EVER SINCE RANGER MET AND vanquished Endeavor in the $11,000-per-minute America's Cup competition of 1937, the big yacht races have all been meticulously planned events. Their outcome is more or less decided, in a sense, months and sometimes years in advance of the starting gun in a low brick building that borders the campus of Stevens Institute of Technology in Hoboken, N. J. There, under the critical eye of Randolph Ashton and other specialists in the aerodynamics of sails and the hydrodynamics of hulls, the fleetest racing sloops on earth first demonstrate their prowess as models in an experimental towing tank without benefit of fanfare, crew, wind or wave.

The initial design of a championship hull, according to Ashton, is still largely an art based on long experience. But when experience has been milked dry, a test of a model of the proposed design in an experimental tank can show the designer where he stands and suggest improvements. A bit of planking is then shaved off here or built up there to achieve the optimum hull shape. In the Experimental Towing Tank at Stevens a racing yacht, however appealing esthetically, is viewed coldly as a pattern of force vectors.

A testing setup like that at Stevens is about as far beyond the financial reach of amateur sailors as the 200-inch Hale telescope is beyond amateur astronomers. Ashton does not hold out much encouragement to amateurs who may be tempted to build their own towing tanks for testing sailboat designs. He does believe, however, that any sailing enthusiast who plans to build a boat can profit from knowledge of the dynamics of sailing craft.

"The days of commercial sailing ships of course are gone forever," writes Ashton, "but sailing for pleasure and adventure has probably never been more popular. This year, in particular, with the sailboat competition a prominent feature of the Olympic games to be held in Australia, enthusiasm for racing is at a high pitch. And such a stimulus may account in part for increased interest in the whole realm of sailing.

"At the Experimental Towing Tank we have seen an unusual demand for sailboat model tests during the past year. Most of this demand has come from individuals and syndicates patriotically eager to build contenders for the Olympic races. We have tested many models of designs for the 5 1/2-meter class. One or more of these boats, it is hoped, will be a winner-just as Llanoria was in the 1952 Olympics. A model of that boat- a 6-meter craft designed by Sparkman & Stephens, Inc., of New York City-was tested in our tank, and a number of beneficial design changes were suggested. The same testing procedure has been applied to the 5 1/2-meter designs-by the Luders Marine Construction Company of Stamford, Conn.-being prepared for this year's Olympics. Incidentally, the 55-meter racing boat, though familiar in Europe for some time, is practically new to American waters. It is nearly as long on the waterline as the 6-meter-about 22 feet as against 24 feet-but has a displacement of only about 5,000 pounds, as against 9,900 pounds for the 6-meter. The 5 1/2-meter boat is accordingly less costly to build and handle. As to speed, it is expected from our tests that the '5 1/2' will closely approach the '6' over all, and may even surpass it when sailing at substantially a right angle to the wind-an attitude known as broad reaching.

"Even when a sailboat is not strictly a racing design, its owner usually wants it to go as fast as possible consistent with reasonable comfort. Many an eastern U. S. yachtsman who ordinarily sails principally for pleasure aspires to win the Newport-Bermuda race and shorter ones. In this year's Newport-Bermuda event (June 17 to 20) the first three boats across the finish line had been tested and developed in the Stevens tank. Bolero crossed the line first despite the fact that her mainsail had been carried away in a 50-knot wind and she was forced to finish the race on her spinaker. All three of the boats are from the Sparkman & Stevens yard.

"Good performance is a primary requirement of almost every sailboat design; in fact, better performance than that attained by previous boats is what the designer and owner really want. Can this performance be predicted from a given design? If so, what are the theories and methods used?

"Accurate predictions of sailboat performance have been made at the experimental Towing Tank for the past 20 years. The work was made possible by the fundamental analysis and research described in 1936 by K. S. M. Davidson, director of the laboratory.

"A boat moving under sail is subjected to a fairly complicated set of wind and water forces. We can simplify the problem, without losing sight of basic principles, by dealing with a model driven by a steady wind in smooth water, ignoring the complications that arise when rough water causes the boat to roll, pitch and heave.

"Broadly considered, a boat responds to three principal systems of forces-those of gravity (weight), air and water. Since the gravity forces all act straight down, the vectors representing them are all in the same direction and can simply be added together to give a single vector acting downward at the center of gravity of the boat. The wind forces on sails, on the other hand, have various magnitudes and directions, so that they cannot be represented by a single vector. The same is true of local water forces acting on various parts of the hull. Further, there are combinations of opposed water, air and gravity forces-called 'couples'-which tend to turn or twist the boat, like the opposing forces applied by a rider's hands to the handle bars of a bicycle. Such couples occur, indeed, whenever the forces set up by the wind and gravity lie in planes different from those created by the water. Equilibrium results only when the water-force system offsets the combined resultant of the separate air and gravity forces.

