TU Delft. Approximation of the Calm Water Resistance on a Sailing Yacht Based on the Delft Systematic Yacht Hull Series

Transcription

1 Approximation of the Calm Water Resistance on a Sailing Yacht Based on the Delft Systematic Yacht Hull Series J.A. Keuning & U.B. Sonnenberg Report 1177-P Project Code: 953 January 1999 TU Delft Delft University of Technology Faculty of Design, Engineering and Production Ship Hydromechanics Laboratory Department of Marine Technology

2 THE F O U R T E E N T H CHESAPEAKE S A LL I N G YACHT S y M P O SI U M JANUARY 30, 1999 THE CHESAPEAKE SECTION OF THE S'PCIETY OF 'NAVAL ARCHITECTS AND ENGINEERS UNITED5TATES SAILING ASSOCIATION. NAVAL ACADEMY S lling SQUADRON \ THE CjrlPSAPEAKE BAY ^^YACHT RACING ASSOCIATION

3 TABLE OF CONTENTS Papers Presented on Saturday, January 30,1999 Developments in the IMS VPP Formulations Andrew Claughton, Wolfson Unit MTIA, University of Southampton, UK 1 Experimental Technique for the Determination of Forces Acting on a Sailboat Rigging F. Fossati, Politecnico di Milano, Milano, Italy G. Moschini, Politecnico di Milano, Milano, Italy D. Vitalone, Harken Italy S.p.a., Lurago Marinone, Italy 21 Fullscale Hydrodynamic Force Measurement on the Berlin Sailing Dynamometer Karsten Hochldrch, Technical University of Berlin, Beriin, Germany Hartmut Brandt, Technical University of Berlin, Berlin, Germany 33 USS Constitution Preparations for Sail 200 Howard Chatterton 45 In Search of Power, Pace and Windward Performance In Square Rigged Sailing Ships Philip Goode 61 The Windward Performance of Yachts in Rough Water Jonathan Binns, Australian Maridme Eng. Coop. Research Centre (AMECRC), Perth, Australia Bruce McRae, Australian Maritime Eng. Coop. Res. Centre (AMECRC), Launceston, Tasmania Giles Thomas, Australian Maritime Eng. Coop. Research Centre (AMECRC), Perth, Australia 75 A Whitbread Sail Program - Lessons Learned Robert C. Ranzenbach, GLM Wind Tunnel, Univ. of Maryland, College Park, Maryland, USA Per Andersson, GLM Wind Tunnel, Univ. of Maryland, College Park, Maryland, USA David Flynn, GLM Wind Tunnel, Univ. of Maryland, College Park, Maryland, USA 87

4 TABLE OF CONTENTS Papers Presented on Friday, January 29,1999 at the SNAME SC-2 "Sailing Craft" Panel Meeting Sailing Yacht Design Using Advanced Numerical Flow Techniques Caponnetto et al, Hydraulic Machines Laboratory, Ecole Poly. Fed. de Lausanne, Switzerland 97 Parametric Design and Optimization of Sailing Yachts Stefan Harries, Teclinical University of Berlin, Berlin, Gennany Glaus Abt, Teclinical University of Berlin, Berlin, Germany 105 An Investigation of the Structural Dynamics of a Racing Yacht Frederic Louarn, Department of Ship Science, University of Southampton, UK Pandeli Temarel, Department of Ship Science, University of Southampton, UK 123 Use of CFD Techniques in the Preliminary Design of Upwind Sails Patrick Couser, Formation Design Systems, Fremantlem, Westem Australia Norm Deane, VP of the Intemational Mirror Class Association, Hobart, Australia 143 On the Application of RANS Simulation for Downwind Sail Aerodynamics William Lasher, Penn State Erie, The Behrend College, Erie, Pennsylvania, USA 157 Wind Tunnel Testing of Offwind Sails Robert Ranzenbach, GLM Wind Tunnel, Univ. of Maryland, College Park, Maryland, USA Chris Mairs, GLM Wind Tunnel, Univ. of Maryland, College Park, Maryland, USA 171 Approximation of the Calm Water Resistance on a Sailing Yacht Based on the 'Delft Systematic Yacht Hull Series' J.A. Keuning, Ship Hydromechanics Lab., Delft Univ. of Tech., Delft, The Netherlands U.B. Sonnenberg, Ship Hydromechanics Lab., Delft Univ. of Tech., Delft, The Netherlands 181 Bibliography of Previous Chesapeake Sailing Yacht Symposia Papers 201 ii

5 THE 14th CHESAPEAKE SAILING YACHT SYMPOSIUM 14th CSYS Committee Members Steering Committee John J. Zseleczky General Chairman Stephen R. Judson Papers Committee Chairman Joseph O. Salsich Treasurer Volker Stammnitz Publicity Chairman Aim Ljone Publicity Nancy Harris Internet Edy Walsh Arrangements Gregory J. Opas Publications Chairman Rhonda D. Kane Publications Michael G. McLaughlin Publications Bruce Johnson CBYRA Representative Karl L. Kirkman US Sailing & NASS Representative Richards T. Miller Advisor Robert W. Peach Advisor C. Gaither Scott Advisor Papers Committee Diane Burton David A. Heigerson Andrew R. Kondracki J. Otto Scherer Jolin J. Slager Thomas H. Walsh ill

