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:

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:

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

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.

Medium Topspin - All Courts
Average Angle In and Angle Out

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

Heavy Underspin - All Courts
Average Angle In and Angle Out

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

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.