SAILING VESSEL DYNAMICS: INVESTIGATIONS INTO AERO-HYDRODYNAMIC COUPLING by GRAHAM TABER SKINNER AB. Brown University (1975) B.M.E., The Catholic University of America (1980) Submitted in partial fulfillment of the requirements for the degrees of Master of Science in Naval Architecture and Marine Engineering and in Mechanical Engineering at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 1982 f, Graham T. Skinner The author hereby grats to .I.T, permission to reproduce and to distribute copies of nii'doqumenV/X whole or in part. Signature of Author DOpartment of O0ean Engineering Certified By J-tip E. Kerwp, Thesis Supervisor ,wIn R enovl--T hesis Reader Accepted By A. Dougtas Carmichael, Chairman Departmental Committee on Graduate Students, Department of Ocean Engineering -la- SAILING VESSEL DYNAMICS: INVESTIGATIONS INTO AERO-HYDRODYNAMIC COUPLING by GRAHAM TABER SKINNER Submitted to the Department of Ocean Engineering and Mechanical Engi- neering, June 1982 in partial fulfillment of the requirements for the degrees of Master of Science in Naval Architecture and Marine Engineering, and Master of Science in Mechanical Engineering. ABSTRACT An investigation was undertaken of the extent to which the motions and added resistance of a vessel sailing in waves could be attenuated by the aerodynamic damping of sails. The analysis used quasi-steady inviscid lifting line and lifting surface approaches to the aerodynamic problems. The primary focus was the attenuation of added resistance by aerodynamic pitch damping, which was 14% for an example. The value depended strongly on the viscous drag. In addition, it was shown that pitching can increase the driving force slightly and that rolling is overdamped by aerodynamics. Thesis Supervisor: Justin E. Kerwin Title: Professor of Naval Architecture -2- ACKNOWLEDGMENTS The author wishes to thank Professor M. Triantafyllou for his helpful hints and Professor J.E. Kerwin and Professor J. Milgram for providing the direction which was needed to conclude this investigation. Thanks also to Professor Hedrick for his advice and encouragement. I am grateful for the excellent typing service provided by Jessa Frankel, Joanne Sullivan and Marilyn Staruch. -3- 'CONTENTS ....... Page Title . . . . . . . . . . . . . . . . . . . . . . 1 . -9 la Abstract . . . . . . . . . . . . . . . . . . . . . . * Acknowledgements . . . . . . . . . 2 0 * Contents . . . . . . . . . . . . . . . . . . . . 3 0 * Nomenclature . . . . . . . . . . . . . . . . . . 5 . 0 I Introduction . . . . . . . . . 7 0 4. 8 I'I Formulation of the Problem . . . . . . . . . . * 0 II'I The Effect of Vessel Motions on the Apparent Wind 11 .......* * IIV Derivation of the Linear.iz.ed. A.er.od.ynamic. P.it.ch.12 Damping Coefficient . . . . . . . V Approximate Calculation of the Aerodynamic Pitch Damping Coefficient Using Lifting Line Theory . . .. . . . 15 fI Numerical Modeling of Sail . . . . . 17 VIII Seakeeping . . . . . . a·· 24 VI]I Reduced Frequencies . . . . . . . . . . . . . · · · 28 IX The Effect of Aerodynamic Pitch Damping on Added Resistance Due to Pitching . . . . . . . . . 30 X The Effect of Pitching on the Average Drive Force . . 32 .. 33 XI Other Motions: Roll ... . . . · · · 0 e* · 0 XII Other Motions: Surge, Sway, Heave, Yaw 39 0 0 * 0 XIII Other Motions: Pitch Coupling . . . 40 · · · * 0 0 0 XIV Conclusions . . . . . . .. 41 * * 0 0 . * * 8 References . . . . . . .. . . . . . 43 ·o· ·· · · ·· Appendices: · · · · 1. Rough Calculation of Aero Pitch Damping 56 2. Explanation of Program Cyclone 58 · · 3. Transformation of PSF2 Output 63 o· · 4. PSF2 Output . . . . . . 65 · · · · 5. MIT 5-D Output . . . . . . . . 86 -4- LIST OF FIGURES Page 1. Vessel-ixedC oordinatSes tems .. ... . 45 2. Wind Triangle . ...... . . . .. . 46 3. Sailplan for Lifting Line Analysis .... 47 4. Geometry for Lifting Surface Analysis . . . 48 -5- NOMENCLATURE a Wave amplitude Aj Added mass coefficients A Aspect ratio s2/S c Chord CD = D/ - SVA Drag coefficient Cji Hydrostatic restoring force coefficients CL = L/- p SV~ Lift coefficient d Vertical distance between hub surface and center of lateral resistance D Drag Force Fji Exciting force (or moment) in jth direction due to motion in in ith direction, i, j = 1,2..6 F Froude number v/vji n FR Driving force Gj. Element of the generalized mass matrix GM Metacentric height GRAD Vertical true wind gradient, sec 1 k Reduced frequency L Lift force n Propeller rpm L,M,N Aerodynamic moments corresponding to i = 4,5,6 p,q,r Aerodynamic notation equivalent to x4, x5, x6 RHUB Radius of Propeller HUB s Span S Sail planform area t Time -6- T Period of oscillation VA Apparent wind velocity VB Steady (average) vessel velocity XCAM Ratio of Maximum camber of section to chord ~X Displacement in jth direction (surge, sway, heave, roll, pitch, yaw) ; YVessel