4th High Performance Yacht Design Conference Auckland, 12-14 March, 2012

USING PARAMETRIC MODELLING, CFD, AND HISTORICAL DATA, TO ESTIMATE PLANING HULL PERFORMANCE ON A LAPTOP

Dr Jérémie RaymondKevin Cudby

Abstract. Existing systematic hull series may not cover all of the requirements for a new project. This is especially problematic for planing sailboats. This paper describes a simple model that allows a designer to quickly estimate the performance of a proposed new design. The system runs on a small laptop computer. It is based on data from a systematic series of planing yacht hulls, which was developed from an existing design of known performance. Several existing planing sailboat hulls were imported into a parametric modelling system. Fourteen new hulls were generated from a parent based on Groupe Finot’s 2007 IMOCA 60 hull by adjusting key hull shape parameters. A CFD VOF-code system (ISIS-CFD) was used to estimate each hull’s performance over a range of Froude numbers from 0.31 to 1.16 (8 to 30 knots for the IMOCA 60). An existing towing-tank model was used to validate the CFD calculations. The results were fitted to a set of equations using a statistical regression procedure. This regression model can be used to estimate drag, vertical force, and trimming moment of any hull within the range of validity defined by the systematic series. The model facilitates rapid performance assessment of proposed new hulls, before proceeding with detailed CFD and towing tank studies. A 4.2-metre dinghy was designed and built. CFD analysis of this design confirmed the performance estimate from the regression model. The extra CFD data can be used to refine the regression model. A generalised parametric hull model is presented.

NOMENCLATURECp Prismatic coefficientDwl Waterline draftBwl Waterline breadthFn Length Froude numberFx Longitudinal force (drag)Fz Vertical force (lift)Lwl Waterline lengthMSA Area of master sectionMy Trimming momentXb Longitudinal position of centre of buoyancyxMSA Longitudinal position of master section

1. INTRODUCTION

This paper introduces a simple design tool that allows data from CFD and tank testing to be applied to multiple design projects. The tool provides a method of linking data from old and proposed new designs. It runs on a small portable computer. Provided that proposed design changes, or new designs, fall within the model’s validity range, the effect of modifications, or the likely performance of a new design, can be estimated without the need for new CFD or tank test data. Although it was designed to address the lack of practical design tools for planing sailboats, this method is applicable to all types. The tool provides data that can be used in a VPP system.

This paper shows how the method was applied to CFD and tank-test data from a study of planing monohull sailboats [2]. The method provides for the assessment of rig forces. The resulting regression model was later used in the design of a small planing dinghy.

Today’s monohull sailboats readily achieve planing speeds. It is vital that sailboat designers can ensure their designs easily climb onto a plane and stay there. Existing design tools do not provide much help.

Figure 1: On-the-water measurements from a Mini 650 show that the boat easily exceeds the performance predicted by a VPP application (WinVPP – Groupe Finot) [2].

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Figure 2a: Drag calculations using established methods of estimating planing hull resistance, compared with towing tank measurements on a model of on IMOCA 60 hull [2].

On-the-water testing showed that an existing hydrodynamic model seriously underestimated the performance of a planing sailboat (Figure 1) [2]. Theoretical methods of assessing planing hull performance were designed for powerboat hulls. They do not accurately estimate sailboat performance (Figure 2a). The Delft Systematic Yacht Hull Series [1] does not cover Froude Numbers greater than 0.75 (Figure 2b).

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Figure 2b: Comparison between drag calculated using DELFT models, and drag measurements from semi-captive tank tests on a model of an IMOCA 60 hull [2].

2. STRATEGY

For the present study, the design process was considered to have three phases. During the first phase, numerous options are defined and compared. In the second phase, the most promising options are further developed. Finally, one option is refined into a practical design.

The scope of the early design phase depends on factors such as the project budget. A large project may justify the investigation of many candidates. This type of in-depth investigation would be beyond the scope of smaller projects.

There is a need for a design tool that rapidly provides a realistic assessment of the performance of proposed planing sailboat hulls. Such a tool would simplify the early phase of large projects. On smaller projects, it would provide performance estimates that would otherwise be uneconomic.

Towing tank models do not satisfy this requirement. Their cost precludes their use in the early phase of most sailboat design projects. A CFD application capable of accurately simulating planing sailboat performance is very heavy on computing resources. It is out of the question for very small projects, and may limit the scope of the early phase of a large project.

