Game Development Reference

In-Depth Information

The aerodynamic drag is primarily skin friction and pressure drag similar to that ex‐

perienced by the projectiles discussed in
Chapter 6
, and the planes and boats discussed

in earlier chapters. Here again, you can use the familiar drag formula:

R
air
= (1/2) ρ V
2
S
p
C
d

Here ρ (rho) is the mass density of air,
V
is the speed of the car,
S
p
is the projected frontal

area of the car normal to the direction of
V
, and
C
d
is the drag coefficient. Typical ranges

of drag coefficients for different types of vehicles are 0.29 to 0.4 for sports cars, 0.43 to

0.5 for pickup trucks, 0.6 to 0.9 for tractor-trailers, and 0.4 to 0.5 for the average economy

car. Drag coefficient is a function of the shape of the vehicle—that is, the degree of

boxiness or streamline. Streamlined body styles have lower drag coefficients; for ex‐

ample, the Chevy Corvette has a low drag coefficient of 0.29, while the typical tractor-

trailer without fairings has a high drag coefficient of up to 0.9. You can use these coef‐

ficients in your simulations to tune the behavior of different types and shapes of vehicles.

When a tire rolls on a road, it experiences rolling resistance, which tends to retard its

motion. Rolling resistance is not frictional resistance, but instead has to do with the

deformation of the tire while rolling. It's a difficult quantity to calculate theoretically

since it's a function of a number of complicated factors—such as tire and road defor‐

mation, the pressure over the contact area of the tire, the elastic properties of the tire

and road materials, the roughness of the tire and road surfaces, and tire pressure, to

name a few—so instead you'll have to rely on an empirical formula. The formula to use

is as follows:

R
rolling
= C
r
w

This gives you the rolling resistance per tire, where
w
is the weight supported by the

tire, and
C
r
is the
coefficient of rolling resistance
.
C
r
is simply the ratio of the rolling

resistance force to the weight supported by the tire. Luckily for you, tire manufacturers

generally provide the coefficient of rolling resistance for their tires under design con‐

ditions. Typical car tires have a
C
r
of about 0.015, while truck tires fall within the range

of 0.006 to 0.01. If you assume that a car has four identical tires, then you can estimate

the total rolling resistance for the car by substituting the total car weight for
w
in the

preceding equation.

Power

Now that you know how to calculate the total resistance on your car, you can easily

calculate the power required to overcome the resistance at a given speed. Power is a

measure of the amount of
work
done by a force, or torque, over time. Mechanical work

done by a force is equal to the force times the distance an object moves under the action

of that force. It's expressed in units such as foot-pounds. Since power is a measure of