568. The Moment of Inertia of Liquid Filled Cylindrical Tanks About Various Axes
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Paper
Abstract
This paper gives the results of a series of experiments performed to determine the moment of inertia of filled cylindrical tanks as they oscillate about various axes. The purpose of this investigation was to find an approximate analytical expression for determining liquid moments of inertia to better predict the dynamic behavior of launch vehicles. The experiments were divided into four categories:
1. Roll Axis about Center of Mass
2. Displaced Roll Axis
3. Yaw-Pitch Axis about Center of Mass
4. Displaced Yaw- Pitch Axis
Torsional and compound pendulums were used for oscillating the tanks. The results of these tests verified the available analytical expressions. These expressions can be applied to Launch vehicle fuel tanks.
By definition, the moment of inertia is the property of a solid which depends on its mass distribution and its axis of rotation. Since liquid is non-rigid, the amount of liquid which participates in rotation depends on the boundary conditions placed on the liquid, the liquid viscosity, the frequency of rotation, and the axis of rotation. The dependency of the liquid behavior on so many variables shows that the terms, liquid and solid moment of inertia, are not synonymous. Therefore, the liquid moment of inertia is normally referred to as the effective moment of inertia. That is. the solid moment of inertia which would yield the same apparent moment of inertia of the liquid.
The experimental results agree well with the analytical expressions derived from classical hydrodynamic theory. The yaw-pitch expression is obtained by using velocity potential theory with the aspect ratio as the only variable. The roll axis moment of inertia is dependent on the liquid viscosity, oscillation frequency, arid the tank geometry, but for cylindrical fuel tanks it is very close to zero. The moment of inertia transfer theorem for solids was proved to be valid for liquids. The equations herein, which have been verified experimentally, can be easily applied, if the proper variables are known.
