Building a
mathematical model is like building other types of
models such as visual models (pictures), verbal models
(speech, articles, or books), and sculptures.
Let us consider a simple example of reverse engineering
by choosing the transmission system of a car, the
mechanisms that convert the circular motion produced by
the engine into the forward or backward motion of the
car. The circular motion of the engine is measured in
rpms, or revolutions per minute using a
tachometer.
In the United States the motion of a car is measured in
mph, or miles per hour using a
speedometer.
Look at your
Bicycle
You may get an
idea of the general principles of transmission system of
a car by considering a bicycle. The
gears,
chain,
and tires
of a bicycle convert the circular motion of the pedals
into the forward motion of the bicycle. There is a
cluster of gears attached to the pedals. The gears have
different numbers of teeth. The rear wheel also has a
cluster of gears and each gear has a different number of
teeths.
If the front
derailler is on the 52 tooth gear and the rear derailler
is on the 14 tooth gear then each revolution of the
pedals causes the chain to move by 52 teeth. Therefore,
the rear gear revolves by 52 teeth. Since the rear gear
has 14 teeth this produces 52/14 revolutions of the rear
wheel. If the diameter of the rear wheel is 27"
then each revolution of the pedals moves the bicycle
315.06 inches = 26.25 feet = 0.0050 miles.
|