Gliding flight in Chrysopelea: turning a snake into a wing

Numerical Analysis of the Aerodynamic Interactions in Tandem Flying Snake Airfoils

During gliding, flying snakes flatten their ribs to create an airfoil-like cross-section and adopt S-shape postures, allowing upstream body segments to generate wake structures that affect the aerodynamic performance of downstream segments. This study investigates these interactions using numerical simulations of two-dimensional snake cross-sectional airfoils. By employing an immersed-boundary-method-based incompressible flow solver with tree topological local mesh refinement, various foil positions and movements were analyzed. The results show that aligning the downstream foil with the upstream foil reduces lift production by 86.5% and drag by 96.3%, leading to a 3.77-fold increase in the lift-to-drag ratio compared to a single airfoil. This improvement is attributed to the vortex-wedge interaction between the upstream vortex and the following foil's leading edge (wedge), which enhances the gliding efficiency of the posterior body. Furthermore, integrating specific pitching motions with coordinated vortex shedding could further optimize its lift production. These findings provide valuable insights into the aerodynamics of tandem flying snake airfoils, offering guidance for configuring optimal body postures for improving gliding efficiency.

Vertical bending and aerodynamic performance in flying snake-inspired aerial undulation

This paper presents a numerical investigation into the aerodynamic characteristics and fluid dynamics of a flying snake-like model employing vertical bending locomotion during aerial undulation in steady gliding. In addition to its typical horizontal undulation, the modeled kinematics incorporates vertical undulations and dorsal-to-ventral bending movements while in motion. Using a computational approach with an incompressible flow solver based on the immersed-boundary method, this study employs topological local mesh refinement mesh blocks to ensure the high resolution of the grid around the moving body. Initially, we applied a vertical wave undulation to a snake model undulating horizontally, investigating the effects of vertical wave amplitudes (ψm). The vortex dynamics analysis unveiled alterations in leading-edge vortices formation within the midplane due to changes in the effective angle of attack resulting from vertical bending, directly influencing lift generation. Our findings highlighted peak lift production atψm=2.5∘and the highest lift-to-drag ratio (L/D) atψm=5∘, with aerodynamic performance declining beyond this threshold. Subsequently, we studied the effects of the dorsal-ventral bending amplitude (ψDV), showing that the tail-up/down body posture can result in different fore-aft body interactions. Compared to the baseline configuration, the lift generation is observed to increase by 17.3% atψDV= 5°, while a preferable L/D is found atψDV= -5°. This study explains the flow dynamics associated with vertical bending and uncovers fundamental mechanisms governing body-body interaction, contributing to the enhancement of lift production and efficiency of aerial undulation in snake-inspired gliding.

Quasi-steady aerodynamic theory under-predicts glide performance in flying snakes

Flying snakes (genus Chrysopelea) glide without the use of wings. Instead, they splay their ribs and undulate through the air. A snake's ability to glide depends on how well its morphing wing-body produces lift and drag forces. However, previous kinematics experiments under-resolved the body, making it impossible to estimate the aerodynamic load on the animal or to quantify the different wing configurations throughout the glide. Here, we present new kinematic analyses of a previous glide experiment, and use the results to test a theoretical model of flying snake aerodynamics using previously measured lift and drag coefficients to estimate the aerodynamic forces. This analysis is enabled by new measurements of the center of mass motion based on experimental data. We found that quasi-steady aerodynamic theory under-predicts lift by 35% and over-predicts drag by 40%. We also quantified the relative spacing of the body as the snake translates through the air. In steep glides, the body is generally not positioned to experience tandem effects from wake interaction during the glide. These results suggest that unsteady 3D effects, with appreciable force enhancement, are important for snake flight. Future work can use the kinematics data presented herein to form test conditions for physical modeling, as well as computational studies to understand unsteady fluid dynamics effects on snake flight.

Petal-shaped femoral lobes facilitate gliding in orchid mantises

To glide in forest canopies, arboreal vertebrates evolved various skin-derived aerodynamic structures, such as patagial membranes or webbing, but no comparable structure has been reported from wingless arboreal arthropods.1,2,3 Orchid mantises (Hymenopus coronatus) have been traditionally considered a textbook example of flower mimicry for ∼200 years due to their highly expanded, petal-shaped femoral lobes. However, the empirical evidence substantiating the petal-mimicry function of the femoral lobes has not been entirely conclusive.4,5,6 Observational and experimental evidence suggests that these lobes do not contribute to flower mimicry for luring pollinators6,7 and likely serve other functions.7,8 After observing their aerial escape initiated with active jumping, we hypothesized that orchid mantises can glide and that their femoral lobes are used for gliding. Through behavioral investigations and morphological analyses, we show that orchid mantis nymphs are excellent gliders, exhibiting the shallowest gliding trajectories observed in terrestrial invertebrates.9,10,11,12,13 The lobe extensions on their femoral segments are cambered airfoils, which increase the mantis projected area by ∼36% and play a vital role in the aerodynamic underpinning of the observed gliding. Despite a 165-fold increase in body mass throughout ontogeny, older female mantis nymphs maintained a persistent gliding capability. We further showed a notable 40%-56% reduction in wing loading attributed to the positive size allometry of these lobes, indicating a clear promotion of gliding throughout ontogeny. This is the first documentation of gliding-adapted "leg wings" in a wingless arthropod. The evolution of such structures is potentially common among arboreal arthropods and demands a systematic re-examination.

