The Gyroscopic Compass: A Non-Mathematical Treatment

by T. W. Chalmers

Let us, however, rotate the bob about the axis at C through something less than 90 deg. from the first position—say, through 45 deg., as indicated in the third sketch. Consider again the two extreme end portions as the bob is passing through the mid position of its swing. Let J K be a line through the centre of the bob parallel with the knife-edge axis. From the centres of the end portions, let lines L N and M P be drawn at right angles to J K. From N and P draw lines upwards parallel with the rod A to meet the knife-edge axis at Q and R. Then Q and R are the points about which the two extreme portions of the bob are swinging. The centrifugal forces on these portions are directed along the lines Q L and R M, and are indicated at S and T. These forces may, as shown, be resolved into vertical components—parallel with Q N and R P—and horizontal components—parallel with N L and P M. Treating the other portions of the bob similarly, it will be seen that while the vertical components of the centrifugal forces, as before, merely tend to bend the ends of the bob downwards, the horizontal components are no longer parallel with the length of the bob, as in the second sketch. They are inclined to the bob and clearly apply to it a moment which will turn it about the axis at C in the direction of the arrow U until the bob reaches the position shown in the second sketch.

It is obvious that any rotation of the bob on the axis at C away from the position shown in the first sketch, even a slight one, will call into action horizontal components of centrifugal force after the manner shown in the third sketch. The equilibrium of the bob in the position shown in the first sketch is therefore unstable. With the bob in the second position a movement of the end L to the left will, as we know, call into action horizontal components of centrifugal force, tending to turn the bob about C in the direction of the arrow U. If the end L is moved to the right the horizontal components, as can easily be verified by repeating the argument, will tend to turn the bob about C in the direction opposed to the arrow U. Thus deflection to either side of the second position calls forth forces which lead the bob to recover that position. We conclude, therefore, that the second position is one of stable equilibrium.

It may further be shown by repeating the argument that if the bob is rotated about C from the first position in such a way as to send the end L to the rear the horizontal components called into action tend to set the bob into the second position with the end L pointing backwards, and that when the bob is so aligned relatively to the knife-edge axis the equilibrium is again stable. Thus, altogether, if the bob is parallel with the knife-edge axis, the equilibrium is unstable. If it is at right angles the equilibrium is stable. If it is set into any intermediate position, forces are called into play which endeavour to align it at right angles to the knife-edge axis.

Let a second cylindrical bob of the same size and weight be attached to the first at right angles to it and in the same plane. Then in all positions of the bobs relatively to the knife-edge axis the equilibrium will be stable, for at any setting of the bobs the rotary force about C developed by the one bob will be equal and opposed in direction to that developed by the other bob.

The above discussion covers a principle of considerable general importance in mathematical physics. Briefly put, it shows us that a body suspended pendulum-wise in the manner sketched will develop a tendency when swung to set its longer axis parallel with the plane of the swing, and that to avoid this tendency in a swinging body mounted in the manner we have indicated, the mass of the body must be distributed symmetrically and equally about the pendulum rod, so that there shall be no “longer axis.”[8] So far as the gyro-compass is concerned, the circumstances described necessitate—at least in the Sperry and Brown compasses—the addition of compensator weights to represent the second cylindrical bob to which we have referred above.

The masses composing the gyro-compass are not disposed symmetrically and equally about the vertical axis—the axis which we have throughout called H J. As seen in plan, the masses are concentrated towards the east and west plane containing the spinning wheel, and are deficient towards the north and south. By virtue of the presence of the pendulous weight, or its equivalent, below the spinning wheel, the whole mass of the compass is capable of swinging pendulum-wise, the axis of this swing being one or other of the axes of the external gimbal mounting. Further, the swinging mass is free—if the wheel is not spinning—to turn about the vertical axis which we have called H J. Reference to [Fig. 31] will make these statements quite clear.

Thus the compass and its system of mounting inevitably reproduce the essential features of the pendulum shown in [Fig. 43]. Taking the second sketch in that engraving, the bob represents the masses of the compass concentrated in the east and west plane. The gyro-axle being at right angles to this plane is parallel with the knife-edge axis B. This axis B may be regarded as representing the longitudinal axis of the external gimbal mounting, so that in the conditions imagined the ship is supposed to be sailing due north or south. It is clear that when the ship rolls on either of these courses, the fact that the mass of the compass is concentrated in the east and west plane will not tend to deviate the axle, for the “pendulum bob” is in its position of stable equilibrium.

The first sketch similarly represents the condition of matters existing when the ship rolls on an east or west course, the knife-edge axis B again being identified with the longitudinal axis of the external gimbal mounting. The pendulum bob is now in its position of unstable equilibrium, so that if the mass distribution of the compass is not corrected by the addition of compensator weights, a tendency for the axle to deviate away from the north may occur.

If we identify the knife-edge axis B with the athwartship axis of the external gimbal mounting, the second sketch in [Fig. 43] illustrates the condition of matters existing when the ship pitches on an east or west course, while the first will represent pitching on a due north or south course.

On quadrantal courses, failure to correct the inequality of the mass distribution, if that distribution is not uniform, will inevitably result in the axle deviating when the ship rolls. Thus, the third view in [Fig. 43] represents the conditions prevailing when the ship rolls on a due north-west—or south-east—course. Looking at the plan, the line J K represents the direction of the longitudinal axis of the external gimbal mounting and therefore the direction of the ship’s course, while a line at right angles to the pendulum bob would represent the gyro-axle, and therefore the north and south direction. When the ship rolls the compass masses oscillate pendulum-wise about the external longitudinal gimbal axis—represented by the bar B—but the directive force of the compass tends to preserve the general plane of the oscillating masses inclined at 45 deg. to the direction of the bar B. As a result, the horizontal components of the centrifugal forces developed in the compass masses apply to the wheel, casing, etc., a turning moment in the direction of the arrow U. This moment, it will be seen, tends to turn the sensitive element in the same direction as that in which the “kicks” of the weight at the out positions of the swing endeavour to deviate the axle on the same course. The centrifugal moment would, however, cause an actual deviation in the direction U in a direct manner only if the gyro-wheel were not spinning. As it is, the centrifugal moment causes the north end of the gyro-axle to precess upwards and therefore leads to a deflection of the pendulous weight of the north. This deflection throws a turning moment on to the wheel about the horizontal axis—the axis we have called E F throughout—and, finally, this turning moment precesses the axle horizontally in the direction of the arrow U. Thus, with the wheel spinning, the centrifugal moment actually does produce rotation in the direction U, but its action is not direct.