Scientific methods in yacht design

SCIENTIFIC METHODS

IN YACHT DESIGN

Lars Larsson

SSPA Maritime Consulting, P.O. Box 24001, S-400 22 Gothenburg, Sweden, and Chalmers University of Technology, Department of Marine Hydrodynamics, S-41296 Gothenburg, Sweden

INTRODUCTION

One of the most remarkable achievements in the history of sport was the victory of the Australian yacht Australia II in the 1983 America's Cup races. The cup, brought to the US from England in 1851 after the victory of the yacht America, had since then been successfully defended 24 times, and was considered permanently bolted to its table in the New York Yacht Club. American technology and financial resources, combined with the skill and experience of some of the most well-known yachtsmen in the world, had always been an insurmountable obstacle to challengers from different countries.

From a scientific point of view the victory of Australia II is of special interest, since the successful outcome of the races was, to a very large extent, the result of a strong technological effort (see van Oossanen 1985). The hull and, particularly, the keel represented radical departures from

the traditional design of the 12-m America's Cup yachts. Before the

breakthrough in 1983 the evolution of the 12-m class had almost ceased,

and there was widespread opinion among designers that the optimum

design had been reached. Furthermore, due to some notable failures in the early 1970s, confidence in yacht research, and tank testing in particular, was very low. After the 1983 races interest was boosted, not only in the

Cup itself but also in yacht research and development. It had become

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'Twelve meters is the rating of the yacht according to the International R-rule. The real

overall length is about 20 m. Yachts of the 12-m class were used in the America's Cup between 1958 and 1987.

obvious to everyone in the yacht-design community that much

prac-tical information could be obtained from the application of scientific

methods, and that there was still room for improvement in the 12-m class design.

In the 1987 campaign most participating syndicates spent large efforts on tank testing and numerical flow calculations. This was particularly true of the US syndicate Sail America, whose leading spokesman, Dennis Connor, had lost the Cup as skipper of Liberty in 1983. More than 30

naval architects, engineers, and scientists were engaged in the development

of the new yacht, and after a very successful campaign Connor was able to bring the Cup back to the US in February 1987. What is interesting in this effort, from a scientific point of view, is that most of the work has been published (see Salvesen 1987, Chance 1987, Letcher et al. 1987a,b, Letcher & McCurdy 1987, Oliver et al. 1987, Boppe et al. 1987, Scragg et al. 1987). Not much has been reported from other US syndicates, although some information

about the research in the America II and Heart of

America campaigns has been released (see Xia & Larsson 1986, van Hem-men 1986, Larsson 1987). Experiences from testing several of the non-US challengers have been collected in two papers on keels by van Oossanen & Joubert (1986) and van Oossanen (1987), and some infolination on the Australian efforts is given in the papers by Cox & Whitaker (1987) and

Klaka & Penrose (1987). Experiences from the design of the first fiberglass

12-m yachts, KZ 3 and 5 from New Zealand, are reported by Bowler &

Honey (1987).

Although the America's Cup has been the source of much recent yacht research, important developments have taken place over the years at

insti-tutions not linked to the Cup. The most comprehensive collection of papers

on yacht research may be found in the transactions from several series of symposia on the subject held regularly in the US and the Netherlands. The Chesapeake Sailing Yacht Symposium is held biannually on the US East Coast, and the AIAA Symposium on the Aero/Hydronautics of Sailing is an annual event on the West Coast. Recently, another series, the Tampa Bay Sailing Yacht Symposium, was started in Florida. The Dutch

Sym-posium on Developments of Interest in Yacht Architecture is held in

Amsterdam biannually. Several decades of yacht research at Southampton University are reported in the excellent books by Marchaj (1979, 1982, 1986), which deal with the fundamental aspects of sailing in a very clear and concise manner. Other books on the same topic are those by Kay (1971), Hammitt (1975), and Gutelle (1984). A book on the principles of yacht design by Joubert & Larsson (1990) is about to be published.

There are two different disciplines that must be mastered by the suc-cessful yacht designer: fluid mechanics and structural mechanics. Bearing

this in mind, it may seem surprising that the vast majority of papers on yacht research deal with only the first area. An important reason for this unbalance may be the 12-m rule, which prohibits exotic materials and

specifies robust scantlings. There has been no room for advanced structural

optimization.

While the fluid mechanics of sailing includes both aero- and hydro-dynamics, the emphasis of this review is on the latter. This is the area where most of the development has taken place in recent years. Readers interested in sailing aerodynamics are referred to Marchaj (1977, 1979), Milgram (1968, 1971a,b,c, 1972, 1978), Thrasher et al. (1979), Wiersma

(1977, 1978, 1979a,b) and Register & Irey (1983).

Today, hydrodynamic data for a hull can be obtained either by improved techniques for tank testing or by means of numerical methods. In either case a computer program is required for predicting the performance of the

yacht, given the hydrodynamic input. In fact, the program may itself

generate such data from semiempirical formulas. The results will be less accurate, but a large number of alternatives may be evaluated in a very

short time. This type of program, called VPP (Velocity Prediction

Program), is now a most important tool for top yacht designers. In the next section the VPP theory is outlined and some examples of applications

are given. Recent developments in the tank testing techniques are described

thereafter, and in the final section the results of application of

com-putational fluid dynamics (CFD) are reported.

VELOCITY PREDICTION PROGRAMS

Davidson (1936), more than 50 years ago, proposed a method for

predicting the close-hauled (upwind) performance of sailing yachts from towing-tank data. Using full-scale measurements on board the yacht Gim-crack, he was able to derive a set of sail coefficients, which has been in use at many towing tanks until recently (Murdey 1978). A more general

evaluation procedure was, however, proposed by Herreshoff (1964),

enabling predictions of all points of sailing to be made.

Methods for predicting performance without access to towing-tank data appeared in the mid-1970s (see Myers 1975, Letcher 1974, 1975a, 1976. Dawson 1976, Curtiss 1977). A few years later, van Oossanen (1979) presented a method especially designed for 12-m yachts. The real break-through of the VPPs did not appear, however, until the early 1980s as a result of the H. Irving Pratt project at Massachusetts Institute of Tech-nology (Kerwin & Newman 1979). The purpose of the project was to

improve the handicap rules for sailing yachts. A VPP was developed, which

System (MHS) and, more recently, for the International Measurement System (IMS) (see Poor 1986, Kirkman 1987). In the development of the

12-m yachts for the 1987 America's Cup the VPPs played a very important role, as explained by Oliver et al. (1987) and van Hemmen (1986). For the special Cup in 1988, where a catamaran competed against a monohull, performance predictions must have been even more important, and since

a new rule has now been adopted for the America's Cup, VPPs will

continue to be imperative as a tool for the designer.

Structure of the VPP

Until recently, all velocity prediction programs have been based on the equations for static equilibrium. The essence of such programs is thus a method for satisfying the equilibrium equations (although usually not in all six degrees of freedom). To accomplish this, info' illation is required

about the hydrodynamic, aerodynamic, and stability properties of the

yacht (see Figure 1). The output of the program is the yacht perfoithance under varying wind conditions.

