THE ACTIVE TYPE OF GYRO SHIP STABILIZER 153
ship aground may be able to free itself if it can roll toward deeper water; a ship stuck in mud may be able to free itself by rolling back and forth till the keel is sufficiently loosened; a ship may be able to break a passage through ice by rolling against the ice sheet.
A vessel equipped with a stabilizer of the active type will roll with gradually increasing amplitude if there be applied to the main gyro a periodic torque that is in opposite phase to the precession of the spin-axle that would be produced by the natural rolling of the ship in the direction in which rolling is desired (Art. 92). By changing electric connections at the switchboard, the apparatus may be caused to operate either as a reducer of rolling or as a producer of rolling.
97. Admiral Taylor's Formula. - The effect of waves on the rolling of a ship is cumulative, each wave contributing a small effect till the total angle of roll may become large. By neutralizing the small increments of roll, the angle of roll will not become large. Admiral D. W. Taylor, U. S. N., has shown that a roll increment ¢ can be neutralized by a gyro-wheel having a moment of inertia relative to its spin-axis of the value
K' = 1225 OD HT (100) n
where KS' is expressed in pound-feet2 units, 0 is the difference in degrees between two successive amplitudes of roll in the same direction, D is the displacement of the ship in tons, H is the metacentric height in feet, T is the period of roll in seconds, and n is the spin-velocity of the gyro in revolutions per minute. The required moment of inertia may be due either to a single gyro or to two or more gyros.
The derivation of this equation never has been published, but it may be seen in the Archives of the U. S. Navy Department in Washington.
Problem. It is required to compute the principal elements of a ship stabilizer of the non-pendulous active type that will quench a roll increment
0 = 5°, where o is the difference between two successive angles of roll in the same direction. The ship has a displacement D = 2200 tons, metacentric
height H = 2.5 ft., period of roll T = 13 sec.
The diameter of the gyro-wheel is to be 8 ft. On account of the limit of
fiber strength of steel, the peripheral speed must not exceed 33,000 ft. per min. Stops are used that limit the amplitude of precession to 60° on each side of
the equilibrium position. A magnetic brake and a motor rotating at 500