Generating hydrodynamic surfaces by families of Lame curves for modelling submarine hulls

This paper investigates the construction of hydrodynamic surfaces, which are defined by algebraic equations and describe the theoretical hull of a vessel. A technique for automation of generating hydrodynamic surfaces is proposed. This technique allows to create a vast variety of hull shapes, for which Lame curves with variable exponents are used as surface generator lines. The surface is constructed by a family of curves in one of the three mutually perpendicular planes, which permits to obtain three algebraically different, but geometrically identical surfaces. This paper introduces parametric equations for each of the three surfaces, generated by families of sections, buttocks and waterlines in the form of Lame curves. The algorithm of modelling a submarine hull with different fore and aft bodies and a parallel middle body by a closed surface is demonstrated and the modelling results are illustrated. The presented technique may be effectively applied at the early stages of ship design when choosing the optimal hull shape, for which a number of surfaces need to be considered.