Mathematical Modelling

Performance prediction of a sailboat is an excellent way to determine the validity of a boat design without having to actually build it (taking both time and money). The trick, however, is being able to come up with decent numerical models that accurately define the boat. Since a boat is a complicated system with many interconnected parts it is impossible to come up with an idealized model. However, by combining both theoretical and empirical data it is possible to come up with a good model (i.e. within 90% accuracy).

Drag Forces
Drag forces are always apparent on a boat, one from the wind, and the other from the water. The general equation for drag is:
 * F = 0.5*p*V^2*C*A (1)

Since density is a major component of drag, and the density of water is 3 orders of magnitude greater than that of air, the drag component of air can be taken to be non-consequential.

Water Drag
The three main components causing drag in the water (in order of signifigance) are the hull, the keel, and the rudder. Important values for GaelForce II are summarised as follows. By subbing all of these values into equation 1, it can be found that the drag force acting on the boat is determined by:

Fd = 4.1*Vboat^2

This is numerically true for all forms of sailing, although it still must be empirically tested.

Downwind Sailing
In terms of modelling, downwind sailing is the easiest as it is impact sailing as opposed to aerodynamic sailing when sailing upwind. As such, the generated lift forces are easily calculated using the following equation.

Fsail = pair*Asail*Vwind^2

The area of the sails currently used on GFII is approximately 1.5m^2, and the density of air is about 1kg/m^3. As such the driving force for downwind sailing