Game Development Reference
In-Depth Information
the car is. Then select the “brake” mode and watch the car slow down. If you want to play with
shifting gears up and down, you can set the mode to “cruise”, which will hold the velocity
constant. If for some reason the entire GUI is not rendered, press the Reset button to redraw
the GUI.
Keep in mind that the Car Simulator uses the maximum possible acceleration of the car
according to Equation (8.20). In the Car Simulator, you're driving “pedal to the metal.”
Wheel Traction
Up to this point, we have been modeling the car tires under the assumption they roll without
sliding along the ground. In certain situations, however, this may not be the case. If a car is
stopped and the accelerator is pushed to the floor, the tires may spin in place for a moment
before the car starts to move forward. If a car tries to drive around a corner at too high a speed,
it may slide outward.
If you recall from the beginning of this section, the tires move the car forward because of
the friction that exists between the tire and the surface of the ground. This force, known as the
traction force
, is equal to the normal force exerted on the tire multiplied by the coefficient of
friction between the tire and road.
FF
=
m
=
m
g
cos
q
(8.32)
T
k
N
k
The traction force, shown in Equation (8.32), is the maximum force that can be applied to
the tire for it to roll without sliding on the ground. The traction force for a given car is typically
determined by putting the car through what is known as a
skidpad
test. The car is driven around
a level, circular track. The velocity of the car is increased until centripetal acceleration of the
car is equal to the traction force of the tires.
2
v
m
mg
=
m
(8.33)
k
r
The
r
parameter in Equation (8.33) is the radius of the track. If the velocity of the car increases
beyond this point, the centripetal force is greater than the traction force, and the car begins to
slide outward on the track. The results of the skidpad test are usually expressed in terms of the
maximum acceleration the tires can be subject to without sliding. On dry pavement, the 2004
Porsche Boxster S has a maximum tire frictional force of 0.91
g
, where
g
is the gravitational
acceleration.
This limiting acceleration applies to straight-line motion as well. If the torque applied to
the wheels results in a force that is greater than the maximum frictional force, the tires will spin
against the ground. The maximum frictional force is therefore a limiting value on the accelera-
tion of the car. No matter how much torque the engine is applying to the wheels, the acceleration
of the car won't be greater than that defined by the maximum frictional force.
For game programming purposes, the implementation of wheel traction effects is fairly
straightforward. The first thing to do is to compute the force applied to the wheels from the
engine, which is a function of the engine torque, gear ratios, and wheel radius.
TTgG
F
==
w
e
k
(8.34)
T
r
r
w
w
