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accuracy in measuring horizontal accelerations. A slight tilt of the stable platform will introduce a
component of earth's gravity as acceleration on the aircraft and will result in incorrect distances and
velocities (Figure 16.4). Keeping the accelerometers level is the job of the feedback circuit. The
computer calculates distance traveled along the surface of the earth and moves the accelerometer
through an equivalent arc. Several factors affect aligning the accelerometer using this method. The earth
is not a sphere, but an oblate spheroid or geoid. Because the earth is not a smooth surface, there are local
deviations in the direction of gravity. The feedback circuit operates on the premise that the arc traversed
is proportional to distance traveled. Actually, the arc varies considerably because of the earth's shape;
the variation is greatest at the poles. The computer must solve for this irregularity in converting distance
to arc.
Figure 16.4. Effect of Accelerometer Tilt.
16.17.1. The accelerometers are kept level relative to astronomical rather than geocentric latitude. Using
the astronomical latitude, the accelerometers are kept aligned with the local horizon and also with the
earth's gravitational field. Feedback from the computer keeps the accelerometers level, correcting for
two types of apparent precession. If the inertial unit were stationary at the equator, it would be necessary
to rotate the accelerometers to maintain them level because of the earth's angular rotation of 15° per
hour. Also, movement of the stabilized platform would require corrections to keep the accelerometers
level. When using a local horizontal system, in which the accelerometers are maintained directly on the
gyro platform, the gyro platform must be torqued by a signal from the computer to keep the platform
horizontal. Apparent precession is illustrated in Figure 16.5.
AFPAM11-216 1 MARCH 2001 335
Figure 16.5. Apparent Precession.
16.17.2. A slight error in maintaining the horizontal would induce a major error in distance computation.
If an accelerometer picked up an error signal of 1/100 of the G-force, the error on a 1-hour flight would
be 208,000 feet (over 34 NM). In 1923, Dr Maxmillian Schuler showed a pendulum with a period of
84.4 minutes could solve the problem of eliminating inadvertent acceleration errors.
16.17.3. If a pendulum has a period of 84.4 minutes, it will indicate the vertical, regardless of
acceleration of the vehicle. He demonstrated that a device with a period of 84.4 minutes would remain
vertical to the horizon despite any acceleration on the device. The fundamental principle of the 84.4-
minute theorem is that if a pendulum had an arm equal in length to the radius of the earth, gravity would
have no effect on the bob. This is because the center of the bob would be at the center of gravity of the
earth and the pendulum arm would always remain vertical for all motions of the pivot point. While it
would be impossible to construct this pendulum, devices with an 84.4-minute cycle can be constructed
using gyroscopes. The Schuler pendulum phenomenon prevents the accumulation of errors which would
be caused by platform tilt and treating gravity as an acceleration. It will not compensate for errors in
azimuth resulting from the precession of the steering gyro. The amplitude of the Schuler cycle depends
upon the overall accuracy of the system. Figure 16.6 shows the Schuler-tuned system.
336 AFPAM11-216 1 MARCH 2001
Figure 16.6. Schuler Pendulum Phenomenon.
16.17.4. A spinning, untorqued gyro is space-oriented and will appear to move as the earth rotates
underneath it. This is undesirable for older systems because the accelerometers will not be kept
perpendicular to the local vertical. To earth-orient the gyro, we control apparent precession. If a force is
applied to the axis of a spinning gyro wheel that is free to move in a gimballing structure, the wheel will
move in a direction at right angles to the applied force. This is called torquing a gyro and can be
considered as mechanized or induced precession. A continuous torque, applied to the appropriate axis by
electromagnetic elements called torques, reorients the gyro wheel to maintain the stable element level
with respect to the earth, and keeps it pointed north. An analog or digital computer determines the torque
to be applied to the gyros through a loop that is tuned using the Schuler pendulum principle. The
necessary correction for earth rate depends on the position of the aircraft; the correction to be applied
about the vertical axis depends on the velocity of the aircraft.
16.17.5. It is important that the stable element be accurately leveled with respect to the local vertical and
aligned in azimuth with respect to true north. Precise leveling of the stable element is accomplished
　
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