6 THE 14th CHESAPEAKE SAILING YACHT SYMPOSIUM The Fourteenth Chesapeake Sailing Yacht Symposium was co-sponsored by: The Society of Naval Architects and Marine Engineers, 601 Pavonia Avenue, Jersey City, NJ The United States Sailing Association, P.O. Box 209, Newport, Rl The Chesapeake Bay Yacht Racing Association, 612 Third Street, Annapolis, MD The U.S. Naval Academy Sailing Squadron, The Robert Crown Sailing Center, U.S.N.A., Annapolis, MD The Fourteenth CSYS was held in the Francis Scott Key Auditorium on the campus of St. John's College in Annapolis, Maryland, USA. The SNAME SC-2 "Sailing Craft" Panel meeting was open to all CSYS attendees and was held in Conference Room 103, Rickover Hall, U.S. Naval Academy, Annapolis, Maryland, USA. Copyright 1999 by The Society of Naval Architects and Marine Engineers iv

7 Approximation of the Calm Water Resistance on a Sailing Yacht Based on the 'Delft Systematic Yacht Hull Series' J.A. Keuning, Ship Hydromeclianics Lab., Delft Univ. of Tech., Delft, The Netherlands U.B. Sonnenberg, Ship Hydromechanics Lab., Delft Univ. of Tech., Delft, The Netherlands ABSTRACT Over the past years a considerable extension has been given to the Delft Systematic Yacht Hull Series (DSYHS) The DSYHS data set now contains infonnation about both the bare hull and appended hull resistance in the upright and the heeled condition, the resistance increase due to the longihjdinal trimming moment of the sails, the sideforce production and induced resistance due to sideforce at various combinations of forward speeds, leeway angles and heeling angles. New formulations for the relevant hydrodynamic forces as function of the hull geometry parameters have been derived to be able to deal with a larger variety of yacht hull shapes and appendage designs. During the past two years some results of this research have already been published. In die present paper an almost complete picftire of the relevant expressions which may be used in a Velocity Prediction Program (VPP) will be presented. i INTRODUCTION The Delft Systematic Yacht Hull Series is a very extensive series of systematic yacht hulls consisting of some 50 modeis by now, all of which have been tested at the Delft Shiphydromechanics Laboratory of the Delft University of Technology over the last 25 years. The aim of these investigations which led to the testing of these 50 models of the DSYHS was the developments of equations that could be used as an approximation method for the assessment of the most important hydrodynamic forces acting on a sailing yacht. The shape of the yacht designs has changed considerably over these 25 years which necessitated the change in the shapes of the hulls tested as well as in the approach and/or method of analysis of the measured data of the DSYHS. Therefore over the total span (in time) of the DSYHS Üiree different parent models have been used. In it's sort the DSYHS is probably the largest systematic series with such a high degree of consistency in both the model shapes and measurement techniques, procedures and analysis. Based on the equations derived from the results of the DSYHS a Velocity Prediction Program was to be developed, which should enable designers of sailing yachts to evaluate their designs and the possible design variations on their performance in an early design stage. In conjunction with this DSYHS a number of smaller systematic series have been tested aimed at solving specific problems not (fully) covered by the DSYHS. In this respect the research on appendage drag and sideforce production should be mentioned. Due to the rather large development in the appendage design and layout in the last decades the standard appendages of Ihe DSYHS did no longer do justice to these new design trends. This research was aimed to derive formulations for the forces on the appendages separately, so lhat a larger variety of designs could be dealt with and was based on a series model experiments containing some 13 different keel configuration placed underneath one particular yacht hull and on a series of experiments with 6 different keels underneath two systematically different hulls. Inevitably also the approach towards the assessment of the forces involved has changed over the past 25 years, which led to additional tests with all the models, also with those already previously tested, for instance to measure bare hull resistance and the change in resistance due to trim and heeling alone. All these changes mentioned above have led to a substantial new set of polynomial expressions suitable for the approximation of the calm water resistance forces involved in the sailing yacht equilibrium in calm water. During the last decades a considerable number of publications on the these subject of calculating the hydrodynamic forces on the sailing yacht have been published by Gerritsma et al., all of which may be found in the List of References at the end of this paper. A part of the newly derived fonmulations have already been presented in some recent publications of the Delft Shiphydromechanics Laboratory. In the present paper however the new calculation schedule and the complete set of equations that goes with this schedule will be presented. 181

