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AN EXPERIMENTAL INVESTIGATION OF THE AERODYNAMIC INTERACTION OF YACHT SAILS BY JAMES G. LADESIC A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1983 Copyright 1983 by James G. Ladesic To Marlene, my loving wife, for all, the time and things in life she sacrificed . ACKNOWLEDGEMENTS I extend my heartfelt thanks to all those who supported and assisted in the work represented by this dissertation: to EmbryRiddle Aeronautical University for the use of their facilities during the test phase; to Dr. Howard D. Curtis, my department chairman at EmbryRiddle, for his considerate support during this lengthy activity; to Mr. Glen P. Greiner, Associate Instructor, for his assistance early on in the equipment development phase, especially for his help with the planetary boundary layer synthesis; to Mr. Don Bouvier for his expert help with advice on hardware fabrication; to Professor Charles N. Eastlake for his insight on wind tunnel testing techniques and to all of my student assistants for their aid during the data collection phase. Finally, I extend special thanks to my committee chairman, Dr. Richard K. Irey, of University of Florida. His love for sailing and his insistence on excellence has left me with a lasting impression which I shall demon strate in all my future work. TABLE OF CONTENTS Page ACKNOWLEDGEMENTS..................................... iv LIST OF TABLES........................................ vii LIST OF FIGURES ............................... ....... viii KEY TO SYMBOLS.................................... .... x ABSTRACT............................................. xiv CHAPTER INTRODUCTION AND GENERAL EXPERIMENTAL APPROACH................................. ... Introduction. ................................ Experimental Motivation...................... Experimental Method......................... EXPERIMENTAL SIMILITUDE FOR THE SAILING YACHT....................................... General Problem of Complete Yacht Similitude................................ Sail Test Similitude........................ YACHT AERODYNAMIC FORCES AND THEIR MEASUREMENT................................. Resolution of Aerodynamic Forces and Moments .................................. Common Measurement Methods.................. OTHER EQUIPMENT AND APPARATUS............... The Wind Tunnel.............................. Data Collection and Reduction............... SYNTHESIS OF THE ONSET VELOCITY PROFILE..... Motivation and Basic Approach............... The Model Atmospheric PBL and Scale Effects. ................................. Profile Synthesis............................ v ONE TWO THREE FOUR FIVE Page SIX YACHT MODEL DESIGN.......................... 35 Planform Geometry........................... 35 Model Geometry and Trim Adjustments........ 42 Sail Construction.......................... 45 Sail Trim, Setting and Measurements........ 48 SEVEN COMMON EXPERIMENTAL PROCEDURE.............. 50 Sail Trim Pretest ......................... 50 Wind Tunnel Test............................ 51 EIGHT MODEL CONFIGURATION TEST RESULTS........... 54 The FinnType Sail Test.................... 54 Variable Jibsail Hoist Series.............. 66 High Aspect Ratio Series................... 67 NINE EXPERIMENTAL AND THEORETICAL COMPARISONS... 82 The Influence of the Simulated Planetary Boundary Layer.......................... 82 Comparisons of Potential Flow Models and Wind Tunnel Results................. 84 TEN CONCLUSIONS AND RECOMMENDATIONS............ 95 Wind Tunnel Test Conclusions............... 95 Recommendations............................ 96 APPENDICES A SAIL TWIST AS RELATED TO THE APPARENT WIND AND THE INDUCED FLOW FIELD................. 98 B AERODYNAMIC FORCES AND THE CENTER OF EFFORT 104 C AERODYNAMIC FORCE MEASUREMENT.............. 110 D WIND TUNNEL DATA REDUCTION COMPUTER PROGRAM "BOAT" ................ ...................... 121 E BOUNDARY LAYER SYNTHESIS................... 126 F CENTER OF EFFORT BY DIRECT INTEGRATION..... 133 LIST OF REFERENCES...................................... 137 BIOGRAPHICAL SKETCH..................................... 140 LIST OF TABLES Table Page 31 Experimental Force and Moment Coefficient Maximum Uncertainties...................... 22 41 Typical Output Format from "BOAT"........... 28 61 Planform Geometries....................... 40 71 Mean Sail Shape and Trim Parameters........ 52 91 Rig Configuration Test and Theoretical Results.................................... 88 92 FinnType Sail Results from Experiment and Theory ...................... ................. 90 93 Masthead Sloop (Tl5MH1) for Various 8, Experiment vs. Theory...................... 91 vii LIST OF FIGURES Figure Page 21 Coordinate Systems and Basic Dimensions... 10 41 ERAU Subsonic Wind Tunnel General Arrangement............................... 24 61 Sail Geometry Nomenclature................ 36 62 Lift Coefficient vs. Angle of Attack for a Thin, Single Cambered Section as Measured by Milgram (ref. CR1767) for Three Reynolds Numbers and as Predicted by Thin Airfoil Theory............................ 41 63 Wind Tunnel Yacht Model Configurations.... 43 64 Sail Surface Description................. 47 65 Typical Sail Camber Lines, Draft and Twist Measurement Locations..................... 49 81 Finn Sail Yarn Observations............... 57 82 Finn Sail Upwash Observation.............. 57 83 Effect of the Planetary Boundary Layer on Sail Test Data........................... 59 84 Finn Moment Coefficients with and without the Planetary Boundary Layer.............. 61 85 Finn Sail Center of Effort Location....... 64 86 Masthead Sloop Test Results.............. 68 87 Masthead Sloop Polars..................... 69 88 Test Results, 7/8 Sloop................... 70 89 Polars, 7/8 Sloop.......................... 71 810 Test Results, 3/4 Sloop................... 72 811 Polars, 3/4 Sloop.......................... 73 812 Test Results, 1/2 Sloop.................... 74 viii Figure Page 813 Polars, 1/2 Sloop........................... 75 814 Catboat Test Results....................... 76 815 Catboat Polars.............................. 77 816 Masthead Sloop, High Aspect Ratio Main and Jib, Test Results........................... 78 817 Masthead Sloop, High Aspect Ratio Main and Jib, Polars................................. 79 818 Masthead Sloop, High Aspect Ratio Jib and Standard Main, Test Results................ 80 819 Masthead Sloop, High Aspect Ratio Jib, Polars..................................... 81 91 Masthead Sloop Theoretical C C CFWD and C /C vs. Test Results............. ...... 85 y x 92 Masthead Sloop Theoretical Polar vs. Test Polars..................................... 86 93 L/D Ratios From Theory and Test. .......... 93 A1 Typical Wind Triangle for the Sailing Yacht 99 Cl Sixcomponent Floating Beam Force Balance In Schematic.... ......................... 115 El Correlation of Screen Impedance with the Resultant Downstream Velocity Distribution. 127 E2 Yarn Spacing and the Resultant Flow Impedance Distribution..................... 127 E3 Dimensionless Velocity Ratios (Measured and Desired) and Turbulence Intensity Distributions (10T) ........................ 131 KEY TO SYMBOLS AA BB numerical solutions to the Glauert and image n n integral equations A.. direction cosine coefficient matrix A Fourier coefficients n AR aspect ratio BAD boom above deck distance B.. general constant coefficient matrix 13 C force or moment coefficient CpF planform chord length E mainsail foot length F() generalized force vector F( magnitude of the force vector components FBA free board area FRF fractional rig factor H height of the mast above the water plane I jib span I(z) flow impedance distribution function J foretriangle base length K von Karman's constant K. any generalized constant 1 L/D lift to drag ratio LOA length overall LP luff perpendicular Lt nondimensional turbulence scale parameter M( generalized moment vector M() magnitudes of the moment vector components OR overlap ratio P mainsail span PBL planetary boundary layer R. force balance strain gauge resistance reading R Reynolds number SA total planform sail area T. local applied sail traction 1 UA apparent wind speed UB boat speed UT true wind speed U (z) true wind velocity profile U30 apparent/true wind speed at 30 feet W() uncertainty weighting factor x' yacht rig parameter group a,b general constants c chord length, straight line distance from luff to leech d depth of draft (%) e exponential base e. 3space unit vectors 1 F. force vector h reference distance from water plane to the force balance 1H geometric scale factor n reference length of the force balance s surface area u* friction velocity u'v' Reynolds stress u', v' turbulent fluctuating velocities w uncertainty w(z) downwash velocity x sail shape and trim parameter group s x,y,z orthogonal coordinate system a angle of attack 8 apparent wind angle Y true wind angle 6 sail trim angle Eijk permutation symbol Si position vector C() magnitude of the position vector components A leeway angle A sail geometry polar coordinate v kinematic viscosity p density T shear stress 6 heel angle turbulence scale correlation coefficient sail twist R Prandtl mixing length xii Subscripts A,B,C,... F HL J M MOD PF PROT i,j,k,l... x,y,z mx,my,mz force balance channel indicators foretriangle heel jibsail mainsail model planform prototype coordinate indices or counters 3space reference coordinates moment subscripts xiii Abstract of Dissertation Presented to the Graduate Council of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy AN EXPERIMENTAL INVESTIGATION OF THE AERODYNAMIC INTERACTION OF YACHT SAILS By James G. Ladesic Chairman: Dr. Richard K. Irey Major Department: Mechanical Engineering Steady flow wind tunnel test results of sail planforms and rig configurations for typical sloops and catboats are presented. Tests were conducted in the subsonic wind tunnel at EmbryRiddle Aeronautical University, Daytona Beach, Florida, from September, 1981, through August, 1982. Force and moment data were collected using a special pur pose sixcomponent force balance. Test generated force and moment coefficient uncertainties are reported for all tests with a maximum uncertainty for lift as 4.3%, for drag as 6.0% and for the moments as 6.1%. Test results are given for the entire yacht. Estimates of the forces and moments attributable to the sails alone are calculated by subtract ing data of hull and rig tested without sails from the total rig data. The onedesign Finn dinghy planform was used to assess the effect of onset velocity profile distribution. A xiv logarithmic distribution of velocity, modeled after the planetary boundary layer (PBL) typical over water, decreased the net lift and drag coefficients approximately 28% com pared with those determined for a uniform onset velocity distribution. The net sail force center with the PBL was 30% farther above the water plane than that with a uniform onset