Inviscid CFD codes applied in sailing yacht design

TECHNISCHE UNIVERSITET Laboratorium voor Scheepshydromechanica

Archief

Mekelweg 2, 2628 CD Delft

O15-78684/f44RK1181CFD Codes Applied in Sailing Yacht Design

Introduction

Computational Fluid Dynamics (CFD) is taking an ever more important place in the design

of ships. This process is not only obvious in the design of merchant vessels where inviscid

CFD codes nowadays are routinely applied at some institutes; but, perhaps surprisingly, also

in sailing yacht design. Especially in the design of yachts for the America's Cup races the increasing use of CFD has been a revolutionary rather than evolutionary process.

The breakthrough of the "scientific approach" to sailing yacht design largely came with the design of the 12-Meter Class yacht "Australia II" in 1981. Its victory in the 1983 America's Cup races was a demonstration of the potential of the integrated use of sophisticated towing

tests and flow calculations to support the designer. The design of the America's Cup contenders

nowadays invariably uses the latest CFD tools and advanced performance analysis techniques.

Within ten years the design procedure for these yachts has gone through the same development

as for merchant ships in several decades, and even beyond.

This paper briefly describes essential elements of the hydrodynamic design of sailing yachts

and the role played by CFD methods, specifically the validity and accuracy of linear and

nonlinear wave resistance codes for sailing yachts. Larsson(1990) gives a more complete review

of the state of the art in this field.

Hydrodynamic Design of Sailing Yachts

2.1 Hydrodynamic Forces

The speed of a sailing vessel is determined by the complicated equilibrium between sail forces and hydrodynamic forces. Forces on sails and hull in longitudinal, transverse, and vertical direction must be balanced. This leads to the yacht not just moving straight ahead, but taking a heel and yaw angle. Sail and hull forces depend on wind speed, ship speed, their relative direction, the heel angle and the yaw.

Hydrodynamic transverse forces act on the keel, the rudder, and the hull. Keel and rudder

have the familiar shape of lifting foils, but the hull usually does not. Its side force contribution

is partly due to wave making effects, partly to the "lift carry-over", the effect of the asym-metric pressure field generated by the keel. Hydrodynamic longitudinal forces consist of wave resistance, viscous resistance, and induced resistance resulting from the side force. The side

force may also contribute to the wave resistance.

The former 12-Meter Class yachts were restricted by the measuring rules to be deep, rel-atively heavy displacement hulls, with a shallow keel with low aspect ratio. The induced resistance and side force generation was of much concern in the design, but wave resistance was also an important quantity. To give an idea of the relative magnitude of resistance com-ponents: at 8 knots on a windward course, induced resistance amounted to about 15%, wave resistance 45%, viscous resistance 40%. Present International America's Cup Class (IACC)

yachts are light-displacement, high-performance hulls with deep-fin keels. At 8 knots to wind-ward, viscous drag may now amount to 65%, wave resistance to 20%, induced resistance 15%, Mzlgrarn and Frirnm. (1993). Downwind substantially higher speeds areoften reached, making wave resistance again dominant above 10 knots.

2.2 The Design Procedure

Designing for maximum speed involves not simply resistance reduction but simultaneously has to consider the side force generated at a certain yaw (leeway) angle, the heel angle and its

'MARIN, P.O.Box 28, 6700 AA Wageningen, Netherlands. e-mail H.C.RavenKuMARIN.NL

160 Schiffstechnik Bd. 41 1994 / Ship Technology Research Vol. 41 1994

effect on resistance, side force and sail forces. etc. On a windward course optimization of the speed made good to windward involves maximization of both the hydrodynamic and aerody-namic lift/drag ratio, Phillips (1973). Stability requirements and the behaviour in waves form important side conditions while the measurement rules, that usually restrict (combinations of)

parameters of hydrodynamic or aerodynamic relevance, further complicate the design problem.

