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

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

T U Delft

T H E F O U R T E E N T H

C H E S A P E A K E

S A LL I N G

Y A C H T S y M P O S I U M

J A N U A R Y 3 0 , 1999

THE CHESAPEAKE SECTION OF

THE S'PCIETY O F 'NAVAL ARCHITECTS

A N D ENGINEERS

UNITED5TATES

SAILING ASSOCIATION

. NAVAL A C A D E M Y

S | l L I N G S Q U A D R O N

\

THE CjrlPSAPEAKE BAY

^ ^ Y A C H T RACING

T A B L E O F C O N T E N T S

Papers Presented on Saturday, January 30,1999

Developments in the I M S V P P Formulations

Andrew Claughton, Wolfson Unit MTIA, University of Southampton, U K 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 1997-1998 Whitbread Sail Program - Lessons Learned

Robert C. Ranzenbach, G L M Wind Tunnel, Univ. of Maryland, College Park, Maryland, USA

Per Andersson, G L M Wind Tunnel, Univ. of Maryland, College Park, Maryland, USA

T A B L E O F C O N T E N T S

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, U K

Pandeli Temarel, Department of Ship Science, University of Southampton, U K 123

Use of C F D 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, G L M Wind Tunnel, Univ. of Maryland, College Park, Maryland, USA

Chris Mairs, G L M 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

THE 14th CHESAPEAKE SAILING YACHT SYMPOSIUM

14th C S Y S 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

THE 14th CHESAPEAKE SAILING YACHT SYMPOSIUM

The Fourteenth Chesapeake Sailing Yacht Symposium was co-sponsored by:

The Society o f Naval Architects and Marine Engineers, 601 Pavonia Avenue, Jersey City, NJ 07306

The United States Sailing Association, P.O. Box 209, Newport, R l 02840-0209

The Chesapeake Bay Yacht Racing Association, 612 Third Street, Annapolis, M D 21403

The U.S. Naval Academy Sailing Squadron, The Robert Crown Sailing Center, U.S.N.A., Annapolis, M D 21402

The Fourteenth CSYS was held in the Francis Scott Key Auditorium on the campus of St. John's College in Annapolis, Maryland, USA.

The S N A M E 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.

Approximation of the C a l m Water Resistance on a Sailing Yacht Based on the

'Delft Systematic Yacht Hull Series'

J.A. Keuning, Ship Hydromeclianics Lab., Delft Univ. o f Tech., Delft, The Netherlands

U.B. Sonnenberg, Ship Hydromechanics Lab., Delft Univ. o f 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. I n 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 publica-tions 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.

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 1. Graphic Representation of Resistance Components Upnghi RciijtaYice o f H u l l wilh Keel i n d Rudder k a i J i u K e o r H i i l l with Keel w i Rudder with Heel = R[(f>

ResLSU/Keot'Hull wiJi Kect md Rudder with

Hed ind Le«wiy •Rl9p

T n c ï ï ö r ü r Resistance Hull RcsidLu/y" Rcsistuicc Hull Viicotu Rcsiiiince Keel VlKOlll R d i s i i n c e Rudder Rejiduary R e j u U n c e Keet Upnght Resiiunce of Hull with Keel

ind Rudder mi Frict. Resiittnce due 10 Heel Hull k e s i i t i n c e o r M ü l l wilh Keel Uld Rudder with Heel = A RJhtp

E5;TÜ

Resiitince iue to Side Force

Hull ind Keel Delti Reiiitmce due to Heel Hull due to Heel 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:

Figure 2. Relative Resistance Contributions

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 Nether-lands. 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. A l l 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

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

Sysscr44

The principal hull parameters varied within DSYHS are presented in Table 1.

Table 1. The Range of Hull Parameters Tested i n the DSYHS

Ranges Length - Beam Ratio

Lwl

Bwl 2.73 to 5.00 Beam - Draft Ratio

Bwl

Tc 2.46 to 19.38 Length - Displacement Ratio

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 Loading Factor

Aw

3.73 to 12.67

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). A l l 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

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.

