The potential problem is solved for the circulation distribution of an optimum propeller with finite number of blades when operating in a cylindrical duct. The effects of the duct on both the circulation and the thrust increase have been calculated for specific cases, showing that they become important for propellers operating in a duct having a diameter which approaches the propeller diameter. The effect of the duct increases with decreasing number of blades and with increasing pitch. The percentage increase in thrust which has been computed is additive to the Woodand Harris correction resulting from the contraction of the slipstream.

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