Calculating Curves of Form Using the Hand-Held Programmable Calculator

Abstract

This paper describes a program which the author has written for a programmable calculator for computing curves of form. The properties of the trapezoid and the mathematical expressions for them, along with expressions for summing the longitudinal and transverse moments of inertia of the elements of area making up a waterplane, form the basis of the program. The author discusses these relationships, shows how they are put in forms most usable by the calculator, and explains their function in the program. The choice of the number and spacing of stations used on a given waterplane to produce offsets or half-breadths for entry into the program is described, along with the three main uses for the program: doing curves of form for a hull in its early stages of design, making a final set of curves for a completed hull design, and computing a set of curves for an existing hull from its lines, construction drawings, or direct measurements. Finally, the advantages to the user of the program are described: a set of curves of form can be computed when and where it is needed, the accuracy is determined by how many trapezoids are used to approximate the waterplanes, and all calculations are performed automatically.