A direction gyro on a ground test at 50 s latitude is found to
have a drift at 6/hr, reading increases, calculate the real wander?
The answer is 5.5"/hr decreases
Assumption: The direction gyro axis is parallel to local North-South during the test.
The direction gyro has teh property of rigidity in space. Which means
that it will maintain its axis direction in relation to space, and not
just in relation to earth. We know earth undergoes one full rotation
(360 degrees) every 24 hrs. Which means the earth rotates at 15 degrees/hour.
Our directions are fixed with earth, so these directions also rotate with earth.
But not all these directions at all the location on earth rotate at 15 deg/hr.
For example on equator, North and South always remain in the
same direction in relation to space, hence its rotation rate is 0 deg/hr.
While close to the poles the earth fixed North/South rotates at 15 deg/hr.
At the intermediate latitudes the formmula is 15*sin(Latitude) deg/hr
(+ Southern Hemisphere, -ve for Northern)
So at the latitude of 50s the rate at which the Local North-South direction rotates
in space is 15*sin(50) = 11.5 deg/hr
Now if the gyro didn't have any mechanical error it would be drifiting by 11.5 degrees per hour (increasing).
But the test says it is drifting by only 6 degrees per hour, this discrepancy is due the mechanical drift error also called as Real Wander, since the observed wander is less than apparent wander, the real wander must be negative.
Real Wander = 6.0 - 11.5 = -5.5 degrees/hr