Now, in the Sperry system the forces P - p and P + p are not allowed to act on the trunnions E F of the wheel casing, but are borne by the phantom ring K ([Fig. 19]) whence they are transmitted back to form part of the load on the follow-up motor. Acting on the casing, therefore, there remains only the force W + w. This force exerts a turning moment about the axis E F strictly equal to that produced by a directly attached pendulous weight. In addition, it exerts a turning moment about the axis H J.
Fig. 21. Action of Excentric Pin in Sperry Compass.
As actually constructed, the wheel casing and bail in the Sperry compass cannot be placed in the position shown in [Fig. 20], for the forks at the end of the bail permit the bail, and therefore the casing, to swing only through a small angle from the vertical position. It is clear, however, that if the parts could be moved into the horizontal position the moment of the force W + w about the axis H J would be a maximum, just as in this position the moment of the same force about the axis E F is a maximum. It is also clear that when the parts are in the vertical position the force W + w has no turning moment about either axis. In an intermediate position ([Fig. 21]) the moment of the force W + w about the axis E F is proportional to a c—that is, to the component of a b perpendicular to the plane of the casing or disc—just as it would be if the pin were central or if the bail formed a rigid part of the casing. The moment of W + w about the axis H J is likewise proportional to the component a c. As the value of the component a c, at least for small angles of swing, is proportional to the angle of swing θ, the net result of making the pin excentric and introducing a phantom ring is to apply to the casing when it is deflected (1) the ordinary moment of the weight W about the axis E F, and (2) an additional moment about the axis H J. This latter moment is proportional to the angle of swing θ, and in the position shown in [Fig. 21] tends to turn the casing in the direction of the arrow R. If the deflection is towards the other side of the axis E F, the moment applied about H J will clearly tend to rotate the casing in the opposite direction, as shown at T. Comparing Figs. [21] and [16], it will be seen that the excentricity of the pin in the Sperry compass secures exactly the same result as the air blast reaction produces in the Anschütz compass.
It is to be noted that the excentric pin in the Sperry compass is displaced towards the east when the axle is resting on the meridian. If it were displaced towards the west the force applied about the vertical axis would be reversed in its effect, and would tend to increase the oscillations of the sensitive element and not to damp them, as is the intention.
CHAPTER VII
THE DAMPING SYSTEM OF THE BROWN COMPASS
In both the Sperry and the early Anschütz compass the natural oscillation of the sensitive element about the vertical axis is damped by applying a retarding moment to the element about this same axis, the strength of the retarding moment being at all times proportional to the velocity with which the element is moving in the course of its vibration. The opposition exercised by the retarding force is not, however, a direct one. The motion of the sensitive element arises from the fact that the spinning wheel, the axle, and the pendulous weight are tilted about the horizontal axis E F. The retarding force is applied about the vertical axis, not because that is the axis on which the sensitive element is oscillating, but because a force so applied produces a movement about the horizontal axis tending to wipe out the tilt and so eliminate the cause of the oscillation.
Fig. 22. Gyro-Pendulum with Axle Tilted.