spin; and the sense of the precession is such that it causes the
plane of the spin to move towards the plane of the torque as if
to secure agreement of sense after one quarter-turn.
The Sperry Compass. The Sperry type being the most universally known is used in the following discussion as a convenient example to illustrate the principles of gyro compasses. It consists essentially of a gyro mounted so as to be free to spin, free to tilt about a horizontal axis and free to turn in azimuth round a vertical axis. The tilting freedom is modified by the addition of a gravity control in the form of a bail weight, fastened to the case by a roller connexion at one point only.
For the present it will be assumed that this roller connexion is in the vertical plane through the gyro-axis, so that whenever the gyro-axis is tilted the gravity control only produces a torque on the gyro in the vertical plane. On account of the earth's rotation the N.
end of the gyro-axis will, whenever it is | ^y^ of the meridian be tilting | downwards ' and as a result of the S ravit y control, whenever
the N. end of the axis is tilted
the horizontal plane it must
be processing < g t . This precession, however, is relative to space
and not relative to the earth.
It follows that such a gyro compass will have, at the equator, a resting-position in which the gyro-axis is horizontal and in the meridian. At a place in N. lat. the gyro-axis, in its resting-position, will be in the meridian with the N. end tilted up slightly, so that the gravity control may provide a torque in the vertical plane sufficient to cause the gyro-axis to precess in azimuth at a rate equal to that at which the meridian is turning round the vertical.
With the Sperry constants the tilt required is about 8' of arc in
lat. 53, for this tilt produces a torque of ^- X ^- X - ft.-pound-
8 Xi6oX36oo , als and so a rate precession equal to degrees per
OO /\ / XN 9OO
hour or about 12 per hour. (Mass of bail = 10 Ib. ; depth of O. G. below tilt axis =6 in.)
Further, if the gyro-axis is disturbed from its resting-position it will oscillate about that position but will not settle again unless there is sufficient friction to damp out the oscillations. Such friction must always be reduced to a minimum as it involves a degree of uncertainty in the resting-position.
In order to damp out any oscillations of the gyro-axis the roller connexion between the bail weight and the case is placed slightly to the E. of the vertical plane through the gyro-axis. This roller con- nexion will, in what follows, be referred to as the " eccentric pivot." With this arrangement whenever the N. end of the gyro-axis is tilted above the horizontal plane there are two torques acting on the gyro, both proportional to the tilt :
(a) one in a vertical plane as before,
(b) the other in a horizontal plane.
The second torque is the damping torque and always acts in the sense opposing the precession in azimuth due to the first torque. Its effect on the gyro is always to reduce the tilt whether above or below the horizontal plane. By reducing the tilt it lessens the torque pro- ducing the azimuth precession and so diminishes the amplitude of the azimuth movement and consequently damps out the oscillations.
The angle between the two planes through the gyro-axis which pass through the slope diameter and the eccentric pivot respectively is called the eccentricity of the pivot, and is usually about 1. By in- creasing this eccentricity the damping can be made heavier, the value 7 being enough to give to the Sperry compass a dead-beat movement in all latitudes.
The damping torque causes the compass to settle, in N. latitudes, with the N. end of the gyro-axis tilted up and E. of the meridian. This damping error, or latitude error as it is sometimes called, varies as the eccentricity of the pivot and the tangent of the latitude. In the resting-position the damping torque maintains the slight pre- cession of the gyro-axis in the vertical plane necessary to keep the tilt constant although the axis is not in the meridian.
The resting-position in any latitude can be adjusted to be horizon- tal and in the meridian by putting out the horizontal balance of the case. Imagine a weight put on the N. side of the case sufficient to produce the torque in a vertical plane required to keep the gyro-axis processing at the same rate as the meridian is turning round the vertical. Then in the resting-position there would be no tilt and so no pressure at the eccentric pivot, no damping torque and no damp- ing error. That is, the gyro would settle with its axis horizontal and in the meridian. This gives a clue to the effect of a change in the horizontal balance on the resting-position making this balance N. heavy reduces the upward tilt of the N. end and causes it to settle to the W. of its normal resting-position.
In a similar way can be seen the effect of a twist in the suspension. This merely introduces an extra torque in a horizontal plane and so either increases or decreases the damping torque and therefore the
damping error. Hence the only effect on the resting -position is to introduce a change in azimuth in the sense of the twist.
