1 PERFORMANCE PREDICTION OF THE PLANING YACHT HULL L A le Clercq and D A Hudson, University of Southampton, UK SUMMARY The performance of racing yachts has increased significantly over the past years without significant changes to the prediction methods used in the early stages of the design. Tank testing or CFD-simulation are not always an option and especially in the early stages of the design a requirement for reliable numerical methods exists. This paper discusses the applicability of these existing numerical resistance prediction methods for modern, high performance yachts based on tank testing of a generic planing hull. NOMENCLATURE B B WL C F C R C T Fn ITTC k L L WL R F R R R T R V R W 1. INTRODUCTION Beam overall (m) Beam at waterline (m) Frictional resistance coefficient Residuary resistance coefficient Total resistance coefficient Froude number (length based) International Towing Tank Convention form factor Length overall (m) Length at waterline (m) Frictional resistance (N) Residuary resistance (N) Total resistance (N) Viscous resistance (N) Wave making resistance (N) Advances in design, materials, methods as well as rules have allowed a significant increase in the speeds modern yachts are able to achieve in flat water, let alone with the help of waves. Using data supplied by Farr Yacht Design , improvements in performance can be illustrated by taking target speeds from sail-selection charts for different designs throughout the past two decades. A 50- foot design in the 1990s would expect to achieve speeds of around 10knots in 20knots of true wind and flat water. A 50 foot IMS-design (late 1990s, early 2000s) would see targets of approximately 12 knots in the same wind conditions, whilst a modern 50 foot race yacht, such as a TP52 (2006 design), will have a target speed of 16 knots for these same conditions. This example merely illustrates a change that can be observed across the entire range of high performance yachts up to 100 foot. The speeds achieved by current grand-prix yachts frequently exceed length-based Froude numbers of 0.7 in sailing conditions, thus venturing into the planing regime. The speed difference between a typical IOR-design and a TP52 represents an increase of around 50% in less than 20 years and raises the question of whether the performance prediction of sailing yachts has been able to keep up with the significant improvements in performance seen on the race course. The importance of a velocity prediction program (VPP) in the early stages of the design process to aid decisions emphasises the quality requirement of the underlying performance prediction method . An investigation of current design practices for this study showed that the VPP alone is still the most used tool by yacht designers , even with the advances in other, physics-based numerical methods such as computational fluid dynamics (CFD). The aim of this study was the evaluation of existing methods for performance prediction of high performance yachts. The investigation is based on a generic design of a representative hull shape, for which a model was tank tested. The scaled results from this testing are compared to the predictions of existing methods, both within their stated range of validity and outside this range since the survey of current design practice indicated that yacht designers are using these methods outside of their intended range. The objective is thus to comment on the applicability of current main-stream performance prediction methods for the prediction of high performance yachts and suggest directions for future work. 2. RESISTANCE PREDICTION METHODS Whilst the prediction of the resistance of ships has been extensively researched with numerous standard series being available for merchant vessels as well as fast craft, there is less research of the resistance properties of sailing yachts. Most of the publications which are available focus on very specific vessels or very particular design features. A notable exception to this is the research conducted by the Delft University of Technology and this has lead to the publication of the Delft Systematic Yacht Hull Series (DSYHS). In addition the designer can use tank testing and now computational fluid dynamics to predict the resistance and thus performance of planing yachts. 2.1 DELFT SYSTEMATIC SERIES The DSYHS is the most extensive standard series available for yacht hulls and with 50 different dedicated models tested, is the most applicable series for the