"The general nature of the three basic systems of forces is illustrated by the simple case of a sailboat with spinnaker running free before the wind. The magnitudes and spatial relationships of the forces are measured relative to the vertical, horizontal and longitudinal axes that pass through the boat's center of gravity; on a diagram these axes are represented by the conventional x, y and z [see drawings on this page]. The air force in this simple case is solely horizontal. The air force (F) and the gravity force (W) can both be considered to lie in the same plane and can therefore be combined in a single force vector (R). Hence no couple, or turning force, results. Equilibrium is established when R is precisely opposed by the combined effects of the boat's buoyancy and of the resistance met by the hull's motion through the water. To attain this precise balance of forces, the magnitude of the resistance encountered by the hull must match that of the opposing air force. This means that the boat must attain a specific 'equilibrium' speed, because the resistance increases with the velocity. In addition, if the directions of the opposing forces are to coincide, the hull must be free to alter its trim (bow up or down). In this simple case the center of the spinnaker's effort lies in the vertical plane that divides the boat into two symmetrical halves. It is assumed that the rudder is centered and that the boat is sailing on a straight course.

"A slight complication arises if the same yacht runs free before the wind without a spinnaker. She is then driven by her mainsail, which is carried to leeward. This shifts the center of the driving force to leeward by the distance y_o, [drawing at upper right of Figure 3]. The air and gravity forces accordingly lie in different planes and cannot be combined as a single force. A couple results. To clarify the picture and make the case analogous to that of running with the spinnaker, it is possible to resort to the simple expedient of introducing two equal but opposite forces, F₁ and F₂ [drawing at lower right of Figure 3]. This device leaves the system unchanged as a whole, but F₁ then corresponds to the air force in the spinnaker case and combines with the gravity force. The air force then combines with F₂ and forms the horizontal 'resultant couple.' Equilibrium is established by giving the boat a leeway angle through the action of the rudder.

"The speed of the boat will not necessarily be the same in the two cases, even assuming the same wind force, because the flow of water past the hull is asymmetrical in the second case. Sailors would say the boat 'yaws.' This increases the effective resistance encountered by the hull.

"Sailboats must sail into the wind far more frequently than they sail before it. Yacht races are usually won or lost on the windward leg. Therefore the designer of a sailboat is concerned mostly with its windward ability. The essential problem is to provide useful floating volume for the passengers together with the least development of water resistance consistent with adequate sail-carrying ability. The ability to carry sail is of special importance. Occasionally it happens that a change in design which improves this characteristic of the boat will actually injure its ability to run before the wind while providing the increased speed to windward so likely to lead to success in racing. Naturally the latter gets the preference.

"When sailing to windward, a yacht is spoken of as 'close-hauled.' Now it is theoretically necessary for a close-hauled boat to heel over [see top drawing in Figure 3] and to make some 'leeway' i.e., turn a little from the strictly windward direction. Obviously the sails must 'stand up' to the wind if it is to create a force against them. The wind force must then be resisted by the water force, equal and opposite in direction. These forces, with their components and resultants, are shown in the bottom drawing in Figure 3. The lateral wind and water forces produce a couple which tends make the boat capsize; but in the equilibrium situation this couple is opposed by another righting couple of equal magnitude and opposite direction comprised of the buoyancy and gravity forces. The righting couple can be created only if the boat heels over, and the lateral water force will develop only if the keel advances through the water at an angle like the close-hauled sails or like the wing of an airplane. For the keel to have this angle of attack the hull must make leeway. Incidentally, while the keel itself has a shape reasonably analogous to an airfoil, its 'lift' tends to increase-the heel of the boat and thus to decrease the effective wind pressure.

"The center of effort exerted by the close-hauled sail lies to leeward of the boat's centerline, of course, as in the case when the boat runs before the wind without spinnaker. In addition, the center of effort of the sail is displaced further from the boat's center of gravity by the angle of heel. The resultant force can be resolved into components one of which acts in the direction of boat's motion (F_r) another in the transverse direction (F_h cos) and the third downward (F_h sin, the angle being the angle of heel [see Figure 5]. These components act parallel to the longitudinal, lateral and vertical axes, respectively. They lie in planes which pass through points 1, 2 and 3 in the diagrams. The water couple required for equilibrium is formed by inequalities in the lateral components of the water forces acting on the hull. As a general rule these component forces must be greater on the lee side than on the weather side to balance the lateral wind force components-which means that the hull must make leeway.

