Legs as linkages: an alternative paradigm for the role of tendons and isometric muscles in facilitating economical gait.

Considerable attention has been given to the spring-like behaviour of stretching and recoiling tendons, and how this can reduce the work demanded from muscle for a given loss-return cycling of mechanical energy during high-speed locomotion. However, even completely isometric muscle-tendon units have the potential to act as tension struts, forming links in linkages that avoid the demand for mechanical work-cycling in the first place. Here, forelimb and hindlimb structures and geometries of quadrupeds are considered in terms of linkages that avoid mechanical work at the level of both the whole limb and the individual muscles. The scapula, isometric serratus muscles and forelimb can be viewed as a modified Roberts' straight-line mechanism that supports an approximately horizontal path of the body with vertically orientated forces, resulting in low work demand at the level of both limb and muscle. Modelled isometric triceps brachii inserting to the olecranon form part of a series of four-bar linkages (forelimb) and isometric biceps femoris cranial, rectus femoris and tensor fascia latae form part of a series of six-bar linkages (hindlimb), in both cases potentially resulting in straight-line horizontal motion, generating appropriate moments about shoulder and hip to maintain vertical ground reaction forces and again low mechanical work demand from the limb. Analysing part of the complexity of animal limb structure as linkages that avoid work at the level of both the whole limb and the supporting muscles suggests a new paradigm with which to appreciate the role of isometric muscle-tendon units and multiple muscle origins.

Limb work and joint work minimization reveal an energetic benefit to the elbows-back, knees-forward limb design in parasagittal quadrupeds.

Quadrupedal animal locomotion is energetically costly. We explore two forms of mechanical work that may be relevant in imposing these physiological demands. Limb work, due to the forces and velocities between the stance foot and the centre of mass, could theoretically be zero given vertical limb forces and horizontal centre of mass path. To prevent pitching, skewed vertical force profiles would then be required, with forelimb forces high in late stance and hindlimb forces high in early stance. By contrast, joint work-the positive mechanical work performed by the limb joints-would be reduced with forces directed through the hip or shoulder joints. Measured quadruped kinetics show features consistent with compromised reduction of both forms of work, suggesting some degree of, but not perfect, inter-joint energy transfer. The elbows-back, knees-forward design reduces the joint work demand of a low limb-work, skewed, vertical force profile. This geometry allows periods of high force to be supported when the distal segment is near vertical, imposing low moments about the elbow or knee, while the shoulder or hip avoids high joint power despite high moments because the proximal segment barely rotates-translation over this period is due to rotation of the distal segment.

Bird wings act as a suspension system that rejects gusts.

Musculoskeletal systems cope with many environmental perturbations without neurological control. These passive preflex responses aid animals to move swiftly through complex terrain. Whether preflexes play a substantial role in animal flight is uncertain. We investigated how birds cope with gusty environments and found that their wings can act as a suspension system, reducing the effects of vertical gusts by elevating rapidly about the shoulder. This preflex mechanism rejected the gust impulse through inertial effects, diminishing the predicted impulse to the torso and head by 32% over the first 80 ms, before aerodynamic mechanisms took effect. For each wing, the centre of aerodynamic loading aligns with the centre of percussion, consistent with enhancing passive inertial gust rejection. The reduced motion of the torso in demanding conditions simplifies crucial tasks, such as landing, prey capture and visual tracking. Implementing a similar preflex mechanism in future small-scale aircraft will help to mitigate the effects of gusts and turbulence without added computational burden.

High aerodynamic lift from the tail reduces drag in gliding raptors.

Many functions have been postulated for the aerodynamic role of the avian tail during steady-state flight. By analogy with conventional aircraft, the tail might provide passive pitch stability if it produced very low or negative lift. Alternatively, aeronautical principles might suggest strategies that allow the tail to reduce inviscid, induced drag: if the wings and tail act in different horizontal planes, they might benefit from biplane-like aerodynamics; if they act in the same plane, lift from the tail might compensate for lift lost over the fuselage (body), reducing induced drag with a more even downwash profile. However, textbook aeronautical principles should be applied with caution because birds have highly capable sensing and active control, presumably reducing the demand for passive aerodynamic stability, and, because of their small size and low flight speeds, operate at Reynolds numbers two orders of magnitude below those of light aircraft. Here, by tracking up to 20,000, 0.3 mm neutrally buoyant soap bubbles behind a gliding barn owl, tawny owl and goshawk, we found that downwash velocity due to the body/tail consistently exceeds that due to the wings. The downwash measured behind the centreline is quantitatively consistent with an alternative hypothesis: that of constant lift production per planform area, a requirement for minimizing viscous, profile drag. Gliding raptors use lift distributions that compromise both inviscid induced drag minimization and static pitch stability, instead adopting a strategy that reduces the viscous drag, which is of proportionately greater importance to lower Reynolds number fliers.