2 resistance prediction of a sailing yacht. Based on the latest model tests, Keuning and Sonnenberg  presented a prediction method for resistance over a range of length Froude numbers from 0.1 to 0.6, for both upright and heeled conditions. The resistance, using this latest prediction polynomial , is calculated using the skin friction coefficient based on the ITTC-57 correlation line combined with the residuary resistance calculated from the model tests. This method has a defined range of ship particulars, presented in table 1, as well as a defined range for length Froude number (0.1 to 0.6) to compute the residuary resistance for the naked hull in the upright condition. The Froude number-specific residuary resistance can be used to create a polynomial to predict the residuary resistance at intermediate speeds. The frictional resistance is based on the ITTC-57 correlation line with a modified length (70% L WL ) to calculate Reynolds number. The DSYHS also includes a method for predicting the change in resistance for heeled conditions based on an empirical formula for the change in wetted surface area and a change of influence of the hull parameters on the heeled residuary resistance. The DSYHS can be used manually, or through many commercially available resistance prediction software tools. 2.2 ALTERNATIVE PREDICTION METHODS The prediction of planing yacht performance using a numerical prediction method intended for planing powered craft has also been considered. Using the work of Savitsky for the prediction of constant deadrise, hard chine, craft in the planing  and pre-planing  conditions an attempt may be made to predict the hull resistance for a range of yacht particulars outside that of the Delft Series. In order to use this method for a roundbilge yacht hull, the hull parameters as used in the Delft Series are supplemented by the addition of a measurement for the equivalent deadrise angle of the hull. The deadrise angle is taken for 50% LWL. The predictions using both of these methods have been included in order to gain some insight as to the likely behaviour of the yacht s resistance beyond the speed range of the existing Delft Series. 2.3 TANK TESTING AND CFD SIMULATION The most accurate resistance predictions should follow from a performance prediction method based on the complete hull geometry. Tank testing and computational fluid dynamics (CFD) both permit analysis of the complete hull geometry, both with and without appendages. Both methods are, however, time consuming and costly thus reducing their usefulness in the early stages of design. For the purpose of this study, an indepth analysis of the hull was paramount and as such the resistance prediction using tank testing and/or CFD was a requirement. The tank testing requires a number of choices on the setup and poses a number of challenges to accurately model the full scale situation. The choice of testing method influences the results, as does the scale of the model and the ballasting during testing.. It is vital to keep as a primary objective for tank testing the assurance of the repeatability of the experiments so as to warrant the quality of the testing . The testing of the DSYHSmodels employed a semi-captive method, and the same method was used for the testing of the representative planing hull design in this work. The use of CFD in the design process is now considerable, however the survey of design practice showed it is still comparatively rarely employed in the early stages of design . It is claimed that CFDsimulations using RANS-code has now surpassed the accuracy of tank testing and that using solely this method is viable for even the highest level of competition such as the America s Cup and Volvo Ocean Race . This is disputed to some degree by Raymond et al.  in their application to an Open 60 design at varying angles of trim. 3. HULL DESIGN To assess the applicability of the Delft Series to current and future high performance yachts a representative hull has been specifically designed as part of this study. The design is based on analysis of current design trends across a wide variety of modern yacht forms, from 24 feet to 70 feet in length. 3.1 LINES PLAN AND HYDROSTATICS The primary goal of the hull design process was to design a hull within the ranges of the Delft Series, closely resembling both the ratios as well as the hull shapes of the basis yacht designs. An analysis of the hull shapes showed that the design required a narrow waterline, significant overhangs aft, relatively little rocker compared to older designs and a flat run aft. The incorporation of a chine has been avoided based on the experiences of professional sailors with both soft and hard chines in conventionally ballasted yachts. Whilst it may have been preferable to use an existing design for tank testing in order to have a better understanding of full scale behaviour and performance, it is believed that the use of a new design has allowed a much broader representation of high performance sailing yachts to be achieved. The designed hull has not been optimised for any particular operating condition in order to keep the design as generic and representative of the range of modern design practice as possible. A lines plan of the final generic hull is shown in figure 1. The fit of the design within the DSYHS range of parameters is presented in table 1, which also includes the principal particulars for the full scale hull.