"One important air-water couple always investigated at Stevens produces an effect we call the 'unbalance arm': the tendency of a close-hauled boat either to nose into the wind or to fall off. An unbalance arm exists when the center of effort of the sail lies either fore or aft of the center of the hull's lateral resistance. When the center of effort lies aft of the center of resistance, the boat tends to nose into the wind and is said to have a 'weather arm.' It behaves like a weather vane, and for the same reason, the sail being analogous to the weather vane's tail, and the center of lateral resistance to the pivot on which the vane turns. If the two forces were perfectly aligned in opposition, the boat would have no unbalance arm and would accordingly sail a straight course when close-hauled without attention from the helmsman. In practice such balance is rarely achieved or even desired. Some rudder action is practically always required. Actually the rudder angle necessary to compensate for a small weather arm increases the drag of the boat little if at all; indeed, because of the flow pattern of the water around the hull it may even decrease the drag up to about two degrees of rudder angle. The yacht designer has a good measure of control over the unbalance arm, by moving the mast or altering the sail arrangement so as to shift the center of effort forward or aft as required. He can learn what change promises improvement in his original design either by a model test or by full-size trials.

"So far we have considered only the forces-the pushes and pulls-acting on the boat. What about their effects in terms of the boat's movement through the water-its speed? In effect, the angle at which the sails are rigged with respect to the center line of the hull and its keel causes the sail-hull combination to act as a kind of aerodynamic-hydrodynamic wedge. Wind force acts against one face of the wedge and water force against the other. The yacht tends to escape from between the opposing forces-much as slick watermelon seed shoots out from between your finger and thumb when you squeeze it.

"The velocity analysis of a boat sailing to windward is shown in the diagram at the right. The boat is headed at a slight angle with respect to its course an makes leeway as indicated. The 'sailing speed' on course (i.e., rate of progress in the direction of its goal) is a vector resultant of the wind speed and the sailing angle. To a person aboard the sailboat the wind has a certain apparent velocity arising from the boat's motion; this velocity differs in direction and magnitude from the wind's true speed. Now the boat's sailing speed toward the goal will be at a maximum when the sailing angle is so increased that the vector of apparent wind speed is brought approximately abeam-the sailing tactic known as broad reaching. Conversely, the sailing speed will be a minimum when the sailing angle is decreased as much as possible-that is, when the boat is sailed as close to the wind as practicable. Somewhere between these extremes (nearer the minimum than the maximum) there is a sailing angle which results in the best compromise-i.e., the best 'speed-made-good.'

"This speed-made-good directly into the wind, when considered in conjunction with the calculated true wind speed, is the final criterion of windward ability in the Stevens model tests. Speed-made-good is a function of the combined hull and rig characteristics; therefore it cannot be determined from model tests of the hull alone. Model tests of the hull determine the magnitude and direction of the force that must be provided by the sails in the actual boat when the hull moves on course at the speed and angle of heel for which the test was made. The designer must also have reliable knowledge of the lift-drag ratio of the rig and of the relationship between the apparent speed and the corresponding total wind force exerted on the sails of the boat. Both the true and apparent speeds can then be calculated. When the test procedure is carried out for a number of values of the sailing speed at the same heel angle, it is found that the calculated speed-made-good increases at first as the sailing speed increases and then falls off. Accordingly there is always found a best speed-made-good, with its corresponding true and apparent velocities; and such findings agree with actual sailing experiences. Obviously, though, the accuracy with which the true speed can be calculated depends on the values used for the constants of full-sized rigs.

"At the Stevens tank these rig-constant values were originally derived by combining the hull data for a particular boat, as determined by model tests, with the results of a long, careful series of tests on the full-sized boat itself sailing to windward. This boat had a well-designed rig, a good set of sails and an expert helmsman. Measurements were made simultaneously of sailing speed and angle, relative wind velocity and angle of heel. The final analysis of data resulting from these tests indicated that the lift-drag ratio and the wind-force coefficient both varied primarily with the heel angle. Accordingly this angle has become a most important independent variable in our tests. By measuring the water forces that act on the hull at various angles of heel-while holding other quantities constant-such as the speed of the model through the water, we can anticipate the magnitudes of the opposing aerodynamic forces that will be required for equilibrium at that angle.

