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

## Mathematical Modeling of the Coefficient of Restitution Typical Data

### by M. Styer,

#### Adapted from a science fair report published March, 2004

This first graph is the elasticity calculated by dropping the balls from various heights (the x-axis values) and visually estimating how high they bounced on a kitchen linoleum tile floor. Note that at lower heights the balls are more elastic, that is, a smaller proportion of the energy is lost for small bounces.

By analyzing the sound track of the bounces, one can determine the bounce velocities and heights, hence the elasticity and COR for fairly small heights (down to about one centimeter.) This graph shows the analysis of the sound track of a table tennis ball dropping from heights of 40 centimeters (velocity 280 cm/sec) down to heights as low as 0.27 cm (velocity 23 cm/sec). Note the variance in the data at the low heights. This variance was typical for every type of ball dropped, whether on kitchen linoleum tiles or on the bathroom hard tiles.

For more information, please see the complete data file (Excel). Other graphs show the elasticity when bounced on a bathroom hard tile floor, and many more graphs at low heights obtained from the sound tracks. The data contain literally hundreds of observations.