Lyle Long and Howard Weiss
Velocity Dependence of Aerodynamic Drag: A Primer for Mathematicians
(1083K, Postscipt)
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.