Fluctuations in auxin levels depend upon synchronicity of cell divisions in a one-dimensional model of auxin transport

Auxin is a well-studied plant hormone, the spatial distribution of which remains incompletely understood. Here, we investigate the effects of cell growth and divisions on the dynamics of auxin patterning, using a combination of mathematical modelling and experimental observations. In contrast to most prior work, models are not designed or tuned with the aim to produce a specific auxin pattern. Instead, we use well-established techniques from dynamical systems theory to uncover and classify ranges of auxin patterns as exhaustively as possible as parameters are varied. Previous work using these techniques has shown how a multitude of stable auxin patterns may coexist, each attainable from a specific ensemble of initial conditions. When a key parameter spans a range of values, these steady patterns form a geometric curve with successive folds, often nicknamed a snaking diagram. As we introduce growth and cell division into a one-dimensional model of auxin distribution, we observe new behaviour which can be explained in terms of this diagram. Cell growth changes the shape of the snaking diagram, and this corresponds in turn to deformations in the patterns of auxin distribution. As divisions occur this can lead to abrupt creation or annihilation of auxin peaks. We term this phenomenon 'snake-jumping'. Under rhythmic cell divisions, we show how this can lead to stable oscillations of auxin. We also show that this requires a high level of synchronisation between cell divisions. Using 18 hour time-lapse imaging of the auxin reporter DII:Venus in roots of Arabidopsis thaliana, we show auxin fluctuates greatly, both in terms of amplitude and periodicity, consistent with the snake-jumping events observed with non-synchronised cell divisions. Periodic signals downstream of the auxin signalling pathway have previously been recorded in plant roots. The present work shows that auxin alone is unlikely to play the role of a pacemaker in this context.

Dynamic gap crossing in Dendrelaphis, the sister taxon of flying snakes

Arboreal animals commonly use dynamic gap-crossing behaviors such as jumping. In snakes, however, most species studied to date only employ the quasi-static cantilever crawl, which involves a whole-body reach. One exception is the paradise tree snake (Chrysopelea paradisi), which exhibits kinematic changes as gap distance increases, culminating in dynamic behaviors that are kinematically indistinguishable from those used to launch glides. Because Chrysopelea uses dynamic behaviors when bridging gaps without gliding, we hypothesized that such dynamic behaviors evolved ancestrally to Chrysopelea. To test this predicted occurrence of dynamic behaviors in closely related taxa, we studied gap bridging locomotion in the genus Dendrelaphis, which is the sister lineage of Chysopelea. We recorded 20 snakes from two species (D. punctulatus and D. calligastra) crossing gaps of increasing size, and analyzed their 3D kinematics. We found that, like C. paradisi, both species of Dendrelaphis modulate their use of dynamic behaviors in response to gap distance, but Dendrelaphis exhibit greater inter-individual variation. Although all three species displayed the use of looped movements, the highly stereotyped J-loop movement of Chrysopelea was not observed in Dendrelaphis. These results support the hypothesis that Chrysopelea may have co-opted and refined an ancestral behavior for crossing gaps for the novel function of launching a glide. Overall, these data demonstrate the importance of gap distance in governing behavior and kinematics during arboreal gap crossing.

Air-to-land transitions: from wingless animals and plant seeds to shuttlecocks and bio-inspired robots

Recent observations of wingless animals, including jumping nematodes, springtails, insects, and wingless vertebrates like geckos, snakes, and salamanders, have shown that their adaptations and body morphing are essential for rapid self-righting and controlled landing. These skills can reduce the risk of physical damage during collision, minimize recoil during landing, and allow for a quick escape response to minimize predation risk. The size, mass distribution, and speed of an animal determine its self-righting method, with larger animals depending on the conservation of angular momentum and smaller animals primarily using aerodynamic forces. Many animals falling through the air, from nematodes to salamanders, adopt a skydiving posture while descending. Similarly, plant seeds such as dandelions and samaras are able to turn upright in mid-air using aerodynamic forces and produce high decelerations. These aerial capabilities allow for a wide dispersal range, low-impact collisions, and effective landing and settling. Recently, small robots that can right themselves for controlled landings have been designed based on principles of aerial maneuvering in animals. Further research into the effects of unsteady flows on self-righting and landing in small arthropods, particularly those exhibiting explosive catapulting, could reveal how morphological features, flow dynamics, and physical mechanisms contribute to effective mid-air control. More broadly, studying apterygote (wingless insects) landing could also provide insight into the origin of insect flight. These research efforts have the potential to lead to the bio-inspired design of aerial micro-vehicles, sports projectiles, parachutes, and impulsive robots that can land upright in unsteady flow conditions.

