Weight of Sensitive Element.
| Anschütz compass | 15 lb. |
| Sperry compass | 100 lb. |
| Brown compass | 7¼ lb. |
| Thomson magnetic compass | 178 grains |
Whether or not the directive force developed will be sufficient to control the movement of the sensitive element in a gyro-compass must clearly depend very largely upon the degree of success reached in banishing friction from the vertical axis about which the sensitive element moves. Without for the present describing the means actually adopted to secure virtually frictionless support in the three types of gyro-compass, we may say that were they other than very refined no compass action whatever would be manifested. In the early theoretical days of the gyro-compass before sufficiently refined practical constructive methods had been developed, the experimental verification of the mathematical results arrived at could not be attempted.
Granted the attainment in practice of a satisfactory frictionless method of supporting the sensitive element, we have next to note that the simple gyro-pendulum system which we have been considering would be quite useless as a direction-finding device either at sea or on land by virtue of the fact that the very absence of friction at the vertical axis would encourage the sensitive element to oscillate from side to side of the meridian under the least provocation. The period of oscillation would be a prolonged one, much too prolonged, in fact, to permit the true north to be determined by taking the mean of the extreme positions reached by the gyro-axle in the course of its oscillation.
We have seen that the simple gyro-pendulum system which we have so far been considering, when placed on the equator, manifests a tendency to set its axle north and south, that if the axle is deflected towards the east a westerly turning directive force is developed, and that if the axle is deflected towards the west an easterly turning directive force is developed.
In an ordinary vertical pendulum ([Fig. 13]), the resting position of the bob is at d. If it is swung to the position e—towards the east, let us say—the weight w of the bob supplies a moment about the axis at g, tending to restore the pendulum to its resting position; while if it is swung towards the position f—towards the west, we may suppose—the moment is reversed and again acts to restore the pendulum to its resting position.
Fig. 13. Pendulum and Compass.
The gyro-pendulum system as set up at the equator is, it will be seen, subjected to an exactly analogous set of forces when its axle is deflected east or west. The system, in fact, constitutes virtually a horizontal pendulum, the vertical axis H J being identified with the axis at g in the ordinary pendulum. Now we know that if we deflect an ordinary pendulum to some such position as e and let it go it will swing through the resting position d to a position f equidistant on the other side, and will continue to vibrate until friction at the axis g, air resistance, etc., sap its original stock of energy communicated to it by the initial deflection. The period of vibration—the time elapsing between two successive passages of the bob in the same direction through the resting position—is determined by the length of the pendulum and remains constant throughout, even when the amplitude of the swing has fallen off virtually to nothing.
An exactly analogous state of affairs exists with the gyro-pendulum system. If the axle is deflected towards the east and then let go it will swing back under the action of the directive or restoring force through the north and south position over to an equal angle on the western side, and will thereafter vibrate back and forth with a constant period, until frictional and other losses cause the motion to die away. The period of vibration is determined by a complication of factors, among which are the speed at which the wheel is spinning on its axle, the speed of rotation of the earth, and the mass of the sensitive element. If the sensitive element can be regarded as consisting solely of the wheel, then, no matter what may be the size of the wheel, so long as it is in the form of a circular disc, the period of vibration is determined solely by the speed of the wheel and the speed of rotation of the earth. For a wheel at the equator running at 20,000 revolutions per minute the period of vibration would be about eleven seconds. In practice, however, the weight of the axle, the inner and outer supporting rings—or their equivalents—the pendulum bob and various other fittings and adjuncts of a secondary nature have to be added to the weight of the wheel in assessing the influence of the sensitive element upon the period of vibration. The greater the mass—or more correctly, the moment of inertia—of the sensitive element the longer will be the period of vibration. In the early—1910—Anschütz gyro-compass the sensitive element had a moment of inertia such that the period of vibration at the equator was just over 61 minutes; that is to say, 334 times as long as it would have been if the sensitive element had consisted of nothing but the spinning wheel.