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It is not so much of a failure but an Heading offset caused by
"Speed Error"
The speed error is an error generated when a vessel/aircraft in which a gyrocompass is installed transits a course other than east or west. Its value is determined depending on the ship's speed, course, and latitude. (It is not related to the kind or type of gyrocompass.)
The north-seeking tendency of a gyrocompass is based on the earth's rotation. When a ship sails, the resultant motion of the ship's motion and the earth's rotation acts on the north-seeking tendency of the gyro. If the course of the ship deviates towards the north or south, the direction of the resultant motion deviates north or south and thus an error occurs because the north-seeking force of the gyro acts perpendicular to this resultant motion. That is, the speed error is the angle of the difference between this resultant motion and the east-west direction.
Determining Speed Error
ϕ: Latitude
K: Speed of the earth's rotation at the
equator (About 900 kt)
V: Vessel/Aircraft speed (kt)
θ: Gyrocompass course
δ: Speed error
In the figure above, AC = Vcos θ = Kcos ϕ • sin δ
Since δ is a small value,
sinδ = δ (radian) = 1/57.3 δ (unit: degree)
From these equations, δ = 57.3 Vcos θ/900 cos ϕ
If we assume, for example, that the ship is at the equator ( ϕ = 0), the gyrocompass course is N ( θ =
0), and the ship's speed is 30 kt, then
δ = 57.3 × 30/900 = 1.91 degrees = 1°54'
When the value of θ is between 270° to 90°, the compass indication increases. Therefore, the
ship's true course is as shown below.
0° − 1°54' = 358°6'
As seen above, if the compass course deviates towards the north, the true course can be obtained by subtracting the speed error from the compass course, and if the course deviates towards the south, the true course is obtained by adding the speed error to the compass course.
Most modern Gyros can automatically compensate for this error when interfaced to a GPS/SatNav/GLONASS (position/Speed) and w or w/o a Speed Log (speed). These values can also be entered in Manually to calculate speed error. See CMZ900 by Yokogawa and marketed by AGMarine. Just a little plug if that's alright?
In the same location when we compare 2 vessels have same heading; we can come to that conclusion from formula "57.3 Vcos θ", higher speed will cause bigger speed error.
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