As can be seen in Figure 1, the info' 'nation required can be obtained in a variety of ways. Static stability calculations are usually carried out by the designer, and some empirical correction for the effect of forward speed is added in the program. Accurate aerodynamic data are more difficult to

find. While it would be possible to obtain such data from either experiments

Empirical data Figure 1 VPPstructure. Either one of d - f can be used Empirical data c a and c very rare Wind tunnel

results Aerodynamicmodel

Numerical results Stability model Solution of equilibrium equalions Speed Heel Leeway et Towing tank results Hydrodynamic model Numerical results

Leeway _Dr angle force App. wind angle Aerodyn side force Hydrodyn side force

or numerical calculations, this is seldom done owing to the high cost

involved. Instead, standard aerodynamic coefficients are used. The hydro-dynamic input may be obtained from three different sources: towing-tank results, numerical predictions, or semiempirical relations. In the latter case

the hydrodynamic coefficients are computed by the VPP itself, and very rapid evaluations of design alternatives may be made.

Equilibrium Equations

Figure 2 shows the forces acting on a sailing yacht under equilibrium conditions. In the top view (left) the horizontal components of the forces are displayed. When the hull is driven through the water, a resistance is developed. Under equilibrium conditions this has to be balanced by a

driving force from the sails. Unfortunately, this cannot be accomplished without at the same time producing a side force, which in turn has to be balanced by the hydrodynamic side force. Since the turning moment under equilibrium conditions must be zero, the resulting aero- and hydrodynamic forces (in the horizontal plane) have to act along the same line.

In the view from behind (right in Figure 2) the force balance in

a

transverse plane (at right angles to the direction of motion) is presented. It is seen that the resulting aerodynamic side force is at right angles to the

mast. This is an assumption that was introduced already by Davidson

(1936) and has been adopted by all sailing-yacht investigators since then. The heeling moment from the side force is balanced by a righting moment

from the couple created by the buoyancy force and the weight of the

yacht.

Apart from the equilibrium equations, the velocity triangle (see Figure

Resistance

Figure 2 Forces on a sailing yacht.

'Heel angle Aerodyn side force angle Heeling force Hydrodyn. side force Weight Buoyancy force App. wind,

1.500

1100G

500

3) plays an important role. As the figure shows, the triangle relates the true and apparent wind velocities via the yachtspeed.

The VPPs generally solve a set of five equations:

,0 Aerodynamic driving force = Hydrodynamic resistance, Aerodynamic side force = Hydrodynamic side force,

is Aerodynamic heeling moment

Hydrodynamic (-static) righting' moment,,

co Apparent wind velocity from velocity triangle, Apparent wind direction from velocity triangle.

Hydrodynamic Model

A typical distribution of resistance components for a sailing yacht beating

to windward is shown in Figure 4. It is seenthat at lower speeds the viscous

Resistance Viscous Reeking induced Wave _Residuary Schoenherr Upright or ITTC -57 1_ :6 7' Speed [knots]

Figure 3 Velocity triangle.

Figure 4 Resistance components ofa 7.6-m cruisingyacht,

=

EN]

resistance dominates, while at higher speeds the wave resistance becomes increasingly more important. Upwind, the induced resistance amounts to about one fourth of the total resistance at low and intermediate speeds,

less at high speed. A fourth component, the heeling resistance, is introduced to take the effect of heel on the viscous and wave components into account.

For some yachts with very inclined ends, this fourth component may be

negative.

VISCOUS RESISTANCE The traditional way to compute viscous resistance

in hydrodynamics is to refer to some empirical formula based on tests with

flat plates. In the US, Schoenherr's formula has always been the most

popular one, but according to the recommendations of the International Towing Tank Conference (ITTC), the ITTC-57 Ship Model Correlation Line should be used (Comstock 1967). This is not a pure flat-plate formula, since it includes some form effect as well.. As a matter of fact, many VPPs use this formula for the total viscous resistance. Some attempts have been made to compute individual "form factors" for each hull (van Oossanen 1979,, 1981), but the accuracy of the empirical formulas is questionable.

When calculating the Reynolds number Ra required for the ITTC-57

formula, some account has to be taken of the fact that the chord lengths of appendages are much smaller than the length of the hull. Therefore :individual calculations are often made of the different parts of the

under-water body (van Oossanen 1979, 1981, Larsson 1981b)..

WAVE (RESIDUARY) RESISTANCE The fact that the computed viscous

resist-ance does not include the full form effect may not be too serious, provided that the formula for computing the rest of the upright resistance takes this into account., This component is normally referred to as the residuary resistance, and it contains essentially wave resistance but also, to some extent, the viscous form effect.

Several different relations for the residuary resistance have been

employed in VPPs. Van Oossanen (1979, 1981) used a semiempirical relation due to van Oortmerssen (1971),, based on tests with 93 different small-craft hull forms at the Dutch towing tank MARIN. An advantage with this formula is that it is based on wave-resistance theory, and very

good predictions applying the formula for Antiope were obtained by

Larsson (1979) and van Oossanen (1981). For 12-m yachts, van

Oort-merssen's relation may be the best but for lighter, more beamy yachts

another expression, derived on purely empirical grounds from a systematic series of sailboat tests by Gerritsma et aL (1981), should be more accurate. This formula, which contains the displacement, displacement/length ratio, prismatic coefficient,' longitudinal position of the center of buoyancy,, The prismatic coefficient is defined as the volume displacement divided by the Maximum

and beam/draft ratio, was shown to give quite good correlation with

measurements when applied to the 22 models of the test series.

INDUCED RESISTANCE The induced resistance may be computed either from slender-body theory or lifting-line theory (see, e.g., Newman 1977). The former approach was chosen in the MIT work (Kerwin 1976). In this approximation the induced resistance is independent of the detailed shape of the underwater part of the yacht, being inversely proportional to the draft squared. A correction for the displacement effect of the hull on the trailing vortex system was, however, applied by Kerwin.

More detailed studies of the effect of varying the shape of the appendages

can be made if the lifting-line theory is adopted, as proposed

by van Oossanen (1979, 1981). The induced resistance is then computed indi-vidually for the hull, keel, and rudder. Since in the lifting-line theory the

induced resistance is inversely proportional to the aspect ratio and an

"induced drag factor" (Abbott & von Doenhoff 1949), dependent on the

load distribution, the planform of the keel/rudder comes into play. In

aerodynamics the influence on the induced drag factor by s-weepback and

taper is known (see, e.g., Hoerner 1965), but for a sailing yacht the influence

is more complex owing to the interaction between the vortex field and the

free surface. A correction for taper was introduced by van Oossanen

(1981).

The aspect ratio is geometrically defined as the span divided by the mean

chord, or, equivalently, the span squared divided by the area. For a lifting surface attached at right angles to an infinite plane, the effective aspect ratio is twice the geometric one, and this assumption is usually adopted for the hull as well as for the keel and rudder. The hull is thus considered reflected in the free water surface, which is a good approximation at low and moderate Froude numbers but less accurate when significant waves

are being generated (see Slooff 1984).

In the most modern VPPs (Oliver et al. 1987, Larsson 1989), the effect of

the keel wings is taken into account. After their introduction on Australia II in the 1983 races, such wings are now always used on 12-m yachts. The

wings are mounted on the tip of the keel, thereby interfering with the

overflow from the pressure to the suction side. The strength of the vortex left behind the keel is then reduced, as is the induced resistance. Larsson's relations were derived by results from systematic numerical predictions by Letcher et al. (1987b), where the size and planform of the wings were varied, and the same data, combined with extensive towing tank infor-mation, were used by Oliver et al.

