It is very clear that assuming all of the sports have an equal swing time (tswing) would be inappropriate
as, for example, tswing for tenpin bowling is 12.5 times greater than tswing for badminton. The difference in
swing time is likely to be partly due to the implement's moment of inertia but it is also partly due to the
actual motion, which limits how fast a swing can be. For example a badminton smash, which produces
head speed almost entirely from a rotational wrist motion, as found by Kwan et al [8], will allow a quick
swing and is a simple motion to analyse. Conversely the forward drive in cricket is a much more complex
movement involving the rotation of both arms and a large amount of translation with the step forwards,
which is naturally a much slower movement and a more difficult motion to simplify for analysis.
Due to the influence of swing time, this was used to normalise the data further. The tip velocity for
each sport was divided by the swing time for that activity to produce a new variable to replace the swing
speed: the apparent acceleration at the tip of the implement (aTIP) or the swing acceleration.
The swing acceleration is a much more appropriate variable to use in analysis when considering
multiple sports because it removes the factor of swing time. Removing the effect of swing time is
important because an athlete performing a swing with a longer swing time can apply an accelerating force
to the implement for a longer period of time, potentially speeding up the implement more than if they
were performing a shorter swing. Taking the acceleration data also draws the data closer together which
produces a more solid relationship as can be seen in Fig. 2. This is shown by the fact that the log data for
the acceleration is much more closely correlated with the moment of inertia than the velocity data (r2
=-
0.82, p=0.006 compared to r2
=-0.66, p=0.06). This new relationship can be defined in a similar manner to