Effect of Aerodynamic Drag Forces

Second draft: 17 February 2000.

Fine tuning: 18 February 2000.

This document was originally writtin in Latex as a single file. A modified
version was processed through latex2html, then the resulting HTML was edited
manually to produce the more familiar linkage into sections and embedded
graphics that you find here and in the following sections.

0. Overview

A Frequently Asked Question in the sci.physics newsgroup concerns how to
include the effect of aerodynamic drag forces in calculations of projectile
motion. As we see in Section 1, all realistic drag forces are sufficiently
complicated that only a numerical solution is feasible for the general problem.
I have done such an analysis for a specific set of questions that arise in
baseball in a separate study. Nonetheless, the equations can be solved
analytically if some plausible assumptions about the v dependence of the
drag force are made. Further, those analytic solutions can be used to estimate
the drag force on some arbitrary object based on a fit to free-fall data as the
first step in a more detailed study of the motion of that object.

Note that the way this new version of latex2html works, equations are made
extra large and then reduced to half-size to fit in the text, which can lead to
invisible equal signs and other defects. Use the right mouse button to "view
image" to see the equation in its original size to be sure you have it right
before using it. Also note that I use italics in the text to minimize graphics
for simple expressions. This makes a v (vee) for velocity look a lot like
a (greek nu) for kinematic viscosity. The right meaning should be clear
from context and whether an image was used within the text. Also note that links
to the references take you to this page, so you should use the "Back" button on
your browser to return after checking one of those (and ditto if you use a link
to check an equation in another section than the one you are reading).

The outline of this document is as follows:

Introduction
to aerodynamic drag forces

1.A Table and
graphs of standard data

1.B Short
rationale for linear or quadratic drag regimes

General
solution for simplified (polynomial) forces

Analytic solution for the K1
v case

Analytic solution for the K2
v2 case

Sample
results

Fitting
data to get CD equation

Bibliography

1

Russell L. Donnelly in Section 12 of "A Physicist's Desk Reference: The
Second Edition of Physics Vade Mecum", ed. Herbert L. Anderson (AIP, New York,
1989), pages 197ff.

2

"The Physics of Baseball" by Robert Adair.

Jim Carr
2000-02-17