3 Figure 1: Lines plan of generic hull design (not to scale) 3.3 MODEL SCALE AND CONSTRUCTION The scale of the model was dictated by the maximum speed of the testing facility, the displacement and the expected mass of the model. A larger model would allow a larger margin in the construction and trim ballast but would reduce the maximum achievable length-based Froude number. The testing facility has an advertised maximum carriage speed of 4.6 m/s, with 4.1 m/s as an achievable constant maximum operating velocity according to experienced operators. The desire to test at a Froude number greater than 1.0 resulted in the model being scaled to an overall length of 1.80 metres. The final scaling factor is thus approximately 1: Delft Series Range Design Length - Beam Ratio Beam - Draught Ratio Length - Displacement Ratio Longitudinal Centre of Buoyancy Longitudinal Centre of Flotation 0.0% % -1.8% % Prismatic Coefficient Midship Area Coefficient Loading Factor Full scale hull properties: Length m - L WL m Beam m B WL m Draught canoe body 0.24 m Wetted area m 2 Water plane area m 2 Volumetric displacement m 3 Table 1: Comparison of DSYHS-ranges to hull design The model was produced from a computer numerically controlled cut female mould by the University of Southampton Engineering Design and Manufacturing Centre (EDMC). The model was constructed in glassfibre reinforced epoxy. The delivered model was finished with a coating and prepared to 600grit in accordance with ITTC recommended procedures . Trip-studs were installed to ensure representative full scale flow characteristics along the majority of the hull, with the location and spacing in accordance with advice from the Wolfson Unit MTIA. 4. RESISTANCE PREDICTION OF HULL Prior to the testing of the model the resistance of the design was predicted for both the upright and heeled conditions of the full scale naked hull. The upright resistance was predicted both manually and using various commercially available software packages, whilst the heeled condition has only been predicted manually. 4.1 UPRIGHT RESISTANCE PREDICTION The upright resistance of the hull was predicted using the Delft method as published in  as well as using the resistance prediction methods offered by the Wolfson Unit MTIA Powering software and Hullspeed, which forms part of the MaxSurf software suite. The three predictions are all based on slightly different versions of the Delft Series and as such provide different predictions. The Delft Series data published in 1981  and 1996  is the basis of the Wolfson Unit MTIA resistance prediction for the naked hull . The FormSYS Hullspeed  Delft Series predictions are based on the papers published by Gerritsma et al. in 1991  and 1992 . The resistance predictions are shown in figure 2 and illustrate the different resistance values predicted by each method for the same length based Froude number. The Hullspeed resistance prediction using the Delft Series is based on the oldest published data of the three methods employed and displays a significantly different resistance trend to the other two prediction methods shown in figure 2. Although the Hullspeed prediction is based on the imported hull shape, it does not predict the resistance based on the lines plan but on the same hull parameters used in the other prediction methods. As a
4 result the decision was made to exclude this method in further analysis of the performance prediction. The prediction methods used are all limited to a relatively small range of length based Froude number. With the Froude number limited to 0.6, higher speed resistance predictions are dependent on extrapolation of the data and, respecting the published limits of the Delft Series, none of the prediction methods used include an extrapolation procedure within the method. A freely available Microsoft Excel Add-In was used in order to interpolate and extrapolate the predicted resistance. The add-in uses a curve fitting technique based on a double parabolic method . This avoids unrealistic values outside the data range as would be experienced using a high order fitted polynomial. The full numerical prediction including the extrapolated resistance is included in the plots of the scaled tank-data. The use of such an add-in is significantly limited as it lacks the possibility of user control. Nonetheless, it will be used to compare the scaled experimental results to the numerical predictions outside the published speed range since designers employ various extrapolation techniques in order to obtain performance predictions from VPPs. 4.2 HEELED RESISTANCE PREDICTION The heeled resistance of the naked hull is based on the manual upright resistance predictions as discussed in section 4.1 using the methods described by Keuning and Sonnenberg . The heeled resistance has been predicted for a heel of the hull of 5 and 10, these values of heel