FEET
PER
SECOND

FEET

Accelerometer Output Intergration
Figure 6

ACCELERATION
VELOCITY
DISTANCE
INPUT
AXIS

Rate Integrating Gyro
Figure 7

EFFECTIVITY
AIRPLANES WITH DELCO INS
CONFIG 1 798 Page 12
34-41-00

 Apr 25/86
 (6)  
Ground speed (GS) is the velocity with which the airplane is moving over the earth's surface.

 (7)  
Drift angle (DA) is the angle between the airplane's true heading and ground track.

 (8)  
Desired track angle (DSRTK) is the angle between true north and an imaginary line on the ground connecting successive position points desired to overfly; this line being the great circle segment that lies between two successive waypoints.

 (9)  
Present position (POS) is the actual latitude and longitude position of the airplane.

 (10)
 Cross track distance (XTK) is the shortest distance between the airplane's present position and the desired track.

 (11)
 Track angle error (TKE) is the angle between the airplane's actual ground track and the desired ground track.

 (12)
 Distance (DIST) is the great circle distance between the present position of the aircraft and the next waypoint or destination.

 2.  Basic INS Principles
____________________
 A.  The basic components of any inertial navigation system include accelerometers, gyros, inertial platforms, and computers. An understanding of INS operation is predicated upon an understanding of these basic devices.
 B.  Accelerometers
 (1)  
An essential component of any inertial navigation system is the accelerometer which senses changes in airplane velocity. In its simplest form, an accelerometer consists of a small weight (proof mass) suspended between two springs (Fig. 5). Acceleration sensed in a horizontal direction causes the mass to compress one of the supporting springs and stretch the other. The compressive force and the equal but opposite tensile force are proportional to the degree of airplane acceleration along the accelerometer sense axis. Spring displacement is directly proportional to the accelerating or decelerating forces which can be read on a scale calibrated in gravity (g) units.

 (2)  
As long as the accelerometer remains with its sense axis perpendicular to the local vertical axis of the earth's gravitational field, only accelerations due to airplane horizontal velocity changes are sensed. Therefore, a simple accelerometer must be kept level at all times so that it will not misinterpret the force of gravity as an acceleration. An accelerometer at rest can be used, however, to sense the direction of gravity as a vertical acceleration. For example, an accelerometer senses components of gravitational acceleration as its sense axis is tilted toward the local vertical axis. In this instance it functions as a level detector.

 (3)  
Mathematically, it is possible to derive functions of velocity and distance from an original acceleration function through a process of successive integration (Fig. 6). In this manner, pulse signals representing airplane acceleration are electronically integrated to obtain airplane velocity. The airplane velocity is then integrated to obtain distance traveled.

 C.  Gyros (Fig. 7)
 EFFECTIVITY
 AIRPLANES WITH DELCO INS  CONFIG 1  03 A Page 13  Apr 25/9734-41-00
 (1)  
Another essential component of an inertial navigation system is the gyro. In its simple form the gyro is an accurately balanced spinning flywheel or rotor (Fig. 7). The rotor spins about a central or spin axis (SA) which passes through its center of gravity. The rotor shaft and its bearings are suspended within a gimbal. The gimbal is free to rotate about an axis which is perpendicular to the rotor spin axis called the gyro output axis (OA). The gyro operates on the principle of gyroscopic inertia which is the characteristic of a rotating mass to resist any forces which tend to change the direction of its spin axis. When a torque is applied around an axis perpendicular to both the SA and OA axis, namely the input axis (IA), the spin axis will tip but not in the direction of the torquing force as would be expected. Instead, the spin axis rotates around the output axis at right angles to the applied torque. This is known as induced gyroscopic precession.

 (2)  
Gyroscopic inertia fixes the spin axis of the gyro in space. However, because the earth rotates in space, the space-oriented gyro appears to rotate with respect to an earth-bound observer. This apparent rotation of the gyro spin axis is called apparent gyroscopic precession. Except for two special cases, this makes the gyro unsuitable for use as an earth-fixed reference unless the gyro is deliberately torqued to rotate at a rate proportional to the earth's rotation rate (earth rate). When torqued in this manner, the spin axis appears stationary and the gyro is effectively slaved to the earth's coordinate system.
　
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