A Generic Mathematical Model for the Maneuvering and Tacking of a Sailing Yacht

Date AUthOr Address

March 2005

Keuning, J.A., K.J. Vermeulen and EJ. de Ridder Deift University of TechnOlogy

Ship Hydromechanics Laboratory

Mekelweg 2, 26282 CD .Delft

TUDeift

DeiftUnlversityol Technology

A Generic Mathematical Model for the

Maneuvering and Tacking of a Sailing

Yacht

by

Keuning, 3.A., KJ. Vermeulen, TUDeift

E.). de Ridder, MARIN Wageningen

Report No. 1458-P

2005

Presented at the 17th Chesapeake Sailing Yacht SymposIum, March 45,'O5, Annapolis, Maryland,

7

SAILING

I

THE SEVENTEENTH

CHE SAP EAKE

SAILING YICHT

SYMPOSIUM

March 4-5, 2005

Annapolis, Maryland, USA

Society of Naval Architects and Marine Engineers Chesapeake Section

US Sailing

THE

1.7th

CHESAPEAKE SAILING YACHT SYMPOSIUM

ANNAPOLIS, MARYLAND, MARCH2005

Table of Contents

Papers Presented. on. Friday, March 4, 2005

Toward Numerical VPP with the Full Coupling of Aerodynamic and Hydrodynamic

Solvers for ACC Yachts.

..,,

. .

Erwan Jacquin, Bassin d'essais. des carens, Vai de Reuil,. France

Yann Roux, Company K-Epsilon, Val de Reuil, France

Bertrand Allessandrini, Ecole Centrale, Nantes, France

Time Domain Simulation of a Y. 'acht Sailing Upwind in Waves

13

D. H. Harris, Reiçhel-Pugh Yacht Design, San Diego, USA

Geometry and Resistance of the IACC Systematic Series "Il Moro di Venezia"

33

Battistin, INSEAN - Italian Ship Model.Basin, Rome, Italy

D.. Peri, 1NSEAN. - Italian Ship Model Basin, Rome, Italy

F.. Campana,. 1NSEAN - Italian Ship Model Basin, Rome, Italy

Sailing Yacht Rig Improvements Through Viscous Computational Fluid Dynamics...53

Vincent G. Chapin, Fluid Mechanics, Department, Ensica, France.

Romaric Neyhousser, Aquitaine Design Team, Arcachon, France

Stephane Jamme, Fluid Mechanics Department, Ensica, France

Guillaume Duihand, Fluid Mechamcs Department, Ensica, France

Patrick Chassaing, Fluid Mechanics Department, Ensica, France

A New Velocity Prediction Method for PostProcessing of Towing Tank Test Results. .

.

67

Kai Graf, Institute of Naval Architecture, University of Applied Sciences Kiel (UAS), Germany

Christoph Bohm, R&D-Centre Univ. Applied Sciences Kiel, Yacht Research Group, Germany

Hull Form OptimizatiOn of Performance Characteristics of Turkish Gulets for Charter. 79

Mark Gammon, DRDC Atlantic,, Dartmouth Nova Scotia, Canada

Abdi Kukner, Istanbul Technical University, Istanbul,, Turkey

Abmet Alkan, Yildiz Technical University, Istanbul, Turkey

The Development of ân Integrated Ship Design Environment for the Naval Architect on

The Linux' Operating System

. . ,

.

91

H. James Parker, Gibbs and Cox, Incorporated, USA

Multiobjective Design Optimization of an LACC Sailing Yacht by Means of CFD

High-Fidelity SOlvers

...,

. ,

.

105

Daniele Peri, INSEAN, Rome, Italy

Fabrizio Mandolesi, INSEAN, Rome, Italy

THE

17th

CHESAPE4KE SAILING YACHT SYMPOSIUM

ANNAPOLIS, MARYLAND, MARCH 2005

Table of Contents

Papers Presented on Saturday, March 5, 2005

Comparison of Tacking and Wearing Performance Between a Japanese Traditional Square

Rig and a Chinese Lug Rig

117

Yutaka Masuyama, Kanazawa Institute of Technology, Japan

Akira Sakurai, Kyushu University, Japan

Toichi Fukasawa, Kanazawa Institute of Technology, Japan

Kazunori Aoki, Kawasaki Shipbuilding Corporation, Japan

Relative Performance of Conventional Versus Movable-Ballast-Racing Yachts

129

Frank DeBord, BMT Scientific Marine Services, USA

Harry Dunning, Reichel/Pugh Yacht Design, USA

The Effect of Mast Height and Centre of Gravity on the Re-Righting of Sailing Yachts. 135

Jonathan R. Binns, Researcher, Australian Maritime College, Australia

Paul Brandner, Research Leader, Cavitation and Fluid Dynamics, Australian Maritime College

A Generic Mathematical Model for the Maneuvering and Tacking of a Sailing Yacht.. 143

A. Keuning, Shiphydromechanics Laboratory, Delft University of Technology

J. Vermeulen, Shiphydromechanics Laboratory, DelfI University of Technology

J. de Ridder, MARIN, Wageningen

Experimental Methods to Evalùate Underwater Appendages

165

Robert Ranzenbach, GLM Wind Tunnel-University of Marylànd, College Park Maryland, USA

Mathew Zahn, Webb Institute of Naval Architecture, Glen Cove New York, USA

A Velocity Prediction Program for a Planing Dinghy

183

Todd Carrico, Naval Surface Warfare Center Carderock Division, Bethesda Maryland, USA

Sail Aero-Structures: Studying Primary Load Paths and Distortion

193

Robert Ranzenbach, GLM Wind Tunnel & Quantum Sail Design Group, Annapolis MD USA

Zhenlong Xii,, GLM Wind Tunnel - University of Maryland, College Park Maryland, USA

Light Weight Sandwich Panels for Yacht Hull Structures

-

205

M. C. Rice,

: C - University of Maryland Baltimore County, Baltimore Maryland, USA

A. Fleischer, UMBC - University of Maryland Baltimore County, Baltimore Maryland, USA

D. R. Cartie, Cranfield University, Crrnfie1d, United Kingdom

Marc Zupan, UMBC-- University of Maryland Baltimore County, Baltimore Maryland, USA

Bibliography of Previous Chesapeake Sailing Yacht Symposia Papers

217

In Mernoriam

The 17th Chesapeake Sailing Yacht Symposium

is dedicated to

Edy Walsh

1949 - 2003

Frederick Wallace wrote:

"Ye can have yer steamboat racin', but gimme the run in a gale,

Of a well geared, able clipper, what is driven by snow white sail.

For I've known the thrill of a pilin' sea an' the sky in cloud flecked gown

An' fourteen knots in a windbag when she's running her Easting down."

Edy Walsh is that well geared, able clipper, driven by snow white

sail

These gifts were showcased every two years at the Chesapeake Sailing

Yacht Symposium, for which she was the Arrangements Chair This Symposium

is the premier technical forum in the world for sailing yacht techiiology and

regularly draws international papers and attendees.

Authors from England,

France, Spain, Italy, Germany, Holland, Switzerland, Argentina, Japan, Australia

and New Zealand are commonplace. All attendees perennially appreciated the

venue, snacks, meals and receptions, which Edy orchestrated.