being chosen based on experience sailing at the higher sustained speeds, which are commonly achieved in a downwind sailing condition with minimal heel. The change in resistance due to heel is predicted to be minimal for the 5 and 10 heeled conditions and the predicted resistance for both conditions is included in the resistance prediction shown in figure 2. The heeled resistance prediction has also been extrapolated beyond the speed range of the Delft Series to allow comparison to the experimental data. The same function was used as described in section EXPERIMENTAL PREDICTIONS In order to judge the accuracy of the Delft Series resistance predictions the constructed model of the design was tested in a towing tank using a method comparable to that described by Keuning and Sonnenberg  and discussed in section 2.3. The testing was undertaken at the Southampton Solent University (SSU) towing tank which has the following properties: Length Breadth Depth Maximum Carriage Speed 60 m 3.7 m 1.8 m 4.6 m/s Although the tank has an advertised maximum velocity of 4.6 m/s, the maximum speed during testing was limited to 4.1 m/s to ensure reliable data could be obtained. The test data is scaled using the same methods as described in for the DSYHS which are based on the ITTC-78 procedures . 5.1 TEST PROCEDURE Different speeds were tested in a random order and the acquired resistance data was checked after each run to ensure signal quality throughout the test sessions. Particular attention was paid during the testing to ensure a number of repeatability tests could be made in the limited time available, in accordance with good testing practice . For the upright condition three speeds were repeated, with a further check at one speed. Both heeled conditions were also repeated at three speeds, but without an additional check of any of the tested speeds. The observed variation between runs was greatest in the upright condition for the higher speeds, with a variation of 7.6% at the same carriage speed setting for a speed close to 4 m/s (run speeds were 3.96 m/s and 4.06 m/s). Further analysis of the data showed a variation in carriage speed of ~3%, hence reducing the error for the same speed to approximately 5%. For the other upright conditions repeatability was approximately 1%. The margin of repeatability for the 5 heeled condition varied slightly more, from 3.3% at a clock speed for 2.75 m/s to 0.15% for a clock speed of 3.75 m/s. All of the measured resistance data is shown at model scale in figure OBSERVATIONS DURING TESTING In addition to the measurements of resistance, the behaviour of the hull was observed and measured. In addition to the resistance, measurements of side-force, trim and sinkage were taken. The results of the trim measurements have been discarded as a result of a faulty sensor in the heel fitting used during testing. The sinkage of the model was also measured in order to check the transition from displacement into planing mode for the varying conditions. The measurement showed at low speeds (Fn < 0.2) a small negative sinkage value indicating that the hull was lifted due to the developing wave system, corresponding to visual observations. At higher Froude numbers, but still within the Delft Series range, sinkage increased to a minimum around Fn = before reducing for increasing speeds. For the upright condition, the static position is achieved at a Froude number of approximately 0.75 whilst for the 10 heeled condition this equivalent point was at Fn This indicates the hull would be in the fully planing regime for Fn > 0.8. In addition to these measurements, a visual observation of the spray was made with the primary focus on the
5 registration of the number of wet trip studs. For a length based Froude number approaching 0.9 it was observed that due to trim and sinkage none of the studs were wet. This observation is used to deduct the correct added resistance of the studs from the model tests during the scaling procedure. Figure 2: Resistance prediction of the planing yacht hull using various methods for both upright and heeled conditions Figure 3: Resistance data as measured for each individual run
6 Figure 5: Scaled resistance (including form factor) and numerical resistance predictions for full range of length based Froude number Figure 6: Focus on the data for Froude number for scaled resistance (including form factor) and numerical resistance predictions