The preceding remarks refer to a compass in a binnacle fixed rela tive to the earth. When the binnacle is mounted in a ship further complications arise. That part of the earth's rotation which is essential to the working of a gyro compass is the tilting movement of the horizontal plane about a N.-S. line. This tilting movement in combination with the gravity control causes the gyro compass to be N.-seeking. If the ship, in which the compass is mounted, is steaming due N., the curvature of the earth's surface causes a tilting movement, sense S.-Z.-N., of the horizontal plane about an E.-W. axis; the gyro compass detects this tilting movement and on ac- count of this alone would point its N. end west. The final result is that the gyro-axis points in the direction of the axis of the resultant angular movement. Since the angular velocity of the horizontal plane due to the ship's speed is only a small fraction of that due to the earth's rotation, this direction will be only slightly W. of N. Hence for northerly speeds the compass has a resting-position which is W. of its normal one. This error is called speed error and its value in radians is given approximately by the expression
Northerly speed of ship
Easterly speed of the latitude circle
For British latitudes it is roughly 1 per 10 knots. The error for southerly courses is E. and for east or west courses it is zero. Thus it is clear that every alteration of course will involve a change in the resting-position of the compass. Take the case of a ship which, when steaming N. at 20 knots, alters course to S. The gyro compass, supposed settled when the ship was on the northerly course, would be pointing some 2 W. of its normal resting-position; at the end of the turn the new resting-position will be 2 E. of the normal one and so 4 E. of that for the northerly course. But during the turn there has been a southerly acceleration, and consequently a tendency for the bail weight, acting as a pendulum in the N.-S. plane, to lag behind to the north. Hence it exerts a pressure (due to the accelera- tion) on the case at the eccentric pivot, and so produces two torques on the gyro:
(1) in a vertical plane' sense N.-Z.-S.;
(2) in a horizontal plane sense W.-S.-E.
The former of these causes the N. end to precess E., that is toward the new resting-position for the southerly speed. The angular dis- placement of the gyro-axis thus obtained is called the ballistic deflexion. If the constants of the compass are so arranged that this deflexion is equal to the difference of the two speed errors, then dur- ing the turn the gyro-axis will have moved in azimuth exactly to its new resting-position. But the ballistic deflexion is independent of the latitude, whilst the change of speed error varies with the latitude. Hence this adjustment can only be made correctly in one particular latitude called the standard latitude. To obtain this effect the con- stants of the compass must be adjusted so that its undamped period is 85 minutes in the standard latitude. This is the reason why all gyro compasses of this type have periods approximating to I j hours.
The torque in the horizontal plane produces no such beneficial results. It causes an upward precession of the N. end during the turn and so increases the tilt. Since the resting-position for the S. speed requires the same tilt of the N. end as that for the N. speed, the gyro-axis will begin to wander, after the turn i$ completed to- wards the west. This wander, called the ballistic tilt effect, is always opposed in sense to the ballistic deflexion. It also occurs in the Anschutz and Brown compasses because the acceleration causes a transference of the oil in the damping mechanism. In order to re- duce this ballistic tilt effect the eccentricity of the pivot is kept small in the Sperry compass.
The mercury-box attachment to the Sperry compass provides a means of making the ballistic deflexion approximately correct in all latitudes, and is noteworthy as being the only practical device which so far has overcome this difficulty. The gravity control con- sists of two cast-iron boxes containing mercury and joined together by a long U tube which enters each box at the bottom. This is. essentially a top-heavy form of gravity control and the magnitude of the torque exerted by it depends on the area of the free surfaces of mercury in the boxes. Each box is divided by vertical partitions into three compartments whose areas are as 1 : 2 : 3. A valve at the bottom of the box, actuated by turning a knob at one bottom corner, en- ables the area of the free surface and so the magnitude of the bail weight to be varied in the ratios 3:4:5:6. By means of this device the bail weight can be so adjusted that the ballistic deflexion is equal to the change of speed error within i in any navigable latitude.
Further complications arise due to the rolling and pitching of the vessel. A swinging ring oscillates stably in its own plane but unstably in a perpendicular plane. This is because the moments of inertia of the ring, about a diameter and about a line through the centre at right angles to the plane of the ring, are not equal. This inequality existed in the original Sperry compass but was removed by the at- tachment of the compensator weights and frame to the vertical ring. In addition, with the ship on an intercardinal course, say N.E., and rolling, the compass in the binnacle is subject to an alternating acceleration in the N.W.-S.E. vertical plane. The E.-W. com- ponent of this causes the compass as a whole to swing in the gimbals in the plane of the case, and so the eccentric pivot swings E. and W.