8 The method by which the hydrodynamic forces have been decomposed in separate components is presented in Figure 1 as a kind of flow chart. The decomposition is as follows: Figure 2. Relative Resistance Contributions Figure 1. Graphic Representation of Resistance Components Upnghi RciijtaYice ofhull wilh Keel ind Rudder kaijiukeorhiill with Keel wi Rudder with Heel = R[(f> ResLSU/Keot'Hull wiji Kect md Rudder with Hed ind Le«wiy Rl9p Tncïïörür Resistance Hull RcsidLu/y" Rcsistuicc Hull Viicotu Rcsiiiince Keel VlKOlll Rdisiince Rudder Rejiduary RejuUnce Keet Upnght Resiiunce of Hull with Keel ind Rudder mi Frict. Resiittnce due 10 Heel Hull Delti Reiiitmce due to Heel Hull due to Heel Keel = A RJhtp kesiitinceormüll wilh Keel Uld Rudder with Heel E5;TÜ Resiitince iue to Side Force Hull ind Keel TkTS Reiiitance due to Tnmming Moment The upright resistance of the bare hull is the starting point of the calculation scheme. In this condition the frictional resistance and the residuary resistance are calculated. Then the resistance of keel and rudder are determined in the same condition also as the summation of a viscous and a residuary part. Then the yacht is heeled over and the 'deltas' of the frictional resistance of the hull and the residuary resistance of the hull, the keel and the rudder are detenmined. Subsequently the yacht assumes leeway and the induced resistance due to the side force is calculated as a function of heeling angle. Finally the change in resistance due to the trimming moment of the crew, adjusting its longimdinal position along the length of the yacht to counteract the bow down trimming moment caused by driving force of the sails in particular at die running and reaching courses, will be brought into the calculation. Finally the summation of all these components yields the total resistance of the yacht in calm water. For each of these components expressions will be presented in the following paragraphs. In fonnula the total resistance as a sum of the various components can be written as: ( 1 ) Rlifp, = RJhif + Rvkr + Rrh + MrhB + ARrhif, + Rrk + Mrjhp + Ri To give an impression of the magnimde and the contribution of all these different resistance components to the total resistance of a sailing yacht with a waterline length of 10 m, under 10 heel, a leeway angle of 3 and with a 4 men crew sitting in the cockpit aft, the relative contributions to the total resistance for Sysser models 1 and 25 are presented in Figure 2. Each line adds the component as labelled in die legend: Model 25 Noticeable is die different influence of the resistance caused by the trimming moment. For model 25 the total resistance decreases when the crew compensates the forward trimming moment of the sail force. While for model 1 this influence is limited to an resistance increase in the middle speed range only. 2 DESCRIPTION OF THE DSYHS The original parent model chosen for the Delft Systematic Yacht Hull Series in 1974 was the well known "Standfast 43" designed by Frans Maas at Breskens, The Netherlands. The Standfast 43 was a typical contemporary racing yacht design. From this parent model (model 1), 21 other systematically varied designs have been derived (model 2 to model 22) using, as far as feasible, an affine transformation technique. All models were consequently tested in the towing tank over a period of 10 years. This sub-series of the DSYHS is known as "DSYHS Series 1". After 10 years the typical yacht designs started to differ considerably from the lines of this original parent and therefore it was decided in 1983 to introduce a new parent model into the DSYHS according to the lines presented to 182

9 the Delft Shiphydromechanics Laboratory by Van der Stadt Design at Wormerveer, The Netherlands. From this second parent hull, model 25, another 6 new variations were derived known as sub-series "DSYHS Series 2" (model 23 through model 28) and later another 12 models based on the same parent with special emphasis on very light displacement and higher Length to Beam ratios (model 29 through model 40; "DSYHS Series 3"). Finally in 1995 yet another parent model was introduced into the DSYHS according to the lines presented tc the Delft Shiphydromechanics Laboratory by Sparkman and Stephens from New York, United States of America, known as the "IMS 40" especially designed for research and which was intended as some "average" Intemational Measurement System (IMS) design. From this third parent model, model 44, another 9 variations have been tested sofar and is now known as sub-series "DSYHS Series 4" (model 42 through model 50). In general it is believed that by this significant variety in hull shapes a sufficiently large area of possible yacht designs is being covered by the DSYHS to make its results and the derivations therefrom applicable to a large diversity of yacht designs. Nevertheless new additions to the DSYHS in the fumre may still be necessary to keep up with (inevitable) developments in yacht design. To give an impression of the hull shapes, the bodyplan of the three parent models are presented in Figure 3. Figure 3. The Parent Hull Forms of the DSYHS The principal hull parameters varied within DSYHS are presented in Table 1. Table 1. The Range of Hull Parameters Tested in the DSYHS Length - Beam Ratio Beam - Draft Ratio Length - Displacement Ratio Lwl Ranges Bwl 2.73 to 5.00 Bwl Tc 2.46 to Lwl VcJ< 4.34 to 8.50 Longitudinal Centre of Buoyancy LCB 0.0 % to 8.2 % Longitudinal Centre of Floatation LCF -1.8 % to 9.5 % Prismatic Coefficient Cp 0.52 to 0.60 Midship Area Coefficient Cm 0.65 to 0.78 Aw Loading Factor 3.73 to A complete oversight of the hull shape parameters of each of the 50 models of die Delft Systematic Yacht Hull Series is presented in Table 2. This Table is of particular interest because it illustrates the range of values of the various hull shape parameters (and parameter combinations) Üiat have been varied and tested within the Series which yields an indication of the range of applicability of the formulations derived from these data. 2-1 TEST SETUP All models have been tested in the tt\ towing tank of the Delft Shiphydromechanics Laboratory with a length of 145 meter, width of 4,5 meter and depüi of 2.5 meter. The model size widiin the DSYHS ranges between 1.6 meter waterline length for Series 1 to 2.00 meter waterline lengüi for die other models (Series 2, 3 and 4). All models have been tested as bare hulls (unappended) in the speed range from Fn = 0.10 to Fn = 0.60 to measure resistance, sinkage and trim in the following conditions: - upright with no trim correction for the driving sail forces - upright with trim correction for die driving sail forces - heeled to 20 degrees heel wiüi no correction for trim due to sail forces Sysscr44 In addition the majority of the models have been fitted with a keel and rudder, identical for all models and according to the plan as presented in Figure 4. For the sake of consistency throughout the series all these models have been fitted with physical the same keel and rudder. 183