HEELING RESISTANCE When the yacht heels, the effective waterline length

predicted in the effective CAD systems now available to yacht designers, but this is not usually done. While very approximate methods are used for the length variation, the change in wetted surface is not considered at all.

SIDE FORCE Obviously, the same theories used for computing the induced

resistance can also be employed for the side force (hydrodynamic lift). Nomoto & Tatano (1979) showed that by combining slender-body theory for the hull with lifting-line theory for the appendages, an accurate

cal-culation of the side force and the center of effort could be made. In this method the side force of the hull and rudder was obtained by extending them through the hull to the waterline, The interaction between the hull and the appendages is then approximately taken into account. A more exact calculation of this interaction wassuggested by van 'Oossanen (1981). When the VPP is used for evaluating experimental data or results from numerical flow calculations, the residuary resistance is usually represented

by a spline function through the data, while the

induced and heeling resistance, as well as the side force, are 'computed using semiempirical formulas, where the constants are determined by regression analysis (see Gerritsma et al,. 1981, Letcher 1975b).

Aerodynamic Model

The most difficult part of the VPP theory is to find a good aerodynamic model. For many years, Davidson's (1936) sail coefficients were the only

ones available, and they have been used until recently for predicting

upwind performance from towing-tank tests. A simple model for all wind directions was proposed by Herreshoff (1964), and Myers (1975)suggested a model based on wind-tunnel data (Marchaj, 1982) and lifting-line cal-culations (Milgram 1971c). To obtain a more reliable model, full-scale data were recorded on two ocean racers, Standfast and Bay Bea, in the

mid-1970s. The results were reported by Kerwin et al. (1974)and Gerritsma

et al. (1,975), and the model proposed was used in the original VPP

developed in the Pratt project at MIT (Kerwin 1976).

A rather serious disadvantage of the proposed model was

that it

pro-vided no means for taking the actual shape of the sail plan into account.

The model was, valid for yachts with a rig not too

different from the

masthead rig of the ocean racing yachts on which the measurements had been made. For very different rigs, as on a 12-m yacht, the model could not be used without corrections. A possible improvement, suggested by Kerwin (1976), was to make use of the sail model

of the International

Offshore Rule. (IOR) for ocean racing. By means of this model, the actual rig could be converted to an equivalent Standfast type of rig, for which the measured coefficients could be used.

The most widely accepted aerodynamic model today is the one presented

by Hazen (1980). As in all other models, the forces are presented as

functions of the apparent wind angle. There are thus no means of trimming

the sails in different ways; they are always assumed to be set at their optimum. Hazen compiled data from various sources, including the Bay BeaStandfast results, and was able to obtain coefficients for lift and parasitic (viscous) drag

for each individual sail. A weighted average based on the area of each sail may then be used for their combined effect. The induced drag is computed

according to lifting-line theory by taking 1.1 times the height of the rig as the

effective span. The most serious disadvantage of Hazen's model is that the interaction between different sails is not included, but it has nevertheless

become accepted as the best choice available.

The effect of heel is taken into account in two principally different ways.

The original Bay BeaStandfast data (Kerwin 1976) indicated a linear force

reduction with heel angle. Kerwin (1976), on the other hand, suggested that the effect of heel could be considered in the velocity triangle. In a coordinate

system heeling with the yacht, the apparent wind angle will depend on the

heel angle, and a fixed set of coefficients that are only dependent on

the apparent wind angle can be used. It should be noted that due to the atmospheric boundary layer, the wind velocity has to be computed at the

actual height of the center of effort of the sails. Thus, the true wind velocity

also depends on the heel angle.

REEFING, FLATTENING, AND TWISTING Most modern VPPs have options for reefing and flattening the sails. In fact, in most programs there are automatic reefing and flattening procedures for finding the optimum per-formance of the yacht under varying conditions. Not only is this possibility a necessary feature for realistic predictions, it also serves as a guide to the

skipper of how to make optimum use of his sails. The reefing R and

flattening F factors in the sail model have different effects on the sail forces.

If R is proportional to some linear dimension of the sails, and the shape of the sail plan is assumed constant, the area and hence the forces will be proportional to R2. At the same time the height of the center of effort is also approximately proportional to R. F, on the other hand, is proportional to the lift of the sails, but it has no influence on the center of effort. Since

the induced drag is proportional to lift squared, decreasing the F-factor means increasing the lift/drag ratio, i.e. rotating the sail force forward. As

most sailors know, it is more beneficial to flatten the sails than to reef them when the heeling moment gets too large.

An interesting feature was introduced in the VPP used by the Sail

America syndicate in the 1987 America's Cup (Oliver et al. 1987). Since

by which the spanwise loading of the sails could be varied. In this way the actual sail trim of the 12 m in the strong winds off Fremantle could be modeled quite well. The effect of the twist parameter was obtained from lifting-line theory.

Flow Diagram

A simplified flow diagram of a typical VPP is shown in Figure 5.. To obtain

the equilibrium solution, an iterative method is required. Thus, the speed

and heel angle of the yacht are first assumed. This yields the apparent wind speed and direction, which are used to find the sail forces. The heel equation is then solved to find a new heel angle, and new sail forces can be calculated.

Upon convergence of the heel iteration, all resistance components can be

computed and the corresponding speed is obtained. This is not usually close enough to the assumed one, so several iterations are required. Know-ing the speed and heel angle one can compute explicitly the leeway angle. The calculations are repeated for varying true wind speeds and directions,,

and the results can be presented in the form of a polar plot (see Figure 6). The polar plot gives the speed of the yacht versus the true wind angle. Each curve represents a certain wind speed. Points of special interest are the upper- and lowermost points of the curves, where the yacht has its maximum speed upwind and downwind, respectively. The corresponding angles can be used by the helmsman to optimize upwind and downwind performance.

Sailing in Waves

A weak point of most VPPs is the prediction of the performance in waves. In many programs the wave effect is neglected, at least explicitly. It may be argued that since the aerodynamic model is based, to some extent, on results from actual sailing conditions, some effect of the waves may be buried in the sail coefficients. However, when obtaining the data, rough sea conditions were avoided. It would have been too difficult to include

the complex effects of a seaway in the simplesail coefficients_

Waves create motions in all degrees of freedom. Additional mean forces

are generated both on thehull and the sails. Furthermore, the sails

influ-ence the motions considerably, thereby rendering standard prediction

tech-niques useless in certain degrees of freedom. Therefore, a complete model for the wave effects is out of reach at present, but in the approach chosen 'by the author (Larsson 1981b, 1989) and some other investigators (Klaka & Penrose 1987, Oliver et aL 1987), the most important effect is taken into account., Thus, the added resistance in waves is calculated using a strip theory (see, e.g.., Frank & Salvesen 1970), and this component is added to

START

True wind direction

given Boat speed guessed Speed cony.? Heel angle guessed

App. wind vet. dir from wind triangle

Heel cony? Leeway angle from '(-equation More 'wind directlions? More wiad velocities? 1 Yes Yes

True wind velocity

given

Aerodyn forces from sail model

I

Heel angle from heel equation

LBoat

speed from X- equation

Figure 5 VPP flow diagram (schematic).

