the towing tank tests, because the hull parameters deviate considerably from the range covered by the DSYHS. To show the considerable difference in Figure 2 the results of the residuary resistance calculation using the expressions derived from the DSYHS for this IACC hull are compared with the results obtained from the towing tank. The hydrodynamic resistance of the appendages, i.e. the frictional resistance and the form drag, is taken from the wind tunnel tests with the appendages. The hydrodynarnic forces in sway on the hull and the appendages under influence of leeway are taken from the towing tank results. in the generic model, the side force is calculated using different procedures: the side force due to the roll and sway velocity are calculated using the p ormu a ions. - or i -calcul'atiuiroftb moment, the distribution of the side force is acquired by 136 2007: The Royal Institution of Naval Architects
calculating the side force distribution in upright condition based on the Equivalent Keel Method (EKM), see Keuning and Venrieulen [Ref 2]. The DSYHS fonnulations were originally not suited for higher aspect ratio keels. After an improvement in the determination of the coefficients [Ref 5] these formulations still were not completely valid for appendages with such a very high aspect ratio like the ones usual on IACC yachts.. Figure 2:.- IACC Tank test values - DSYHS Calculated values Velocity Residuary resistance comparison 8. For the rudder, a reduction of the effective angle of attack on the rudder due to downwash of the keel is added, as described in [Ref 5], according to: Ic D=a0 I_ A Re With the following values for the coefficient ao: 00 150 a0 0.136 0.137 In [Ref 5] also a velocity reduction near the rudder due to the wake of the keel is used. In the case of the IACC this is not deemed appropriate due to the large keel - rudder separation and the high aspect ratio of the keel, the small chord of the keel (c) and the low relative thickness (tic) of the keel. The hydrodynamic forces due to the roll and yaw motions, i.e. the velocities and accelerations, are determined using the generic expressions of the original model. The hydrodynamic yaw moment on the hull due to the leeway angle is taken from the towing tank results, the effects of the trim tab are taken from the wind tunnel tests and the yaw moment due to the yawing angular velocity is taken from the generic method of the original model. Il. The hydrodynamic roll moment on the hull due to the drift and roll angular velocity is talcen from the towing tank tests. 12. In the generic model the heeling angle was restricted to 30 degrees, due to the fact that this was the limiting heeling angle used in the tests of the DSYHS. From full scale experience however it was known that this was not enough for an IACC yacht. An increase in the maximum allowable heeling angle was deemed necessary. To enable this increase the necessary extra information was generated. 2.2 AERODYNAMIC MOD[FICATIONS For the determination of the aerodynamic forces and moments on the sails the following calculation methods are used: The aerodynamic forces and moments on the sails are determined from results of Computational Fluid Dynamics (CFD) calculations and from wind tunnel tests. This was necessary because the sail plan of the present IACC designs deviates so much from the "usual" sail plans, that the IMS sail coefficients, which are used in the original generic model, were considered to be inapproprfate. The actual lift and drag coefficients of the IACC rig, as used in the simulations, are presented in Figure 3. From these results it may be seen that the lift coefficients are becoming smaller with increasing wind speed to achieve the desired "de-powering" effect. With these coefficients and the associated shifts of the Center of Effort of the aerodynamic forces on the sails both in height and in longitudinal direction, it was found that the modeled sailing parameters, i.e. forward speed and heeling angle, corresponded sufficiently with the results obtained from the full scale measurements. The drag coefficients below an apparent wind angle (AWA) of 7 degrees are tailored to take into account the additional resistance of the sails due to flogging and back windage during the tack. 1.6 1.4 -- 1.2 - - o08-00.6 0.4-0.2 0.0 Figure 3: Aerodynamic Coefficients 0 30 60 90 120 150 180 AWA [deg] The lift and drag coefficients of the sails for true windspeeds 8, 12 and 16 knots The aerodynamic inertia of the sails such as the added mass and the added mass moment of inertia in roll and yaw are taken from potential flow approximations. 2007: The Royal Institution of Naval Architects 137