Everyone,

including some of the most well known names in the sailing world, knew her and

were delighted to see her again. She needed a sailbag sized for a spinnaker on a

70 foot long International America's Cup Class yacht to carry home all the

compliments she received each time

Excerpt from the eulogy for

Edy Walsh

December 10, 2003

THE

17th

CHESAPEAKE SAILING YACHT SYMPOSIU

ANNAPOLIS, MARYLAND, MARCH 2005

th

17 CSYS Steering Committee

Executive Committee

John Zselecky

Stephen R Judson

Andy Ulak

J. Bergquist

Jaye Falls

Brent Canaday

Veronique Bugmon

Luke Shingledecker

Alon Finklestein

Marc Zupan

Advisors

Bruce Johnson

Richards T. Miller (Founder)

'Robert W. Peach (Foùnder

Papers Committee

Jesse Falsone

David A. Helgerson

J. Otto Scherer

John J. S lager

Thomas H. Walsh

Special Thanks to

Nancy A. Harris

Rick Harris

Edy Walsh

General Chairman

Papers Committee Chairman

Treasurer/Registrátion

Past Proceedings

CD Archive

Webmaster

Arrangements

Publicity

Publicity

Proceedings

THE

17th

_{cms4PiìÁxi SAILING YAChT SYMPOSIUM}

ANNAPOLIS, MARYLAND, MARCH 2005

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

The Society of Naval Architects and Marine Engineers

601 Pavonia Avenue1 Jersey City, NJ 07306

¡Ai

$AIL!N&

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

The U.S. Naval Academy Sailing Squadion

The Robert Crown Sailing Center, U.S.N.A., Annapolis, MD 21402

The Chesapeake Bay Yacht Racing Association

612 Third Street, Annapolis, MD 21403

TheSeventeenth CSYS was held on March 4-5, 2005

The papers were presented in the Francis Scott Key Auditorium Located on the campus of St. Johnt]s College

Annapolis,Maiyland, USA.

A Generic Mathematical Model for the Maneuvering and Tacking of a Saffing Yacht

J.A. Keuning, Shiphydromechanics Laboratory, Deift University of Technology

K.J. Vermeulen, Shiphydromechanics Laboratory, Deift University of Technology

E.J. de Ridder, MARIN, Wageningen

Summary

In the present report an extension of the mathematical model for the tacking maneuver of a sailing yacht, as previously described by the same authors in Reference [1], will be presented.

There is a need for such a mathematical model because the tacking maneuver and more in particular the speed loss during

such a maneuver, is of interest for handicapping purposes. If

this speed loss of a large variety of sailing yachts can be

calculated the

differences may be

incorporated in their

respective handicaps. This implies however also that this

mathematical model should incorporate

only

the use of

formulations based on "generic" parameters, which describe the hull form and the sail plan of the yacht under consideration. In the present report a more complete description of this model,

as available so far, will be presented. The accent is on the

hydrodynamic part of the model. As much as possible the

results obtained within the Dclii Systematic Yacht Hull Series

(DSYHS) will be used. In a future report also the aerodynamic part will be more extensively elaborated so that a wider variety of sail plans may be dealt with.

A number of simulations with the model have been performed and checked with the results obtained during a series of full

scale measurements.

i

Introduction

Formulating a maneuvering model of a sailing yacht under sail

has been the subject of research by various authors for some time now. In general these research projects have been carried

out for different reasons. Some authors were focusing on

finding the optimal tacking procedure (i.e. rudder action) for finding the minimal speed loss of a particular yacht during a tack. Others, van Oossanen in Reference [8], were aimed at

putting the influence of the applied rudder angle in the Velocity Predictions.

Most of these studies were in general conducted for specific yachts or group of yachts such as for instance IACC yachts. After the defmition of a reliable set of equations of motions

THE

17th

CIIIESAPEAJ SAILING YACHT SYMPOSIUM

ANNAPOLIS, MARYLAND, MARCH 2005

describing the maneuvering behavior of a sailing yacht most of the necessary hydrodynamic coefficients in the equations were

determined using dedicated experiments, such as forced

oscillation tests.

Other authors were more interested in obtaining insight in the

general maneuverability characteristics of sailing yachts under

sail. These later studies gained importance due to the ever

increasing scale of the cruising sailing yachts. Due to their size the draft restrictions imposed on them led to generally shallow

draft and so low aspect ratio's of the appendages. Both the

demand for proper "balance" of the hydro- and the aerodynamic forces and moments when sailing on a straight course as well as

the obliged safe operation of these yachts when sailing in

confined areas, where sudden maneuvers may be necessary to

avoid collisions etc., called for more insight in their

maneuvering behavior under sail. Here, often also the necessary

coefficients for the mathematical models, which were used,

have been generally determined using model tests.

In the present study the emphasis has now been put on

formulating a set of equations containing only coefficients, which could be determined using the design data of the ship

under consideration without the necessity of experiments. This

implies that these coefficients must be expressed in what is

called "generic" formulations containing only parameters

describing the hull form, appendages and the sail plan.

One of the possible applications of such a maneuvering model would be the use of the obtained results of simulations carried out for different yachts in some kind of "speed loss" calculation

during a tack. In its turn this could be used to refine the

handicapping procedures used around the world. In those

procedures it has been found that just considering the straight line up wind speed potential of the yacht alone, as it is being

predicted by the Velocity Prediction Programs (VPP),

is

actually not sufficient. Different yachts (even with similar speed potential on a steady course) may have different values for the "speed losses during a tack" and therefore the total time lost in

an up-wind leg may differ considerably. In order to be able to

calculate the differences between a large variety of yachts, the development of a simulation model is necessary which yields a

reliable prediction of the behavior of a sailing yacht during a

To develop such a "generic" model it was decided to make use of the available data obtained from extensive tests and analyses ofthe Deffi Systematic Yacht Hull Series (DSYHS).

The goal of the present study was to generate generally

applicable appmximations for

all the

coefficients in the equations ofinotions based on this well-established series.

The first action ¡n the present study was the selection of an

appropriate mathematical model from the existing literature.

It is evident that the tacking maneuver of a sailing yacht is a

rather complex maneuver. The by far most important difference with "normal" maneuvering models used for commercial ships

is the incorporation of the heel angle and roll motion and the large change of the propulsive aerodynamic forces during the

process. Also the in-stationary effects on the forces on both the

sails and the hull with appendages may complicate the things

even further.

After a literature survey and analysis it was decided that the model as previously presented by Y Masayuma in 1995, Ref [2], presented an excellent starting point. He showed in his

study that with a fair determination of the hydrodynamic

coefficients a very good correlation between the actual tacking maneuver measured at full scale and the results obtained by the simulation could be obtained. In his study he also used a neural

network technique to predict results on a more generic basis. This approach however will not be followed in the present

report. The idea is to use the extensive results and the database

as obtained within the Delft Systematic Yacht Hull Series

(DSYHS) and all the formulations and expressions based

hereon for the "generic" determination of the coefficients

To determine these generic formulations for the coefficients some results obtained within the DSYHS and presented by Keuning and Sonnenberg in 1998 and 1999, Reference [4], could be used straight away, such as the determination of the upright resistance and the resistance increase due to heel of an

arbitrary hull.

Another usable result came directly from the report published by Keuning and Vermeulen in 2002, Reference [1]. In this

report they presented a calculation method for the yaw balance

of (large) sailing yachts on a straight course. They formulated

generally applicable expressions for side force and yaw moment both in the upright condition and under heel of an arbitrary hull with and without the appendages.

In the present study these expressions from Reference [1] have

been further elaborated and refined. In addition they have also

been verified by means of a series of dedicated experiments in the towing tank of the Delft Shiphydromechanics Laboratory. The results of these tests showed the validity of the expressions

for a variety of hulls. Only the formulations for the side force

production of the appendages needed a correction to make them

more applicable for the higher aspect ratio appendages as

normally found on racing yachts.

Further an extensive series of dedicated forced oscillation tests with a 6-degrees of freedom forced oscillator, the "Hexamove", have been carried out with a number of models of the DSYHS to validate both the validity and the accuracy of the expressions

developed for the added mass in sway and the added mass

moment in yaw again both upright and under heel. From these

tests it became apparent that the presented expressions yield reliable results for the foreseen purpose. A summary of these

results will be presented here.

Finally, to be able to check the results of the full simulations for a variety of yachts, full-scale measurements have been carried out on the tacking maneuver with three quite different yachts.

The results of these tests confirmed the validity of the

mathematical model for the assessment of the speed and time

loss of sailing yachts during a tack and the use of these results for handicapping purposes.

2

The mathematical Model

As stated before the first action was to choose an appropriate set

of equations for simulating the tacking maneuver. Aller some study the model as proposed and used by Y Masayuma was

selected, Reference [2]. On his turn he made use of the model

and coordinate systems as presented by Hanainoto

et.al.

Reference [3].

