Schuler tuning

As Schuler period is called the oscillation period of approximately 84.4 minutes. The analyzes are based on Maximilian Schuler, who sought to minimize the influence of the rolling motions of a ship on a gyrocompass.

Examples of its occurrence are:

• Period of oscillation of a pendulum with the length of the Earth's radius 6370 km
• Period of a theoretical satellite orbits at sea level
• Total time it would take a stone, until he returns to the starting point, if he cut through the earth by one, airless tunnel falls. The centrifugal force is neglected. If the tunnel axis is not the same as the axis of rotation of the earth side contact forces ( Coriolis force ) which must be added, for example by rail. Here, the tunnel does not have to pass through the center of the earth, each other straight connection of two points on the earth's surface results in the same time period. Again, the body must slide on rails, so as not to collide against the walls.

Application and derivation

A pendulum, as used for example in a gyrocompass, defines the perpendicular direction. Accelerations along the pendulum axis are without influence. Movements perpendicular to it put into violent vibrations that make a determination of the solder impossible. A special case is a pendulum with the length of the Earth's radius of 6,370 km. It remains at rest when it is moved along the surface. In practice, designed the system so that the natural frequency coincides with the Schuler period.

The Schuler period is also observed with a permanently mounted on the earth inertial navigation system (INS ). A rotation of the Earth around the angle φ also rotates the INS on the Earth's surface and exerts a torque. The force applied to the tilted axis of the INS acceleration dV / dt ( V: velocity, g: gravitational acceleration) is:

Or for small angle changes:

The angular velocity of the Earth is ( R: radius):

This according to the wave equation follows the oscillation period T:

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