Appendage spacing and stroke kinematics in metachronal swimming of crustaceans

Oscillatory paddling of multiple appendages is a swimming strategy used by a large number of ecologically important crustacean species. Species that use their swimming legs (pleopods) for routine swimming, such as krill, typically perform a metachronal stroke in which pleopod pairs move with a phase lag relative to the neighboring pairs. In contrast, species that use other methods of routine swimming (e.g. copepods) use their swimming legs for rapid escape responses and perform a hybrid stroke consisting of a metachronal power stroke (PS) followed by a synchronous recovery stroke (RS). Non-dimensional inter-pleopod spacing for over 30 crustacean species, defined as the distance between adjacent appendages (D) divided by appendage length (L), was reported by Murphy et al. (Mar. Biol., 158, 2011) to range from 0.2-0.65. Krill species were at the higher end of this range (D/L>0.4) and copepods were at the lower end (D/L<0.3). We hypothesized that a metachronal stroke with higher D/L may be better suited for cruising, while a hybrid stroke with lower D/L may be better suited for escaping. To test this hypothesis, we examined the effects of varying D/L and stroke kinematics (metachronal, synchronous, hybrid) on forward swimming performance (thrust, swimming speed, and acceleration) of a self-propelling paddling robot. For a metachronal stroke, decreasing D/L results in increasing swimming speed for constant stroke amplitude (SA). However, decreasing D/L also reduces the maximum SA achievable for a given non-zero phase lag while avoiding collisions between adjacent appendages. Regardless of phase lag during PS, the use of a hybrid stroke allows for a SA of nearly 180 degrees by delaying recovery until all appendages have completed PS. The use of a hybrid stroke also allows organisms to accelerate faster and swim farther per stroke than when using a metachronal stroke.