Optimizing the forces and propulsive effciency in bird-scale flapping flight

This paper presents first-principle and numerical studies of flapping flight with the objective of optimizing the force production and propulsive efficiency. Strouhal number is identified as a critical parameter affecting all of these variables, and the optimum ranges of Strouhal number are calculated. The results of the calculations, in particular, explain why a value in the range of 0.2-0.4 is usually preferred by nature's flyers. Next, an attempt is made to quantify the effects of wing flexibility on force generation and propulsive efficiency, and it is shown that there exists a critical value of wing elasticity at which propulsive efficiency is maximized, and moreover, this value is driven primarily by the dynamics of the bending motion of the wing rather than twisting.