The complicated trade-offs to be made require insight in the force equilibria. Suppose that

for a windward sailing condition a certain design modification (e.g. a reduction of the keel area)

would reduce the viscous resistance but decrease the side force. To find out whether this will

improve the performance or not, one could simply determine the speed made good to windward

at that particular course angle. But it is likely that a fair comparison must first determine the optimum course to windward which e.g. might be further off the wind than for the original design. In that case all force components will change as a result of this single modification.

This simple example illustrates that a method is desired to determine the sail forces and

hydrodynamic forces, boat speed, heel and yaw angles, in a certain wind speed: and to determine the optimum course angle and speed made good to windward. Such a method is a VPP, Velocity

Prediction Program, a relatively simple tool which plays an important role in the optimization and performance prediction.

A VPP requires as input the dependence of all forces and moments on speed, heel, and yaw.

This can either be supplied by empirical rules, or by more sophisticated tools, or using towing tests. The straightforward way of_ carrying out model tests is to determine a full matrix of resistance data against speed, heel and yaw angle. But the VPP then establishes the relation between these parameters. and only a small fraction of the test data actually plays a role. A

more efficient approach is permitted by a sail force dynamometer, Van Oossanen (1985), meant

to make each test a realistic combination of ship speed, heel and yaw angle. In the test rig as

developed at MARIN, the model is towed in the center of effort of the sail forces at a small tow

mast. Speed and yaw angle are fixed; the heel angle is left free. A servo mechanism adapts the longitudinal position of the tow point relative to the model. and its height above the water surface, such that true sail forces are simulated. These forces are measured and determine to what wind speed the data apply. This test set-up has later been extended for tests in waves.

2.3 Application of CFD

While towing tests are most useful for the final evaluation of the design and optimization (fine-tuning) with respect to aspects not covered by theoretical approaches, a large part of the optimization nowadays can be done using CFD methods. CFD allows to predict and optimize

the hydrodynamic side force, the wave and induced resistance, and to systematically investigate the effect of complicated appendages or design modifications on these quantities within a short time; it also provides the insight necessary to find new solutions to design problems. Although similar methods can also be applied to predict aerodynamic forces, we shall not consider these

here and will only address the prediction and optimization of hydrodynamic forces.

Application of flow calculations to sailing yachts is more complicated than to motor ves-sels. Yacht geometries are quite complicated, with keel and rudder, possibly winglets making complicated intersections with each other that need to be discretized most carefully to avoid

numerical problems. Heel and yaw make the geometry and flow asymmetric. The induced resistance related to the side force on keel and rudder plays is important and must be deter-mined accurately. The representation of the lift carry-over, the numerical treatment of the hull/keel junction, the interference between the keel wake and the rudder, and the effect of the free surface on the side force are further complicating factors for calculations and their analysis. But similar complications would almost prohibit to make the right choices without using computational tools.

3. Inviscid flow codes for sailing yachts

3.1 Some history

Sailing yacht design used to be based mainly on the experience of the designer and some-times on full-scale experiments. Especially in the USA, tank-testing sailing yachts was rather unpopular in the seventies. The victory of the Australia II in the 1983 America's Cup contest, making the Cup leave the US after 132 years. was demonstrated what could be achieved by proper use of towing tests and flow calculations. Its design was a radical departure from that of

previous 12-Meter Class yachts, which would have been hard to develop based on design

experi-ence alone. Extensive towing tests at MARIN and flow calculations by the National Aerospace Laboratory NLR proved most helpful in devising and refining the new concepts involved.

The NLR evaluated several design variations using the NLR panel method. Labrujere et al. (1970), predicting trends of side force and induced resistance. This allowed to confirm and explain the favourable effect of the famous winglets mounted to the keel, which was simulta-neously found and further optimized in towing tests for several configurations. Van Oossanen (1985). The wave resistance, however, could not be predicted and was not particularly re-duced: No treatment of the free surface was available at that time, except a simple reverse mirror image technique appropriate for very high Froude numbers.

