range of craft geometries. In fact, in recent times the world sailing speed record has been held by a sail-board for which a significant component of the sail force is vertically upward.

The focus here is on the aero/hydrodynamics used in support of the design of monohulled yachts. However, several of the approaches have application to the less common sailing craft mentioned above.

The history of aero/hydrodynamic research related to sailing vessels can be divided into two categories. The first is the set of individual research programs of varying intensity and longevity whose modern history covers more than 50 years. The second category is the applied hydrodynamic research on sailing vessels stimulated by competition in the America's Cup yacht races. These events, typically held once every 3 to 5 years, have attracted extraordinary and unique international interest and intense competition. As a result, very substantial resources have been applied to every known way to increase the sailing speed of vessels which meet the specified requirements for the competition. Applied aero/hydrodynamic research is one of them. Most of the material to be presented herein is drawn from this category.

Since a sailing vessel is a complex interconnected “system”, most design changes influence more than one kind of fluid force. For example, suppose one wishes to reduce the frictional resistance of the hull by reducing its wetted surface. For most hull shapes, if length is maintained, the reduction in hull wetted surface requires a reduction in beam. This in turn reduces the heeling stability which, for prescribed sail shapes, leads to an increase in heel angle. The change in heel angle not only changes the hull shape, but also changes the sail forces. How does one determine whether the sum of all these effects is advantageous or disadvantageous? More importantly, how can one evaluate the effects if the sail shapes are simultaneously changed to optimize them for the altered hull? Short of complete full scale sailing experiments, answering these questions must be done with a numerical method of predicting performance. A computer program that does this is called a *Velocity Prediction Program* (VPP). One can think of a VPP as ”sailing a boat in the computer”.

The primary purpose of a velocity prediction program is to predict the boat speed for any prescribed wind conditions and sailing angle, *β*_{T}*,* between the wind direction and the course of the boat. This is achieved in a computational model by balancing counteracting aerodynamic and hydromechanic forces and moments. The course of the vessel differs from the heading of its centerline by the yaw (leeway) angle, λ.

A few preliminary definitions and descriptions are needed before proceeding further. The true wind speed varies with the distance, *z,* above the water. Here, we will consider logarithmic wind velocity profiles described by:

(1)

where V_{10} is the wind speed at a height of 10 meters and *z*_{o} is the roughness height which is taken here as 0.001 meters (1 mm). Hence the wind velocity profile *v(z)* is described by the single parameter *V*_{10}. The *deck plane* is defined as a plane perpendicular to the centerplane of a vessel. Figure 1 shows the aerodynamic and hydromechanic force and moment components in the deck plane. Those involved in the VPP force and moment balance are:

*F*_{af}*,* the aerodynamic forward force in the course direction,

*F*_{ah}*,* the aerodynamic heel force which is perpendicular to the forward force and the parallel to the deck plane. The aerodynamic force is presumed to be parallel to the deck plane. Thus the aerodynamic forces perpendicular to the deck plane are neglected in our model for evaluating performance here,

*M*_{ah}*,* the aerodynamic heeling moment whose vector is along the centerline of the yacht,

*F*_{wr}*,* the resistance of the yacht in the direction opposite to the course direction,

*F*_{wh}*,* the hydromechanical force component which is perpendicular to the course and parallel to the deck plane, *F*_{wh} is exclusive of components of that part of the buoyancy force which balances the weight of the yacht.

*M*_{wh}*,* the righting moment of the water on the yacht. Its vector is in the direction of the yacht centerline. It includes both hydrostatic and hydrodynamic components.

For any equilibrium sailing condition there are three “balance equations” involving these forces and mo-