Schuler tuning

Schuler tuning describes the fundamental functional conditions for a gyrocompass.

As first explained by Max Schuler in his classic 1923 paper, a
pendulum whose period exactly equals the orbital period of ahypothetical satellite orbiting just above the surface of the
Earth (about 84 minutes) will tend to remain pointing at thecenter of the Earth when its support is suddenly displaced.This is the basic principle of Schuler tuning that mustbe included in the design of any inertial guidance systemthat will be operated near the Earth, such as in ships and aircraft.

Consider three hypothetical objects:
# A simple gravity pendulum, whose length equals the radius of the Earth, suspended near an enormous flat plate such that it encounters a uniform gravitational field of the same strength as that experienced by a small pendulum near the Earth's surface;
# A small body orbiting very near the surface of an airless perfect sphere the size and density of the Earth;
# A small body falling down an airless tunnel running from the North Pole to the South Pole through the center of the Earth.

Each of these will have the same period: about 84 minutes — though the third body only if the density of the Earth is assumed constant (in which case its movement is a harmonic oscillation).

A physical pendulum can be constructed to have an arbitrarily long period by having a large rotational moment of inertia about its pivot point in proportion to its bob weight. (In the two dimensional case consider a large and heavy disk with a slightly off-center center of mass. Such a device can be tuned to the specified period and placed in an initial state with the center of mass downward.) However physical pendulums are not used for Schuler tuning in practice.

In practical applications, Schuler tuning provides the inertial platform of a
navigation system with a feedback loop between its velocityoutput and its stabilizing gyros such that it behaves asthough it were such a pendulum. This makes it remain verticalas the vehicle moves from place to place on the surface ofthe Earth.

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