flow. The sloop configuration was used to assess the effect of jib hoist. Results are compared to theoretically derived lift and drag coefficients. Good agreement was obtained for lift at attack angles less than 350, the stall angle. Theore tical drag estimates are underpredicted but agree in trend. Drive force coefficients from the tests have been found to be more realistic relative to current sailing wisdom and suggest that the omission of pressure, viscous,and boundary layer interference drag in the analytical models is significant. Further experimental research is needed to assess the effects of Reynolds number. Force center movement relative to sail trim, especially for the close reach and beat, also requires further investigation. Continued effort towards empirical stall prediction is called for. Finally, full or fractional size onthewater tests are suggested to advance both sail and yacht design. xv CHAPTER ONE INTRODUCTION AND GENERAL EXPERIMENTAL APPROACH Introduction Sail design and fabrication have relied heavily on the talent of the naval architect and sailmaker (1). Effective sail production has been the result of an individual sail maker's intuitive understanding of fluid dynamics, his knowl edge of prevailing weather conditions for the locality of in tended use and his adroitness in developing complicated three dimensional surfaces from twodimensional patterns (2). In recent times, stateoftheart sailmaking has gone through a renaissance with the application of mathematics and digital computers to the geometric aspect of this transformation task (3). As a result, the accuracy and speed of sail shape develop ment has been significantly improved allowing the sailmaker to market his products as "computer designed". The computer has also been applied to the more complex task of sail aerodynamics with limited success. Computeraided applications of lifting line and vortex lattice flow models provide a theoretical link between desired pressure distributions and the related surface geometry (4, 5, 6, 7). Recent computerized application of the vortex lattice approach by Register (7) has extended this model in two re spects: it includes a logarithmic nonuniform onset velocity 1 patterned after that expected over open water; in addition, no linearizing assumptions are made with respect to sail shape or wake geometry. The latter is particularly signifi cant with respect to modelling the strongly interacting sails of the sloop rig. While application of the potential flow concept shows great promise, it must be understood that such analyses are applicable only for angles of attack less than that of the sail stall point. Superficially this encompasses the beat, close reach and beam reach headings. However even at these headings performance is determined by the ability to maintain maximum sail lift without incurring large scale separation. As such, identification of the stall point and determination of lift and drag coefficients in the vicinity of the stall point are a necessary part of a comprehensive sail study. In this range potential flow theory does not provide useful infor mation. Furthermore, applications of lifting line and vortex lattice theories to the sail have in some instances predicted results that are contrary to accepted sailing beliefs. As a result, controversy shrouds the credibility, practicality and usefulness of predictions made by these analytical methods for sails. Experimental Motivation Motivation for research is usually coupled with national security and/or commercial enterprise. Admittedly, sail research has almost no application to the former and the association with the latter is on a rather small financial scale. As such, experimental efforts have been infrequent. What has been done has often been the guarded property of the designer, naval architect or sailmaker. In the public domain one rarely finds reference to specific documentation. The most dedicated group for altruistic experimental sail research has been that of Marchaj (8) and Tanner (9) at the University of Southampton. Much of this work has been undertaken in a large lowspeed wind tunnel using fabric model sails. No apparent attempt has been made to develop an onset velocity gradient and tests have been run at Reynolds numbers based primarily on distortion and shape control rather than model similitude. The results reported are significant from a qualitative point of view. However, they have limited quantitative applicability because experimental uncertainties are unreported. Many of the tests are performed for specific yacht or planform configurations and thus are not applicable to a wide range of yachts or configurations in general. Milgram (10, 11) has provided general, normalized, two dimensional sail coefficients with and without mast effects at appropriate Reynolds numbers. (His experimental uncertainty is also unreported.) Methods for applying such twodimensional sail data to a threedimensional sail configuration for forces and moments are, at present, unclear in that no corrections for such factors as aspect ratio and sail geometry variations are provided. Milgram proposes a scheme for estimating three dimensional pressure and viscous drag effects from two dimensional data but admits the need for experimental verification of the method. Such techniques do exist for air foil sections and wings (12) but whether they apply directly to the sailboat has not been established. In short, experi mental sail characteristics that can be readily employed to verify analytical results are necessary to further the advance ment of sail aerodynamic research. One fact agreed upon by both proponents and opponents of the analytical approach is the need for experimental research. Such research would not only quantify the performance of the sails tested, they would also complement the theoretical efforts by validating their range of applicability. For the sloop rigged vessel (jib and mainsail), the aerodynamic interaction associated with the close proximity of the headsail and main sail has not been fully explored. Specifically, how performance is affected by the amount of jibsail overlap and the percentage of jib hoist has not been reported. Nor has the effect of nonuniform onset velocity. These topics are principal ob jectives of this research. How this experimental information compares with analytical results is also of keen interest. Experimental Method Measurements are made in a lowspeed subsonic wind tunnel into which a flow impedance distribution can be introduced to model the nonlinear onset velocity profile at a scale compat ible with the yacht model. All sails are cylindrical surfaces. Such shapes are easy to characterize geometrically, but they do not match the shapes offered by present day sailmaking technology. Sails are constructed from aluminum sheets which are cut and rolled to shape. Once fastened to the yacht model's standing rigging, the builtin shapes are maintained throughout the tests. Yacht rig configurations tested fall into three categories: a cat rigged, Finntype sail which is tested without a hull model in order to assess the influence that onset velocity profile has on the sail force magnitude and its location relative to the water reference plane; a variable hoist series, hull present, in which the headsail hoist is decreased at a constant main sail size; and a rig aspect ratio series, hull present, for the masthead sloop. Tests are conducted at velocities that model a 4 to 6 kt true wind speed at the masthead. All data are corrected for wall effects, solid blocking and wake blocking. Each datum point displayed is presented with its estimated experimental uncertainty. Some salient aspects of sail testing and theo retical extension into very low Reynolds number regimes are discussed. In the present effort, threedimensional sails are em ployed to assess the effects of trim and rig under steady flow conditions. These trends are compared to the vortex lattice analysis completed by Register for identical configurations and trim and to the vortex line model developed earlier by Milgram for similar rig configurations and trim. CHAPTER TWO EXPERIMENTAL SIMILITUDE FOR THE SAILING YACHT General Problem of Complete Yacht Similitude Experimental efforts in yacht testing are classically divided at the airwater interface. That is the hydro dynamics of the hull are evaluated independently of the aero dynamics of the sails. This division is convenient in that it permits a reduction in the number of parameters required for model similarity but it cannot assess interactive effects that are a consequence of the airwater interface. As such, hull hydrodynamic results must be partnered with sail aero dynamic results on the basis of assumed interface conditions. It has not been practical to attain complete experimental similitude in either sail aerodynamics or hull hydrodynamics (13, 14). It is standard practice for these methods to de part from strict compliance with similarity laws. For con venience the inference is often made that sail theory is an extension of the body of literature developed for aircraft wings. As such, differences in the governing parameters are sometimes assumed trivial and design parameters are deduced from existing airfoil data, such as that collected in Abbott and von Doenhoff (12). However, applications of such data even to the single cambered, flexible sail must be done with caution as significant differences between the two exist. As differentiated from the rigid aircraft wing, cloth sails are normally highly loaded and generally have large geometrical twist. In addition, the criterion for optimum sail performance must be related to the projections of lift and drag to the vessel's center line that resolve into the driving force; whereas wing optimum performance is governed primarily by lift alone. Also, the sail is sub ject to a nonuniform onset velocity resulting from the atmospheric boundary layer; while in contrast, the air craft wing moves through an air mass that is to the first order stationary. As a consequence of these effects, the variation of lift with attack angle cannot be considered a constant for sails, whereas this is a typical assumption in wing design. In addition, tests for aircraft are usually conducted at Reynolds numbers much larger than those en countered on yacht sails. These differences clearly justify a treatise on sail test similitude based on the pertinent variables and conditions that are unique to the sailing yacht. For the work presented herein, the hydrodynamic effects of the hull are ignored. The scaled true wind magnitude is determined by the available wind tunnel capacity for the model size selected, with the profile impedance screen in place. This wind speed is equivalent (based on Reynolds number) to prototype onthewater wind speed of 4 to 6 kt. As such, heel effects for the yacht being modeled can be ignored and an assumption of no waveair