Game Development Reference

In-Depth Information

work done over time, its units are, for example, foot-pounds per second. Usually power

in the context of car engine output is expressed in units of
horsepower
, where 1 horse‐

power equals 550 ft-lbs/s.

To calculate the horsepower required to overcome total resistance at a given speed, you

simply use this formula:

P = (R
total
V) / 550

Here
P
is power in units of horsepower, and
R
total
is the total resistance corresponding

to the car's speed,
V
. Note, in this equation
R
total
must be in pound units and
V
must be

in units of feet per second.

Now this is not the engine output power required to reach the speed
V
for your car;

rather, it is the required power delivered by the drive wheel to reach the speed
V
. The

installed engine power will be higher for several reasons. First, there will be mechanical

losses associated with delivering the power from the engine through the transmission

and drive train to the tire. The power will actually reach the tire in the form of torque,

which given the radius of the tire will create a force
F
w
that will overcome the total

resistance. This force is calculated as follows:

F
w
= T
w
/r

Here
F
w
is the force delivered by the tire to the road to push the car along,
T
w
is the

torque on the tire, and
r
is the radius of the tire. The second reason the installed engine

power will be greater is because some engine power will be transferred to other systems

in the car. For example, power is required to charge the battery and to run the air

conditioner.

Stopping Distance

Under normal conditions, stopping distance is a function of the braking system and

how hard the driver applies the brakes: the harder the brakes are applied, the shorter

the stopping distance. That's not the case when the tires start to skid. Under skidding

conditions, stopping distance is a function of the frictional force that develops between

the tires and the road, in addition to the inclination of the roadway. If the car is traveling

uphill, the skidding distance will be shorter because gravity helps slow the car, while it

will tend to accelerate the car and increase the skidding distance when the car is traveling

downhill.

There's a simple formula that considers these factors that you can use to calculate skid‐

ding distance:

d
s
= V
2
/ [2g ( µ cos φ + sin φ)]