Errors due to a practical Green function for steady ship waves

Abstract

Errors that stem from a practical analytical approximation La to the local flow component L in the Green function associated with steady linear potential flow around a ship hull are considered. Although the approximation La is not very accurate, the flow potentials evaluated via the exact local flow component L or the approximation La for Froude numbers F=0.15, 0.3 and 0.5 cannot be distinguished, except at F=0.15 for which relatively small differences can be observed. Moreover, the sinkage, the trim angle and the wave drag predicted by the Neumann–Michell (NM) theory, with the local flow potential evaluated using L or La, are in very close agreement. Despite its remarkably simplicity, the analytical approximation La can then be used to compute the local flow component L in the Green function, in the entire flow region, within the framework of the NM linear potential flow theory and the related Hogner approximation. The practical analytical approximation La is far more practical than the basic integral representation of L, and is an important element of the NM theory. Indeed, the analytical approximation La, and other features of the NM theory, make it possible to compute the flow around a steadily advancing ship hull in a highly efficient way, as required for routine practical applications to design and hull-form optimization.