The Eulerian equations of motions for the respective motions

become:

m(û - vi,) = X, + X,,11 + X,,,,,,, + X,,,,,

m(i' - u i') = Y,,,, + Y, +

J,,çii = K,,,, + K,,,, + K,,,, + K,,,,,,,,, J,,yi = N,,,,, + N,,dfr, + N,,,,

in which:

u = velocity along the X axis y = velocity along the Y axis

q' = roll angle = yaw angle

I = (total) roll mass moment of inertia J "(total) yaw mass moment of inertia

The origin of the coordinate system is located on the centerline

of the ship at the still waterline in the midship section at zero heel. The X-axis lies along the centerline of the ship with the

positive direction forwards. The positive Y-axis points to

starboard and the positive Z-axis points downwards.

Ignoring the pitch and heave motion of the yacht the

mathematical model cont'ins equations for four degrees of

motion, i.e. surge, sway, yaw and roll.

Masayuma modified this set of equations in the horizontal body

axes first through omitting the higher order terms considering

that these were not significant iii the present approach. He then modified the equatiOns for taking into account the effects of the

(large) heeliñg angle and the transformation of the added

masses and added moments of inertia from the body axes of the

boat to the horizontal body axes (figure 1) of the boat. In

addition we assume now that the centroid of the added mass is

located in the Center of Gravity of the yacht and therefore no additional moments and forces originate from the possible distance between these two centers. The possible effect of a non-symmetric added mass distribution over the length of the

yacht may be taken into account in a later stage or further

development. In order to be able to compare the results from the

mathematical model with trajectories derived from real scale

tests, the results of the mathematical model are transformed to an earth fixed co-ordinate system. The definition of this system is presented in figure 2.

Figure 2 Earth bound co-ordinate system The set of equations now becomes: Surge:

(m+ m,jù - (m+.m cos2

q+

in, sin2

9)vy'

=X,,+ X,,,,, +X,,vV/+ X,,, + X,,,,, Sway:

(mmcos'ço+m,sin29)1)+(m+m,,)uy

+2(m, - m ) sin cos q, vçb zrY,,ffl Ro1l

(I,,,+

» {(J,,

_jR,J(

+J)}sin çocosça. vçi

K,,,,,+K0çi +K,.,,,,,,,+ K,,,,, + K,,,,,,,,

Yaw:

{2, + .J,, )sin2«i +(I,,,+ J,,,)cos2 q,)ì

+2{(J2, j»(,. +J,,)}sinçocosço.yiçò

= N,,,,,, +N,y. + N,,, + N,,,,,

In the present approach the transformation of the added mass

terms from thebody axes ofthe boat to the horizontal body axes (figure 1) of the boat, as it is being used in the above equations

from Masayuma, is

no longer necessary since we now

approximate the sway added mass of the asymmetric 2-D

sections of the heeled yacht hull: in the horizontal plane directly. This method will be further described and verified later in this report. The method Used here follows the approachas suggested by Keuning and Vermeulen in Reference [1].

The terms with X, Y, K and N and their respective suffixes in

the equations stand for the forces in X and Y direction and the moments around the X- and Z-axes of the body fixed coordinate system The suffbc denominate where they originate.

Masayuma showed in his report, Reference [2], that the results

obtained from iinulations using this set of equations and the coefficients, such as he obtained them from towing tank tests (and calculations), showed close resemblance with the results obtained from full scale measurements. He concluded that

therefore that no immediate action was necessary for a further

extension of the equations in order to obtain valuable and

reliable results for the purpose of track simulation and speed

loss assessment. This is in particular true when considering the formulated aim of the present study, i.e. the ability to compare a large variety of yachts in a qualitative sense. This implies that a

broad range of validity is more important than a very high

accuracy.

So in the present study Masayuma's model was adopted. This was also stimulated by the fact that an approximation seemed

feasible for most of the contributions in this model. The goal of the present report is to be able to express all these contributions

now by existing formulations or expressions derived from the

data and results as obtained within the Delft Systematic Yacht Hull Series.

3

The added mass in surge, sway, yaw and

roll

The equations contain on the left hand side terms with the

added mass and added mass moments of inertia in the sway, yaw, roll and surge motion. So for an assessment of the sway,

yaw and roll added mass an approximation of the 2-D sectional added masses is called for.

The distribution of 2-D sectional added mass in sway is

necesaiy for determining hull yawing moments. Keuning and

Vermeulen presented in Reference [1] a suitable approximation

method for the sway added mass of an arbitrary 2-D section.

Their expressions are based on the simplifying assumptions that the area of a half circle element may approximate the 2-D added mass. Nomoto, amongst others, formulated this approximation.

Using this in conjunction with a correction factor taking into

account the effect of the cross sectional area coefficient of the section (as formulated by Keuning and Vermeulen) yields valid results for both the upright and the heeled section. So the total sway added mass may now be obtained by integration of this 2-Dvalúeover the length of the yacht, i.e.;

in which:

h)

drafi of the section under heel

Cyz(x) sectional area coefficient of the section

p

densizy of water

Lw! length of the static water line

The added mass in sway of the keel and the rudder may be

expressed as for that of a-simple oscillating plate, i.e.:

2p7rbksk

m k

= ______ for the keel and

I 2

Iaek +1

m,,r

_I 2

2pths

,Iae, +1

for the rudder.

2(bk+Tc)

a,

-I crei + ctfr L 2

a

2(br+Tc)

" [cre, + ci, L 2 In which:

x x-distance of midpoint section

The influence of the heel angle on the sway added mass is (again) accounted for by using h(x), which is the maximum

draft of the particular section under consideration when heeled.

The influence of the keel and rudder on the yaw added mass

moment of inertia may be found by multiplying their respective added masses with the distance to the center of gravity squared,

i.e.:

J,kr

=

mk

* ¡2+

mr

¡2

in which:

'k x-distance of keel(*) with respect to CoG

ir x-distance of rudder(*) with respect to Cog

the point on the keel from which the distance is

measured equals the 0.25 chord length at 43% of the

span of the appendage

Finally using a rather simple formulation as presented by Jacobs and which has proved valid for commercial ships, approximates the added mass in surge.:

Tc m =

2m

Loa in which: m

=pÍh(x)2C(x)dx

C(x)

= (3.33c,(x)2 -3.05c,,(x) + 1.39)

Loa length over all of the vessel

m solid mass of the vessel

4

The hydrodynamic forces in the model.

Masayuma described the forces and moments acting on the hull and the appendages due to leeway and heel by means of the

following expressions:

X,, = Xv2 + Xvb + Xçb2 + X,,v4

Y,,v + + Yv2 + Yv2q + Y,vt2 + Yçb3

KH K,v + IÇçb + K,v3 + Kv2 1b + K,vØ2 + Kq3

N,,. =N,v+N6+N_v3 +Nv2+Nv2+ 1VØØ

Within the framework of his study he found that using these expressions yielded good results for the sailing yacht under consideration. It should be noted however that all (or most) of

these coefficients describing the hull forces were determined by

applying regression on the results obtained from dedicated

experiments in the towing tank for the one particular yacht, that was the subject of his study. These tests comprised such tests as forced oscillation tests in sway and yaw or stationary tank tests

under heel and yaw. The formulation of the forces in Taylor

expansions is common in naval architecture when dealing with

maneuvering coefficients and also

based on the use of

regression on the experimental results. The sail forces and rudder forces were derived separately and largely based on

well-established "thin airfoil" theories and available wind

tunnel data.

In the present study the approximations of these forces will now be derived from the results of the DSYHS. This will imply that

some of the usual expressions for the forces such as they are formulated above will be replaced with other formulations

yielding similar results.

