  1Earlier form as in use in 1910. 2Approximate. Differs in different compasses. 3The value of the latitude error is b tan L, where L is the angle of latitude and b a constant dependent upon the design of the compass. In the Sperry correction mechanism the value of the quantity b is represented by the distance between the centre of the dial B and the centre of the pin C when the radial slot in the dial is lying at right angles to the bar DE. 4The value of the north steaming error is numerically equal to (a K cos C)/cos L, where K is the ship’s speed, L the angle of latitude, C the angle between the course and the north and south direction, and a a constant involving the speed of rotation of the earth. In the Sperry correction mechanism the value of the quantity a is represented by the radius at which the pin L lies from the centre of the latitude dial. 5The ballistic deflection is dependent upon the rate at which the northerly component of the ship’s speed is being changed. The difference in the north steaming errors is dependent upon the initial and final values of the speed towards the north, and would not appear to be affected by the length of time occupied in changing the speed. It would seem, therefore, that the ballistic deflection can only be dead-beat in the chosen latitude if the speed towards the north is reduced or increased at one particular rate. Thus if the ship is steaming due north at 20 knots and changes its speed to 10 knots in (a) 10 minutes or (b) 5 minutes, the initial and final values of the north steaming error will be the same in both cases, since the initial and final speeds are the same, but the ballistic deflection will be greater in the second case than in the first, since the rate at which the speed is changed is greater. If, then, the ballistic deflection is dead-beat in the first case it cannot be so in the second. The statement that the ballistic deflection in the chosen latitude is dead-beat thus appears, it may be suggested, to require qualification. On the other hand, the British Admiralty in connection with the use of gyro-compasses on destroyers and similar fast-manoeuvring vessels wherein the ballistic deflection is a factor of very great importance has carried out lengthy experiments on the matter, and, although the results have not been divulged, it is understood that the ballistic deflection was found to be dead-beat independently of the rate at which the speed was changed. 6The wheels in the two designs being similar in form, their moments of inertia—the real factors determining the magnitude of the directive forces—are proportional to the fourth powers of their diameters. The fourth power of 5 is to the fourth power of 6 as 1 is to 2 approximately. 7The directive force is proportional to the sine of the angle of deflection. The gyros KLM therefore supply at 30 deg. deflection a total directive force of D sin 30 deg. + D sin 60 deg. + D sin 0 deg., or 1.366 D. For a single-gyro compass, having a wheel of twice the inertia of KL or M separately, the directive force at 30 deg. deflection would be 2 D sin 30 deg. or D. |
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