Parametric design opens up a new approach. The final design can be considered a unique point on a multidimensional continuum, or design space. Any unique hull shape occupies a unique point on this design space. This means that any characteristic of the parametric hull can be described by a simple polynomial equation, as a function of the hull design parameters. This may include performance characteristics such as the drag, lift, and pitching moment, at specific operating conditions such as speed and trim angle. Any small computer can evaluate this type of polynomial equation in real time.

This approach eliminates the need for detailed CFD or towing tank analysis of every candidate, which, in any case, is not possible because the continuum contains an infinite number of options. Instead, a systematic series of hulls was developed from the parametric hull model. These were then analysed. Finally, the coefficients for the polynomial equation were calculated using a regression algorithm.

Constructing this polynomial equation (regression model) involved the following activities:

• Create a systematic series of hulls• For each hull, obtain a close estimate of the lift,

drag, and trimming moment across a range of boat speeds and trim angles

It was desirable to use a CFD code to characterise the hull series. So, it was necessary to identify a CFD code that could accurately compute forces and moments at planing speeds. This required a towing tank campaign to validate the CFD computations.

3. CREATING THE SYSTEMATIC SERIES

The parent hull for the systematic series was Groupe Finot’s 2007 IMOCA 60 hull (Generali, Hugo Boss, Brit’Air & DCNS). The systematic series was created by modifying the following parameters of the parent hull:

• longitudinal position of the master (maximum area) section

• hull volume, centreline curvature; vertical and longitudinal position of the lowest point of the centreline

• shape of the aft sections• bow shape• transom shape and draft

The systematic series was created from a parametric hull model using the Friendship Framework®. The model is built on skeleton of fair curves, mainly fsplines and ksplines. The fspline was introduced by Harries and Abt [3]. It defines a fair curve by optimizing a b-spline against fairness criteria. The kspline is an inherently fair curve with intuitive controls introduced by Cudby [4].

Figure 3: Simple parametric hull model.

The skeleton is built on a foundation of longitudinal “rail” curves such as the centreline curve CPC (kspline), datum waterline DTL (fspline), and deck edge curve DEC (fspline).

The transverse sections are defined by ksplines (underwater) and fsplines (topsides) (Figures 3, 4). Another set of longitudinal fsplines defines the values of section control parameters along the hull. This includes the area coefficient curve ACC), bilge factor curve (BFC), floor factor curve (FFC), and deadrise curve (DRC).

Figure 4: Effect of kspline shape controls.

Finally, the skeleton is skinned with a metasurface. This defines a fair b-spline surface based on a fair skinning interpolation algorithm.

Figure 5: Sections in the parametric hull were adjusted to match curves imported from an existing IGES hull surface.

To create the parent hull, twenty sections were sliced from the original hull surface (Figure 5). The parametric model was adjusted to conform to these section shapes. This hull was CFD tested and the results compared to the original. The differences were less than 0.1%, confirming the validity of the parametric method.

Figure 6: Hulls # 0 (top) and # 1(bottom). Hull # 1 is deeper and has more rocker.

A series of fourteen new hulls was designed (Table 1). Design time was approximately ten minutes per hull.

Hull # Modifications made0 Parent hull1 More curvature in the centreline2 Lowest point of the centreline moved forward3 Lowest point of the centreline moved aft4 Maximum area section moved forward5 Maximum area section moved aft6 Rounder sections (lower bilge factor)7 Flatter sections (higher bilge factor)8 Intermediate centreline curvature (less than #1,

more than #0)9 Narrower transom10 Higher area coefficient in the centreline abaft

the maximum area section11 Lower area coefficient in the centreline ahead

of the maximum area section12 Higher area coefficient in the centreline ahead

of the maximum area section13 Finest forward sections14 More rocker abaft the maximum area section

Table 1: Systematic hull series.

4. TOWING TANK TESTING

The towing tank tests provided reference measurements for comparison with, and validation of, the CFD simulations.

The towing tank measurements were taken from captive testing, in which the trim angle and nominal displacement are held constant throughout each test run.

This technique was chosen because it allows direct measurement of hull forces and moments. A key objective of this project was to develop a technique for simulating a yacht’s equilibrium attitude and performance in a range of scenarios representing variations of rig design and wind conditions.

Captive testing is especially relevant to planing yachts, because their performance depends critically on the vertical force and trimming moment. Neither of these parameters can be obtained from the semi-captive technique, which is more commonly used for model testing of sailing yachts. In semi-captive testing, the hull is free to trim and sink. The pitching moment is corrected by moving a mass along the longitudinal axis of the boat. The displacement of this mass is calculated to take into account the estimated position of the application point of aerodynamic loads.