The relative contributions of multiarticular snake muscles to movement in different planes

Muscles spanning multiple joints play important functional roles in a wide range of systems across tetrapods; however, their fundamental mechanics are poorly understood, particularly the consequences of anatomical position on mechanical advantage. Snakes provide an excellent study system for advancing this topic. They rely on the axial muscles for many activities, including striking, constriction, defensive displays, and locomotion. Moreover, those muscles span from one or a few vertebrae to over 30, and anatomy varies among muscles and among species. We characterized the anatomy of major epaxial muscles in a size series of corn snakes (Pantherophis guttatus) using diceCT scans, and then took several approaches to calculating contributions of each muscle to force and motion generated during body bending, starting from a highly simplistic model and moving to increasingly complex and realistic models. Only the most realistic model yielded equations that included the consequence of muscle span on torque-displacement trade-offs, as well as resolving ambiguities that arose from simpler models. We also tested whether muscle cross-sectional areas or lever arms (total magnitude or pitch/yaw/roll components) were related to snake mass, longitudinal body region (anterior, middle, posterior), and/or muscle group (semispinalis-spinalis, multifidus, longissimus dorsi, iliocostalis, and levator costae). Muscle cross-sectional areas generally scaled with positive allometry, and most lever arms did not depart significantly from geometric similarity (isometry). The levator costae had lower cross-sectional area than the four epaxial muscles, which did not differ significantly from each other in cross-sectional area. Lever arm total magnitudes and components differed among muscles. We found some evidence for regional variation, indicating that functional regionalization merits further investigation. Our results contribute to knowledge of snake muscles specifically and multiarticular muscle systems generally, providing a foundation for future comparisons across species and bioinspired multiarticular systems.

Material properties of skin in the flying snake Chrysopelea ornata

In snakes, the skin serves for protection, camouflage, visual signaling, locomotion, and its ability to stretch facilitates large prey ingestion. The flying snakes of the genus Chrysopelea are capable of jumping and gliding through the air, requiring additional functional demands: its skin must accommodate stretch in multiple directions during gliding and, perhaps more importantly, during high-speed, direct-impact landing. Is the skin of flying snakes specialized for gliding? Here, we characterized the material properties of the skin of Chrysopelea ornata and compared them with two nongliding species of colubrid snakes, Thamnophis sirtalis and Pantherophis guttatus, as well as with previously published values. The skin was examined using uniaxial tensile testing to measure stresses, and digital image correlation methods to determine strains, yielding metrics of strength, elastic modulus, strain energy, and extensibility. To test for loading orientation effects, specimens were tested from three orientations relative to the snake's long axis: lateral, circumferential, and ventral. Specimens were taken from two regions of the body, pre- and pos-tpyloric, to test for regional effects related to the ingestion of large prey. In comparison with T. sirtalis and P. guttatus, C. ornata exhibited higher post-pyloric and lower pre-pyloric extensibility in circumferential specimens. However, overall there were few differences in skin material properties of C. ornata compared to other species, both within and across studies, suggesting that the skin of flying snakes is not specialized for gliding locomotion. Surprisingly, circumferential specimens demonstrated lower strength and extensibility in pre-pyloric skin, suggesting less regional specialization related to large prey.

Hang in there: comparative arboreal prey-handling in boa constrictors and ball pythons

Snakes are a diverse group of reptiles, having colonized almost every environment on the planet. Multiple snake lineages have independently evolved semiarboreal or completely arboreal species. As snakes lack limbs, the challenges of moving and feeding in an arboreal environment are numerous. Here we compare the prey-handling ability of the semiarboreal boa constrictor to the terrestrial ball python in a simulated arboreal context. Snakes were allowed to strike at rodent prey and attempt to swallow that prey while suspended. Boa constrictors were successful in feeding, using a complex suite of behaviors to maintain their position and manipulate their prey. Boa constrictors positioned rats so that swallowing occurred in the direction of gravity, and would use loops of their body to support the rat during swallowing. Ball pythons were frequently not successful in feeding, lacking the complex behaviors that boa constrictors frequently employed. Ball pythons would attempt to swallow, but in the majority of feeding attempts were ultimately unsuccessful. These unsuccessful feeding attempts were typically characterized by the ball pythons hanging upside-down, trying to swallow the prey against the direction of gravity. We suggest that behavioral modifications to feeding encouraged successful invasion of arboreal habitats, but more sampling of snake diversity is needed to explore the range and types of feeding behaviors that arboreal snakes employ.

Dynamic movements facilitate extreme gap crossing in flying snakes

In arboreal habitats, direct routes between two locations can be impeded by gaps in the vegetation. Arboreal animals typically use dynamic movements, such as jumping, to navigate these gaps if the distance between supports exceeds their reaching ability. In contrast, most snakes only use the cantilever crawl to cross gaps. This behavior imposes large torques on the animal, inhibiting their gap-crossing capabilities. Flying snakes (Chrysopelea), however, are known to use dynamic behaviors in a different arboreal context: they use a high-acceleration jump to initiate glides. We hypothesized that flying snakes also use jumping take-off behaviors to cross gaps, allowing them to cross larger distances. To test this hypothesis, we used a six-camera motion-capture system to investigate the effect of gap size on crossing behavior in Chrysopelea paradisi, and analyzed the associated kinematics and torque requirements. We found that C. paradisi typically uses cantilevering for small gaps (<47.5% snout-vent length, SVL). Above this distance, C. paradisi were more likely to use dynamic movements than cantilevers, either arching upward or employing a below-branch loop of the body. These dynamic movements extended the range of horizontal crossing to ∼120% SVL. The behaviors used for the largest gaps were kinematically similar to the J-loop jumps used in gliding, and involved smaller torques than the cantilevers. These data suggest that the ability to jump allows flying snakes to access greater resources in the arboreal environment, and supports the broader hypothesis that arboreal animals jump across gaps only when reaching is not mechanically possible.

