Last month, we examined how a ball's approach angle affects its outbound angle as spin rates varies on 4 different court surfaces (hard, green and red clay, grass). Four types of balls were used: Wilson US Open (hard court), Roland Garros (red clay), Slazenger Wimbledon (grass), and Wilson clay court.

This month we'll look at rebound height and distance for these same balls and courts . Next month we'll wrap things up and examine ball velocity on these different surfaces.

You may know from playing tennis that a ball hit with topspin bounces higher than a flat (no spin) ball. Balls hit with underspin bounce lower than flat balls. How much higher does it bounce and how does this vary with the amount of spin?

In the charts below we define "Rebound Height" as the ball's maximum vertical height obtained (in inches) and the "Rebound Distance" is the horizontal distance it took the ball to reach that height. (NA means there was no data available in that category.) Click on the thumbnail charts for full sized graphics.

These were the pre-bounce spin rates used. There was quite a variation within each range, but these numbers can be used as a guide.

Does topspin bounce higher than flat and underspin balls?

Does topspin bounce higher than flat and underspin balls? Definitely! Note the grass court. If you have played on grass you know how low that ball bounces up and how little time you have to get to it.

Below are the graphs for ball height and distance by court type for each spin rate tested. Even without expanding the charts its easy to see that topspin bounced higher than the flat balls and underspin less than the flat balls.

In the diagrams below blue designates the flat balls, red and grey the topspin balls, and green the underspin balls. The chart on the left represents the ball's maximum height and the one on the right is the distance the ball traveled to reach the maximum height.

The green clay court had the highest rebound height and longest rebound distance, followed by the hard court, red clay court and last, the grass court. Is it the court, spin type and rate that generates the longer distance? Doesn't the velocity out affect these distances? We'll look at velocity next month.

One last general comment, with the exception of the US Open ball on the grass court, medium underspin balls bounced higher than heavy underspin balls.

Green Clay Court Results: In general, both the US Open ball and the Wilson Clay ball followed the expected trend: topspin higher than flat, flat bounced higher than underspin. It's interesting to note that the low and medium topspin averages were slightly lower than the flat ball average. However, the high topspin and underspin performed as expected. The green clay court had the highest average rebound height for all ball spins: flat, low, medium and high topspin, medium and high underspin. Except for the low topspin, the green clay also had the longest rebound distance.

Hard Court Results: The US Open ball followed the expected trend: topspin higher than flat, flat bounced higher than underspin. Low topspin bounced an average of 4 inches higher than the medium and heavy topspin. The hard court had the second highest average rebound height for all ball spins. It had the second longest distance for all balls except the low topspin where it was ranked first.

Grass Court Results: Clearly much different but not unexpected results. The grass court rebound height was significantly lower than the rebound height for other courts. In general it bounced about 50% less than the balls on the other courts. The grass court also had the shortest rebound distance for all spin types and rates except the medium underspin. The grass court ranked fourth (last) in rebound height and distance.

Until Next Month ... Jani

References

Brody, H., Tennis Science For Tennis Players, University of Penn. Press, 1987.

Cislunar Aerospace, Inc., wings.avkids.com/Tennis, 1997-2002.

Acknowledgement to NASA Ames Research Center for their assistance through agreements NCC2-9010 and NCC2-9014.