Analytical Approximations of Projectile Motion for Linear and Quadratic Air Drag

Report No. ARL-TR-6218
Authors: Richard Saucier
Date/Pages: September 2012; 48 pages
Abstract: The purpose of this report is to provide closed-form solutions to projectile motion while accounting for, or approximating, the effect of air resistance. The plan is to first quickly review the solution when air resistance is neglected, and then to approximate the effect of air drag. Making the assumption that the drag force varies linearly with air speed allows us to solve the equations of motion exactly. The more realistic assumption that air drag varies as the square of the speed can also be solved analytically, provided that we restrict it to shallow launch angles. This analytical approximate solution is compared to the exact numerical solution using a fourth-order Runge-Kutta method.
Distribution: Approved for public release
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Last Update / Reviewed: September 1, 2012