# Calculating wind force and drag force on a falling object

I'm trying to numerically integrate the motion of an object (say, a falling vertical cylinder). Here, there's a drag force: the wind "acting" on the body (presumably adding horizontal velocity) and the air itself slowing down the vertical motion.

Is it correct to calculate both forces with the drag equation, $F_D = \frac{1}{2} \rho v^2 C_D A$? Here I suppose the velocity would be the relative velocity between the falling object (i.e. initially $(0, -15)\ m/s$) and the "air" (i.e. $(5, 0)\ m/s$). If that's the case, where would the drag force point towards to? $-\hat{v}_{relative}$?

• Yes that's right. In the case of a cylinder of height $h$ and radius $r$, when apparent wind is at an angle $\theta$ to the vertical the projected area is $A = \pi r^2 \cos\theta + 2rh\sin\theta$ (doing this in my head, think it's correct... draw yourself a diagram). Incidentally there may be some torque on the object because of asymmetry w.r.t. the direction of the air flow, but I assume you can neglect that. It's one reason why guns have rifling so the bullet spins (keeps its trajectory stable in the presence of this torque). – Floris Apr 16 '15 at 18:30