First calculations for varying keel taper ratio's had suggested the usefulness of inverse taper, a so-called -upside-down" keel, having maximum chord length at the tip. This is theoretically advantageous at very high Froude numbers, Slooff (1984), but increases the induced resistance

at lower Froude numbers due to the larger loading at the tip. Winglets were tried to compensate

this, and in fact were found to increase the side force and reduce the induced resistance; but

they increased the wetted surface and thereby the viscous resistance. However, the inverse taper

and the volume of the winglets allowed a deeper position of the ballast, and a reduction of the ballast weight was possible. Consequently a large part of the keel could be cut away (reducing again the wetted surface), the stability was increased and displacement reduced. The 12-Meter Class measuring rules then require a smaller waterline length but permit a larger sailarea. All

these factors contributed to an increased performance, in particular on windward courses in

light winds, Milgrarn, (1984). The close cooperation between the designer Ben Lexcen. MA.RIN

and initially NLR thus not only led to a revolutionary keel but to an entirely different design

overall.

The success of this joint effort made eight different syndicates for the 1987 America's Cup

races use MARIN's services. All of them applied CFD, water tunnel tests, and towing tests in an

integrated approach. Also the challenger "Stars and Stripes" that eventually won the races had been designed using similar tools. For the inviscid flow prediction, MARIN used a predecessor

of the current code DAWSON. the NLR-developed code HYDROPAN. Free-surface effectswere

taken into account in the hull and appendage design, although the wave resistance predictions were rather poor for today's standards. This partly resulted from insufficient resolution which was almost unavoidable using the computers then available. Therefore the code was again primarily useful to optimize side force and induced resistance. The actual wave resistance work at MARIN, starting in 1986. soon resulted in important code modifications leading to the DAWSON program. which was subsequently extended for sailing yacht calculations and validated in a study for the Australia II (Section 4.1).

However. 12-Meter ClaSs yachts soon became obsolete: after the 1988 races. new rules for the America's Cup contest were agreed upon. The new IACC yachts have entirely different dimensions and hull forms. posing new problems and design trade-offs. New experience and insight had to be collected within a short time. and CFD methods proved extremely useful for systematically investigating many parameters and possibilities. Especially in the USA a huge effort was made to collect the necessary data and experience on the design. Cooperative

projects in the PACT (Partnership for America's Cup Technology) involved extensive use of

potential flow codes. studying details of the hull and appendages, wave resistance effects, and ship motions and diffraction forces. Sclavounos and Nako.s (1993). While the research efforts for America's Cup yachts are almost unrivalled, some research has been carried out fore.g.

IOR Maxi yachts and for a few other yachts to be built in larger series. CFD has played a role in such work as well.

3.2 A linearized free-surface panel method

To illustrate the capabilities of present flow calculation methods, we will now consider two

particular codes for calculating the inviscid flow around a ship hull, and their application to

cases relevant to sailing yacht design.

For studying wave making, side force generation and induced resistance, neglecting viscosity

effects on the flow is a practical and valid simplification. A potential flow is then assumed, subject to boundary conditions on the hull (zero normal velocity) and on the water surface. The latter conditions state that the flow must follow the wavy water surface, and that the pressure must be equal to the atmospheric pressure. All boundary conditions can be expressed in the (unknown) potential and its spatial derivatives.

The solution can be found by a panel method. We cover the boundaries of the flow domain (i.e. the underwater part of the hull surface, and a surrounding part of the water surface) with

source panels. The total flow field is defined to be the sum of the velocity fields induced by all

source panels plus the incoming undisturbed flow. The boundary conditions lead to a closed

set of algebraic equations in the unknown source strengths. After solving this system we easily

deduce the velocity and pressure field, the wave pattern and all derived results such as the forces and moments on the hull.

