Effects of varying number of paddles in a metachronal paddling system

Many aquatic invertebrates use a locomotion strategy known as "metachronal paddling" in which a series of appendages ("paddles") are stroked in a coordinated – but not synchronized – fashion. A number of previous studies have examined how the metachronal coordination of a fixed number of paddles can increase the propulsive forces relative to synchronous paddling. However, another interesting aspect of this strategy as observed in nature is that the number of paddles varies both across species and across stages of development – many crustaceans that employ metachronal locomotion undergo larval and juvenile development stages during which they grow additional swimming legs. In this study, we examine how changing the number of paddles affects the swimming speed, tip vortex dynamics and pressure in the wake of the metachronal paddling system. We found that increasing the number of paddles results in a decrease in circulation in the paddle-tip vortex generated during the paddle's thrust-generating power stroke, likely due to destructive interactions between high- and low-pressure zones on opposite sides of adjacent paddles. Additionally, we found that increasing the number of paddles resulted in linearly increased swimming speed, but a nonlinear decrease in swimming speed per paddle.