Page 10 - Electronic Navigation Cyber Book

Latitude (Damping) Error
Latitude error is a constant error, the magnitude of which is directly
proportional to the earth's rotation at any given latitude. It is, therefore,
present even when the ship is stationary. As has previously been stated,
a gyrocompass will always settle close to the meridian with an error in tilt.
To maintain the gyro pointing north it must be precessed at an angular
rate varying with latitude. At the equator, the earth's linear speed of
rotation is about 900 knots and rotation from west to east causes a fixed
point to effectively move at 900 x cos (latitude) knots in an easterly
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direction. For any latitude (A.) the rate of earth spin is to = 15° h . This
may be resolved into two components, one about the true vertical at a
given latitude (to sin A) and the other about the north/south earth surface
horizontal at a given latitude (to cos A).

The component of the earth's rotation about the north/south horizontal
may be resolved further into two components mutually at right angles to
each other. The first component is displaced a° to the east

Correction for latitude error requires that a torque be applied to precess
the gyro at an angular rate, varying with latitude, to cancel the error. This
will be an external correction that can be either mechanical or electronic.
For mechanical correction, a weight on the gyro case provides the
necessary torque. The weight, or 'mechanical latitude rider', is adjustable
thus enabling corrections to be made for varying latitudes. Another
method of mechanical correction is to move the lubber line by an amount
equal to the error. Latitude correction in a bottom-weighted compass is
achieved by the introduction of a signal proportional to the sine of the
vessel's latitude, causing the gyroball to precess in azimuth at a rate
equal and opposite to the apparent drift caused by earth rotation.

Speed and course error
If a vessel makes good a northerly or southerly course, the north end of
the gyro spin axis will apparently tilt up or down since the curvature of the
earth causes the ship to effectively tilt bows up or down with respect to
space. Consider a ship steaming due north. The north end of the spin
axis tilts upwards causing a westerly precession of the compass, which
will finally settle on the meridian with some error in the angle, the
magnitude of which is determined by the speed of the ship. On a cardinal

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