For planing sailboats, hydrodynamic forces and moments are very sensitive to trim and heel. To characterise a planing sailboat with semi-captive testing, it would be necessary to run many tests covering all the possible

attitudes corresponding to the aerodynamic loads under the various conditions of navigation and sail trim.

In contrast, captive testing provides direct measurement of hydrodynamic forces and moments at discrete values of sink and trim. Provided that the initial testing covers an adequate range of conditions, the forces and moments at intermediate values of sink and trim may be estimated by interpolation.

The tank testing campaigns used two models (overall length 4 m, scale 1:4.5) built for Groupe Finot-Conq’s 2007 IMOCA 60 programme (Generali, Hugo Boss, Brit’Air & DCNS). The models were tested at fixed trim angles of 0° and 1° (positive when bow is up), at speeds ranging from 1 to 7 m/s corresponding to length Froude numbers up to 1.3 and real speeds between 8 and 30 knots. These models were used because of budgetary considerations. However, they were built for a larger tank, so the tests were influenced by tank boundary effects and more specifically by bottom effects. As no solitons were generated in the tank during the tests, those effects were considered as slight [2].

4.1 Captive Model Test Technique

The towing tank campaign used an isostatic six-component dynamometer. This was designed at l’Ecole Centrale de Nantes in 2005 for testing submarines. It was later adapted for surface ships. The dynamometer has six transducers: One for the x-component, rated at 1kN FS1; two for the y-components (1kN FS); and three for the z-components (2kN FS). All transducers have a precision of 0.008% FS.

The dynamometer frame is mounted on a “Hexapode” movement generator, which was used in this study to fix the model’s attitude and vertical position during the run.

Figure 7: IMOCA 60 model on six-component dynamometer in the towing tank at l’Ecole Centrale de Nantes.

Displacement is fixed by measuring the hydrostatic forces acting on the model when in the water. The Hexapode provides for adjustment within 0.01mm, which corresponds to 0.3N (0.03%) for the IMOCA 60 model. The attitude is checked by measuring moments to find the hydrostatic centres, verifying that the model is

1 Full scale.

positioned at zero heel and trim angles as defined in the architect’s plan.

The principal disadvantage of captive model testing is that the hydrodynamic forces and moments depend on five parameters (three for attitude, one for vertical position and one for speed). Regular precise calibration is necessary to minimise measurement errors. Rigorous experimental planning is necessary to ensure satisfactory and coherent results. Even so, the technique requires a significant number of tests.

5. CFD ANALYSIS

This study required a CFD system capable of accurately comparing the forces and moments acting on the various hulls, across the full range of boat speeds. Three CFD systems were investigated (Table 2).

System DeveloperREVA G. Delhommeau, Fluid Mechanics

Laboratory, Ecole Centrale de Nantes (ECN), France.

ICARE ECN, with support from the French Navy (DGA / Bassin d'Essais des Carenes).

ISIS-CFD Equipe Modélisation Numérique (EMN), Fluid Mechanics Laboratory, ECN.

Table 2: CFD systems investigated.

Computations from these CFD systems were compared with captive towing tank measurements, during which the model’s displacement and trim were held constant throughout the test run. This method permits direct measurement of the vertical force and pitching moment, as well as the longitudinal force.

5.1 REVA

Initial testing of REVA showed a significant discrepancy between the vertical force and the towing tank measurement for Fn > 0.5.

The predicted height of the bow wave differed noticeably from the bow wave observed during tank testing. To correct for this discrepancy, the code was modified by implementing a wave height description based on experiments by Delhommeau and Noblesse. This is a simple analytical expression for the bow wave’s height above the mean free-surface plane [5]. This seems to improve computation of bow pressures and vertical force. It does not significantly affect longitudinal force computation.

REVA estimates viscous drag using the formula in ITTC57. It then calculates total drag as the sum of computed drag and viscous drag. This requires an estimate of the form factor k, which is difficult to determine. Resistance was calculated with form factor ranging from 1.0 to 1.2. At low speeds, a correct estimation of the form factor can increase precision

significantly. At higher Froude numbers, REVA is not precise, irrespective of the form factor.

The modified REVA code computes longitudinal force and vertical force within about 5% relative to towing tank measurements for Fn < 0.5. This is fairly reasonable given the very low computation time.

