Fairing of High Speed Displacement Hull Forms by B‐spline Approximation and Fitting

ABSTRACTThis paper presents flexible numerical procedures for fairing hull form design curves which form the three dimensional ship body. The traditional solution to the problem of fairing ship hull forms is to reduce the problem to simultaneous fairing of two dimensional curves on three orthogonal planes, called the section lines, waterlines and buttock lines. However, this process requires excessive time and experienced personnel. Fairing procedures employed in most Computer Aided Ship Design (CASD) software are computerised versions of the manual method and hence have similar drawbacks. The approach adopted in this study is based on approximation of ship lines by B‐splines that are already fair. It is shown that the degree of fairness can be improved by increasing the order of the B‐spline; however, this may result in excessive deviations from the original offset points. A balance between closeness and fairness can be identified by successive applications of B‐spline to original offsets in an iterative manner. Alternatively, B‐spline fitting instead of B‐spline approximation can be applied in order to minimize the deviation from original offset points. For ship hull forms, in order to obtain three dimensional fairness, two dimensional ship lines on three orthogonal planes need to be faired simultaneously The fairing process is first applied to waterlines and the modified offsets are transferred to other planes. The iterative process is repeated until specified degree of fairness is achieved. This procedure is applied for fairing the lines of a distorted mathematical hull form and the parent hull of a high speed hull form series. The results indicate that these procedures are particularly useful for high speed displacement hull forms and can be used as practical design tools in the early stages of ship design.