The aerodynamics of flying snake airfoils in tandem configuration

Flying snakes flatten their body to form a roughly triangular cross-sectional shape, enabling lift production and horizontal acceleration. While gliding, they also assume an S-shaped posture, which could promote aerodynamic interactions between the fore and the aft body. Such interactions have been studied experimentally; however, very coarse models of the snake's cross-sectional shape were used, and the effects were measured only for the downstream model. In this study, the aerodynamic interactions resulting from the snake's posture were approximated using two-dimensional anatomically accurate airfoils positioned in tandem to mimic the snake's geometry during flight. Load cells were used to measure the lift and drag forces, and flow field data were obtained using digital particle image velocimetry (DPIV). The results showed a strong dependence of the aerodynamic performance on the tandem arrangement, with the lift coefficients being generally more influenced than the drag coefficients. Flow field data revealed that the tandem arrangement modified the separated flow and the wake size, and enhanced the lift in cases in which the wake vortices formed closer to the models, producing suction on the dorsal surface. The downforce created by the flow separation from the ventral surface of the models at 0 deg angle of attack was another significant factor contributing to lift production. A number of cases showing large variations of aerodynamic performance included configurations close to the most probable posture of airborne flying snakes, suggesting that small postural variations could be used to control the glide trajectory.

Osteology, relationships and functional morphology of Weigeltisaurus jaekeli (Diapsida, Weigeltisauridae) based on a complete skeleton from the Upper Permian Kupferschiefer of Germany

BACKGROUND

Weigeltisauridae is a clade of small-bodied diapsids characterized by a horned cranial frill, slender trunk and limbs, and a patagium supported by elongated bony rods. Partial skeletons and fragments are definitively known only from upper Permian (Lopingian) rocks in England, Germany, Madagascar and Russia. Despite these discoveries, there have been few detailed descriptions of weigeltisaurid skeletons, and the homologies of many skeletal elements-especially the rods supporting the patagium-remain the subject of controversy.

MATERIALS & METHODS

Here, we provide a detailed description of a nearly complete skeleton of Weigeltisaurus jaekeli from the upper Permian (Lopingian: Wuchiapingian) Kupferschiefer of Lower Saxony, Germany. Briefly addressed by past authors, the skeleton preserves a nearly complete skull, postcranial axial skeleton, appendicular skeleton, and patagial supports. Through comparisons with extant and fossil diapsids, we examine the hypotheses for the homologies of the patagial rods. To examine the phylogenetic position of Weigeltisauridae and characterize the morphology of the clade, we integrate the material and other weigeltisaurids into a parsimony-based phylogenetic analysis focused on Permo-Triassic non-saurian Diapsida and early Sauria (61 taxa, 339 characters).

RESULTS

We recognize a number of intriguing anatomical features in the weigeltisaurid skeleton described here, including hollow horns on the post-temporal arch, lanceolate teeth in the posterior portion of the maxilla, the absence of a bony arch connecting the postorbital and squamosal bones, elongate and slender phalanges that resemble those of extant arboreal squamates, and patagial rods that are positioned superficial to the lateral one third of the gastral basket. Our phylogenetic study recovers a monophyletic Weigeltisauridae including Coelurosauravus elivensis, Weigeltisaurus jaekeli, and Rautiania spp. The clade is recovered as the sister taxon to Drepanosauromorpha outside of Sauria (=Lepidosauria + Archosauria).

CONCLUSIONS

Our anatomical observations and phylogenetic analysis show variety of plesiomorphic diapsid characters and apomorphies of Weigeltisauridae in the specimen described here. We corroborate the hypothesis that the patagial ossifications are dermal bones unrelated to the axial skeleton. The gliding apparatus of weigeltisaurids was constructed from dermal elements unknown in other known gliding diapsids. SMNK-PAL 2882 and other weigeltisaurid specimens highlight the high morphological disparity of Paleozoic diapsids already prior to their radiation in the early Mesozoic.

A Quantitative Analysis of Micrurus Coral Snakes Reveals Unexpected Variation in Stereotyped Anti-Predator Displays Within a Mimicry System

Warning signals in chemically defended organisms are critical components of predator–prey interactions, often requiring multiple coordinated display components for effective communication. When threatened by a predator, venomous coral snakes (genus Micrurus) display a vigorous, non-locomotory thrashing behavior that has previously been qualitatively described. Given the high contrast and colorful banding patterns of these snakes, this thrashing display is hypothesized to be a key component of a complex aposematic signal under strong stabilizing selection across species in a mimicry system. By experimentally testing snake response across simulated predator cues, we analyzed variation in the presence and expression of a thrashing display across five species of South American coral snakes. Although the major features of the thrash display were conserved across species, we found that predator cue type, snake body size, and species identity predict significant inter- and intraspecific variation in the propensity to perform a display, the duration of thrashing, and the curvature of snake bodies. We also found an interaction between curve magnitude and body location that clearly shows which parts of the display vary most across individuals and species. Our results suggest that contrary to the assumption that all Micrurus species and individuals perform the same display, a high degree of variation exists despite presumably strong selection to conserve a common signal. This quantitative behavioral characterization presents a new framework for analyzing the non-locomotory motions displayed by snakes in a broader ecological context, especially for signaling systems with complex interaction across multiple modalities.