"In the last analysis, we are interested in values of speed-made-good of various boats for the same true wind speed. A series of measurements made with respect to heel angle leads us directly to this desired information.

"The standard test procedure for a sailboat model at Stevens comprises (1) 'upright' tests and (2) 'close-hauled' or 'heeled' tests. Usually the upright tests are run first. They simulate the condition of a boat sailing before the wind. The model is made of a western sugar pine, varnished and very carefully rubbed down to a uniform finish, with a deck parallel to the designed load water line and a standard distance above it The model is towed the length of the tank by a motor-driven carriage which rides on the underside of a monorail suspended above the center of the tank. The attitude of the model with respect to the water is determined by a set of adjustable mechanical linkages which connect it to the carriage. It is pulled by a horizontal tow-bar fastened to its foredeck and to a resistance dynamometer ahead of it [see photograph above]. The model is accelerated to any one of a long series of test speeds by a post which extends down from the carriage. When the desired speed is attained, the post is disengaged from the model. Equilibrium is then established for the given speed by adjusting the force exerted by the dynamometer so that it just balances the opposing force of the water on the model. From the test data, predictions are made of the resistance of the full-sized sailboat over the whole speed range. From these predictions the designer can immediately compare his design with others in the preliminary and rather inconclusive case of sailing before the wind.

"Another consideration of special importance in both upright and heeled tests is that of establishing turbulent, as opposed to laminar, flow in the boundary friction layer of the model. Without turbulent flow the model tests would be useless. Now small models, particularly models of sailboats, with their extremely 'easy' bow characteristics, require close attention as to turbulent flow. We have developed a method of inducing the essential turbulence by applying a strip of coarse sand along the stem from the water line to the bottom of the keel.

"When a sailboat is close-hauled, the fundamental variables are speed of advance, angle of heel and leeway. If each of these variables remained independent, a veritable network of tests would be required for each model, and the interpretation of the test data would be extremely difficult. As a primary simplification, therefore, the model rudder is kept in its central position. The leeway is then fixed by the values of the other variables. At a particular speed of advance and angle of heel, the leeway must be such that the lateral water force will establish equilibrium precisely between the overturning and righting couples. The magnitude of the righting couple depends solely on the angle of heel. At Stevens tests are made over a range of speeds at heel angles of 10, 20 and 80 degrees, with the leeway adjusted at each speed to produce the lateral force corresponding to the heel angle. The 10-degree heel simulates close-hauled sailing in a light wind; the 20-degree heel represents average windward sailing, and the 80-degree heel simulates sailing into a strong wind with the lee rail almost awash but with full sail. Normally three speeds of advance are tested for each angle of heel, and three values of a mechanically applied lateral force corresponding to that developed by the wind are used for each speed. Two lateral dynamometers apply this lateral force at a height considerably below that of the normal center of effort, but the test technique allows for this, in part, by moving a standard sliding weight laterally above the model deck. This, together with the leeway adjustment, balances the applied force at the particular angle of heel. Other components of the wind force are compensated for by similar techniques.

"The ultimate objective of these heeled tests, as previously mentioned, is to predict the best speed-made-good to windward for the hull and rig under consideration at each of the three angles of heel. Values of speed-made-good are then plotted against true speed and the resulting curve becomes one of the designer's guides in making modifications and improvements. The designer is also supplied with charts showing the characteristics of resistance, leeway, center of lateral resistance and unbalance arm, so that he can compare the predicted performance of the model with that of other designs.

"Although each sailboat design will exhibit its special characteristics, the test and calculation techniques are carefully standardized to afford, as far as possible, rigorous comparisons between designs. In this way the designer learns quickly just how his boat is likely to perform.

"If any reader is by now stimulated to try some experiments of his own, it is recommended that he use full-sized sailing craft rather than models. Accurate construction of models and experimental equipment is difficult to the point of being impracticable. Moreover, data on full-sized boats are scarce at present and would be of great interest. Experiments to test sail coefficients, centerboard designs and locations and racing strategy-to mention only a few of the problems- offer challenging opportunities for ingenious and enthusiastic amateurs."

Bibliography

SOME EXPERIMENTAL STUDIES OF THE SAILING YACHT. Kenneth S. M. Davidson in Transactions of the Society of Naval Architects and Marine Engineers, Vol. 44, pages 288-334; 1936.

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