98-694 Lyle Long and Howard Weiss

Velocity Dependence of Aerodynamic Drag: A Primer for Mathematicians (1083K, Postscipt) Oct 30, 98

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Abstract. Many elementary ordinary differential equation and calculus texts contain a model of the motion of a body (like a baseball or skydiver) subject to a drag force that depends linearly on the velocity, along with a calculation of the body's terminal velocity. Unfortunately, the physical assumption regarding the linear dependence of the drag force on velocity is often incorrect, and thus the model's predictions are physically implausible. The purpose of this note is to explain the dependence of the drag force on velocity for a general mathematical audience and to present a few realistic models. The appendices contain an interesting model (which has a closed-form solution) of the re-entry for the space shuttle into the earth's atmosphere and a dimensional analysis proof of the Pythagorean theorem.

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