The Journal of Online Mathematics and Its Applications, Volume 7 (2007)
Bouncing Balls and Geometric Series, Robert Styer and Morgan Besson

## How a Ball Actually Bounces

We claimed that a golf ball or a super ball bounces so that the height of each bounce is a fraction of the height of the previous bounce, in other words, the elasticity is constant. The middle school daughter of the first author did not believe this, and wrote her spring 2004 award winning science fair project on bouncing balls. She bounced several types of balls from several heights on different types of surfaces. The links below are to the science fair report and the accompanying data and graphs:

Like most experimental science, her results are not clear and definitive. But they definitely suggest that the elasticity coefficient and the closely related coefficient of restitution rise somewhat as the height falls (roughly 0.01 to 0.06 change in the coefficient of restitution per meter change in height). Somewhat surprisingly, the elasticity does not seem to rise all the way to 100% as the height approaches zero (the limit for very small heights seems to be 0.8 to 0.9).

For very small heights, the data had a large variance. She thought this might be a function of irregularities in the balls, but the Paul Ryan reference below used steel ball bearings on a granite surface, and his data showed very similar variance. So there is plenty of room for more experimenting by bright young students!

Selected web references from the report:

1. Hwang, Fu-Kwun. Bouncing Balls
2. Johnson, Porter W. Bouncing Balls"
3. Ryan, Paul. Computerized Technique to Determine and Analyze the Coefficient of Restitution