10 Table 2. Huil Form Parameters of DSYHS Lwl/Bw Bwl/Tc Lwl / LCB LCF Cb Cp Cw Cm Aw/ Sysse r VOLCIf i % % VOLc'2/ J ; 0, E 0, C 3.04: 4.77e -2.3C -3.3^ 0, S -2.3C -3.3: 0,37C S : 0, ' 3 4C Ê ,4C , , , , , Ü.OÜ ^ , , , , , , , , , ^ , , , , , , , , , , , ,724 3, ,736 7, ,751 9, ^ , ^ , , , , , , ^ , , , , Ö ; This implies that the relative magnitude of die keel and rudder on the full scale yachts with 10 meter waterline length is dependent on die model size and the scale factor used. Figure 4. DSYHS Keel and Rudder Configuration Table 3. DSYHS Keel and Rudder Model Dimensions syrobol unit Keel Rudder Profile NACA 63,A Root Chord tn Tip Chord "m m Span bk br m Volume Vk Vr m' O23 Wencd Area Sk Sr Swcepback Angle AJc Ar All diese appended models have been tested in the following conditions: 184

11 upright with no trim correction for driving sail forces (Fn = ) heeled, yawed and trimmed condition in a matrix consisting of all combinations of - 4 heeling angles at least three different speeds 4 different leeway angles (i.e. 0, 10, 20 and 30 degrees) (i.e. ranging from Fn = 0.25 to 0.45) (i.e. ranging from 0 to 12 degrees) During the experiments the following values were measured: - forward speed of the model - resistance force - heeling angle - heeling moment - leeway angle - side force and yawing moment - sinkage and trim (at speed) - trimming moment The standard measurement technique developed for sailing yachts experiments at the Delft Shiphydromechanics Laboratory has been used throughout the whole series. This technique implies that the model is connected to the towing carriage in such a way that it is free to heave, roll and pitch but restrained in all other modes of motion. The connection to the towing carriage is established by means of two balanced arms siniated at equal distances fore and aft of the longimdinal position of the Centre of Gravity of the model at deck level. A schematic presentation of die measurement set-up is presented in Figure 5. Figure 5. Test Set-up under Towing Carriage On die hull three strips are placed which are 4.0 cm wide each and placed at equal separation with die first strip at the forward end of the waterline and the after most one approximately at station 6'/^ just forward of the leading edge of die keel. On die keel and rudder one single strip is placed close to die leading edge of the appendages and diese have a widüi of 3.0 cm for the keel and for the rudder 2.0 cm. To correct for the extra resistance originating from die presence of die strip itself all resistance tests are carried out twice: once with half width and once widi ftill width of die strips. The difference in resistance between these two conditions is used to determine die resistance of die strips. The model resistance is obtained by subtracting die extra resistance from die strips from the measured model resistance. All model data are extrapolated to a ftill scale 10 m wateriine lengdi yacht. The extrapolation is carried out according to Fronde's extrapolation technique. For die determination of die frictional resistance 'RT use is made of die followmg expression: where: p V S density of water die fonvard velocity of die yacht the wetted area at zero speed Cf friction coefficient (2) kg/m^ m/s m^ In die determination of die frictional resistance use is being made of die well known ITTC-57 extrapolation line, according to: (3 ) (log(^)-2)' in which die hull Reynolds number Rn is determrned by: (4) in which: V During die measurements the model is fitted with carborundum strips for hirbulence stimulation, both on die hull and the appendages. Lwl V waterline lengdi kinematic viscosity m mvs 185

12 As may be seen from this expression for the reference length necessary for the determination of die Reynolds Number 'Rn' 70% of die waterline lengdi is taken. For the appendages the average chord lengdi is used for die determination of the Reynolds Number. 1.5 Prohaska plol Uprighl For the upright conditions a so-called Prohaska plot is made to determine die formfactor of the hull. As a typical example of such a Prohaska plot of die DSYHS in Figure 6 the plots are presented for die diree parent models of the Series. From diese figures it may be concluded diat the formfactor is generally small. In general die formfactor using this described turbulence sthnulation technique and derived from die Prohaska plots has been found to be in die range from 'k' = 0.03 to 'k' = 0.07 in most cases and only in one or two exceptional cases 'k' exceeded these values. Figure 6. Prohaska Plots for the Parent Model Hull Measurements Prohaska plol Uprighl P 0.5 C J. i,, Fn«4/cr Plot for Sysser 44 Since no well based or generally accepted formulation is known (nor could it be derived from die results widi die DSYHS) determining die formfactor 'k' as function of die hull geometry parameters of any arbitrary hull, it was decided, from die beginmng of the series, not to use a formfactor for die calculation of the viscous resistance in die extrapolation procedure. This would make such a calculation mediod of 'k' necessary in order to be able to calculate die resistance of a specific yacht under consideration. 3 CALM WATF.R RRSISTANCF 0 5 hi CANOEBODY RESISTANCE 0 J.,, Fn»4/Cf Plot for Sysser 1 As shown in die flow component chart for die definition of die various resistance components (Figure 1) die fu-st resistance to be assessed is die bare hull canoe body resistance UPRIGHT RESISTANCE First die resistance in die upright sailmg condition will be calculated. Two separate parts of die resistance m die upright condition will be considered: i.e. die frictional (or viscous) resistance and the residuary resistance VISCOUS RRSTSTANrP The frictional resistance of die bare hull is determrned usmg die followmg expression: Plot for Sysser 25 ( 5 ) in which: 186

