# Propeller Efficiency - Simple Methods

## DOI:

https://doi.org/10.31224/osf.io/zdgcn## Keywords:

advance ratio, aircraft, angular momentum, aviation, blade, design, disc loading, efficieny, lift-to-drag ratio, Mach number, performance, performance factor, propeller, speed, thrust loading, tip## Abstract

In order to produce thrust, the air needs to be accelerated by the propulsor (the propeller or the jet engine). The more the air gets accelerated from flight speed v = v_1 to exit speed v_4 (i.e. the higher v_4/v_1), the lower the efficiency. However, without accelerating the air, no power or thrust is produced. The efficiency depends on the non-dimensional thrust, called thrust loading, c_S, which is a function of aircraft speed. Disc loading k_P is calculated from power, P air density, rho and propeller disc area, A_S. k_P is independent of speed and as such a good characteristic parameter of a propeller. Together, this makes the propulsive efficiency a function of disc loading, k_P and flight speed, v. Further losses come from angular momentum. The efficiency calculated considering angular momentum in addition dependents on the ratio of forward speed, v and tip speed u (v/u). A constant speed propeller can run at a favorable speed for the piston or turboprop engine at a limited Mach number of the blade tips. At higher speeds, v and also v/u increases and hence required engine torque. This increases the angular momentum and reduces the efficiency. At low speeds, the ratio v_4/v_1 gets unfavorably high and the efficiency is low. At zero speed v_4/v_1 goes to infinity and the efficiency to zero. For an example calculation, optimum efficiencies were obtained at v/u between 3 and 5 depending on disc loading. Not considered is the limited lift-to-drag ratio (L/D) of the propeller blades and losses at blade tip (which could be accounted for by a performance factor between 0.85 and 0.9).### Downloads

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