interaction is reasonable. Thus, it is not necessary to model motions that would result from a wind driven sea state. A major discrepancy between this work and on the water conditions is that the onset flow has zero twist which, in turn, implies the assumption of zero boat speed. This limi tation is a practical necessity in wind tunnel testing. To model the effect of boat speed, one could either move the model at constant speed in a direction oblique to the tunnel flow during data collection or modify the wind tunnel air flow in both direction and magnitude with the yacht model stationary. Either procedure could simulate the vectorial addition of boat speed and true wind speed. The former would require a suitably wide tunnel test section and would intro duce uncertainties associated with model inertial response. The latter concept would complicate the synthesis of the onset velocity profile. For present purposes, the added complexity of either procedure is unwarranted in terms of what it would contribute to the results. Therefore, the distortion of re sults that are a consequence of zero boat speed are accepted. The effect of this distortion on the overall test results is assessed in Appendix A; it is shown to be small. Finally, the apparent heading (BX) of a yacht sailing to weather is different from the true heading measured re lative to the apparent wind by the angle X. This small dif ference is measured from the yacht center line and is referred to as the leeway angle. This angle is the effective angle of incidence for the keel. While X is small (on the order of 4 degrees), it is necessary for the development of the keel reaction to the sailproduced heel force. Consequently, the desired component resolution of the aerodynamic sail forces are taken parallel and perpendicular to a plane passed vertically through the yacht and rotated X from the yacht center line. Since the hydrodynamic properties of the hull and keel are unknown and, therefore, ignored in the pre sent work, the aerodynamic sail forces are resolved parallel and perpendicular to the boat center line. This is equiva lent to assuming A = 0. It is seen from Figure 21 that this assumption will slightly decrease the component of lift and increase the component of drag in the selected driving force direction and is therefore conservative with respect to the net predicted driving force. Sail Test Similitude Dimensionless variables can be formulated by applica tion of Buckingham's Pi Theorem (15). This is the approach adopted here. For the sailing yacht, forces and moments of interest are resolved with respect to the wind tunnel flow direction. Figure 21 illustrates the Cartesian coordinate frame selected for this purpose. From the assumption that X = 0, the force coefficient is then defined functionally as F UT(z) UB UT UC  2__ CF[ X',xS Lt,lH 2 CF[,e, U (z ) U U V 'S t H pUA(SA) UT(MAX A UA (2la) Lift C Boat ] Heading? _ CIIL e"x Drag ea( Cx Mi Boat Center mz Line Note: Force coefficients shown are resolved about an arbtirary point. Masthead Level FIGURE 21 Coordinate System And Basic Dimensions Where the nondimensional arguments of this function are defined as 8 = heading angle from the apparent wind to the boat center line 8 = heel angle U (z)/U (zMAX) = onset velocity profile normalized for zM at the masthead MAX U /UA = boat to apparent wind speed ratio UT/UA = true to apparent wind speed ratio UAc/v = inertial to viscous force ratio (Reynolds number, Re) X' = rig parameters such as (cat, sloop, cutter, or ketch), vertical or raked masts), (standing rig ging area to sail area), (free board area to sail area), (rig aspect ratio H2/2SA), (etc.) I x = sail shape and trim parameters such as draft, draft position, foot curve, roach curve, sail dimension ratios (I/P, J/E ,.. ), trim angles (6M,6 ), twist parameters (J ,4M), etc. Lt = dimensionless scale of turbulent 1H = the geometric scale factor. It is evident from Figure 21 that a smaller yacht "sees" a lower portion of the profile shown. Thus, scale similarity is dependent on the mast height (H) relative to the onset velocity function U(z). Writing the relation between homo logous model (MOD) and prototype (PROT) dimensions defines the geometric scale factor or 1 PROT H HMOD Application of the conditions of negligible leeway, zero heel, and zero boat speed yields U UT 6=0, = 0 and 1 A A For the test results reported, the same sloop hull model with standing rigging is used except for those in which the sail is tested without a hull model. Therefore, in comparing one set of test results with another among the rig parameter variable group (X') the most significant variables are the rig aspect ratio (H /2SA) and freeboard to sail area ratio (FBA/SA). Only these will be reported. Of all the sail shape and trim parameters (xs) only s those that are related to the overall planform shape and the sail trim adjustments furnished on the yacht model are reported. Sail parameters such as the foot and roach curves are proportional for each model and therefore are not listed. Similarly, the draft positions for cylindrical sails are constant and are located at the 50% chord point. As such, they are not parametrically varied and, therefore, are not reported. The sail shape and trim parameter group can then be written as xs = xs'(I/P, P/E, J/E 6, 6M' J' M' dj, dM) and equation 2la becomes 2 FBA  C = C (8, R H /2SA, SA ', Lt' 1 ) (21b) F F eS s t H Free stream turbulence is known to effect both laminar to turbulent transition and separation of the boundary layer attached to a lifting surface. Increased free stream turbu lence normally results in increased drag and decreased lift. This phenomenon is an interactive one, it is thought to be a function of the scale of the free stream turbulence relative to the scale of the lifting surface turbulent shear layer (16, 17). Specifically, evidence suggests that if the free stream scale is large relative to that of the shear layer, the interaction is negligible. Referring to yacht sails, the free turbulence scale of the majority of the atmosphere is large; however, the scale of the lower regions of the air water interface boundary layer is small. The actual and tunnel simulated velocity profiles are of classical logarith mic form. The portion of that boundary layer normally inci dent on the sails is generally within the "overlap layer" (18). In this region the scale of turbulence is proportional to elevation, z. Investigation within the atmospheric boundary layer over open water by Ruggles (19) and later Groscup (20)included measurements of the Reynolds stress. Groscup (20)gives a value for the planetary boundary layer Reyonolds stress per unit density of 0.328 ft2/s2 at a height near that of the prototype yacht midchord. This Reynolds stress was measured in a true wind velocity of 4 to 8 kt at a 30 ft elevation. This is compatible with the conditions of interest here. To compare this to the sail boundary layer, assume it to the that 14 of an equivalent flat plate so that a convenient length scale for comparison is the Prandtl mixing length (). Then using the one seventh power velocity distribution for the sail boundary layer, one can estimate that the max imum mixing length for the sails is about 0.2 in. at the trailing edge. A similar mixing length calculation, made for the planetary boundary layer, incorporating the measured Reynolds stress provided by Groscup gives a mixing length of about 30 in. Defining the prototype dimensionless para meter (Lt) for turbulence scale as PBL Lt (22) SAIL gives for the velocity range of interest here Lt = 150. This suggests two orders of magnitude difference between the two scales. The preceding estimates refer to actual sailing conditions of a prototype yacht. If this were also the case for the model sail in the simulated wind tunnel boundary layer, then Lt could be eliminated from the perti nent governing parameters. Turbulent intensity rather than Reynolds stress was experimentally measured in the wind tunnel. Thus to eval uate the same ratio, the Reynolds stress must be inferred from the turbulence intensity measurement. The correlation coefficient is defined by u'v' u = (23) rrsrr As suggested by Schlichting (16), it is taken as 0.45 in the overlap layer, and the lateral perturbation velocity v' is assumed directly proportional to u consistent with the experiments performed by Reichardt (16). Given a measurement of 4 for the mean velocity profile, one can evaluate the Reynolds stress using equation 23 with the above assumption and approximate the mixing length as (BL)m = u'v (24) PBL m ;u/az where au/3z can be found directly from the measured mean velocity profile at an appropriate height (z), taken here as the height of the planform geometric chord. Equation 24 gives a model mixing length (PBL)m of about 2.0 in. at U30 = 80 ft/s. The sail model shear layer is considered in the same manner as the prototype; this yields a sail model mixing length ( SAIL)m of 0.02 in. The dimensionless turbulence scale for the model (Lt)m is thus estimated to be about 100. This is sufficient to allow turbulent inter actions to be ignored. As a result, equation 21b simpli fies to H FBA C = C (H, R H', 1 ) (25) F F e' 2SA' SA x 1H) The threedimensional moments may also be written in coefficient form similar to equation 2la or 2 M = C (8, Re, A A x' 1H) (26) PU2 SA Cp m 2SA 'SA s H pU SA C A PF where CpF is the planform geometric chord. The moment co efficients represented by equation 26 are subject to the same dimensionless groups as those of equation 25. For the experiments reported here, UA is taken as the wind speed measured at the masthead of the model and the three principal force coefficients (reference Figure 21) are *C  drag, parallel to and positive in the direction of the apparent wind *C  lift, perpendicular to the apparent Y wind and to the mast *C  heave, parallel to the mast and z mutually perpendicular to C and C x y The corresponding moments C C and C represent moments mx my mz about the same xyz coordinate system. Referring once more to Figure 21, the forward and side (heel) force coefficients relative to the boat center line are then defined respec tively (for X=0) as CFWD = C sin (8) C cos (8) (27a) FWD = x CHL = C cos (8) = C sin (8) (27b) Equations 27 will be used in later discussions regarding potential yacht performance. Finally, only one size yacht model is correct rela tive to the fixed onset velocity distribution [UMOD(2)] used here. However, slight extensions of the scale factor (1H) may be assumed without appreciable error. For example, to represent a 30 ft prototype mast height while maintaining the same velocity distribution, the scale fac tor would increase to approximately 13. Conversely, for a 26 ft prototype mast height, 1H becomes approximately 11. Corresponding to these stretched scale factors, the esti mated error in the net forces is 2.0% of the nominal 28 ft prediction. The uncertainty in