7 5.3 TEST RESULTS AND SCALING Scaling of the acquired data was conducted using the adapted ITTC-method as described by Keuning and Sonnenberg for the Delft Series . However, it was decided that with the available data a form factor (1+k) could be derived, allowing a comparison between scaling methods and potentially greater accuracy in full scale predictions. The form factor may be derived using a Prohaska plot of the low speed resistance data. The form factors have been derived for each of the tested conditions individually . The Prohaska relationship for these conditions is shown in figure 4. The form factors for the individual conditions are: (1+k) = (upright) (1+k) = (5 heeled) (1+k) = (10 heeled) The form factors found for both heeled conditions are within the typical range of (1+k) = 1.1 to 1.2 , but large compared to older yacht designs . The form factor for the upright condition, however, falls outside this typical range. It is possible that this could be the result of the flow behaviour at slow speeds, as higher form factors are commonly measured on immersed transom designs . Although the transom was observed to stay dry throughout the tests, at lower speeds the flow did appear to remain attached to a significant part of the stern overhang. This may explain, at least partially, the higher form factor measured for the upright hull. The use of low speed tests to derive form factors for high speed hulls with immersed transoms is known to cause difficulties for powered craft and leads the ITTC to recommend a (1+k) = 1.0 for scaling purposes for such vessels . As mentioned previously, C F is based on the Reynolds number as calculated for 70% waterline length and the ITTC-57 correlation line, C R is constant for both model and full size yacht. The scaled resistance from tank testing is shown in figure 5, together with the results of the prediction methods based on the Delft Series discussed in section 4. For speeds corresponding to Froude numbers greater than 0.6, the predicted results are extrapolated for illustrative purposes using the method described in section COMPARISON OF SERIES-BASED AND TANK TESTING PREDICTIONS In order to assess the usefulness of the existing Delft Series methods for the prediction of modern high performance yacht hulls, a comparison of the scaled data and extrapolated resistance predictions was undertaken. Both the upright and heeled resistance predictions were scaled and compared individually. 6.1 UPRIGHT RESISTANCE COMPARISON A comparison of the scaled resistance data of the upright tank testing with all resistance predictions using the Delft Series resulted in discarding all but the Wolfson Unit MTIA software and manual predictions (seen in figure 5). These two methods showed a relatively constant variation (in %) from the scaled resistance, whilst other methods showed both less consistent as well as larger differences. Figure 6 presents the data from figure 5 for a reduced Froude number range (<0.5) and shows the variation between the experimental data (scaled with form factor) and the Delft Series resistance predictions within their range of applicability. The calculated variation between series-based predictions and experimental data is presented in figure 7. The percentage difference between the Delft Series predictions and the testing was approximately 10%, with the smallest differences within the range (0.2<Fn<0.6) and at the lower extrapolated speeds. The extrapolated manual resistance data at these speeds (Fn ) over-estimates the measured resistance (up to ~6%). Figure 4: Prohaska plots to obtain form factors for individual conditions Prior to scaling the results the additional drag of any wet trip studs was deducted from the measured total resistance. Using Froude s extrapolation technique , the data was subsequently scaled for the full size hull: R T = R V + R W = (1+k) R F + R R C T = (1+k) C F + C R Figure 7: Margin of difference between numerical and experimental resistance values (upright)
8 The resistance curve of the model at higher Froude numbers bears a great resemblance to that of the NPLseries  for power craft. Although the range of parameters for which the NPL-series has been validated varies significantly from the Delft Series, it seems logical that the resistance characteristics at higher Froude number are comparable, as both transom sterns will run dry. The total resistance coefficient increases to a Froude number of approximately 0.45, slightly decreases for Fn = and then increases again for Fn > 0.8. As a result the resistance curve for the hull will go from an approximately exponential increase, through a closely linear increase before continuing to increase in an exponential manner. 