Reduction in efficiency of propellers due to slipstream

In the slipstream behind a propeller there is a considerable amount of kinetic energy which has been imparted to it by the engine without producing any corresponding propeller thrust. The increased absorption of power reduces the propeller efficiency. Attention has been previously directed to this question by Bendemann and Madelung and other writers. Their contribution serves to verify a simple method of calculating the reduction in the propeller efficiency due to the slip stream. That method of calculation is given here. Explanations and examples are given for as single propeller and for two propellers mounted in tandem.