WIND DIRECTION BOAT SPEED [knots' 10 8 10

SPEED MADE GOOD MIN

12

Figure 6 Polar plot (example).

To investigate whether or not strip theory is appropriate for motions

and added resistance of yachtlike hulls, Gerritsma & Moeyes (1973), Klaka

& Penrose (1987), and Gerritsma & Keuning, (1988) carried out tests in waves and compared them with calculations. In general, fairly good correspondence was noted. For heavy hulls a considerable reduction in added resistance with heel angle was found, indicating that the strip-theory calculations should be carried out for varying heel. This turned out to be unnecessary, however, for lighter, more beamy hulls. The effect of leeway was found to be negligible.

Skinner (1982) investigated numerically the influence of the aerodynamic

damping of the sails on the pitch motion and the added resistance. A

reduction of the latter of about 14% due to damping for a 12-m yacht was obtained. He also carried out a simple calculation for the effect of pitching on the driving force from the sail and found it to be negligible. While Skinner's investigation involved important simplifications, it still lends some support to the approach used in the VPPs.

I

LW*SPEED MADE 600030°

ir

gs'

ri441,

t6M/s

1111/

1200 OM s 60° 90°

urgdX)

Pitch Yaw

Sway `11), _{Heave '(Z)}

Figure 7 Yacht motions (definitions),

New Developments of the VPP

DYNAMIC VI)13 A new type of VPP has recently been developed at SSPA

Maritime Consulting in Sweden. The purpose of the new development has been to be able to predict the dynamics of maneuvers and other unsteady conditions apart from wave motions. Such effects are of great importance in match racing and should be taken into account when investigating the

performance of, for example, America's Cup yachts.

-The mathematical model is based on the one presented by Rutgersson

& Ottosson (1987) and Kallstrom & Ottosson (1983) for ship-maneuvering

studies. Four dynamic equations are solved (cf, Figure 7, where the

ter-minology is defined):

a Surge acceleration from total surge force, Sway acceleration from total sway force,

Roll acceleration from total roll Moment, Yaw acceleration from total yaw moment.,

These nonlinear ordinary differential equations in time are integrated using the SIMNON computer program for nonlinear systems (Astrom 1982). On the SSPA Masscomp 5400 microcomputer, updating can be achieved up to 10 times per second, so real-time simulations can be made. This possibility is utilized in the SSPA sailing simulator, where match racing between two yachts can be practiced. The simulator, seen in Figure 8, consists of two identical setups, each with two screens for displaying the yacht in a horizontal and a vertical view. On the latter screen, which has a zooming facility, the competing yacht and the marks on the course are

displayed too. All instruments used on a real yacht are shown in the

horizontal view. A steering wheel and controls for sails

and trim tab' are

included.

Figure 8 The SSPA sailing simulator (two identical setups).

Not only does the dynamic VPP require a

completely new solution procedure, but also many new empirical relations are needed. Since the

yaw equation is considered, a rudder model including stall must be

provided, and stall effects of the keel at low speeds must be taken into account as well. The aerodynamic model includes the interference between the two yachts, and there is a sheeting model, which takes into account

the movement of the center of effort

for different sheeting angles.

Obviously, added masses for hull, keel, and rudder must be computed for all motions considered.

The sailing simulator has been in operation since the summer of 1988, but no extensive report on the basic theory has yet been published. A brief

description is given by Larsson (1989). The dynamicVPP has now replaced

the static one (Larsson 1981b) for all performance predictions at SSPA, including the ones based on towing-tank data and numerical flow pre-dictions. When the dynamic program is used as a VPP, an autopilot steers the yacht, and a prescribed number of tacks is automatically performed. As in the manually operated simulator, a wind spectrum with variations

EXTENDED USE OF THE VPP _{Extensive use of a VPP is reported by Oliver} et al. (1987) in the development of the America's Cup contender Stars

and Stripes. With knowledge of the wind statistics for Fremantle, the

probability of winning a race against a known opponent could be calcu-lated. In fact, in one approach, quasi-steady time-domain studies were

carried out where the two yachts were raced around the full course, using the wind history from statistical data. A matrix of win/loss probabilities

could then be obtained by systematically varying the sizes of the two

yachts. Table 1 gives one example, where Stars and Stripes as well as the opponent were varied in size, the waterline lengths being changed in steps of 1 ft from 46 ft to 49 ft. Obviously, when the sizes are equal (identical yachts), the probability must be 50%. It is seen that the best chance of winning is when Stars and Stripes is 48 ft and the opponent 46 ft.

In order to make the most rational decision regarding the hull size, game theory was applied. Thus, match racing was considered a two-person, zero-sum game. For the probabilities of Table 1 (the "game matrix"), this theory leads to a "single strategy" with 48 ft as the best option. Choosing this length there is no way the opponent can get a higher probability of winning. Other game matrices may lead to a "mixed strategy," where a weighted random selection between the choices must be made. It is also possible to compute the result of a series of match races where the fleet of competing yachts has an assumed composition of lengths.

TOWING-TANK TESTING

The first reported extensive tank test of a sailing yacht was a disaster. The British designer G. L. Watson spent nine months tank testing his America's Cup challenger Shamrock II, only to be beaten in three straight races by the Herreshoff-designed defender Columbia in 1901. Watching the losing

Table 1 Percentage win probabilities for Stars and

Stripes (Perth, January)

Opponent Waterline (ft) 46 47 48 49 46 50 45 41 44 Stars and 47 48 55 59 50 53 47 50 47 52 Stripes 49 56 53 48 50

-battle, Watson made his now classic remark: "I wish Herreshoff had a

towing tank" (Burgess 1935).

While this may not be a fair verdict on the towing tank, it is quite clear that the early tests with sailing-yacht models were not entirely reliable. It was not until Davidson (1936) pointed out the importance of measuring

not only the resistance but also the side force that

more accurate pre-dictions could be made from the tank. There are, however, still a number of pitfalls in the sailboat test technique, which in many respects is con-siderably more complex than regular ship model testing.

Testing Techniques

As pointed out many years ago by Davidson (1936), there are two prin-cipally different techniques that can be used when investigating a sailing-yacht model. The apparently most straightforward way is to tow the sailing-yacht at the center of effort of the sails and let it attain its equilibrium condition under heel. By measuring speed, heel, and leeWay for a given sail force, the merits of the design can be evaluated.

This method was not, however, adopted by Davidson, who favored the other technique, in which the hull is fixed in all degrees of freedomexcept

heave and pitch, and where a matrix of speeds, heels, and leeways is

covered in each test. By applying suitable interpolation routines and using

a VPP type of approach, the equilibrium of the yacht under different

conditions can be determined.. This semicaptive technique was adopted by other towing .tanks and is still the most popularone.

