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)]