predicted force center is 0.7%, while the moment uncertainty is 5.3%. The dif ference in average velocity that the sails would see is 1.0%. All of these percentages are within the estimated experi mental uncertainty of the tests conducted. Accordingly, the test results presented here may be considered applicable within reported uncertainty to sailboats from 18 to approxi mately 26 ft LOA as a function of their mast height off the water. CHAPTER THREE YACHT AERODYNAMIC FORCES AND THEIR MEASUREMENT Resolution of Aerodynamic Forces and Moments In steady flow, the net aerodynamic forces and moments experienced by the sails, rigging and above water hull of the sailing yacht are reacted by hydrodynamic forces on the keel, rudder and hull underbody surfaces. These aerodynamic forces and moments are transmitted to the sails, rigging and above water hull via nearfield airflow pressure distri butions and viscous boundary layer shear stresses on every free surface exposed to the flow. From the equations for static equilibrium three components of force and three com ponents of moment are needed to define the net reaction of all the applied aerodynamic loads. Therefore, the direct measurement of orthogonal force and moment triples at any preselected location, on or off the yacht, would yield the net aerodynamic reactions. In order to assess the contribution that the aerodynamic forces make towards the balance and stability of a yacht it is necessary to know both the magnitude and the location of these forces. For this purpose, the center of effort is commonly defined as a point in space where the applied aero dynamic forces may be resolved so that the net aerodynamic moment about this point is zero. Appendix B discusses, in detail, resolution of the sail aerodynamic loads and the ex perimental determination of the yacht's center of effort. In general, it is demonstrated in Appendix B that direct measurement of forces and moments relative to an arbitrary global origin will not uniquely yield the center of effort location. As such, the center of effort must be known a priori or must be estimated from some physical constraints of the experiment. Common Measurement Methods The measurement of forces and moments resulting from flow about the sailing yacht model may be accomplished by any of three different methods: 1) Measure the pressure distribution over the free surfaces (Equation B2) and sum the measurements as a function of area (Equation B3); 2) Survey the upstream and downstream flow for momentum difference and evaluate the stream wise static pressure distribution upstream and downstream of the model (valid for steady flow only); 3) Measure the three orthogonal components of force and moment via a force transducer or balance directly. Pope and Harper (21) discuss each of these methods in detail relative to wind tunnel tests of aircraft. They indi cate that three forces (lift, drag and yaw) and their companion moments completely describe the local spectrum of interest for aircraft. Symmetry and aircraft design experience indicate that the point of resolution for these forces and moments is normally considered to be known a priori. These restric tions admit a unique solution for the aircraft. However, as discussed in Appendix B, this is not the case for the sailing yacht. Most sails, including those tested, are thin. As a result surface orifices for pressure measurement are impractical. Wake survey methods are of use but require the measurement of both static and dynamic pressure at each survey point. Hence, the accuracy of any calculated force from such a survey is a func tion of the number of survey points selected. In order to reduce the number of measurements, it is common practice to measure only stagnation pressure at each of the survey points and to measure the static pressure at the wind tunnel wall. It is then assumed that this static pressure is uniform across the section of the tunnel where the measurements are made. This assumption is valid providing the distance downstream from the model is sufficiently far to allow static pressure recovery. Unfortunately, this is not often possible due to changes in wind tunnel geometry downstream of the test section. These can cause appreciable wall effect losses that must be accounted for with the consequence of an increase in the level of exper imental uncertainty. Direct measurement with a force balance is the simplest and most straightforward method of attaining net force and moment data. However, as discussed above, spe cific details as to local force and moment distribution are not possible. In the present work, a sixcomponent force balance has been used to measure the aerodynamic response of various model sailing yacht rig configurations. A general discussion on sixcomponent force balances is given in Appendix C with de tails of the sixcomponent floating beam balance used here. The net maximum uncertainty for each force and moment coeffi cient range discussed in Appendix C is calculated employing the methods of Holman (22) and is given in Table 31. In addi tion to these direct measurements, the static pressure through the wind tunnel test section was surveyed both upstream and downstream of the model to establish correction parameters for solid blocking and horizontal bouyancy. TABLE 31 Experimental Force and Moment Coefficient Maximum Uncertainties Coefficient Cx Range 0.0 to 0.2 0.2 to 0.4 0.4 to 1.0 Uncertainty 4.3% 3.9% 3.1% Coefficient Cy Range 0.0 to 0.5 0.5 to 1.0 1.0 to 1.5 Uncertainty 6.0% 4.9% 3.8% Coefficient Cz Range 0.4 to 0.2 0.2 to 0.1 0.1 to 0.0 Uncertainty 2.0% 2.1% 2.2% Coefficient Cmx Range 3.0 to 2.0 2.0 to 1.0 1.0 to 0.0 Uncertainty 4.8% 5.8% 5.9% Coefficient Cmy Range 0.0'to 0.2 0.2 to 0.5 0.5 to 1.5 Uncertainty 6.1% 5.8% 4.6% Coefficient Cmz Range 0.2 to 0.2 0.2 to 0.4 0.4 to 0.6 Uncertainty 3.1% 2.6% 2.1% CHAPTER FOUR EQUIPMENT AND APPARATUS The Wind Tunnel The most essential piece of equipment used for the tests reported herein is the subsonic wind tunnel at EmbryRiddle Aeronautical University, Daytona Beach, Florida. This wind tunnel is a closed circuit, vertical, single return design which has an enclosed, lowspeed and highspeed test section. Flow is produced by a 6blade, fixed pitch, laminated wood propeller, 56 in. in diameter, that is driven by a 385 horsepower, 8cylinder internal combustion engine. Speed control is provided by throttle and a 3speed fluid drive transmission. Figure 41 illustrates the overall dimensions, general arrangement and location of the main features of interest. The operational range of the tunnel is from 0 to 190 ft/s, 0 to 96 ft/s in the lowspeed and 0 to 190 ft/s in the highspeed test sections. The lowspeed test section is octagonal, 36 in. high by 52 in. wide, with a crosssectional 2 area of 11.5 ft To permit easy access to the model area and force balance, the entire lowspeed section is mounted on a wheeled frame and can be removed from the tunnel proper. The sixcomponent floating beam balance was installed on the under side of this test section, external to the tunnel I M >o 0  coq a)O Q)OlE) I ~  interior. The rectangular highspeed test section is 24 in. 2 wide by 36 in. high with an area of 5.96 ft2. Considering the effects of solid blocking together with the size of model needed for reasonable scale similitude, the lowspeed test section allows the most flexibility and was used for all the results presented. The lowspeed test section was designed with 1/2 degree diverging walls to maintain a constant streamwise static pres sure through the section as the wall boundary layer thickens in the streamwise direction. For the range of velocities of concern here, the turbulence intensity of the mean flow is less than 0.004 and is considered well within acceptable limits for lowspeed testing. The velocity distribution through the test section is uniform to within 1%. This, of course, was intentionally modified along with the turbulence intensity to produce the model velocity profile discussed in the next chapter. Data Collection and Reduction The experimental data presented were collected with the sixcomponent floating beam force balance discussed in Chapter Three via a tenchannel BaldwinLimaHamilton (BLH) Model 225 Switching and Balancing Unit and interpreted with a BLH Model 120C Strain Indicator. Each of the flexural elements of the force balance was fitted with a matched pair of Micro Measurement EA06250BG120 precision 120R gauges which were wired as two arms of a fourarm Wheatstone bridge circuit on the Model 225 Switching and Balancing Unit for each of the six channels monitored. The remaining bridge circuit was com pleted using two precision 1200 "dummy" resistors. Strains were read directly from the Model 120C Strain Indicator in microinches per inch, pin./in. The backup and calibration check unit used for the BLH system was a Vishay Instruments BAM1 Bridge Amplifier and Meter. System calibration checks were made monthly to ensure that experimental accuracy was maintained. Flow air temperature was measured upstream of the low speed test section at the inlet contraction cone by a mercury bulb thermometer probe connected to an external dialtype indicator which reads to 10F precision. Flow velocities were inferred from direct measurement of the local static and dynamic pressure with a common Pitotstatic tube and a 50 in. water manometer. A Thermonetic Corporation HWA101 hot wire anemometer was used for backup and to augment velocity survey measurements. The force balance calibration equations were incorporated into a Fortran computer program along with all the pertinent flow relations for Reynolds number, yacht rig configuration sail area calculation, wind tunnel solid blocking and hori zontal buoyancy corrections. The strain gauge resistance data for all six strain channels at each heading angle tested were loaded to a computer disc file. In addition, flow air tempera ture, the static and dynamic pressure at the masthead and the 27 rig configuration geometry were stored in this file. All of this information was subsequently processed through the Fortran program BOAT (a listing BOAT is given in Appendix D) on a Hewlett Packard HP1000 minicomputer. A sample of the typical output information is shown in Table 41. The xyz coordinate system is global; x being in the flow direction and z vertical while the boat coordinates of "Drive", "Heel" and "Vertical" are those as illustrated in Figure 21. TABLE 41 Typical Output Format From "BOAT" RU,BOAT INPUT NAME OF FILE RUN DATA IS STORED IN (UP TO SIX CHARACTERS,FIRST CHARACTER START IN COLUMN 1, JUSTIFIED LEFT, INCLUDE TRAILING BLANKS, IF ANY) T15MH1 WIND TUNNEL DATA REDUCTION PROGRAM SAIL BOAT DATA INPUT INPUT SAIL DIMENSIONS (for model) I J 25 8 22.5 9 P E (inches) INPUT PERCENT OVERLAP, FRACTIONAL RIG FACTOR 1.5 ,1 WIND TUNNEL EXPERIMENT, DATA REDUCTION OUTPUT TEST MODEL : SAIL BOAT 7/12/82 STD 150 SLP, W/PBL, FLOOR SEALED, STD ASPECT RATIO. SAIL DIMENSIONS : I = 25.00 E 9.00 8.00 P 22.50 SAIL AREA (ACTUAL) = 1.82ft**2 SAIL AREA (100 Z F.T.) = 1.40 PERCENT OVERLAP = 1.50 FRACTIONAL RIG FACTOR = 1.00 J = TABLE 41 continued SAIL ANGLES(DEG),VELOCITY(FPS),REYNOLDS NUMBER, DYNAMIC FORCE Delta Delta jib main 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 0.'0 0.0 0.0 0, 0.0 0.0 0.0 0.0 VELOCITY '78.41 79.36 80.06 81.35 81.50 82.01 82.34 82.71 REYNOLDS NUMBER 402566. 