4.1

The determination of the hydrodynamic

coefficients

The forces on the hull and appendages are approximated by

making use of the results of the DSYHS. It should be noted

however that there is a significant difference in the

formulations, which has to do with the difference in coordinate systems used between the DSYHS reports so far and the present study. The expressions presented so far in the framework of the

Dclii Systematic Yacht Hull Series are derived for the use in

Velocity Prediction Programs, which implies that the X-axis is parallel to the velocity vector of the ship through the water and the side force is perpendicular to that direction along the Y axis.

in the present report however all the forces are described in a

body fixed coordinate system with the X-axis pointing forward

along the centerline of the ship. This is common practice in

maneuvering models. So the difference between the two set of

formulations lies primarily in the effects due to the leeway

angle of the yacht, if applicable. In general with sailing yachts however, even during a tacking maneuver, the leeway angle will

remain rather small when compared with the drift angle

of

"normal" commercial ships during a maneuver, Where it may

reach values as high as 30 -40 degrees.

In the followmg paragraphs for each direction and for all of the various components the derivation will be presented.

4.2

The forces acting up on the yacht along

the X-axis due to forwaid velocity

The forces in the X direction are actually the resistance

forces due to the forward speed of the yacht, incremented by the

effects of the heel angle, the leeway angle and the side force

produced The expressions for these resistance forces are similar to those as previously formulated by Keuning and Sonnenberg in Reference [4].

For the frictional resistance of the hull use is being made of the

well-known ITTC-57 formulations for the extrapolation

coefficient. In correspondence with the procedure used in the

DSYHS the Reynoldsnumber of the hullis based on 70% of the waterline length. No form factor for the bare hull is being used, because such an expression foran arbitrary hull isnotavailable. In the expressions for the viscous resistance of the appendages

the generally expression based on relative thickness of the

section is used, see or instance Hoerner, Reference [9].

The polynomial for the residuary resistance of the bare hull used in the present model is the làtest version as presented in 1999, Reference [4]

The residuary resistance of the keel

appendage is from the same origin.

The total force due to the forward velocity along the X-axis (i.e the resistance with no leeway) as taken from Reference [4] now becomes: Fx,=-Rfh, - Rrh, Rvk, - Rv, - Rrk RJh, =pu'ScCf (Iog(Rn) .2)2 Rik, =Rfk/'l+kk) RJk =i-pu2S,Cf,, (1+ kk)

=[+

2.i_60(!5-]]

Rvr,= Rfr(1k,) Rfr, =fpu2scf.

(1 k,)

_{={1+2!+60(!!_Ij']} Rrk Tc bk Tc i- Zcbk Vc

'--A,A,

+A

+4-Vkpg Bwl _Vk4 Vk In Which:

6.

Fn2ço LCB Vc BwI Vc

a, +a2Cp+a,

-Lw! Aw

+a +a

'Lw! Sc Rrh Vc =a,+ Vcpg _{LCB (LCB2} Lw!

+a+aI----I

+aCp'

'LCF ..Lw1) 8 /

Rrh residuaryresistance of canoe body N RJh frictional resistance of canoe body N

Rvk viscous resistance of/cee! N

Rvr viscous resistance of rudder N

Rrk residuary resistance of keel N Cf frictional resistancecoefficient of canoe body

Rn reynolds nuber of canoe body

Vc volume of displacement of canoe body

g acceleration ofgravity ,Ws2

Bwl beam of waterline m LCB longitudinal position center of buoyancy tofpp m LCF longitudinal position center offlotation tofpp rn

Aw water plane area'at zero speed

Sc

wetted surface canoe body at zero

Cp prismatic coefficient

speed m2

m2

upright

Cfk frictional resistancè coefficient keel kk form factor keel

tk mean thickness keel

4

meanchordlength keel m

CjÇ frictional resistance coefficient rudder

kr form factor rudder

l mean thickness rudder m

mean chord rudder m

m3

17c volume of displacement of keel

Zcbk vertical positionof centerof buoyancy of keel m

0.075

Suffixes:

u longitudinal velocity rn/s

y transyerse velocity rn/s

q; heeling angle

rad

w yaw angle

rad

The coefficients of the various polynomials in the formulations above are presented in appendix.

The resistance due to the heeling angle of the yacht alone, so without the forces originating from the induced resistance, as

caused by the liii force generation, ingiven by:

Fx,,,, =zlRrhço,9 + 4.Rrkço,, + z1Rjhq Lwl Bwl

u0 + u, - + u2

8w! Tc

+u:cB+uLCB'

(Tc±bk)

Tc Tc Bwl

_+114-

Lwl

(Tc+ bk) Tc

Vc LIRTh,9 Vcpg LlRrk,9 Vkpg

u

Fn

=

in which:

ARrhço change in residuary resistance N

of canoe body due to heel

4Rfhço change in frictional resistance N

of canoe body due to heel

4Rrkço change in residuary resistance N

of keel due to heel

Scço Wetted surface of canoe body m'

Fn under heel

Cm Froude number

midship section coefficient

and the coefficients of the polynomials for the additional

resistance due to heel for the bare hull, the appendages and the change in wetted area due to heel are presented in the appendix:

4.3

Forces along the X-axis due to the sway

velocity

The forces in the ship bound X-direction originating from

the side force production on the hull and the appendages are the

summation of two components: one (small) component due to

the lift itself and the second (larger) component which is due to the induced resistance. So:

Fx,,

Fh cos(ço) sin(._LJ

- RÇ cosi - I

-u)

1+ I

loo

2''

Bwl (Bwl

s0+sj-+s2I

Tc Tc + s3Cm

ßJLpJÌ52S

ßFh.o=O.0092Thhhl Tc ço2Fn

Tc (Tc+bk)

Drag = Ri 2 Ri

- ,rTe1pVs

(Tc+bk)

( \2

\

A Tc +A Tc

'(Tc+bk)

(T+bk)J +

Thy! A3 + A4TR . Tc Fyuv

Figure 3: Side force due to the transverse velocity of the yacht

It should be noted that in the present formulations the leeway

angle is now defined as the fracture of the transverse velocity y and the forward velocity u, according to:

B0 +B1Fn)

4.4

The forces along the Y-axis due to the

sway and roll velocity

The forces on the yacht along the Y-axis are the swnniatiofl

of components associated with the body fixed lift- and drag

forces also. The lift is generated by the sway velocity (O

Fhcos(qo) =

'

(Tc+bk)2

'(Tc+bk)"2

Tc b1 _+b,i Sc

₎

Tc (Tc+bk)' +b (Tc+bk)

i

4(Tc+bk) Sc =

- Rjk

RJh =

2CJ3c Te In which: Fh Heeling force N Ri Induced resistance N

TR Taper ratio of keel

Fn Froude number based on waterline length

leeway angle) of the yacht and also by the change in the angle

of attack that originates from the combination of the induced

velocities by the roll motion (combined with the fOrward

velocity) Similar to the situation when dealing with the forces

alòng the X-axis here also a component of the rèsistance enters

in the equations. The principal parts of the formulations again

are obtained from Reference [41:

So the Y forces dueto the sway velocity now becomes:

Fy9 =Fh cos( q'),

cos{.'_J

+ RÇ0

sin(-'_Jj

(Tc +bk)2

+ b

((Tc + bk)2

Sc 2 Sc

₎

Dc

+b

Tc

(Tc+bk)2

(Tc + bk)

(Tc + bk)

Sc

*tI+

ßFh=oJ+pVs2Sc

Fhcos(ço)

= Fh R J irTe7 pVs2

fi

_,Fh-O = 0.0092 Bwl Tc ço2Fn Tc

(Tc+bk)

Te

(Tc+bk)

(

Tc f Tc A

+Al

'(Tc+bk)

2(Tc+bk)

+A .

3Tc

(B, + B,Fn)

and the additional lift forces dueto the roll velocity transformed to the horizontalbody axes:

Fy,

=[Fhcos(o).4 cosf:!!fJ +Ri Fhcos(ço) = Te (Tc+bk) f Tc A (Tc+bk) +A Tc Fxr =

Fhr cos(qi)sin

and for the force in Y direction:

Fyr =

Fhr

coS()cos(_ b,

(Tc±bk)'

b[(Tc +bk)2

j

Fhr =

pVs2Alat, lr

b3

(Tc+bk) Tc (Tc+bk)2 Sc

*fJJLPVS2SC

Tc (Tc+bk)

Figure 4 side force due to Roll velocity

B3 +B,Fn)

4.5

Forces along theX and Y-axis dueto the

yaw velocity

The assumption is now made that the sailing yachts under consideration have a more or less traditional appendage layout. This implies that the keel is positioned close to the longitudinal

position of the center of gravity of the yacht. This makes the

assumption justifiable that the inflúence of the yaw velocity on

the forces on the keél is neglect able So the forces on the

appendages dUe to the yaw velocity are restricted to the forces on the rudder only.

