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How BallCheck measures bounce from sound

Last checked · 2 min read

Short answer

BallCheck times the gaps between a ball's bounces by listening to them. Each gap is shorter than the one before, and the ratio between gaps gives the ball's coefficient of restitution (COR), the share of speed it keeps on each bounce. Comparing that with a new ball of the same type on the same court gives the score.

Bounce, in one number

The coefficient of restitution (COR) is the ball's speed just after a bounce divided by its speed just before. A perfect bounce would be 1 and no bounce at all would be 0. For a straight drop, COR is the square root of rebound height divided by drop height.

Physicist Rod Cross puts a tennis ball on a hard court at about 0.75. Working back from the official rebound ranges gives about 0.73 to 0.76 for new tennis and padel balls, and about 0.62 to 0.66 for pickleballs. These are our calculations from the specs, ignoring air resistance.

Why sound works

A ball's flight time between two bounces depends only on how fast it left the floor. So the ratio of one gap to the gap before it equals the COR. You do not need to see how high the ball went: you only need to hear when it lands.

This is a well known method in physics teaching, published in the American Journal of Physics in 1977, 1981, 2001 and 2003. The 2001 paper did it with an ordinary PC sound card. A phone microphone times each bounce to well under a millisecond.

What BallCheck adds

  • It waits for the room to go quiet, then learns the background noise for a few seconds so it can ignore it.
  • It finds each bounce and rejects knocks, racket taps and footsteps that do not fit the pattern of a bouncing ball.
  • It measures every bounce separately, because COR drops slightly at higher impact speeds.
  • It compares your ball with a new ball of the same type on the same court type, because a soft or sandy floor takes energy out of every bounce.
  • With Precision check, it averages three drops and tells you how far to trust the result.

What it does not do

BallCheck gives an estimate, not a certified lab measurement. The ITF and FIP measure rebound on granite with video in a temperature controlled room. Your court, the temperature and how you drop the ball all affect the result, which is why BallCheck always compares like with like.

Sound is analysed on your phone and thrown away straight after. Nothing is recorded or uploaded.

Questions

How accurate is it?

Timing is very precise. Most of the variation comes from the drop itself and the court. Precision check uses three drops and shows an accuracy rating, so you can see how consistent they were.

Does it work in a noisy place?

It learns the background noise before each drop and ignores sounds that do not match a bouncing ball. A very loud spot, like next to a court with play on it, can still make results less reliable.

What is the official test rebound in the app?

It is an estimate of how high your ball would bounce in the official 254 cm drop test, worked out from its COR, and shown on the official range for that ball type.

Sources

  1. Rod Cross: Tennis physics, anyone? (Physics Today, 2008)
  2. Aguiar and Laudares: Listening to the coefficient of restitution and the gravitational acceleration of a bouncing ball (Am. J. Phys. 71, 2003)
  3. ITF: Ball Approval Tests

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