velocity in ith direction a Apparent wind angle to vessel centerline A Displacement (lbs.) AF Added resistance 1 Y True wind angle to vessel centerline X Leeway angle between course and vessel centerline P Density of fluid e Pitch angle Frequency of oscillation X Angle of incidence of waves (for head seas - 108°) Damping ration between actual damping coefficient and damping coefficient required to just damp out oscillations Superscripts & Subscripts -A Aerodynamic -H Hydrodynamic -n Natural (frequency or period) -p Derivative with respect to p -q Derivative with respect to q -7- I. INTRODUCTION Analysis of sailing vessel performance in a seaway is complicated by the coupling of hydrodynamic and aerodynamic forces and motions. Performance of a vessel sailing in calm water has been analyzed by Kerwin3. Behavior of a yacht hull moving through waves has been analyzed by Gerritsma and Moeyes4. A program has been written to combine these analyses for performance prediction for a vessel sailing in a seaway5, but neglects the contribution of the rig to the equations of motion. For downwind sailing results have been reported for studies of hull-sail interaction, such as the coupling between wave induced roll and wind induced sway moment, which can lead to the instability known as broaching6 '7 For upwind sailing the possibility exists that aerodynamics provides substantial damping of wave excited motions. If so, then added resistance due to wave radiation should be less than that predicted by models which neglect this coupling. No investigations of this phenomenum are known to have been reported. Such an investigation was the primary purpose of this work. A corollary result of this work was the development of a program to facilitate the analysis of a single sail using numerical lifting surface techniques. Use of such techniques for sail design has been reported1, and such techniques have been used for wing and propeller blade analysis8 However, no previous use of this technique for sail analysis is known. -8- II. FORMULATION OF THE PROBLEM Observation of the motions of vessels sailing in waves shows that pitch is the most severe motion and probably contributes most to added resistance due to wave radiation. These observations are supported by the results of the seakeeping analysis of a sailing vessel hull moving through waves, (see later chapter). Since pitch motions seem to make the largest contribution to added resistance, the initial and primary focus of this investigation was in:terms or the aerodynamic contribution to pitch damping. It is easiest to model this flow using quasi-steady inviscid theory9 First, however the relative importance of viscous and unsteady effects must be evaluated. The most significant effect of viscosity is separation of the boundary layer from the sail surface. When this condition is severe the sail has -"stalled", and the effective mean camberline of the sail is so different from the actual sail shape that inviscid flow modelling based on the actual shape is invalid. Experiments have shown that stall occurs when the lift coefficient exceeds a value of about 1.9.2 For a sail of fixed shape the lift coeffi- cient varies with angle of attack. Then as long as the pitch induced change in angle of attack is small, separation is insignificant. Unsteady effects include periodic changes in sail shape. Because the sail is a flexible membrane, its shape is pressure distribution dependent. -9- When the angle of attack is "ideal" the fluid velocity at the leading edge is directed along the mean camberline at the leading edge. Below ideal angle of attack the pressure drop across the fabric at the leading edge will tend to deform (or "luff") the sail. For small pitch induced changes in angle of attack not much less than ideal, the change in sail shape due to luffing can be neglected. Unsteady effects also include periodic changes in the inviscid flow alone. Outside the boundary layer the flow is essentially inviscid. Here the vorticity must be constant so that vorticity must be shed into the flow as the lift coefficient varies. As this vorticity is convected downstream it changes the effective angle of attack. If the rate of convection is large with respect to the pitch rate, then this effect can be neglected. A measure of the importance of this unsteady effect is the reduced frequency, k TV A For small k unsteadiness of the flow can be neglected. The magnitude of all the effects considered above is proportional to the magnitude of the change of angle of attack due to pitch. This change is small in high winds. Since high winds generate the large amplitude waves which excite large pitch motions, the simplification of the problem to a quasi-steady inviscid analysis should be valid. Further assumptions, which will be repeated later as they are applied, are