2459. The Moment of Inertia of Fluids


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Richard Boynton: 2459. The Moment of Inertia of Fluids. 1999, (L. R. ‘Mike’ Hackney Award).



This paper describes a first step in trying to measure the MOI of fluids in tanks. The results I measured were not what most mass properties engineers would expect to find. There is a common assumption among mass properties engineers that a tank rotates independently of the fluid contained within it, so that the mass of the fluid has a small effect on the MOI. For this reason, they ignore the mass of the fluid when calculating moment of inertia, even though the mass of the fluid often is a large percentage of the total mass of the vehicle. Although this is often a safe assumption when rotating about the cylindrical axis, the effect of fluid mass on rotation about a transverse axis is usually large enough to be a major contributor to MOI. For a straight walled tank with an aspect ratio of about 3 filled with hydrazine, the MOI is 72% of the value the fluid would have if it were solid. Since the weight of fuel is as much as 85 % of the entire vehicle weight of a rocket, this means that the pitch and yaw MOI of the fuel is more than four times as large as the MOI of the entire rocket before filling it with fuel. If the effect of rocket fuel had been ignored, then the calculated pitch and yaw MOI would be less than 20% of true MOI. The results of a number of different types of experiments are summarized in this paper. It appears that the roll MOI of a rocket can be predicted by knowing the viscosity of the fuel. Additional experiments are necessary to establish a numerical relationship. Also additional work is needed to establish formulas which define the pitch and yaw moment of inertia of fluid-filled tanks of different aspect ratios. I hope that someone reading this paper will take up this cause.


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