Approximation method for the loss of speed during tacking maneuver of a sailing yacht

Transcription

1 Date March 25/26, 2004 wriitenby E.J. de Ridder, J.A. Keuning and K.J. Vermeulen Address Delft University of Tecfinology i y Sliip Hydromeclianics Laboratory I I 1"^/^^ If ^ Mekelweg 2, 2628 CD Delft L^O IT L The Nerlands Delft University of Technology Approximation method for loss of speed during tacking maneuver of a sailing yacht By E.J. de Ridder, J.A. Keuning & K.J. Vermeulen Report 1383-P

2 Approximation metiiod for loss of speed during tacking maneuver of a sailing yacht. E J de Ridder\ J A Keuning^ K J Vermeulen^ Abstract In present report first results of a study on speed loss of a sailing yacht during a tacking maneuver are presented. The study alms at development of a generally applicable generic mamatical model for determination of speed loss of an arbitrary sailing yacht during a tack. The results of such a simulation model for various yachts may be implemented In a VPP to make an assessment of differences in speed loss of various designs into account for handicapping purposes. The simulation model should n be made generally applicable to an arbitrary yacht without extensive and complicated calculations. In an earlier study Keuning and Vermeulen, Reference [1], presented an approximation method for yaw force and sway moment of an appended sailing yacht hull under steady forward motion and under influence of leeway and heel. In present study se formulations are slightly modified to improve correlation with types of yacht under consideration and implemented in mamatical model for maneuvering of sailing yachts as presented by Y Masayuma, Reference [2]. Also resistance curve as developed within DSYHS is taken into mamatical model. The goal of all this is to develop a relatively easy to use and generally applicable maneuvering model of which necessary "hydrodynamic coefficients" in model may be obtained from calculations derived from results obtained with models of Delft Systematic Yacht Hull Series (DSYHS). The velocity terms are ^introduced now acceleration terms follow later. Validation of results is presently executed with measurements from Masayuma but will be extended to foreseen full scale ' MSc student Delft Shiphydromechanics Department ^ Associate Professor Delft Shiphydromechanics Department ^ Researcher Delft Shiphydromechanics Department measurements within this project in near future. Introduction A manoeuvring model of a sailing yacht has been subject of research by various authors during some time now for a variety of reasons. Some authors were focussing on finding optimal tacking procedure (or rudder control) for minimal speed loss during a tack. More often n not this was carried out only for a very specific (type of) yacht such as for instance America Cuppers. Ors researchers were more aiming at obtaining insight in general manoeuvrability characteristics of sailing yachts when under sail. This became of particular interest with ever-increasing size of some yachts and demand for both good balance between hydrodynamic and aerodynamic moments on yacht when sailing on a straight course as well as for save operability of se yachts in confined and/or congested waters, when sudden collision avoiding manoeuvres may be called for. The present study tries to look In more detail Into speed loss of a sailing yacht during a tacking manoeuvre. For handicapping procedures it has been considered for some time now that just judging differences in upwind performance by only comparing optimal VMG of yachts on such a course obtained from a Velocity Prediction Program (VPP) might not be sufficient to yield a proper assessment of ir mutual capabilities, because loss of VMG during a tack may also be strongly dependent on particular design under consideration and refore different. In order to be able to calculate possible differences in this respect between a large(r) variety of yachts development of a simulation model is necessary which yields a reliable prediction of behaviour of a sailing yacht during a tack and also allows an approximation of necessary various hydrodynamic coefficients in that particular