THE SEVIICAPTIVE TECHNIQUE _{While most tanks have stuck to the .original.}

idea of releasing only heave and pitch in the semicaptive techniques (Kirk-man 1974, 1979, Murdey et al. 1987, DeBord 1987, Takarada & Obokata

1987, Gonzalez 1987, Campbell & 'Claughton 1987), an alternative

approach is to release also the roll motion and

measure the heel angle during the run.. By applying a weight sliding transversely, a static moment can be applied to the hull to vary the heel angle. This technique has been used particularly for large models to avoid _{an excessive roll moment in} the supporting mechanism due to the hydrodynamic force (see Herreshoff & Newman 1967, Kirkman 1974, 1979).. There are, however, many other ways of avoiding this problem. In Figure 9 the equipment used at SSPA for testing large models is presented. The towing force is applied

_{to a}

vertical mast, approximately at the center of effort of the sails in the upright

condition. The horizontal component of the heeling force is measured at the same position.. Fore and aft, the hull is guided by vertical posts, giving the model the freedom to heave and pitch. Side-force transducers. are fitted

force Yaw and Pitch free Y force Universal joint X force Y force Hinge Carriage

Figure 9 SSPA's yacht dynamometer (principle).

forces on the hull. In this design the lever arms for heel and yaw moments are very large, and the setup is quite stiff, enabling accurate setting of the angles. When the heel angle is changed, the foot of the mast, pivoting around a bolt at deck level, is moved sideward. Since the side forces are applied horizontally in this equipment, a weight has tobe put on the hull to account for the vertical component of the sail force. No correction is applied to account for the slightly too large pitching moment from the mast force when the model is heeling.

THE FREE-SAILING TECHNIQUE

Davidson's free-sailing idea was first

developed by Allan et al. (1957). A force was applied at the center of effort

of the sails, and the hull was free to attain equilibrium heel and leeway angles corresponding to the towing speed.

Care was taken to apply the

towing force at right angles to the mast. Unstable as this setup may seem, steady conditions were obtained in most cases. Some restraining moment (which was measured) at the top of the mast was however, occasionally

needed.

Equipment, in principle very similar to that used by Allan et al., was developed at the National Research Council (NRC), Canada (see Murdey 1978, Murdey et al. 1987). The major difference is that in the NRC tests, the rudder angle is used as an independent variable. By varying the rudder angle, the heel is changed systematically. The main reason for including the rudder is that in practice it is very important for balancing the yacht.. More realistic conditions can then be obtained in the tank.,

universal

joint

Some instability was reported by Murdey (1978), and to avoid this

problem a slightly different approach was chosen at MARIN, the Nether-lands, where the most modern free-sailing equipment has been built (see Gommers & van Oossanen 1984, van Oossanen 1985). The equipment is seen in Figure 10. In this system the yaw angle is fixed. The towing force is applied at a vertical position corresponding to the center of effort of the sails. When the hull starts moving, a side force is developed. This causes the model to heel and a yawing torque to be developed. By using servo-motors, the mast structure moves longitudinally until the torque is elim-inated, and the tow point moves axially along the mast until there is no axial component left of the tow force. Equilibrium conditions are obtained after 15-20 s.

The major advantage of the free-sailing systems is that fewer test points are required. Rather than one needing to interpolate in the speed-heel-leeway matrix, each test condition represents a realistic combination of the three variables. According to Murdey et al. (1987), experiences from the NRC system indicate that about half as many test points are required as compared with the conventional semicaptive systems. On the other hand, predictions of prototype perfoi mance can be made only for the stability tested. In the semicaptive approach, stability is taken into account

in the VPP prediction and can thus be varied arbitrarily. Another

dis-advantage of the free-sailing tests is that the cost of producing a model is

Vertical carriage attached to main carriage

Y force

Universal joint (pitch, heel free)

X force

Yaw angle

Most movable

increased, since a cast lead keel is required to give the correct stability. In fact, Murdey et al. (1987), after more than 10 years of experience of the free-sailing system, conclude that the semicaptive procedure combined with a state-of-the-art VPP is the optimum combination. An implemen-tation of such a system at NRC is planned for the future.

Model Size and Turbulence Stimulation

An issue that has been discussed extensively in the past 15 years is the required size of the models. For almost 40 years after Davidson's pio-neering work, models at 1:13 scale were used in the Davidson Laboratory at Stevens Institute of Technology, and eight successful America's Cup defenders were developed in that way. The disappointing performance of the two 12-m yachts Mariner and Valiant in the early 1970s, however, cast doubt on the usefulness of the towing-tank technique itself, and the failures were attributed by many to the misinterpretation of the tank data due to scale effects.' An extensive test program had already been launched by the panel H-13 (sailing yachts) of the Society of Naval Architects and Marine Engineers, and a standard test case had been defined (Society of Naval Architects and Marine Engineers 1971). Different sizes of this hull, the Antiope, were tested at many different organizations in the late 1960s and early 1970s (Herreshoff & Newman 1967. Kirkman 1974). In a landmark paper, based on these and a number of other geosim tests from different

laboratories, Kirkman & Pedrick (1974) were able to draw important

conclusions regarding the required size of the models. These conclusions and recommendations were later reinforced in a paper by Kirkman (1979). In essence, the results were as indicated in Figure 11. Here the correlation between the model and its prototype, or (in some cases) a larger model, is

given as a function of the waterline length of the (small) model. Two

important conclusions can be immediately drawn: The scatter is very

large for the small scales, with many errors in the 10-20% range; and a considerable reduction in error is obtained at larger scales.

To obtain the results of Figure 11 the small-model data were extrapo-lated to full scale or largest model scale using the standard procedure in yacht testing. The upright resistance is assumed to consist of two parts:

the viscous resistance and the residuary resistance (cf. Figure 4). For

the same Froude5 number, the latter component is proportional to the

'Brown & Savitsky (1987) have recently shown that the Mariner predictions were correct. It was predicted to be considerably slower than the competitor Courageous, which had been tested in the same tank, but this information could not be released to Mariner's designer for

proprietary reasons.

'The Froude number F, is defined as the speed divided by the square root of the waterline

Correlation error in percent 20 10 0 -10 -20 20 10 0 -10 -20 So Resistance, Fn = 0.20 Approximate bounds 2 3 4 5 6 7 2 3 4 5 6 7

Model waterline length in meters

Figure 11 Correlation between results at model and full scale (or a large model scale). From Kirkman & Pedrick (1974).

displacement, while the former is scaled Using a standard foimula such as Schoenherr's (used by Kirkman) or the ITTC-57 correlation. The resist-ance components due to heel and leeway, as well as the side force, are scaled as the residuary resistance. It should be noted that more accurate scaling_ procedures, with individual extrapolation of the appendage drag and with the fotin-factor approach (see Lindgren & Dyne 1980), are used

at some towing tanks.

There may be several reasons for the low accuracy of the small-scale data in Figure 11. Some of them are inevitable. For instance, if the stern is very full, different separation patterns will appear in the different scales, with a large influence on the drag as a consequence. Even if separation does not appear, the relative boundary-layer thickness on a 1:10 scale model is twice as large as on the prototype. The interaction between the boundary layer and the stern waves may thus be different. The most likely

sources of error, however, are the influence of laminar flow and the parasitic

drag of turbulence stimulators.

Two of the author's students (Liden & Sallin 1975) carried out an

Side force

Figure 12 Location of the start of transition (neutral stability point) at F = 0.12. Cal-culations are for Antiope at three different scales. From Liden & Sallin (1975).

interesting calculation of the boundary layer around Antiope at different Reynolds numbers; the frictional resistance was obtained by integrating the skin-friction coefficient along the hull. In Figure 12 the location of the

neutral stability point, computed according to Granville (1953), is shown for different scales at a constant Froude number. This point should be somewhat upstream of transition, but measurements (Xia et al. 1985) have shown that, in practice, it is a relatively good representation of the start of the transition region. It is seen in the figure that at 1: 3 scale the neutral stability point has moved from a location near the bow at full scale to

almost amidships. This change in the extent of the laminar region is

accompanied by a drop in friction, as can be seen in Figure 13.6 It is also

clear in the figure that the measured low-speed data get extremely scattered

below the critical Reynolds number.

