Game Development Reference

In-Depth Information

Here ρ is the mass density of air,
V
the speed of the hovercraft,
S
p
the projected frontal

area of the craft normal to the direction of
V
, and
C
d
the drag coefficient. Typical values

of
C
d
for craft in operation today range from 0.25 to 0.4.

The next drag component, the induced drag, is a result of the craft assuming a pitched

attitude when moving. When the bow of the craft pitches up by an angle τ, there will

be a component of the aerostatic lift vector that acts in a direction opposing
V
. This

component is approximately equal to the weight of the craft times the tangent of the

pitch angle:

R
induced
≈ W (tan τ)

Finally, momentum drag results from the destruction of horizontal momentum of air,

relative to the craft entering the lift fan intake. This component is difficult to compute

unless you know the properties of the entire lifting system such that the mass flow rate

of air into the fan is known. Given the mass flow rate,
R
momentum
is equal to the mass flow

rate times the velocity of the craft:

R
momentum
= (dm
fan
/dt) V

Mass flow rate is expressed in units such as kg/s, which when multiplied by velocity in

m/s yields
N
.

In
Chapter 9
we mentioned that it is beneficial to have the center of this drag be behind

the center of gravity. This gives directional stability, as the vessel will tend to try to point

into the apparent wind. Consider if the vessel yaws some angle, the forward velocity is

creating a wind that is now hitting the side of the hovercraft. If the center of effort of

this force is forward of the center of gravity, it will want to yaw the vessel more, increasing

the side force and causing even greater drag until the vessel spins 180 degrees! If the

center of effort of the wind is aft of the center of gravity, the vessel will spin back into

the wind. You don't want the center of effort so far aft that it is too difficult to turn the

vessel, but it is generally better to have the vessel naturally straighten out than to require

constant steering input to maintain a steady course. This is also true of sailboats and is

called
weather helm
. This also occurs in airplanes. The solution in airplanes is similar

to that of hovercraft: to fit tail fins that move the center of the area aft, increasing its

directional stability. If you choose to model damage in your simulation, the loss of a tail

fin will cause the vessel to be very difficult to control.

In addition to these three drag components, hovercraft will experience other forms of

resistance when operating over water. These additional components are
wave
drag and

wetted
drag. The equation for total drag can thus be revised for operation over water as

follows:

R
total
= R
viscous
+ R
induced
+ R
momentum
+ R
wave
+ R
wetted