Artificial mass loading disrupts stable social order in pigeon dominance hierarchies.

Dominance hierarchies confer benefits to group members by decreasing the incidences of physical conflict, but may result in certain lower ranked individuals consistently missing out on access to resources. Here, we report a linear dominance hierarchy remaining stable over time in a closed population of birds. We show that this stability can be disrupted, however, by the artificial mass loading of birds that typically comprise the bottom 50% of the hierarchy. Mass loading causes these low-ranked birds to immediately become more aggressive and rise-up the dominance hierarchy; however, this effect was only evident in males and was absent in females. Removal of the artificial mass causes the hierarchy to return to its previous structure. This interruption of a stable hierarchy implies a strong direct link between body mass and social behaviour and suggests that an individual's personality can be altered by the artificial manipulation of body mass.

Upwash exploitation and downwash avoidance by flap phasing in ibis formation flight.

Many species travel in highly organized groups. The most quoted function of these configurations is to reduce energy expenditure and enhance locomotor performance of individuals in the assemblage. The distinctive V formation of bird flocks has long intrigued researchers and continues to attract both scientific and popular attention. The well-held belief is that such aggregations give an energetic benefit for those birds that are flying behind and to one side of another bird through using the regions of upwash generated by the wings of the preceding bird, although a definitive account of the aerodynamic implications of these formations has remained elusive. Here we show that individuals of northern bald ibises (Geronticus eremita) flying in a V flock position themselves in aerodynamically optimum positions, in that they agree with theoretical aerodynamic predictions. Furthermore, we demonstrate that birds show wingtip path coherence when flying in V positions, flapping spatially in phase and thus enabling upwash capture to be maximized throughout the entire flap cycle. In contrast, when birds fly immediately behind another bird--in a streamwise position--there is no wingtip path coherence; the wing-beats are in spatial anti-phase. This could potentially reduce the adverse effects of downwash for the following bird. These aerodynamic accomplishments were previously not thought possible for birds because of the complex flight dynamics and sensory feedback that would be required to perform such a feat. We conclude that the intricate mechanisms involved in V formation flight indicate awareness of the spatial wake structures of nearby flock-mates, and remarkable ability either to sense or predict it. We suggest that birds in V formation have phasing strategies to cope with the dynamic wakes produced by flapping wings.

The grazing gait, and implications of toppling table geometry for primate footfall sequences.

Many medium and large herbivores locomote forwards very slowly and intermittently when grazing. While the footfall order during grazing is the same as for walking, the relative fore-hind timing-phasing-is quite different. Extended periods of static stability are clearly required during grazing; however, stability requirements are insufficient to account for the timing. Aspects of relatively rapid rolling and pitching-toppling due to the resistance of the back to bending and twisting-can be included in a simplifying geometric model to explain the observation that, in grazing livestock, a step forward with a forefoot is consistently and immediately followed by a step forward from the hind; but not vice versa. The same principles and geometry, but applied to the footfall pattern of walking primates, show that toppling would occur at a different point in the gait cycle. This provides a potential account for the distinctive diagonal-sequence footfall pattern of primates, as it prevents the instant of toppling from being at forefoot placement. Careful and controlled hand positioning would thus be facilitated, presumably beneficial to walking on top of branches, despite a slight energetic cost compared with the usual lateral sequence pattern of horses.

Matching times of leading and following suggest cooperation through direct reciprocity during V-formation flight in ibis.

One conspicuous feature of several larger bird species is their annual migration in V-shaped or echelon formation. When birds are flying in these formations, energy savings can be achieved by using the aerodynamic up-wash produced by the preceding bird. As the leading bird in a formation cannot profit from this up-wash, a social dilemma arises around the question of who is going to fly in front? To investigate how this dilemma is solved, we studied the flight behavior of a flock of juvenile Northern bald ibis (Geronticus eremita) during a human-guided autumn migration. We could show that the amount of time a bird is leading a formation is strongly correlated with the time it can itself profit from flying in the wake of another bird. On the dyadic level, birds match the time they spend in the wake of each other by frequent pairwise switches of the leading position. Taken together, these results suggest that bald ibis cooperate by directly taking turns in leading a formation. On the proximate level, we propose that it is mainly the high number of iterations and the immediacy of reciprocation opportunities that favor direct reciprocation. Finally, we found evidence that the animals' propensity to reciprocate in leading has a substantial influence on the size and cohesion of the flight formations.

Flying in a flock comes at a cost in pigeons.