407417. 411020. 417675. 418426. 421015. 422739. 424646. FORCE AND MOMENT COEFFICIENTS RELATIVE TO COURSE ANGLE 8.0 15.0 20.0 25.0 30.0 35.0 40.0 46.0 Cx .2607 .2727 .3207 .3542 .4592 .5641 .7103 .9575 Cy .3778 .6533 .8607 1.1499 1.3206 1.4165 1.4891 1.4652 Cz .0427 .0773 .1086 .1402 .1672 .1878 .2095 .2202 Cmx .0800 .3655 .6114 .7936 .9597 1.1360 1.0961 1.1495 THE WIND Cmy .0569 .0698 .0727' .1124 .1241 .1755 .2723 .4645 FORCE AND MOMENT COEFFICIENTS RELATIVE TO THE BOAT COURSE ANGLE 8.0 15.0 20.0 25.0 30.0 35.0 40.0 46.0 DRIVE COEF. .2056 .0943 .0070 .1649 .2626 .3503 .4130 .3887 HEEL COEF. .4104 .7016 .9185 1.1918 1.3733 1.4840 1.5973 1.7066 VERT. COEF. .0427 .0773 .1086 .1402 .1672 .1878 .2095 .2202 HEEL MOMENT COEF. .0871 .3711 .5994 .7668 .8932 1.0313 1.0148 1.1327 PITCH MOMENT COEF. .0675 .1620 .2774 .4373 .5873 .7953 .9132 1.1495 COURSE ANGLE 8.0 15.0 20.0 25.0 30.0 35.0 40.0 46.0 DYNAMIC FORCE 12.50 12.78 13.01 13.44 13.46 13.58 13.69 13.81 Cmz .0769 .0538 .0206 .0032 .0430 .0571 .0408 .0164 YAW MOMENT COEF. .0769 .0538 .0206 .0032 .0430 .0571 .0408 .0164 CHAPTER FIVE SYNTHESIS OF THE ONSET VELOCITY PROFILE Motivation and Basic Approach The sailing yacht is subject to a nonuniform onset velocity resulting from the vector addition of the atmos pheric planetary boundary layer (PBL) and the yacht's for ward velocity. This summation produces what is termed the yacht's apparent wind. The magnitude of this apparent wind varies as a function of vertical height while its direction tends to rotate aft from the deck to the masthead of the yacht. Proper modeling of this boundary layer with respect to a sail rig configuration is essential for achieving scale similitude. Previous tests of sails and rig configurations (8, 9, 10, 11, 13) both two and threedimensional, have not used such an onset velocity. As such, conclusions re garding lift, drag and center of pressure could be signi ficantly different than with nonuniform onset. Modeling both the variation and direction in the wind tunnel is difficult. Modeling only magnitude variation with respect to one geometric axis is commonplace. Well developed methods for modifying a wind tunnel velocity profile exist (23, 24, 25). When the size of a particular wind tunnel is fixed in shape upstream of the test section, methods which develop a desired velocity distribution by artificial fetch (roughness pegs, counter jets or, simply, the length of upstream convergent section) must be discarded. A more direct approach in such cases is to progressively impede the flow in the geometric direction of the desired velocity variation. That is if U = U(z) (51) the direction of impedance (I) would also be I = I(z) (52) This simple approach implies that a desired distribution could be synthesized by physically obstructing the flow up stream of the test section. In principle this is correct. However, the level of turbulence introduced into the flow due to the upstream obstruction(s) must be within some pre determined limits. Similarly, the pressure drop across the obstruction equates to an overall reduction in tunnel operat ing efficiency. With these considerations in mind, a direct impedance scheme can be planned to provide a desired velocity distribution and a reasonable turbulence intensity in the wind tunnel test section. The Model Atmospheric PBL and Scale Effects The measurement and formulation of the atmospheric boundary layer above the ocean has been the topic of numer ous research efforts (19, 20, 26, 27). For modeling such a boundary layer in the wind tunnel with respect to the sailing yacht, only the first 100 ft, measured from the water surface, is of interest. In this first 100 ft, often referred to as the surface layer, the characteristics of the actual PBL that are of significance towards such test ing, for steady flow, are as follows: *The wind direction is essentially constant and Coriolis effects may be ignored. *The long duration vertical velocity distribution is logarithmic in form to within a 95% certainty. *The scale of turbulence in the PBL is large re lative to that of the sail boundary layer (this is verified in Chapter Two). *Vertical variation of stresses and other fluxes can be neglected. *The friction velocity (u*) can be assumed a linear function of the wind speed rate of shear and is defined as u* = where Tw is the shear stress at the boundary (water plane) and p is the local flow density. Neglecting convective terms, the generally agreedupon form of the long duration, stable surface layer PBL is U(z) = ln( ) (53) K z where z = vertical distance above the water plane U(z) = velocity at height z K = von Karman Constant taken to equal 0.42 z = roughness length From this form Kerwin (28) has developed a useful average wind gradient formula applicable to the sailing yacht in terms of the wind velocity at a height of 10(m) above the water surface [U10] and the vertical position (z) for any profile velocity as U(z) = 0.1086 UI0 ln[304.8z(m)] (54) Since equation 54 was that adopted by Register in his vortex lattice scheme, it will similarly be the profile shape syn thesized in the wind tunnel. As mentioned in Chapter Two, similarity requires that a specific size yacht be determined for test that simultan eously sizes an explicit portion of the PBL which must be synthesized. Converting equation 54 to scale (1H = 12) yields U(z) = 0.1086 lnz(in.) + 0.4918 (55) U30 where z is measured above the wind tunnel floor. Equation 55 is considered the desired shape of the scale velocity profile to be synthesized in the wind tunnel. Profile Synthesis The details of the direct impedance method used to syn thesize the velocity profile described by equation 55 are given in Appendix E. The profile obtained by this method 34 fits the desired profile to a confidence of 96.5% using a least squares logarithmic curve fitting scheme on the measured velocity values. The turbulence intensity dis tribution through this synthesized profile has also been measured and it has been found to be in reasonable agree ment with classical turbulent boundary layer measurements. CHAPTER SIX YACHT MODEL DESIGN Planform Geometry As discussed previously, the overall model dimensions were selected as a function of the wind tunnel test section size relative to the type of yacht data desired. Consis tent with popular sailcraft nomenclature, the primary geometric dimensions of the sail planform are I, J, P, and E as illustrated in Figure 21. The right triangle formed by the horizontal "J" and vertical "I" dimensions is termed the sail platform "foretriangle". The vertices of any foresail and the edges between these vertices are shown in Figure 61. The luff perpendicular (LP) is drawn from the luff to the clew as shown. Foresails or headsails which exceed the foretriangle area are named or "rated" as a percent of "J". Ergo the 150% genoa headsail is a sail with LP=1.5J. The region of the sail area which extends beyond the J dimension is termed the "overlap". For the research reported here, it is convenient to define the overlap ratio (OR) factor where LP OR = L Y Similarly, sloop rigs which have foretriangles that do not extend to the vessel masthead are termed "fractional 35 Luff Clew Foot FIGURE 61 Sail Geometry Nomenclature. C l rigs". To classify these geometries, one can define a fractional rig factor (FRF) (I) FRF = (P+BAD) where (P+BAD) is the distance from the yacht deck to the masthead and for convenience is set equal to H. The foresail triangular area (SAF) can then be written as SAF =(I 2+ 2(OR)(J) The mainsail dimensions are designated P and E, Its triangu lar area (SAM) is SAM =PE. The rig planform area used for all of the force and moment coefficients is the sum of the foresail and mainsail area SA = SAF + SAM This area is slightly smaller than the actual sail area due to the curvature or "roach" of each sail's trailing edge. It is common practice to omit this area when defining sail area. Rig aspect ratio is another quantity of interest and is somewhat more arbitrary in definition. The classical definition of aspect ratio used in the sailing community is defined by the particular sail being referenced. The main sail aspect ratio is taken as AR ME while the foretriangle aspect ratio is I AR J J For the present work, it is desirable to use an aspect ratio that adequately represents the entire rig configuration re flecting both mainsail and jibsail aspect ratios. For this purpose, a rig aspect ratio is defined here (for H=P+BAD) as (H) AR = 2SA It is believed that this definition is compatible with the classical individual sail aspect ratio definitions while satisfying the need for a single representative value for the rig. The mean planform chord length is taken to be 1 SAF SAM SAM PF 2 P ]Jib PF P Main Test Reynolds numbers for each wind tunnel test run are cal culated using this chord length. It is reasoned that CpF represents a realistic average length for the evaluation of the flow related viscous forces as opposed to other charac teristic lengths which could be offered. This is thought to be significant when comparing such test results to other wind tunnel data, either sail or airfoil, where the Reynolds number characteristic length can easily be ascertained. Table 61 lists the planform geometry of the rigs investigated. Comparing the mean planform chords for the different configurations permits an interpretation of the similitude scaling problems discussed in Chapter Two. Indeed, if the mean planform chord provides a representa tive flow Reynolds number and if the effect of Reynolds number variation on the aerodynamic performance of a rig is strong, then results for the catboat (CPF = 4.6 in.) compared with those of a sloop (Cp = 5.3 in.) for the same wind velocity at the masthead, could be quite differ ent than at the same Reynolds number. This observation would, in effect, make the Reynolds number a significant design parameter and somewhat removes the regimelike con clusions often made for wing and airfoil theory. There is strong evidence that both of the premises offered above are valid. For Reynolds numbers less than 10 , the viscous flow effects are strong and the amount of sur face area exposed to the flow is increasingly important; that is, the force coefficients produced by a thin single cambered surface in the flow are nonlinear and vary with samll changes in Reynolds number. Figure 62, reproduced here from NASA CR1767 (10), is an illustration of this * k ,v ,i 0000 00 O O O ( e N C N (N (N (N (N (N C C C) C) C C C) CD 00 on V) u?) Ln ur t n NO NO NO O *. . o o o co m o o O L CO CO C) L LA C O r4i O in in CN C14 1N C4 Cd O 4 ) 0 < 14 < F<: " (d . .H r(d * 1 a  0i U) E r "r C mS tr) ) > I I I I 4 I 0 0) C 1O C 4 a 4 04 ,i o 0 ra Q4 F: C O O O O O O r 0 0 0 0 0 0 n cr O O O O p O 0. H H 4 4 ,I .1 rd , ' I  I' ) U) U) LA LA) P) r 0 (0 C .l ( O7 0) 0 . 