2415. Generalized Mass Properties Formula Development for Submarine Analysis

Paper

Abstract

Throughout the normal process of analyzing mass properties data, it becomes apparent that the ordinary geometric shapes and their corresponding mass properties formulas normally published in textbooks and handbooks do not always adequately describe the component you are analyzing. This will present a problem if you are attempting, for instance, to determine the moments of inertia of a shell segment of a spheroid, cylinder, cone, etc. The geometric shapes that are analyzed in this paper are segments of some of the solids shown in the SAWE Weight Engineers Handbook under Section 4.2, Section Properties – Solids. The mathematical methods of determining the generalized formulas for volume, mass, moment as referenced from the axial planes through the object’s origin, centroid, and moment of inertia as referenced about axes through the object’s geometrical principle origin and centroid are described. The resulting derived formulas are somewhat long and complex. Therefore, to utilize them effectively and easily, they were incorporated into a spreadsheet format where only a few easily obtainable parameters are required for input. These formulas and samples of the spreadsheet format for each geometric shape are included as an appendix. This paper will also demonstrate that these sets of generalized formulas are able to effectively replace many of the formulas of solid shapes depicted in the Handbook, depending on the parameters which are chosen. This paper also recommends enhancements to the geometric shape codes and ”second-line” input data used for item moment of inertia calculation, as described in the SAWE Recommended Practice Number 12.