Flying birds often form flocks, with social, navigational and anti-predator implications. Further, flying in a flock can result in aerodynamic benefits, thus reducing power requirements, as demonstrated by a reduction in heart rate and wingbeat frequency in pelicans flying in a V-formation. But how general is an aerodynamic power reduction due to group-flight? V-formation flocks are limited to moderately steady flight in relatively large birds, and may represent a special case. What are the aerodynamic consequences of flying in the more usual 'cluster' flock? Here we use data from innovative back-mounted Global Positioning System (GPS) and 6-degrees-of-freedom inertial sensors to show that pigeons (1) maintain powered, banked turns like aircraft, imposing dorsal accelerations of up to 2g, effectively doubling body weight and quadrupling induced power requirements; (2) increase flap frequency with increases in all conventional aerodynamic power requirements; and (3) increase flap frequency when flying near, particularly behind, other birds. Therefore, unlike V-formation pelicans, pigeons do not gain an aerodynamic advantage from flying in a flock. Indeed, the increased flap frequency, whether due to direct aerodynamic interactions or requirements for increased stability or control, suggests a considerable energetic cost to flight in a tight cluster flock.

Children and adults minimise activated muscle volume by selecting gait parameters that balance gross mechanical power and work demands.

Terrestrial locomotion on legs is energetically expensive. Compared with cycling, or with locomotion in swimming or flying animals, walking and running are highly uneconomical. Legged gaits that minimise mechanical work have previously been identified and broadly match walking and running at appropriate speeds. Furthermore, the 'cost of muscle force' approaches are effective in relating locomotion kinetics to metabolic cost. However, few accounts have been made for why animals deviate from either work-minimising or muscle-force-minimising strategies. Also, there is no current mechanistic account for the scaling of locomotion kinetics with animal size and speed. Here, we report measurements of ground reaction forces in walking children and adult humans, and their stance durations during running. We find that many aspects of gait kinetics and kinematics scale with speed and size in a manner that is consistent with minimising muscle activation required for the more demanding between mechanical work and power: spreading the duration of muscle action reduces activation requirements for power, at the cost of greater work demands. Mechanical work is relatively more demanding for larger bipeds--adult humans--accounting for their symmetrical M-shaped vertical force traces in walking, and relatively brief stance durations in running compared with smaller bipeds--children. The gaits of small children, and the greater deviation of their mechanics from work-minimising strategies, may be understood as appropriate for their scale, not merely as immature, incompletely developed and energetically sub-optimal versions of adult gaits.

Leap and strike kinetics of an acoustically 'hunting' barn owl (Tyto alba).

Barn owls are effective hunters of small rodents. One hunting technique is a leap from the ground followed by a brief flight and a plummeting 'strike' onto an acoustically targeted - and potentially entirely hidden - prey. We used forceplate measurements to derive kinetics of the leap and strike. Leaping performance was similar to reported values for guinea fowl. This is likely achieved despite the owl's considerably smaller size because of its relatively long legs and use of wing upstroke. Strikes appear deliberately forceful: impulses could have been spread over larger periods during greater deflections of the centre of mass, as observed in leaping and an alighting landing measurement. The strike, despite forces around 150 times that of a mouse body weight, is not thought to be crucial to the kill; rather, forceful strikes may function primarily to enable rapid penetration of leaf litter or snow cover, allowing grasping of hidden prey.

Constraints on muscle performance provide a novel explanation for the scaling of posture in terrestrial animals.

Larger terrestrial animals tend to support their weight with more upright limbs. This makes structural sense, reducing the loading on muscles and bones, which is disproportionately challenging in larger animals. However, it does not account for why smaller animals are more crouched; instead, they could enjoy relatively more slender supporting structures or higher safety factors. Here, an alternative account for the scaling of posture is proposed, with close parallels to the scaling of jump performance. If the costs of locomotion are related to the volume of active muscle, and the active muscle volume required depends on both the work and the power demanded during the push-off phase of each step (not just the net positive work), then the disproportional scaling of requirements for work and push-off power are revealing. Larger animals require relatively greater active muscle volumes for dynamically similar gaits (e.g. top walking speed)-which may present an ultimate constraint to the size of running animals. Further, just as for jumping, animals with shorter legs and briefer push-off periods are challenged to provide the power (not the work) required for push-off. This can be ameliorated by having relatively long push-off periods, potentially accounting for the crouched stance of small animals.

Vaulting mechanics successfully predict decrease in walk-run transition speed with incline.

