Yacht research at NRC

SUMMARY

This report outlines work carried out at the National Research Council, Marine Dynamics and Ship Laboratory in the field of research into sailing yacht performance. Model test philosophy and techniques are discussed and comparisons made between results of model experiments and full scale data. Projects to compare the performance of two Albacore dinghies and alternative rudder designs for Tornado catamarans are described.

1.0 INTRODUCTION

Research in the field of sailing yacht performance has long been of interest not only to professional aero and hydrodynamicists who find the problem of the behaviour of a yacht under the action of complex air and water forces a fascinating one, but also to yacht architects seekingspecific answers to the many questions raised during the design process. Unfortunately, the development of this branch of research in naval architecture has been restricted, largely by commercial considerations. Because of the complexities of the yacht design problem, the cost of a research and development project may well exceed that for a large ocean going ship, yet the funds available are much less, even

for the most expensive yacht.

Nevertheless, progress has been made and facilities developed. Pioneer work was done by K.S.M. Davidson at the Davidson Laboratory in the 1930's and subsequently developments have been made at hydrodynamic research institutions and universities in the United States, UnitedKingdom,

Australia, The Netherlands, Sweden, Canada and elsewhere. Much of the impetus behind these

devel-opments has been the America's Cup Challenges. More recently, the very high level of competition in races for boats built to the International Offshore Rule, such as the Admirals Cup, S.O.R.C. and level

rating championships, has increased the demands made by yacht designers and builders on the research organizations.

Although the Marine Dynamics and Ship Laboratory of the National Research Council has always done its best to answer queries from industry, and had carried out some upright resistance

tests with a model of a 30-ft. waterline offshore racer in 1968, involvement in the sailing yacht field in a systematic way did not start until a year later under the stimulus of a proposed Canadian chal-lenge for the America's Cup. This date saw the start of three related but separate research programs. The first was to study scaling laws for resistance, the second was to develop the specialized apparatus required for testing sailing boat models heeled, and the third was an investigation into the

hydro-mechanics of sailing.

The latter investigation lead to a mathematical model, incorporating empirical factors based on published tank test results, to predict full scale heeled performance. A computeralgorithm of this model was found to be most useful for investigating the effects on performance of changes in basic parameters which are known at the earliest stages of design. It could not, of course, be used to study the effects of changes in hull shape explicitly. The program was made available to industry for a nominal fee, and was regularly in use until 1973 when changes in hull form brought about by the IOR Rule rendered the empirical data base obsolescent.

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D.C. Murdey

Marine Dynamics and Ship Laboratory

Division of Mechanical Engineering

Technische Hogeschool Delft

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Unfortunately, when the Canadian challenge for the America's Cup was withdrawn, research

effort in the Laboratory was put into other fields and there _{were no developments for some three}

years, the heeled testing apparatus remaining incomplete.

In 1974, C & C Yachts of Port Credit, Ont., expressed their desire to have available a

Cana-dian research facility to assist in the development of yacht design. As a result, a joint research project was started in which C & C contributed a member of their own design staff for a year to work at NRC as a guest researcher. The objective of this project was to complete the design and construction of apparatus for heeled testing, and to develop methods of analysis to give data of immediate use to the practicing designer.

This task was accomplished, and the apparatus and analysis procedures inuse are described

in Sections 2.0 and 3.0 of this report.

Although the major thrust of NRC projects have been directed towards the solution of design problems associated with offshore racing yachts, NRC has also carried out projects of interest to the designers and builders of smaller craft.

One of these was an investigation of the effect _{on performance of differences in hull shape} of a nominally one-design dinghy and involved the testing of two full size Albacore dinghies in the tank. Another was to study alternative rudder designs for the Tornado Catamaran. This_{project was} carried out in order to assist the Canadian team for the Montreal Olympic Games._{Outlines of these} projects are given in Sections 3.0 and 4.0 of this report, respectively.

The scope of the work that has been undertaken, and will be done in the near future at NRC, is determined to a large part by the facilities available at the Laboratory. The major facility, the Towing Tank, is 450 ft. long X 25 ft. wide X 10 ft. deep, and is equipped with a carriage capable of speeds in excess of 20 ft./sec. and a wavemaker which _{can produce waves over one foot in height.} The carriage is fitted with a computer controlled data acquisition and analysis system. A _Cavitation Tunnel and a Manoeuvring and Seakeeping Basin, the potential of which are yet to be exploited for yacht research projects, are also available. The basic facilities are backed up by model making, in-strumentation, electronics and computer laboratories. These facilities are being continually updated to meet the needs of the Marine Industry in Canada.

2.0 UPRIGHT TESTING 2.1 Introduction

It was demonstrated by Davidson (Ref. 1) in the classic "Jack and Jill" experiments, that upright testing could not give any indication of merit for windward performance, and upright _tests are carried out today for the purpose of predicting downwind performance only.

Whilst the carrying out of such tests is no problem for any towing tank, several decisions have to be made before testing can be started.

2.2 Model Size

One such decision is the choice of model size. From the point of view of accurate prediction of full scale resistance, the model should be _{as large as possible. Unfortunately, the time to} manufac-ture a model and its cost increase as model size increases, as does the difficulty of handling the model, and the effect of tank boundaries on the results obtained.

