Instabilities of a gyroscope produced by rapidly rotating, highly viscous liquids

A series of experiments were conducted to determine the yaw behavior of a gyroscope that contained a liquid-filled rotor. Spin rates, liquid viscosities, and cylinder geometries were selected to produce a wide range of Reynolds numbers (5 < RE < 12,000). Three cylinder aspect ratios (height/diameter) were tested: 1/1, 3/2, and 3/1. Coning frequencies for the free gyroscope were selected to be typical of spin-stabilized projectiles. Two distinct types of yaw behavior were observed with Reynolds number being the major controlling parameter. For RE > 1,000, the motion of the gyroscope was reasonably well predicted by classical liquid-filled shell theories that postulate a resonance between a natural frequency of the spinning liquid and the yaw frequency of the gyroscope. For these conditions the maximum yaw growth rate will occur when an eigenfrequency of the liquid is approximately equal to the gyroscope yaw frequency. For cases where RE< 1,000, the behavior of the gyroscope was not characterized by a resonant mechanism. Instead, the liquid-induced yaw moments and yaw growth rates grew monotonically with increasing yaw frequencies.