MPXM2102AS datasheet(126/670 Pages) MOTOROLA

126 / 670 page

AN1635

2–90

Motorola Sensor Device Data

www.motorola.com/semiconductors

CAPTURE

WINDOW

POINT

IMPACT

THRESHOLD

LEVEL

SYSTEM AT 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

Eq. 1

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

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?

Freescale Semiconductor, Inc.

For More Information On This Product,

Go to: www.freescale.com

MPXM2102AS Datasheet(PDF) 126 Page - Motorola, Inc

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