13 p density of water V die forward velocity of die yacht Sc the wetted area of die hull at zero speed Cf friction coefficient kg/m^ m/s The wetted area of die hull is considered to be known from die hydrostatic calculations. If this is not die case die wetted area of die hull Ln die upright and zero speed, condition may be approxhnated by the following expression derived from regression using die hydrostatic calculations carried out for all the models of die DSYHS; m RESIDUARY RESISTANCE Based on the experience gained widi previous expressions for die determination of the residuary resistance of die hull of a sailing yacht, see Ref. 1, Ref 2 and Ref 3, die following expression for the residuary resistance of a yacht hull in the upright condition at one specific Froude number has been found to yield sufficient accuracy as well as "robustness": (7) in which:.c = ri ^].fm5f (,,.,,,^. V Tc j {CmJ ^ ' (6; Rrh I LCB - = a.+\ a, Vc-p-g in which: Vc'^ Bwl] Vc^ -I-a, Cp + Qj ha, --^^-^ -^-^ + Lwl Aw Lwl j Lwl ( Vc«LCB,, (LCB, Sc i-cf, ' I Lwl + a,-cp' Lwl Bwl beam of waterline m Tc draft of canoe body m Cm midship section coefficient - Vc volume of displacement of canoe Lwl length of waterline m Fully turbulent flow along the hull bodi during the experiments as in real life is assumed and dierefore die friction coefficient Cf is detennined using die ITTC-57 extrapolation line. Aldiough die choice of 70% of die waterline lengdi as die reference length in die Reynolds Number, as shown before, is quite justifiable for die hull geometry's of Series 1 die choice remains debatable. Particularly for Lhe more contemporary shapes of Series 2, 3 and 4, 90% of the waterline lengdi would appear more appropriate. For the sake of consistency however 70% of Lwl has been used throughout die whole DSYHS for the determination of die frictional resistance. It should be noted that this dierefore effects also the magnitude of the residuary resistance part. As explained before no "form" factor 'k' is used m die DSYHS for the transformation of the frictional mto die viscous resistance of die hull. This decision is based on die absence of a generally accepted formulation of die form factor as a function of hull parameters for an arbitrary hull. Such a fonnulation could also not be derived from die results of the DSYHS. This implied diat 'k' = 0 was die best approach leaving any differences in die viscous resistance due to hull shape m die residuary resistance. Rrh residuary resistance of canoe body N Vc volume of displacement of canoe body P density of water kg/m^ g acceleration of gravity m/s^ Lwl lengdi of waterline m Bwl beam of waterluie m LCBfpp longitudinal position centre ofbuoyancy to fpp m LCFfpp longitudinal position centre of notation to fpp m fpp forward perpendicular (ordinate 10) Cp prismatic coefficient - Aw waterplane area at zero speed Sc wetted surface canoe body at zero speed Some principal considerations which led to die presented shape of die parametric terms contained in the polynomial are: 1 The parameters m die terms are coupled with the displacement length ratio to make diem dependent on displacement. The terms are composed in such a way that their supposed contribution to die residuary resistance has a similar trend as die displacement length ratio. 2 The beam to length ratio is introduced for all speeds involved as an contributmg factor. 3 The beam to draft ratio is replaced by die ratio between the displacement and die wetted area of the hull, which term is considered to yield more robustoess and less sensitivity to small changes in midship section shape. 187

14 4 The LCB-LCF separation is introduced as a possible measure of hull distortion. 5 Higher order terms of boüi Cp and LCB are introduced to yield optimum values of Cp and LCB as function of speed within the range covered by the polynomial. The coefficients of this polynomial expression have been determined at constant forward speeds and are presented for a number of different Froude numbers using a least square fit through die measured data. Since die original presentation of this expression in 1996, Ref. 3, die number of models tested within die DSYHS has increased therefore leading to differences in die coefficients compared to diose presented before. Also diis time not all models of the DSYHS have been included in the regression but only 39 out of die total of 50 models available have been used, leaving some of die more extreme or highly distorted models out. The coefficients 'ao' to 'ag' are presented in Table 4 for 11 different Froude numbers from Fn = 0 10 to Fn = Table 4. Coefficients for Polynomial: Residuary Resistance of Bare Hull Fn O h a* O , ^ ^ , The resistance curves obtained for the models widiin the DSYHS using this polynomial expression all showed quite satisfactory correlation widi the measured data and they do so over the entire speed range. As a demonstration of this fit, the measured and calculated residuary resistance curves of the diree parent models of die series, some additional models of Series 2 and four models not belonging to the DSYHS are presented in Figure 7. Figure 7. Comparison Hull Residuary Resistance Measured and Approximated Rialfhixy RniliMic* Bar* HuN MMxnd i C«(culM*d 10 m 1*1 a loooo 23 moa ,r 20 eooo ^ * t > ^ ^ ^ rr- ^ ',- - 1, \, 1 _, / a 27 cajc fl Fn 27 Models of Series RMkkJwy RMiiUncf B«ra Hull msai: 10O0O _ RwhJuwy RMtmnca Oar* Hul mea ' 329 oooo? e = «00. / ' / '.-^^^ 27- eooo. * / / ^ « _ S« I 0.2 0, O.S Fn Parent DSYHS Models \, 0.3 0, ,6 Fn 117 Non DSYHS Modeis 188

