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Follow The Bouncing Ball
Ball/Court Interaction - Part I

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

Ball physics studies would certainly be a lot simpler if we could narrow the variables down - for example, just count the ball spin (which has its own unique issues). However, the majority of ball physics studies must monitor a multitude of simultaneously changing factors to obtain results. Such is the case with ball/court interaction studies.

Aside from environmental factors and atmospheric conditions like wind, altitude, temperature, humidity and air pressure, the ball's trajectory after its bounce is affected by:

  • the velocity before bounce;
  • the angle the ball strikes the court (angle of incidence or angle in);
  • court surface material;
  • ball spin type and rate;
  • the behavior of the ball's materials.
  • Why examine ball/court interaction at all? These components affect the angle and velocity off of the court, the distance the ball travels after the bounce and the maximum rebound height. With a variety of court surfaces available, ball/court interaction affects the amount of time you have to get to the ball and the height the racquet can approach and strike the ball. If you have played on a variety of surfaces you know grass courts are considered "fast" (you typically have less time to get to the ball and the angle after the bounce is typically low) and clay courts are "slow." Hard court speeds are somewhere in between.

    As a guideline, what results would we expect? According to Professor Howard Brody's book, Tennis Science for Tennis Players, friction between the ball and the court:

  • causes the angle out (the rebound bounce) to change from the angle in;
  • the smaller the friction the smaller the rebound angle;
  • the smaller the friction the faster the court;
  • the larger the friction the greater the rebound angle;
  • the greater the friction the slower the court.
  • In a study done as part of a cooperative educational project between NASA Ames Research Center and Cislunar Aerospace, Inc. ball/court interaction affects were investigated.

    High speed cameras captured ball action at 250 frames per second. Balls were marked with a black line around the ball's circumference so spin rates could be examined. Different types of spin and rates of spin (flat, low topspin, medium topspin, high topspin, medium underspin and high underspin) and four court surfaces (hard, red clay, green clay and grass) were used in this investigation. Wilson "US Open" balls were used on each court. In addition, court specific balls (Wilson clay court balls on the green clay, Roland Garros balls [the French Open ball] on the red clay and Slazenger [Wimbledon] balls for the grass court) also were tested. A ball machine able to control ball spin and speed was used to launch the balls.

    Results - Angles Before And After The Bounce

    Results for flat (no spin) balls are summarized below. (You can click on the graphs for larger versions).

    Flat (No Spin) Ball - All Courts
    Average Angle In and Angle Out

    Court: Ball: Angle In: Angle Out: Difference
    Green Clay Wilson US Open26.8 37.5 10.7
    Green Clay Wilson Clay 28.2 41.0 12.8
    Red Clay Wilson US Open 26.5 37.5 11.0
    Red Clay Roland Garros24.3 34.7 10.4
    Hard US Open 23.9 32.9 9.1
    Grass US Open 24.9 29.4 4.5
    Grass Wimbledon 24.2 28.6 4.4

    Is this what we expected? Yes! Notice the difference between the rebound angle and the angle before the bounce. We expect grass to be fast and clay to be slow. The grass surface has a tendency to let the ball skid.

    The trend we expected and observed with the flat (no spin) continues with the topspin. Based on the difference between the angle in and angle out, grass is fastest by far, than the hard court and then the clay courts.

    However, there are some major differences. As the spin rate increases, the difference in the angles out is decreasing. While the angle out was always greater than the angle in for the flat (no spin) case, that trend disappears for the grass court with medium topspin. For heavy topspin, the angle out is significantly lower than than angle in.

    Looking at the other courts - red and green clay and the hard court - as the spin rate increases, the angle before the bounce is almost identical to the angle out. Determining the fastest court speed based on these numbers is no longer as easy as it was for the no spin case.

    Low Topspin - All Courts
    Average Angle In and Angle Out

    Court: Ball: Angle In: Angle Out: Difference
    Green Clay Wilson US Open27.5 35.5 8.0
    Green Clay Wilson Clay 29.2 36.4 7.2
    Red Clay Wilson US Open 25.5 34.4 8.9
    Red Clay Roland Garros25.2 32.7 7.5
    Hard US Open 26.6 33.1 6.5
    Grass US Open 25.3 28.7 3.4
    Grass Wimbledon 24.3 25.8 1.5

    Medium Topspin - All Courts
    Average Angle In and Angle Out

    Court: Ball: Angle In: Angle Out: Difference
    Green Clay Wilson US Open-NA- -NA- -NA-
    Green Clay Wilson Clay 25.4 30.4 5.0
    Red Clay Wilson US Open 22.8 28.3 5.5
    Red Clay Roland Garros -NA- -NA- -NA-
    Hard US Open 21.9 27.4 5.5
    Grass US Open 22.8 23.2 .4
    Grass Wimbledon 23.5 22.1 -1.4

    Heavy Topspin - All Courts
    Average Angle In and Angle Out

    Court: Ball: Angle In: Angle Out: Difference
    Green Clay Wilson US Open28.0 27.7 -.3
    Green Clay Wilson Clay 29.2 28.8 -.4
    Red Clay Wilson US Open 24.1 24.5 .4
    Red Clay Roland Garros25.2 26.4 1.2
    Hard US Open 25.1 24.8 -.3
    Grass US Open 24.8 18.6 -6.2
    Grass Wimbledon 23.4 16.8 -6.6

    In analyzing the underspin results, it was important to remember that after the bounce the ball would have topspin. Although it is observed from time to time, the majority of underspin balls change direction into topspin after the bounce.

    While balls with no spin or topspin before the bounce will naturally follow the direction of flight and generate topspin after the bounce, balls with underspin before the bounce change spin direction after the bounce and have topspin.

    Medium Underspin - All Courts
    Average Angle In and Angle Out

    Court: Ball: Angle In: Angle Out: Difference
    Green Clay Wilson US Open25.1 39.9 14.8
    Green Clay Wilson Clay 25.9 41.7 15.8
    Red Clay Wilson US Open 23.7 37.9 14.2
    Red Clay Roland Garros23.9 38.1 14.2
    Hard US Open 24.6 40.8 16.2
    Grass US Open 21.6 24.4 2.8
    Grass Wimbledon 22.9 26.1 3.2

    Heavy Underspin - All Courts
    Average Angle In and Angle Out

    Court: Ball: Angle In: Angle Out: Difference
    Green Clay Wilson US Open20.8 31.5 10.7
    Green Clay Wilson Clay 21.1 31.2 10.1
    Red Clay Wilson US Open 20.1 30.1 10.0
    Red Clay Roland Garros22.1 33.2 11.1
    Hard US Open 20.6 29.7 9.1
    Grass US Open 23.1 29.1 6.0
    Grass Wimbledon 22.9 25.6 2.7

    There are several interesting observations to make:

    1. The grass court balls did not behave like the balls on the slower courts.
    2. Medium underspin balls for the red and green clay and hard court had the steepest angles out and largest angle differences for any spin type and rate including heavy underspin.
    3. The heavy underspin balls had the lowest angles in.

    Why would the grass court behave differently? Unlike the slower courts the grass surface allows the balls to skid. There is less friction and interaction between the ball and the grass court.

    In Part II of this article, we'll look at how these angles affect the height and distance of the ball's trajectory after the bounce and the amount of time this gives you to get to the ball.

    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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