On the other hand too small a model makes it more difficult to predict full size performance and demands extreme precision of manufacture and measurement.

At NRC a compromise has been adopted with the choice of a standard model length of about 9 ft. on the waterline, giving scales around 1/3 to 1/4 for typical modern yachts. This size is also convenient for heeled testing. It is also about the minimum size for which separate keel and rudder combinations may be tested with a reasonable anticipation of avoiding excessive scale effects on the rudder. Rudders are fitted for all, the tests.

2.3 Turbulence Stimulation

A problem which exists with all ship model testing, and is particularly important for yachts is that of stimulating turbulent flow conditions over the model so that flow conditions over the full scale hull may be properly represented. Kirkman (Ref. 2) presents a detailed discussion of this prob-lem as it affects yacht model testing and this section will be limited to a description of the procedure adopted at NRC.

Early work at NRC had followed the Davidson Laboratory in the use of sand strips, testing with two widths of strip in order to extrapolate to zero sand. conditions. It was felt that non-uniformity of sand grain size and concentration could cause discrepancies in results between two similar models and that the presence of a one-inch wide sand strip near the critical leading edge of a keel could have an overall disturbing effect on keel hydrodynamic behaviour.

For these reasons the decision was made to use tripwires, located as shown in Figure 1. Studs were considered, but rejected in favour of tripwires for which NRC had had long experience on other types of ship models. The tripwires are set vertically so as to minimize the inducement of downwash over the keel.

Models are run first without tripwires then the test repeated with the tripwires in position. The difference between the two resistance curves at higher speeds (where the flow should be turbulent in both cases) is taken as a measure of stimulator drag.

2.4 Apparatus for Upright Tests

The apparatus used for upright tests is shown in Figure 2. Apart from the high location of the towing point, the set up is exactly the same as that used for ship models. The model is restrained by guiders to maintain a straight course down the tank but is free to heave and pitch.

The longitudinal position of the tow point is at the longitudinal position of the nominal sail centre of effort and the vertical position is taken to be one half of the height of the nominal sail centre of effort above the waterline. This allows, to some extent, for the lifting effect of a spinnaker and for the aft movement of the crew when sailing downwind. Towing from the full height of the centre of effort was found to give an unrealistically large depression of the bow. The nominal centre of effort is defined as the centre of area of the main triangle and 170% of the fore triangle.

2.5 Upright Test Data

Examples of resistance curves measured with and without tripwires, are given in Figure 3. The data in Figure are typical both as to density and scatter of measured points and charac-teristics of the curves faired through them. Each curve takes about one day of test work to define.

The increased scatter and droop at low Froude number in the data are due to laminar flow; which occurs at very low speed (Froude number 0.05), even with tripwires in position.

2.6 Prediction of Full Scale Performance

Prediction of full size resistance is made according to Froude's hypothesis, that resistance can be broken down into two parts, one a function of Reynolds number only, and the other a function

of Froude number. Although there is a mounting body of evidence which suggests this is not strictly true, it is the only method presently available for producing predictions on a routine basis.

It is further assumed that the part of the resistance coefficient dependent on Reynolds

number may be defined by a correlation line, which is the same for all models tested. In early work, the correlation line was called a skin friction line, which represented the resistance of a smooth flat plank of the same length as the hull. Considerable effort was put into deciding an appropriate length of a yacht hull to use in the calculations. It is now recognized that with modern fin keel configura-tions, consideration of actual skin friction must await further research, and that the name correlation line is more appropriate. Since the ITTC 1957 line is in routine use at the NRC tank, this line was chosen for yacht work also.

For routine test analysis, Reynolds numbers are calculated using a length equal to 0.7 of the waterline length, which is a standard adopted for yachts by many test establishments. This proce-dure is only an interim measure however, and alternatives are being considered. For example calcula-tions may be made of skin friction drag for the rudder, keel and fairbody hull separately. For the rudder and keel Reynolds number lengths equal to the wetted surface area divided by the span (depth) are appropriate, and for the hull, wetted surface area divided by the maximum girth. For a modern IOR design, this leads to the following lengths:

The Reynolds numbers associated with flow over the keel and rudder (wake and entrained water effects being neglected) are much smaller than for the hull alone, and the Reynolds number dependent part of resistance and the scale effect (difference in Reynolds number dependent resistance between model and full size) are therefore bigger for the appendages than the hull. This results in a lower resistance predicted full scale than when 0.7 LWL is used for the combined hull, keel and rudder. However, experience with several models indicates that, for small changes in design, predicted differences in performance full scale are about the same for both prediction methods.

2.7 Comparison of Model Predictions with Full Scale Data

The final test of any prediction scheme must be a comparison with full scale. Full scale data are available for the 5.5 metre Antiope towed at the David Taylor Naval Ship Research and Develop-ment Centre and these have been analyzed by Letcher (Ref. 3). A 1/2.5 scale model of Antiope was constructed and run at NRC to enable comparisons to be made. Unfortunately, the design of Antiope is not modern, and in particular, the keel is quite long with the rudder attached. For this reason, predictions using 0.7 LWL and separate hull, keel, rudder are almost identical.

