184 SOME GRAPHIC STUDIES OF THE ACTIVE GYRO STABILIZER. 



This gives the maximum wave slope in degrees, or the inclining angle due to the 

 maximum of a sinuous couple, against which a stabilizer with the characteristics 

 k^WR would hold very closely a vessel pendulum with the characteristics DTh. 

 When unrestricted the roll increments equal 



IT 



For each half period the individual roll increments quenched would be 



^j[_ k' WR 2 sin 4, ' 

 ^ 2 DTh 2,^22 ' 



Should the precession angles be 90 degrees the precession velocity could be 

 constant and equal to the phase velocity of the wave, or — . Since the maxi- 

 mum of the stabilizing couple must also be equal to that of the wave, we have 



224oDksma = k'^^%, 

 g Zo T 



and again 



k' WR 



DTh j.()\i' 



which gives the same result as the general formula for 2 sin a = 2. 



The work done by the gyros depends on the angular velocity of the body on 

 which they act and would become a maximum when the entire momentum was 

 exerted at the center of the roll. This would give an effect of the stabilizer of 



^ 4 TT y^' WR 2 sin 4, 

 ^ ^2 DTh i2>22 



as unity. This, however, is largely of theoretical interest, but useful as establishing 

 a base line. 



The properties of the pendulum from which the curves were taken were: 



Total pendulic weight, 615 pounds, or .2746 ton. 



Pendulic height, found from inclining experiments, .36 feet. 



The period was 2.9 seconds giving the characteristic DTh = .287. 



Suppose this model represented a ship reduced at the ratio of \ = 30, it would 

 then represent a ship with the characteristic 



DTh = \^ x^x v/x'x. 287 = 1,273,000 



{D== 19,000 tons. 

 7= 14 seconds. 

 h = 4.78 feet. 



Each of the gyro rotors had the following properties: /^' fF=,2i881bs.-feet^ 

 and therefore an impulsive or maximum roll quenching power of 



_ .2188 X 1-732 ;p _ R 



9^ max ^ n ■^ ' 



1911 X .287 1450 



