20 



THE POPULAR SCIENCE MONTHLY 



SOME PEACTICAL ASPECTS OF GYEOSTATIC ACTION" 



By Professor W. S. FRANKLIN 



LEHIGH UNIVERSITY 



r 



iHE Brennan monorail car and the Schlick device for the prevention 

 of rolling of ships at sea have recently attracted popular attention 

 to the gyrostat, and gyrostatic action has recently become vitally inter- 

 esting to a large group of men because an automobile-engine fly-wheel 

 shows serious gyrostatic reactions when the automobile rounds a curve 

 rapidly or rises suddenly upon a bump in the road. The following 

 discussion will therefore be welcomed by many readers. Let no one 

 imagine that gyrostatic action is mysterious and difficult to analyze; 

 it is really quite simple 1 and the discussion of Fig. 10 makes this action 

 as clear, physically, as the simple inertia reaction of a heavily loaded 

 wagon or boat. The formula for calculating the numerical value of 

 the torque reaction of a gyrostat, as given at the end of this paper, is 

 simple enough for any one to use. 



The rotation of a wheel on an axis is called spin, and the axle upon 

 which the wheel rotates is called the axle of spin. The spin of a 



wheel may be completely repre- 

 sented in both magnitude and 

 direction by an arrow drawn par- 

 's y ■ allel to the axle of spin, pointing 

 in the direction in which a right- 

 handed screw would travel if 

 turned with the spinning wheel, 

 and having a length which repre- 

 sents the number of revolutions 

 per second of the wheel. Thus, 

 the arrow S, 2 Fig. 1, represents the spin of the wheel WW. 



Let the arrow S', Fig. 2, represent the spin of a body, imagine a 

 large turning force to act upon the body for a short time, and let the 

 arrow S" represent the spin which would be produced by the turning 

 force if the body had been initially at rest. The actual resultant spin 



1 When the angular velocity of precession is small as compared with the 

 velocity of spin and when the gyrostat wheel is symmetrical with respect to 

 its axis of spin. 



2 To appreciate the geometrical meaning of the arrows S, AS and T in the 

 vector diagrams given in this paper, the reader should thrust his hand in the 

 direction of the arrow head and move the hand as if turning a right-handed screw. 



Fig. 1. 