Figure 4 shows the comparison between model and full scale data. A 0.0003 correlation allowance would have to be added to the model data to achieve agreement. This bias may be due to any one of several factors. First, the model was towed from a centre of effort position 8.7 ft. above the waterline full size, whereas the full scale Antiope was towed from near deck level, resulting in different bow down trim in each case. Second, the ITTC friction line may be too high for this type of hull and third, there may be scale effects due to transitional flow (inadequate turbulence stimula-tion).

Further work will be undertaken to investigate these problems. In the meantime, it is felt that it would be unduly pessimistic to await the solutions before carrying out tests on a routine basis.

Waterline length (ft.) 32.7

0.7 LWL 22.9

Fairbody effective length 22.7 Keel effective length 5.9 Rudder effective length 2.0

3.0 HEELED TESTING 3.1 Fundamental Assumptions

The prediction of windward performance is made by solving the equalities between sail and water forces and moments, Figure 5. In general, the water forces depend on the attitude of the hull, rudder angle and speed. Practical conditions are defined in the transverse plane by the relationship between the stability of the hull, heeling force and heel angle. Sail forces are determined by the rela-tive wind angle and wind speed, sail configuration and setting, and the attitude of the sail plan. In order to reduce the number of variables in those relationships to a manageable number, it is usual to make some simplifying assumptions.

Since a primary object of tank testing is to compare predictions of performance of different hull designs, it is assumed that the relative performance of two hulls may be assessed without deter-mining the optimum sail configuration for each hull. The aerodynamic forces may be then convenient-ly represented by a standard nominal force, whose magnitude depends on sail area, relative wind speed and heel angle only and whose direction depends on heel angle and apparent wind direction only. The sail force is assumed to act through a nominal centre of effort position. The effects of sail settings or details of sail design are then not considered. The well known `Gimrack' sail coefficients are of the form described, and are believed to give realistic performance figures. These coefficients are employed as a standard for comparison in NRC work.

It is further assumed, following Davidson, that the sail force acts perpendicular to the mast. This assumption is not only physically reasonable, but also simplifies hull testing, since it defines a relationship between heel angle, vertical force and side force and means that it is only necessary to determine the effects of changing two of these three quantities.

In order to scale model force measurements to full size, it is assumed that there are no scale effects on the side force and vertical force, which may be, therefore, scaled directly to full size. It is assumed that scale effects will be present on resistance in exactly the same way as for upright tests, and that the same scaling laws apply.

Once these assumptions have been made, the windward performance of a hull may be predicted from measurements of resistance and side force on a model at a given heel angle and speed. 3.2 Alternative Test Approaches

Even with the assumptions described in the previous section, there is scope for alternative measuring schemes which differ primarily in the choice of parameters which are either held constant or changed systematically throughout the tests, and the parameters to be measured during a test run. In the test methods based on that used by Davidson, the rudder is fixed on the hull centre-line, and tests carried out over a range of stability, speed, heel angle and side force. Leeway angle and resistance are measured. The model, whilst free to take up any attitude is restrained by the dynamom-eter and yawing moment is balanced by suitable placing of the point of application of the side force. A weight, placed inside the mode, corresponds to vertical force and allows for the fact that the forces are applied to the hull at a point much lower than the nominal centre of effort. The test procedure is iterative and several runs are required to achieve a satisfactory arrangement of forces and model attitude.

In a scheme used by Allan and Doust (Ref. 4), the model, built with a fixed representative stability, was fitted with a mast and towed by forces at a nominal position of centre of effort. The forces were adjusted to give a resultant force perpendicular to the mast. As the model heels, the tow point moves to the leeward side and the resulting yawing moment was balanced by a couple applied

to the mast. The rudder was fixed on the centreline. Doust found that the model would run at a

At NRC a development of the latter system is employed, where the rudder itself is used to provide the moment required to enable the model to run on a steadycourse. The object of this devel-opment is that, subject to the simplifying sail assumptions, each test run would be representative of full scale sailing, and that it is believed that the effect of the rudder on performance should not be neglected, as it was in other methods. The degree of realism of the leeway angles obtained with the test method would indicate if major scale effects on the rudder were affecting the results obtained. Tests are carried out at several fixed rudder angles and at various speeds, and the resulting tow force vector measured together with the heel and leeway angles. The model is completely free (except for the tow force) throughout a test run. A major advantage of this method of testing is that each run down the tank provides valid data representative of a realistic sailing condition. This reduces the time required for testing compared with iterative systems.

However, there are disadvantages in the testing approach adopted by NRC, The first is that, by carrying out tests with a model with scale stability, effects of changing stability can only be deter-mined by repeating the test program after the model has been re-ballasted, and second, that foria particular rudder angle, there is a unique relationship between speed, heel and leeway angle. It is not possible to change, for example, leeway angle at a given heel angle while keeping speed constant. This makes comparison between NRC model results and results of tests carried out using other test ap-proaches or with hydrodynamic theory somewhat difficult, but this is considered of little importance

compared with the requirement to make all test runs meaningful. 3.3 Heeled Apparatus

The heeled test apparatus was developed in a way consistent with the general approach described in the previous section. The test arrangement is shown in Figure 6.