Modified REVA is less accurate at Fn > 0.5. A comparison of the pressure map and force repartition showed that REVA over-estimates depression at the stern because it does not directly compute viscous effects.

5.2 ICARE

ICARE seems to correctly compute longitudinal force (drag) and vertical force for Froude number up to 0.7~0.8. At higher speeds it under-estimates the drag, but correctly computes vertical force and pitching moment. Except for drag, the differences are within the tank test uncertainties.

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Figure 8: Longitudinal force from CFD computations compared with measurements from towing tank tests.

This is probably because ICARE uses an energy dissipation function to avoid computing spray. Because the bow wave creates most of the drag, this limitation very likely affects the longitudinal force (drag) computation. Its effect on the vertical force is less significant, because the lift is significantly influenced by depression at the stern.

5.3 RANSE Solver Using VOF Method: ISIS-CFD

ISIS-CFD appears to correctly compute longitudinal and vertical forces for high Froude numbers. The overall relative differences are 6% in drag and < 4% for absolute vertical force (sum of hydrostatic vertical force and dynamic vertical force).

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Figure 9: Dynamic vertical force from CFD computations compared with measurements from towing tank tests.

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Figure 10: Pitching moment from CFD computations compared with measurements from towing tank tests.

5.4 Effect of Tank Boundaries

Budget constraints required the use of existing IMOCA 60 towing tank models, which were built for a large towing tank. However, the study required a tank equipped for captive testing. The tank tests were conducted in the towing tank at l’Ecole Centrale de Nantes which is 140m long, 5m wide and 3m deep. According to the ITTC recommendation, the models were too large for this tank, because the results might be influenced by the tank walls and bottom.

Two important effects need to be considered:• A hydraulic effect resulting from the obstruction

of the water cross section leads to a higher relative velocity and therefore greater resistance. The model’s cross-section was less than 1% of

the tank cross-section area, so this effect is weak.

• Propagation of waves is highly affected by water depth.

The effect of tank boundaries was investigated. All three CFD codes were sensitive to tank boundary effects. Most significantly, the vertical force computations are affected by the presence of tank bottom.

Figure 11: Bow wave simulations from ISIS-CFD and ICARE.

Figure 12: Bow wave and wave pattern description (ISIS-CFD) at Fn = 0.96, trim = 0°.

There was a significant difference between the bow wave simulations from ICARE and ISIS-CFD (Figure 11). The simulation from ISIS-CFD (Figure 12) closely resembled the bow wave recorded on video cameras during towing tank tests. This suggests ISIS-CFD correctly computes bow pressure and forces. There were small differences between the longitudinal force computed by ISIS-CFD and the towing tank measurements. These were probably caused by the effect of tank walls at high speeds. Unfortunately, because ISIS-CFD could not simulate the effect of tank walls at that time, it was not possible to investigate this hypothesis.

5.5 Evaluation of CFD Codes

To be useful at the pre-design stage, a CFD code must correctly classify candidate designs. This means the

computation must show whether one design has more, or less, drag than another.

To test each code’s ability to correctly classify two designs, it was convenient to compare two configurations of the same model. Because the angle of trim and the displacement were held constant throughout the test run, the model’s hydrodynamic configuration could be changed by changing the trim angle. So, the results from the parent hull with no trim, were compared with results from the same model with no heel but 1° of trim (positive when bow is up) (Figure 13).

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Figure 13: Comparison of parent hull longitudinal force (top) and vertical force (bottom) at trim angles of 0° and 1°.

In terms of longitudinal force, it appears that, up to Fn = 0.6, all codes correctly classify the two cases. ISIS-CFD is more precise than ICARE which is more precise than REVA. At higher speeds, only ISIS-CFD reliably classifies these cases.

Concerning the vertical force, REVA provides good classification except at Fn = 0.39, and acceptable evaluation of the difference between two test cases.

REVA offers very fast computation time. However, it will probably have trouble comparing two hull models at high Froude numbers, and when the vertical forces differ by only a small amount between test cases.

ICARE offers a better compromise between accuracy and computation time. However, it does not accurately

simulate spray, which implies it will give misleading results at the highest speeds.

ISIS-CFD provides a good comparison with more precise computation of the differences between two test cases. It was chosen for the systematic study, because it offers acceptable accuracy at high Froude numbers.