Table 2. Huil Form Parameters of DSYHS Sysse Lwl/Bw Bwl/Tc Lwl / LCB LCF Cb Cp Cw Cm Aw/ Sysse r V O L C I f i % % Cp Cm VOLc'2/3 1 3.15J 3.992 4.77£ -2.2£ -3.3; 0,365 0.564 0.68E 0,646 4.976 2 3.62C 3.04: 4.77e -2.3C -3.3^ 0,367 0.567 0.691 0.646 4.349 3 2.747 5.34£ 4.77S -2.3C -3.3: 0,37C 0.572 0.696 0.647 5.776 4 5 3.50S 2.747 3.947 3.957 5.097 4.366 -2.25 -2.4' -3.3: •3 4C 0,367 0 361 0.568 0.691 0.646 5.119 6 3.155 2.979 4.339 -2,4C •3.42 0.363 0.55Ê _0.561 0.683 0.686 0.647 0.646 4.719 4.091 7 3.155 4.953 5.143 -2,29 •3.36 0.362 0.561 0.685 0.646 5.743 8 3.279 3.841 4.775 -2,40 -3.32 0.379 0,586 0.707 0.647 4.921 9 3.049 4.131 4.776 -2,20 •3.34 0.353 0,546 0.672 0.646 5.026 10 3.155 3.992 4.775 Ü.OÜ -1.91 0.365 0.564 0.694 0.646 5.017 11 3.155 3.992 4.775 -1.98 ^.97 0.365 0,565 0.682 0.646 4.928 12 3.509 3.936 5.104 -0.01 -1.93 0.364 0,564 0.693 0.647 5.149 13 3.509 3.936 5.104 -5.01 -5.01 0.364 0,564 0.681 0.646 5.057 14 3.509 3.692 5.104 -2.30 -3.47 0.342 0,529 0.657 0.646 4.879 15 3.165 3.683 4.757 -2.29 -3.45 0.343 0,530 0.658 0.646 4.708 16 3.155 2.810 4.340 -2.30 •3.48 0.342 0,529 0.657 0,646 3.926 17 3.155 4.244 4.778 -0.01 •1.79 0.387 0,598 0.724 0,647 5.241 18 ^ 3.155 4.244 4.778 -5.00 4.89 0.387 0,599 0.712 0,647 5.152 19 3.155 3.751 4.777 0.01 -2.06 0.342 0,530 0.664 0,646 4.802 20 3.155 3.751 4.778 -4.99 -5.09 0.342 0.530 0.651 0,646 4.712 21 3.509 4.167 5.099 -2.29 -3.22 0.387 0.598 0.718 0,547 6.322 22 _{2.732 4.231 4.337 -2.29 •3.22 0.387} 0.599 0.719 0,647 4.947 23 3.472 4.091 5.001 -1.85 -5.29 0.394 0.547 0.673 0,721 4.850 24 3.497 10.958 6.935 -2.09 -5.84 0.402 0.543 0.670 0,739 9.215 25 4.000 5.388 6.003 -1.99 •5.54 0.399 0.548 0.671 0,727 6.048 26 3.994 12.907 7.970 -2.05 •6.33 0.407 0.543 0.678 0,749 10.791 27 4.496 2.460 5.011 -1.88 -5.24 0.395 0.546 0.677 0,724 3,780 28 4.500 6.754 6.992 -2.05 •5.95 0.400 0.544 0.672 0,736 7,305 29 4.000 10.870 7.498 -4.59 -7.63 0.413 0.549 0.671 0,751 9,437 30 4.000 7.082 6.500 ^.56 -7.66 0.413 0.549 0.672 0,751 7.096 31 4.000 15.823 8.499 ^.53 -7.81 0.412 0.548 0.674 0,752 12.172 32 4.000 10.870 7.498 -2.14 -6.22 0.413 0.549 0.687 0,751 9.651 33 4,000 10.870 7.498 -6.55 •8.73 0.413 0.549 0.659 0,751 9.266 34 4.000 10.373 7.491 -4.37 -7.55 0.395 0.522 0.649 0,757 9.106 35 4,000 11.468 7.472 ^.49 -7.58 0.440 0.580 0.694 0,758 9.686 36 4.000 10.163 7.470 •4.36 -7.29 0.390 0.551 0.663 0,707 9.249 37 4,000 9.434 7.469 4 , 4 2 -6.93 0.362 0.552 0.654 0.667 9.117 38 3.000 19.378 7.503 •4.53 •7.86 0.413 0.547 0.675 0.755 12.666 39 5.000 6.969 7.499 •4.55 -7.54 0.413 0.549 0.670 0.753 7.534 41 4.000 5.208 5.927 -Ö.16 -9.51 0.400 0.540 0.652 0.741 5.722 42 3.319 3.711 4.699 -3.28 •6.41 0.394 0.554 0.670 0.711 4.460 43 2.784 6.291 4.983 -3.28 •6.49 0.394 0.553 0.672 0.712 5.991 44 3.319 4.424 4.982 -3.29 -6.25 0.394 0.554 0.668 0.712 4.996 45 4.175 2.795 4.982 -3.28 -6.24 0.394 0.554 0.668 0.711 3;969 46 3.319 5.569 5.379 -3.29 -6.26 0.394 0.553 0.668 0.712 5.825 47 3.337 6.042 5.474 •6.02 -8.40 0.410 0.548 0.699 0.749 6.278 48 3.337 5.797 5.426 -0.65 •5.03 0.404 0.557 0.690 0.725 6.084 49 3.352 6.307 5.523 -6.34 -8.43 0.421 0.566 0.699 0.743 6.359 50 3.333 6.342 5.521 -7.90 -9.14 0.419 0.639 0.688 0.777 6.291