The model, ballasted to scale stability is fitted with a mast at the nominal centre of effort position, which is free to rotate about its longitudinal axis. A collar, whose vertical position may be adjusted to correspond to the sail centre of effort, serves as the point of application of the tow force and as an indicator to show when the force is perpendicular to the mast. The tow line is attached to the carriage at a force measuring block, mounted on a lead screw so that its vertical position may be changed during a test run. The angles between the tow force and the tank centreline and the angle between the tow force and the hull centreline in the plane of the deck (mast angle) are sufficient to define the direction of the tow force and the leeway angle of the hull. Heel angle is measured with reference to a pendulum hanging vertically. A locking pin serves to locate the rudder at chosen angles. With the exception of rudder angle all measurements use electromechanical transudcers, the outputs of which are interfaced with the carriage data logging system.

All cables are taken from the model from amidships to minimize residual forces due to their stiffness.

3.4 Test Procedure

The test method is as follows. Before a run, the rudder angle is chosen, and speed selected on the basis of previous experinece with similar models to give a run near a required heel angle. The model is hand held while the carriage accelerates to the selected speed, then carefully released. Under the action of the tow force, it takes up a heeled, yawed attitude. The vertical position of the force block is adjusted until the operator can see the tow string is aligned with the pointer showing it is perpendicular to the mast. Finally, the carriage data logging equipment is switched on and reads the output of all the transducers. At the end of the test run average values of the measured parameters, and values of predicted full scale apparent wind angle are listed. The latter is used to check that the range of tests covers optimum performance.

Testing continues until data covering the optimum performance have been measured over the range of heel angles from 5 to 25 degrees. This usually required rudder angles from -2 to +5 degrees.

In a typical test, some 20 to 25 runs are made. Intervals between test runs are usually 10 minutes, except at higher speeds, (in excess of 5 ft./sec.) for which water disturbance is greater and a 15-minute interval is preferred.

The attitude taken up by the model during a run is determined by the equalities of forces and moments acting. The model is heeled by the moment between the tow force acting high up and the forces generated by the hull and keel and rudder acting low down and balanced by its transverse stability.

The directional stability depends on the position of the tow point (centre of effort), effec-tive centre of lateral resistance (centre of hydrodynamic force), the size and location of the rudder and the particular relationship between resistance, side force, leeway, rudder angle and speed for the design being tested.

For most modern designs tested, negative rudder angles are associated with a stable equilib-rium. That is, the model will return to its course after a slight disturbance. Negative rudder angles (lee helm) are near the optimum at heel angles 10 degrees or less, and are a necessary part of the tests. At positive rudder angles (weather helm), the equilibrium is unstable (that is, the model moves away from the equilibrium point if disturbed), and the model has to be prevented, by a gentle touch from time to time, from falling away from the balance point. The force required to do this is very small, applied only for a very short period of time and is not believed to have any effect on the results.

3.5 Results and Analysis

No attempt is made during the tests to take runs precisely at optimum performance. The concern is rather to ensure, over the range of heel angle covered, that tests range from low apparent wind angles (pinching) to apparent wind angles up to 30 degrees (sailing free). The first stage in the analysis procedure is to set out the data in such a way that interpolations can be made for those

conditions not actually tested. For each rudder angle, the data are plotted in ways suggested by

fundamental hydrodynamic and hydrostatic theory.

Figures 7 to 10 show typical data for a modern design. Figure 7 shows speed plotted on heel for each rudder angle. This shows different trends associated with negative and positive rudder angles. At negative rudder angles, increasing speed increases heel angle and with positive rudder, increasing speed reduces heel angle. At some intermediate angle near zero, the heel angle is indeterminate, and tests are not carried out using that angle. The reason for the different trends is that negative rudder angles tend to turn the model away from the tow point, increasing heel, an effect which will become greater as speed increases while for positive rudder angles, the reverse is true. These effects depend on the same parameters which define the course stability, and on the extent to which the flow into the rudder tends to be aligned with the hull.

The resultant of the vertical and side forces, heeling force (FH), is plotted on heel angle in Figure 8, which shows FH differs little with changing rudder angle, indicating that the change in stability due to changes in wave profile at the higher speeds associated with higher rudder angles is not large in this case.

For resistance it is expected that the drag associated with lift may be nearly proportional to the square of the lifting force. The resistance measured during the test also includes components dependent primarily on speed, and in order to establish the relationship with lifting force, it is neces-sary to subtract the upright resistance (which is taken as a measure of the speed dependent compo-nents). A plot of CR - CR (U) on C2 F H is shown in Figure 9. The changes from rudder angle to rudder angle are due in part to the increased drag of the rudder itself and in part to differing flow conditions and free surface effects as speed changes compared with conditions for the upright model. Coefficients are defined by dividing the forces by 05pw SH v2 where pw is the density of water, SH the wetted surface area of the hull and v the speed.