4 U 0 U  44 r4 4 (N UEmmrd C4 U S N Cn) ,m U z o Ln Ln Ln LLn LAn O r ,4 ,4 , 0  H EH l H EH l H U) i4 .,I 4J I E ED 0 C) 44 Cd 4 (^ (U 0) u Q) l 4J O U) 4, mo 0 HO 1a O U 0 CO C4 O) .C0 A O  *.4 4 S0n a, .U 0 4) U) a) 4U4 a) Q) P C 0 r) Q) 4a C o 0 441 C4 Z*l a _________________________ 41 2.8 I .. ....".. .. S 20% Change in CL for 0 .8", ARe= 53.0x105 S.. Re 6 x 105  I 0 o I tx Io.e 3 1 __ x05 Re = 1.2 x106 0.4 . 0.8 24 20 16 12 8 4 0 4 8 12 16 20 Angle of Attack (degrees) FIGURE 62 Lift Coefficient vs. Angle of Attack for a Thin, Single Cambered Section as Measured by Milgram (ref. CR1767) for Three Reynolds Numbers and as Predicted by Thin Airfoil Theory. effect. For the sailor though, the point of interest is normally the rig performance at a given wind speed. Thus, increasing or decreasing the Reynolds number can play an important role as a practical performance parameter. For the results presented here, comparisons are made for the same masthead velocity on each of the rigs tested. Each will, therefore, be at a different Reynolds number as a function of CPF. Model Geometry and Trim Adjustments The geometric scale factor (1H) is taken as 12 to per mit a model size that is within acceptable limits relative to wind tunnel test section blocking requirements. This size also provides a fair representation of actual sailboats ranging from 18 to 25 ft LOA for the wind velocity profile being simulated. A scale mast height above the water sur face of 28 ft is chosen to allow a reasonable fit with the planform geometries previously defined. Figure 63 gives the overall model and standing rigging dimensions. The different planform geometries are also shown for clarity. Deck size is arbitrary and is selected to permit a reasonable arrangement of sail trim control and adjustment devices. The standing rigging acts as the structural sup port for the sail and consists of upper shrouds and a backstay. The upper shrouds are adjustable to maintain the mast perpendicular to the deck in the athwartship direction and to control the shroud tension. Backstay tension is also 04 0 I O 0 r t rP f1 o P, SIN0 0 H ' 0 0 0N Q * Zd N H 0: Nd( r a, k6 Wc3 kco 05 S C's C'S o 0 0 0 CM Nu S0) *H ghO 43 o oH 0 00) *H r l S*a 0 U > *H 00 P *H .0) ADo $ 943 Y 3o ) ry a0 <;v adjustable and can be used to bend the mast in the fore and aft plane. The mast is rigidly fastened to the deck to prevent its base from rotating about the athwartship axis. No forestay is used. Instead, the metal foresail head is attached directly to the mast by a threaded fastener and the tack is connected to a throughdeck adjust ment screw. Tensioning the luff via this screw controls the fore and aft position of the masthead and opposes the back stay. In contrast to cloth sails, an increase in luff ten sions on the metal sail does not move the sail draft forward and only the lower onethird to onehalf of the sail draft is adjustable by means of sheet trim and clew downhaul. Upper section headsail draft is rolled into the sail prior to installation on the model and can only be altered by re rolling. Headsail sheet trim is achieved by means of a threaded rod adjustment device that is fastened to the deck. When the length of the rod is reduced, it draws the sail clew aft. This decreases the trim angle and flattens the lower portion of the sail. Headsail leech downhaul is attained using a second device fastened directly to the sail clew and to the model deck. Therefore,the clew vertical position can be changed, secured and maintained throughout testing. The mainsail boom is equipped with a traveler/downhaul that permits the trim angle and sail twist to be controlled adequately. A downhaul adjustment permits the leech tension to be eased or tightened as needed. Finally, a mainsail clew may be trimmed independent of the trim angle or leech tension. Sail Construction All the sails are made of 2024T3 aluminum sheet, 0.020 in. thick, cut to the planform described above. Each sail is then rolled parallel to its luff to produce a cylin drical surface such that any camber line drawn perpendicular to the sail luff is a circular arc or constant radius of curvature. The LP, the longest such camber line, and the sail draft depth (d) as a proportion of straight line chord lenght are used to define a characteristic radius of curva ture or 2 1 LP 14(d) r = P [ARCCOS( )] (61) 2 1+4(d) For the headsail, (I2 +J2 ) is taken as the cardinal surface ruling. Then the total surface is easily defined in cylin drical coordinates by equation 61 for the intervals 2 0 < A < 2 ARCCOS[ 4(d)] 1+4 (d) and (62) S(1 r) < z,' < (I2+2 z (1 r F LP F LP O O where z' =J [ F 2+1 zo (I/J) +1 Figure 64 illustrates the coordinate system and the surface bounds. The z' coordinate system is rotated and translated relative to the previously described global coordinates. z' and z' are foot and leech bounds respec F L tively. Equations 61 and 62 in the defined intervals of A and z' describe the cylindrical headsail in terms of its rated dimensions. Similar intervals can be written for the mainsail in terms of its P, E dimensions and the d proportion. With the geometry of the sail defined as indicated, it is clear that the deepest draft point of each sail is located at 50% chord. While this is farther aft than suggested by current sailing wisdom for the headsail, it is approximately correct for the mainsail. This divergence from current sail set philosophy is considered acceptable for the comparisons made here, since it is consistently applied throughout all of the rig configurations tested and is similarly employed for the vortex lattice models discussed later. Certainly, such comparisons should establish performance trends and it seems probable that these trends should be preserved as the deepest sail draft point is moved moderately further forward. 4 2) 1/2 C FIGURE 64 Sail Surface Description. Sail Trim, Setting and Measurements The model deck is equipped with two protractor scales; one to measure the headsail trim angle (6 ) and one to mea sure the mainsail trim angle (6 ) relative to the boat cen terline. The trim angle is defined as the angle between the boat centerline and a line drawn from tack to clew along the foot of the sail in question. Each sail has camber lines drawn at selected zlocations as shown in Figure 65. Once the sail is fitted to the model, a sail "set" may be de scribed by measuring the leech position of each camber line relative to the vertical plane that contains the foot trim angle line, thus yielding the sail twist. The draft position and depth of draft are measured directly from a line drawn from the camber line luff the camber line leech. In total, these measurements provide a mapping of sail shape which characterizes a particular set. Finally, each sail is equipped with tufts along both the luff and leech on both windward and leeward sides. By direct visual observation of tuft motion, any sail set may be assessed for attached or separated flow. This visual observation is useful prior to test data collection to ensure that reasonable trim has been attained and that no large scale flow separation exists over the planform. Mainsail Twist 1 M3= 210 2 = 160 M2 >M = 70 , = 00 Headsail Tvsist 240 3 2 22.50 24.0 20.0 16.0 12.0 , = 210 8.0 4.0 0o o 12 Mainsail Chords 2.4 3.7 5.1 6.3 Model Deck Level FIGURE 65 Typical Sail Camber Lines, Draft and Twist Measurement Locations. (Dimensions shown are in inches.) CHAPTER SEVEN COMMON EXPERIMENTAL PROCEDURE Sail Trim PreTest Prior to each configuration test, the model was placed in the wind tunnel with an approximate sail set and trim. A first order approximation of trim was established at pre selected trim angles for the jib and main with draft and twist selections estimated from sailing experience and judgement. An observation test run was then conducted to assess the twist and draft set. The sails were inspected for windward or leeward separation. For this purpose, a large mirror was installed on the far wall of the wind tun nel test section; this allowed simultaneous observation of both sides of the sails. If flow separation was noted from the motion of the sail tufts, appropriate trim adjustments were made. Such adjustments were analogous to their counter parts of the full scale yacht, each adjustment having the corresponding effect. For example, if large separation was noted aloft on the leeward side of the jib, a correction was to ease the leech downhaul which induced increased sail twist. This is analogous to moving the jib sheet fairlead aft on a full scale sailboat which relaxes leech tension and increases twist on the upper portions of the sail. With the wind tunnel operating at approximately the speed of the intended test, the model was slowly rotated through a range of heading angles from approximately 100 to 450. Leading edge and trailing edge separation points were noted using the tufts as indicators as a function of B and a few strain gauge resistances were recorded at the maximum yforce point. Small adjustments were then made to the trim to maximize the lift force as indicated by a maximum resis tance reading. The model was rechecked for leading and trailing edge separation heading angles. Finally, the wind tunnel was shut down, the model removed and sail trim measure ments were recorded (reference Table 71). Wind Tunnel Test The model was reinstalled in the wind tunnel and the force balance was nulled on each of the six channels with the model set at a heading angle of B=100. The model was ro tated through 450 to indicate if any weight balancing was necessary to maintain each of the six channel null points. Variations in resistances that correspond to more than 5pin. were corrected by the addition or removal of weights from the model. The correct model center of gravity having been determined relative to the force balance, the wind tunnel was started and brought up to test speed. Raw test data were recorded manually for each channel at each heading angle and checked for repeatability in an updown reading sequence. Head ing angles were indexed in approximately 50 increments from 10 to 45 S dP dP oP dP dP dP dP dP Il (N (CN rI r i 04 0 0 0 0 0 0 0 0 I rJ. ( 0 ,q m u, tD (N lq 0 0 0 0 0 0 0 0 '0 0 0 0 0 0 0 0 0 dP dP ctP cdP d dP dP I c o o r ri r C o o 0 0 0 0 0 0 Ft& o o o0 co 0 o  Loooooo Z 1 Z rA 'i (N rrl .t o o o o o 0 o o '0 a. (N M zN (I N m DN tN 44 E E H E4 E4 E4 0  I l II l U E 'r. I 1 M (0 ( E 4 'U a During each test, the static and dynamic pressure of the flow at the calibration point (3.00 in. above the model masthead) were noted along with the airflow temperature. At the end of