AN ANALYTICAL WINDAGE EXPRESSION FOR BALL-BEARING GYROSCOPE WHEELS. VOLUME I. CONTINUUM REGIME. VOLUME II. SLIP REGIME,
MASSACHUSETTS INST OF TECH CAMBRIDGE INSTRUMENTATION LAB
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A study was made of the windage contributions of typical free surfaces and gaps found in the gyro wheel-motor-gimbal geometry with ball-bearing spin-axis support. A series of tests varying geometry and gas conditions was performed to verify the validity of the theoretical derivations. Correlation was generally better than 85. The results are presented in graphical form to show comparison of theory and test results whenever possible. A constriction drag coefficient was derived to express the windage effect due to the close-fitting gimbal shell. A study was also made of the gas-surface slip effect that results in a considerable reduction in gyro wheel windage at low operating gas pressures. Exact mathematical derivations of the slip factors are presented for the four types of wheel surfaces 1 Vertical gap between flat surfaces of wheel and motor, 2 outer face or side rim, 3 wheel OD, and 4 annular gap between wheel and motor. Test data are presented for windage measurements with helium from 5080 microns .2 inches Hg to 500 microns Hg. An empirical constriction drag coefficient is derived from the data for the narrow gap between wheel OD and float enclosure when operating in the slip flow regime.
- Fluid Mechanics