REVA modified

ICARE ISIS-CFD

Method Linear potential flow

RANSE finite difference

RANSE volume of fluid (VOF)

Computer Laptop Power5 4 x 2.4 GHz BiOpteron, 4GB RAM

Meshing time

30 min 4 hours 4 hours

Mesh type Half-mesh Half-meshMesh tool ICEM-CFD ICEM-CFD No. of cells 200,000 800,000Comput-ation time

5 min 5 hours 24 hours

Limit Froude Number

0.5~0.7 0.8~1 1.2

Tank boundaries

Bottom only

Bottom only Bottom only

Table 3: Comparative performance of CFD systems.

6. REGRESSION

The regression model links the parametric hull model with the performance data from CFD testing. For any set of hull shape parameters, the regression model provides numerical values for lift, drag, and trimming moment across a range of speeds.

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00Hull 05

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Figure 14: Vertical force (Fz/V²) calculated from the regression model for five different designs.

The use of a polynomial equation is a classical approach, used, for example, for the Delft systematic series. However, Gerritsma, Keuning, et al. [7], [8], [9], consider that the CAD geometry represents the hull from

a hydrodynamic point of view, and use correction functions to account for heel and trim.

From the dynamic perspective, the underwater shape is a function of parameters such as heel, trim, leeway, and immersed volume, as well as the CAD geometry. In this study, each unique underwater shape was treated as a separate “hull”. This eliminates the need for correction functions for the trim angle. The same approach can be used to evaluate the effect of heel. Correction functions are not required. The model described in this paper does not cover the effect of heel.

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Hull 0Hull 1Hull 2

Figure 15a: Longitudinal force comparison for 3 different designs.

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Figure 15b: Vertical force comparison for 3 different designs. Note increased down force on Hull 1 at Fn > 0.8.

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Figure 15c: Pitching moment comparison for 3 different designs.

At each speed, the regression model provides a separate equation for each performance characteristic: longitudinal force (Fx), vertical force (Fz), and trimming moment (My). The systematic series has 15 hulls, and each hull was tested at two trim angles. The CFD campaign investigated thirty test cases at each speed.

The model was created by step-by-step regression. A variable is added to the formula only if the correlation coefficient (R²) is higher and its Pearson coefficient is lower than 0.4. To ensure that this procedure is stable and reliable, the equations must be restricted to a maximum of ten terms.

Each of these ten terms contains one hull shape parameter. It was necessary to choose the most significant ones. The CFD campaign evaluated the following parameters:

,DwlBwl,

DwlLwl,

BwlLwl,

MSADwlBwl,

Vol

Sf,Vol

Sw,MSA

Sf,MSASw

32

32

⋅

XfDwl,

LwlSAx,

SfSw,

XbDwl,Cp,Cb,

SfDwlVol,

SwDwlVol,

LwlXf,

LwlXb M ⋅

⋅⋅

Many of these parameters were defined separately for the forebody (immersed volume ahead of the maximum section area), and the afterbody. This led to a total of 54 hull shape parameters.

The regression model was assembled by adding one parameter at a time. Each parameter was included only if its addition improved the correlation coefficient. The final regression model was checked by conducting a sensitivity analysis. The value of each parameter was altered by one percent, and the effect on forces and moments calculated. The maximum impact on calculated drag was three percent.

The key parameters are: • L/B, characteristic of the general hull shape• Xb/L, characteristic of the centreline shape

which is a key parameter for the pressure distribution

• Lfwd/Bfwd, characteristic of the forward part of the hull which generates most of the drag.

This analysis yielded a set of equations with eight terms per equation.

aft7fwd6aft

aft5

fwd

fwd4

aft

aft3

fwd

fwd210

CpaCpaDwlBwla

DwlLwla

BwlLwla

BwlLwla

LwlXba

BwlLwlaFx

++

+++++=

aft7fwd6aft

aft5

fwd

fwd4

aft

aft3

fwd

fwd210

CpbCpbDwlBwlb

DwlLwlb

BwlLwlb

BwlLwlb

LwlXbb

BwlLwlbFz

++

+++++=

aft7fwd6aft

aft5

fwd

fwd4

aft

aft3

fwd

fwd210

CpcCpcDwlBwlc

DwlLwlc

BwlLwlc

BwlLwlc

LwlXbc

BwlLwlcMy

++

+++++=

Fn 0.31 0.58 0.77 0.96 1.16R² (Fx) 0.9997 0.9998 0.9995 0.9996 0.9997MSE (Fx) 0,04% 0,06% 0,075% 0,1% 0,1%R² (Fz) 0.986 0.996 0.992 0.971 0.982MSE (Fz) 0,05% 0,06% 0,16% 0,65% 1,3%R² (My) 0.9996 0.9996 0.9995 0.9986 0.999MSE (My) 2,1% 3,1% 3,3% 3,6% 4,1%

Table 4: Correlation coefficient (R²) and mean square error (MSE) for each force and speed.

