The extinct ocean-going plesiosaurs were unique within vertebrates because they used two flipper pairs identical in morphology for propulsion. Although fossils of these Mesozoic marine reptiles have been known for more than two centuries, the function and dynamics of their tandem-flipper propulsion system has always been unclear and controversial. We address this question quantitatively for the first time in this study, reporting a series of precisely controlled water tank experiments that use reconstructed plesiosaur flippers scaled from well-preserved fossils. Our aim was to determine which limb movements would have resulted in the most efficient and effective propulsion. We show that plesiosaur hind flippers generated up to 60% more thrust and 40% higher efficiency when operating in harmony with their forward counterparts, when compared with operating alone, and the spacing and relative motion between the flippers was critical in governing these increases. The results of our analyses show that this phenomenon was probably present across the whole range of plesiosaur flipper motion and resolves the centuries-old debate about the propulsion style of these marine reptiles, as well as indicating why they retained two pairs of flippers for more than 100 million years.

The propulsive performance of a pair of tandem flapping foils is sensitively dependent on the spacing and phasing between them. Large increases in thrust and efficiency of the hind foil are possible, but the mechanisms governing these enhancements remain largely unresolved. Two-dimensional numerical simulations of tandem and single foils oscillating in heave and pitch at a Reynolds number of 7,000 are performed over a broad and dense parameter space, allowing the effects of inter-foil spacing (S) and phasing (ϕ) to be investigated over a range of non-dimensional frequencies (or Strouhal number, St). Results indicate that the hind foil can produce from no thrust, to twice the thrust of a single foil depending on its spacing and phasing with respect to the fore foil, which is consistent with previous studies that were carried out over a limited parameter space. Examination of instantaneous flowfields indicate that high thrust occurs when the hind foil weaves in between the vortices that have been shed by the fore foil, and low thrust occurs when the hind foil intercepts these vortices. Contours of high thrust and minimal thrust appear as inclined bands in the S − ϕ parameter space and this behaviour is apparent over the entire range of Strouhal numbers considered (0.2 St 0.5). A novel quasi-steady model that utilises kinematics of a virtual hind foil together with data obtained from simulations of a single flapping foil shows that performance augmentation is primarily determined through modification of the instantaneous angle of attack of the hind foil by the vortex street established by the fore foil. This simple model provides estimates of thrust and efficiency for the hind foil, which is consistent with data obtained through full simulations. The limitations of the virtual hind foil method and its physical significance is also discussed.

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.