Continuous body 3-D reconstruction of limbless animals

Limbless animals such as snakes, limbless lizards, worms, eels and lampreys move their slender, long bodies in three dimensions to traverse diverse environments. Accurately quantifying their continuous body's 3-D shape and motion is important for understanding body-environment interactions in complex terrain, but this is difficult to achieve (especially for local orientation and rotation). Here, we describe an interpolation method to quantify continuous body 3-D position and orientation. We simplify the body as an elastic rod and apply a backbone optimization method to interpolate continuous body shape between end constraints imposed by tracked markers. Despite over-simplifying the biomechanics, our method achieves a higher interpolation accuracy (∼50% error) in both 3-D position and orientation compared with the widely used cubic B-spline interpolation method. Beyond snakes traversing large obstacles as demonstrated, our method applies to other long, slender, limbless animals and continuum robots. We provide codes and demo files for easy application of our method.

Jumping Locomotion Strategies: From Animals to Bioinspired Robots

Jumping is a locomotion strategy widely evolved in both invertebrates and vertebrates. In addition to terrestrial animals, several aquatic animals are also able to jump in their specific environments. In this paper, the state of the art of jumping robots has been systematically analyzed, based on their biological model, including invertebrates (e.g., jumping spiders, locusts, fleas, crickets, cockroaches, froghoppers and leafhoppers), vertebrates (e.g., frogs, galagoes, kangaroos, humans, dogs), as well as aquatic animals (e.g., both invertebrates and vertebrates, such as crabs, water-striders, and dolphins). The strategies adopted by animals and robots to control the jump (e.g., take-off angle, take-off direction, take-off velocity and take-off stability), aerial righting, land buffering, and resetting are concluded and compared. Based on this, the developmental trends of bioinspired jumping robots are predicted.

Visual acuity in the flying snake, Chrysopelea paradisi

Visual control during high-speed aerial locomotion requires a visual system adapted for such behaviors. Flying snakes (genus: Chrysopelea) are capable of gliding at speeds up to 11 m s-1 and perform visual assessments before take-off. Determining nuances of control requires a closed-loop experimental system, such as immersive virtual arenas. To characterize vision in the flying snake Chrysopelea paradisi, we used digitally reconstructed models of the head to determine a 3D field of vision. We also used optokinetic drum experiments and compared slowphase optokinetic nystagmus (OKN) speeds to calculate visual acuity and conducted preliminary experiments to determine whether snakes would respond to closed-loop virtual stimuli. Visual characterization showed that C. paradisi likely has a large field of view (308.5 ± 6.5° azimuthal range), with a considerable binocular region (33.0 ± 11.0° azimuthal width) that extends overhead. Their visual systems are broadly tuned and motion-sensitive, with peak OKN response gains of 0.50 ± 0.11 seen at 46.06 ± 11.08 Hz, and a low spatial acuity, with peak gain of 0.92 ± 0.41 seen at 2.89 ± 0.16 cpd (cycles per degree). These characteristics were used to inform settings in an immersive virtual arena, including framerate, brightness, and stimulus size. In turn, the immersive virtual arena was used to reproduce the optokinetic drum experiments. We elicited OKN in open-loop experiments, with a mean gain of 0.21 ± 0.9 seen at 0.019 ± 6x10-5 cpd and 1.79 ± 0.01 Hz. In closed-loop experiments, snakes did not exhibit OKN, but held the image fixed, indicating visual stabilization. These results demonstrate for that C. paradisi responds to visual stimuli in a digital virtual arena. The accessibility and adaptability of the virtual setup make it suitable for future studies of visual control in snakes and other animals in an unconstrained setting.

Lateral Oscillation and Body Compliance Help Snakes and Snake Robots Stably Traverse Large, Smooth Obstacles

Snakes can move through almost any terrain. Similarly, snake robots hold the promise as a versatile platform to traverse complex environments such as earthquake rubble. Unlike snake locomotion on flat surfaces which is inherently stable, when snakes traverse complex terrain by deforming their body out of plane, it becomes challenging to maintain stability. Here, we review our recent progress in understanding how snakes and snake robots traverse large, smooth obstacles such as boulders and felled trees that lack "anchor points" for gripping or bracing. First, we discovered that the generalist variable kingsnake combines lateral oscillation and cantilevering. Regardless of step height and surface friction, the overall gait is preserved. Next, to quantify static stability of the snake, we developed a method to interpolate continuous body in three dimensions (3D) (both position and orientation) between discrete tracked markers. By analyzing the base of support using the interpolated continuous body 3-D kinematics, we discovered that the snake maintained perfect stability during traversal, even on the most challenging low friction, high step. Finally, we applied this gait to a snake robot and systematically tested its performance traversing large steps with variable heights to further understand stability principles. The robot rapidly and stably traversed steps nearly as high as a third of its body length. As step height increased, the robot rolled more frequently to the extent of flipping over, reducing traversal probability. The absence of such failure in the snake with a compliant body inspired us to add body compliance to the robot. With better surface contact, the compliant body robot suffered less roll instability and traversed high steps at higher probability, without sacrificing traversal speed. Our robot traversed large step-like obstacles more rapidly than most previous snake robots, approaching that of the animal. The combination of lateral oscillation and body compliance to form a large, reliable base of support may be useful for snakes and snake robots to traverse diverse 3-D environments with large, smooth obstacles.