The wave making problem is substantially complicated by the nonlinear free-surface bound-ary conditions which are to be imposed on a wave surface not known beforehand. To circumvent

these difficulties, until recently the problem was always linearized. In most methods this was done by assuming the flow to be a relatively small perturbation of the flow around the hull

without waves. the "double-body flow". Dropping terms quadratic in the perturbation removes

the nonlinearities and the need to impose conditions on an unknown boundary. In most lin-earized methods. panels are therefore put on the undisturbed water surface. and the solution can be found in a single step.

The most popular method in this class is Dawson's (1977) method, a particular imple-mentation of the approach outlined above. Many codes for Dawson's method exist, differing mostly in certain numerical details. At MARIN we use the code DAWSON. Raven (1988),

routinely in commercial ship design work. As it reliably predicts the complete flow field (wave

pattern, flow direction and hull pressure distribution), it provides the information permitting

a most efficient. directed optimization of the hull form design. Although for merchant vessels,

in particular for full hull forms, the wave resistance predicted usually is not quite reliable, for the relatively slender hulls typical of sailing yachts most useful resistance predictions can be

obtained, see below. Side force predictions for sailing yachts generally are accurate.

3.3 Application to sailing yachts

To apply such a method to sailing yachts. several extensions and additions have to be made.

In the first place, the side force (lift) working on keel and rudder must be modeled. The implementation in DAWSON is entirely analogous to that in the NLR Panel method. Labrujere et al. (1970). Because lift cannot be represented by source panels alone, we add a dipole distribution in the camberplane of the lifting components and extending aft from their trailing edges as a "wake sheet". The shape of the wake sheet is specified and is not iteratively adapted. a linearization in the lift coefficient.

The source panels on the outer surface of the foils are arranged in chordwise strips. In the camberplane under each strip are strips of dipole panels. The dipole strengths have a specified distribution over the chord, such that only a single unknown is added for each strip of dipole panels. This unknown is the circulation around that spanwise location. There are as many additional unknowns as there are panel strips on the lifting components.

A Nutta condition (smooth flow off the trailing edge) is imposed in a point just aft of the trailing edge in the middle of each strip. In this point we require zero velocity normal to the trailing dipole sheet. a linear formulation consistent with the restrictions in the code. The Kutta conditions, expressed in all source and dipole strengths, are simply added to the set of equations, and the circulations to the unknowns. The system is again closed and can be solved, although the solution method requires some modifications, Raven (1988). Thus the simultaneous solution for all source and dipole strengths is found. The computed flow field incorporates all interference effects mentioned before: the effect of the free surface on the side force, the effect of the side force on wave making, the side force acting on the hull.

Although the prescribed distribution of dipole strengths over the chord might at first sight seem restrictive, the lift distribution found may well be entirely different, due to the effect of the source distributions on both sides of the foil. An odd dipole distribution will produce large source strength gradients, to be avoided for reasons of numerical accuracy, but will still give approximately the correct lift distribution.

A difficulty arises at the hull/keel junction. The hull cannot simply be treated as a lifting surface, as a Kutta condition generally does not apply. Letting the dipole distrbution of the keel end right at the junction would seem rational but causes numerical trouble, the edge of the dipole panel inducing infinite velocities on the hull. The usual solution is to continue the dipole sheet with equal strength inside the hull for some (arbitrary) distance; in DAWSON usually all the way up to the undisturbed water plane. The precise distance fortunately has rather little effect.

Another problem arises in the shape of the wake. Should the trailing vortices just be horizontal lines, should they follow the hull contour? This does have an effect on the predicted side force and induced drag, though a not too drastic one, Boppe (1991). Consistency in treating these problems may be the best option.

For a flow with waves the induced resistance cannot simply be found from pressure integration. The pressure resistance found is the sum of induced and wave resistance, and the analysis is hampered by the inability to distinguish between these components.

Therefore we derive the induced resistance from a far-field analysis (Trefftz-plane analysis)

based on the strength of the trailing dipole sheet. Additionally a better accuracy is obtained than pressure integration would allow.

