The Gyroscopic Compass: A Non-Mathematical Treatment

by T. W. Chalmers

It is clear that whether the bob S remains radially below the centre of the wheel, as in [Fig. 32], or remains vertically below it, or swings past the vertical, as in [Fig. 33], the effect of rolling when the ship is on a due north course is as established in connection with [Fig. 29]. Either a tendency to rotate the wheel about an axis coincident with its axle or an actual rotation of the wheel about this axis results from the kicks of the weight S at the out positions. Whichever it is, there is no gyroscopic effect called into play, and the axle is not subjected to any influence causing it to move away from the due north direction.

We have now to discuss what happens if the vessel rolls or pitches when sailing on an inter-cardinal or quadrantal course.

In [Fig. 34] we show in plan a vessel steaming on a north-west course. When the ship rolls the compass oscillates in the path A D, a path, that is to say, at right angles to the ship’s centre line and curved upwardly by reason of the fact that the compass is mounted above the rolling centre of the ship. The axle of the compass during this movement tends to point steadily towards the north under the action of the directive force. The wheel therefore oscillates from A to D with its axle askew relatively to the path of oscillation, and not at right angles to it, as in [Fig. 29], or parallel with it, as in [Fig. 30]. The oscillation A D can, however, be resolved into two components, namely, a north and south oscillation D K, in which the axle is parallel with the path, and an east and west oscillation K A, in which it is at right angles to the path, both paths being curved upwardly.

Fig. 34. Ship Rolling on N.W. Course.

The oscillation D K, taken by itself, is clearly exactly equivalent to that shown in [Fig. 30]. The southward kick of the weight at the “out position” D ([Fig. 34]) just neutralises the disturbing effect of the northward kick at the “out position” K.

Similarly, the oscillation K A, taken by itself, is exactly equivalent to that shown in [Fig. 29] or its modification, [Fig. 33]. The eastward kick of the weight at A and the westward kick at K cannot do more than turn the mounting round the axle of the spinning wheel. They do not tend to change the direction of the axle.

Hence, taken separately, each component oscillation D K and K A is without disturbing effect upon the direction in which the axle is pointing. Taken together, however, their united effect is not the sum of their separate effects, as we might hastily assume. We must not suppose that the north and south kicks proper to the north and south component of the oscillation are without effect upon the east and west component or vice versa. At the out position D of the component oscillation K D the weight is not only kicked southwards, but also receives a westward kick from the other component oscillation A K. At K it receives both a northward kick and an eastward kick. Similarly, at the out position K of the component oscillation A K the weight is kicked not only to the west but also to the south, by virtue of the oscillation from K to D. At the other out position A of this component the weight is kicked eastwardly, and also to the north. If we take cognisance of these additional kicks, we may treat the component oscillations separately and add the separate results to get the true effect of the actual oscillation A D.

Returning, then, to [Fig. 30], let us suppose that in the oscillation there shown, the equivalent of the component K D, we apply a westward kick to the weight S when the ship reaches its port out position—that is to say, a kick out of the paper—and that at the starboard out position it receives an eastward kick into the plane of the paper. It is clear that these additional kicks do nothing more than tend to rotate the wheel about its axle or an axis coincident or parallel with its axle. They cannot therefore call any gyroscopic effect into action, and as a result do not disturb the direction in which the axle is pointing. The component oscillation D K, even with the extra kicks added, is thus harmless.

Taking [Fig. 33] rather than [Fig. 29] as the equivalent of the component oscillation A K, let us suppose that at the port out position the weight is subjected to an additional kick to the south—that is, into the plane of the paper—and that at the starboard out position it receives an extra kick to the north, or out of the plane of the paper. The southward kick on the weight at the port out position will tend to cause the end B of the axle to turn down towards J, but, in accordance with the fundamental gyroscopic rule, the actual motion of the sensitive element will not be a rotation about the axis E F, but a precession about the axis H J, the end B of the axle moving in the direction K. Similarly, the northward kick at the starboard out position will tend to cause the end B of the axle to rise towards H, and will therefore produce precession in the direction L. Now these two precessional movements, K and L, can be resolved into horizontal and vertical components N M and Q P respectively, as shown separately, and of these components it is clear that the movement N cancels the movement Q. On the other hand, the two components M and P are in the same direction, and therefore do not cancel each other. Their effect is cumulative, and with each succeeding roll the end B of the axle tends to rise higher and higher in the true vertical plane B R. It may be explained, perhaps, that this motion is possible, in spite of the fact that there is no actual axis in the mounting of the compass at right angles to the true vertical plane, except at the instant when the compass is passing through the even keel position in the course of its swing from side to side. As the rolling of the ship starting from zero increases up to a more or less steady value, the end B of the axle rises slowly at first and then at a constant rate, as exaggerated at T. Such of this upward movement as occurs while the compass is passing through the even keel position can be effected by means of a rotary motion purely about the axis E F. Elsewhere in the swing of the compass from side to side it is accommodated by a partial rotation on E F and a partial rotation about H J. These two axes between them permit the end B of the axle to rise in a vertical plane at any point of the compass swing just as effectively as would an axis which was at right angles to the vertical plane B R.