Water striders Gerridae are insects of characteristic length 1 cm and weight 10 dynes that reside on the surface of ponds, rivers, and the open ocean. Their weight is supported by the surface tension force generated by curvature of the free surface, and they propel themselves by driving their central pair of hydrophobic legs in a sculling motion. Previous investigators have assumed that the hydrodynamic propulsion of the water strider relies on momentum transfer by surface waves. This assumption leads to Denny's paradox: infant water striders, whose legs are too slow to generate waves, should be incapable of propelling themselves along the surface. We here resolve this paradox through reporting the results of high-speed video and particle-tracking studies. Experiments reveal that the strider transfers momentum to the underlying fluid not primarily through capillary waves, but rather through hemispherical vortices shed by its driving legs. This insight guided us in constructing a self-contained mechanical water strider whose means of propulsion is analogous to that of its natural counterpart.

In this experimental and theoretical study, we investigate the slithering of snakes on flat surfaces. Previous studies of slithering have rested on the assumption that snakes slither by pushing laterally against rocks and branches. In this study, we develop a theoretical model for slithering locomotion by observing snake motion kinematics and experimentally measuring the friction coefficients of snakeskin. Our predictions of body speed show good agreement with observations, demonstrating that snake propulsion on flat ground, and possibly in general, relies critically on the frictional anisotropy of their scales. We have also highlighted the importance of weight distribution in lateral undulation, previously difficult to visualize and hence assumed uniform. The ability to redistribute weight, clearly of importance when appendages are airborne in limbed locomotion, has a much broader generality, as shown by its role in improving limbless locomotion.friction ͉ locomotion ͉ snake L imbless creatures are slender and flexible, enabling them to use methods of locomotion that are fundamentally different from the more commonly studied flying, swimming, walking, and running used by similarly sized limbed or finned organisms. These methods can be as efficient as legged locomotion (1) and moreover are particularly versatile when moving over uneven terrain or through narrow crevices, for which the possession of limbs would be an impediment (2, 3). Limbless invertebrates such as slugs propel themselves by generating lubrication forces with their mucus-covered bodies; earthworms move by ratcheting: propulsion is achieved by engaging their hairs in the ground as they elongate and shorten their bodies (4, 5). Terrestrial snakes propel themselves by using a variety of techniques, including slithering by lateral undulation of the body, rectilinear progression by unilateral contraction/extension of their belly, concertina-like motion by folding the body as the pleats of an accordion, and sidewinding motion by throwing the body into a series of helices. This report will focus on lateral undulation, whose utility to locomotion by snakes has been previously described on the basis of push points: Snakes slither by driving their flanks laterally against neighboring rocks and branches found along the ground (6-11). This key assumption has informed numerous theoretical analyses (12-17) and facilitated the design of snake robots for search-and-rescue operations. Previous investigators (7,9,18,19) have suggested that the frictional anisotropy of the snake's belly scales might play a role in locomotion over flat surfaces. The details of this frictionbased process, however, remain to be understood; consequently, snake robots have been generally built to slither over flat surfaces by using passive wheels fixed to the body that resist lateral motion (18,(20)(21)(22). In this report, we present a theory for how snakes slither, or how wheelless snake robots can be designed to slither, on relatively featureless terrain, such as sand or bare rock, ...

We consider the hydrodynamics of creatures capable of sustaining themselves on the water surface by means other than flotation. Particular attention is given to classifying water walkers according to their principal means of weight support and lateral propulsion. The various propulsion mechanisms are rationalized through consideration of energetics, hydrodynamic forces applied, or momentum transferred by the driving stroke. We review previous research in this area and suggest directions for future work. Special attention is given to introductory discussions of problems not previously treated in the fluid mechanics literature, with hopes of attracting physicists, applied mathematicians, and engineers to this relatively unexplored area of fluid mechanics.

Why does a single fire ant Solenopsis invicta struggle in water, whereas a group can float effortlessly for days? We use time-lapse photography to investigate how fire ants S. invicta link their bodies together to build waterproof rafts. Although water repellency in nature has been previously viewed as a static material property of plant leaves and insect cuticles, we here demonstrate a selfassembled hydrophobic surface. We find that ants can considerably enhance their water repellency by linking their bodies together, a process analogous to the weaving of a waterproof fabric. We present a model for the rate of raft construction based on observations of ant trajectories atop the raft. Central to the construction process is the trapping of ants at the raft edge by their neighbors, suggesting that some "cooperative" behaviors may rely upon coercion.cooperative animal behavior | surface tension | adhesive | emergent | differential equation

