A Performance Analysis System for the Sport of Bowling

The ball's angular velocity increases until the discrepancy between the angular and linear
velocities is resolved (a condition called roll out). If the ball rolls out before reaching the
pins, it is no longer skidding, and the continuing decrease in its linear velocity due to
rolling friction also directly impacts the angular velocity (it begins to monotonically
decrease, as well). Under normal circumstances, the ball does not roll out before hitting
the pins, and therefore, the angular velocity generally increases until the ball hits the pins.
Given a uniform light distribution along the length of the lane, the light level seen by
SMARTDOT will be at its highest (brightest) when the module faces directly towards the
ceiling, and at its lowest (darkest) when the module faces directly towards the floor, with
a smooth transition occurring between those two points. Under these circumstances, a
graph of the light waveform appears as an increasing frequency "chirp". The peaks and
valleys of the sinusoid are spaced further apart near the release point, and get closer
together as the ball approaches the pins. Figure 3-5, which is a capture of the filtered
"Waveform" screen from the MASTER program, depicts this waveform.
If the ball rolls out, its angular velocity reaches a maximum at the roll out point, and then
begins decreasing. It is possible to use this information to detect whether or not roll out
has occurred by looking for a decrease in the angular velocity.
Recall also that friction-reducing lane oil is regularly applied to the first 30-40 feet of the
lane. Therefore, the ball is more prone to sliding on the upper half of the lane (nearer the
foul line), with the majority of the increase in angular velocity occurring on the lower
half of the lane (nearer the pins). Therefore, a graph of the angular velocity of the ball
versus time (or distance from the foul line) will have a hyperbolic or exponential shape,
assuming roll out has not occurred. The graph of the linear velocity will mirror that of
the angular velocity, starting high and falling off at the end. Figure 3-7, which is a
capture of the "Analysis" screen from the MASTER program, depicts these two graphs.
If the ball had rolled out, the graph of its angular velocity in Figure 3-7 would display an
inflection point at the point of roll out, decreasing after roll out, while the graph of its
linear velocity would continue to decrease. Figure 3-9 depicts a waveform that resulted
from the ball rolling out before hitting the pins.
3.1.2 The "Real" Waveform
The "jagged" appearance of the raw data waveform, as shown in Figure 3-1, indicates
that a good deal of high frequency "noise" has been captured along with the desired
waveform. Since the module filters out the 120 Hz flicker of the overhead fluorescent
lights while capturing the waveform, this noise must have another cause. In fact, the
noise could be the result of three additional sources: the non-homogenous nature of the
overhead lighting; the directionality of the light sensor that was introduced by placing the
SMARTDOT module at the bottom of a finger hole, 1 3 / 8 inches below the surface of the
ball; and from "aliasing" of frequencies greater than one-half the sampling frequency.
These higher frequencies might result from flash bulbs, reflections, etc. Other than these
transient sources, aliasing should have minimal impact, since there are no significant
sources of flickering light greater than 120 Hz in a bowling center.
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