It is clear that pitching of the ship when on a due west course has the same effect—or lack of effect—on the compass as rolling on a due north course, and that pitching on a due north course has the same effect as rolling on a due west course. It is further clear that due south and due east courses are similar in this respect to due north and due west courses. Thus when the ship is on a cardinal course neither pitching nor rolling disturbs the axle of the spinning wheel from its north resting position.
Matters are quite otherwise, however, when the course is an inter-cardinal, or quadrantal, one. The discovery of this unlikely fact was in large part due to the investigations of the Compass Department of the British Admiralty. It does not appear to have been known, or at least its full significance does not seem to have been appreciated, in the earlier days of gyro-compass construction. At least one early design of compass—the Anschütz of 1910—did not include means of eliminating or allowing for the “quadrantal error,” and soon became obsolete as a result primarily of the omission. That the later design of Anschütz compass successfully overcomes the difficulties introduced by this error is shown by the admitted excellence of the navigation of the German submarines, which vessels were universally fitted with compasses of this design, and which, like all their class, suffer much from rolling and pitching.
Fig. 31. External Gimbal Mounting.
So far we have been able to use a very simple model to demonstrate the properties and errors of the gyro-compass. We have now reached a subject which, if it is to be explained correctly, requires us to adopt a model of a more elaborate nature, one in which the outer square frame of our simple model is itself mounted on a pair of gimbal axes. We have already referred to this type of mounting in our second chapter and above in connection with [Fig. 29]. In [Fig. 31] we show it with the pendulous weight added to the sensitive element. We may take it that the axis T U, about which the entire compass system may swing, is parallel with the longitudinal centre line of the ship, and that the frame Y is fixed to the deck.
Fig. 32. Effect of Rolling on a Due North Course (Simple Mounting).
Fig. 33. Effect of Rolling on a Due North Course (External Gimbal Mounting).
In order to make quite clear the difference between the two forms of mounting, we give in Figs. [32] and [33] two corresponding sets of views showing the compass system on a ship while steaming due north and rolling. With the simple mounting ([Fig. 32]) the weight S constantly remains radially below the centre of the spinning wheel, and the kicks which it applies at the out port and out starboard positions merely stress the compass mountings. With the more elaborate mounting ([Fig. 33]) the weight tends to remain constantly in the vertical below the centre of the spinning wheel, but the kicks occurring at the out positions, if the rolling is continued for any length of time, cause it to swing beyond the vertical, so that as the ship rolls the whole compass system acquires an oscillation on the axis T U ([Fig. 31]) in tune with the rolls. It is to be noted that the period of vibration of the compass system about the axis T U is very much less than that of the sensitive element about the axis H J. The latter, as we have seen, is about 85 minutes, and is determined, in part at least, by the high speed of the spinning wheel. About T U the vibration, however, does not call any gyroscopic force into play, for it takes place without causing the axle of the spinning wheel to alter its direction. The period of this vibration is therefore not affected by the speed of the spinning wheel. It may be quite small—from one to two seconds—and therefore comparable with the ship’s rolling period. If, then, no steps are taken to prevent it, the compass system as a whole will acquire a swing on the axis T U ([Fig. 31]) when the ship is steaming north—or south—and rolling. Its period of vibration on this axis is not strictly that which it would have were it set oscillating about the axis T U with this axis mounted on a fixed frame, for the vibration is not a free one, but is a forced vibration under the impulses communicated by the rolling of the ship. Whatever may be the exact free period of swing of the compass system on the axis T U, so long as it is somewhere near that of the ship’s roll or a small sub-multiple of the rolling period, the tendency is for the compass swings to settle down in such a way that, as represented in [Fig. 33], the pendulum weight S reaches its extreme out positions simultaneously with the ship’s arrival at its extreme port and starboard heels. In the course of one complete roll of the ship, however, the compass system may make more than one complete vibration about T U.