The Gyroscopic Compass: A Non-Mathematical Treatment

by T. W. Chalmers

Fig. 27. Ballistic Force on Compass when Ship’s Speed Changes.

If the ship changes speed while on a west to east course, the change is similarly without effect on the compass. Strictly speaking, we ought to say that the change of speed will have no effect on the compass if the ship’s course is at right angles to the direction in which the axle of the wheel is pointing. Only at the equator would this course be due east or west. In other latitudes the latitude error has to be reckoned with, so that the particular course on which changes of speed are without effect on the compass must be slightly south or north of due east or west.

If, now, the ship is steaming due north, as indicated in [Fig. 27], a reduction of its speed will tend to make the pendulum weight swing forward about the east and west axis E F in the direction P. This tendency is clearly equivalent to the application of an upward force to the end B of the axle, and hence, as we know, will cause the wheel to precess, the end B of the axle going eastwards. As this precession continues it is opposed by the ever-increasing restoring moment of the directive force, so that in the end the axle assumes a position in which the directive force just balances the ballistic deflective force. This ballistic deflection remains constant all the time the ship’s speed is falling. When the speed reaches the new steady value the axle slowly oscillates back to the true resting position.

It is clear that a reduction of speed on a northerly course and an increase of speed on a southerly produce ballistic deflections in a like direction, the north end of the axle moving towards the east. An increase of speed on a northerly course or a decrease of speed on a southerly produces a westerly ballistic deflection. On intermediate courses deflections of a like kind, but of intermediate value, are caused, for the north and south component of the change of speed is alone effective in tilting the wheel about the east and west axis E F.

Imagine a ship steaming due north at 20 knots and changing its speed to 10 knots during a period of five minutes. As it is steaming north there will be a north steaming error, the axle pointing westwards of true north by an amount dependent upon the speed of the ship and the latitude in which it is sailing. Let O N ([Fig. 28]) be the direction of true north, and let O A be the direction in which the axle of the gyro-compass aligns itself when the speed is 20 knots, the angle N O A being the combined latitude and north steaming errors. Let O B be the resting position for the axle when the ship’s speed is 10 knots, the angle N O B being the latitude error—which has not altered—plus the north steaming error—which is now less because of the reduced speed. As the speed is being reduced, the ballistic action of the pendulum weight causes the axle temporarily to turn eastwards from the true resting position and to align itself in some direction O C. When the ship has settled down to 10 knots, the axle leaving the position O C vibrates about O B with amplitudes which are being continually reduced by the action of the damping system.

Fig. 28. Ballistic Deflection.

The point of importance to notice is that the temporary ballistic deflection O C is eastward of O A, just as is O B the new resting position for the axle. This result is a general one. Had the speed been increased instead of decreased, the ballistic deflection would have been westward of O A, just as would be the new resting position for the axle at the increased speed. Similarly, on due southerly courses or on quadrantal courses the ballistic deflection produced by any change of speed is always in the same direction as that in which the axle moves in passing from the old to the new north steaming error. This being so, it is conceivable that at least, under certain conditions, the ballistic deflection position O C may coincide with the new position O B for the axle under the new north steaming error. Should such a result be obtained, the ballistic action will, on a change of speed occurring, swing the axle straight away into the new resting position. Thus O C and O B being coincident, there will be no tendency for the axle to oscillate about O B when the speed assumes the new steady value, so that the axle will swing into the new resting position in a “dead-beat” manner. The effect of the ballistic action will thus be confined to the period during which the speed is being changed—five minutes in our example—and will not influence the readings of the compass for a period of anything up to two or three hours after the new speed is reached.

The ballistic deflection of a pendulum hung from the roof of a railway carriage is dependent upon the length of the pendulum, and therefore upon its period of natural vibration. So, too, the ballistic deflection of the gyro-compass is dependent upon the period of its vibration about the north and south direction. Once the characteristics of the compass are determined, therefore, the angle A O C ([Fig. 28]) of the ballistic deflection is settled by (1) the direction of the ship’s course, and (2) by the rate at which the ship’s speed towards the north or south is being changed. It is not affected by the latitude in which the ship is sailing, the deflection produced by a change of 10 knots in five minutes being the same at the equator as in 60 deg. or any other latitude.

Coming to the difference between the old and the new north steaming errors, it will be seen from our previous explanation of the errors themselves that the magnitude of the angle A O B is independent of the design of the compass in use. It will vary with (1) the direction of the ship’s course, and (2) the extent by which the ship’s speed is changed. In addition, it will also vary with (3) the latitude in which the ship is sailing.