Visualization of the pressure distribution gives an idea of the quality of the viscous flow and the generation of the side force. The vertical distribution of the side force can be plotted, giving important keys for the minimization of induced drag. Also the forces and moments are given: the wave and induced drag, the side force, the yawing and heeling moment, the sinkage and trim.

Sailing yachts require more care in grid generation than usual ships. The intersections of keel. hull. and winglets are 3D curved lines that must be properly discretized since overlapping or intersecting panels could produce numerical difficulties. Also the dipole distribution in the lifting surfaces and the trailing vortices must be appropriately defined. Any lack of care in the discretization for sailing yachts immediately results in useless or

164 SchilIstechnik Bd. 41 1994 / Ship Technology Research Vol. 41 1994

misleading solutions for e.g. the induced resistance. or even in no solution at all.

Tools for quickly adapting the paneling to a change in heel, trim or sinkage are necessary for efficiently dealing with different conditions.

3.4 RAPID

a nonlinear free-surface panel method

While considerable success has been obtained using linearized methods for sailing yachts, in

principle the linearization is less reliable. Linearization assumes that vertical variations of the

flow field and hull geometry are small near the waterline. This allows to reduce the free-surface

boundary conditions to conditions on the undisturbed free surface, to discretize only the part of the hull under the still water line, and to perform the pressure integration over that area only. The hull is virtually cut off at the still waterline. But sailing yacht hulls usually have pronounced flare and a large stern overhang ("counter stern"), often because the rating rules restrict the waterline length. At speed the stern wave reaches the overhang and lengthens the wetted part of the hull by several meters. The counter stern restricts the height of the stern wave and absorbs a longitudinal force in forward direction. If the stern wave is large enough it will reach the edge of the transom, and a somewhat different flow regime occurs locally, which cannot be properly represented by a linear method, Raven (1993). All these aspects are absent in linearized calculations. Therefore these applications call for a fully nonlinear_

method, in which the free-surface boundary conditions are not simplified but imposed in their.

exact form; not on the undisturbed water surface but on the actual wave surface; in which-. dynamic trim and sinkage are determined and their effect is fully incorporated; and in which the hull boundary conditions are app-lied on the part of the hull that is actually wetted at the

condition considered.

Since a few years such nonlinear methods are available, e.g. SHALLO (Jensen et al. (1989)),

RAPID (Raven (1992,1993)), and SHIPFLOW (Larsson et al. (1989)). A RAPID (RAised

Panel Iterative Dawson) calculation basically is an iterative process, each iteration constituting a problem similar to the Dawson problem. However, the free-surface condition is not linearized

with respect to a flow without waves, but to the flow found in the previous iteration; and it is

imposed on a wave surface deduced from the previous iteration. Repeatedly solving this linear

fixed-domain problem makes the result converge to the solution of the exact problem without

any linearization, with the free surface boundary conditions imposed on the actual free surface.

The method has been found to be quite robust and to converge usually without any trouble

even for severely nonlinear cases or with bad initial guesses. This makes the code a very useful

tool in design, and it has already been successfully applied in several practical design studies. It still seems to be a general belief that nonlinearities primarily affect the wave making for full hull forms such as tankers. However, we find that including the nonlinear effects often gives a surprisingly large improvement of the wave pattern prediction, even for slender ships:

in particular for diverging wave components. In several cases an unexpected level of agreement with experimental data has been obtained. For full, slow ships on the other hand. the nonlinear

effects on the wave pattern seem to be fairly small. although on the resistance prediction they can be quite substantial.