3 mamatical model to be based on general hull parameters only. To develop this it was decided to make use of availability of data base obtained from extensive tests and analyses of Delft Systematic Yacht Hull Series (DSYHS) and to try to generate generally applicable approximations for se coefficients from this well established series. The first part of present study consisted of development or selection from existing literature of an appropriate mamatical model. It is evident that tacking of a sailing yacht is a complicated manoeuvre. Many factors influence manoeuvre such as general manoeuvrability of yacht but also stability and roll characteristics of yacht and sail geometry and performance. After a literature survey and analyses it was considered that model as previously presented by Y Masayuma in 1995, Reference [2] yielded a good starting point. He showed in his study that with a fair approximation of various coefficients a good correlation between actual manoeuvre at full scale and simulation could be obtained, suggesting that all relevant and significant parameters were taken into account in his model. Some results of DSYHS are presented in 1998 and 1999 by Keuning and Sonnenberg, Reference [3], could be used straight away in mamatical model, such as determination of upright and heeled resistance of an arbitrary yacht hull shape. Anor results came from report published earlier on yaw balance of large sailing yachts. In this study presented in 2002 Keuning and Vermeulen, Reference [1], presented a method for assessing balance (in yaw) of a sailing yacht in steady fonward motion yielding generally applicable expressions for side force production and associated yaw moment of an arbitrary hull with appendages. The expressions formulated were suitable for both upright and heeled condition. For present study expressions for side force and yaw moment of bare hull under a heeling angle have been furr elaborated and also validated against some dedicated model tests in Delft Shiphydromechanics Laboratory with models of DSYHS, which results were not available at time of printing of original report in These measurements showed that formulations were in good agreement with measurements. Only formulations, which y presented for side force production of appendages, needed a small adjustment to make m more applicable to high aspect ratio appendages such as se are generally found on racing yachts. In ir original study authors were more focussed on very large sailing yachts, which tend to have draft restrictions imposed on m and refore have in general lower aspect ratio appendages. Using formulations as presented now a considerable part of coefficients in present mamatical model could be calculated for arbitrary designs. The formulations for acceleration terms in equations at present still have to be evaluated. A large number of dedicated forced oscillation tests in yaw and sway with a number of models of DSYHS are presently carried out both upright and heeled. For se tests a hydraulically actuated forced oscillator In six degrees of freedom of Delft Shiphydromechanics Department is being used. The IVIamatical Model used For formulation of an appropriate mamatical model use is being made of model as presented by Y Masayuma, Reference [2]. On his turn he made use of model and system of axes as presented by Hamamoto et. al.. Reference [4]. In this ordinate system Origin Is located In still water plane at centerline in midship section and X-axis lies along centerline of ship positive direction forwards. The Y axis positive direction Is to starboard and Z axis points downwards. Ignoring pitch and heave motion of yacht model contains equations for four degrees of freedom, i.e. surge, sway, yaw and roll. Addition of latter degree of freedom was considered necessary due to large distance between centers of effort of aerodynamic and hydrodynamic forces and so generating coupling effects between roll, sway and yaw but also in surge (heeled resistance and reduced sail forces). The equations of motion n become:

4 Kali Masayuma modified his equations after omitting higher order terms as being insignificant for present approach. These have been furr simplified for present study by placing origin of coordinate system and centrold of added mass in Center of Gravity of yacht and so omitting all terms with Xg in original equations. In a later phase a nonsymmetrical added mass distribution and effect on yaw moment may again be taken into account. This yields following simplified equations: Surge : {m + )ii -{m + my cos^ (p + m^ sin^ (j))vy/ Figure 1: Coordinate system equations Y, = Y,v + Y^^ + Y^y + Y /(P + Y^^^vf + Y^,/ N = N^v + N^<p + N^v' +N^y<p + N,^^vf +N^j' Determination of hydrodynamic coefficients = X ^ + XMI + X^^W + ^rudder + ^.,7 Sway: (m + niy cos^ (p + m^ sin^ (j))v +(m+m^ )u\j/+2(m^ - ) sin cos ^ v{i Roll: -{(1^ +Jyy)- (4 Yaw: + J.. )}sin <ö COS (!> In which: u and V are velocities along X and Y axis respectively ( ) and \)/ are Eulerian angles for roll and yaw as defined in Figure 1. 5 is rudder angle and Xh, Yh, Kh and Nh stand for respective hydrodynamic forces and moments on hull due to leeway and heel according to : Masayuma used this set of equations to calculate tacking behavior of one particular sailing yacht. In his report he showed that using his model toger with a set of experimentally obtained hydrodynamic coefficients a good correlation with a full-scale experiment with same yacht could be obtained. This led to adoption of same set of equations for present study. However to make model more generally applicable for a larger range of arbitrary hulls and appendages it was decided to try to determine necessary coefficients not through a series of towing tank experiments but by making use of results as obtained from extensive studies on Delft Systematic Yacht Hull Series (DSYHS). This implies that right hand side of equations of motions Is determined using formulations obtained from DSYHS. The forces in X-direction, I.e. resistance forces due to forward speed, heel and leeway, are approximated by making use of formulations as presented by Keuning and Sonnenberg In Reference [3]. These expressions read: For viscous resistance use is being made of ITTC-57 formulations:

5 Rfli = ^pv'' -Sc-Cf with cf = ^^^^ ^"'^ " factor is being tal<en (log(^«)-2f into account. and Rn = ^^^^J-^^ The residuary resistance of bare hull is V determined by: Rrh Vc-pg + a. Sc LCB fpp LCB fpp LCF. fpp + «4 Aw 'LCB,p''' Bwl ^ + in which: Rrh Vc P g Bwl LCBfpp LCFfpp fpp Cp Aw Sc residuary resistance of canoe body volume of displacement of canoe body density of water acceleration of gravity length of waterline beam of waterline longitudinal position centre of buoyancy to fpp longitudinal position centre of flotation to fpp forward perpendicular (ordinate 10) prismatic coefficient waterplane area at zero speed wetted surface canoe body at zero speed N m kg/m^ m/s^ m m m m m' m^ Table 1: Coefficients for Polynomial: Residuary Resistance of Bare Hull Fn , ao ai as as ae a? as And viscous resistance of appendages with: The residuary resistance of appendages is approximated by: Rv = Rf-{l + k) and {l + k) = with c Rf = \-p-v^-s-cf Rrk Vk-p-g In which: Tc + Zcbk +A ' ' Bwl ' Vyt>^ Vc

6 Rrk residuary resistance of l<eel N Vk volume of displacement of keel m^ T total draft of hull with keel m Bwl beam of waterline m Tc draft of canoe body m Zcbk vertical position of centre of buoyancy of keel m Vc volume of displacement of canoe body m^ And: Table 2: Coefficients for Polynomial: Residuary Resistance of Keel Fn Ao Ai A A At present changes in resistance due to change In heeling angle during tacking maneuver are not taken into account. This was decided in this stage of project for sake of simplicity. The effect of se components is considered to be rar small. This simplification however may be easily omitted by implementing expressions from Reference [2] covering se components. For calculation of Y-forces toger with moments around Z- and X-axes on hull with appendages, under influence of leeway and heel angle and surge- and sway-velocities, procedure as suggested by Keuning and Vermeulen in Reference [2] was used. For side force on heeled hull expression from Reference [3] was used for hull with appendages under heel: [' Sc ' ^Sc) T T Sc ^ in which: b b b b And: B3 = * (Bwl/To)* (Tc/T) When applying th ese expressions series of hulls with appendages some calculated s Therefore a new "construction" using aspect keels typica on a rar high-aspect ratio anomaly was found in ide force production. regression is under more data of more high lly outside planform DSYHS. The range of planforms within DSYHS Is rar limited. This work was not yet finished at time of writing. In Reference [1] Keuning and Vermeulen assume total yawing moment of appended hull to be composed of three

7 separate contributions : tlie l<eel, tlie rudder and bare hull. The side force on appendages was located at quarter chord length of each foil and ir respective contribution to yawing moment calculated using se positions with respect to CoG of yacht. The yaw moment on bare hull was determined using following strings of expressions. For derivation of and rationale behind se expressions, reference is being made to study reported by Keuning and Vermeulen in Reference [3] In principle this method for calculating yaw moment consists of determination of so-called "Munk moment" on bare hull using Nomoto's method as described In Reference [5], but now with an integration of sway added mass, corrected for Cm value, carried out over entire length of model. The sway added mass of each section is approximated by taking actual maximum depth of heeled sections and is multiplied with correction coefficient C(x). An additional leeway angle in shape of peff is added to Nomoto's expression to account for lift generated due to asymmetry of heeled hull of yacht. So: In which sway added mass ^22 L 1 \ a22 = -np \h\xyc(x)dx Cix) = (3.33c (xf-3.05c,, (x) ) The additional effective angle of leeway due to heeled canoe body assymetry reads: Pe/f in which: and from regression In DSYHS data base magnitude of C^^o was found to correlate to: CmzO = 0.01 Bwl2/*Tc These approximations were shown in Reference [ ] to yield good results when compared with measurements in DSYHS. At that time however no additional test data derived from experiments with bare hulls under heel and leeway were available for validation of this yaw moment approximation. A number of se measurements have now been carried out in context of this study in towing tank of Delft Shiphydromechanics Laboratory with 4 models belonging to DSYHS and 2 additional models, which do not belong to this Series. In se tests models have been towed at leeway angles ranging form 3 to 9 degrees and at speeds corresponding to Fn = 0.30, 0.35 and 0.40 respectively. From se results it could be concluded that: The prediction of yaw moment using described procedure yields good results, in particular for lowest fonward speed. A significant effect of forward speed can be observed tending to increase yawing moment with increasing speed. A few remarks about se observed effects can be made: The Munk moment is a fully inviscid or potential flow phenomena. In a real viscid flow it Is assumed that generated side force by fluid momentum over aft part of body is reduced due to viscous effects such as vortex shedding and flow separation. This reduces yaw moment when compared with a full potential flow approximation. This effect increases with increasing leeway angle. In literature this effect is associated with athwart forces with respect to ships longitudinal axis related to so called "cross flow drag", i.e. drag forces arising from a cross flow over sections due to sway velocity of ship. The sway velocity and cross flow drag coefficient Cdc of each section determine magnitude of force according to: Fy= l/2pv'acdc

