The Unsteady Loading on a Marine Propeller in a Nonuniform Flow

The lifting-surface integral equation governing the unsteady loading on a marine propeller in a nonuniform free stream is derived using a classical vortex model. The induced downwash is split into a part corresponding to a locally tangent flat finite wing and wake, plus parts corresponding to the effects of the "helicoidal deviation" from this, of the true blade and wake, and the interference from the other blades and their wakes. Strip-type approximations are tolerated on these terms while a lifting-surface formulation is retained for the dominant finite flat-wing portion. A simple numerical example is carried out and these effects are indeed found to be quite small; so small, in fact, that it may suffice to retain only the flat finite-wing terms in practical applications.