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Follow The Bouncing Ball
Ball/Court Interaction - Part II

Jani Macari Pallis, 
Ph.D. Photo
Jani Macari Pallis, Ph.D.

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.

Flat : 0 rev/min
Low Topspin: 900 rev/min
Medium Topspin: 1500 rev/min
Heavy Topspin: 3000 rev/min
Medium Underspin: 1500 rev/min
Heavy Underspin: 2500 rev/min

Does topspin bounce higher than flat and underspin balls?


Graph Graph

Court: Ball: Rebound Height: Rebound Distance:
Green Clay Wilson US Open50.8 121.7
Green Clay Wilson Clay 60.2 126.5
Red Clay Wilson US Open 45.3 103.6
Red Clay Roland Garros44.5 109.1
Hard US Open 45.5 115.8
Grass US Open 26.5 87.2
Grass Wimbledon 27.6 93.6

Low Topspin

Graph Graph

Court: Ball: Rebound Height: Rebound Distance:
Green Clay Wilson US Open58.1 148.4
Green Clay Wilson Clay 58.0 143.0
Red Clay Wilson US Open 50.6 129.7
Red Clay Roland Garros49.3 135.8
Hard US Open 57.3 162.6
Grass US Open 33.1 114.0
Grass Wimbledon 31.6 122.6

Medium Topspin

Graph Graph

Court: Ball: Rebound Height: Rebound Distance:
Green Clay Wilson US Open-NA- -NA-
Green Clay Wilson Clay 58.4 185.7
Red Clay Wilson US Open 48.6 145.9
Red Clay Roland Garros-NA- -NA-
Hard US Open 52.8 183.5
Grass US Open 29.9 127.7
Grass Wimbledon 30.5 140.4

Heavy Topspin

Graph Graph

Court: Ball: Rebound Height: Rebound Distance:
Green Clay Wilson US Open61.1 209.0
Green Clay Wilson Clay 65.9 213.0
Red Clay Wilson US Open 49.1 185.7
Red Clay Roland Garros50.6 176.3
Hard US Open 52.9 204.2
Grass US Open 26.2 143.9
Grass Wimbledon 24.6 148.2

Medium Underspin

Graph Graph

Court: Ball: Rebound Height: Rebound Distance:
Green Clay Wilson US Open44.3 97.7
Green Clay Wilson Clay 43.9 91.5
Red Clay Wilson US Open 40.9 95.2
Red Clay Roland Garros36.9 78.4
Hard US Open 38.9 81.4
Grass US Open 20.5 83.3
Grass Wimbledon 21.1 78.8

Heavy Underspin

Graph Graph

Court: Ball: Rebound Height: Rebound Distance:
Green Clay Wilson US Open33.5 101.4
Green Clay Wilson Clay 34.1 103.8
Red Clay Wilson US Open 31.4 98.6
Red Clay Roland Garros33.1 95.1
Hard US Open 26.3 81.1
Grass US Open 23.1 77.2
Grass Wimbledon 18.6 71.7

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.

Green Clay Court
Height - Distance

Graph Graph

Red Clay Court Results: Both the US Open ball and Roland Garros ball followed the expected trend: topspin higher than flat, flat bounced higher than underspin. The topspin heights (low, medium and heavy) for both balls were very close in height - about 50 inches. The red clay court had the third highest average rebound height and distance for all ball spins.

Red Clay Court
Height - Distance

Graph Graph

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.

Hard Court
Height - Distance

Graph Graph

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.

Grass Court
Height - Distance

Graph Graph

Next month we'll conclude this series of articles on ball/court interaction and focus on ball velocity.

Until Next Month ... Jani


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.

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This column is copyrighted by Jani Macari Pallis, Ph.D., all rights reserved.

Dr. Jani Macari Pallis is the founder and CEO of Cislunar Aerospace, Inc., an engineering and research firm in San Francisco. In addition to her engineering practice, she has led two collaborations between NASA and Cislunar, creating educational materials on the aerodynamics of sports for pre-college students and educators. As the head of NASA's "Aerodynamics in Sports" project, she has led a team of researchers investigating the aerodynamics, physics and biomechanics of tennis. The group has conducted high speed video data capture at the US Open and research of ball/court interaction, footwork, serve speeds, trajectories and ball aerodynamics. Pallis received a BS and MS from the Georgia Institute of Technology, an MS in mechanical engineering from the University of California, Berkeley and a Ph.D. in mechanical and aeronautical engineering from the University of California, Davis. She is a member of the Executive Committee of The International Sports Engineering Association.

Questions and comments about these columns can be directed to Jani by using this form.


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