Extension of the formation time concept to general planforms and trajectories

We propose a generalization of the concept of formation time for flapping wings and appendages, that overcomes the drawbacks of Strouhal number and paves the way to the development of a unified theory for the unsteady aerodynamics of flapping propulsion. We show experimental evidence of the universality of the generalized formation time concept coming from results on flapping flat plates, shape optimization of flapping wings, and trajectory optimization for the caudal fin of an arrtificial fish.