Hydrodynamic Modeling Of Sailing Yachts.pdf

Hydrodynamic Modeling of Sailing Yachts

Stefan Harries, Technical University of Berlin

Claus Abt, Technical University of Berlin

Karsten Hochkirch, Friendship Systems, Berlin

ABSTRACT

the optimization of a keel-bulb-winglet conﬁguration so

as to ﬁnd a minimum drag solution for a given sideforce

and (b) the optimization of the bare hull with respect to

wave resistance.

The examples can be regarded as representative for

both racing and touring yachts with draft restrictions and

illustrate the methodology of hydrodynamic modeling.

In modern yacht design geometric modeling is regarded

to be directly related to the hydrodynamic performance

of the shape of the hull and its appending elements –

usually the keel, often with winglets, and the rudder.

While the traditional way of shape design – i.e., draw-

ing, model building, tank testing, modifying . . . – is both

time consuming and expensive, a complementing ap-

proach shall be discussed within this paper. The ap-

proach is called hydrodynamic modeling since it tightly

combines the hydrodynamic analysis and the geomet-

ric modeling in the design process. It is based on ad-

vanced Computational Fluid Dynamics (CFD) methods

for ﬂow ﬁeld analysis and unique parametric modeling

techniques for shape generation.

The geometry of a yacht is entirely described via im-

portant form parameters as discussed in detail by the au-

thors at the 1999 CSYS. The canoe body of the yacht is

modeled from a small set of longitudinal curves which

provide all parameters needed for sectional design. The

longitudinal curves themselves being created via form

parameters, a fully parametric description of the hull is

achieved which allows to create and modify the geom-

etry in a highly sophisticated manner. The fairness of

the shapes is an intrinsic part of the form generation

procedure. Apart from the canoe body the keel repre-

sents the most pronounced hydrodynamic design ele-

ment, dominating lift and righting moment of a yacht

but also causing a non-negligible resistance component

called induced drag. Keel, bulb and winglets are also

speciﬁed in terms of form parameters.

An application of hydrodynamic modeling is given

for an IACC-yacht. Formal optimization can be suc-

cessfully employed to identify improved and, eventu-

ally, optimal conﬁgurations. A reasonably small set of

parameters (free variables) was selected and systemati-

cally varied making use of a fully-automatic optimiza-

tion scheme. Two optimization examples are presented

in order to demonstrate the potential of the approach: (a)

NOMENCLATURE

B max

maximum beam at deck level

C B

block coefﬁcient

C P

prismatic coefﬁcient

E 2

fairness criteria

F n

Froude number

IACC

International America’s Cup Class

L PP

length between perpendiculars

V PP

Velocity Prediction Program

x B max

longitude of maximum beam

x CB

longitudinal center of buoyancy

T max

maximum draft

INTRODUCTION

Designing a yacht, in particular its hull geometry and

appendages, is a process of creativity, skill, experience

and art – independent of whether the naval architect

chooses to express his or her ideas by means of a tra-

ditionally drawn lines plan or whether the designer de-

cides to apply a computer aided design (CAD) system to

create a product model. Full beneﬁt can be gained from

the latter when an integrated process of modeling and

analysis is established in which design variations can be

evoked and assessed efﬁciently.

In geometric modeling and particularly in yacht de-

sign many CAD systems are now built on an outstand-

ing mathematical curve and surface representation tech-

nique known as B-splines. Originating in free-form de-

sign, the underlying methodology of most of these sys-

tems is the interactive shape generation where points –

e.g. the vertices of the B-spline’s deﬁning polygon or

polyhedron – are positioned in three-dimensional space.

Achieving the desired form generally is a laborious un-

dertaking since the results need to be suitably fair while

speciﬁc constraints have to be taken into account, e.g.

the displacement or the length of a water line important

to the rating rules under consideration. Then the pro-

cess of manual vertex manipulation becomes rather te-

dious and systematic modiﬁcations in order to improve

the shapes with regard to their hydrodynamics become

inapt.

Instead of interactively handling the lowest entities

of the underlying mathematical model (i.e., the vertices)

a different approach has been pursued which is aimed at

expressing the geometry in terms of high level descrip-

tors for the intended shapes (i.e., form parameters).

Following the stage of shape creation, the design

may be analyzed for its various characteristics. The hy-

drodynamics being of supreme importance to racing

yachts, a state-of-the-art system of Computational Fluid

Dynamics can be used to examine the performance.

Modern ﬂow codes have reached the maturity to rank

different designs in respect to resistance and lift (i.e.,

side force). A potential ﬂow code with good response

time was therefore applied to numerically analyze the

ﬂow about the hull and a keel-bulb-winglet conﬁgura-

tion.

The potential of linking the two stages of geometric

modeling and hydrodynamic analysis tightly together,

becomes apparent when utilizing an integrated envi-

ronment in which modeling, analysis, evaluation and

modiﬁcation can be repeated systematically within short

turn-around time.

Within this paper the parametric approach will be

discussed and examples will be shown for an IACC

yacht, see section on geometric modeling. The hydrody-

namic optimization of an IACC canoe body and its keel-

bulb-winglet conﬁguration by means of a formal strat-

egy and a fully-automatic process will be presented, see

section on optimization. A full optimization in the light

of a velocity prediction program (VPP) is discussed.

tures (e.g. angle of entrance of the design water-

line),

Positional form parameters like points to be interpo-

lated (e.g. breadth of the waterline at the transom),

Integral form parameters like area, volume and cen-

troid information (e.g. center of ﬂotation).

Well-deﬁned parameters facilitate the modeling process

since the designer can focus his or her attention on the

outcome rather than on the input, assuming that the

form generation procedure automatically brings about

the speciﬁed geometry by itself.

