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Compass precession

It is often said that since the earth rotates 15 degrees per hour, any gyrocompass will move by that much also - hence the regular DI resetting needed on the clapped out PPL training planes.

However I can't get my head around why it should be 15 degrees/hr regardless of where you are. I can see it would be that much if overflying the N or S pole (ignore the fact that the magnetic compass won't work up there anyway). But everywhere else?

Administrator
Shoreham EGKA, United Kingdom

The earth rotates by 360 degrees per day. 360/24 = 15.

The gyrocompass is rigid in space. The earth is not rigid in space, it rotates. Take your old wooden globe, mark the magnetic north pole, suspend a paper aircraft on your ceiling, measure the angle to the north pole, rotate your globe while not moving your airplane and measure again.

Perhaps it's because we try to keep the gyro wheel vertical inside the instrument over time (the internals of the DI have to be able to move in any direction, otherwise if we made a banked turn then it would precess like crazy, but at the same time we want the wheel to stay pretty much vertical over a long duration, a bit like we want an attitude indicator to correct to horizontal when we spin it up, I hope I'm explaining my thoughts not too unclearly here!) The act of trying to keep the DI's wheel upright over time will cause it to precess as the earth moves underneath it regardless of where you are, especially if the wheel's axis is perpendicular to the earth's axis.

However, this will depend on the direction - if you're at the equator and the gyro's wheel is aligned also with the equator, the earth moving under it can't possibly make it precess since both the gyro's axis and the earth's axis are parallel. (This assuming ideal bearings and no drag inside the instrument).

So I don't believe a DI will precess 15 degrees regardless. How much the earth causes the reading on the DI to change (assuming the mythical DI with ideal dragless internals) will depend on the angle of the DI's axis relative to the Earth's axis - 0 degrees difference and the reading will be rock steady, 90 degrees difference and it'll precess at 15 degrees per hour.

Andreas IOM

if you're at the equator and the gyro's wheel is aligned also with the equator, the earth moving under it can't possibly make it precess since both the gyro's axis and the earth's axis are parallel.

That's exactly what I had in mind - it must be location dependent.

That also makes a mockery of the often talked about "adjustment nut" which the avionics shop supposedly tweaks for your latitude when they overhaul the instrument.

Actually I think most training plane DIs drift so much (anything up to 10 degrees in 10 minutes, on the ones I flew) because they are shagged, not because of any precession effects

Administrator
Shoreham EGKA, United Kingdom

all you need to know:

EDxx, Germany

because they are shagged, not because of any precession effects.

That's the most likely explanation - it'll probably be a precession effect but caused by the gimbals being worn out and ending up applying a force to the gyro wheel as you manuever the aircraft.

(I only have to adjust the old World War II gyro on the Auster twice an hour)

Andreas IOM

From Nobbi's URL:

A free gyroscope situated at the North Pole with its axis horizontal will have an apparent movement, which is entirely in the horizontal plane.

Its axis will appear to move in a clockwise direction when viewed from above. This would be due to the real counter clockwise rotation of the earth beneath.

This circular motion causes the gyroscope to drift through 360? in one sidereal day.

That is at a rate of 15? per hour.

A free gyroscope situated at the equator with its axis horizontal will not drift at all, irrespective of whether its axis is set in the North – South or East – West line.

The rate of drift for a gyroscope with its axis horizontal thus varies from a maximum at the poles to zero at the equator.

That is the rate of drift varies as the sine of the latitude. For a free gyroscope with its axis horizontal:

Rate of Drift in degrees per hour = 15? sine Latitude

So it depends on the latitude, as I suspected.

Administrator
Shoreham EGKA, United Kingdom
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