585. The Graphical Solutions of Oblate Spheroid Shell Intersection

Paper

Abstract

When elliptical bulkheads are used for cylindrical tank ends, certain problems arise in relation to the calculation of exposed surface area and enclosed volume of the tank ends. The case of a single bulkhead resolves itself into the solution of the surface area and volume of an oblate spheroid, for the bulkhead is essentially an oblate spheroid shell that has been split in half by the plane of the major axes. The solution of the problem is readily available and can be expressed in fairly simple mathematical terms.
A more serious and complicated problem arises when two tanks are clustered in such a way that the walls and bulkheads intersect. This condition results whenever the distance between the longitudinal axes of the tanks is less than the diameter of the individual tanks. Tanks would be arranged in this fashion to obtain better volume utilization within a given structural envelope.
This paper deals with a graphical approach to determining surface areas and volumes of intersecting elliptical bulkheads. A rigorous mathematical solution of the problem requires very complicated calculus techniques and the solution resolves itself into elliptic integral power series. Even assuming that one is familiar with the techniques Involved, the solution for even only one set of conditions is exceedingly time consuming and because of the difficulty the chance of error high. The use of the curves derived in this paper reduces the problem to one of extreme simplicity. Someone without the slightest awareness of the complexities of the problem can obtain exact answers for the volume and answers within ~ 3 % for the surface area of intersecting elliptical bulkheads. The total time required to do this is mere minutes.