As an example. Fig.1 compares calculated and measured longitudinal cuts through a wave pattern for a recent practical case. The cut is at 20% of the ship length off the centerplane. The bow is at x11, = 0.5, the stern at xIL = +0.5. RAPID overestimates the depth of the

first bow wave trough and the stern wave amplitude far downstream. The first deviation will at

least partly be a result of the wave breaking visible in the experiment, the latter one is due to

viscous effects, specifically the small dead-water region aft of the transom. Otherwise RAPID

reproduces the experimental data in almost all details. DAWSON appears to substantially underestimate the bow wave system here and misses several shorter components. This has

_

experiment

.§11

cr.7

Fig..1: Longitudinal cuts through measured and computed wave pattern, for a RoRo vessel Similar results have been obtained in other cases. RAPID predictions virtually alwaysare

closer to experimental data than linearized predictions, and the _{more so for cases dominated by} diverging rather than transverse waves. While applying RAPID to sailing yachts thus seems

attractive, at present lifting surfaces have not yet been included and no provision has been made for asymmetric flows and geometries. Both restrictions _{can easily be removed..}

4. Results

4.1 Australia II

In 1987 an extensive validation study for DAWSON waS carried out for the Australia II. Nowadays larger panel numbers would probably be used and better results obtained, but the

study seems worthwhile. to review. Measurements

Calculation - - RAPID DAWSON

\I

Calculated wave resistance and experimental residuary resistance coefficient,

Australia II,. zero heel and. leeway .

Calculations were made for the vessel upright and with. zero leeway angle at 7, 8.5 and 10 knots speed, conditions relevant for downwind sailing. Experimental trim and sinkage were used in the geometry definition. Fig.2 compares the calculated and measured _{wave resistance.}

166 _{Schiffstechnik Bd. 4t} 11994 Ship. Technology Research VOL 41, 1994

_ -0.5 -0.5 C in 10 Fig. 2: -1.0 0.0 1.0

A fair result is obtained for the lower _{speeds, but, a 30% overestimate}

at. 10 knots. The _most likely explanation for this is the favourable effect of the counter stern _{on wave making and} resistance, which is_{absent in these linearized calculations.}

8014

STERN

Fig 3: Wave profile Australia II, case 3. Wave _{height 10 times magnified.}

weather side; - - - lee side.

For windward sailing

conditions, combinations of speed, heel and leeway _{were taken from}

experimental data. Fig.3

shows the asymmetry of the wave profile along the hull, with a larger bow wave at the lee side, a deep wave trough at the weather side (amplified _{by the keel suction),}

and a substantial longitudinal shift of the _{stern waves.}

In absence of an experimental form factor for _{the heeled and yawed}

conditions, the same

viscous drag as in upright _{condition has been added to the calculated}

wave resistance. This is the "calculated" total _{model resistance entered in Table I. It}

appears that for the two conditions for which experimental_{data are available, the}

model resistance prediction _{is within 9% of the}

experimental value; the large increase with heel angle is _{well represented. The}

side force is

within 8%. The lift/drag _{ratio is extremely close}

to the value found in the experiment, the deviation being less than_{3%. The side force with waves is much larger than in the}

double-body flow _{0). This is largely due to the asymmetry}

of the wave forces _{on the hull. The hull} here carries _{up to 45% of the side force due}

to these wave forces and the lift carry-over. Table I: Calculated forces _{and moments. Australia II,}

windward sailing conditions. speed 1 _{speed 2 speed 3}

heel angle _{13.5 21.3 33.0} leeway angle 2.33 4.19 5.89 C,,, . 103 _{1.18 2.89} 6.00 Ctnd - 103 _{0.28 0.80 1.28} C, - 103 _{16.58 28.27} 34.55 Czi(Cz)F----.o 1.25 1.27 1.35 (Fz),1,1(F,..),, (Fx)carcl(Fx)exp 0.92 0.91 -1.06 1.06 / /

\

/

4.2 IOR Maxi Yacht

For this study a geometry was selected having several features in common with IACC yachtS

a small displacement, flat sections, a relatively narrow transom and a deep-fin keel. Again,

a counter stern of substantial length is present. The calculations with the nonlinear code concerned the hull at zero heel and leeway (downwind sailing), with keel but without rudder,

at F, = 0.272,0.341 and 0.408. Trim and sinkage were iteratively determined.

