Froude number, hull shape, and convergence of integral representation of ship waves

Abstract

Abstract The Fourier–Kochin representation of the oscillatory part of the flow pressure at the hull surface of a ship that travels at a constant speed in calm water of large depth – and the related Fourier–Kochin representations of the wave drag, hydrodynamic lift and pitch-moment experienced by the ship – are considered within the framework of the potential flow theory based on the Green function that satisfies the Kelvin–Michell linear boundary condition at the free surface. The convergence of the Fourier integrals in these Fourier–Kochin representations of the flow pressure, the wave drag, the lift and the pitch-moment are studied via a parametric numerical analysis, based on Hogner’s approximate theory, for two families of 120 simple ship models at Froude numbers F within the range 0 . 15 ≤ F ≤ 2 . The analysis shows that the cutoff wavelength λ ∞ associated with negligible short waves is significantly influenced by the Froude number and the hull shape, and yields an analytical relation that explicitly determines λ ∞ in terms of F and three major hull-shape parameters: beam/length ratio, draft/length ratio, and (nondimensional) bow or midship lengths.