6.2 HEELED RESISTANCE COMPARISON The resistance curves for the heeled conditions, seen in figures 5 and 6, are comparable to the upright with an exponential-like increase at low Froude number, a linearlike region for the middle region of the tested speeds and a further exponential-like increase for the higher Froude numbers. When this data is compared to the extrapolated manual resistance predictions, the complete curve has an exponential-like behaviour. Although the manual predictions are under-predicting the resistance for the lower speed range (Fn ), the continuing exponential-like curve crosses the experimental resistance curve at a Froude number just above the predicted range. The experimental data not only implies a longer linear-like region but for this design also a relatively significant increase of resistance in the change from linear-like to exponential-like behaviour. The variation between numerical predictions and experimental data is presented in figure 8. For the range of speeds appropriate to the Delft Series, the heeled resistance predictions are within a margin of approximately 10% of the experimental data. At speeds immediately above this (0.6 < Fn < 0.8), the extrapolated series predictions remain within 10% of the experimental data for the 5 degree heel case, and 20% for the 10 degree heel angle, but the difference increases with speed. 6.3 DISCUSSION OF RESULTS The comparisons between predictions based on the Delft Series and tank test results for both heeled conditions and the upright condition show an underestimation for the resistance using the standard series method compared to the scaled tank test results over the speed range for which the standard series data are validated. For both cases the error is relatively constant over this speed range, but distinctly unsteady once the data had to be extrapolated. Comparing the total resistance coefficient curve to other existing standard series, the qualitative characteristics of the curve correspond closely to those of the NPL-series, with a significant increase in the resistance coefficient for higher Froude numbers (Fn > 0.75). This corresponds to the transition from displacement to planing and is a typical feature of round bilge hull shapes at higher Froude numbers. The increase in the resistance coefficient for higher Froude numbers means that the near linear relationship between resistance and Froude number at the lower speeds becomes exponential. This requires any extrapolation to estimate an exponential function based on near-linear behaviour for the upright condition. A larger data-set including a wider variety of designs for this extended speed-range could allow for either an extension of the existing prediction method or an addition specifically for this higher range. Without such data, velocity prediction programmes based solely on the Delft Series and including a basic extrapolation for the resistance at higher Froude numbers will likely underestimate the yacht hull resistance. The same VPP will, using the same extrapolation techniques, most likely over-estimate the resistance of the hull in the heeled condition. In this case the prediction forms an exponential curve, whilst the experimental data suggests a near-linear region extending over a greater speed range. As a result the extrapolated points of the numerical prediction result in an increasing over-estimation of the resistance at higher Froude numbers. This again requires a larger data-set to extend the existing methods for this higher speed region. With the analysis of a larger data-set it should be possible to improve the numerical prediction method so that it can be effectively and confidently used in the early design stages of high performance sailing yachts. 7. CONCLUSION Figure 8: Margin of difference between numerical and experimental resistance values (heeled) The analysis of a single hull and a limited number of conditions cannot by itself provide sufficient evidence on the applicability of existing prediction methods for high performance yachts. For this particular design, the resistance within the range of the Delft Series is underestimated by a margin of ~10% relatively consistently over the full tested range. This implies that for comparison of preliminary high performance designs,
9 which fit within the Delft range of parameters and speeds, the use of the Delft Series is as reliable as it is for more conventional, heavier displacement boats and as such is suitable as the basis of a VPP. From this study it can be concluded that predictions for designs towards the boundary of a particular range can be expected to be less accurate whilst the resistance of the hull at higher Froude numbers corresponds qualitatively to that of the NPL-series, thus indicating that any simple extrapolation techniques will not be sufficiently accurate for the prediction of the resistance for the transitional and planing regimes. As a result, further data is a definite requirement in order to develop reliable resistance prediction techniques for high performance yachts. 