The optimum efficiency of a screw propeller, with or without end plates, depends on the geometry of the generator lines of blades and end plates. Quality numbers of propellers have been calculated for a variety of generator lines. The shape of the planform of end plates is discussed in order to minimize their viscous resistance.
On the Influence of Choice of Generator Lines on the Optimum Efficiency of Screw Propellers
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de Jong, K., and J. A. Sparenberg. "On the Influence of Choice of Generator Lines on the Optimum Efficiency of Screw Propellers." J Ship Res 34 (1990): 79–91. doi: https://doi.org/10.5957/jsr.1922.214.171.124
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