8 Model 366 S 3 A 5 B 7 D 9 Ï0 li Ï2 IB IB 19 2Ö S3 2T Model H 15 IB 17 IB 19 EO Model IB Model IB Results Model 366 Results Model 329 Yaw moment-area bare hull Uprighl, Model 366, Model scalel Yaw moment-area bare hull Upriaht, Model 329, Model scale Fn=0.3 measured Fn=0.35 measured Fn=0.4 measured Calculated CSYS2003 Fn=0.3 measured Fn=0.35 measured Fn=0.4 measured Calculated CSYS2003 Beta (dei Beta [deg]

9 Model 424 (SYSSER 62) Results Model 424 Yaw moment-area bare hull Upright, Model 424, Model scale Beta [deg] Model 433 (SYSSER 63) Results Model 433 Yaw moment-area bare hull Uprioht, Model 433, Model scale Beta [deal

10 For commercial vessels effect of this on yaw moment will be different from effect on a sailing yacht hull. The more V- shaped sections In bow will have a higher drag coefficient than flat bottom and rounded sections in stern of a yacht hull. This will tend to increase yaw moment. Also influence of bow wave will be significant. It is known from visual observation that re Is a strong asymmetry in bow wave for a yacht sailing with leeway. This effect will increase with forward speed. The resulting pressure distribution over bow will also tend to increase yaw moment, in particular at higher Froude numbers. At present no attempt has been made to asses this forward speed influence on yaw moment in more detail. Finally forces on rudder are approximated using well known expression for lift and drag on a foil. The effective angle of attack of flow on rudder during a tack will depend on : Rudder angle The leeway angle The induced velocities due to sway and yaw. So following expression for effective rudder angle is applied: S=6+tm In which: 3. 5, U is effective angle of attack radder angle Y lateral velocity (driftangle = ) u yaw velocity distance between radder and CG. of yacht Finally it should be noted that usual transverse stability data have been used for equations in roll. The forces on sails and appendages were assumed to have ir CeO In geometrical centroid of sail plan and on 43% of total draft of appended canoe body. The sail forces The sail forces in tacking model are calculated using a slightly adopted procedure to be able to take into account effect of very small incidence angles on sails as well as effective angle of attack due to combined effect of sway, yaw and roll velocities. The roll- and yaw velocity will increase apparent wind angle. The leeway angle decreases angle of attack on sails. The roll- and yaw velocity will increase apparent wind angle. The leeway angle decreases angle of attack on sails. The apparent wind angle and apparent wind velocity are calculated at a representative height. In present study at supposed Center of Effort (CoE) of sails. Zee Is vertical distance and Xce horizontal distance with respect to origin of coordinate system to CoE of sail. Sail Coefficients -^Cy»e-«Cx In a steady state equilibrium condition, i.e. sailing at a steady course, apparent wind velocity and apparent angle of attack are calculated by: V,, = C + 2 V, Cos{l5,^+P) P.. = tan- V, + Cos{P^+p) These expressions are modified by taking roll- and yaw velocities into account. This yields following expressions for apparent wind angle and velocity in tacking situation:

11 =pzce + Xce + F., sin )f +{v^^ cos {fi^, )f (^Zce+ ifrxce+ V^, sin(/?,j) ^.. = tancos In present maneuvering model, used to simulate a tack, aerodynamic coefficients of sails decrease from values In close-hauled condition to values even smaller n zero until apparent wind angle shifts to or side (tack). From re on it will take a few seconds to trim sails again for new situation and to get a steady flow around sails. During this time-lag, in present model, sail forces are assumed to Increase linearly. Obviously this time lag will depend on all kind of parameters and procedures such as steering procedure, i.e. rudder angle as function of time. In following simulations of tacking procedure of half ton yacht this time lag Is set on 5 seconds. Comparison measurements with full scale To check wher present model yields comparable results with model as formulated by Masayuma use is being made of his full scale measurement data. This measurement is very well documented and recorded in his papen The measurements were carried out with a half ton yacht. The tacking procedure measurements included track of boat, speed, rudder angle, heeling angle, course of boat etc. All relevant input data was retrieved from his measurements and resulting tacking procedure calculated using present model. From results it may be concluded that correlation between measurements and simulation are quite satisfactory. Differences are present but se may also be due to slight differences between input of two maneuvers. accuracy of formulations presently used. These tests will be carried out in sway and yaw motion at various speeds. Also te Influence of heeling angle will be Investigated. The results obtained will be compared to existing calculation routines. These may be adapted or modified if considered necessary. Also a number of full scale trials will be carried out with at least two significantly different yachts to validate results of presented tacking model. Finally an assessment will be made between a number of different yachts in principal parameters such as displacement, sail area, stability and appendage lay out, of differences in time needed for a tack. Based on this maybe a formulation can be derived for handicapping purposes which makes it possible to account between difference between yachts in this respect c omp arise m of Fact ingi raje( tori( S «\ \\ tartc f \\ x\ t ickin \) Wi id ve Dclty i.3 m/s > simulated measured Xolm] Future Developments In foreseeable future an experiment will be carried out at Delft Shiphydromechanics Laboratory to measure added mass and damping of a number of models In DSYHS to establish

12 List of Symbols List of References A CLR Cm GM g ^xx,yy,zz m SA Tc u V Vs V aw Pa U V p.. S S. - distance between keel and CG. of yacht - distance between rudder and CG. of yacht - centre of lateral resistance - midship section coefficient - Height of metacenter - acceleration of gravity - moments of inertia about x, y and z-axis in body axes system - added moments of inertia about x, y and z-axis in body axes system - length of water line - mass of yacht - added masses along x, y and z-axis in body axes system - sail area - mean draft of canoe body - longitudinal flow velocity - transverse flow velocity - yacht velocity - true wind velocity - apparent wind velocity - sway, surge force due to steady forces on canoe body and fm keel sway, surge force due to rudder - sway, surge force due to sails - roll, yaw moment due to steady forces on canoe body and fin keel - roll, yaw moment due to rudder - roll, yaw moment due to sails - roll moment due to stability of yacht - water density - air density - longitudinal flow velocity - transverse flow velocity - leeway angle - true wind angle - apparent wind angle - yaw angle - rudder angle - effective rudder angle - roll angle - course of yacht [1] Keuning, J.A. Vermeulen, K.J. The yaw balance of sailing yachts upright and heeled 16'" Chesapeake Sailing Yachts Symposium SNAME 2003 [2] Masayuma, Y.e.a.Dynamic Performance of Sailing Cruiser by Full Scale test 11'" Chesapeake Sailing Yacht Symposium SNAME 1995 [3] Keuning, J.A., Sonnenberg, U.B. Approximation of Hydrodynamic Forces on a Sailing Yacht based on Delft Systematic Yacht Hull Series Inetrnatlonal HISWA Symposium on Yacht Design and Construction 1998 [4] Nomoto, K. Tatano, H.Balance of Helm of Sailing Yachts International HISWA Symposium on Yacht Design and Construction 1975 [5] Masayuma, K. Fukusawa, T. Sasagawa, H. Tacking Simulation of a sailing yacht 12'" Chesapeake Sailing Yacht Symposium SNAME 1995

13 Appendix Comparison witfi full scale measurements Comparison of yaclit Velocity SOjime [sec]35 Comparison ofyachtvmg o o > Sim ulated 1" " «measured 1 1 i T Comparison of Course 25 SOTime [sec]35 - ï 0 U -50 i-100 ^^^^^vs im u Iat6d - -.Measured SOTime [sec]35 Comparison of Heelangle 30Time [sec] a) 20 O) s (=» 10 O) ra d) 1=. a i> a 0 o 3-10 o; 20 The ( effective) Rudder angle Rudderangle «fifaoeoeffective rudder angle Time [sec]35