The Physics of Roller Coasters

The Reynolds Number

The coefficient of drag unfortunately does not remain constant, but instead varies with the Reynolds number.


The above is a graph relating the coefficient of drag on a sphere with the Reynolds number, which is given by the equation

$$R_e=\frac{ρvL}{µ}$$
where D is a required linear dimension, µ is dynamic viscosity of the fluid, and L is the characteristic linear dimension, which is itself given by


where A is the cross sectional area and P is the perimeter. All together, this means that as a body moves faster and faster, the coefficient of drag goes down, but it also means that for Reynolds numbers outside of the order of E3 to E5, the value of the coefficient of drag changes rapidly as velocity changes.