Despin of a Liquid-Filled Cylinder Caused by Coning

The effect of coning on the despin of a liquid-filled cylinder is investigated experimentally, and the results are analyzed using a linear theory of forced coning motion. Liquids with different viscosities are used to fill a cylinder of 60.3-mm internal radius and 258.7-mm half-height, which is then spun up to equilibrium at 66.67 Hz about its symmetry axis (tilted 20 deg from the vertical) and despun with the axis forced to cone about the vertical at 8.33 Hz. Spin rates are recorded from 66.67 to 33.33 Hz, decay constants are determined, and the despin moment is calculated by subtracting the previously determined frictional decay component. The results are plotted as a function of the logarithm of the relative viscosity. Analytical expressions describing the coning effect are derived, numerical computations are performed, and good qualitative agreement is found between theory and experiment for viscosities corresponding to Ekman numbers of 0.1 or lower.