15 3-1-2 CHANGE IN RESISTANCE DUE TO HKKI. When the yacht heels over there will be a change in the resistance of the yacht. In real circumstances this heeling will be caused by die arthwarth forces on die sails. This implies lift forces on die hull and its appendages also and dierefor die induced resistance component will be a large part of the change in total resistance. However to be able to calculate diis induced resistance more accurately fu-st an attempt has been made to assess the change in resistance due to heel alone, i.e. no sideforce mvolved. This resistance change is split in a viscous and a residuary part, each being treated separately CHANGE IN VISCOUS RESISTANCE The change in viscous resistance due to heel of die canoe body is solely attributed to a change in wetted area of the yacht hull. This implies no change in viscous resistance, i.e. no change in formfactor, is taken mto account. This approach originates from two considerations: Bwl Tc Cm beam of waterline draft of canoe body midship section coefficient With the coefficients 'Sg' to 'Sj' being determined using a least square fit regression analysis in Table 5: Table 5. Coefricients for Polynomial: Wetted Surface under Heel h t Sl h A typical result of diis expression is shown in Figure 8 for one "average" and two "more extreme" models of die DSYHS. Both the accuracy of the fit using die polynomial expression for such widely different hulls as die significant difference in die magnimde of die change of wetted area itself is clearly demonstrated. Figure 8. Calculation of Wetted Surface 30 Measured and Calculaled Welted Surface 1 A formfactor is not taken into account in die upright condition as well. 2 A change in form factor due to heel alone can hardly be established based on towing tank measurements alone. The model could be towed wiüi heel and widiout total sideforce (possibly implying a small drift angle) but this does not mean that diere is no sideforce distribution along the lengdi of die model which sums up to zero. This implies a possible "mix up" between a complicated induced resistance component and a possible change in formfactor. Based on die hydrostatic calculations which have been carried out for all models of die DSYHS die change in wetted area of he hulls with heeling angle has been determined. This change m wetted area of die yachts could be approximated widi a high degree of accuracy by die following expression: (8) FT 22 - ^ m ftlodol 1Ö 2A model 3! model 28 W 18 - a calculaled 18, M !. a !! Heeling Angle PHI [DEG CHANGE IN RESIDUARY RESISTANCE Due to the asymmetry of the hull when heeled and a corresponding change in the distribution of displaced volume along the lengdi a change in residuary resistance will most probably occur. To asses this change in resistance approaches have been tried: two possible in which: Tc [Tc ) To use die same polynomial expression as used for the upright resistance of the canoe body but determine new coefficients based on die measured data under heel. The result is not a change in residuary resistance but the changed residuary resistance due to heel. 189

16 The change of residuary resistance due to heel is determined from die measured data and a simplifled polynomial expression is formulated for just this delta resistance alone. Bodi approaches have dieir pro's and con's. The results of die first approach have been published in Ref 5 but predicting die total residuary resistance of die heeled hull widi die upright geometrical properties of die upright hull seems less justifiable dian predicting die upright resistance widi die upright parameters and using only some of diese to predict die generally small change (delta) due to heel. So die second approach is presented and used throughout diis report, aldiough die differences widi die first approach are generally small for die cases investigated. The change in residuary resistance of die canoe body due to heel is derived from die measurements at zero and 20 degrees of heel wiüi all models used for die upright condition polynomial by determming die viscous resistance upright and heeled and subtracting diese from the total resistance of die hull upright and heeled respectively. According to: ^Rrh<p Rrhtp mtas) Rrh^ calc) (9) fit was obtained using a dependency of die delta resistance on the heeling angle. The change is calculated to be equivalent widi die heeling angle to die power 1.7, according to: ARrh^ =ARrh^,,.-6.0-p'- (11) widi die heel angle 'yj' in radians. The fit dirough die experimental data for a few DSYHS models is shown in Figure 9 and Figure 10 and demonstrates to be quite satisfactory. It should be noticed in Figure 9 and Figure 10 that die delta part is small compared with the upright resistance. The scale of the vertical axes in the graphs differ with factor 10, Figure 9. Delta Resistance due to 20 Heel of Bare Hull SCO D«IU R«>liL 0»rt Hufl dui 2tr h«*4 O The delta residuary resisumce at 20 degrees of heel (as an average sailing angle) could dien be approximated by a polynomial expression given by: ( 10) J" ' a " ""^ ' "^a t^k-n- Lwl Bwl > = U. + U, + li, Vc-p-g ^ ' Bwl ^ Tc with die coefficients for Uq du-ough Uj (Bwl\ ^u,lcb + u^ LCB' \ Tc ) -* I 0,S ,45 0,5 0,55 Fn -H 0.6 Figure 10. Residuary Resistance of Bare Hull at 20 Heel 50 Table 6. Coefficients for Polynomial: Delta Resistance Hull due to 20 Heel _ Rtald. RitliL Ban Hull 20 daq haal mea» and cat (Rrh drrtiw) lom M a meia: ^3 CocfTlc ents ajc multiplied bv 1000 Fn "o U u, O O u' OO4 O The dependency on die heeling angle which is necessary to obtain values of die resistance mcrease due to heel for any odier angle of heel has been determined using a much smaller database of measurement data. In general a good 190

