On the inter-foil spacing and phase lag of tandem flapping foil propulsors

The aim of this article is to provide a theoretical basis upon which to advance and deploy novel tandem flapping foil systems for efficient marine propulsion. We put forth three key insights into tandem flapping foil hydrodynamics related to their choreography, propulsive efficiency, and unsteady loading. In particular, we propose that the performance of the aft foil depends on a new nondimensional number, s/Utau, which is the inter-foil separation s normalized by the distance that the freestream U advects in one flapping period tau. Additionally, we show how unsteady loading can be mitigated through choice of phase lag