8. FUTURE WORK This study was an initial investigation of the applicability of existing resistance prediction methods to modern high performance yachts. There is thus considerable scope for further work. Increased confidence in the use of prediction methods for planing yacht hulls can be obtained in a number of ways: Design and testing of a variety of high performance yacht hull designs. The effect of volume distribution, narrower designs (L WL /B WL >5) and variation of prismatic coefficient would be particularly useful to represent on-going design trends. Investigation of the effects of appendages and sail trimming moment on total resistance in the towing tank and compared to the prediction methods. At higher speeds the influence of trim angle on resistance is particularly important and the inclusion of the sail trimming moment is thus likely to be more necessary to better represent actual sailing conditions. Testing and validation of this and other high performance designs using virtual towing tank CFD predictions. Further optimisation of the extrapolation techniques for the standard series prediction methods may be warranted to allow a more representative prediction at speeds above a length Froude number of ACKNOWLEDGEMENTS Too many people have been important in the research that has formed the basis of this paper to be named individually here. A special acknowledgement, however, must be given to the help given by Britton Ward of Farr Yacht Design in providing performance prediction data for various 50 foot designs, as well as his extensive help throughout the course of the research. 10. REFERENCES 1. Ward, B., 50 footer target speed comparison, Farr Yacht Design, 2010 (Private communication). 2. Claughton, A., Shenoi, R., & Wellicome, J., Sailing yacht design: theory (2 nd ed.), University of Southampton, Clercq, L. le, Performance prediction of the planing yacht hull, MEng Individual Research Project, University of Southampton, Keuning, J. & Sonnenberg, U., Approximation of the hydrodynamic forces on a sailing yacht based on the 'Delft Systematic Yacht Hull Series', 15 th International Symposium on Yacht Design and Yacht Construction (pp ), Savitsky, D. Hydrodynamic design of planing hulls, Marine Technology, Vol. 1 (71-95), Mercier, J. & Savitsky, D., Resitance of transom stern craft in the pre-planing range, Davidson Laboratory, Report 1667, Stevens Institute of Technology, Raymond, J., Finot, J., Kobus, J., Queutey, P., & Delhommeau, G., A research program on performance of planing sailing yachts, International Conference on Innovation in High Performance Sailing Yachts, Lorient, RINA, Larsson, L. & Eliasson, R., Principles of yacht design (Second ed.), International Marine, Teeters, J., Refinements in the techniques of tank testing sailing yachts and the processing of test data, Proceedings of the 11th Chesapeake sailing yacht symposium, SNAME, Azcueta, R. & Rousselon, N., CFD applied to super and mega yacht design, Design, Construction and Operation of Super and Mega Yachts, RINA, International Towing Tank Conference, Model manufacture ship models, ITTC Recommended procedures and guidelines , Gerritsma, Prof J., Onnink, R. & Versluis, A., Geometry, resistance and stability of the Delft Systematic Yacht Hull Series, 7 th HISWA Symposium, Keuning, J., Onnink, R., Versluis, A. & Gulik, A. van, The bare hull resistance of the Delft Systematic Yacht Hull Series, 14 th HISWA Symposium, Wolfson Unit MTIA, Winpow help-file, Wolfson Unit MTIA power prediction Version Cat Beta 1.1, Formation Design Systems, Hullspeed helpfile, Formation Design Systems Hullspeed Version 14.01, Gerritsma, J., Keuning, J. & Onnink, R.,
10 Sailing yacht performance calm water and in waves, The tenth Chesapeake sailing yacht symposium, Gerritsma, J., Keuning, J. & Onnink, R., The Delft Systematic Yacht Hull (Series II) experiments, 12 th HISWA Symposium, Advanced Systems Design and Development, XlXtrFun extra functions for Microsoft Excel, m (retrieved14 May, 2010), Banks, J., Charlotte-Gaillard, A., Randall, R., Webb, A. & Williams, R., The design of an America s Cup AC90 yacht, MEng Group Design Project, University of Southampton, International Towing Tank Conference, High speed marine vehicles, ITTC Recommended procedures and guidelines , Bailey, D., The NPL High Speed Round Bilge Displacement Hull Series, RINA Maritime Technology Monograph No. 4, AUTHORS BIOGRAPHIES Lucas le Clercq is currently a Ship Science student (MEng Yacht and Small Craft) at the University of Southampton. This research project was the basis of his third year, individual research project. He has gained practical experience with yachts through race-boat preparation, tuning and racing of high performance yachts and currently races in a variety of classes including the TP52-class. Dr Dominic Hudson is a Senior Lecturer at the University of Southampton with research interests in all aspects of ship hydrodynamics. He is currently course coordinator for the Ship Science degree programmes at the University. Dr. Hudson is a member of the Performance Sports Engineering Laboratory within the School of Engineering Sciences, leading research into the performance of sailing yachts and small craft. He is also a member of the 26 th ITTC specialist committee on high speed craft.