17 hl APPENDAGE RESISTANCE The resistance of the bare hull and die appendages are dealt with separately. The viscous resistance of die appendages has been found to be independent of the heel angle and therefore only one expressions is fonnulated for die calculation of this viscous part. Based on die DSYHS experiments with systematic keel variations underneadi various hulls it was concluded diat the residuary resistance of die appendages is significantly influenced by the (immediate) presence of die free surface and dierefore definitely has a heeling dependency. So die residuary resistance of the appendages is determined in die upright condition first and a delta resistance due to heel is formulated thereafter. combination of laminar and turbulent flow over die chord of the appendage. There are no principal procedural problems however for taking diese mixed flow possibilities in account except maybe the conect formulation of die frictional and form effects. The viscous and formdrag is taken into die calculation by making use of the well known formulation for 'k' as given by Hoemer's "Fluid Dynamic Drag" Ref 7 and generally accepted in the aeronautical sciences, which determines die formfactor a sole function of the relative thickness of die sections, according to: UPRIGHT APPENDAGE RESISTANCE VISCOUS RESISTANCE The viscous resistance 'Rv' of the appendages is considered to be a summation of die frictional resistance and "other" viscous effects accounted for by die introduction of a "form" factor. Rv=Rf-{\ + k) ( 12) Each of die appendages, i.e. keel and rudder(s), is treated in a similar manner using die same fonmulations. For the "straight course" upright resistance a possible wake effect from die keel on the rudder may be introduced. From experiments, in which die wake behind die keel on sufficient distance aft of the keel has been measured on a 3.5 meter Lwl model, an acceptable mean reduction value of 0.80 times the free stream velocity has been found for the water velocity over the rudder, see Ref. 8 and Ref. 9. The general applicability of this value may be disputed however and because the rudder will only be in the wake completely if the yachts sails with absolutely no heel and no leeway, die necessity of such an approach is also questionable. For the calculation of die frictional resistance 'Rf use is made of the following expression: in which Rf = j-p-v'-s-c/ (log(rr,)-2f ( 13 ) ( 14 ) originates from the ITTC '57 extrapolation line and is valid for a fully turbulent flow. For die determination of the Reynolds number 'Rn' die average chord length ofthe appendage may be used or, if the appendage is span wise divided in several segments, the local chord lengdi of such a section. No attempt is being made here to take into account more complex dependency on die cross section profiles of die appendage and so possibly for mixed flow, i.e. a APPENDAGE RESIDUARY RESISTANCE The very existence of a significant residuary resistance of the appendages beneaüi the hull in the upright condition has long been disputed. A report in 1975 by Beukelman and Keuning Ref 10 however already showed an influence of the keel sweepback (i.e. longimdinal distribution of the displaced keel volume over Üie length) on the upright resistance of a yacht. From analysis of die results of die experiments widi bare hull and die appended model within die DSYHS, in which series one and die same keel has been tested underneadi a wide variety of hulls, it became obvious diat a residuary resistance of the appendages should be taken into account. Straight forward comparison of die appended and unappended results widiin the DSYHS however necessitated the subtraction of two big quantities to produce the residuary resistance of die keels. This yielded too much scatter in die relatively small keel residuary resistance component to justify a reliable assessment. 191

