Mathematical programming basis for ship resistance reduction through the optimization of design waterline

It has been more than a decade since Calisal et al. (J Ship Res 46(3):208–213, 2002) presented their concept of wave resistance reduction by allowing an increase in the beam of a ship accompanied by smoothing the shoulders. Since then a series of computational and experimental studies have been performed to provide evidence for the design idea that an increase in the beam with waterline parabolization may give reduced wave resistance for moderate Froude numbers in most cases in contrast to the common understanding among naval architects. The procedure in the design concept mentioned has been based on a systematic search supported by computational work and validated by experimental studies. The present study attempts to rationalize the introduced design concept by establishing a mathematical programming basis which employs the thin-ship approximation for wave resistance and a quadratic programming in finding the optimal shape of the design waterline (DWL), for minimum wave resistance, for the given design constraints. In this case, the shape of the DWL and in turn the hull shape in accordance with DWL is determined by a well-defined optimization procedure, which is dictated by the mathematical programming routine. Computational tools are employed to check the hydrodynamic characteristics of the hull form determined by the optimization routine, before tank testing. An experimental work is carried out to confirm the computational results and to validate the proposed methodology. Both the computational and the experimental work point out that the present design approach is effective particularly for Froude numbers greater than 0.21 and less than 0.4 where the ship-generated wavelength along the hull is less than the body length.