In the subsections to come, ﬁrst the parametric mod-

eling of (bare) hulls shall be brieﬂy reviewed as intro-

duced by H ARRIES AND A BT (1999b) and H ARRIES

(1998). New features will be presented so as to cope

with additional constraints originating from class rules.

Following this, the parametric modeling of appendages

shall be outlined as needed for hydrodynamic optimiza-

tion.

Hull

In the novel parametric approach to the design of sailing

yachts by H ARRIES AND A BT (1999b) the process of

modeling surfaces of complex geometry is based on lay-

ing out a set of cross-sectional curves and, subsequently,

generating a surface by means of lofting (L ETCHER ,

1981) or skinning (W OODWARD , 1986, 1988). Follow-

ing the classic naval architect’s technique of describing

a ship’s geometry in terms of longitudinal curves (i.e.,

basic curves) from which design sections are derived,

the design sections (i.e., the cross-sectional curves) de-

ﬁne the interpolating surfaces and determine the shape

of the envisioned hull.

A new system called FRIENDSHIP Modeler , 1 has

been introduced which is based completely on paramet-

ric design principles. One of the key features of the

1 Form parameter oRIENteD SHIP Modeler http://www.

friendship-systems.com

GEOMETRIC MODELING

HYDRODYNAMIC

OPTIMIZATION

PERFORMANCE

CONSTRAINTS

FREE VARIABLES

In parametric modeling design ideas are usually ex-

pressed by descriptors that imply higher level informa-

tion about the object to be created. Often, relationships

and possible dependencies between entities are consid-

ered. In addition, the descriptors may also represent

complex features that the product is to assume. When

modeling geometry, the descriptors are called form pa-

rameters, three types of which can be distinguished:

GEOMETRIC

OPTIMIZATION

HULL

FAIRNESS

CONSTRAINTS

FREE VARIABLES

PARAMETRIC

HULL GENERATION

CURVE

FAIRNESS

CONSTRAINTS

FREE VARIABLES

OBJECTIVE

FUNCTION

IACC-FRIEND

Differential form parameters like tangents and curva-

F IGURE 1: Levels of the hydrodynamic modeling sys-

tem

Layer

Objective function

Constraints

Design/Free variable

2 Hydrodynamic

optimization

Performance

Feasible domains of the

design variables

Properties deﬁned by the

constraints of layer 1 e.g.

C P , x CB

1 Parametric hull

generation with implicit

measurement constraints

and physical properties

from form parameter

deﬁned basic curves

Fairness of basic curves

and sectional fairness

Displacement, x CB ,

interpolation of the deck,

design waterline ,

centerplane, tangents,

tangent plane, shape

modiﬁcation curves,

measurement marks

Direct geometrical

properties of the basic

curves e.g. B max , T max ,

L PP , x B max , x T max , B stern ,

B bow

0 Parametric B-spline

generation

E 2 Fairness

Interpolation, enclosed

area, centroid position,

tangential properties,

curvature

Vertex coordinates,

vector sizes

T ABLE 1: Direct parametric modeling

Layer

Objective function

Constraints

Design/Free variable

3 Hydrodynamic

optimization

Performance

Feasible domains of the

design variables

Properties deﬁned by the

constraints of layer 2

(e.g. C P , x CB ) and free

variables of layer 1

2 Geometric optimization

Global and local fairness

of the hull

Displacement, formula

constraints, form

parameters e.g. C P , C B ,

x CB , lateral area,

waterplane area, center

of ﬂotation, convexity

A subset of the free

variables from layer 1

1 Parametric hull

generation with implicit

measurement constraints

and physical properties

from form parameter

deﬁned basic curves

Fairness of basic curves

and sectional fairness

Displacement, x CB ,

Interpolation of the deck,

design waterline ,

centerplane, tangents,

tangent plane, shape

modiﬁcation curves,

measurement mark

Direct geometrical

properties of the basic

curves e.g. B max , T max ,

L PP , x B max , x T max , B stern ,

B bow

0 Parametric B-spline

generation

E 2 Fairness

Interpolation, enclosed

area, centroid position,

tangential properties,

curvature

Vertex coordinates,

vector sizes

T ABLE 2: Advanced parametric modeling

approach is the generation of B-spline curves and sur-

faces by means of variational calculus. Instead of in-

teractively manipulating the B-spline’s control points,

the (free) vertices are computed from a geometric op-

timization which employs fairness criteria as measures

of merit and captures the speciﬁed form parameters as

equality constraints.

Modeling a hull thus becomes the task of selecting

the form parameters to be taken into account and assign-

ing suitable values to them. This can be done by evalu-

ating an existing design and remodeling it or, alterna-

tively, specifying a set of form parameters from scratch.

As soon as an initial shape is produced changes can be

systematically brought about by varying one or several

parameters.

Form parameters can be individually addressed and

changed. Nevertheless, the interdependency of form pa-

rameters needs to be considered. For instance, pushing

the center of ﬂotation aft while pulling the center of

buoyancy forward can only be accommodated within

subtle limits unless non-yacht like shapes are intended.

Within hydrodynamic optimization, the direct use

of physical properties like displacement and center of

buoyancy can be successfully employed, see H ARRIES

AND A BT (1999a). Variations can be evoked efﬁciently

but the initial guess should be reasonably close to where

F IGURE 2: Parametrically designed IACC yacht with circular sections

F IGURE 3: Parametrically designed IACC yacht with trapezoidal sections

F IGURE 4: IACC canoe body designed by parametric modeling

F IGURE 5: Perspective view of an IACC canoe body designed by parametric modeling

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