The evolution of helicopters

Here, we show that during their half-century history, helicopters have been evolving into geometrically similar architectures with surprisingly sharp correlations between dimensions, performance, and body size. For example, proportionalities emerge between body size, engine size, and the fuel load. Furthermore, the engine efficiency increases with the engine size, and the propeller radius is roughly the same as the length scale of the whole body. These trends are in accord with the constructal law, which accounts for the engine efficiency trend and the proportionality between "motor" size and body size in animals and vehicles. These body-size effects are qualitatively the same as those uncovered earlier for the evolution of aircraft. The present study adds to this theoretical body of research the evolutionary design of all technologies [A. Bejan, The Physics of Life: The Evolution of Everything (St. Martin's Press, New York, 2016)].