to the y-coordinate. By looking at figure 7-31, you

detecting a positive acceleration. It also shows the

y-accelerometer detecting a negative acceleration

during this interval. If the vehicle maintains a

constant speed throughout the turn, the detected

acceleration results from a velocity change. This

change is due to a change in direction rather than

a change in speed. This acceleration is radial

(centripetal) acceleration (AR). The direction of

the radial acceleration is toward the center of the

turn and perpendicular to tangential velocity (VT).

Find coordinates (17.5, 17) in figure 7-30. If the

speed hadn't been constant during the turn, a

This acceleration would parallel the tangential

velocity (VT) vector and be normal (at a right

direction of the tangential acceleration would

depend upon whether the speed was increasing

or decreasing, positive or negative. If the

turning vehicle's acceleration is due to changes

in speed and direction, the accelerometers detect

the x and y components of the resultant of

the two accelerations.

Remember, when detecting acceleration of an

accelerating body, accelerometers detect only

the component of the resultant acceleration along

their sensitive axis. Accelerometers can't tell if the

Figure 7-31 is an illustration of a typical set

detected velocity change is due to a speed change

of acceleration and velocity curves from the INS

or a direction change or both, Nor does it matter

shown in figure 7-30.

what forces cause the velocity changes. The result

Referring to figures 7-30 and 7-31, the

is the same, provided the accelerometers maintain

operation of the plane inertial navigation system

correspondence with the coordinate axes.

is explained as follows: The vehicle aligns

Refer to the acceleration and velocity curves

(initializes) on the coordinate system with a

in figure 7-31. Notice the integration of the

displacement of 3 on the x and y axes. That is,

x-component of acceleration for the interval t15

both x and y displacement indicators read 3. At

to t20. It shows an increase in the x-component

time t3, the vehicle experiences an acceleration,

of velocity and, therefore, a corresponding

A, in a direction of 45 from the x-axis. The ac-

increase in displacement along the x-axis.

celerometers detect only that portion of the

Integration of the y-component of acceleration

acceleration that lies along its sensitive axis. This

over the same interval shows that the velocity goes

means the x-accelerometer detects the component

to zero at time t20. Therefore, the displacement

of acceleration along the x-axis. This is A cos a.

along the y-axis ceases to change. Hence at time

The y-accelerometer detects the component of A

t15, the displacement is (15, 15). At time t20, the

along the y-axis, which is A sin a. The vehicle

displacement is (20, 15) and at time t25, the

continues in a direction of 45 until time t15. At

displacement is (25, 15), etc.

this time it begins a turn to the right. Since sine

The INS just described navigates very well on

and cosine are equal at an angle of 450, the

a flat surface. However, navigation on the earth

displacements along x and y are equal at time t15.

requires a highly complex inertial system. The

This says x = 15 and y = 15. Also, it means the

earth, of course, is not flat, neither is it exactly

acceleration and velocity along the x-axis is equal

round. Its radius at the poles is less than its radius

to the acceleration and velocity along the y-axis.

at the equator. It also spins about its polar axis

At time tl5, the vehicle begins a right turn, it

and orbits around the sun. You must take all of

completes the turn at time t20. The new direction

these factors into account and correct them

is parallel to the x-coordinate and perpendicular