SOME GRAPHIC STUDIES OF THE ACTIVE GYRO STABILIZER. 183 



period insures perfect lubrication throughout the pressure-free bearing surfaces 

 so that ordinary bearings with liberal allowance for oil space are found to run cool 

 under extremely high, periodic, specific pressure, while both the very high velocity 

 and pressure insure the very low frictional coefficient which is realized in practice. 

 Theoretically a synchronous wave of the apparent slope a will produce, when 

 passing a floating body, a maximum amplitude of wa , or result in two single 



roll increments of — a° each, when considered as frictionless. Correspondingly, 



if the maximum plus and minus moments of our mechanical wave producer, when 

 at rest, inclined the pendulum a from the vertical, corresponding increments, 



— a , should be obtained for synchronous conditions. This was indeed very nearly 



the case; the minute deviations found are due to the slight friction, and also the 

 difficulty of starting the wave-maker instantly at full speed. 



The angular momentum that a sinuous couple, the maximum value of which 

 would incline a vessel at , will impart to such a vessel, during one-half of an har- 



o / / *!? o /I o frh Q1 n /V 



monic oscillation, is equal to — x its maximum value x — > or ^ 



2 "■ 



in pounds, feet, seconds, when, 



T = full period of vessel and of the couple in seconds. 



D — displacement of vessel or weight of pendulum in tons. 



h = metacentric height or pendulic height in feet. 

 This momentum must be balanced, for close stabilization, by that produced by 

 the stabilizer, which according to the well-known formula is equal to 



k 2 sm ^ , 



g 30 



in which 



k'^ radius of gyration of the rotating mass in feet^. 



W=^ weight of rotating mass in pounds. 



R= number of revolutions per minute of this rotating mass. 



^= angle of precession from the center position of the gyro to each side, 



therefore. 



2240 — Dh sin a = k" 2 sin <f>. 



g 30 



For small angles va , we can substitute 



IT 



—5- a = sm a, 

 180 ' 



consequently, 



Z? 7^3822 ' 