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 N A C A _{63,A015 0012} Root Chord tn 0.414 0.124 Tip Chord "m m 0.262 0.096 Span bk br m 0.219 0.266 Volume Vk Vr m' 0.00262 0.00O23 Wencd Area Sk Sr 0.1539 0.0550 Swcepback Angle AJc Ar 45 5.4

A l l diese appended models have been tested in the following conditions:

upright with no trim correction for driving sail forces (Fn = 0.10....0.60)

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 o f 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.

A l l 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:

( 2 )

where:

p density of water

V die fonvard velocity of die yacht

S the wetted area at zero speed

Cf friction coefficient

kg/m^

m/s

m^

During die measurements the model is fitted with carborundum strips for hirbulence stimulation, both on die hull and the appendages.

In die determination of die frictional resistance use is being made of die well known ITTC-57 extrapolation line, according to:

( 3 ) 0.075

( l o g ( ^ ) - 2 ) '

in which die hull Reynolds number Rn is determrned by:

( 4 ) V in which: Lwl waterline lengdi V kinematic viscosity m mVs

185

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.

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

0 5

0 J . , ,

0 1 2 3

Fn»4/Cf

Plot for Sysser 1

Prohaska plol Uprighl

1.5

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 C A L M WATF.R RRSISTANCF

hi CANOEBODY RESISTANCE

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.

Plot for Sysser 25

3-1-1 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.

3-1-1-1 VISCOUS RRSTSTANrP

The frictional resistance of die bare hull is determrned usmg die followmg expression:

( 5 )

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

m2

The wetted area of die hull is considered to be known from die hydrostatic calculations. I f 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;

( 6 ;

.c = r i . 9 7 . 0 . 1 7 1 . ^ ] . f M 5 f ( , , . , , , ^ .

V Tc j {CmJ ^ '

3-1-1-2 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 ) Rrh I LCB - = a.+\ a, Vc-p-g Vc'^ Bwl] V c ^ — -I-a, • Cp + Qj • ——ha, --^^-^ • -^-^ + Lwl Aw Lwl j Lwl ( V c « LCB,, (LCB, Sc i-CF,„ ' I Lwl + a,-Cp' Lwl in which: in which: Bwl beam of waterline m

Tc draft of canoe body m Cm midship section coefficient

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 L w l 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 LCBfpp

ofbuoyancy to fpp m LCFfpp longitudinal position centre LCFfpp

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.

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 = 0.60.

