A Performance Analysis System for the Sport of Bowling

• The ball takes the shortest path from the foul line to the head pin: In
actuality, the ball is rarely thrown straight at the head pin from the center of the
foul line. Instead the ball is rolled with some amount of hook, and is released
from some place other than the center of the lane, and is initially directed
somewhat toward the right gutter (for a right-handed bowler). If the ball were
thrown from the outside edge of the right gutter in a straight line 45-50 feet down
the lane, and then suddenly hooked straight toward the pocket, it would travel an
extra 7 / 8 ". At the other extreme, if the ball were released at the left gutter, and
traced a regular arc to the right gutter at 30 feet, and then back to the head pin, it
would travel an extra 6". This is an extreme amount of hook, but will be factored
into the error budget as ±3".
• The ball and pins each have fixed diameters: The ABC maintains tight control
over the allowed dimensions of the ball and the pins. The ball has a nominal
diameter of 8.547 ±0.047", resulting in a nominal circumference of 26.853
±0.149". The diameter of the ball contributes a negligible error. However, the
circumference of the ball, which is used in later calculations to estimate the
amount of sliding and the coefficient of friction, could be multiplied by the total
number of revolutions the ball makes during a shot, which can total 20 or more.
In this case, the error contribution due to the ball's circumference could contribute
up to ±3".
At the height that the ball strikes a bowling pin (8.77"), the pin must have a
nominal diameter of 4.766 ±0.031". This is an insignificant contribution to the
error calculations.
Combining the three significant errors (at the foul line, at the pins, and the ball path),
yields a total of approximately ±12" of error in the distance the ball travels. For a
nominal distance of 60 feet, the total error works out to ±1.67%. For a ball thrown at 15
mph, this error will manifest itself in the velocity calculations as a difference of 0.25
mph.
This error could be reduced further by supplying the appropriate information to the
MASTER program. The bowler could input their normal release point as a configuration
parameter. Then, during normal play, they would indicate the approximate board where
the ball was released, the extreme right (or left) board that the ball crossed on its path to
the pins, and the first pin the ball hit, along with the type of hit (head on, right, left, graze,
etc.) and/or the board the ball was on at the time of impact. The analysis software would
utilize this information in its calculations. This type of input could reduce the margin of
error to less than 6", increasing the velocity resolution to 0.1 mph.
3.5.2 Time
Another assumption is that the microprocessor's clock is accurate. If the clock is based
on a quartz crystal, it will be accurate over temperature to at least ±200 ppm (0.02%), or
600 µsecs over a 3-second shot, which is an insignificant error contribution. If a ceramic
resonator is used (because it is much cheaper and much more durable), a ±2% error over
temperature is possible, which is ±60 msecs over a 3 second shot. This is not
insignificant, and would be additive to the distance error in any calculation of velocity.
However, this error could be calibrated out by measuring the actual clock rate with a
more precise clock and compensating for the difference in the MASTER software.
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