Restitution
Though this is not a formal definition of the
term, restitution involves the ball losing energy
upon impact with the floor, resulting in it bouncing
lower than the height from which it was dropped. To
measure this effect, the balls were dropped from a
fixed height beneath an ultrasound position sensor
to accurately record its height (see diagram).
As expected, the data
clearly exhibits the behavior of a damped harmonic
oscillator (see graph).
Our tests showed that the synthetic ball bounces
back lower by 5-8% when dropped from a height of
little over four feet, depending on the hardness of
the floor. Specifically, for a hard linoleum floor
with concrete underneath, the conditioned leather
ball bounced back an average distance of 2.2 inches
higher compared to the synthetic ball, when dropped
from a height of 4 feet 3.7 inches. The coefficient
of restitution is 0.81 for the leather ball at this
height, increasing monotonically to 0.85 for
successive bounces till they reach approximately one
third of the drop height. The coefficient of
restitution for the synthetic ball was 0.79-0.84
over the same range of heights. The difference in
bounce was more pronounced (increasing to 4 inches)
on softer, more pliant floors (see graph).
In order to compensate for the difference in bounce,
we re-tested the basketballs by over-inflating the
synthetic balls. The synthetic ball had the same
bounce characteristic as a conditioned leather ball
when over-inflated to 14 psi (the required
over-inflation depends on the hardness of the
floor). The leather ball was inflated to the
recommended pressure of 8.5 psi for comparison.
The bounce test was repeated with a new
(unconditioned) leather ball. We found that the
unconditioned leather ball had similar coefficient
of restitution to the synthetic ball at same
inflation -- that is, both bounced back essentially
to the same height. We conclude that the
conditioning of leather balls increases their
bounce. However, thus far, we have not attempted to
condition our new leather ball and repeat the tests.
While performing these tests we had a harder time
keeping the new synthetic ball underneath our
position sensor. This suggested that the new ball
was more prone to erratic bounces, prompting further
tests. One possible explanation is that this is a
result of the deep embossing used on the new
synthetic ball.
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