7. VALIDATION

The regression model was used to study a series of six hull shapes for a 4.2m dinghy. The design objective was to obtain a fast planing hull similar to the IMOCA 60. Table 5 shows the main dimensions of one of these hulls, compared with the range of values covered by the regression model (Table 5).

Coef. Min Dinghy MaxL/B 2,54 3,01 4,40

Xb/L 0,33 0,41 0,52L/B fwd 1,67 1,95 3,19L/B aft 0,58 1,05 1,75

L/D fwd 30,43 25,01 55,10B/D aft 11,47 13,20 27,64Cp_fwd 0,44 0,52 0,60Cp_aft 0,61 0,71 0,96

Table 5: Hull parameters of a dinghy hull compared with the regression model’s validity limits.

The design process began with an initial hull (design01), scaled from an existing IMOCA 60 hull. A series of five additional hulls were created, and their performance estimated from the regression model. Two hulls were selected for further study, and their performance estimated using ISIS-CFD. Figures 16a-16c compare results from the regression model and the CFD analysis.

Figure 16a: Longitudinal force comparison for 3 different designs using regression model.

Figure 16b: Longitudinal force comparison for 3 different designs using CFD.

The tendencies predicted by the regression model were confirmed by the CFD study. Design01 is better at high speeds than design02 and design03.

Figure 15c compares the CFD and regression results for design03.

Figure 16c: Longitudinal force comparison for design03 using regression and CFD.

As expected, the absolute value of the longitudinal force (drag) given by the regression model is different from the longitudinal force obtained after CFD calculations but the tendency is the same. This means that the regression model can be used to study performance differences in the pre-design phase.

Figure 17: Prototype sailing dinghy developed using the regression model described in this paper.

Finally, this study allowed the designer to study different hull shapes quickly and chose the best compromise for this new dinghy. Prototype testing (Figure 17) confirmed that the boat performs as expected. No modifications were required after completing the sailing tests.

8. GENERIC HULL MODEL

The regression model’s range of applicability depends on the parametric hull model’s versatility. The wider the scope of the hull model, the wider the potential scope of the regression model. To illustrate the versatility of this hull design technique, we present two examples from a generalised hull model developed from the model used for the CFD campaign.

Figure 18a: IMOCA-style hull from a new parametric model using the Friendship Framework.

Figure 18b: Another hull from the same parametric model used for Figure 18a.

9. CONCLUSIONS

This study demonstrates a practical method for estimating planing sailboat performance, overcoming the main deficiencies of previous design tools.

The system allows a designer to estimate the performance of a proposed new design by interpolating between hulls for which performance estimates are available from CFD and/or towing tank data. This allows data from previous projects to be applied to new projects.The regression model allows the results of CFD and towing tank studies to be applied to small projects whose budget would not otherwise justify detailed performance investigations. On larger projects, the regression model allows designers to quickly compare a range of possibilities before any new CFD or towing tank work is started. Data from new CFD or towing tank studies can be incorporated into the model, enhancing its accuracy for future projects.

Both the regression model and the parametric model require minimal computing resources. This means that preliminary concepts can be studied in real time without the need for large, expensive computing systems. It can be used in a cafe or yacht club.

The captive method of CFD and towing tank analysis ensures the model can be used to assess the position and dimensions of rig and ballast tanks, the disposition of crew weight, and other practical variables. It also provides some insight into planing dynamics.

The versatility of the parametric hull model ensures this approach is equally applicable to other sailboat types, such as retro cruisers and perhaps, multi-hulls.

Acknowledgements

The authors thank the following people for their generous assistance: Jean-Marie Finot, Pascal Conq and the Numeca Team.

References

1. Keuning, J.A. & Katgert, M. (2008), “A bare hull resistance prediction method derived from the results of the delft systematic yacht hull series extended to higher speeds”, Proceedings of the International Conference on Innovation in High Performance Sailing Yachts, Royal Institution of Naval Architects, London, 2008, 1–21.

2. Raymond, J. (2009), Estimation Des Performances Des Voiliers au Planing et en Manoeuvre (Estimated Performance of Sailing in Planing and Manoeuvring), Ecole Centrale de Nantes, Nantes, France, 2009.

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