-For interpolating leeway (yaw) angles, use is made of the expected relationship between lift coefficient and the attitude of the hull, which is that CFH is expected to depend on X Cos 0 and (X Cos 0)2 where X is the leeway angle and 0 the heel angle. In this case CFH is known and it is more useful to plot X on CFH /COSO, as in Figure 10. The curve of the lines at constant rudder angle is indicative of cross flow effects. Leeway angles corresponding to the optimum sailing condition (2 to 4 degrees) are considered realistic.

The second stage in the analysis is the interpolation of the curves fitted to the experiment data at selected values of heel angle at each rudder angle. The resistance associated with lift is added to the upright resistance predicted for the full size yacht, and all the other parameters scaled to full size directly. The full scale sailing performance is then calculated at each interpolated point.

It remains to find the optimum performance. Alternative methods of defining the optimum are defined by Crewe (Ref. 5). For the NRC test data, an appropriate definition of the optimum is the point at which the ratio of speed made good to windward (Vm G ) to true wind speed (VT) is a maximum.

The procedure in use at NRC is illustrated graphically in Figure 11 in which apparent wind angle (g) is plotted on the ratio of apparent wind speed to yacht speed (VA /Vs ) against a grid of lines at constant Vm G /VT. The contact point between the lines of constant Vm G /VT and the experiment curve is the optimum performance. This method avoids the well known sharp hooks associated with the determination of optimum performance by plotting VmG or VT directly.

3.6 Comparison with Full Scale

As with uptight tests, the only valid proof of a model test method is to compare the results with full scale data. For heeled tests this may be done at two levels. One is to compare predicted full scale sailing performance, and the other to compare forces measured on a full scale yacht at the same speed, heel, leeway and rudder angle as the model.

The former suffers from the disadvantage that the prediction involves nominal sail forces. Useful comparisons may be made, however, between predicted differences in performance of two boats to establish if the relative performance of one to the other is predicted correctly. Unfortunately, such data are not yet available for boats tested at NRC.

On the other hand, the 5.5 metre Antiope has been tested heeled and yawed, including some runs at positive rudder angles, and these data have been analyzed by Letcher (Ref. 3), into a form most suitable for comparison with model test results.

The full scale data suffer the inconvenience that, although the nominal heel angle and leeway angle were set for tests at a range of speeds, in practice both heel and leeway changed with speed. Since for the model results heel, leeway, speed and rudder angle are correlated, it was necessary to interpolate the full scale data for values of side force and resistance coefficient at the same heel and leeway angles as the model. Comparisons are then made at slightly different speeds, and it is assumed that the speed squared term in the coefficient formulae will take into account first order effects of speed differences.

Small differences in speed would be expected to have a negligible effect on lift coefficient,

but for drag CR - CR (U) was interpolated, and CR (U) from Antiope at the speed of the

corre-sponding model test run added to give a full scale value of CR . The full scale data are such that only four spots inside the rnage of the model experiment data may be interpolated. These data are com-pared with the line smoothed through the model results in Figure 12.

For side force, the model and full scale data, agree very well at 0 degree rudder, but at 3 degrees rudder model side force is greater than full scale.

The resistance data agree well, better than for the upright resistance, probably due to the fact that a greater proportion of resistance is due to factors not too dependent on Reynolds number. The process of interpolation of the Antiope full scale data is not entirely satisfactory, and another approach, that of regressing to find the coefficients in theoretical equations representing the hydrodynamic behaviour may give a more meaningful, if less explicit, comparison.

For lift, a regression on leeway angle and rudder angle gives the result

CIH = 0.00533Cos 0 (1.04X + 0.476) ( 1)

compared with the full scale equation

CFH 0.00533Cos 0 (1.03X + 0.276) (2)

where 6 is the rudder angle.

The similarity in the coefficients of X in the model and full scale equations shows that the model accurately represents the effect of changing leeway angle on side force. The greater coefficient of rudder angle from the model confirms the effect found from the interpolated data, that the model tests tend to overpredict the effect of changing the rudder angle.

For resistance, an analysis of the increase in resistance coefficient above that for the same speed upright in terms of lift gives

CR - CR (U) = 0.305CFH 2/0.52 7r (3)

in which 0.52 is an effective aspect ratio. Letcher's similar analysis of the full scale data leads to an effective aspect ratio 0.59, which is in close agreement with the model result.

It is considered that these comparisons are sufficiently encouraging to justify continued development of the test method.

4.0 DINGHY HULL FORM 4.1 Introduction

One recent project which has produced some unique data has been the testing of two

Albacore sailing dinghies in the tank.

This study was undertaken in order to resolve a particular question in a nominally one design class. Does a boat built with slightly greater rise of floor than that laid down in the class rules differ in performance from a boat complying with the rules in all respects?

4.2 Hulls

Two hulls were tested. Boat A was normal in all respects. Boat B, although built on a standard mould, had had the sides drawn together somewhat when the deck and internal structure was fitted, resulting in a slightly narrower beam at a measurement point 9 inches above the keel than the minimum defined in the class rules. This implies a greater rise of floor and increased prismatic coefficient over that for the standard hull.