Table 4. Coefficients f o r Polynomial: Residuary Resistance of Bare H u l l Fn 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 -0.0O14 0.0004 0.0014 0.0027 0.0056 0.0032 -0.0064 -0.0171 -0.0201 0.0495 0.0808 0.0403 -0.1808 -0.1071 0.0463 -0.8005 -0.1011 2.3095 3.4017 7.1576 1.5618 -5.3233 h _{0.0470 0.1793 0.0637 -0.1263 0.4891 -0.0813 -1.5152 -1.9862 -6.3304 -6.0661 -1.1513} -0.0227 -0.0004 0.0090 0.0150 0.0269 -0.0382 0.0751 0.3242 0.5829 0.8641 0.9663 a* -0.0119 0.0097 0.0153 _{0.0274 0.0519 0.0320 -0.0858 -0.1450 0.1630 1.1702 1.6084} 0.0061 0.0118 0.0011 -0.0299 -0.0313 -0.1481 -0.5349 -0.8043 -0.3966 1.7610 2.7459 -0.0O86 -0.0055 0.0012 0.0110 0,0292 0.0837 0.1715 0.2952 0.5023 0.9176 0.8491 ^7 -0.0307 0.1721 0.1021 -0.0595 0.7314 0.0223 -2.4550 -3.5284 -7.1579 -2.1191 4.7129 ^1 -0.0553 -0.1728 -0.0648 0.1220 -0,3619 0.1587 1.1865 1.3575 5.2534 5.4281 1.1089

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 H u l l Residuary Resistance Measured and Approximated

10000

RMkkJwy R M i i U n c f B«ra Hull

msai: / ' oooo ? e °= « 0 0 .

/ '

. - ^ ^ ^

Parent DSYHS Models

Rialfhixy R n i l i M i c * Bar* HuN

M M x n d i C«(culM*d 10 m 1*1 a lOOOO moa 23 9000 24 , r 20 eooo € a 27 °^ *000 caJc — •

/

RwhJuwy RMtmnca Oar* Hul

• 10O0O _ mea ' 329 3S« eooo. * / 332 6000 . / 117 ^ «000 . 329 2000 . _. 366 0 \ , 232 0.3 _{0,25 0.3 0.35 0.4 0.45 0.5 0.35 0,6} Fn 117

3-1-2 CHANGE I N RESISTANCE DUE TO HKKI.

When the yacht heels over there will be a change in the resistance of the yacht. I n 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.

3-1-2-1 CHANGE I N 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:

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 )

Bwl beam of waterline

Tc draft of canoe body

Cm midship section coefficient

With the coefficients 'Sg' to ' S j ' being determined using a least square fit regression analysis in Table 5:

Table 5. Coefricients f o r Polynomial: Wetted Surface under Heel 5 10 15 20 25 30 35 h -4.112 -t.522 -3.291 1.850 6.510 12.334 14.648 Sl 0.054 -0.132 -0.389 -1.200 -2.305 -3.911 -5.182 h -0.027 -0.077 -0.118 -0.109 -0.066 0.024 0.102 6.329 8.738 8.949 5.364 3.443 1.767 3.497 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 28 - ^ m fTlOdol 1Ö 28 2A model 3 ! FT 2 2 W 18 -model 28 ° a calculaled 18 ,

°

Heeling Angle PHI [ D E G |

3-1-2-2 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 two possible approaches have been tried:

in which: 1 + 1

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.

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:

( 9 )

^Rrh<p Rrhtp mtas) •Rrh^ calc)

The delta residuary resisumce at 20 degrees of heel (as an average sailing angle) could dien be approximated by a polynomial expression given by:

( 1 0 ) t^K-n- Lwl Bwl > = U. + U, + li, Vc-p-g ^ ' Bwl ^ Tc (Bwl\ — ^u,LCB + u^ \ Tc ) LCB'

with die coefficients for Uq du-ough Uj

Table 6. Coefficients for Polynomial: Delta Resistance H u l l due to 20° Heel

CocfTlc ents ajc multiplied bv 1000

Fn 0.25 0.30 0.35 0.40 0.45 0.50 0.55 "o .0.0268 0.6628 1.6433 -0.8659 •3.2715 -0.1976 1.5873 U| .0.0014 .0.0632 -0.2144 -0.0354 0.1372 •0.1480 •0.3749 u, .0.0057 .0.0699 -0.1640 0.2226 0.5547 -0.6593 -0.7105 0.0016 0.0O69 0.0199 0.0188 0.0268 0.1862 0.2146 -0.0070 0.0459 •0.0540 •O.5800 -1.0064 -0.7489 •0.4818 u' -0.0017 -0.0OO4 •O.0268 •0.1133 -0.2026 •0.1648 -0.1174

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. I n general a good

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:

( 1 1 )

ARrh^

=ARrh^,,„.-6.0-p'-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

1000

D«IU R«>liL 0 » r t Hufl d u i 2tr h«*4

O •00 ₂₅ SCO § J" 700 29 50 -300 . ' a— " " " ^ ' " ^ a 25 -*00 29 0. I 0,S5 0.3 0.35 0.4 0,45 0,5 0,55 Fn - H 0.6 — 50

Figure 10. Residuary Resistance of Bare H u l l at 20° Heel

10000 _

Rtald. R i t l i L B a n Hull 20 daq haal

mea» and c a t (Rrh • dRrtiW) lOm M a

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 o f 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.

