Remember from elementary physics that

acceleration, whose units are ft/sec2, multiplied

by time in seconds is velocity in ft/sec. Also, that

velocity (ft/sec) multiplied by time (sec) is

displacement (ft). The integration of acceleration,

for example, is the mathematical process of

summing all minute acceleration-time increments

over a given period. The result of the integration

of acceleration is velocity over the same period.

The same integration process performed on

velocity gives displacement or distance traveled

over the same period.

train returns to point A by traveling backwards.

Thus, the simple inertial device is not disoriented.

At point A the readout device shows the value that

was chosen as a reference. This is the displace-

ment at point B minus the distance traveled from

point B to point A.

An example of how a simple single-axis INS

Figure 7-28, view A, is a graph of the detected

operates is illustrated as follows: Assume a

acceleration. View B is the velocity curve obtained

person is on an INS-equipped train on railroad

by integrating the acceleration curve shown in

tracks at the equator. The tracks run in a straight

view A. View C is the displacement curve obtained

line east and west only, The INS consists of an

by integrating the velocity curve shown in view

acceleration detecting device (accelerometer), an

B. All three curves are plotted as a function of

integrating device, and a displacement readout

time.

device. The accelerometer can sense movement in

The acceleration curve (fig. 7-28, view A)

only one direction, along its sensitive axis. The

begins at time to as the train begins to travel from

sensitive axis is an imaginary line parallel to the

point A. Look at view C. The acceleration at time

movement of the mass within the detecting device.

to has a value of al, and it remains at that value

The acceleration detecting device is oriented in the

until t1. At t1 the train ceases to accelerate.

train so that it detects accelerations when the train

Therefore, acceleration goes to zero. At this point,

is moving forward or backward. Figure 7-27 is

the train reaches a steady velocity. The train

a block diagram of such a device.

continues traveling at a constant velocity until

If the train starts moving at point A, you will

time t2 where the train begins to stop. The

note a specific reading on the displacement

acceleration detector detects an acceleration equal

readout device. When the train reaches point B

in value to a1, but its direction is opposite. This

and stops, the readout device will show the new

position. The distance traveled from point A to

now stationary and standing at its destination--

point B added to the reference value noted at point

A will show on the displacement indicator. The

point B.