Forthe force in X direction we find:

Dr cos

)

w + Dr

sin1--u)

r RL.= Th3 ,rTe2 -1-pVs

B

vr

4Fyr

Figure 5: side force dueto Yaw velocity

in which the lift curve slope is calculated using the well known expression from Faulkner:

5.7a,,

4.6

Moments atound the X axis due to heel

angle and the sway- and roll velocity

The moment around the X-axis due to the heel angle of the

yacht is the obvious and well-known hydrostatic stability

moment of the yacht. From the results of the DSYHS it is

known, that the influence . of the forward speed on the

hydrostatic stability (loss of stability) for speeds below Froude numbers of O45 for not extreme hull shapes as far as beam. to draft is concerned, is well Within a few percent. In the present

model therefore this effect is neglected. Since detailed

information of the yacht is not assumed necessary yet a feasible simplification is used So thestability moment is assessed using the GM value as a starting point. This modest simplification has

been proven quite accurate for a large variety of yachts for

heeling angles up to 30 or 40 degrees. So:

K,, =GMsin(p)zlg

For the approximation of the heeling moment due to the _sway velocity use is being made of the approximated vertical position of the center of effort of the total side force on the hull, rudder

and keel as also derived from the results obtained within the

Delft Systematic Yacht.Hull Series, i.e.:

K,, Fy,, * _{43(bk + Tc)}

cos(sp)

For theside force due to sway velocity the expression as

described earlier in this paper is used. In thiscase however, the term PFI.O is omitted.

The same approximation forthe center of effort of the side force is used when approximating the additional heel moment due to the induced roll velocities, i.e.:

K,,,

Fy,,,

*043(bk+Tc)

cos(ço)

The side force due to roll velocity is calculated using the

expression for the side forçe due to sway velocity, in thiscase

we use the angle of attack induced by the roll velocity

çj,*043(bk_{+ Tc)}

u

Due to the fact that the roll velocity induces an angle of attack on the rudder, the resulting rudder force will generate a yawing moment. This yawing moment is calculated by using the saine

approximation for the yaw moment due: to yaw velocity, but nowthe angle of attack on the rudder isgivenby:

* O. 43br u

ôß

J.8+cosfl

/ a,,2 +4 V cos4 Ar

2 br

a=

cre, + cl, L 2

and for theadditional induced resistancethe thin airfoil theory is usedto yield the followingexpression:

=LpVs2Alat,Cdi Cdi = Fh2 =

-pVs2Alat,,ra,, In which:

Fhr

heeling force rudder _N

Ri induced resistance rudder _N Alat lateral area ruddder

Cdi induced cfrag coefficient rudder Cir 4/i coefficient rudder

4.7

The yaw moment due to the sway velocity

For the approximation of this Yaw moment extensiVe use is

beingmade of the results reported by Keuning and Vermeulen

in Referenee[1].

They assumed the total yawing moment ofthe appended hull to

be composed of three separate contributions: the hull, the keel

and the rudder.

So the principal contributions to the yaw moment read:

N9

=N 9Keel + N 9Rudder + NHu11

N,9kee1=FyIç9 *1k

NRudder

=Fyç9 *Ir

Due to the fact that the DSYHS expression given in Reference

[41 is used to calculate the total side force, the separate side

force contributions of keel and rudder are not known. So, in

order to account for the separate contribution of keel and

rudder, a distribution between the side force on the (extended)

keel: and the rudder is assumed, similar to that used in the

upright case. Using this distribution, the side force contribution from hull and keel can be separated from the contribution of the rudder. There are two reasons for using the DSYHS expression instead of the Extended Keel Method to determine the hull, keel and rudder contributions to the total side force:

The extend keel method does not take in account the

effect of heel on the lift generating capabilities

The 'downwash effect'

from the keel on the lift

generated by the rudder is implicitly incorporated in

the DSYHS expressions,

The downwash of the keel diminishes the effective angle of attack of the rudder. The effect will be dependent on the keel

loading, the aspect ratio and the distance between the two foils.

In particular when the tip vortex "hits" the rudder a strong

reduction may be expected. For the usual layout with moderate to high aspect foils and a reasonably large distance between the two, the following formulation has been proven to bevalid:

1.6Cl 4i

The procedure to determine the side force distribution in the

upright case is given in the 4 steps below:

i Calculation of the induced drag and side force for the

known velocities, in the upright case, using the DSYHS formulation Reference [4]:

Te(ço=0)

(Tc+bk)

2 Calculation of the side force and related induced drag

hull and keel, using the Extended Keel Method, note

that for the upright case, the Extended Keel Method is valid: C1k 5.7a,, aß 1.8+ cosA cose A+

2(bk+Tc)

= crek + Cik

[21

Fhk = p Vs2Alatk 2

_ôßLu

Fhk2

Rik=

- pVs'Alatk;7rak

3 Calculation of the fration of keel+hulI side force and

inducedresistance with respect to the totalside force:

jhk

Fhk,,

frk=--4 The contribution of the rudder now becomes:

jhr =1 jhk

frr =1 frk

This distribution of the side force and induced resistance for the upright situation in terms offllk, fr/c Jhr and frr is now used to

calculate the separate contributions of keel and rudder under

(Tc+bk) 3.6246f Tc J' (Tc+bk) +0. Tc 0. 0296TR 1.2306 0.7256Fn) Fh f 2.025(Tc+bk)3+9551

(Tcbk)2j

Sc Sc Tc Tc (Tc+bk)2 +0.631 6575 (Tc+bk) (Tc+bk) Sc _, IJL)LpVs2Sc Fhc2 'rTe2-pVs2 Tc

heel, using the DSYHS formulation Reference [4] for th total

sideforce under heel:

Keel: Rudder:

Drag,

Fh 2 Ri =

'

irTe'4pVs'

Fyç, =

Bwl Tc çû2Fn =000P2 Tc (Tc+bk) (.Tc A Tc ' (Tc+bk) Te

f

Tc ' +bk)

2jTc+bk)

+A

'Tc

_i Fh cos(q,),,,, (Jhr)cos

+ RÇ,(frr)sii

/ ., -V

,u

B, +B,Fn) Fhcos4o),,, in which: Te (Tc + bk) ' (TO+bk) Tc

(Tc+bk)2

'fTc+bk)

Sc ,}LPVS2SC Bwl Tc ço2Fn = 0.0092 Tc (Tc+bk) Drag = Ri,, Fh 2 R0Ç

-

_j

rTe'-2-.pVs' b, (Tc

c2 ±

b2['Tc +bk)2 2" Tc I Tc A, +A,I (Tc+bk) ,(Tc+bk) Bwl Tc

fhk

fraction of the total side force

-due to hull and keel

frk

fraction of the total induced

-resistance due to hull and keel

fhr

fraction of the total side force

due to rudder

frr

fraction of the total induced

-resistance due rudder

2\

I

(B, +B,Fn)

The side force on the appendages is located on the quarter cord

length of each foil and their respective contribution to the

yawing moment is calculated using these positions with respect to the center ofgravity of the yacht.

The yaw moment on the bare hull was formulated 'by an

improved method for the assêssment of the Muñlt moment and based on the theory formulated by Nomoto in Reference [6] for

the yaw moment of an arbitraiy hulL For the improved

forniulátion' of the Munk moment use is being made of the integration of the change in sway added mass over the entire

length of the hull instead of over just half the length, as is

common practice with commercial vessels The sway added

mass is calculated using the approximation method of NomotO with a correction for different Cm valües ofthe sections. Under

heel the sway added mass is approximated using the actual

maximum depth of the section when heeled

Fmally a"

additional' leeway angle is introduced m the NomOtO expression to take care of the "additional" yaw moment of a

yk,,, = +

Rc,(frk)siii(iL)

I-2"

b,

(Tc+bk)'

+b

1(Tc)2

Sc _2L Sc Fhcos(ço),, = Tc

'(Tc+bk)

Tc (Tc+bk)2 +b (Tc+bk) Sc

_I

yacht hUll caused by the just asymmetty of the hull alone when heeled over.

