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Trans RINA, Vol 153, Part B2, Intl J Small Craft Tech, 2011 Jul-Dec E Outer point distance of boom (m)

MGL main girth measurement at P/4 above boom (m) MGM main girth measurement at P/2 (m) MGU main girth measurement at ¾ P (m) MGT main girth measurement at 7/8 P (m) HB

MSA main sail area (m²) J




main girth measurement at P (m) fore triangle base (m)

jib luff perpendicular (m)

jib hoist point above deck (m) jib sail area (m²)

AMG spinnaker half width (m) ASL ISP


A conventional velocity prediction program for sailing yachts (VPP) relies on a set of aero- as well as hydrodynamic coefficients, describing the


properties of the yacht for a given set of state variables, velocity u, heeling angle , leeway angle  and rudder angle . These coefficients are usually provided as tabulated values, derived from towing tank tests or flow simulations. Here the generation of hydrodynamic coefficients using a RANSE flow simulation method resembles procedures from towing tank testing: Within a predefined test matrix, flow forces for a permutation of boat speeds, heel, leeway and rudder angles are analyzed. This approach necessitates interpolation and usually causes a large number of computational runs carried out, necessary

to be including many for off-equilibrium states, interpolation purposes, however rarely

encountered by the sailing yacht. This results in large computational overhead.

A remedy to the drawbacks of the method described above is to calculate aerodynamic forces conventionally, however directly include

the prediction of sailing

equilibrium into a RANSE solver, which calculates the hydrodynamic forces on the fly. This approach avoids interpolation and calculates hydrodynamic forces only for a combination of yacht states for which sailing force equilibrium exists, This reduces the computational cost for the calculation hydrodynamic properties while maintaining fully accuracy. In addition solving for sailing force equilibrium by including the equation of motion into the RANSE solution, the window is opened wide to predict boat performance not only in calm water conditions but also in dynamic, instationary states, for example in natural seaways or while maneuvering. The R&D-project RVPP, carried out by YRU-Kiel, addresses this topic.

While RVPP obviously calculates hydrodynamic forces from a RANSE simulation, aerodynamic forces are predicted from wind tunnel data or empirical (Hazen-like [7])


The hydrodynamic part of the database can be generated in two ways. Firstly, one can use empirical regressions derived

from results of towing tank tests on

systematically varied hull forms (e.g. Delft Systematic Yacht Hull Series). This approach is rather often used for custom builds with a limited budget, but due to its generic approach it obviously lacks the accuracy of dedicated investigations of the individual hull form. The second approach is to investigate the individual hull by means of towing tank testing, be it numerical or physical. Here the different components that make up total resistance and total lift of a sailing yacht have to be considered. The total resistance can be decomposed into:

RR R  R R R force models. This approach does not only Tot U H I   PP Waves (1)

Here RTot is total resistance, RU upright resistance at non- lifting condition, RH added resistance due to heel, RI induced resistance due to production of lift and RPP

B-82 ©2011: The Royal Institution of Naval Architect The aerodynamic database usually compromises

coefficients of drag and lift, cD and cL, as functions of the apparent wind angle (AWA). These coefficients are stored for various single sails or sail sets and are generated by means of wind tunnel testing or numerical investigation.

spinnaker foot length (m) spinnaker foot leech (m)

spinnaker hoist point above deck (m) asymmetric spinnaker sail area (m²)

reduce the computational costs of the method, it allows to easily involve the implementation of the necessary optimization to reflect the sail trimming process carried out in the wind tunnel or by the sailor on board a racing yacht.

The paper describes the method and discusses pros and cons. First implementation steps are presented and some first results will be shown.

2. A sailing yacht

PERFORMANCE PREDICTION is a complex physical

system of

aerodynamic as well as hydrodynamic wings positioned in the interface of two fluids, air and water. It interacts simultaneously

with them and relies solely on the

interaction of fluid forces for its propulsion, which in turn depend on changing environmental conditions, in particular wind speed and direction. This makes it difficult to predict the velocity of sailing yachts. Thus the need

for special calculation

Velocity Prediction Programs (VPPs), arises to predict the yachts performance.


Conventional VPPs usually rely on a pre-calculated database

of aerodynamic and hydrodynamic

characteristics of a yacht. Using input values of true wind speed (TWS) and true wind angle (TWA) the force components are then balanced by setting up and solving the resulting non-linear system of equations. In order to maximize the velocity of the yacht, an optimizer is used to simulate the trimming of the sails.

procedures, so called

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