. 3. VALIDATION OF TILE MODEL USING FULL SCALE MEASUREMENTS In order to be able to validate the results of the simulations, full scale measurements taken onboard the actual boat have been compared with the results of the calculations. in order to be able to do this the results of the -onboard measurement system have been used. The full scale IACC boat was equipped with Racing Bravo, which is an electronic and computer navigation system with distributed acquisition and centralized processing. It consists of a network of modules that transfer the information from the instruments or sensors by means -of, a single cable with CAN technology to a PC on which all the data processing for navigation is performed. For the tracking of the boat a high precision GPS system "OmniSTAR" was used, which is a wide-area differential GPS service, using 10 Hz satellite broadcast techniques. Data from many widely-spaced reference stations are used in a proprietary multi-site solution to achieve submeter positioning. For the course angle and for the correction of the mast twist electronic compasses "MicroStrain 3DM-GX1" were used: one in the boat and one at the mast top. It provides with its 3D-accelerometer3D magnet field, and 3D-gyro the 3D-acceleration-, 3D-magnetic field-, and 3D-position-vector as an RS232 output. The boat speed through the water was measured by a standard B&G paddle wheel log. The wind speed, the wind direction and the inclinometer are also standard B&G instruments. Rudder and trim tab angle were measured by a "wire over potentiometer" type of displacement meter, with the string attached to the rudder shafi and to a trim tab tiller. respectively. The parameters recorded for the analysis of the stationary motions and the tacks are listed below. Also presented is a -short summary of those variables that should preferably also be measured to get the full picture but which were not during the present study. Parameters recorded Boat speed Rudder angle Trimtab angle Heeling angle Apparent wind angle Apparent wind speed Calculated true wind angle Calculated true.wind speed Heading (Course angle) Longitude Latitude -Parameters not recorded Wind shear Wave height Wave front direction Current strength - Current direction Leeway angle The same instrumentation is used later in the project to compare the results of the simulations with those of onboard recordings (measurements) durng the various executed tacks. Due to the limited available space in this presentation results will only be presented of these comparisons during the tacks. It can be stated however that the comparison between the measured data, obtained during full scale trials on board the IACC boat sailing on a steady straight line course in a constant wind speed, and the simulated results using the dedicated model showed that these were close enough to consider the use of the model simulations quite adequate for the envisaged optimization of the tacking procedure. 4. UTILISATION OF THE MODEL TO OPTIMIZE 'ihi TACK BY VARIATION OF THE RUDDER AN]) TRIM TAB ACTIONS To optimize the tack a few starting conditions had to be chosen: the investigation was carried out for a true wind velocity of 11.Skn, the steady state rudder angle was chosen to be +1-4.5 degrees and the trim tab angle was chosen to be +1-6 degrees, which corresponds to the numbers used on the real AC boat. The purpose of the present project was to optimi2'e tacks by varying the rudder and trim tab action. Input for the so called rudder- and trim tab scenes were polygons of angle over the time. The corners of the polygons were rounded by splines. Since the polygons were planned to have up to 12 comer points, an optimization strategy was needed besides monitoring the, resulting distance loss. Since the effective angle of attack of the rudder is a combined measure of rudder action and the (resulting) boat motion, this parameter was chosen as an indicator of a successful modification of the rudder scene. Therefore the initial target was to vary the rudder scene to achieve a smooth effective rudder angle vs. time curve, which is assumed to minimize rudder and keel resistance. The optimization process started with RSO. The resulting pattern of the effective rudder angle was analyzed and the rudder scene was modified to RS 1. This process was r-epeated in 9 more s1c'ps h, Figure 4 the input anles of the four most illustrating rudder scenario's are presented, 138 2007: The Royal Institution of Naval Architects
'i and in Figure 5 the geometric, change in rudder angle, i.e. the actually applied rudder by the helmsman, during the tack as function of the time is shown. 25 20 15 0Ec o cl)< CD..5 Figure 4: 25 20 ' 15.10 e C)5 <0-5 -10 35-10 35 Figure 5: 8 G, O) C < 4-.0 - O) Ee O 0 E o e (D - TSO TS 1 - TS2 Rudder Scenes Geometric Rudder Angle 40 45 50 55 60 65 Time [sec] Applied rudder scenes Since the boat is normally sailing with a trim tab angle of 6. degrees to leeward, this angle was also used for the steady state condition at the steady course just before and after the tack. All the optimization variations were done by using the trim tab scenario TSO. It should be noted that the trim tab scenario, i.e. change in trim tab angle, started 10 seconds after the beginning of the actual rudder action. To assess the effect of a delayed trim tab action, trim tab scenario's TS1 and TS2, with 2.5 and 5 sec. delay respectively when compared to scenario TSO, are presented also and depicted in Figure 6. These varied trim tab scenarios were also used for the simulation together with the rudder scenario's RSO to RS9. igure-6: Tnmtab Scenes 40 4550 55 Time [sec] Geoinetrictrimtab..scenes -.-RS1 --RS4 RS7 -.- RS9 40 45 50 55 60 65 Time [sec] Input rudder scenes RS1 -*-RS4 RS7 -.