3-2-1 UPRIGHT APPENDAGE RESISTANCE

3-2-1-1 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.

( 12)

R v = R f - { \ + k)

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:

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 intro-duced. 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 ' R f use is made of the following expression:

( 13 )

Rf = j-p-V'-S-C/

in which

( 14 )

(log(Rr,)-2f

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, i f 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

3-2-1-2 A P P E N D A G E R E S I D U A R Y 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.

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 resistance-and 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 l A C C Model 329 H u l l

Figure 12. Drawing of l A C C Model 366 H u l l

////

_{i t}

Mod 66

1 1 \—1

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. I n 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

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 A R T R A DSYHS Model 1

DSYHS Model 23..28 DSYHS Model 43

Slandard DSYHS keel 0.63 0.63 43.0 15.0

Model 117 20' sweep back version 0.94 1.00 20.0 15.0 Model 232 'IOR' keel 0.92 0.51 28.0 12.5 Model 232

'Shoal Draft' keel 0.28 0.79 33.0 11.0 Model 232

Up Side Down' keel 0.92 1.98 28.0 12.5 Model 329 ' l A C C 1' Uld Model 366 'lACC 2' [10 configurations) 1 1.62 0.73 4.0 lO.O Model 329 ' l A C C 1' Uld Model 366 'lACC 2' [10 configurations) 3 0.70 0.84 7.2 6.6 Model 329 ' l A C C 1' Uld Model 366 'lACC 2' [10 configurations) 4 0.70 0.84 7.2 15.0 Model 329 ' l A C C 1' Uld Model 366 'lACC 2' [10 configurations) 5 1.62 2.30 4.0 10.0 Model 329 ' l A C C 1' Uld Model 366 'lACC 2' [10 configurations) 5 1.62 0.40 4.0 10.0

Table 8 M a i n H u l l Form Parameters of Different Yacht Test Series

Yacht L w l Bwl L w l L C B L C F C b Cp Bwl T c V c ' " % %

Cp DSYHS Model 1 3.15 3.99 4.78 -2.3 -3.3 0.36 0.36 DSYHS Model 28 4.50 6.75 6.99 -2.1 -6.0 0.4O 0.54 DSYHS Model 43 2.78 6.29 4.98 -3.3 -6.3 0.39 0.55 Model 117 3.19 5.27 5.05 -4.2 -1.6 0.42 0.58 Model 232 3.35 5.22 5.46 -4.2 -4.5 0.4O 0.35 Model 329 ' l A C C I ' 4.52 4.82 6.63 -5.0 -6.4 0.34 0.53 Model 366 ' l A C C 2' 3.73 3.00 6.63 -5.0 -6.4 0.34 0.33

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 l A C C type

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 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 A. -0.00104 -0.00550 -0.01110 -0.00713 -0.03581 -0.00470 0.00553 0.04822 0.01021 A, 0.00172 0.00597 0.01421 0.02632 0.08649 0.11592 0.07371 0.00660 0.14173 A j 0.00117 0.00390 _{0.00069 -0.00232 0.00999 -0.00064 0.05991 0.07048 0.06409} A) -0.00008 -0.00009 0.00021 0.00039 0.00017 0.00035 -0.00114 -0.00035 -0.00192

193

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. ( 1 6 ) Rrk Vk-p-g A„ + A, Bwl Tc + Zcbk •+ A. Vc Vk in which:

Rrk residuary resistance of keel Vk volume of displacement of keel

T total draft of hull with keel Bwl beam of waterline

Tc draft of canoe body

Zcbk vertical position of centre

of buoyancy of keel Vc volume of displacement of canoe body m-^ m m m m

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

3 i M CHANGE I N 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

Figure 16. Total Upright Resistance, Measured and Calcuiated f o r Model 43

0 » öRrtprt

Figure 17. Total Upright Resistance, Measured and Calculated for Model 366.1

TuLiI VjLlrt W t i i l n j i i n

R «

appendages, in particular the keel, is strongly influenced by die fact that the volume o f 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 o f 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 o f 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.