Running a nonlinear code for a case like this may be problematic: Due to the flat sectionS and large stern overhangs, the waterline changes quickly for each change of thestern wave

height in the course of the iteration. This may destabilize the iterative process. Also a careful treatment of the geometry and paneling on both the hull and the free surface_{near the waterline} is imperative. Nevertheless, no serious problems were met and the results converged within

to 15 iterations for all speeds.

DAWSON was also run for comparison for thesame trim and sinkage. The height of the

diverging waves from the bow is again larger in RAPID, Fig.4, but _{not as much as in Fig.l. The}

bow wave near the hull predicted by DAWSON is lower and less steep, a typical shortcoming 'of the linearization. The wave, profiles along the hull, Fig.5, show the stern wave being pushed down by the counter stern, an effect absent in the DAWSON calculations, There is a large difference in the shape of the body as felt by the two codes, _{as the stern wave increases the} wetted length of the hull by 15% and the _{wave trough alongside the hull reduces the actual} waterline beam. -

Ej

...

11"."...0

...

_{V....,... ,....}

...w_... _....__...=

...--y..,

_,..w...

_{..."'''''.w Iiii"}

... ..w....

_{..."...""'"° ..."Z.L. ...n MOMO'n.,%,.LVia'...a.. ...}

,M ... MONW

".1-1 -00"an.4.11.01V.ki0/._ 11 611W..& IHIII").1%11Z&L VI,n 0M,14,..

,OWINMM.L VW, VI& ..iono

.. ,,,,p,

,,,

Fig.,4; Wave pattern of IOR Maxi yacht for Fa = 0.341,

computed by DAWSON (top) and RAPID (bottom)

168 _{'Schiffstechn* Bd. 41 1994 / Ship Technology Research VOL 41 .1994.}

Fig.5: Computed wave profiles of IOR Maxi yacht, at F = 0.272,0.341,0.408

ç.

exp. residual resistance I

0 RAPID wave resistance

DAWSON wave resistance

8. 10. 12.

ship speed [knots]

Fig.6: Computed wave resistance and experimental residual resistance of IOR Maxi yacht

Fig.G compares the wave resistance predicted by DAWSON and RAPID with the experi-mental residuary resistance. Both codes give results in fair agreement with the data, without

These results suggest that, notwithstanding the expected strong nonlinearities in this ap-plication, fair results can also be obtained with a linearized method. This may be due to the slenderness of the hull which reduces the magnitude of the nonlinear contributions, or due to fortuitous error canceling. In any case, the nonlinear prediction is more reliable as the effect of the counter stern and flare and the flow off the stern are completely included.

This is further emphasized by the results of additional DAWSON calculations for the yacht with heel and leeway, at FT, = 0.341. In this case the rudder was included. There is a marked asymmetry of the wave pattern, Fig.7. Results reproduced the relative resistance increase with heel well, although showing a 14% difference in side force with the experiment. However, a strong dependence was found on whether or not a transom flow was supposed. This detail of the modeling appeared to make a significant difference in the angle of incidence on the rudder and thus in the side force. As opposed to this ambiguity, a nonlinear method in the course of the iteration would find out whether or not the stern wave reaches the transom edge, and would model the transom flow much more appropriately.

Fig.7: Wave pattern of IOR Maxi yacht; heel angle 26', leeway 3.67°

5. Conclusions

Since the victory of the Australia II in the 1983 America's Cup races, a revolutionary increase of the use of CFD and towing tests in the design of sailing yachts has taken place. Simultaneously the development of CFD itself has progressed greatly. In particular, a much more complete and reliable prediction of wave resistance, induced resistance and side force is possible nowadays, as the case studies discussed here show.