For a more detailed description of the method developed to

assess the yaw moment, reference

is made to the report

presented by Keuning and Vermeulna on this subject in

Reference [1].

The Munk moment is a fully inviscid flow phenomenon and calculàted using the change of momentum of the oncoming

fluid In a real fluid however it is assumed that this type of side

force generation reduced by viscous effects, such as vortex shedding and flow separation. This reduces the yaw moment

when compared to the full pQtentiai flow. This effect increases

with increasing leeway angle. In the literature this. effect is

associated with athwart forces related tothe so called cross flow drag, i.e dÈag forces arising from across flow over the sections due to the sway velocity of the ship. For commercial ships this.

effect will be different from a yacht hull., The more V shaped

sections at the bow will have a higher drag than the flat bottom

or rounded sections m the stem of the yacht This will tend to

increase the yaw moment. Also the effect of the bow wave due to the higher Froude numbers will be more significant.

Finally the yaw moment on the bare hull is approximated using

the expressions as derived in Reference [1], presenting the

corrected MUsik moment and the additional moment due to the

asymmetiyofthehull when heeled, i.e.:

Nhull =

Lw!

*Jh(x)2(333c(x)2 .3.O5c(x)+ J39»

+ MzO MzO = CMZOLpVSlLw1A, CMzO O. O1Bw12 LwlTc

4.8 Yaw moment due to yaw velocity

Once again assuming the "normal" layout

of the

appendages the side force generated on the keel due to a

rotational velocity in yaw is considered neglóctible, because it is

positioned close to the centre of gravity of the yacht. Also in a

turn there is supposed to be no down wash effect from the keel on the rudder. Under these assumptions the yaw moment.due to

the yawvelocity reducesto:

N, = Fyil

in which the force in the Y direction is composed of both a lift

and adragcomponeataccording to:

Fxç,. = Fhç,,.cos(ço)

sin(-J

- Dr

and for the force in Y direction: Fyi = Fhr cos(ço)cos + D,. smi _L_..

w

Fhç,

LpVs2Alat

in which the lift curve slope is calculated using the well known expression from Faulkner and for the additional induced resistance airfoil theory is used toexpress:

Dr. =

LPVS2AIa,Cdi

Cdi

=

Dç,

₌

Fh'

-pVs2Alat,ira,

4.9

Additional forces on the rudder.

For the lift forces on the rudder the lift curve slope

approximation of Faulkner is being used, quite similar to the

procedure used with the keeL As explained in Reference [lithe Extended Keel Method as presented by Gerritsma m Reference

[5] is used to take into account the end plate effect of the hull

and the increased velocity over the keel being below thehull The rudder however is situated in the steady state condition (i.e

on a steady close hauled course) in the downwash of the keel.

This effect is felt by a reduction of the effective angle of attack on the rudder when compared with the keel and in a reduction of the "free flows' velocity over the rudder, i.e. the wake of the

keel and hulL A typical velocity reduction over a rudder is presented in the Table below based on results obtained by

Gerritsma in Reference[5] Table 1: velocity measurements

UfmIs] 0.90

i2O 15Ó

1.80

U2[m/sj 0.83 1.02 1.30 1.63

Based on these results a wake factor of minus 10% of the free

flow velocity is implied on the rudder velocity.

Besides the effective rudder angle due to the leeway of the yacht in the present model account has to be taken of active rudder manipulation by the helmsman or course controL This

implies additional lift and drag forces on the rudder as function

of the rudder angle applied'. These can be divided in force

componeutsalong the X-axis and the Y-axis respectively. The forces along the X-axis are:

Fxr = Fhi cos(ço) sin

- m

_cos1tL

uJ

Fyr5 = Fhi5

cos()cos(._]

+ Di

Fyr5

=!p(O.9Vs)2Ala12&

In these expressions the lift cûrve slope is calculated using the well known expression from Faulkner as presented here for. The additional induced resistance is approximated using thin

airfoil theory. This yields:

Di =i-pVs2Alat,Cdi Cdi =

Di Fyr,52

L

_pVs2Ala1,ra,

In which:

rudder angle

rad

The yaw momentdue to rudder angle now becomes:

N,8 = Ir * Fyr,6

And the roll moment due to rudder angle: K,., =_O.43br*Fyr,5

5

The sail forces.

The mathematical model presented in this report only

contains a limited version of the full aerodynamic model as it is

presently used in many Velocity Prediction Programs. This model described here is only used fòr determining the lift and

drag forces on the sails of various sail plans and the drag forces

on the rigging and the superstructure. In the present model the customary optimization routines such as "flat", "twist" and

"reef' are not incorporated because this was not felt necessary

in this stage of the project. Since the maneuvering model may

be used for the comparison of a much larger variety of sailing

yachts in the foreseeable future this certainly is considered to be a draw back. In the near future this will therefore be overcome by implementing the fur more versatile and' extensive sail force model similar to those presently used in the Velocity Prediction ProgI!1ps. By doing so, two other possible applications of this

time dothain thaneuvering model become available: first the

time domain simUlation of the "steady state" sailing conditions

under the influence of for instance fluctuating wind velocities and secondly the starting condition of the tacking maneuver

might be closer to the result of the velocity prediction obtained so far;by the use of VPP's.

For the sake of speeding up the calculations in the simulations

the forces on the sails in the present model are approximated

using a slightly adapted and simplified procedure. The model is based on the well.known approach from George Hazen. In later

years this method has been extensively modified by, amongst others, authors as Andy Claughton c.s. and a considerable

amount of effort has been put into this within the frame work of the International Measurement System,.Reference[7].

The basics of this aero model lie in a lift and drag coefficient

curve of the individúal sails (in this case mainsail and jib) over

a range of apparent wind angles, say between 30 and 180

degrees. For application in the present model this range of

angles of attack is slightly different from the usual range in the VPP environment because now these coefficients also need to

be defined for very small angles of attack between O and .30 degrees apparent wind angles. These angles do occur during a

tacking procedure. The values of the lift and the drag coefficient in the "usual" range of angles of attack for functional sails are taken from publicationsabout the IMS sail force modeL The plot of the lift and drag coefficients values used in the calculations ispresented below. It should be noted that there is a significant resistance force due to thesails at very small:angles of attack toaccount forthe resistance of the flapping:sails.

6, .

06

20 120

App,tI.d - [4.11

ISO

Figure 5: The Ifl añdd,lag coefficienst of the sails

The sail plan options in the present approach consists of the full

main sail and a 100% fore triangle. The choice can be made

between.a fractional and a masthead rig.

An addition to the usual approach is found in the fact that the apparent wind speed and the apparent angle of attack on the sails is affected by the forward velocity of the yacht and the induced velocities at the assumed center of effort of the sail by the roll- and the yaw motions1 The center of effort of the sails IS

assumed to be at a height of 39% of the height of the sail

is found from the geometrical centroid of the areas. In the

formulations Zce is the vertical distance and Xce the horizontal distancewith respect to thecenter of gravity ofthe yacht.

X

Figure 6: Definition of the sailforceson the yacht

So the expressions for the areas and the center of efforts of the sails now read:

mainsail:

A =05PE

Zce,

=039P + BAD jib: Ab =0.

5JJl

+ J2 ZceJb =0.391

To obtain the total lift and drag of the sails the coefficients of each sail are multiplied with theft respective area and added.

The lift and' drag coefficients of the total sail plan are found by division through the nominal sail area. This yields the following expressions: (C/rn *A, + Cl) * AN (Cdnm * A + Cdpj * AN AN=

A, + AF

AF=0.5 * J * J

Cdp='

Interaction betweefl the two sails is ñormally taken into account by the a rather simple approach usina "blanketing functions". In the present model however these are not relevant because these

blanketing functions only come into play at apparent wind

angles considerably larger then those found in the close hauled sailing conditions.

