Zach Milbradt    Physics 212    Spring 2015

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 equation

FD=12*ρ*v2*CD*AF_D=\frac{1}2*ρ*v^2*C_D*A

where 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.