Cameron Davis

AERO 211 Dynamics

April 29, 2008

Aerodynamic Effects Due to the

Spin of a Baseball

Signature Page

Table of Contents

Introduction…………………………...... / 4
Project Description………...... / 4
Preliminary Calculations…...... / 5
Experimental Results…………………… / 6
Comparison of Results and Analysis…… / 7
Works Cited…………………………….. / 7

Introduction

Many explanations can be offered about the true form of the “curveball.” Some pass it off as an optical illusion, that the baseball merely appears to curve in midair because of the angle of observation and the parabolic path due to gravity. However, this experiment sets out to prove that the baseball’s spin affects the air flowing around it. The resulting force can have a very real effect on the path, velocity, and acceleration of the baseball.

However, the wind effects don’t need to completely alter the direction of motion or anything drastic for this to be relevant. A baseball bat is only inches in diameter, so being able to create movement of only a few inches is very valuable. Still, pitching can be different every time a pitch is thrown, so the magnitude of this effects is often confused with other events during the balls flight path; thus the need for the controlled system.

A baseball swinging from a pendulum has three main forces acting on it: gravity, the attached rod or string, and air. The object of this experiment is to gain understanding about this force due to air: possibly the direction, magnitude, and how it affects a baseball’s path.

Project Description

The first order of business in setting up the experiment is to find a standard way of setting the baseball in motion, so that the path can be systematically analyzed and the setup repeated. The system to be analyzed is a baseball, hung by string, acting as a pendulum. The string is lightweight and thin, so its effects are neglected here. A hole was drilled into a baseball and then string was forced inside and glued in place.

First, the system is treated in two dimensional motion, to capture the normal effects of air drag and friction on the pendulum. Now the system is captured in motion by three cameras simultaneously, one each on the x, y, and z axis. All cameras captured fifteen frames per second accurately, and this is how the period of oscillation was measured.

Computers were then used to quantify the data. Many measurements needed to be taken to determine specific values for variables to be given later. The coordinate systems and variables used in analysis are represented in the following figure:

Preliminary Calculations

Mostly, we know almost all of the information needed for 2-D calculations. When it is moved into 3-D motion, the object of the experiment is to determine the effects of the forces.

Experimental Results

The data for height reached as viewed from the x and y axis was taken using similar triangles viewing from the x and y direction. I really had a problem here, because the distortion of the viewpoints made it excruciating to come out with a good answer for the height. After a while the best approach was to use similar triangles, and come to a consensus by basically counting pixels on the screen for each swing and the numbers came out reasonably. Using Pythagorean Theorem and the two values obtained from the two viewpoints, you can find the true distance of the baseball from the z-axis. This took a lot of number crunching and re-measuring of individual frames for the numbers to come out reasonably. The pendulum was about 1.1 meters long, and often it would come out that the length was equal to approximately 2 meters, or it would suggest that suddenly the pendulum swung five inches higher than the previous oscillation.

You can find the results on the following pages, but there is a lot of data to trudge through, so here are a few comments.

One interesting result is that the spin caused the pendulum to lose energy faster than swinging a baseball with no spin, by the two graphs on the results summary page. The theta dot and double theta dot graphs look very chaotic, but that is because the measurements were very dependent on tiny measurements, such as of single pixels. However, averages found on the results summary page is trustworthy because those are two measurements over a long period of time, so it would only be off by a small percent, while the individual measurements for each point on the graphs have a larger room for error.

Comparison of Results and Analysis

The most obvious difference is that the pendulum used was not perfect, so the period varied with each oscillation. Every swing caused the system to lose energy to due friction between the string and the support, and also to drag as the ball and string cut through the air.

The calculations for the period of a simple pendulum were actually about right even though the amplitude was large. The measurements of the period did vary depending on the captured frame, but the largest difference was only two frames, which is only 2/15ths of a second.

Works Cited

Adair, Robert K. The Physics of Baseball. NY: Harper Collins, 1990

Armenti Jr., Angelo. The Physics of Sports. NY: American Institute of Physics, 1992

Halfman, Robert L. Dynamics, Particles, Rigid Bodies and Systems. Ed. Howard W.

Emmons. London: A.W. PC, 1962

Watts, Robert G., and A. Terry Bahill. Keep Your Eye on the Ball. NY: W. H. Freeman

& Company, 1991

Tongue, Benson H., and Sheri D. Sheppard. Dynamics Analysis & Design of Systems in

Motion. J. W. & Sons, Inc., 2005

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