Relation between the lifting surface theory and the lifting line theory in the design of an optimum screw propeller

A theory on an optimum screw propeller is described. The optimum means optimum efficiency of a propeller, that is, maximizing thrust horse power for a given shaft horse power. The theory is based on the propeller lifting surface theory. Circulation density (lift density) of the blade is determined by the lifting surface theory on a specified condition in general. However, it is shown that, in the case of optimum condition, the circulation density is not determined by the lifting surface theory, although the circulation distribution which is the chordwise integral of the circulation density is determined. The reason is that the governing equation of the optimization by the lifting surface theory is reduced to that by the lifting line theory. This theoretical deduction is the main part of this paper. The importance of the lifting line theory in the design of the optimum propeller is made clear. Numerical calculations support the conclusion from the deduction. This is shown in the case of freely running propellers and in the case of wake adapted propellers.