2–90
Motorola Sensor Device Data
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A
B
CAPTURE
WINDOW
POINT
OF
IMPACT
THRESHOLD
LEVEL
SYSTEMAT STEADY RATE
OSCILLATIONS THAT RESULT
AS ENERGY IS DISSIPATED
Figure 2. Typical Crash Pattern for the Baseball Pitch Speedometer Demo
THEORY OF OPERATION
When a ball is thrown against the target, the accelerometer
senses the impact and produces an analog output signal,
proportional to the acceleration measured, resulting in a crash
signature. The amplitude and duration of the crash signature
is a function of the velocity of the ball. How can this crash
signature be correlated to the velocity of the baseball By
making use of the principle of conservation of momentum (see
Equation 1). The principle of conservation of momentum
states that the total momentum within a closed system
remains constant. In our case, the system consists of the
thrown ball and the target.
mball *Vball,initial + mtarget *Vtarget,initial =
mball *Vball,final + mtarget *Vtarget,final
When the ball is thrown, it has a momentum equivalent to
mball *Vball,initial. The target initially has zero momentum
since it is stationary. When the ball collides with the target,
part of the momentum of the ball is transferred to the target,
and the target will momentarily experience acceleration,
velocity, and some finite, though small, displacement before
dissipating the momentum and returning to a rest state. The
Eq. 1
other portion of momentum is retained by the ball as it bounces
off the target, due to the elastic nature of the collision. By
measuring the acceleration imparted on the target, its velocity
is computed through integration. Ideally, if the mass of the ball,
the mass of the target, and the final velocity of the ball are
known, then the problem could be solved analytically and the
initial velocity of the baseball determined.
The analysis of the crash phenomenon is, however, actually
quite complex. Some factors that must be taken into account
and that complicate the analysis greatly, are the spring
constant and damping coefficient of the target. The target will
be displaced during impact because it is anchored to the frame
by a thick rubber mat. This action effectively causes the
system to have a certain amount of spring. Also, though the
mat is very dense, it will deform somewhat during impact and
will act as shock absorber. In addition, the ball itself also has
a spring constant and damping coefficient associated with it,
since it bounces off the target and, though not noticeable by
the naked eye, will deform during the impact. Finally, and of
even greater significance, the mass of the ball, the mass of the
target, and the final velocity of the ball are neither known nor
measured. So how can the system work
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