Armed with our knowledge of the structure of the pressure fields arising from propeller loading and thickness effects (in the absence of blade cavitation) we can seek to determine blade-frequency forces on simple “hulls”. There are pitfalls in so over-simplifying the hull geometry to enable answers to be obtained by “hand-turned” mathematics, giving results which may not be meaningful. Yet the problem which can be “solved” in simple terms has a great seduction, difficult to resist even though the required simplifications are suspected beforehand to be too drastic. One then has to view the results critically and be wary of carrying the implications too far.

From our knowledge that most of the terms in the pressure attenuate rapidly with axial distance fore and aft of the propeller we are tempted to assume that a ship with locally flat, relatively broad stern in way of the propeller may be replaced by a rigid flat plate. The width of the plate is taken equal to that of the local hull and the length extended to infinity fore and aft on the assumption that beyond about two diameters the load density will virtually vanish. As we shall note later, this assumption of fore-aft symmetry of the area is unrealistic as hulls do not extend very much aft of the propeller. We shall also assume at the outset that the submergence of the flat surface above the propeller is large so we might ignore the effect of the water surface.