Distribution Functions of Mass Properties: A Tool for Naval Architecture

Abstract

Dynamic sea load calculations require the lumping of the ship into a number of mass sections. For each such section, its mass, center of gravity and some components of its tensor of inertia must be calculated. Previously, this problem was solved by tedious methods. This paper presents a general method of calculating these data out of a database containing the mass data of all ship items. The method is based on the notion of distribution functions of mass properties. It is shown that two types of mass distribution functions can be used for representing all possible distributions. These functions are the step mass distribution and the second-degree mass distribution functions. Distribution functions of moments and moments of inertia can be calculated from the mass distribution functions by analytic integration and/or multiplications. The distribution functions are also an easy means of calculating the mass properties of a jumboized ship, starting from the data of the original ship.