each test, the force balance was checked for zero return. Any zero drift error found was investigated. If the error was in excess of Spin., that set of test data was discarded. For such cases, the same configuration was rerun. Each configuration test required approximately two hours of wind tunnel run time. After each run, a calibration check was made on the force balance and the calibration equations were adjusted accordingly. CHAPTER EIGHT MODEL CONFIGURATION TEST RESULTS The FinnType Sail Test The Finn is a simple, onedesign catboat rigged, sail ing dinghy which offers an easily modeled sail planform (reference Table 61). Marchaj (8) has used a oneseventh scale (1 H=7) fabric scale model of the Finn sail to experi mentally investigate the effects of boom vang tension and resulting sail sha: on the total sail lift and drag coef ficients. His test results were achieved under uniform onset flow conditions and they are reported at scale Reynolds numbers that are in the range reasonable for similitude. In the present work, a geometric scale factor of 1 =9 yields a Finn model of appropriate size to fit the wind tun nel test section without severe blocking. This model was constructed absent of a hull and deck to permit an accurate determination of the sail force center both with and without a simulated nonuniform onset velocity. The nonuniform velocity profile that was used in these tests is described in Chapter Five and,; thus, is slightly distorted relative to the portion of the true PBL that the fullsize prototype Finn sail would actually "see". This distortion, however, is believed to be unimportant for the comparisons presented. The sail planform is given in Table 61, Configuration Code TOOCB1. The sail model was rolled to a cylindrical shape parallel to the luff and fastened to a cylindrical shape parallel to the luff and fastened to a mast/boom assembly. The mast/boom assembly was stiffened using a small spreader and shroud combination. This stiffening was necessary since the mast section modulus must be small in order to conform to the prototype mast. Its contribu tion to the resultant drag has been verified by measuring the drag of bare poles (mast and boom alone). This test indicated that the mast drag contribution was negligible. Camber lines at 4 in. intervals starting at the boom were used to define draft and twist. Since this model had no hull or deck, the adjustments of the sloop model tests were not available and the sail set capability was correspond ingly limited. Angles of attack measured between the boom and the wind tunnel center line were used in place of head ing angles. Partial sail twist control was realized by using a boom topping lift and vang but at a slight drag increase. At large angles of attack, the stress on the sail was observed to be sufficient to slightly alter the initial sail twist. Naturally, the effect increased with increasing flow velocity. The same effects would occur on the prototype Finn but vang, sheet and mast bend have not been modeled propor tionately for the wind tunnel test. Therefore, at large flow velocities (Reynolds numbers) there would be some de parture from geometric similitude. Direct flow observations on the windward side of the sail were of particular interest both with and without the PBL velocity profile. Figure 81 illustrates a side view of the model and the positions long yarn tufts assumed when placed in a 40 ft/s flow with the sail model at an angle of attack of 250. Using the camber lines for approxi mate measurement, a yarn tuft was estimated to be near the windward side of the sail pressure center if it was not deflected up or down relative to the horizontal plane. This observations was made with the nonuniform logarithmic ve locity profile in the tunnel and tuft #2, approximately 0.36 H above the floor, was estimated to be at the windward side center of pressure. Similar observations of the leeward side of the sail were not as informative because of large random yarn motion. As expected, two strong votices were seen; one near the masthead and one near the boom. A top view of the leeward side, Figure 82, reveals the strong upwash which was ob served upstream of the leading edge and smooth flow to about the 3/4 chord point where turbulence and the shed trailing edge vortex displaced the yarn. Near the 0.36 H height noted, an upwash angle of approximately 100 at the sail leading edge was measured relative to the wind tunnel centerline. This angle appeared to vary along the leading edge as a function of vertical position. z(in.) 30 Tuft #6 #15 20 #4 #3 #2 o.  10 #1 \ SWind Tunnel Floor FIGURE 81 Finn Sail Yarn Observations. Observed yarn motion for the Finn sail at an attack angle of 25, V=40 ft/s, without the simulated PBL. Wind Tunnel Center iLine 10 (Approx.) Edge FIGURE 82 Finn Sail Upwash Observation. Position assumed by a long yarn on the leeward side of the sail as viewed from above. Flow While the above observations come as no surprise, they do provide insight and evidence in support of concepts suggested later in this work. For instance, the strong upwash noted is in agreement with the arguments offered in Appendix A for quantifying the magnitude of relative wind twist that results solely from the sail circulation and is almost independent of boat speed. The results of the force balance data collected for the Finn sail, both with and without the simulated PBL onset velocity profile, are given in Figure 83 as lift (Cx) and drag (C ) coefficients along with the lift to drag ratio (C /Cx) plotted against the attack angle. Selected data points from Marchaj's work are superposed for comparison and are seen to be in fair agreement considering the large differences in models used (metal to fabric) and the unre ported uncertainty of the earlier work. The second stall or "bump" seen in both C plots at approximately 30 attack angle for uniform and logarithmic onset velocities is thought to be a result of sail trim changes caused by the pressure distributions in these high loading conditions. Both tests were conducted for a velocity of 80 ft/s at the model mast head and a Reynolds number of 3 x 10 The simulated PBL had the effect of decreasing the lift and drag values over those measured for uniform flow at the same attack angle. As a point of interest, the negative vertical force coefficient is also plotted in Figure 84 for the case with LEGEND SWith PBL Without PBL    Marchaj's Data  o0 Cx 0 Cy V Cy/Cx / +#x 4 / A/ I,^ ; n 0 r8' I I I I i I i1 10 20 30 40 50 HEADING ANGLE(Degrees) FIGURE 83 Effect of the Planetary Boundary Layer on Sail Test Data. Finn sail for Re= 1.8 x 105 vs. Marchaj's data for Re= 2.2 x 105. I SAIL SHAPE AND TRIM 6J = N/A Pj = N/A dj = N/A 6M= 00 M1= 320 aM= 11% 3.5 3.0 2.5 1.5 1.0 0.5 ``Hn the simulated PBL. Because of mast and sail deflection under load, a small projection of sail area can be ob tained in the xyplane. The centroid of this projected area is not necessarily the same as the planform centroid. The negative vertical force.related to this coefficient (C ) can be thought of as the net reaction of the span z wise flow momentum on this projected area. This inter pretation is supported by the yarn observations made earlier and would also be true for the prototype Finn. The x and y moment coefficients are shown in Figure 84. While the overall trends of the coefficients are preserved, the net effect of the nonuniform onset velocity is seen to reduce the values of C and C. mx my In an attempt to resolve the sail force center, it is conservative to assume that each of the forces represented by the coefficients Cx, C and Cz are concentrated at dif ferent x, y, z locations or Fx = x(xl y1, z) F = Fy(X2' 2' z2) and Fz = Fz(x3' y3' Z3) LEGEND With PBL Without PBL  0 Cmx O C my C z Y SAIL SHAPE AND TRIM 6J = N/A 6M = (j = N/A M= 32 dj = N/A dM= 11/o k6'  * I' I I ~ ' / '1 I I 10 20 30 40 50 HEADING ANGLE(Degrees) FIGURE 84 Finn Moment Coefficients With and Without the Planetary Boundary Layer. 3.5 3.0 2.5 1.5 1.0 0.5 If the vertical force is taken as the vertical component of the total lift vector, where the total lift vector is normal to the sail surface at its center of pressure, one obtains x2 = x3 and y2 = y3 0 (81) The resultant moments of the three forces in coefficient form can be written as Cmz = (CyX2 + CxY1)/CPF Cmx = (Cy2 + Czy3)/CPF (82) Cy =(Cxz + Cx)/CPF Applying the conditions of equation 81 to equation 82 gives C C S=mx PF 83) 2 C y From the plots in Figure 83 it is noted that C > C y x It is logical to assume yl < x2, therefore, the zmoment coefficient can be approximated as Cmz Cy X2/CPF Solving for x2 yields C C mz PF x2 C (84) y Using equations 81, 82 and 84 the vertical height to the xforce location can be approximated as C mz CmC ( ) my z C ( z, =  (85) x It is clear that the uncertainty of z2 is less than that of z1 which, in turn, is greater than the uncertainty of any one of the contributing coefficients. The uncertainty of z2 is calculated as 7.87% while z1 is estimated at 11.09%. Using these uncertainties to generate weighting factors W1 and W2, a sensible vertical distance to the force center is defined as 2 2 z(nominal) = 1 + (W22(86) 1 2 Where W1 = 9.02 and W2 = 12.71 based on the above uncer tainties. Since the plane of the projected sail planform rotates relative to the x,y,zcoordinated system, the hori zontal distance from the mast to the force center is a function of x,y and the attack angle. Figure 85 shows the force center locations as calculated by equations 84 and corrected for the attack angle. 