The Gyroscopic Compass: A Non-Mathematical Treatment

by T. W. Chalmers

It might be thought that the system would without further addition serve as a compass, for if it maintains its axle constantly pointing in one direction it is just as good as a compass which always points its needle towards the magnetic north. In the magnetic compass, however, the needle has a directive force applied to it which enables it to recover its standard direction if it should be accidentally deflected from it. In the gyroscopic system we have been considering there is no such directive force. The axle will remain pointing in one direction, it is true, but the system is indifferent as to what that direction may be. If the axle is accidentally deflected it will remain pointing in the new direction as consistently as it did before in the originally set direction. As a substitute for the ordinary compass, then, the success of the device would depend upon the success with which accidental deflecting forces were prevented from acting on the axle after it had been set in a known direction. In practice, as Dr. Anschütz found in his early investigations, it is excessively difficult, if not quite impossible, to construct a gyroscopic system in which the centre of gravity and the centre of suspension are absolutely coincident. As a result a very minute gravity torque is thrown on the system, and in consequence the axle very slowly precesses away from the original set direction. This fact and the complication of parts required to give practical effect to the idea led Dr. Anschütz to abandon his early attempts at providing a compass substitute of the apparently simple nature described above.

Fig. 9. Elementary Gyro-Compass.

An addition to the system of a very simple kind in itself not only endows the axle with directive force, but makes the direction which it seeks the north and south one, and thus converts the system into a device possessing the familiar property of the compass. This addition consists of a pendulum-like weight S ([Fig. 9]), attached below the wheel by a stirrup fixed to the inner ring so that the weight, stirrup, inner ring, axle, and wheel may swing as a whole on the horizontal axis E F.

Let us suppose that the system with this addition is set up at the equator and that the axle this time is aligned at right angles to the equator so that the end B, as shown at I ([Fig. 10]), points due north. In this condition the inner ring is horizontal and the weight S is vertically below the pendulum axis E F. No turning moment is therefore being applied by gravity to the wheel. If through imperfection of workmanship the centre of suspension of the system is not absolutely coincident with the centre of gravity before the weight S and its stirrup are attached, then the minute gravity torque arising from the lack of coincidence will be balanced automatically by the weight, the inner ring taking up some position minutely inclined to the horizontal. There will thus under all conditions be no resultant turning moment applied by gravity to the system as thus set up. In addition, the axle, lying north and south as it does, is aligned parallel with the earth’s polar diameter. Consequently the rotation of the earth can only move it parallel with its original position, and therefore does not tend to cause relative motion between it and the square frame. We conclude, then, that in this north and south position of the axle the system is not acted upon by any force or influence tending to cause the axle to depart from the north and south position.

Fig. 10. Elementary Compass at Equator.

Now let us suppose that the axle by some agency is forced into parallelism with the equator so that the end B points due east as indicated at II ([Fig. 10]). Immediately after it takes up this position the tendency of the axle to remain parallel with this, its new original, direction becomes manifested in attempted relative motion between the axle, wheel, and inner ring on the one hand and the square frame on the other. Thus as the earth rotates the axle, etc., tend to set themselves relatively to the frame in the position shown at III. In this position, however, the weight S being rigidly suspended from the inner ring, is no longer vertically below the pendulum axis E F. Gravity acting upon the weight therefore applies a turning force to the wheel, etc., about the axis E F. The system is thus under the same conditions as those represented in [Fig. 1], when the weight W is hung on the inner ring at B. Precession about the vertical axis therefore sets in, in the direction M ([Fig. 1]), so that the end B of the axle swings round from the east towards the north.

Let us reset the system in position I, and then by some agency cause the axle again to align itself parallel with the equator, this time, however, with the end B pointing due west as shown at IV ([Fig. 10]). As before, the rotation of the earth combined with the tendency of the axle to remain parallel with the new west and east position results in attempted relative motion between the axle, etc., and the square frame, so that in a little time the system would adopt the configuration shown at V. In this configuration, however, gravity as before applies through the weight S a turning force about the pendulum axis E F. Now, comparing the two configurations III and V, it will be seen that, mere reference letters or similar distinguishing marks being washed out, they are indistinguishable except for one fact: the wheel is rotating in opposite directions. If with the system as arranged in [Fig. 1] we reverse the direction of spin of the wheel without reversing the direction of the applied force W, then, as we know already, the direction of the precession will be reversed. Precession about the vertical axis will take place in the direction opposed to the arrow M. Hence in the configuration shown at V ([Fig. 10]), the precession induced by the action of gravity on the weight S causes the end B of the axle to swing up from due west towards the north.

We are thus led to identify the end B of the axle as the north-seeking end and the end C as the south-seeking. With B pointing due north as at I, there is no force acting on the system tending to make the axle depart from the north and south direction. If B is swung over to the east or west—or intermediately, as may be taken for granted—a force is called into play tending to move the end B back towards the north. It follows, therefore, that the resting position of the axle is the north and south one with the end B pointing north.