Algebraic Surfaces with Three Super Ellipses for Formation of Submarine Hull Surfaces

Abstract

_ Definite stereotype for the outward look of submarines was worked out in the process of evolution. It is very difficult to take into account all inner and outside factors having an influence on the choice of submarine hull shape. Choosing either factor, designers’ model a great variety of outside lines. A light hull of a submarine is the outer nonwatertight hull which provides a hydrodynamically efficient shape. The pressure hull is the inner hull of a submarine; this holds the difference between outside and inside pressure. Closed algebraic surfaces with the main cross-sections in the form of three superellipses lying in three coordinate planes can help to select a submarine form during early-stage design. Having used a parallel middle body, one can extend considerably the choice of suitable shapes. In this paper, a method of modeling smooth compound closed algebraic surfaces that approximates the outside lines of a submarine is presented. The authors offer to form an outside submarine hull from six fragments of algebraic surfaces. The whole hull surface and its fragments are given by the same parametric equations. A method is illustrated in three examples, and it is realized easily in the form of a computer program. The initial data contain large quantities of constants, and it gives an opportunity to consider an infinitely large quantity of variants of submarine hull surfaces. Keywords submarine hull surface; superellipse; compound algebraic surface; buttock line; waterline; midship section