In the preceding chapter we calculated the force generated by intermittent cavitation on simple forms. It was necessary to model not only the ship as a simple form but also the cavitating propeller. Although these simplifications gave useful information it was also obvious that the results could not be used for practical purposes. This was the price we had to pay for being able to obtain results by “hand-turned mathematics”.

When we now wish to obtain results for actual, intermittently cavitating propellers behind real ship forms of given (arbitrary) shape we must expect the mathematics to be too complicated to be manipulated into closed expressions for forces and pressures. Instead, we shall describe a general, computer-effected method for solving the problem for a propeller behind a ship and we shall also present results of this theory for cavitating propellers. Furthermore, we shall correlate these results with those obtained by model experiments.

REPRESENTATION OF HULLS OF ARBITRARY SHAPE IN THE PRESENCE OF A PROPELLER AND WATER SURFACE

It has been demonstrated in the foregoing that a propeller operating in a temporally uniform but spatially varying hull wake produces, through the concerted action of all the blades, a potential flow and pressure field composed of many components, all of which are at frequencies qZω. As these frequencies are large compared with those which can give rise to wave generation on the free water surface, the appropriate linearized boundary condition, imposed by the presence of the water surface, is that the total velocity potential in the undisturbed locus of that surface must be zero.