handbook of modern sensors

8
Velocity and Acceleration
Acceleration is a dynamic characteristic of an object, because, according to Newton’s
second law, it essentially requires application of a force. In effect, the position,
velocity, and acceleration are all related: Velocity is a first derivative of position
and acceleration is the second derivative. However, in a noisy environment, taking
derivatives may result in extremely high errors, even if complex and sophisticated
signal conditioning circuits are employed. Therefore, velocity and acceleration are
not derived from the position detectors, but rather measured by special sensors. As
a rule of thumb, in low-frequency applications (having a bandwidth on the order of
1 Hz), position and displacement measurements generally provide good accuracy. In
the intermediate-frequency applications (less than 1 kHz), velocity measurement is
usually favored. In measuring high-frequency motions with appreciable noise levels,
acceleration measurement is preferred.
Velocity (speed or rate of motion) may be linear or angular; that is, it shows how
fast an object moves along a straight line or how fast it rotates. The measure of velocity
depends on the scale of an object and may be expressed, say, in millimeters per
second or miles per hour. Currently, the speed of a large object, especially of a land or
water vehicle, may be very efficiently determined by a GPS (Geo Positioning System)
that operates by receiving radio signals from a number of the Earth’s satellites and by
computing the time delay of signals received from one satellite as compared with the
other. When the position of a vehicle is determined with a periodic rate, computation
of its velocity is no problem. For smaller objects and shorter distances, GPS is not
a solution. Detecting the velocity for such objects requires different references. A
basic idea behind many sensors for the transduction of velocity or acceleration is a
measurement of the displacement of an object with respect to some reference object
which, in many cases, is an integral part of the sensor. Displacement here is a keyword.
Many velocity or acceleration sensors contain components which are sensitive to a
displacement. Thus, the position and displacement sensors described are the integral
parts of the velocity sensors and accelerometers. In some instances, however, velocity
sensors and accelerometers do not use an intermediate displacement transducer
because their motions may be directly converted into electrical signals. For example,
moving a magnet though a coil of wire will induce a voltage in the coil according