In order to make a valid comparison between the two hulls, both were ballasted to the same displacement, 600 lb., and trimmed to be nominally level (judged by expert sailors to be a realistic sailing condition). Boats were tested without centreboards (but with slot rubbers in position) and without rudders. Both hulls were in first class racing condition.

4.3 Tests

Owing to the size of the craft, it was not possible to make any tests representative of wind-ward sailing, but downwind performance could be compared by carrying out resistance tests. Each hull was towed by a line fixed to the top of the transom and the resistance measured with a standard force block. The towing point was much lower than that used for yacht models (Section 2.0) but it is considered that the tests are representative of the situation in which the crew have moved aft to counteract the additional pitching moment caused by the sail force.

4.4 Results

The resistance values are shown plotted in Figure 13. Because of the range of resistance measured, the resistance is divided by the square of the speed in the figure, in order that small dif-ferences in performance would not be obscured.

The results show that the reduction in beam does lead to a significant reduction in resist-ance at hull speeds in excess of about 6 ft./sec., although Boat B has slightly higher resistresist-ance at low speeds. This is in agreement with the experience of development classes, such as the International 14. There is a possibility that the difference in performance could be due to the choice of test trim being closer to the optimum for Boat B than for Boat A. This was investigated by running tests

with Boat A at 4 ft./sec. and 10 ft./sec. with a ballast weight moved to lower and then raise the

transom by one inch. Although increasing the aft trim was beneficial at the higher speeds, very large changes in trim would be required to explain the difference in performance of the two hulls.

A feature common to the results from both hulls is the very low resistance measured at speeds below 4 ft./sec. The implication of this is that any change in hull resistance or sail driving force can make a very large difference to hull speed in this region. In particular, the drag of poorly designed appendages can be significant. It also explains why a boat, successful in seeking out only marginally improved wind speed, can make very large gains.

5.0 RUDDER DESIGN 5.1 Introduction

One area in which very little has been published concerns small boat rudders and centre-boards. Design of these appendages is usually carried out with the aid of data measured on aerofoil sections. This may be misleading because the flow regime in which the rudders operate is so very different to that for which most data are available. A typical dinghy rudder has a mean chord of less than a foot, and at normal speed, operates at Reynolds numbers between 105 and 106, the range in which the flow is transitional. Most wind tunnel data on aerofoils does not extend below Reynolds number 106. It is well known that both lift and drag characteristics depend on Reynolds number. A further disadvantage of wind tunnel results is that they do not take into account wavemaking and

spray making drag.

There are so many variables in practical sailing that it is difficult to make an objective assessment of alternative rudder designs; and for this reason, early in 1976, the Marine Dynamics and Ship Laboratory carried out a project to compare three alternative designs for Tornada catamarans. 5.2 Rudder Designs

In general, rudders differ in size, profile, thickness and section shape, but for the Tornado catamaran, the class rules specify the size and profile, which leaves just thickness and section shape as variables. In practice, most rudders in use in this class are of similar thickness, so the problem is reduced to one of comparing section shapes.

The profile and section shapes investigated are shown in Figure 14. Design A has maximum thickness at 30% from the leading edge, and a constant thickness/chord ratio over the span. Design B has the maximum thickness at 40% chord but is otherwise similar toDesign A. The third design has a "laminar flow" section with maximum thickness at 33% of chord from the leading edge and a con-cave trailing section. The thickness is maintained constant, so that thickness/chord ratio increases towards the tip.

All three rudders were presented with a smooth, racing finish. 5.3 Experiments

The rudders were mounted in a stock so that the leading edges were vertical and their depth of immersion in the tank corresponded to a static load waterline when the rudders are fitted to the catamaran. The stock was itself mounted on a plate which was fixed to the carriage through three force blocks. Two blocks measured side force and turning moment, and the third resistance.

This apparatus was originally designed for testing models of ship rudders, which were about half the area, and much less deep, and it was necessary to strengthen the structure to withstand the higher side forces expected and the moment due to the lower point of application of the force relative to the force blocks. Despite this strengthening, the test program was limited to side forces less than 150 lbs.

Tests were run at speeds 2.5, 5, 10, 15 and 20 ft./sec., at rudder angles0, 1, 2, 3, 4, 5, 8 and 10°, except at 20 ft./sec. where the strength limitation restricted the maximum to 4°, and at 10 ft./sec. when additional angles up to 15° were tested in order to define the stall point.

5.4 Results

To be consistent with presentation of aerodynamic data, the results were evaluated as lift and drag coefficients based on profile area and speed. Because the turning moment of the rudder itself is negligible compared with the turning moment due to the action of the side force, (less than 2%), the analysis was concerned with lift and drag only.

Figures 15, 16 and 17 show lift and drag data for rudders A, B and C respectively. The scatter in the data at low speeds is due to the small forces being measured. At 4° rudder angle the drag increases from 0.15 to about 10 lbs. as speed increases from 2.5 to 20ft./sec. Corresponding lift data are 2 lbs. to 120 lbs.