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Water-walking insects and spiders rely on surface tension for static weight support and use a variety of means to propel themselves along the surface. To pass from the water surface to land, they must contend with the slippery slopes of the menisci that border the water's edge. The ability to climb menisci is a skill exploited by water-walking insects as they seek land in order to lay eggs or avoid predators; moreover, it was a necessary adaptation for their ancestors as they evolved from terrestrials to live exclusively on the water surface. Many millimetre-scale water-walking insects are unable to climb menisci using their traditional means of propulsion. Through a combined experimental and theoretical study, here we investigate the meniscus-climbing technique that such insects use. By assuming a fixed body posture, they deform the water surface in order to generate capillary forces: they thus propel themselves laterally without moving their appendages. We develop a theoretical model for this novel mode of propulsion and use it to rationalize the climbers' characteristic body postures and predict climbing trajectories consistent with those reported here and elsewhere.

Limbless organisms like snakes can navigate nearly all terrain. In particular, desert-dwelling sidewinder rattlesnakes (C. cerastes) operate effectively on inclined granular media (like sand dunes) that induce failure in field-tested limbless robots through slipping and pitching. Our laboratory experiments reveal that as granular incline angle increases, sidewinder rattlesnakes increase the length of their body in contact with the sand. Implementing this strategy in a physical robot model of the snake enables the device to ascend sandy slopes close to the angle of maximum slope stability. Plate drag experiments demonstrate that granular yield stresses decrease with increasing incline angle. Together these three approaches demonstrate how sidewinding 1 arXiv:1410.2945v1 [physics.bio-ph] 11 Oct 2014 with contact-length control mitigates failure on granular media.The majority of terrestrial mobile robots are restricted to laboratory environments, in part because such robots are designed to roll on hard flat surfaces. It is difficult to systematically improve such terrestrial robots because we lack understanding of the physics of interaction with complex natural substrates like sand, dirt and tree bark. We are thus limited in our ability to computationally explore designs for potential all-terrain vehicles; in contrast, many of the recent developments in aerial and aquatic vehicles have been enabled by sophisticated computationaldynamics tools that allow such systems to be designed in silico (1).Compared with human-made devices, organisms such as snakes, lizards, and insects move effectively in nearly all natural environments. In recent years, scientists and engineers have sought to systematically discover biological principles of movement and implement these in robots (2). This "bioinspired robotics" approach (3) has proved fruitful to design laboratory robots with new capabilities (new gaits, morphologies, control schemes) including rapid running (2, 4), slithering (5), flying (6), and swimming in sand (7). Fewer studies have transferred biological principles into robust field-ready devices (4, 8) capable of operating in, and interacting with, natural terrain.Limbless locomotors like snakes are excellent systems to study to advance real-world allterrain mobility. Snakes are masters of most terrains: they can move rapidly on land (9, 10) and through water (11), burrow and swim through sand and soil (12), slither through tiny spaces (13), climb complex surfaces (14), and even glide through the air (15). Relative to legged locomotion, limbless locomotion is less studied, and thus broad principles which govern multi-environment movement are lacking. Recently developed limbless robotic platforms (5), based generally on the snake body plan, are appealing for multi-functional robotics study because they are also capable of a variety of modes of locomotion. These robots can traverse confined spaces, climb trees and pipes, and potentially dive through loose material. However, 2 the gaits that carry these robots across fir...

We present the results of a combined experimental and theoretical investigation of the dynamics of water-walking insects and spiders. Using high-speed videography, we describe their numerous gaits, some analogous to those of their terrestrial counterparts, others specialized for life at the interface. The critical role of the rough surface of these water walkers in both floatation and propulsion is demonstrated. Their waxy, hairy surface ensures that their legs remain in a water-repellent state, that the bulk of their leg is not wetted, but rather contact with the water arises exclusively through individual hairs. Maintaining this water-repellent state requires that the speed of their driving legs does not exceed a critical wetting speed. Flow visualization reveals that the wakes of most water walkers are characterized by a series of coherent subsurface vortices shed by the driving stroke. A theoretical framework is developed in order to describe the propulsion in terms of the transfer of forces and momentum between the creature and its environment. The application of the conservation of momentum to biolocomotion at the interface confirms that the propulsion of water walkers may be rationalized in terms of the subsurface flows generated by their driving stroke. The two principal modes of propulsion available to small water walkers are elucidated. At driving leg speeds in excess of the capillary wave speed, macroscopic curvature forces are generated by deforming the meniscus, and the surface behaves effectively as a trampoline. For slower speeds, the driving legs need not substantially deform the surface but may instead simply brush it: the resulting contact or viscous forces acting on the leg hairs crossing the interface serve to propel the creature forward.