The calculations by Liden & Sallin (1975) were made withoutturbulence

stimulation, as were the measurements in Figure 13. However, Kirkman (1979) reported that even for a hull with stimulators, peculiar trends of the viscous resistance were observed in the critical-Reynolds-number range, indicating that the stimulators were not fully effective.

The most common type of stimulator in yacht investigations is a row of studs, usually 3 mm in diameter and 1-2.5 mm high, with a

pitch of 10

25 mm. The studs are applied either on the hull or the appendages or both. Frequently, several rows are put on the hull at different stations, while on the appendages the studs may be applied either close to the leading edge

or at the 25% chord

line (sometimes even further aft; see Campbell &

Claughton 1987). The positioning on the appendages is particularly tricky,

since the size of the stimulator is considerable for the smaller models, as compared, for instance, with the leading-edge radius of a keel or rudder. An unintended change in shape of the foil section may thus be caused by studs placed too close to the leading edge. Furthermore, since the use of

'Coefficients for skin friction (CO, wave resistance (Cw), lift (CD, and drag CD) inthis

7 6 5 4 3 2 CF ITTC-57 a a a 1:6 / Calculated CF a °

Mean curve through

measured total resistance

A

/

1:3 Measurements at different Fn's 1,1 6.0 6.5 7.0 icitog Rn

Figure 13 Calculated skin friction for Antiope compared with the ITTC-57 correlation line and measurements at three scales. From Liden & Sallin (1975).

laminar sections has become more common for keels, positioning of studs in front of the expected full-scale transition would be a mistake.

There is no generally accepted simple procedure for checking the effec-tiveness of the stimulators. Hot-film measurements were made at South-ampton (Campbell & Claughton 1987) on a 1: 4 scale 12-m yacht, but this is hardly possible in general within the rather limited budgets available. The only realistic way seems to be to look at the behavior of the resistance curve at low speeds (Kirkman 1979) to see whether the slope is in accord-ance with the skin-friction curve.

Another problem is the correction for the parasitic drag of the stimu-lators. Traditionally, this is obtained by changing the number of studs, under the assumptions that the flow is turbulent for both configurations

and that the difference in drag is due to the studs themselves. If the

comparison is made at high speed, all studs may be removed. Alternatively,

the drag of the stimulator may be computed by assuming a velocity (inside the boundary layer) and a drag coefficient. Kirkman (1979) showed that this results in good agreement for large models but poorer agreement for small ones. He also showed that the determination of the stimulator drag is vital for the smaller models, since it may amount to more than 10% of the total resistance. Differences between different test objects are often of the order of a few percent, so the determination of the stimulator drag

becomes critical.

It should be apparent from this discussion that tests with small models require extreme caution, and that even with an experienced and careful

test crew, some scale effects are unavoidable. This is the reason why most America's Cup syndicates have turned to 1: 3 scale (corresponding to 1:1.5

scale for Antiope) in recent years. For the typical yacht designer

this

trend is unfortunate, since the cost of testing such large models is often

prohibitive. The designer therefore has to accept the somewhat lower

accuracy of the smaller tank.

APPLICATION OF COMPUTATIONAL FLUID

DYNAMICS

Computational fluid dynamics (CFD) has appeared recently as a tool for the yacht designer. Chance & Company started an ambitious program in

1973 to apply calculation methods to the flow around a series of yacht hulls (see Boppe et al. 1987), but owing to the difficulties encountered, the only results obtained were from a potential flow solution at zero heel and.

leeway and under the assumption of a flat free' surface. One step further was taken by Liden & Sallin (1975), who also included the calculation of the boundary layer at several Reynolds numbers. More complete were the Antiope results presented by the author in 1979 (Larsson 1979), where the

viscous wave, and induced resistance as well as the side force were pre-dicted using CFD. Different methods were used, however, for the lift and the free-surface calculations,, and thus the important interaction between

the vortex system from the keel and the generated waves was

not

considered. A simplified method for taking this interaction into account was used in the development of the Australia II keel (van Oossanen 1985), but it was not until the wing-keel boom of the 1987 America's Cup that complete methods for lift-generating hulls in the presence of a free surface Were developed (see van Beek et al. 1985, Xia & Larsson 1986, Larsson

1987, Boppe et al. 1987). However, quite interesting systematiccalculations

were also carried out in the 1987 campaign that neglected the free surface/ vortex interaction (Letcher et al. 1987b, Boppe et al. 1987, Scragg et al.

1987). These calculations are described below, followed by a survey of the

more exact methods. A short account is also given of recent viscous-flow

calculationS.

Calculations at Zero Froude Number

In the Sail America technology team for the 1987 America's Cup, two different groups were engaged in CFD development. Both used essentially . the same method for computing the induced resistance and the side force, assuming no waves. In this zero-Froude-number approximation the free water surface is simply considered as a symmetry plane. The calculations were carried out using the. public-domain code VSAERO, developed. by

Maskew (1982) at NASA. This is a first-order panel method in which the flow around the body is simulated using constant distributions of sources and/or doublets on flat panels on the body surface. Thick components of a configuration, like the hull, are represented by sources proportional to the normal component of the free-stream velocity and an unknown doublet strength. Thin lifting surfaces, like the keel, are represented only by doub-lets, whose unknown strength is determined from the zero-normal-velocity condition on each panel. Doublet panels with a strength computed from the trailing-edge conditions are located in the wake, the position of which

can be either iteratively determined by the program or specified by the user.

Interestingly, the two groups ![Letcher et al. (1987b) at Science Appli-cations International Corporation (SAIC) and Boppe et al. (1987)] spent considerable efforts on validating the code but arrived at different con-clusions. The most extensive validation was made at SAIC, where three simple cases, for which analytical results could be obtained, were inves-tigated.. Comparisons were also made with measurements for three 12-m models tested earlier. The results seem to prove, convincingly, that the method for obtaining drag from a summation of the pressure forces on all panels is too inaccurate. A method for 'determining lift and drag from the trailing vortex system was therefore developed and proved, to be very robust. Boppe's group, on the other hand, carried out a systematic panel-ization study for a model-tested 12-m yacht and concluded that reasonable convergence using pressure summation had been obtained, for the densest

arid used.

Analyzing the results, one notes that both groups favored uniform grids. The finest 'one used by SAIC contained' 24 chordwise panels, whereas 5-4 panels were used by Boppe's group. The panel lengths in the chordwise direction were thus approximately 4% and 2%, respectively, of the chord.

Small as these panel lengths may seem, they are not small enough to

resolve the leading-edge suction. Recent panel-method calculations in the author's CFD group have indicated that for a proper resolution, the nose panels have to be only a fraction of the leading-edge radius. Panels smaller by 5-10 times than those reported in the VSAERO calculations are thus, required, and this is difficult to achieve with a uniform grid. Considerable stretching, with rather large panels (10%) in the middle of the profile, may be applied without loss of accuracy.