Despite the increased scatter, there are differences between results at 2.5and 5 ft./sec. and those obtained at higher speeds. It is believed these are mainly due to wavemaking effects reducing lift and increasing drag at higher speeds, but Reynolds number effects may also be present. The rudders stall at an angle of about 15°, and maximum lift/drag ratio occurs at an angle of about 4°.

It is evident that for a given lift, design A is associated with less drag at all speeds tested, and that design C, with laminar flow type sections does not show any evidence of the expected 'bucket' in the curve of drag against lift. The maximum lift/drag ratio are 15.0, 12.6 and 13.1 for rudders A, B and C respectively.

It was clear throughout the tests that the wave disturbance caused by therudders was very large, especially at high speeds. It may be worthwhile to design to minimize this effect, perhaps by cutting down blade thickness near the free surface or, in classes where rudder shape is free modifying the design near the free surface. Adequate strength must be provided in any such design of course, since the forces could easily exceed in practice the limit of 150 lbs. set for these tests. Rudderfittings

6.0 FUTURE WORK

Apart from specific contract studies, work at the laboratory in the field of yacht research will concentrate on continuing development of techniques of experiment and analysis.

Much remains to be done to improve the prediction of full scale performance. There is room for improvement of turbulence stimulation on the models, and further investigation into correla-tion lines. Consideracorrela-tion must be given to scale effects on rudders and on side force during heeled tests.

Methods will be studied for making meaningful comparisons between hulls without recourse to Trimrack' or similar coefficients, and, as data are accumulated, the mathematical model of per-formance will be updated to predict the behaviour of moderndesigns.

The possibility of carrying out instrumented full scale trials is being investigated.

7.0 REFERENCES 1. Davidson, K.S.M. Kirkman, K.L. Pedrick, D.R. Letcher, J.S. Allen, J.F. Doust, D.J. Crewe, P.R. CD CFS CFH CL CR CR (U) CE FH Fn R

Some Experimented Studiesofthe Sailing Yacht.

Trans. SNAME, Vol. 44, 1936, p. 288.

Scale Effects in Sailing Yacht Hydrodynamic Testing. Trans. SNAME, Vol. 82, 1974, p. 77.

Sailing Hull Hydrodynamics, with Reanalysis of the Antiope Data.

Trans. SNAME, Vol. 83, 1975, p. 22.

Yacht Testing.

Trans. SNAME, Vol. 83, 1957, p. 136.

Evaluation of Sail Performance on Yacht Close Hauled Behaviour. Trans. RINA, Vol. 106, 1964, p. 287.

SYMBOLS

Drag coefficient

Coefficient of side force Coefficient of heeling force Lift coefficient

Coefficient of resistance

Coefficient of upright resistance and same speed as heeled test Coefficient of upright resistance

Heeling force, lb. Froude number Resistance, lb. 2., 3. 5. 4.

SYMBOLS (Cont'd)

SH Heeled area of hull, sq. ft. Model speed, ft./sec.

Vs Yacht speed, kts.

VA Apparent wind speed, kts.

VT True wind speed, kts.

VmG Speed made good to windward, kts.

0 Apparent wind angle, deg.

0 Heel angle, deg.

X Leeway angle, deg.

6 Rudder angle, deg.

TRIP WIRES

LEADING EDGE DIVIDED INTO 3 EQUAL PARTS

FIG. 1: LOCATION OF TRIPWIRES

TRIP

.11

1111°

raw. L.

AFT GUIDE

5 LB. TENSIONtrA

WEIGHT

TOWLINE RESTS ON _{FORCE BLOCK}

COLLAR AROUND MAST _{(50 LB. MAX. FORCE)}

MAST STEPPED ON MAST ANGLE POTENTIOMETER STAYS TO SUPPORT MAST MAST 3/411 Ot.D. ',DURAL' TUBE ,v40 TOW HEIGHT = 1/2 C.E.. HEIGHT AS SPECIFIED FWD. GUIDE

MAST 'POSITION AFT OF FWD END, OF WATERLINE SELECTED TO GIVE

SPECIFIED LONGITUDINAL POSITION OF SAIL, ,C.E,

FIG. 2 EXPERIMENT ARRANGEMENT FOR UPRIGHT TESTS

STOPPING

CR x1000

14

0

0 NAKED MODEL

10 MODEL WITH TRIPWIRES

RESISTANCE INCREMENT DUE TO TRIPWIRE

-01

0

FIG. 3: TYPICAL UPRIGHT RESISTANCE DATA 0.35 005 0.10 0..15 0.20 0.25 18 16 12 8 6 4 0

0-0- 9

-FIG. 4: UPRIGHT RESISTANCE FOR "ANTIOPE"

5.0 4.8 4.6 4.4 4.2

103CR 4.0

3.8 3.6 3.4 3.2 3.0

^

+

FULL SCALE "ANTIOPE" (REF. 3)

PREDICTIONS FROM 1/25 SCALE MODEL

/

HULL EFFECTIVE LENGTH 0.7 LWL HULL AND KEEL SKIN FRICTION SCALED SEPARATELY

28 0.1 0.2 0.3 0.4 FROUDE NUMBER

-RUDDER MOMENT (WEATHER HELM)

HORIZONTAL PLANE

WATER FORCES

PROFILE PLANE

SAIL FORCES SAIL FORCES

LONGITUDINAL RIGHTING MOMENT

YACHT SPEED V5

p APPARENT WIND

FORCES

WATER FORCES HEEL ANGLE

FIG. 5: FORCES AND MOMENTS ACTING ON A YACHT SAILING

TO WINDWARD

ON STARBOARD TACK

SAIL FORCES

TRANSVERSE PLANE

TOW POSITION AT ESTIMATED C.E.

