Boats and Things That Float - Physics for Game Programmers - page 255

Aerodynamic Drag
So far we have been discussing how to model the hydrodynamic drag forces experienced by a
boat. Part of a boat will be above water and will be subject to the forces of aerodynamic drag.
Generally speaking, aerodynamic forces for boats traveling at low to moderate speeds don't
contribute significantly to the overall drag resistance experienced by the boat. Aerodynamic
drag is significant, however, for high-speed planing powerboats.
To model the aerodynamic drag on a boat, the familiar drag equation can be applied
once again.

1
2

2

FCv A = r (9.25)

D

The area, A , in Equation (9.25) is the frontal area of the boat that is above water. Aerodynamic
drag coefficients for displacement hull boats tend to range from 0.6 to 1.1 depending on the type
of boat. Supertankers, obviously, have higher aerodynamic drag coefficients than do powerboats.
Computing the aerodynamic drag of a high-speed boat with a planing hull is complicated
by the fact that when the boat lifts up, its frontal area and drag coefficient will change and will
be a function of how much of the hull is out of the water and the angle of the boat relative to
the water.

Modeling the Acceleration and Velocity of a Boat
In the previous sections, we have discussed some of the theoretical aspects of boat thrust and
drag. To create a boat simulator, a model must be developed to predict the acceleration profile
for the boat, ideally an expression that relates the potential acceleration of the boat as a func-
tion of the current velocity of the boat.
One way to come up with an acceleration profile is to try to model the various thrust and
drag components. The problem with this approach is that so many unknowns are involved. For
example, to compute the drag, we need to calculate not only the wetted area, but also the time
history of the wetted area, because the value will change as the speedboat begins to plane. The
aerodynamic drag coefficient and frontal area of the boat will similarly change as the boat
begins to plane.
A similar situation exists with trying to evaluate the thrust produced by the boat engines.
Using Equation (9.16) requires knowledge of the engine power level, wake fraction, and the
coefficients of propulsive and hull efficiency. The engine power level will likely be a function of
the engine turnover rate. The wake fraction will be a function of boat velocity. As you can see,
it takes a lot of research and a lot of information to realistically model the forces and accelera-
tions of a boat.
Fortunately, there is a much simpler approach for game programmers, one that will gener-
ally give pretty accurate results as well. Most speedboats are performance tested either by the
manufacturer or by publications such as Powerboat magazine. The performance data typically
includes things such as velocity vs. time and engine rpm vs. velocity data. The performance
data represents experimental measurements on the performance of the boat. From this data,
an acceleration profile can be determined for the boat that includes all of the various thrust
and drag components experienced by the boat.