Dynamic testing of tennisballs - Cross, R. (2001)
A standard test of a tennis ball is to measure the compression under a certain load, then compress it further, then measure the compression again while the ball is unloaded. This provides a measure of the ball stiffness and it also provides a measure of the energy loss in the ball. However, the results of this test are not consistent with the results from a standard drop test. A ball dropped from a height of 100 inches must bounce to a height of about 55 inches. It therefore loses about 45% of its energy during the bounce. But it loses only about 15% of its energy during a compression test. Furthermore, the ball is about twice as stiff during the bounce as it is in a quasi-static compression test. To investigate this further, a force plate was constructed, using four large piezo ceramic 50 mm squares connected electrically in parallel to form a larger plate of dimensions 100 mm x 100 mm x 4 mm. The voltage output from a piezo is proportional to the applied force. A tennis ball was dropped on the plate, giving an output signal which represents force vs. time on the ball. Since force = mass x acceleration, one can integrate the signal to give ball velocity vs. time, then integrate again to get the displacement of the centre of mass vs. time. A plot of force vs. displacement therefore gives a dynamic hysteresis curve that is analogous to the quasi-static force vs. compression curve but it is more directly relevant to the bounce properties of the ball. The force rises to about half its peak value in the first 0.2 ms, due to compression of the cloth cover and the rubber which remains very stiff under compression. The ball then buckles, and the initial contact region pops up inside the ball. During this phase, the ball stiffness suddenly drops.