Modelling the impact of tennis balls on court surfaces.

A model of tennis balls impacting obliquely on tennis courts was developed in this study.
Balls were impacted normally on a force plate to read impact force data, and filmed at high
speed during oblique impacts. A normal model was created and then extended to cover
oblique impacts. The experimental data was used to verify the model in each case.
A study of surface testing methods found that tennis courts are significantly stiffer than
tennis balls; so much so that they can be considered rigid. A coefficient of friction between
ball and surface was all that was necessary to define a surface.
Normal impacts were performed on a force plate for four different ball constructions at
speeds between 3 and 20 ms-I
. Impact speed had a significant effect on coefficient of
restitution (ratio of rebound speed to inbound speed) - for example for a pressurised ball,
from about 0.8 at an impact speed of 3 msI
to about 0.6 at 20 msI. Pressureless balls
bounce at a similar speed to pressurised balls at low impact speeds, but slower at high
impact speeds. Punctured balls bounce slower throughout the range of impact speeds. All
balls showed a rapid increase in force during the initial part of the impact.
An iterative model was created to simulate normal impact. A numerical method was used
to find the effect of deformation shape on the relationship between centre of mass
movement and ball deformation. A total force during impact was created by combining
structural stiffness, material damping and impulsive reaction forces. This model worked
well for all ball types and used quasi-static compression data and a low speed drop test to
find the parameters. The impulsive force simulated the initial increase in force well.
A thorough experimental study of oblique impacts was performed by isolating in turn each
of the key incoming properties of impact. The incoming speed, spin and angle, together
with the ball and surface construction were individually varied in turn and the effect on
outgoing characteristics measured using high speed video footage. In most cases there was
a distinct change in rebound properties when rolling happened. Footage at up to 7000
frames per second was used to qualitatively explain the effect of deformation shapes on
energy losses. It was found that impacts with backspin caused more deformation and an
increased energy loss compared to normal impacts with the same vertical velocity. Impacts
with topspin had a reduced vertical energy loss.
The normal model was extended to include the horizontal and rotational forces necessary
to simulate an oblique impact. A damping compensation factor was included to adjust the
vertical energy losses at different spin rates. The oblique test data was used to verify the
model, and there was a very good correlation.