Force of Drag
Obviously,
in order to find how much energy is lost to the air, one
needs to know what force the air is applying to the roller
coaster car. The force of drag is given by the equationwhere rho is
the density of the fluid, air, v is the velocity of the
body relative to the fluid, A is the cross sectional
area, and C sub D is the coefficient of drag. And so
with this, it should be easy enough to calculate the
force of drag. There are two problems, though. The first
is that we do not know the coefficient of drag of a
roller coaster, and the value is actually rather
difficult to find with a simple search. The other is
that the force varies with the square of velocity, which
itself is going to vary with the height of the car.
However, there is a simplification that can be made for the coefficient of drag - a roller coaster has roughly the same shape as a passenger train. Looking through a table of drag coefficients, a passenger train has a coefficient of drag of 1.8. Short of using a wind tunnel to get an exact value, this should be close enough to the real value. However, there is another problem when it comes to calculating coefficient of drag, one that unfortunately will have to be ignored for the purposes of calculations here, but at the same time is an important factor in calculations involving air resistance.
However, there is a simplification that can be made for the coefficient of drag - a roller coaster has roughly the same shape as a passenger train. Looking through a table of drag coefficients, a passenger train has a coefficient of drag of 1.8. Short of using a wind tunnel to get an exact value, this should be close enough to the real value. However, there is another problem when it comes to calculating coefficient of drag, one that unfortunately will have to be ignored for the purposes of calculations here, but at the same time is an important factor in calculations involving air resistance.