Reaction Forces and Rib Function During Locomotion in Snakes

Locomotion in most tetrapods involves coordinated efforts between appendicular and axial musculoskeletal systems, where interactions between the limbs and the ground generate vertical (GV), horizontal (GH), and mediolateral (GML) ground-reaction forces that are transmitted to the axial system. Snakes have a complete absence of external limbs and represent a fundamental shift from this perspective. The axial musculoskeletal system of snakes is their primary structure to exert, transmit, and resist all motive and reaction forces for propulsion. Their lack of limbs makes them particularly dependent on the mechanical interactions between their bodies and the environment to generate the net GH they need for forward locomotion. As organisms that locomote on their bellies, the forces that enable the various modes of snake locomotion involve two important structures: the integument and the ribs. Snakes use the integument to contact the substrate and produce a friction-reservoir that exceeds their muscle-induced propulsive forces through modulation of scale stiffness and orientation, enabling propulsion through variable environments. XROMM work and previous studies suggest that the serially repeated ribs of snakes change their cross-sectional body shape, deform to environmental irregularities, provide synergistic stabilization for other muscles, and differentially exert and transmit forces to control propulsion. The costovertebral joints of snakes have a biarticular morphology, relative to the unicapitate costovertebral joints of other squamates, that appears derived and not homologous with the ancestral bicapitate ribs of Amniota. Evidence suggests that the biarticular joints of snakes may function to buttress locomotor forces, similar to other amniotes, and provide a passive mechanism for resisting reaction forces during snake locomotion. Future comparisons with other limbless lizard taxa are necessary to tease apart the mechanics and mechanisms that produced the locomotor versatility observed within Serpentes.

Rib Motions Don't Completely Hinge on Joint Design: Costal Joint Anatomy and Ventilatory Kinematics in a Teiid Lizard, Salvator merianae

Rib rotations contribute to lung ventilation in most extant amniotes. These rotations are typically described as bucket-handle rotation about a dorsoventral axis, caliper rotation about a craniocaudal axis, and pump-handle rotation about a mediolateral axis. A synapomorphy for Lepidosauria is single-headed costovertebral articulations derived from the ancestral double-headed articulations of most amniotes. With a single articular surface, the costovertebral joints of squamates have the potential to rotate with three degrees-of-freedom (DOFs), but considerable variation exists in joint shape. We compared the costovertebral morphology of the Argentine black and white tegu, Salvator merianae, with the green iguana, Iguana iguana, and found that the costovertebral articulations of I. iguana were hemispherical, while those of S. merianae were dorsoventrally elongated and hemiellipsoidal. We predicted that the elongate joints in S. merianae would permit bucket-handle rotations while restricting caliper and pump-handle rotations, relative to the rounded joints of I. iguana. We used X-ray reconstruction of moving morphology to quantify rib rotations during breathing in S. merianae for comparison with prior work in I. iguana. Consistent with our hypothesis, we found less caliper motion in S. merianae than in I. iguana, but unexpectedly found similar pump-handle magnitudes in each species. The dorsoventrally elongate costovertebral morphology of S. merianae may provide passive rib support to reduce the conflict between locomotion and ventilation. Moreover, the observation of multiple DOFs during rib rotations in both species suggests that permissive costovertebral morphology may be more related to the biological roles of ribs outside of ventilation and help explain the evolution of this trait.

Control of gliding in a flying snake-inspired n-chain model

Flying snakes of genus Chrysopelea possess a highly dynamic gliding behavior, which is dominated by an undulation in the form of lateral waves sent posteriorly down the body. The resulting high-amplitude periodic variations in the distribution of mass and aerodynamic forces have been hypothesized to contribute to the stability of the snake's gliding trajectory. However, a previous 2D analysis in the longitudinal plane failed to reveal a significant effect of undulation on the stability in the pitch direction. In this study, a theoretical model was used to examine the dynamics and stability characteristics of flying snakes in three dimensions. The snake was modeled as an articulated chain of airfoils connected with revolute joints. Along the lines of vibrational control methods, which employ high-amplitude periodic inputs to produce desirable stable motions in nonlinear systems, undulation was considered as a periodic input to the system. This was implemented either by directly prescribing the joint angles as periodic functions of time (kinematic undulation), or by assuming periodic torques acting at the joints (torque undulation). The aerodynamic forces were modeled using blade element theory and previously determined force coefficients. The results show that torque undulation, along with linearization-based closed-loop control, could increase the size of the basin of stability. The effectiveness of the stabilization provided by torque undulation is a function of the amplitude and frequency of the input. In addition, kinematic undulation provides open-loop stability for sufficiently large frequencies. The results suggest that the snakes need some amount of closed-loop control despite the clear contribution of undulation to glide stability. However, as the closed-loop control system needs to work around a passively stable trajectory, undulation lowers the demand for a complex closed-loop control system. Overall, this study demonstrates the possibility of maintaining stability during gliding using a morphing body instead of symmetrically paired wings.