The following figure presents how the measurement data from die 'heel and leeway' experiments have been split in the components for pure Heeled Residuary Resistance 'Rr^j' and the Induced Resistance ' R i ' ;

Figure 18. Offset f o r Heeled Residuary Resistance and Slope for Resistance due to Sideforce

Table 10. Coefficients for Polynomial: Delta Resistance of the Keel due to Heel

HBSiduary K o a i s u n c » and Hesled horco 20 b«*. (or oo« valoaty

Induced Resistance due to Sideforce

Heeled Residuary Resistance at no Sideforce

. fit through msasuremants

OOEtOO 5.06-KM 1.0E*07 I.SE+07 2.0E-KI7 2.5EMJ7 3.0E-M)7 3.5E-MJ7 Fh*2 [N^2]

Consequently to further separate the effects contributed by the keel alone, the resistance components associated widi the upright condition and the delta through heel of die hull itself should be subtracted from this heeled residuary resistance:

^''^'P{„„os) = ^'P -Rr- hRrhtp

Where 'Rr^p' and 'Rr' represent the values for the hull with keel and rudder. Hence the following expression has been used to approximate diese data:

( 17)

ARrkp

Vk-p-g Ch-Fn'-cp

where die following expression has been found for the assessment of Ch:

( 1 8 )

T ' Tc ' T Tc ' Vc'^'

of which die coefficients H , through H4 have been determined using a least square fit regression analysis. These coefficients are presented in Table 10. The heeling angle '^o' in radians.

The data set to determine die coefficients widi included tests widi die following models: 24 models of die DSYHS, 10 configurations of die DVKS and 3 configura-tions of die DVKS.

H , -3.5837 H , -0.0518 H , 0.5958

H4

Some results of calculations executed with this polynomial are presented in the following chapter in together with the Induced Resistance component in Figure 20 and up.

INDUCED RESISTANCE

The results from previous studies on the induced resistance as presented amongst odiers by Gerritsma et al. in Ref 1 and Ref 2, have been completely revised in the present study. This is primarily due to a change in the definition of the induced resistance itself and partly due to taking the effect of other parameters in assessing it into account.

In the initial approach the induced resistance was simply defined as the difference in die total resistance of die sailing yacht in its upright condition and sailing at die same speed under heel and leeway (wiüi sideforce). By doing so a number of changes in die total resistance were considered to be part of the induced resistance, which were however not directly related to die sideforce production itself.

In the present approach most of the components of die resistance difference between diese two conditions (i.e. the upright and die heeled and yawed condition) are dealt with separately, i.e, die changes in both die residuary-and viscous resistance due to heel alone residuary-and no sideforce involved are considered, as it is extensively described in the previous chapters. The induced resistance is now solely related to die actual sideforce generation of die huil and die appendages.

The present approxunation mediod however is still based on the same fundamental physical principles as they are originating from the aeronautical sciences, i.e. the "effective span" approach as presented in Ref 1. The basic idea behind this approach is as follows;

As known from the aeronautical sciences the induced resistance, i.e. die additional resistance component due to die sideforce production of a wing widi finite span, is related to the circulation around the foil and its geometry by die following set of expressions :

( 19 ) ( 22 ) Fh' Ri = Cr,rjpV-Alat i J ; = — °' ''^ n-AR,-\pV'-Alat Fh = C,-\pV'-Alat in which: n-Te'-\pV' ( 2 0 )

Alat = ck-T illustrated in Figure 18

The induced resistance is proportional to the slope ' R C i ' of the line fitted through the measurement data as

and:

Ri induced resistance N Cpi induced resistance coefficient

Mat lateral surface of hull with Iceel

Fh heeling force N C L lift coefficient

ck mean chord of keel m T total span of hull with keel m

The induced drag coefficient Cpj is related to the loading of the foil by:

( 2 1 )

c

TTAR.

