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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/Uτ, which is the interfoil separation s normalized by the distance that the freestream U advects in one flapping period, τ. Additionally, we show how unsteady loading can be mitigated through choice of phase lag. 1. Introduction Marine propulsion has been an important engineering problem since the time of Archimedes (287–212 BC) (Carlton 1994). The evolution of propulsor design from the classic Archimedes screw to the modern screw propeller has primarily been driven by considerations of efficiency. A hydrodynamically efficient propulsor has low friction losses, low turbulent losses, an ability to manipulate incident vorticity, and a stable and persistent jet-type wake. it is composed of lifting surfaces with high aspect ratio and large lift-to-drag ratio. Although screw propellers offer advantages with regard to mechanical simplicity (just need to turn the shaft!), they have practical limitations that place upper bounds on the overall hydrodynamic efficiency, such as the limitations of aspect ratio due to cavitation at high tip speeds. Research with isolated flapping foils has demonstrated up to 87% propulsive efficiency (Anderson et al. 1998), nearly achieving the ideal efficiency of an actuator disk. However, single-foil propulsion is not practical due to shortcomings, such as large oscillations in thrust, large unsteady side forces, and no mechanical redundancy. Many other nontraditional propulsors also suffer these flaws or are simply inefficient. Biomimetic concept designs and trade-offs have recently been reviewed by Fish (2013). One promising nontraditional propulsor concept involves in-line tandem flapping foils (two hydrofoils, one aft of the other). Recent research indicates that the high efficiency of a single flapping foil may be possible with a tandem foil arrangement (Akhtar et al. 2007; Boschitsch et al. 2014). Tandem flapping foils may also solve the operational problems associated with a single foil, such as inconsistent thrust and side force.