Propeller Efficiency - Simple Methods
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
AbstractIn 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).
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