A Parametric Design Method for Unstepped Planing Hulls Using Longitudinal Functions and Shape Coefficients

This paper proposes a specifically parametric design method for planing hulls using longitudinal functions and shape coefficients in order to meet the requirements for optimizing the hydrodynamic performance of planing hulls. To fully define the geometry of the planing hull, a series of design parameters and a set of longitudinal functions and shape coefficients are introduced to define key geometric features. The main frame curves of the hull are designed from bottom to top to ensure the priority and independence of parameters related to the planing surface. The mathematical equations of the control points of the keel curve, chine curve, sheer curve, and surface station curve of the hull framework are established and solved based on B-spline theory. This configures the basis for generating a continuous smooth surface of the hull. Finally, based on the frame curves, the hull surface was generated by using NURBS surface interpolation. The design parameters, especially the longitudinal functions and shape coefficients, can intuitively and independently control the key features of the hull form, which allow control over key geometric features that are highly relevant to the hydrodynamics of the planing hull. By utilizing this approach, rapid production of deep-V and radial planing hulls is achievable, resulting in closed and smooth hull surfaces. Case studies have provided evidence that the modeling of monohull unstepped planing hulls with diverse characteristics can be effectively accomplished through the definition of these parameters.