Going around the bend to evaluate the role of coalescence in metachronal swimming

Metachronal swimming is achieved by sequentially beating closely spaced flexible appendages. The distinct differential stiffness of the appendages keeps them rigid during the power stroke to maximize thrust but enables significant bending during the recovery stroke. The effect bending has on the near flow and forces during the recovery stroke has received little attention despite being crucially important in reducing drag. We combine μ-CT measurements with in vivo velocimetry experiments on shrimp (Palaemonetes vulgaris) and their robotic analog to explore the underlying mechanisms enabling differential stiffness and drag reduction during metachrony. We find that the concave geometry of the legs (pleopods) makes them twice as flexible during the recovery versus the power stroke. Simultaneous kinematics and particle image velocimetry data show that bending enables inter-pleopod interactions causing three legs to coalesce at any time during the recovery stroke. Contrary to the power stroke, these complementary mechanisms shed no observable wake. We used these results to design a scaled robot with five morphologically accurate pleopod analogs mounted in series that integrate differential stiffness. We compare the thrust and drag forces against rigid pleopods to test the hypothesis that bending and coalescence effectively reduce the drag of three legs to that of only one. Considering appendage stiffness leverages our understanding of metachronal propulsion for designing novel underwater robots.