The indtced drag of the sails is computed using the thin airfoil

theory once again. This implies that the induced drag

is

proportional to the

lift coefficient of the sail squared and

inversely proportional to the effective aspect ratio of the sails. Since we will be looking here only at close hauled courses the follöwing expression has been used:

Cdi = Cl' * ( ¡ + 005 ir* A Re

ARe

(1.1(EHM+F4))

AN

The drag of the;rigging and topsides is approximated by: CdO= ¡

13(BMAX*FAEHM* EMDC)

AN

The total drag coefficient now becomes:

Cd='Cdp + Cdi+ CdO

The expressions for the apparent wind' speed and direction in

the present model taking into 'account the induced velocities by the roll and the yaw mbtioñsnow read:

= «j(Øzce+

yilce v

sin(ß.))2+ (v cos (ß,))2

(Zce+ yiXce+ V, sin('ß)

vcos(ß)

The X and Y forces of the sails as well as the Kand'N moments induced by the sails are expréssedby the following equations:

X,mi= )PA V .Sa.Ç

}Ç!.PA.VWSaCY

K,,,, = Y,,, Zce cos

N,,,,=X,1 .Zce.sinço+}Ç,1, Xce In which:

C, =Cl.sin(ß)Cd.cos(f3)

C, =Cl.cos(/33+Cd.sin(ß)

Apart from the heeling moment due to the sail forces also a yawing moment is introduced when the boat is heeled over, a

rather significant component in the'equations

6

Results from the forced oscillation

experiments.

In the framework of the present study forced ,oscillation

Shiphydromechanics Department of the Deffi University of

Technology.

The aim of these tests was to validate the approach as presented

by Keuning and Vermeulen

in Reference [1]

for 'the

approximation of the sway added mass both in the upright

condition as under heel. It wa& decide to investigate the

influence ofthe following parameters on the sway added mass. The influence of hull depth

The 'influence of heel' angle

The influence of the forward velocity The influence of the frequency of oscillation

Hereto four very different models of the DSYHS, one from

Sub-Series i

and three of Sub-Series 2, have been tested

underneath the new 6 degrees of freedom oscillator from the Department. The principal dimensions of these models are depicted in the table 'below. For more detailed information about the body plans of these models reference is made to the

literaturedealing with the DSYHS, such asReference [4].

Table 2 Syssers usedfor the validation

The tests have been carriedoutat three different heal angles, 'i.e. 0, 20 and 30' degrees, at two different speeds, je. Fiv"0.30 and

Fn0.40 and at a number of different oscillation frequencies

between 0.447 rad/sec to 0.373 rad/sec.

SYS Lwl/B BwLic' Lw1fVo1c

6 3.155 2.979 4.339

24 3.497 10958 6.935

25 4:000 5.388 6.003

o

Ome (rad/s] Added mass in Sway

SYSSER 25Heel=0 a a

:

X X * U Fn0.3 En0.35 XFs=0.4 CSYS 2003

Figure 7. Added, mass .derivedfrom oscillation tesis compared tocalculation of added mass according to CSYS2003

formulations upright

0rne (radis]

-Figure 8: Added mass.derivedfrom oscillation tests compared to calculation of added mass according toCS YS2003

formulations at 20. degrees of heel.

O 0.5 1.5

0me (rad/s] Added mass in Sway

SYSSER25HeeI2O 4000 3000- a a aFn=0.3 Fn0.35 2000 XFnO.4 CSYS 2003 1000 o 0 0.5 I I.S 10000

8000-Added mass in Sway SYSSER 6 Hee1=0 e

_.

a a

.

a 12000 10000 80005

Added mass in Sway SYSSER 6 HeeI2Q

.

Fn0.3 Fn0.3 w 6000- A A a Fn=O.3S 6000 - A A AFn0.4 LFn=0.4 4000 _ICSYS2003 4000 - CSYS2003 2000 2000 -o o 1500 1000 500 o

Added massin Sway

SYSSER24HIO a x X

I

_x 2500-2000! 1500-1000 500 -o

Added mass in Sway SYSSER24 Hee120

I.

* o X Fn0.3 Fn0.35 S CSYS 2003 aFn0.3 Fn0.35 * Fn0.4 CSYS 2003 lnm 6000 4000 2000 o

Added mass in Sway SYSSER 27 HeeI=0

s

I.

X X 8000 6000-to . 40002000 -o

Added mass in Sway SYSSER 27 Hee120 5, a L U X Fn0.25 a Fn=0.3 AEn0.33 Fn0.35 * Fn0.4 CSYS2003 Fn0.3 AFn0,33 Fn0.35 XFn=0.4 CSYS2òO3 o 0.5 1.5 Omega (radis] 0.5 15 0.5 I'S

0m (rad/s] Omega (rad/s]

0.5 1.5 0 0.5 I 1.5

Om (radis] Omega (radis]

3000

-u

2000 X 1000

Someof the results of these tests are presented in Figures 7 and 8. In these figures the added mass in sway is compared against the results of the calculations using the procedure as presented in Reference [1]. The results are shown for the four models and

for the zero degrees of heel and the 20 degrees of heel

condition. The results are depicted for a number of different

forward speeds and oscillation frequencies. The thick spot at the omega O axis is the result of the approximation, which is

independent of speed and oscillation frequency.

From these results it is obvious that the approximation for the

upright condition is reasonably accurate. It should be reminded that the actual value used inthe calculations is the value at zero

frequency of oscillation which value obviously may only

obtained from the measurements by significant extrapolatiOn of

the results. From the results however it is obvious that in. the frequency range investigated there is no strong dependency of

the sway added mass on the frequency of oscil1ation

The results of the measurements also show a considerable

influence of the forward speed on the added mass in sway. In general it may be seen that the added mass in sway decreases

with increasing forward speed. This is not accounted for by the

present method. Where this speed dependency originates from is not exactly clear. Part of it may be due to the wave system

generated by the forward speed and in particular the bow wave.

Also it should be noted that during all the experiments no free vertical motion of the model was allowed, so no sinkage and

trim during the experiments at speed. This also will have

increased the height of the wave system around the hull at

speed.

In general the effect of the heeling angle is properly accounted for by the approximation method used. This conclusion seems not valid for Sysser 24, which is a very high beam. tè draft ratio model. For this model the increase in added mass due to heel is predicted much higher than the measurements indicate.

The overall conclusion so far however is that the presented approximation method yields very usable results in the frame work of the presentstudy.

7. Compaiison

of

the

rèsuits

of

the

simulations with full-scale measurements.

The validation process of the maneuvering model has been split in two separate parts:

the validation of the accuracy and reliability of the

hydrodynamic model using the approximated coefficients and forces

the validation of the tacking model including all the

aerodynamic forces and moments.

The first validation may be carried out by performing regular maneuvering tests for ships i.e. zig-zag and turning circles

tests.

These measurements have been carried out at full scale with

three different sailing yachts. To eliminate the influences of the

aerodynamic forces these tests have been carried out with the

yachts being propelled by their own engines (and thus no sails). The yachts used for these full-scale experiments were:

Bashford4l

J-35

Staron42

In additiön the results as presented by Masayuma for his half ton yacht Fair V have been used. In all cases the differences between the turning circle diameters measured and computed

were within 5%, which was considered to be quite accurate. A typical example of such a comparison is presented in Figure 9 for the Bashford 41 "Checkmate". Therudder angle input signal was taken directly from the full-scale measurement results.

