In this paper a propeller having all sections operating at supersonic speeds is designated a supersonic propeller regardless of flight speed. Analyses assume subsonic flight speeds but very high rotational speeds. A very elementary analysis of the efficiency of a jet-propeller system is presented. A propeller analysis based on conventional vortex blade element theory is presented and reduced to a single point method which leads to an expression for optimum advance ratio in terms of hub-tip diameter ratio and airfoil fineness ratio.