Moment on a liquid-filled spinning and nutating projectile: Solid body rotation

The moment exerted on the casing by a completely spun-up liquid filling a spinning and nutating right circular cylinder is evaluated. Among the restrictions of the theory are (1) assumption of small yaw angle, and (2) constant spin and nutational frequencies and timewise exponential yaw growth. The new feature of this work is the inclusion of viscous shear in the liquid force on the cylinder walls. It is found that the viscous shear contributes significantly to the overturning moment in many instances. Outputs are compared with those of the theory of Murphy, which makes the additional assumption of inviscid flow except for boundary layers near the walls. Results of the two theories agree well for high Reynolds numbers (>or=5x0.0001) but diverge increasingly as Reynolds number is decreased. Comparisons of calculated yaw growth rates are made with measurements taken in gyroscope experiments for aspect-ratios of 1.0 and 3.1. The differences between theory and experiment are greater for the 3.1 aspect-ratio cylinder than for the 1.0 case. The present theory generally shows better agreement with experiment at the lower Reynolds numbers than does the Murphy theory. Both theories demonstrate a strong sensitivity of yaw growth rate to variation in cylinder aspect ratio.