-RS9 60 65 In Figure 7 the effective angle of attack of the rudder for the various rudder scenarios is depicted. This was the value to which the rudder scenarios were optimized. In Figure 8 the effective angle of attack of the rudder for one rudder scenario and the various trim tab scenarios is shown. These graphs clearly show the difference between the geometrical and effective rudder angle. It can also be seen that the trim tab changes the effective rudder angle, because it alters the turning motion of the boat. Rudder scenario 9 (RS9) delivers the smoothest effective rudder angle curve. This should have its effects on the results of the tacking maneuver. In Figure 9 the 'Distance Lost' due to the tacking maneuver, can be found. This is the distance the boat could have been sailing extra if it had not tacked, maintaining its speed before the tack. The calculation of this distance is shown in Figure 10; method i is used in the model. The influence of the trim tab scenarios on the distance lost is shown with this graph: the difference in the distance lost for the various trim tab scenarios is greater than the difference due to rudder scenario. 0 C, 10-10 -15 Figure 7: 15 e0 C) C 10 - -10 Figure 8 Effective Rudder Angle During Tack with TS2 35 40 45 50 55 60 Time [sec] Effective rudder angle during tack for various rudder scenes Effective Rudder Angle During Tack with RS9 -u- ISO -*-TS1 - TS2-15 35 40 45 50 55 60 Time [sec] Effective rudder angle during tack for various trim tab scenes 65 65 2007: The Royal Institution of Naval Architects 139
Figure 9: Distance lost during tacks RS i RS4 :RS7 RS9 Rudder Scenes LTSO UTSI L1TS2 Distance lost duriñg tack for various rudder and trim tab scènes W.IND.0) - 4.9 4.7 45 43 4.1.3.7 3:5 35 Figure Ii: 4.8 4.6 ' 4.4 Boat: Velocity During Tack With 1S2 --RS1 -*-RS4 RS7 -.-RS9 40 45 50 55 60 65 70 75 Time [sec]. Boat velocity during tack for various rudder scenes Boat Velocity During Tack With RS9 ti VsI to VsO s ti Methød2 TI = sonso + stnst dt TI.ti-tO} ds VsldTC08(betaij 4.0 3.8 3.6. 3.4 35 40 45 50 55 60 65 70 75 Time [sec] Figure 12: 4.5 Boat velocity during tack for various trim tab scenes VMG DúrinLg Tack With TS2 Figure 10: Ssthod1: s2 = VsO'tt-W) ds (s2 - sorcos(betao) - StCOS(betai) The calculation of the distance lost 4.0 'o. 3.5 o- 3.0 > 2.5 Finally, a look at the boat velocity during the tack and the velocity made good (VMG), the velocity towards a windward point, based on boat velocity and course, shows the differences between the rudder- and trim tab scenarios; In Figure 11 and 12 the influence of the rudder and trim tab scenarios on the boat velocity can be seen and in Figure 13 and 14 the influence of the rudder änd trim tab scenarios on the VMG is shown. Regarding the boat velocity, it is clear once again that with RS9 the boat has regained its speed alter the tack earlier than the other rudder scenarios. Here, also the influence of the trim tab scenario is evident: with TS2 the boat regains its speed earlier and yields the highest speed after the tack. The influence of the trim tab on the VMG is rauch less pronounced than its influence on the boat velocity. 2.0 35 Figure 13: 4.5 4.0. (n 3.5 o 3.0 > 2.5-2.0 35 Figure F4: 40 45 50 55 60 65 70 75 Time [sec] Velocity made good (VMG) during tack with variousrudder scenes VMG During Tack With RS9 TSO -*- TS1 - TS2 40, 45 50 55.60 65 70 75 E Time [sec]. Velocity madjuçydurmg tack with various trim tab scenes 140' 2OQ7 The Royal Institution ofnaval Architects
5. CONCLUSION From the results of the simulations compared with the real time measurement data, it may be concluded that the dadicated model can be used to quantify and qualify the influence of variation of parameters on the outcome of a tacking procedure. Based on the combination of the model with the experimental data, a parameter otherwise very difficult to measure, the effective attack angle of the rudder, could be simulated in order to find the best tacking maneuver. This will make the model suitable for comparable exercises in the future. 6. ACKNOWLEDGMENTS The writers of this paper would like to show their gratitude to the United Internet Team Germany for making theirmeasurement data available for this paper. 8. AUTHORS BIOGRAPHIES Axel Mohnhaupt is principal designer of the German AC challenge United Internet Team Germany. He is also research advisor of the 1TC of the Ocean Racing Congress. Lex Keuning is associate professor at the Ship Hydromecharncs Laboratory of the Delfi University of Technology. He has been responsible for research on the Deffi Systematic Yacht Hull Series and also research advisor of the ITC of the Ocean Racing Congress. Michiel Katgert is member of the research staff of the Ship Hydromechanics Laboratory of the Delfi University of Technology. He is responsible for carrying out towing tank research. 7. REFERENCES Keuning, J. A., Vermeulen, K J. and de Ridder, E. J.. A generic mathematical model for the manoeuvring and tacking of a sailing yacht. Chesapeake Sailing Yacht Symposium, 2005 Masuyama, Y. Fukasawa, T. and Sasagawa, H. Tacking simulation of a'sailing yacht - numerical integrations of equations of motion and application of neural network technique. Chesapeake Sailing Yacht Symposium, 1995 Keuning, i A. and Vermeulen, K J. The yaw balance of sailing yachts upright and heeled. Chesapeake Sailing Yacht Symposium, 2003 Whicker, L. F. and Fehiner, L. F. Free-stream characteristics of a family of low aspect ratio control suifaces. Technical report 933 David Taylor Model Basin, 1958 Keuning, J. A., Katgert, M and Venneulen, K J. Further analysis of the forces on keel and rudder of a sailing yacht. Chesapeake Sailing Yacht Symposium 2007 2007: The Royal Institution of Naval Architects 141