Game Development Reference
In-Depth Information
The highest wave velocity will occur when the length of the wave is equal to the waterline
length of the boat. It turns out that wave drag is a limiting factor in the maximum speed of a
boat with a displacement hull. The reason is that for the boat to travel faster than the wave it is
generating, it essentially has to pull the wave along with it, causing the wave drag to increase
dramatically. The velocity described by Equation (9.23) is also known as the
hull speed
. The
hull speed limitation on maximum boat velocity only applies to boats with displacement hulls.
A boat with a planing hull can overcome the hull speed limit by lifting itself on top of the bow
wave. The lifting action greatly reduces the wave (and friction) drag experienced by the boat.
To compute wave drag for a boat analytically requires knowledge of the size and frequency
of the wave pattern. Many attempts have been made to develop an analytical wave drag model.
The models involve horrible-sounding things like “weight integrals” and “thin ship theory.”
For game programming applications, you probably won't want to tackle anything so involved.
A commonly used approach to estimating wave drag is through experimental measure-
ments. The total drag resistance of a boat is measured, the contribution due to skin friction is
subtracted out, and what's left is the resistance due to wave drag, form drag, and any other drag
that might be present. The remainder is also called the
residual drag
. Under this system, the
total drag coefficient,
C
R
, is expressed as the sum of the skin friction drag coefficient,
C
f
, and
the residual drag coefficient,
C
r
.
CCC
=+
(9.24)
R
f
r
For large displacement hulls, the residual drag coefficient can range from 0.001 to 0.003.
1
Other Hydrodynamic Drag Components
The main components of hydrodynamic drag are skin friction, form, and wave drag, but there
are other things going on in the water that can contribute to hydrodynamic drag. If wind-generated
waves are present, they will increase the drag. If there are any boat appendages in the water
such as keels, rudders, struts, and so on, they will add to the hydrodynamic drag. If the boat is
traveling in shallow water, it will affect the drag experienced by the boat by changing the wave
pattern generated by the hull of the boat.
Unless you are developing a highly accurate boat simulation, you can probably ignore the
“other” hydrodynamic drag components. If you want to include the effects of some or all of
them, one way to do so would be to add a factor onto the residual drag coefficient to account
for them.
Determining the Wetted Area
The drag force equations presented in the previous sections are a function of the wetted area
of the boat, the surface area of the hull that is in contact with the water. For displacement hulls,
the wetted area can be determined from the hull geometry and from the draft of the boat (the
depth of the hull that is underwater) at a given time.
For planing hulls, estimating the wetted area is a bit more complicated. When the boat
reaches a certain speed, part of the hull will lift out of the water. This action reduces the wetted
area (which is the whole point of a planing hull). Determining the wetted area for a planing hull
requires information on when the boat begins to plane and how much of the hull lifts out of the
water at a given boat velocity.
