naca-report-210
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National Advisory Committee for Aeronautics, Report - Inertia Factors of Ellipsoids for Use in Airship Design
This report is based on a study made by the writer as a member of the Special Committee
on Design of Army Semirigid Airship RS—I appointed by the National Advisory Committee
for Aeronautics.
The increasing interest in airships has made the problem of the'potential flow of a fluid
about an ellipsoid of considerable practical importance. In 1833 Green, in discussing the
effect of the surrounding medium upon the period of a. pendulum, derived three elliptic inte-
grals, in terms of which practically all the characteristics of this type of motion can be expressed.
The theory of this type of motion 1s very fully given by Lamb, ’ and applications to the theory
of airships by many writers.8 Tables of the inertia coefficients derived from these integrals are
available for the most important special cases.‘ ' These tables are adequate for most purposes,
but occasionally it is desirable to know the values of these integrals in other cases where tabu-
lated values are not available. For this reason it seemed worth while to assemble a collection
of formulae which would enable them to be computed directly from standard tables of elliptic
integrals, circular and hyperbolic functions, and logarithms without the need of intermediate
transformations. Some of the formulae for special cases (elliptic cylinder, prolate spheroid,
oblate spheroid, etc.) have been published before, but the general forms and some special cases
have not been found in previous publications.
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