Extensive parametric studies of keels with wings were carried out by both Sail America groups. It was found that the induced drag is relatively

'insensitive to the detailed shape of the wings, while the wingspan has a large

impact on efficiency. Boppe et al. (1987) found that a forward mounting of

the keel wings is favorable, but that this advantage is offset by the increased trim-tab efficiency with the wings aft. A comparison was also made between

the traditional 12-m yacht Liberty and Australia II with wings. Lifting-surface calculations for an ideally loaded wing/winglet combination had

indicated much larger reductions in drag as compared with the ones

obtained for Australia II. This difference could be explained by the very unfavorable side-force distribution of the hull-keel-winglet combination. In Figure 14 the distributions are given for both yachts, and it is seen that neither one of them is close to the ideal elliptical one, although that of Australia II is the worst, with a large droop near the keel-hull juncture. This droop is associated with vortex shedding, which increases the drag. Obviously, in neither case is the hull a good side-force producer.

Wave-Resistance Calculations at Zero Heel and Leeway

The introduction of the free surface complicates calculations considerably. Whereas on a solid boundary the only (inviscid) condition required is that the flow be tangential to the surface everywhere, a free surface must be given the freedom to deform in such a way that the pressure is constant at all points on the surface. Since no flow is allowed across this deforming boundary, the same kinematic boundary condition as on a solid wall also has to apply.

There are thus two conditions to be satisfied, one kinematic and one

dynamic, and the location where they should be applied is unknown a priori.

In practice, this problem is always solved using some kind of perturbation technique. An obvious first guess of the location of the free surface is the undisturbed water level. In the linear methods this location is not updated, whereas in the nonlinear methods the boundary condition is applied to

the free surface computed in a previous iteration. The kinematic and

dynamic boundary conditions are usually combined and linearized about

a basic, known flow, which is not updated in the linear methods. Nonlinear

Lift

Australia II

Figure 14 Lift distribution for Australia

II and Liberty. Calculations by Boppe et

effects may be taken into account iteratively by using the previous solution as the basic flow.

The choice of the (initial) basic flow may be made in two different ways. In the traditional thin-ship theory, the linearization is simply made about the undisturbed flow. Disturbances due to the hull then have to be small, which makes this theory less accurate for beamy hulls. Another possibility

is to linearize about a double-model solution, obtained (as explained

above) by considering the free surface to be a reflection plane. The major disturbances to the onset flow are then considered already in the basic flow, and more beamy and full hulls can be examined. A brief introduction and evaluation of the different methods may be found in Bai & McCarthy

(1979), and a more detailed analysis of the theory is given by Yeung (1982).

While there are several techniques for the solution of the free-surface problem, only panel methods are considered here. These are by far the most common ones, and they are the only ones that have been applied in sailing-yacht investigations.

Havelock (1928) found a Green function that satisfies the free-surface boundary condition, linearized about the free-stream velocity. If this Have-lock source is employed, source strengths must be adjusted in such a way

that the hull boundary condition is satisfied, while the free-surface boundary

condition is satisfied automatically. One disadvantage of the Havelock source is that the potential function is relatively complicated. Therefore,

methods employing standard Rankine sources have recently become

increasingly popular, particularly since double-model linearized solutions can then be obtained.

An interesting study using Havelock' sources, distributed on panels at the centerplane of the hull, was presented by Scragg et al., (1987). The purpose was to find the optimum section area curve' for given speeds and waterline lengths. Taking the unknown ,constant source strengths on the panels as design variables and the wave resistance, computed from the

energy flux through a control surface behind the hull, as the object

function, the optimum source distribution could be obtained by the method

of Lagrange multipliers. Two constraints could be applied: the

dis-placement and the longitudinal position of the center of buoyancy. By integrating the volume flux from the sources in front of a particular station, the cross-section area of the hull at that station could be found. In Figure 15 an example is given where the optimum section area has been computed

for varying speeds. (For proprietary reasons, actual speeds are not revealed.)

The strategy adopted by the Sail America syndicate was first to compute

The section area curve represents the longitudinal ,distribution of the displacement of the

Area

A11414\4\

/ High speed

Stern Bow

Figure 15 Optimum section area curves.

The center of buoyancy is located amid-ships. Calculations by Scragg et al..(1987)..

the optimum section area curve,, thereafter giving an experienced yacht designer freedom to develop detailed hull lines based on the computed displacement distribution. Once this had been done, another numerical check was made before it was decided whether or not the hull should be model tested. This second calculation was carried out by a method slightly

more exact than the thin-ship approximation used in the optimization

procedure (see Scragg et al. 1987).. Rather than the source panels being located on the centerplane, they were now moved to the surface of the hull and assumed proportional to the normal component of the free-stream velocity. Several tests of this method were made against measured data,

and it was found that the computed wave resistance was consistently

overpredicted. On the other hand, the correct trends were apparently

obtained. The hulls were always ranked in the right order by the numerical method, which could then be used for screening the proposed hull forms, before they were accepted for the relatively expensive model test program. If the Kelvin sources on the hull surface are computed from the exact zero-normal-velocity condition (Neumann condition), the Neumann-Kel-vin approximation is obtained. Calculations based on this theory were carried out by M.-S. Chang and the author (Larsson 1979) for the Antiope hull. The results, may be seen in Figure 16, where the predicted wave resistance is compared with measurements of the residuary resistance.

A different method for solving free-surface potential-flow problems was developed by Dawson (1977). This method has been extensively tested and generalized in the author's CFD group (Larsson et al. 1989a), and several applications to sailing yachts have been made (see Larsson. 1987). Daw-son's method is linearized about the double-model solution, and Rankine sources are distributed on the hull as well as on. part of the free surface. Figure 1,7 shows typical panel distributions.. (The free-surface grid is for the yawed case, to be discussed in the next section.) The calculated wave

cor-Strip

Herreshoff & Newman (1967)

measurements Larsson (1979) calculations Larsson (1987) _A calculations Kirkman (1974) measurements

Figure 16 Comparison between measured and calculated wave resistance for Antiope.

WimmiMMIMINIIIIWr

\1111111111111MMIIINE

'11M1111111111EMENNI IIIIM11111111/

Figure 17 Panel distribution for Antiope. (Top) free surface; (bottom) hull.

6 0 4 0 2 0 0.1 0.2 0.3 0.1+ .10 0

/

Cw .10 0.20 0.25 0.30 Cakutationso 0 0.35 040 Fn Measurements

Figure 18 Comparison between measured and calculated wave resistance for a 12-m yacht.

respondence with measurements may be noted. Considerably worse results were obtained for a 12-m yacht, as seen in Figure 18. These results are consistent with the ones obtained by Scra2g et al. (1987). Computed values are much larger than measured ones, particularly at higher speeds. As a

matter of fact this situation is inevitable when one uses a linear free-surface

method. In this approximation the surface is always kept at its undisturbed level, which means that the large effects of the overhangs at both ends of the hull are not considered. At full speed the waterline length of a 12-m yacht increases by at least 25% owing to the generated wave system. This reduces the wave resistance considerably. It should be noted that the effect is much smaller for Antiope, which has less inclined ends. The only way that the change in waterline length can be taken into account is to make use of a nonlinear method, where thefree surface, as well as the submerged part of the hull, is allowed to change. Such a method has recently been

developed by Kim (1989).