ENCODER AND PENDULUM TO

MEASURE HEEL ANGLE

POTENTIOMETER TO MEASURE MAST ANGLE

TRANSVERSE PLANE CONTAINING TOW FORCE

HEEL ANGLE ENCODER TOWING CARRIAGE PLANE OF DECK ENCODER TO MEASURE TOTAL FORCE ANGLE

RUDDER ANGLE SET BY LOCKING PIN ON TILLER (WEATHER HELM DEFINED

POSITIVE)

BEARING AND CALIBRATION

PLATE FOR MAST ANGLE

%

-LEAD SCREW

TOWING CARRIAGE

FIG. 6: EXPERIMENT ARRANGEMENT FOR HEELED TESTS

FORCE BLOCK

(VERTICAL POSITION ADJUSTABLE DURING

0.40 0,38 0.36 0.34 0.32 0.30 Fn 0.28 0.26 0..24 0.22 0.20 0.18 0..16 0.14

FIG. 7: TYPICAL HEELED TEST DATA: FRDUDE NUMBER

RUDDER ANGLE

25

20 HEEL

ANGLE

FH (LB.) 26 24 22 20 18 16 14 12 10 10 15

FIG. 8: TYPICAL HEELED TEST DATA: HEELING FORCE

20 25 HEEL ANGLE RUDDER ANGLE 0 -4 2 4 6 8 6 4

6 5 4 2 -0.5 0 RESISTANCE COEFFICIENT

FIG. 9: TYPICAL HEELED TEST DATA: RESISTANCE COEFFICIENT 0

; 3

4

2

I0 ^

11

RDD/i)

iteleari

_illittlafar

_Ha/a"

0

FIG. 10: TYPICAL HEELED TEST DATA: LEEWAY

-32 30 28 26 24 0.55 0 60 -0.65 X5 0.40

OPTIMUM WINDWARD PERFORMANCE

x\20

1

FIG. 11: NON-DIMENSIONAL DIAGRAM FOR DETERMINING OPTIMUM

WINDWARD PERFORMANCE NIAG/Vi-1 6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 VA/ VS

103CFS 15 10

FIG. 12: COMPARISON OF MODEL AND FULL SCALE HEELED TEST DATA FOR "ANTIOPE"

30 1 1 X

25

20

0 35 0.20 015 2 0 DINGHY X DINGHY 0 4, 5 It 6 7 8

.HULL SPEED V (FT/SEC:)

'FIG. 13: ALBACORE SAILING DINGHIES

'COMPARISON BETWEEN BASIC RESISTANCE DATA

10 12 , 45 0 AMIE 0.30 0.25 "B" 0 3 9

SPAN 21.05"

AREA 177.8 SO. IN.

MEAN CHORD 8.45"

ASPECT RATIO 2.49

MAX. THICKNESS 1.0"

LOCATION OF

TYPICAL SECTION

FIG. 14: TORNADO RUDDER DETAILS

PROFILE FOR DESIGNS A, B AND C

TYPICAL SECTION DESIGN 'CI

TYPICAL SECTION DESIGN .1:1'

ao6 0.07' 0.05 0.04 CD 0.03 0.02 0.01 PL 0.5 0.3 0.2 0.1 0.4 F 0 0.7

0.6

0

0

=MEAN LINE THROUGH

DATA AT 10, 15 AND 20 FT/SEC.

11 11 I' 0 -_ _ 11 -- _1

-1-2 4 6 8 110 12 14 16 18

a

FIG. 15: LIFT AND DRAG COEFFICIENTS FOR RUDDER DESIGN 'A'

0

0

0

CL 0.0P _ 0.7 0.6 0.4 0.3 0.2

Ar"0

MEAN UNE THROUGH

DATA AT 1005 AND 20 .FT/SEC. fl P _II 1 PI d 0 _II IDESIGN 'B' 0 0.8

FIG. 16: LIFT AND 'DRAG COEFFICIENTS FOR RUDDER DESIGN '6'

11 0 2 4 6

_a

CD 0.0 7 0.0 6 - DESIGN, 'CI' 0.05 0.04 0.03 0.02 )3e8(0 0.01ILL-4---(46 ° Of-0 0 OJ 0,2 0.3 0.4 0.5 CL II

0

MEAN LINE THROUGH'

DATA AT 110,15 AND 20

FT/SEC..

11 ii _ _II ___ il _ 11 I I .

2 4 6 8 po

a

FIG.. 17: LIFT AND DRAG COEFFICIENTS FOR RUDDER DESIG,N ''C'

0.9 18 116 42 ,14 0.7

0.6 -

0.5

0.4

0.3

0.1