Ship waves: the calculation of wave profiles

1. The surface disturbance produced by a ship is usually analysed into two parts : one is called the local disturbance and the other forms the wave pattern, the supply of energy required for the second part giving rise to the wave resistance of the ship. For a direct comparison between observed and theoretical surface elevation it is necessary to calculate both parts of the disturbance. This has been carried out recently for a certain case by Mr. W. C. S. Wigley,* working at the William Froude Laboratory. The model was of uniform horizontal section and sufficiently deep to be treated as theoretically of infinite draught, while the section consisted of a triangular bow and stern connected by a straight middle body ; the surface elevation along the side of the model was observed at various speeds, and compared with the theoretical calculations. The following paper deals with the calculation of the surface elevation in cases of this type. The theory is developed here from the velocity potential of a doublet at any given depth below the free surface of the water ; this has the advantage of being capable of wide generalisation, and, moreover, the introduction of a small frictional term, which is ultimately made to vanish, keeps the expressions determinate throughout the analysis.