Parametric generation of planing hulls

This paper presents a mathematical method for producing hard-chine ship hulls based on a set of numerical parameters that are directly related to the geometric features of the hull and uniquely define a hull form for this type of ship. The term planing hull is used generically to describe the majority of hard-chine boats being built today. This paper is focused on un-stepped, single-chine hulls. B-spline curves and surfaces were combined with constraints on the significant ship curves to produce the final hull design. The hard-chine hull geometry was modeled by decomposing the surface geometry into boundary curves, which were defined by design constraints or parameters. In planing hull design, these control curves are the center, chine and sheer lines, as well as their geometric features including position, slope and, in the case of the chine, enclosed area and centroid. These geometric parameters have physical, hydrodynamic and stability implications from the design point of view. The proposed method utilizes 2D orthogonal projections of the control curves and then produces 3D definitions using B-spline fitting of the 3D data points. The fitting considers maximum deviation from the curve to the data points and is based on an original selection of the parameterization. A net of B-spline curves (stations) is then created to match the previously defined 3D boundaries. A final set of lofting surfaces of the previous B-spline curves produces the hull surface.