18 Therefore an additional Delft Systematic Keel Series (DSKS) has been set up, in which so far a family of 6 different Iceels has been tested underneadi two lacc type hulls with different Beam to Draft ratio's. These experiments are extensively described in Ref. 9 and Ref. 4. Also the results of recent investigations on die DSKS by R W M Meulemans, Ref 12, are included. Therefore this research will only be summarised briefly here. During diese experhnents widi the DSKS the resistanceand liftforces on the appendages were measured directly and separately as well as the forces on the model as a whole. The tests program contained experiments both widi die bare hulls as widi die hulls equipped widi die various appendages. The standard measurements and test program of the Delft Shiphydromechanics Laboratory have been used during diese experiments. The profiles and main dimensions of die keels used in die experiments are presented in Figure 14 and Table 7 and for die two model hulls in Figure 11, Figure 12 and Table 8. Figure 11. Drawing of lacc Model 329 Hull development and future extensions are foreseen, which are intended to lead to an increased reliability of the keel residuary resistance assessment. Anodier systematic keel series has been tested, which consisted of a series of 13 widely different keels underneadi one and die same hull, described in Ref 11. This series is refered to as the Delft Various Keel Series (DVKS). In diis series die hull of a IOR type maxi has been used to compare die usual IOR type keel wiüi a number of altematives bodi for racing and cruising, like an Elliptical keel, keels widi Winglets, Cend-e boards, Shallow Draft keels, Upside-down keels etc. etc. In die present assessment of the keel residuary resistance only die IOR-, die Upside-down- and the Shallow Draft keel are being used because the odiers are not sufficiently consistent with the rest of the keels used. A side view and the main particulars of these keels are presented in Figure 15 and Table 7. The particulars of die IOR type hull. Model 232, are presented in Table 8. Table 7. Main Form Parameters of Keels YachI Keel AR TR A DSYHS Model 1 DSYHS Model DSYHS Model 43 Slandard DSYHS keel Figure 12. Drawing of lacc Model 366 Hull //// i t / Model ' sweep back version Model 232 'IOR' keel 'Shoal Draft' keel Up Side Down' keel Model 329 'lacc 1' lo.o Uld Model 366 'lacc 2' [10 configurations) Mod \ 1 Table 8 Main Hull Form Parameters of Different Yacht Test Series 1' The parameters tested for dieir influence on this residuary resistance of the keel in the upright position were: die span of the keel, the displaced volume and the vertical height of the centre of buoyancy of the keel, die beam to draft ratio of the hull and the taper ratio of the keel. In die analysis die keel resistance was determined as die difference between the resistance of die appended and die unappended condition, so possible interference effects between hull and appendage are contained in die keel resistance component. These results are used to develop the polynomial expression for the keel resistance. It should be noted that diis DSKS is still under Yacht Lwl Bwl Lwl LCB LCF Cb Cp Bwl Tc Vc'" % % DSYHS Model DSYHS Model O 0.54 DSYHS Model Model Model O 0.35 Model 329 'lacc I' Model 366 'lacc 2' This selection was supplemented widi die measurements carried out widi the standard DSYHS keel undemeadi die diree parent models and the half span standard keel as tested undemeath Model 1. So the expression for the residuary resistance of the keel is derived from the following data: The IOR-, die Shallow- and the Upside-down keel in die Delft Various Keel Series (DVKS), 5 of die 6 keels tested in the Delft Systematic Keel Series widi die lacc type 192

19 hulls (DSKS) and die parent models of die DSYHS of which Model 1 with half span keel also. The plan views of these keels are presented in Figure 13 through Figure 15, in which figures all die keels are shown in correct relative size. Figure 13 DSYHS keel (model Lwl = 2.0 m), DSYHS half span (model Lwl = 1.6 m) and Model 117 keel Figure 14 Keels of die Delft Systematic Keel Series Figure 15 Keels of die Delft Various Keel Series Table 9 Coefficients for Polynomial: Residuary Resistance of Keel Fn A A, Aj A)

20 The following expression yielded a quite satisfactory fit through all the data and is based on die relation between keel and hull volume, die taper ratio of die keel, the Beam to Draft ratio of die hull, die vertical distance of the centre of buoyancy of the keel volume to die free surface Zcb and the ratio of canoe body volimie to keel volume. Figure 16. Total Upright Resistance, Measured and Calcuiated for Model 43 ( 16) Rrk Vk-p-g A + A, Bwl Tc + Zcbk + A. Vc Vk in which: 0» örrtprt Rrk Vk T Bwl Tc Zcbk residuary resistance of keel volume of displacement of keel total draft of hull with keel beam of waterline draft of canoe body vertical position of centre m-^ m m m Figure 17. Total Upright Resistance, Measured and Calculated for Model TuLiI VjLlrt Wtiilnjiin of buoyancy of keel m R«Vc volume of displacement of canoe body For die lower Froude numbers the contribution of the residuary keel resistance in the total resistance is not very large, but it increases for the high speeds. The data set however is still radier limited for such a delicate resistance component and further research will certainly contribute to increasing die reliability of diese expressions. With the data set described above the following coefficients were found for die coefficients of die polynomial expression: Calculated- compared widi Total Measured Upright Resistance for two models: See Figure 16 and 17 3iM CHANGE IN APPENDAGE RESISTANCR DTIF. TO HEEL The viscous resistance of die appendages is considered not to be influenced by die heeling of die yacht. This is a quite justifiable assumption. Things are different however when considering die residuary resistance of die appendages. This residuary - or wavemaking resistance of die appendages, in particular the keel, is strongly influenced by die fact that the volume of the appendage is brought closer to the free surface due to die heel angle of die yacht. All experimental data strongly confirm diis change. This was already clearly demonstrated by Beukelman and Keuning in dieir paper of 1975 Ref 10 in which amongst odiers photos of die heeled hull widi resulting die free surface waves widi and widiout sideforce production of die keels were shown. The approach used for die assessment of diis resistance in die present study is along two lines of diought. Firstly the amount of wavemaking resistance of die keel due to heel (no sideforce!!) is considered to be dependent on how close die volume is brought to die free surface, i.e. to be dependent on die beam to draft ratio of die hull and die relative submergence of the keel volume, i.e. die ratio between keel span and hull depth and secondly to die amount of wavemaking of die hull itself, i.e. related to die length displacement ratio. These influences of course will be dependent on die heeling angle but in addition to diis also on die speed of die yacht and hence to its primary wave generation, i.e. die Froude number. 194