AR = Alat

In the formulation the "effective" aspect ratio 'AR^' is used radier than die aspect ratio ' A R ' itself. This "effective" designation is meant to take account of the free surface effects. The effective span is in agreement with die effective aspect ratio and is die equivalent total effective draft of the hull plus keel combination 'Te'. The addition "effective" originates from die fact that a reduction (or sometimes increment) of die geometrical aspect ratio is found which is dependent on die free surface-, hull-keel interaction- and endplate effects associated with die keel - hull combination moving wiüi forward speed in and in die close proximity of die free surface (such as waves, pressure relief and "talk-over" effects etc.).

With die expressions for AR^, C L and C^i combined die induced resistance may now be written as:

Now the effective span 'Te' of the hull widi appendages is determined from the measurement data with:

( 2 3 ) Te = Fh' Te: \K-Ri-\pV' 1 n:-RCi-\pV'

From the measurements it became obvious diat the effective draft Te and its change widi heeling angle '<j)\ was strongly dependent on die Beam to Draft ratio of thé hull above it as well as widi die relation between die canoe body depdi and die keel span. In addition to this a speed dependency was found. For each of die heeling angles tested, i.e. 0 ° , 10°, 20° and 3 0 ° , diis relationship could be satisfactory established with die following expression: Te_ T ( 2 4 ) TcV Rwl V Y j +Ar — +A,-TR .{B.+B.-Fn)

Figure 19. Heeling Force and Sideforce

SF Fh:

cos(p)

Heeling Force 'Fh'

Sideforce ' S F

Where 'TR' is die Taper Ratio of die keel:

TR:

The coefficients of this expression have been detemiined using a least square fit regression analysis dirougJi die measured data. The data set included tests widi the following models: 20 models of the DSYHS, 10 configurations of die DVKS and 3 configurations of die DVKS. The coefficients are presented in Table 11.

Table U . Coefficients for the Polynomial: Effective Span

9

0

10

20

30

A|

3.7455

4.4892

3.9592

3.4891

A?

-3.6246

-4.8454

-3.9804

-2.9577

A,

0.0589

0.0294

0.0283

0.0250

-0.0296

-0.0176

-0.0075

-0.0272

Bo

1.2306

1.4231

1.5450

1.4744

B,

_{-0.72561 -1.2971 -1.5622 -1.3499}

Figure 21. Measured and Calculated Resistance at 30° Heel and Leeway for Model 25 at F n = 0.32,

0.36 and 0.45 0500 MOO 2500 • JOOO liOO 1000

KislduaiY f l « i l i U n c t i n d HMlad l-orct 30 dtQ hMt. *adi Int a W10C31Y

o.oe*oo i.oe«j7 2.oe<oF ioe>o7 FIT>2 [N«2|

Figure 22. Measured and Calculated Resistance at 30° Heel and Leeway for Model 33 at Fn = 0.32,

0.36, 0.41 and 0.45

A typical illustration of the obtained accuracy of die fit to the measured data of die resistance due to heel of both the hull and the appendages and the induced resistance is presented in Figure 20 and following. In diese figures a graphical representation is given of the resistance as a function of the generated sideforce squared for 3 different models belonging to die DSYHS, i.e. Model 1, 24 and 25 and two different angles of heel, i.e. 20° and 30°.

Figure 20. Measured and Calculated Resistance at 20° Heel and Leeway for Model 1 at Fn = 0.30,

0.35, 0.35 and 0.45

HMlduary Uasiilanca and Hxllng Tore. 30 4«g tt*^ f adl in* I vt4oatr

- W for tacn vatodtY O.OEHM 3,0€MM 1.oe«37 1.5E.07 2 OEM)/

Ft\^2 1N>2|

M t J I d u a r y H a a i a l a n c a a n d Haallng l-ofca 30 <,*4 r>M< t B d , ana • v«4oa(y

X mtaturad _{. n fiy aach valocrty} O.OEKO 1.0EMJ7 iOEWJ? 3.0EWJ7 4.06M7 S 0E«I7

Fh'2 1 N ' 2 |

Figure 23 Measured and Calculated Resistance at 20° Heel and Leeway for l A C C Model 329 with Keel

5 (Up Side Down) at F n = 0.27, 0.35 and 0.39