Cars and Motorcycles - Physics for Game Programmers - page 224

The force of rolling friction can be computed from Equation (8.4).

N

F

= 0.015*1393*9.81 = 205 (8.29)

In comparing the results from Equations (8.28) and (8.29), the aerodynamic drag force is
10 times as large as the rolling friction force when the car is traveling at 271.5 km/hr . The rolling
friction force is not a function of velocity. If the car were going 10 km/hr , the rolling friction
force would still be 205 N , whereas the drag force would only be 2.8 N .

Braking
Driving a car is not all acceleration; sometimes you need to slow down, too. In this section, we
will discuss two general ways a car can slow down (and no, one of them is not running into a
tree). It turns out that an engine will slow itself down just by the nature of how the cylinders
move up and down inside the engine. This effect is known as engine braking . The torque due
to engine braking, T eb , is modeled mathematically by a constant known as the engine braking
coefficient , m eb , multiplied by the turnover rate of the engine in rev/s .

m Ω T =

e

(8.30)

eb eb

60

It can be difficult to obtain the value of the engine braking coefficient for a given car. For
an F1 race car, the coefficient has a value of 0.74. 3 If this value is applied to the Boxster S, the
torque due to engine braking at 6000 rpm is equal to 74 N-m corresponding to an acceleration
of -0.17 m/s 2 . If you want to include the effects of engine braking in your car simulation and
don't have the precise value of engine braking coefficient for the car you are modeling, assuming
a value of 0.74 is probably a reasonable estimate.
Another way a car can be slowed down is if its brakes are applied. When the driver steps on
the brake pedal, a brake pad is pressed up against a flat metal disk attached to the wheel. Friction
between the brake pad and disk generates a torque that slows the wheels down. The torque
caused by the brake pad acts in the opposite direction that the wheel is rotating.
It can be difficult to find information about brake torque for a given car. Information on
braking is usually presented as the distance it takes to brake a car from an initial velocity to a
full stop. For example, the Boxster S requires 34 m to brake from a velocity of 26.8 m/s (60 mi/hr )
to a full stop. If braking distance data is available, the braking acceleration, a b , can be obtained
from the Newtonian mechanics as a function of the initial velocity, v 0 , and braking distance, x .

2
0

v m

s

a =− =− 10.4

(8.31)

b

2

2 x

Keep in mind when looking at the results in Equation (8.31), the driver who performed this
test was trying to get the shortest braking distance possible, so he or she probably slammed on
the brakes. The -10.4 value therefore can be considered the maximum braking deceleration for
the Boxster S.
For game programming purposes, if the value for the brake torque for a given car isn't
available, you can calculate the braking acceleration from braking distance data and apply that
in your code. Keep in mind that the braking distance is based on the maximum braking force—
if you slammed on the brakes. To simulate a more gentle braking action, you could simply take
some fraction of the maximum braking acceleration.