The Gyroscopic Compass: A Non-Mathematical Treatment

by T. W. Chalmers

Fig. 42. Plans of Gyros.

If we neglect the two gyros L M for the moment, imagining them to be replaced by simple deadweights to counterbalance the weight of the gyro K, it will be seen that this system differs from that of the early Anschütz compass only in the fact that the gyro-wheel has been reduced in size, and has been displaced from the centre of the horizontal ring to the southern edge. The displacement of the wheel in this manner in no way affects the essential working of the compass. In a single-gyro compass we might with some advantage similarly displace the spinning wheel, for by so doing and by counterbalancing the displaced weight we should, at least partially, get rid of the concentration of mass about the east-west axis, which, as we shall see, introduces, if not corrected, an additional source of error into the compass readings when the ship rolls on quadrantal courses.

The reduction in the size of the gyro-wheel would, of course, reduce the magnitude of the directive force. In the 1912 design the wheels of all three gyros run at 20,000 revolutions per minute—that is, at the same speed as the wheel in the 1910 design. But each wheel is only 5 in. in diameter instead of 6 in., and weighs, with its axle, 5 lb. 2 oz., or only half as much as the wheel in the earlier form. The gyro K considered alone would therefore supply a directive force of but half the former amount.[6]

It follows, obviously, that if a second gyro of the same speed and size as that at K be fixed in accurate alignment at the north end of the meridional diameter of the horizontal ring the directive force at any angle of horizontal deflection away from the north will be doubled, that is, will be made equal to that developed in the 1910 design. Such a compass might be constructed, but it would exhibit the quadrantal error—or at least the inertia force portion of that error—just as badly as did the early Anschütz.

The essence of the 1912 design lies in the fact that not one but two gyros are attached to the north side of the horizontal ring, and in the additional fact that the axles of these two gyros are not parallel with but are inclined to the axle of the south gyro K.

When the sensitive element of this compass is in the north resting position, the axle of the gyro K is aligned with the meridian and therefore the rotation of the earth—the compass being supposed at the equator—merely moves the axle parallel with itself. On the other hand, with the sensitive element in the north resting position, the axles of the gyros L M are inclined to the meridian at 30 deg. The gyro L is virtually in the condition of a single-gyro compass, with the north end of its axle partially turned towards the east. Under this condition, as we know, the rotation of the earth will tend to make the north end B of the axle rise above the horizontal plane. Conversely, the gyro M is in the condition of a single-gyro compass, with the north end of its axle partially turned towards the west. The earth’s rotation in this case tends to make the north end of the axle dip below the horizontal plane. Thus, in the 1912 Anschütz compass, when the sensitive element is in the north resting position, the gyro K under the rotation of the earth is without effect on the pendulous weight S, the gyro L is striving to swing it towards the north, and the gyro M is trying with an equal effort to swing it towards the south. The weight, therefore, remains in the plumb line and applies no turning moment to any of the gyros. As there is no turning moment, there is no precessional tendency. The sensitive element remains directed towards the north. This alignment, as in a single-gyro system, is the true resting position, and under it no directive force is applied to the sensitive element.

To study how the three gyros act together to restore the sensitive element to the north resting position should it be deflected therefrom, let us suppose that the deflection suffered is one of 30 deg. towards the east. As shown in the second plan in [Fig. 42], the effect of such a deflection is to place the three gyros K L M in the condition respectively of a single-gyro system when the axle is (k) deflected 30 deg. to the east, (l) deflected 60 deg. to the east, and (m) aligned on the north. At this deflection, then, the gyro M contributes no restoring force. The directive force contributed by the gyro K is half that contributed by the single gyro of the 1910 design when the deflection is 30 deg., for the mass—or moment of inertia—of the wheel is half the earlier value. The directive force contributed by the gyro L is something greater than that contributed by the gyro K, for the virtual deflection eastwards is 60 deg. instead of 30 deg., and, as we know, the directive force increases with the deflection. Thus, the three gyros taken together supply a directive force, when the sensitive element is deflected through 30 deg., which is somewhat greater than that supplied by the single double-sized wheel of the 1910 design.[7] This result is a general one. Whatever the deflection may be, the directive force supplied by the three-gyro compass is always about one-third greater than the directive force of the 1910 design at the same deflection. This increased force is developed even if the deflection be less than 30 deg. In such cases the gyro M will, of course, supply a force, a non-restoring force, to the sensitive element. Only when the deflection exceeds 30 deg. eastwards does the gyro M assist the gyros K and L to restore the sensitive element to the north resting position. If the deflection be to the west, however, the gyro M is the chief assistant of the gyro K, a laggard’s part being played by the gyro L until 30 deg. of westerly deflection is reached.

The manner in which this three-gyro system avoids the quadrantal error can now be discussed. The quadrantal error, it may be recalled, arises when the ship rolls on an intercardinal course, and is primarily caused by the fact that the whole compass system can swing on its external gimbal axis in tune with the rolls of the ship. If we could so arrange matters that during the roll of the ship from side to side the compass system would swing on the external gimbals, no more and no less than the amount required just to keep the axis H J truly vertical at all points of the roll, then the north and south “kicks” received on the weight S at the out positions of the roll would cause the sensitive element to precess first one way, then the other, but always in a horizontal plane. There would be no vertical component in the precession, the cumulative effect of which, as we have seen, produces the quadrantal error.

In the Brown compass, the quadrantal error is eliminated by delaying the effect of the “kicks” on the weight S until the axis H J is truly vertical—that is to say, the “kicks” on the weight are not transmitted to the spinning wheel until the compass system is passing through the even keel position. In the Sperry compass the weight S is virtually shifted back and forth from east to west of the axis H J in tune with the rolling of the ship in such a way as to introduce a second component of vertical precession, which in amount and direction is just sufficient to nullify the vertical component causing the quadrantal error. In the 1912 Anschütz compass, the object aimed at is the maintenance of the axis H J truly vertical at all times during the rolling condition.