T.).d,,y

f

1-1

-- -- --J-- -- --I---- -- --J -- -- L i i r I r I I - - -1- - - r- - -4 - - I-r i r r r I t -r r i i -r-r i i 0 10 20 30 40 50 60 70 60 X ('J

Figui-e 9 ZigZag measurements

f1 i I I i I r i r i -\4ii

T'r

i r r r r r r r -' 4 I -r

Figure lO Turning cirkie measurements

Similar results were obtained with the other yachts and under

different conditions as far as forward speed and rudder angle is

concerned. Therefore in general it may be concluded that the hydrodynaniic model appears to work well and at least yields

almost similar results as obtained by Masayuma with the

coefficients and forces obtained from model experiment& To check whether the present model with the calculated forces

and hydrodynamic coefficients under sail yields also similar

results when compared with results obtained by Masayuma, bis

full-scale tacking maneuver measurements of the half-tonner

Fair V have been recalculated using the present model.

Masayuma found a good correlation between his simulation and the full-scale measurement and so does the present model. The

simulated and measured track of this yacht in

a tacking

maneuver may be seen in Figure lO Although not shown here It

1 b -r

j

L. O IO 20 30 40 50 60 70

is mentioned that similar agreement was found with the results of the speed-loss, the heeling angle, thecourse etc.

O 10 20 30 40 50 60 70 80 90

X, (ml

Figure 11 Tacking maneuver "Fair V"

In the scope of the present

study also some full-scale

measurements on the tacking maneuver have been carried out for validation purposes with the same yachts as mentioned

before.

The measurements with one of these yachts, i.e. those with the

Bashford 41 "Checkmate", produced the most accurate and

reliable results due to the very good environmental conditions at

the time of the measurements and due to

the excellent

equipment onboard. This consisted of a very sensitive and highly accurate dedicated GPS receiver, capable of measuring displacements with accuracy in the order of magnitude of 10 centimeters and with a very high sampling rate. The result of one of the tacking maneuvers carried out with Checkmate is

presented iii Figure! 1.

Trajectory

58 rn/s

- Simulated boatyosilion - Simulated sail position

- Simulated CoG position

r Measured CoG position

L

X [m(

Figure ¡2 Tacking maneuver "Checkmate"

Some more results as time histories of :boat speed and heeling angle obtained from the same maneuver are presented in figure

13 and 14. 3.5 2.5 0.5 Bo.I.pred tO 20 30 40

Figure 13 Boat speed during tacking maneuver "Checkmate"

Had

-,

- - L - - - L

Simulated boat poioton

-Simulated sail poaitioo

-i- Simulated CoG position

r Measiaed CoG position

1 o o o 1 - - .5 - - - I - - - L. o i I I - - .1 I I I I 1 i r--40 -20 0 20 X (ml

Figure ¡5 Tacking maneuver "J-35"

Sioslaled

4 Measured

Sim,lut,d

è Measured

Ted '1

Figure 14 Heel angle during tacking maneuver "Checkmate"

The results of the full-scale measurements with the J-35

compared to the simulation results are presented in the figures below.

Trajectory Coriorlsai of. ach Ing rajettorIes

WPed vabolty 0.5mO simulated - measured

-Startof ttcldng go 80 10 60 50 E 40 30 20 10 -10 100 -50 o 50 40 60 80 -80 -60 120 -loo -80 E -60 5. -40 -20 o o 20 4° 60 3-80 loo 120

3.5 IO 20 Thrs) Bo.e .e4 -SiusrIsIed Measured

Figürel6 and 17 Boat speed and heel during tacking

maneuver "J-35

8.

Applications

The model may be used for handicapping purposes if

required. To show already one of the possible results of súch a comparison a number of tacking simulations have been made

flm. Io.. n. sali .re.-diapì.eement rulo

Figure 18 Time loss

for a number of quite different boats and their speed loss düring a tacking maneuver assessed.

The main dimensions ofthe boats used for this comparison are presented in table3.

The comparison was made fOr oñe single tack in 10 knots of

true wind.

One important aspect of the application of the model for such a complex maneuver as tacking should be mentioned. At present

the rudder input signal was manipulated "by hand" to find the

smallest speed loss during the'pròcedúre in a reasonable period of time. This resulted among other things in a considerable wider turn for the heavy boat when compared to the lightones. It is obvious of course that the fmal result of the maneuver is

strongly dependent on this input. To'makethe outcomemore objective some kind of autopilot or optimization routine may be developed. Atpresent this is considered outside thescope of the project.

The results ofthe time loss calculations as a demonstrator aïe presented in the figure above and table 4 at the end of this

paper.

From these results it is possible to derive some, more general

information such as the dependency of the speed löss on design parameters, Le.: the relation between the average speed loss and

the' sail area displacement ratio

of the

yachts under consideration.

Such an analysis becomes feasible with this tool and may result in more insight in these phenomena amongst the designers and

the users. This kind of relationships could also be usefull for race organizers. and racing rule makers or "handicappers"

9.

Conclusions.

From the results obtained in the present study it may be concluded that a reasonably reliable tool for the prediction of

the maneuvering behavior of'a sailing yacht is developed. The

simulation of for instance the tacking maneuver and the

assessment of associated speed loss ofa large variety of sailing yachts' is possible within the restraints oftheoverali accuracy of

the model. The results obtained indicate' that in particular the 'mutual differences between various designs may be assessed

with an acceptable degreeofaccuracy.

Since only calculated coefficients and/or hydrodynamic

derivatives are used the model is easily applicable and 'does not require the mput from dedicated experiments

An shortcoming ofthemodelat this moment is still the 'lack of a

more refined aerodynamic model, which is capable of, taking into account 'the differences between various sail setting and

trimming more accurately. This is one of the extensions of the model foreseen in the near future.

Simulured e Measured L s s s r OAD500/3 (-1

Table 3 main particulars

Table 4 Time los

References.

Keuning, J.A. and Vermeulen, K.J.

"On the Yaw Balance of Large Sailing Yachts" 17th International HIS WA Symposium on Yacht Design and Consiruction

Amsterdam November 2002

Masayuma, Y. ; Fukasawa, T. and Sasagawa, H. "Tacking simulation of a sailing yacht- numerical integration of equations of motion and application of neural network technique."

12th Chesapeake Sailing Yacht Symposium

Annapolis SNAME 1995

Hanamoto, M, and Akiyoshi, T.

"Study on Ship Motions and Capsizing in Following Seas"

Journal of the Society of Naval Architects of Japan No

147 1988

Keuning, J.A. and Sonnenberg, U.B.

"Approximation of the Hydrodynamic Forces on a Sailing Yacht based on the

Delf Systematic Yacht Hull Series"

International HIS WA Symposium on Yacht Design and Construction

Amsterdam November 1998

Gerritsma, J.

"Course Keeping Qualities and Motions in Waves of a Sailing Yacht"

Report # 200 Dclii Shiphydromechanics Department Deift University of Technology May 1968

Nomoto, K. and Tatano, H.

"Balance of Helm of Sailing Yachts"

4th_{International HIS WA Symposium on Yacht Design}

and Construction

Amsterdam September 1975 Claughton, A.

"Developments in the IMS VPP Formulations" 14th Chesapeake Sailing Yacht Symposium Annapolis January 1999

Oossanen, P van

"Improvements of Sailing Yacht Performance

Prediction by Including Force Moment Equïlibrium for the Calculation of Helm Angle in a VPP"

12th Chesapeake Sailing Yacht Symposium Annapolis 1995

Hoerner, S F

"Fluid Dynamic Drag" and

FairV 1checkmte3

112 tonnet Sydney 41

8wan48

Des

$taron

Hwsman 42 Design

Déde

cte i-35 Lwl (ml 8,55, 11,50 9,24 8,70 9,73 9,47 Bwl (ml 2,42! 3,14 3,17 2,90 3,10 2,85 Displ (mA3J 3,69! 7,77 9,01 7,00 6,31 5,37 SA (mA2l 56,341 89,00 64,53 66,50 70,00 63,90 SAmlspI _{(-] 23,591} 22,68 14,90 18,17 20,50 20,84

Time loss in seconds for a tack in 10 knots of breeze

FniV :Chackmate3I Swan48. taror 1

beign

0MG loss (m] 8,9 10,4 14,1 11,4 11,6 10,9

0MG total [ml 113,5 152,2 106,7 112,5 131,7 153,3

DMGconst [m/sec] 2,0 2,7 2,0 2,1 2,4 2,4