Free-Surface Calculations Including Lift

Three well-known aerodynamic potential-flow methods with lift have been generalized to include the free surface. Van Beek et al. (1985) and Raven (1987, 1988) developed the Dutch NLR method (Labrujere et al. 1970),

Xia & Larsson (1986) extended the Douglas method (Hess 1972), arid

Boppe et al. (1987) modified VSAERO (Maskew 1982). In all cases a

Dawson type of approach was chosen. Considerable

differences do,

however, exist between the methods. Van Beek et al. and Boppe et al. use a combination of sources and doublets on the free surface, whereas Xia & Larsson and Raven have stuck to Dawson's original idea of using only sources. The free-surface boundary condition in the VSAERO

generaliza-tion is different from that of the other two; it is modified to fit VSAERO's

way of satisfying the solid boundary condition by an internal

zero-perturba-tion approach, rather than the regular Neumann condizero-perturba-tion. Other differ-ences are related to the free-surface grid, finite differencing on the free surface, and wave damping at the lateral edges of the paneled part of the

surface. In the following, some more details are given of the Xia & Larsson

method.

As in the original Hess (1972) method, the body is divided into "lifting" and "nonlifting" sections. The keel, which is obviously lifting, is divided

into longitudinal strips (see Figure 17), each containing a number of panels.

On the hull the panels may be arranged more arbitrarily. In Dawson's

method the free-surface boundary condition is expressed in terms of

deriva-tives of potentials along the double-model streamlines on the undisturbed surface. Therefore, a grid based on these streamlines may be convenient. During the development of the lifting method, it was found that such a grid could not be used for hulls at a yaw angle, since the bow and stern regions became inaccurately resolved. An algebraic body-fitted grid was therefore developed, and the boundary condition was rederived to include derivatives in the longitudinal and transverse directions of the grid.

Each panel on all sections, including the free surface, has a constant-density source distribution, which is initially unknown. In addition, the panels on the lifting sections have an unknown doublet distribution. The

latter is constant spanwise on each strip but is proportional to the arc

length along the strip chordwise. The arc length is measured from the trailing edge on one side around the leading edge and back to the trailing

edge on the other side. From this position, the doublet strength is continued

unchanged on a few dummy panels placed in the wake behind the strip. In this way a constant bound vorticity on each strip is simulated, with free vortices shed at the common boundary between two strips. In the wake, the bound vorticity is zero.

The unknowns of the problem are the source strengths and the doublet derivatives, one on each strip. A closed system of equations is obtained from the boundary conditions on the hull and the free surface and from the Kutta condition applied at each strip. The latter condition, which is nonlinear, is satisfied by specifying that the pressure is to be the same at the control points of the panels closest to the trailing edge on the two sides. As in the original Hess method, the problem is solved by a technique

that avoids the solution of a large nonlinear system. A set of linear solutions

is obtained under the assumption of zero doublet strength, except on one strip, where the derivative is unity. In each of these calculations, the onset flow is set to zero, but there is also one solution for the right onset flow with all doublets set to zero. All solutions are linearly combined with the

CL x 102 40 2.0 0.0 CL 0.05 0.00 °35G 0.3 0.0 o CL Catcutations A o _x102 Measurements

Figure 19 Comparison between measured and calculated lift and drag for Antiope. (Left) lift vs leeway angle; (right) lift-drag polar.

doublet derivatives as unknowns. One such linear combination for each Kutta condition yields a small nonlinear system that can be solved fairly easily. The free-surface condition is expressed in such a way in each linear calculation that it is satisfied in the combined solution. For more details,

see Xia & Larsson (1986).

Results from calculations for Antiope are given in Figures 19 and 20.

Four Froude numbers and five leeway angles have been calculated. In Figure 19 a small Froude number dependence on the lift can be seen in

the computed results, but such a dependence is difficult to judge from the

5.00 4.0 2.0 0.0 0/ d.° Fn = 0.35 0.3 0.0 Leeway angle 10.00 co .10 Calculations a } Measurements Fn.

Figure 20 Computed lift-drag polars for Antiope for varying Froude numbers.

5.0 a° 2.0 4.0

0

CF

x103 4

2

measurements due to scatter. The predictions are nevertheless quite good

considering the neglect of viscous effects. A very regular pattern is observed

in Figure 20, where lift-drag polars are plotted for different Froude

numbers. The slopes of the lines of constant leeway indicate a Froude-number dependence.

Viscous Flow Calculations

Very few calculations of the viscous flow around sailing yachts have been

reported in the literature. The early attempt by Liden & Sallin (1975) has already been referred to, as have the Antiope calculations by the author in 1979. Apart from these, two recent calculations have also been reported. Both were aimed at predicting the location of separation near the stern.

Boppe et al. (1987) attempted to

_{use two-dimensional boundary-layer}

theory at first but found it to yield results quite different from experimental data. They therefore turned to Navier-Stokes solutions and designed _a grid that extended approximately half a waterline length upstream and

downstream of the hull and one length sideways and downward. The

calculations were carried out by the method due

to Pulliam & Steger (1980), and the results are in qualitative agreement with data for the _extent of the separated zone for a 12-m hull.

The other set of separation predictions

_{was presented by the author}

(Larsson 1987) using three-dimensional boundary-layer theory (Larsson

1976). One purpose of the investigationwas to check the Reynolds-number

sensitivity of the separation. The question had arisen whether

or not

separation would occur on a small model, although it had not been

observed either at full scale or at a large (1: 3) model scale. The calculated

skin-friction coefficient along one critical streamline is shown in Figure 21.

1

Figure 21 _{Skin-friction distribution along a representative streamline for a 12-m yacht.} Results are given for four different scales.

0.5 1.0

Results are given for four scales, and it it seen that although there is a large droop close to the stern for the smallest scale, the skin friction is always positive. This indicates that separation will not occur.

Arguments may be raised against each of the two sets of calculations reported. Obviously, the accuracy of boundary-layer solutions deteriorates close to separation, but it has still been frequently

used in the past for

rough estimates of the separation point, at least on two-dimensional and axisymmetric bodies (Chang 1970). There is every reason to believe that three-dimensional boundary-layer theory is adequate in other regions of the hull, as large curvatures are generally avoided on sailing yachts. This theory has been proven to be very useful for ship boundary layers, except

close to the stern (Larsson 198 la). On the other hand, it is essential that the major effect of the three-dimensionality, namely streamline convergence, is

accounted for. Two-dimensional methods are bound to fail.

A Navier-Stokes calculation might seem the ideal way to find separation,

but great caution must be exercised. In order to resolve the boundary layer properly, the grid must have several points within the viscous sublayer, if wall functions are not used as the internal boundary condition. If wall functions are used, several points must be located inside the logarithmic region of the boundary layer (Broberg 1988). With a global grid like that used by Boppe et al. (1987), these requirements cannot be met without

excessive computer requirements. In fact, Boppe et al. state that the closest

grid point was 0.04 ft away from the surface. This distance is one to two

orders of magnitude too great to

resolve the boundary layer properly. With today's computers, it seems

that the only way to overcome

this problem is to resort to a zonal approach where potential flow/boundary layer/Navier-Stokes methods are matched. Such a system has recently been developed in the author's CFD group (see Larsson et al. 1989a,b).

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