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Abstract Numerous species of aquatic invertebrates, including crustaceans, swim by oscillating multiple closely spaced appendages. The coordinated, out-of-phase motion of these appendages, known as “metachronal paddling,” has been well-established to improve swimming performance relative to synchronous paddling. Invertebrates employing this propulsion strategy cover a wide range of body sizes and shapes, but the ratio of appendage spacing (G) to the appendage length (L) has been reported to lie in a comparatively narrow range of 0.2 < G/L ≤ 0.65. The functional role of G/L on metachronal swimming performance is unknown. We hypothesized that for a given Reynolds number and stroke amplitude, hydrodynamic interactions promoted by metachronal stroke kinematics with small G/L can increase forward swimming speed. We used a dynamically scaled self-propelling robot to comparatively examine swimming performance and wake development of metachronal and synchronous paddling under varying G/L, phase lag, and stroke amplitude. G/L was varied from 0.4 to 1.5, with the expectation that when G/L is large, there should be no performance difference between metachronal and synchronous paddling due to a lack of interaction between vortices that form on the appendages. Metachronal stroking at nonzero phase lag with G/L in the biological range produced faster swimming speeds than synchronous stroking. As G/L increased and as stroke amplitude decreased, the influence of phase lag on the swimming speed of the robot was reduced. For smaller G/L, vortex interactions between adjacent appendages generated a horizontally oriented wake and increased momentum fluxes relative to larger G/L, which contributed to increasing swimming speed. We find that while metachronal motion augments swimming performance for closely spaced appendages (G/L <1), moderately spaced appendages (1.0 ≤ G/L ≤ 1.5) can benefit from the metachronal motion only when the stroke amplitude is large. 

ABSTRACT Miniature insects must overcome significant viscous resistance in order to fly. They typically possess wings with long bristles on the fringes and use a clap-and-fling mechanism to augment lift. These unique solutions to the extreme conditions of flight at tiny sizes (<2 mm body length) suggest that natural selection has optimized wing design for better aerodynamic performance. However, species vary in wingspan, number of bristles (n) and bristle gap (G) to diameter (D) ratio (G/D). How this variation relates to body length (BL) and its effects on aerodynamics remain unknown. We measured forewing images of 38 species of thrips and 21 species of fairyflies. Our phylogenetic comparative analyses showed that n and wingspan scaled positively and similarly with BL across both groups, whereas G/D decreased with BL, with a sharper decline in thrips. We next measured aerodynamic forces and visualized flow on physical models of bristled wings performing clap-and-fling kinematics at a chord-based Reynolds number of 10 using a dynamically scaled robotic platform. We examined the effects of dimensional (G, D, wingspan) and non-dimensional (n, G/D) geometric variables on dimensionless lift and drag. We found that: (1) increasing G reduced drag more than decreasing D; (2) changing n had minimal impact on lift generation; and (3) varying G/D minimally affected aerodynamic forces. These aerodynamic results suggest little pressure to functionally optimize n and G/D. Combined with the scaling relationships between wing variables and BL, much wing variation in tiny flying insects might be best explained by underlying shared growth factors. 

Synopsis Numerous aquatic invertebrates use drag-based metachronal rowing for swimming, in which closely spaced appendages are oscillated starting from the posterior, with each appendage phase-shifted in time relative to its neighbor. Continuously swimming species such as Antarctic krill generally use “pure metachronal rowing” consisting of a metachronal power stroke and a metachronal recovery stroke, while burst swimming species such as many copepods and mantis shrimp typically use “hybrid metachronal rowing” consisting of a metachronal power stroke followed by a synchronous or nearly synchronous recovery stroke. Burst swimming organisms need to rapidly accelerate in order to capture prey and/or escape predation, and it is unknown whether hybrid metachronal rowing can augment acceleration and swimming speed compared to pure metachronal rowing. Simulations of rigid paddles undergoing simple harmonic motion showed that collisions between adjacent paddles restrict the maximum stroke amplitude for pure metachronal rowing. Hybrid metachronal rowing similar to that observed in mantis shrimp (Neogonodactylus bredini) permits oscillation at larger stroke amplitude while avoiding these collisions. We comparatively examined swimming speed, acceleration, and wake structure of pure and hybrid metachronal rowing strategies by using a self-propelling robot. Both swimming speed and peak acceleration of the robot increased with increasing stroke amplitude. Hybrid metachronal rowing permitted operation at larger stroke amplitude without collision of adjacent paddles on the robot, augmenting swimming speed and peak acceleration. Hybrid metachronal rowing generated a dispersed wake unlike narrower, downward-angled jets generated by pure metachronal rowing. Our findings suggest that burst swimming animals with small appendage spacing, such as copepods and mantis shrimp, can use hybrid metachronal rowing to generate large accelerations via increasing stroke amplitude without concern of appendage collision. 

Negatively buoyant freely swimming crustaceans such as krill must generate downward momentum in order to maintain their position in the water column. These animals use a drag-based propulsion strategy, where pairs of closely spaced swimming limbs are oscillated rhythmically from the tail to head. Each pair is oscillated with a phase delay relative to the neighbouring pair, resulting in a metachronal wave travelling in the direction of animal motion. It remains unclear how oscillations of limbs in the horizontal plane can generate vertical momentum. Using particle image velocimetry measurements on a robotic model, we observed that metachronal paddling with non-zero phase lag created geometries of adjacent paddles that promote the formation of counter-rotating vortices. The interaction of these vortices resulted in generating large-scale angled downward jets. Increasing phase lag resulted in more vertical orientation of the jet, and phase lags in the range used by Antarctic krill produced the most total momentum. Synchronous paddling produced lower total momentum when compared with metachronal paddling. Lowering Reynolds number by an order of magnitude below the range of adult krill (250–1000) showed diminished downward propagation of the jet and lower vertical momentum. Our findings show that metachronal paddling is capable of producing flows that can generate both lift (vertical) and thrust (horizontal) forces needed for fast forward swimming and hovering.