1.13 ll 0.93  0.73 0 4 1 0 hH (d 0.13 Wind Tunnel Floor Ratio of Foot to Boom Length S/ 7 ///////////////// /////////////////////////777 FIGURE 85 Finn Sail Center of Effort Location. Center of effort locations at various attack angles with and without the simulated PBL. Note: Because the PBL is distorted slightly for the model used the effect on the c.e. translation as shown is less than it would be for a correctly scaled PBL. For: P = 24.8 and E = 15.3 Center of Effort: (z/P) = 0.46 Without PBL (z/P) = 0.52 With PBL 1.0 0.8 r) 0 4P 0 o.6 0 *d 0.2 PBL The concentration of points around the planform cen troid for the uniform velocity is logical and suggests an analytical check using a direct integration scheme. Such a scheme is presented in Appendix D for both with and without the modeled PBL. Without the planetary boundary layer model the calculated center of effort is shown to be 0.39 H, which is identical to the planform area centroid and agrees with the location indicated in Figure 85 for attack angles of 250 to 35. With the nonuniform onset velocity the method requires an approximate model for the lift coefficient variation as a function of span position. Approximating polynomials are selected for this purpose to allow a convenient form for integration by parts. For the selected precision the results are nearly invarient with the assumed lift coefficient models and the net center of effort is shown to be0.48 H. This value is also in close agreement with the measured value as indicated by Figure 85. Finally, the Finn model was used in an effort to assess the effect of Reynold's number on C values at or near stall. At an angle of attack of 300, three tests were conducted cor responding to Reynolds numbers of 2.3 x 10 2.9 x 10 and 5 3.3 x 10 The C values obtained show no variation beyond that of the expected uncertainty, see Table 31. The same results were found for C and C values. Therefore within x mx the range of Reynold's numbers investigated, this parameter's effect is negligible. Variable Jibsail Hoist Series Employing the full yacht model described in Chapter Six, a variable headsail hoist series of tests was conducted. The results of this series were intended to be compared with theoretically derived lift and drag coefficients. For this purpose, the yacht model was fitted with a mainsail (P = 22.50 in. and E = 9.00 in.), common to all tests. A series of jibsails, all of the same aspect ratio but with various hoists, was fitted to the model and tested as described in Chapter Seven. Tests start with the masthead sloop as an arbitrary upper limit on headsail size with the catboat, no headsail, as a lower limit. Table 61 lists the planform geometries for the configurations tested. The configuration code of interest are T15MH1  Full hoist masthead sloop T15781  7/8 hoist headsail sloop T15341  3/4 hoist headsail sloop T15121  1/2 hoist headsail sloop TOSCB1  catboat (no headsail) A general "bareboat" test was made to determine the lift, drag and vertical force of the hull and standing rigging. This force data has been reduced to coefficient form using the area of each respective configuration and they have been subtracted from the total configuration coefficients to give an estimate of the force and moment contribution made by the sails alone. Since drag associated with boundary layer interactions between the sails and rigging are present in the full configuration tests, such estimates for the sails alone are considered to be conservative. Figure 86 through 815 give the results of these tests. In each case, both the "complete rig" and the "sails alone" data are displayed. As such, it is evident that the hull and rigging not only contribute to drag but to lift as well. Therefore, conclusions directed towards overall on thewater boat performance could be misleading, if only the aerodynamics of the sail were considered. [The same obser vation was made earlier by Marchaj (8).] On a macro scale the maximum value of the lift coefficient appears to in crease monotonically as the jib hoist is decreased. This is seen to be true for both the complete rig and the sails alone. However, the drag is also seen to increase porpor tionately, somewhat offsetting the useful component of lift. This will be discussed in greater detail in Chapter Nine. High Aspect Ratio Series A 150% masthead sloop configuration is chosen to assess the effects that different rig aspect ratios have on the resultant sail forces and moments. Configuration Reference codes T15MJ2 and T15MJ3, given in Table 61, were tested for comparison with the standard sloop T15MH1. The results of these tests are given in Figures 816 through 819 and are discussed in the next chapter. LEGEND Sails Alone  Complete Rig Cx O Cy V Cy/Cx A CFWD SAIL SHAPE AND TRIM 6M= 0 TM= 300 dM= 120/ I  8 ...A~1 _ i i FIGURE 86 I I a I a 10 20 30 40 50 HEADING ANGLE(Degrees) Masthead Sloop Test Results. R = 280,000., FBA/SA = 0.23 (T15IH1) e 3.5 3.0 2.5 [ U2. L. 0 u 1.5 1.0 0.5 I I I I 2.0 Cy vs.C OC vs.C OCFWDVS' CHL 5 U * 1.0  0.5 0.5 1.0 5 2.0 Cx or CHL FIGURE 87 Masthead Sloop Polars. Re= 280,000., FBA/SA = 0.23 (T15MH1) LEGEND Sails Alone Complete Rig D Cx 0 Cy V Cy/Cx A CFWD SAIL SHAPE AND TRIM 6J =12 6M. 0 jJ =18 M= 31 dM= 12~/ 6A SI I , FIGURE 88 I I I I I I 10 20 30 40 HEADING ANGLE(Degrees) 7/8 Sloop Test Results. Re= 240,000., FBA/SA = 0.27 (T15781) 3.5 3.0 2.5 1.5 1.0 0.5 1 2.0 C vs.C y x OC vs.C OCFWDV. CE 1.5 1.0 0.51r 0.5 El I I '^J51 14 0.5 1.0 1. 2.0 Cx or CHL FIGURE 89 7/8 Sloop Polars. Re= 240,000. , FBA/SA = 0.27 (T15781) LEGEND Sails Alone Complete Rig Cx 0 Cy V Cy/Cx A CFWD SAIL SHAPE AND TRIM 6J =12 6M= 0 =J =20 #M =35 j =1 1% dM= 11%  a I I I Li I _ 10 20 30 40 HEADING ANGLE(Degrees) FIGURE 810 3/4 Sloop Test Results. Re= 210,000. FBA/SA = 0.32 (T15341) 3.5 3.0 2.5 1.5 1.0 0.5 I I I I I ~h' I I I I I 2.0 OC vs .Cx ." OC vs.C OFWDS CH: 1.5 1 o"U .1 1.0 0.5  Cx or CHL x HL FIGURE 811 3/4 Sloop Polars. Re= 210,000. , FBA/SA = 0.32 (T15341) LEGEND Sails Alone  Complete Rig  x C D Cx O Cy V Cy/Cx A CFWD SAIL SHAPE AND TRIM 6j .12 ij =18 'a =11% 6M= 0 Mi= 350 dM= 1 2% LI f i I  10 20 30 40 HEADING ANGLE(Degrees) FIGURE 812 1/2 Sloop Test Results. Re= 90,000. , FBA/SA = 0.43 (T15121) 3.5 3.0 2.5 1.5 1.0 0.5 ! I I I LEGEND Sails Alone Complete Rig 2.0 OC yVs.Cx *I 0 CFWDVS. CHL .1.5 / U .! 1.0 I 0.5 0.5 1.0 1.5 2.0 C or C, x HL FIGURE 813 1/2 Sloop Polars. Re= 90,000. , FBA/SA = 0.43 (T15121) LEGEND Sails Alone Complete Rig  D Cx O Cx 0 Cy v VC A CFWD SAIL SHAPE AND TRIM 6J = N/A 0 6M = 0 aM 360 dM= 13/o S A I, I I i I 20 HEADING 30 ANGLE(Degrees) FIGURE 814 Catboat (with hull) Test Results. R = 90,000. FBA/SA = 0.60 (TOSCB1) 3.5 3.0 2.5 1.5 1.0 0.5 i I iI i I Iieel 2.0 C vs.C / OCFWD VSCHL 1.5  S4 / 0 / 1.0 I 0.5 I I I I I 0.5 1.0 1.5 2.0 C or CHL x HL FIGURE 815 Catboat Polars (with hull). Re= 90,000. FBA/SA = 0.60 (TOSCBI) 3.5 3.0 i / V \ 2.5 \ o \ TT t/ \ "2.0 0 I A I / rQ 1.5 / k/ 1.0 7 0.5 10 20 30 40 50 HEADING ANGLE(Degrees) FIGURE 816 Masthead Sloop, High Aspect Ratio Main and Jib. R = 260,000. FBA/SA = 0.32 (T15MJ2) 2.0 C vs.C y x O CFWVS. CHL O J1.0 4 I I ! 0.5  0.5 1.0 1.5 2.0 C or CHL FIGURE 817 Masthead Sloop, High Aspect Ratio Main and Jib, Polars. Re= 260,000. FBA/SA = 0.32 (T15MJ2) LEGEND Sails Alone  Complete Rig D Cx  O C O Cy V Cy/Cx A CFWD SAIL SHAPE AND TRIM 6J = 120 6= 0 j 14 M = 24 dj =10% dM= 11% 1A A A L 1 I I 10 FIGURE 818 20 HEADING Masthead Standard (T1 5MJ3) I I I I I S 30 40 50 ANGLE(Degrees) Sloop, High Aspect Ratio Jib and Main. Re= 270,000. FBA/SA = 0.28 3.5 3.0 2.5 1.5 1.0 0.5 1 I I I I h I I I I I 2.0 DC Cvs.Cx y x 0 CL FWD VS'CHL >1.5 0 ^ I 1.0I El 0.5  0.5 1.0 1.5 2.0 C or CHL x HL FIGURE 819 Masthead Sloop, High Aspect Ratio Jib, Polars. Re= 270,000. FBA/SA = 0.28 (T15MJ3) CHAPTER NINE EXPERIMENTAL AND THEORETICAL COMPARISONS The Influence of the Simulated Planetary Boundary Layer Wind tunnel tests of yacht models made with and with out a simulated PBL indicate that the influence of the PBL is significant, accounting for reductions on the order of 28% in the lift and drag coefficients relative to those without the PBL for the same trim and attack angles. In addition, the effective force center with the PBL is 30% farther above the deck than with no PBL model while yield ing approximately the same moment coefficients about the water plane. This is important in that test work which does not model the PBL properly will tend to over predict yacht potential performance relative to lift and drag for the same vessel heel limitations. The assessment of the PBL onset profile by direct integration suggests that tests conducted with a uniform onset velocity model can be analytically corrected for any given onset velocity profile providing a functional formulation of that profile is possible and that some knowledge of the lift coefficient variation with height is available. Such a correction scheme could allow the test results of one model configura tion to be applied to any size prototype independent of similitude requirements for the PBL with all such require ments evaluated by analysis. The direct impedance method offered for onset velocity profile synthesis is effective and practical, giving reason able control over the velocity distribution and the turbulence in the wind tunnel test section. As pointed out earlier, the scale of turbulence for the test must be large relative to the turbulence scale of the sail model viscous shear layer. The evaluation provided here indicates that a rea sonable PBL model should have approximately two orders of magnitude difference between these turbulence scales. For the prototype yacht, it can then be concluded that the scale of turbulence in the overthewater PBL is insignificant and can be ignored relative to the sail aerodynamic performance. A review of previous two and threedimensional sail test data (8, 9, 10, 11, 13, 29) for lift and drag reveals a sensitivity to Reynolds number. This indicates a further complexity in a complete treatise on sail aerodynamics. Re call that in subsonic airfoil theory where the Reynolds numbers are large the viscous properties of flow may be neglected in the determination of lift and have only limited impact on drag. In contrast, experimental evidence for sails suggests that both lift and drag are strongly affected by their much lower Reynolds numbers at all angles of attack. It is speculated here that this Reynolds number sensitivity is closely related to boundary layer stability. Specifically, the sharp edges of the single camber sail are simultaneously subject to an adverse pressure gradient and a fairly large free stream turbulence intensity; both of these effects could cause boundary layer instability. More research dealing with flow separation on sails at Reynolds numbers of 5 x 105 and less is needed. Comparison of Potential Flow Models and Wind Tunnel Results A potential flow analysis of the sail rig configurations described in Chapter Six has been made employing Register's SAIL3 computer program. SAIL3 produces numerical solutions to the classical potential flow problem of the Neumann ex terior type by means of a discrete vortex lattice distribution. Register has shown SAIL3 to be convergent to the exact solu tion of the governing equations in terms of detailed wake geometries as well as force coefficients with upper bound uncertainties for lift coefficients of 6% and 17% for drag coefficients for the specific sail discretization reported. This same discretization is used here. Therefore, the same uncertainty estimates are applicable. Rig configuration T15MH1 has been evaluated using SAIL3. The results are given in Figure 91. Upon comparing these calculated results with the wind tunnel test results for the "sails alone" (see Figure 86) remarkable agreement is observed in lift up to the region of sail stall (8=350). In this same region, the drag coefficient values are seen to be under predicted. This is to be expected with an inviscid solution. 3.5 3.0 2.5 Y SAIL SHAPE AND TRIM 6j =12 ~j =16 6M= 0 Mi= 30 LEGEND Sails Alone (Theory) Complete Rig (Test) O Cx OCY V C /Cx A CFWD A / / / V / /,' I I I II /4 (Test) EI__~EJ I I A I I I I I I 10 20 30 40 50 HEADING ANGLE(Degrees) FIGURE 91 Masthead Sloop Theoretical Cx, C CFWD, and C Cx vs. Test Results. (ref. T1511I1) Uj =121% dM= 12% z "2. u 0 u., 1.5 1.0 0.5 