These sensors provide reference outputs that are

processed to develop navigation data.

To illustrate the principle of inertial navigation,

consider the accelerometer device illustrated in

Figure 17.1; this is formed with a mass and two

springs within a housing. Newton’s second law of

motion states that a body at rest (or in motion)

tends to stay at rest (or in motion) unless acted

upon by an outside force. Moving the

accelerometer to the right causes a relative

movement of mass to the left. If the applied force

is maintained, the mass returns to the neutral

position. When the accelerometer is moved to the

left, or brought to rest, the relative movement of

the mass is to the right. The mass continues in its

existing state of rest or movement unless the

applied force changes; this is the property of

inertia. Attaching an electrical pick-up to the

accelerometer creates a transducer that can

measure the amount of relative movement of the

mass. This relative movement is in direct

proportion to the acceleration being applied to

the device, expressed in m/s2. If we take this

Figure 17.1 Accelerometer

electrical output and mathematically integrate

the value, we are effectively multiplying the

acceleration output by time; this can be expressed

as:

Time × acceleration = s × m/s2 = m/s = velocity

If we now take this velocity output and

mathematically integrate the value, we are once

again multiplying the output by time; this can be

expressed as:

Time × velocity = s × m/s= m = distance

In summary, we started by measuring

acceleration, and were able to derive velocity

and distance information by applying the

mathematical process of integration. To illustrate

this principle, consider a body accelerating at 5

m/s2, after ten seconds the velocity of the body

will be 50 m/s. If this body now travels at a

constant velocity of 50 m/s for ten seconds, it will

have changed position by 500 m.