Global dynamics of non-equilibrium gliding in animals

Gliding flight-moving horizontally downward through the air without power-has evolved in a broad diversity of taxa and serves numerous ecologically relevant functions such as predator escape, expanding foraging locations, and finding mates, and has been suggested as an evolutionary pathway to powered flight. Historically, gliding has been conceptualized using the idealized conditions of equilibrium, in which the net aerodynamic force on the glider balances its weight. While this assumption is appealing for its simplicity, recent studies of glide trajectories have shown that equilibrium gliding is not the norm for most species. Furthermore, equilibrium theory neglects the aerodynamic differences between species, as well as how a glider can modify its glide path using control. To investigate non-equilibrium glide behavior, we developed a reduced-order model of gliding that accounts for self-similarity in the equations of motion, such that the lift and drag characteristics alone determine the glide trajectory. From analysis of velocity polar diagrams of horizontal and vertical velocity from several gliding species, we find that pitch angle, the angle between the horizontal and chord line, is a control parameter that can be exploited to modulate glide angle and glide speed. Varying pitch results in changing locations of equilibrium glide configurations in the velocity polar diagram that govern passive glide dynamics. Such analyses provide a new mechanism of interspecies comparison and tools to understand experimentally-measured kinematics data and theory. In addition, this analysis suggests that the lift and drag characteristics of aerial and aquatic autonomous gliders can be engineered to passively alter glide trajectories with minimal control effort.

Touchdown to take-off: at the interface of flight and surface locomotion

Small aerial robots are limited to short mission times because aerodynamic and energy conversion efficiency diminish with scale. One way to extend mission times is to perch, as biological flyers do. Beyond perching, small robot flyers benefit from manoeuvring on surfaces for a diverse set of tasks, including exploration, inspection and collection of samples. These opportunities have prompted an interest in bimodal aerial and surface locomotion on both engineered and natural surfaces. To accomplish such novel robot behaviours, recent efforts have included advancing our understanding of the aerodynamics of surface approach and take-off, the contact dynamics of perching and attachment and making surface locomotion more efficient and robust. While current aerial robots show promise, flying animals, including insects, bats and birds, far surpass them in versatility, reliability and robustness. The maximal size of both perching animals and robots is limited by scaling laws for both adhesion and claw-based surface attachment. Biomechanists can use the current variety of specialized robots as inspiration for probing unknown aspects of bimodal animal locomotion. Similarly, the pitch-up landing manoeuvres and surface attachment techniques of animals can offer an evolutionary design guide for developing robots that perch on more diverse and complex surfaces.

A Species-Level Phylogeny of Extant Snakes with Description of a New Colubrid Subfamily and Genus

BACKGROUND

With over 3,500 species encompassing a diverse range of morphologies and ecologies, snakes make up 36% of squamate diversity. Despite several attempts at estimating higher-level snake relationships and numerous assessments of generic- or species-level phylogenies, a large-scale species-level phylogeny solely focusing on snakes has not been completed. Here, we provide the largest-yet estimate of the snake tree of life using maximum likelihood on a supermatrix of 1745 taxa (1652 snake species + 7 outgroup taxa) and 9,523 base pairs from 10 loci (5 nuclear, 5 mitochondrial), including previously unsequenced genera (2) and species (61).

RESULTS

Increased taxon sampling resulted in a phylogeny with a new higher-level topology and corroborate many lower-level relationships, strengthened by high nodal support values (> 85%) down to the species level (73.69% of nodes). Although the majority of families and subfamilies were strongly supported as monophyletic with > 88% support values, some families and numerous genera were paraphyletic, primarily due to limited taxon and loci sampling leading to a sparse supermatrix and minimal sequence overlap between some closely-related taxa. With all rogue taxa and incertae sedis species eliminated, higher-level relationships and support values remained relatively unchanged, except in five problematic clades.

CONCLUSION

Our analyses resulted in new topologies at higher- and lower-levels; resolved several previous topological issues; established novel paraphyletic affiliations; designated a new subfamily, Ahaetuliinae, for the genera Ahaetulla, Chrysopelea, Dendrelaphis, and Dryophiops; and appointed Hemerophis (Coluber) zebrinus to a new genus, Mopanveldophis. Although we provide insight into some distinguished problematic nodes, at the deeper phylogenetic scale, resolution of these nodes may require sampling of more slowly-evolving nuclear genes.

How animals glide: from trajectory to morphology

Animals that glide produce aerodynamic forces that enable transit through the air in both arboreal and aquatic environments. The relative ease of gliding compared with flapping flight has led to a large diversity of taxa that have evolved some degree of flight capability. Glide paths are curved, reflecting the changing forces on the animal as it progresses through its aerial trajectory. These changing forces can be under control of the glider, which uses specific aspects of anatomy to modulate lift, drag, and rotational moments on the body. However, gliders share no single anatomical or behavioral feature, and some species are unspecialized for gliding, producing aerodynamic forces using posture and orientation alone. Animals use gliding in a broad range of ecological roles, suggesting that multiple performance metrics are relevant for consideration, but we are only beginning to understand how gliders produce and control their flight from takeoff to landing. In this review, we focus on the physical aspects of how glide trajectories are produced, and additionally discuss the range of morphologies and postures that are used to control aerial movements across the broad diversity of animal gliders.

