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In recent years a number of Dynamic Velocity
Prediction Programs (DVPPs), which allow studying the
behaviour of a yacht while tacking, have been developed.
The aerodynamic models used in DVPPs usually suffer
from a lack of available data on the behaviour of the sail
forces at very low apparent wind angles where the sails are
flogging. In this paper measured aerodynamic force and
moment coefficients for apparent wind angles between 0°
and 30° are presented. Tests were carried out in the
University of Auckland’s Twisted Flow Wind Tunnel in a
quasi-steady manner for stepwise changes of the apparent
wind angle. Test results for different tacking scenarios
(genoa flogging or backed) are presented and discussed
and it is found that a backed headsail does not necessarily
produce more drag than a flogging headsail but increases
the beneficial yawing moment significantly. The quasisteady
approach used in the wind tunnel tests does not
account for unsteady effects like the aerodynamic inertia in
roll due to the “added mass” of the sails. In the second part
of paper the added mass moment of inertia of a mainsail is
estimated by “strip theory” and found to be significant.
Using expressions from the literature the order of
magnitude of three-dimensional effects neglected in strip
theory is then assessed. To further quantify the added
inertia experiments with a mainsail model were carried out.
Results from those tests are presented at the end of the
paper and indicate that the added inertia is about 76 % of
what strip theory predicts.

The Effect of Pitch Radius of Gyration on Sailing Yacht Performance

Traditionally a racing yacht is designed with as low radii of gyration as possible, especially regarding the pitch radius. A small radius normally provides less relative velocities between hull and water and thus less added resistance. Recent model tests at SSPA with a sailing yacht in head seas have indicated that a minimum of the added resistance can be found for a certain radius of gyration. The relation between the radius of gyration and the added resistance is of course best investigated by extensive model tests. However this is expensive and time consuming. A cost effective procedure is to combine model tests with computer based velocity predictions. There are a number of different Velocity Prediction Programs (VPP’s) available around the world today. Most of them are based on equations of equilibrium, one for each degree of freedom, that are explicitly solved. These programs work well as a basis for the judgment of the calm water characteristics for a sailing yacht. Many of them also have algorithms for estimating the added resistance in waves, which is normally based on regression formulas, derived from frequency based strip theory calculations. At SSPA a time domain dynamic prediction program has been developed, a DVPP (Dynamic VPP), that provides possibilities to study also the dynamic characteristics of a sailing yacht. The input data are the same as for a conventional VPP, however, also the hull form is entered in the form of sectional coordinates. The principles for the program is that all the horizontal hydrodynamic forces are expressed in the same way as in the conventional program, however the velocities in the different degrees of freedom are corrected for the wave particle velocities. Additional wave induced forces are also obtained from wave particle accelerations and by pressure integration over the whole momentary wetted surface.

Implementation, Application and Validation of the Zarnick Strip Theory Analysis Technique for Planing Boats

Mathematical-physical expressions, the primitives, for the driving forces for all sailboats, result in a general theory capable of closely predicting speeds of sailboats on smooth waters. The general theory, while inspired by catamarans hull a-fly, applies as an example to a 40-ft. monohull sailboat. The theory applies to a maximal-minimal problem to define limit speeds for all sailboats in true wind speeds from 10 to 100 knots on smooth waters.

The Effects of Flare and Overhangs on the Motions of a Yacht in Head Seas

The coupled heave and pitch motions of hull forms
with flare and overhangs are examined numerically. The
presence of flare and overhangs is numerically modelled
with nonlinear hydrostatic and Froude-Krylov forces based
on integrals over the instantaneous wetted surface. Forces
due to radiation and diffraction are computed with a linear
strip-theory. These forces are combined in two coupled
nonlinear differential equations of motion that are solved in
the time domain with a fourth-order Runge-Kutta integration
method. An assessment of the impact of flare and overhangs
on motions is obtained by comparing these nonlinear
solutions with solutions of the traditional linear equations of
motion, which do not contain forces due to flare and
overhangs. For an example based on an International
America's Cup Class yacht design, it is found that the
nonlinear heave and pitch motions are smaller than the linear
motions. This is primarily due to reduced first-order
response components, which are coupled with nonlinear
response components. Comparisons of these results with
towing tank data demonstrate that the nonlinear procedure
improves prediction quality relative to linear results. In
support of this numerical work, the hydrostatic and Froude-Krylov force integrals are expanded in Taylor series with
respect to wave elevation. These results indicate how
hydrostatic and Froude-Krylov forces change with changing
flare and overhang angles, revealing that sectional slope has
second and third-order effects on forces while sectional
curvature and overhang angles produce third-order effects.