Game Development Reference

In-Depth Information

Here
d
s
is the skidding distance,
g
the acceleration due to gravity, µ the coefficient of

friction between the tires and road,
V
the initial speed of the car, and φ the inclination

of the roadway (where a positive angle means uphill and a negative angle means down‐

hill). Note that this equation does not take into account any aerodynamic drag that will

help slow the car down.

The coefficient of friction will vary depending on the condition of the tires and surface

of the road, but for rubber on pavement the dynamic friction coefficient is typically

around 0.4, while the static coefficient is around 0.55.

When calculating the actual frictional force between the tire and road, say in a real-time

simulation, you'll use the same formula that we showed you in
Chapter 3
:

F
f
= µ W

Here
F
f
is the friction force applied to each tire, assuming it's not rolling, and
W
is the

weight supported by each tire. If you assume that all tires are identical, then you can use

the total weight of the car in the preceding formula to determine the total friction force

applied to all tires.

Steering

When you turn the steering wheel of a car, the front wheels exert a side force such that

the car starts to turn. In terms of Euler angles, this would be yaw, although Euler angles

aren't usually used in discussions about turning cars. Even if the car's speed is constant,

it experiences acceleration due to the fact that its velocity vector has changed direction.

Remember, acceleration is the time rate of change in velocity, which has both magnitude

and direction.

For a car to maintain its curved path, there must be a
centripetal
force (“center seeking”

in Greek) that acts on the car. When riding in a turning car, you feel an apparent

centrifugal
acceleration, or force directed away from the center of the turn. This accel‐

eration is really a result of
inertia
, the tendency of your body and the car to continue on

their original path, and is not a real force acting on the car or your body. The real force

is the centripetal force, and without it your car would continue on its straight path and

not along the curve.

One of the most important aspects of racing is taking turns as fast as possible but without

losing control. The longer you can wait to decelerate for the turn, and the sooner you

can start accelerating again, the higher your average speed will be. It is interesting to

note that when people ride in racecars, what really surprises them isn't the acceleration

but the massive decelerations they can create through braking forces. A Formula One

car regularly experiences decelerations of 4g, with 5-6g being the extreme value for

certain race courses. Most road-legal sports cars can achieve about 1g of braking force.

This allows the racecars to maintain speed until just entering the corner.