A theoretical analysis of pitch stability during gliding in flying snakes

Flying snakes use their entire body as a continuously morphing 'wing' to produce lift and shallow their glide trajectory. Their dominant behavior during gliding is aerial undulation, in which lateral waves are sent posteriorly down the body. This highly dynamic behavior, which is unique among animal gliders, should have substantial effects on the flight dynamics and stability of the snakes, resulting from the continuous redistribution of mass and aerodynamic forces. In this study, we develop two-dimensional theoretical models to assess the stability characteristics of snakes in the pitch direction. Previously measured force coefficients are used to simulate aerodynamic forces acting on the models, and undulation is simulated by varying mass. Model 1 is a simple three-airfoil representation of the snake's body that possesses a passively stable equilibrium solution, whose basin of stability contains initial conditions observed in experimental gliding trajectories. Model 2 is more sophisticated, with more degrees of freedom allowing for postural changes to better represent the snake's real kinematics; in addition, a restoring moment is added to simulate potential active control. The application of static and dynamic stability criteria show that Model 2 is passively unstable, but can be stabilized with a restoring moment. Overall, these models suggest that undulation does not contribute to stability in pitch, and that flying snakes require a closed-loop control system formed around a passively stable dynamical framework.

Aerodynamics of the flying snake Chrysopelea paradisi: how a bluff body cross-sectional shape contributes to gliding performance

A prominent feature of gliding flight in snakes of the genus Chrysopelea is the unique cross-sectional shape of the body, which acts as the lifting surface in the absence of wings. When gliding, the flying snake Chrysopelea paradisi morphs its circular cross-section into a triangular shape by splaying its ribs and flattening its body in the dorsoventral axis, forming a geometry with fore–aft symmetry and a thick profile. Here, we aimed to understand the aerodynamic properties of the snake's cross-sectional shape to determine its contribution to gliding at low Reynolds numbers. We used a straight physical model in a water tunnel to isolate the effects of 2D shape, analogously to studying the profile of an airfoil of a more typical flyer. Force measurements and time-resolved (TR) digital particle image velocimetry (DPIV) were used to determine lift and drag coefficients, wake dynamics and vortex-shedding characteristics of the shape across a behaviorally relevant range of Reynolds numbers and angles of attack. The snake's cross-sectional shape produced a maximum lift coefficient of 1.9 and maximum lift-to-drag ratio of 2.7, maintained increases in lift up to 35 deg, and exhibited two distinctly different vortex-shedding modes. Within the measured Reynolds number regime (Re=3000–15,000), this geometry generated significantly larger maximum lift coefficients than many other shapes including bluff bodies, thick airfoils, symmetric airfoils and circular arc airfoils. In addition, the snake's shape exhibited a gentle stall region that maintained relatively high lift production even up to the highest angle of attack tested (60 deg). Overall, the cross-sectional geometry of the flying snake demonstrated robust aerodynamic behavior by maintaining significant lift production and near-maximum lift-to-drag ratios over a wide range of parameters. These aerodynamic characteristics help to explain how the snake can glide at steep angles and over a wide range of angles of attack, but more complex models that account for 3D effects and the dynamic movements of aerial undulation are required to fully understand the gliding performance of flying snakes.

A phylogeny and revised classification of Squamata, including 4161 species of lizards and snakes

BACKGROUND

The extant squamates (>9400 known species of lizards and snakes) are one of the most diverse and conspicuous radiations of terrestrial vertebrates, but no studies have attempted to reconstruct a phylogeny for the group with large-scale taxon sampling. Such an estimate is invaluable for comparative evolutionary studies, and to address their classification. Here, we present the first large-scale phylogenetic estimate for Squamata.

RESULTS

The estimated phylogeny contains 4161 species, representing all currently recognized families and subfamilies. The analysis is based on up to 12896 base pairs of sequence data per species (average = 2497 bp) from 12 genes, including seven nuclear loci (BDNF, c-mos, NT3, PDC, R35, RAG-1, and RAG-2), and five mitochondrial genes (12S, 16S, cytochrome b, ND2, and ND4). The tree provides important confirmation for recent estimates of higher-level squamate phylogeny based on molecular data (but with more limited taxon sampling), estimates that are very different from previous morphology-based hypotheses. The tree also includes many relationships that differ from previous molecular estimates and many that differ from traditional taxonomy.

CONCLUSIONS

We present a new large-scale phylogeny of squamate reptiles that should be a valuable resource for future comparative studies. We also present a revised classification of squamates at the family and subfamily level to bring the taxonomy more in line with the new phylogenetic hypothesis. This classification includes new, resurrected, and modified subfamilies within gymnophthalmid and scincid lizards, and boid, colubrid, and lamprophiid snakes.

The effects of three-dimensional gap orientation on bridging performance and behavior of brown tree snakes (Boiga irregularis)

Traversing gaps with different orientations within arboreal environments has ecological relevance and mechanical consequences for animals. For example, the orientation of the animal while crossing gaps determines whether the torques acting on the body tend to cause it to pitch or roll from the supporting perch or fail as a result of localized bending. The elongate bodies of snakes seem well suited for crossing gaps, but a long unsupported portion of the body can create large torques that make gap bridging demanding. We tested whether the three-dimensional orientation of substrates across a gap affected the performance and behavior of an arboreal snake (Boiga irregularis). The snakes crossed gaps 65% larger for vertical than for horizontal trajectories and 13% greater for straight trajectories than for those with a 90 deg turn within the horizontal plane. Our results suggest that failure due to the inability to keep the body rigid at the edge of the gap may be the primary constraint on performance for gaps with a large horizontal component. In addition, the decreased performance when the destination perch was oriented at an angle to the long axis of the initial perch was probably a result of the inability of snakes to maintain balance due to the large rolling torque. For some very large gaps the snakes enhanced their performance by using rapid lunges to cross otherwise impassable gaps. Perhaps such dynamic movements preceded the aerial behavior observed in other species of arboreal snakes.