Propeller efficiency and the spectrum of propulsor form with speed, from pike to tuna, vulture to swift

Tail fins, flukes, flapping wings and propellers are propulsors that generate thrust with foils. Efficient thrust production requires suitable foil design and operation. Simplified propeller theory allows the interactions between foil shape and kinematics to be addressed within the context of mechanical or 'propeller' efficiency. Efficient thrust at low forward speeds and/or high motor power is shown to require high foil area and/or lift coefficient. This offers an account for the relatively broad foils of the slow pike and birds requiring take-off at low speeds and high power. The efficiency benefit of high lift coefficients is consistent with the separated emarginate primaries forming multi-slat aerofoil sections observed not only in competent thermal soarers (vultures, storks, etc.) but also many game birds. Efficient thrust at high speeds requires relatively small foil area and/or low lift coefficients, consistent with the simple, high-aspect-ratio foils of tuna and swifts. The spectrum of relatively high-area to low-area foils does not imply a compromise between acceleration and efficiency; both ends of the scale may result in efficient propulsors, with high thrust capacity for given power supply, but with differences in form relating simply to speed.