Unsteady Lifting Surface Theory for a Marine Propeller of Low Pitch Angle With Chordwise Loading Distribution

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Abstract
This study is third in a series of investigations applying the unsteady lifting-surface theory to the marine propeller case. In the present investigation, the surface integral equation is solved for a mathematical model where the chordwise loading is taken as the first term of Birnbaum's lift distribution (flat-plate chordwise distribution), in conjunction with Glauert's lift operator, which, in essence, satisfies the chordwise boundary conditions by a weighted average. It is shown that this model is an improvement over the modified Weissinger model used previously in this series, because it contains as a nucleus the exact two-dimensional solution, and thus it provides a sounder basis for determining the three-dimensional effects. The blade-loading is determined for a propeller operating in flow disturbances induced by the presence of a hull and by the blade-camber and incidence-angle effects. The stationary loading obtained by the present model is less than that obtained by the modified Weissinger model, whereas the nonstationary loading is slightly larger. The results of numerical calculations are applied to the problem of propeller vibratory thrust and torque, and comparison is made with previous theoretical and experimental values. Conclusions of the earlier studies as to the dependence of loading on the important parameters—blade-area ratio, aspect ratio and pitch—are confirmed by the present results.

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