For yachts with wing keels, computational tools are almost indispensable for optimizing the design. There is a very large number of parameters having effects on resistance and side force,

e.g. winglet position, planform, incidence, dihedral angle and twist; keel taper, sweep, and thickness; trim tab planform and setting. Determining optimum values for all these parameters

using towing tests would be impossible, not only because of the time needed but, also since small

effects would probably not be isolated in a physical experiment. CFD here proves invaluable for quickly and systematically investigating their effects.

While linearized wave resistance methods are in principle somewhat dubious in these

appli-cations, they seem to work fairly well at. least for prediction of overall forces. Nonlinear methods are far more complete, including the hull form above the waterline (with the important. counter

stern), the trim and sinkage of time hull, and the change of the wetted part of the body due to 170 _{Schiffstechnik Bd. 41 1994 / Ship Technology Research Vol. 41 1994}

the wave making. Robust and accurate nonlinear methods such as RAPID therefore allow an

even further refinement of the design of large sailing yachts.

Further advances may be expected in the application of viscous flow CFD (boundary layer or Xavier-Stokes methods) to sailing yachts, which has rarely been done up to now. This may permit to reduce flow separation. the generation of longitudinal vortices or the interference drag arising from the keel-hull intersection. Also the use of prediction methods for added resistance and ship motions in waves is likely to be extended in future design studies.

Therefore, for the foreseeable future competitive sailing yacht design will entail extensive

use of CFD tools for a quick evaluation of the effect of variations and prediction of drag and lift.

a Velocity Prediction Program for determining the consequences for the boat speed and time spent on the race course, and sophisticated towing tests for studying physical effects otherwise

not represented and for fine-tuning the design. It is the optimally integrated use of these three components that is the best support for today's yacht design.

References

BOPPE, C.W. (1991), Sailboat hydrodynamic drag source prediction and performance assessment. 10th Chesapeake Sailing Yacht Symp., Annapolis

DAWSON, C.W. (1977), A practical computer method for solving ship-wave problems, 2nd Int. Conf. Num. Ship Hydrodyn., Berkeley

JENSEN,G., BERTR.kM, V., SoDING, H. (1989), Ship wave-resistance computations, 5th Int. Conf. Num. Ship Hydrodyn., Hiroshima

--LABRUJERE, T.E., LOEVE, W., SLOOFF, J.W. (1970), An approximate method for the calculation of the pressure distribution on wing-body combinations at subsonic speeds, NLR Report MP70014 U. AGARD-CP-71

LARSSON, L., KIM, K.J., ZHANG, D.H. (1989), New viscous and inviscid CFD-techniques for ship flows, 5th Int. Conf. Num. Ship Hydrodyn., Hiroshima

LARSSON, L. (1990), Scientific methods in yacht design, Annual Review of Fluid Mechanics

MILGRAM, J.H. (1984), The speed potential of Australia II, 14th AIAA Symp. Aero/Hydronautics of Sailing, Long Beach

MILGRAM, J.H., FRIMM, F.C. (1993), Elements of resistance of IA CC yachts, 11th Chesapeake Sailing Yacht Symp., Annapolis

OOSSANEN, P.van (1985), The development of the 12 meter class yacht Australia II, 7th Chesapeake Sailing Yacht Symp., 1985

PHILIPPS, R.W. (1973), Faster, the technological tune-Up, 4th AIAA Symp. Aero/Hydronautics of Sailing, Los Angeles

RAVEN.H.C. (1988), Variations on a theme by Dawson, 17th Symp. Naval Hydrodyn., The Hague RAVEN, H.C. (1992), A practical nonlinear method for calculating ship wavernaking and wave resistance, 19th Symp. Naval Hydrodyn.. Seoul

RAVEN, H.C. (1993), Nonlinear ship wave calculations using the RAPID Method, 6th Int. Conf. Num. Ship Hydrodyn., Iowa City

SCLAVOUNOS. P.D., NAKOS, D.E. (1993), Seakeeping and added resistance of IA CC yachts by a three-dimensional panel method, 11th Chesapeake Sailing Yacht Symp., Annapolis