There is an ongoing debate about the reasons underlying gait transition in terrestrial locomotion. In bipedal locomotion, the 'compass gait', a reductionist model of inverted pendulum walking, predicts the boundaries of speed and step length within which walking is feasible. The stance of the compass gait is energetically optimal-at walking speeds-owing to the absence of leg compression/extension; completely stiff limbs perform no work during the vaulting phase. Here, we extend theoretical compass gait vaulting to include inclines, and find good agreement with previous observations of changes in walk-run transition speed (approx. 1% per 1% incline). We measured step length and frequency for humans walking either on the level or up a 9.8 per cent incline and report preferred walk-run, walk-compliant-walk and maximum walk-run transition speeds. While the measured 'preferred' walk-run transition speed lies consistently below the predicted maximum walking speeds, and 'actual' maximum walking speeds are clearly above the predicted values, the onset of compliant walking in level as well as incline walking occurs close to the predicted values. These findings support the view that normal human walking is constrained by the physics of vaulting, but preferred absolute walk-run transition speeds may be influenced by additional factors.

The collisional geometry of economical walking predicts human leg and foot segment proportions.

Human walking appears complicated, with many muscles and joints performing rapidly varying roles over the stride. However, the function of walking is simple: to support body weight as it translates economically. Here, a scenario is proposed for the sequence of joint and muscle actions that achieves this function, with the timing of muscle loading and unloading driven by simple changes in geometry over stance. In the scenario, joints of the legs and feet are sequentially locked, resulting in a vaulting stance phase and three or five rapid 'mini-vaults' over a series of 'virtual legs' during the step-to-step transition. Collision mechanics indicate that the mechanical work demand is minimized if the changes in the centre-of-mass trajectory over the step-to-step transition are evenly spaced, predicting an even spacing of the virtual legs. The scenario provides a simple account for the work-minimizing mechanisms of joints and muscles in walking, and collision geometry allows leg and foot proportions to be predicted, accounting for the location of the knee halfway down the leg, and the relatively stiff, plantigrade, asymmetric, short-toed human foot.

Dynamics of hinged wings in strong upward gusts.

A bird's wings are articulated to its body via highly mobile shoulder joints. The joints confer an impressive range of motion, enabling the wings to make broad, sweeping movements that can modulate quite dramatically the production of aerodynamic load. This is enormously useful in challenging flight environments, especially the gusty, turbulent layers of the lower atmosphere. In this study, we develop a dynamics model to examine how a bird-scale gliding aircraft can use wing-root hinges (analogous to avian shoulder joints) to reject the initial impact of a strong upward gust. The idea requires that the spanwise centre of pressure and the centre of percussion of the hinged wing start, and stay, in good initial alignment (the centre of percussion here is related to the idea of a 'sweet spot' on a bat, as in cricket or baseball). We propose a method for achieving this rejection passively, for which the essential ingredients are (i) appropriate lift and mass distributions; (ii) hinges under constant initial torque; and (iii) a wing whose sections stall softly. When configured correctly, the gusted wings will first pivot on their hinges without disturbing the fuselage of the aircraft, affording time for other corrective actions to engage. We expect this system to enhance the control of aircraft that fly in gusty conditions.

Microparticle formation after co-culture of human whole blood and umbilical artery in a novel in vitro model of flow.

Cardiovascular disease (CVD) is now the largest killer in western society, and the importance of interactions between vascular endothelium and circulating blood components in disease pathogenesis is well established. Microparticles are a heterogeneous population of <1 µm blood borne particles that arise from blebbing or shedding of cell membranes. The microparticle population includes several classes of apoptotic bodies; however, increased numbers of procoagulant microparticles have been described in plasma from people with CVD. We have previously demonstrated that interactions of monocytes and platelets with isolated inflamed endothelial cells lead to production of pro-coagulant tissue factor bearing microparticles under laminar flow conditions. Here we have investigated microparticle production after perfusion of human whole blood through intact inflamed human umbilical artery. When blood was perfused through umbilical arteries which had been pre-stimulated with tumour necrosis factor (TNFα) for 18 h under flow conditions, there was significantly increased production of microparticles from both platelet and non-platelet sources, in particular from erythrocytes. To determine whether microparticles generated during interactions with inflamed endothelium could induce a pro-inflammatory response in trans, we isolated microparticles by centrifugation after co-culture and incubated with isolated quiescent endothelial cells followed by measurement of reactive oxygen species formation. Microparticles derived from co-culture with inflamed endothelium induced significantly enhanced levels of reactive oxygen species (ROS). These data suggest that presence of an inflamed endothelium causes release of pro-inflammatory microparticles from circulating blood cells, which could contribute to prolonged endothelial activation and subsequent atherosclerotic changes in blood vessels subjected to inflammatory insult.

The extraordinary athletic performance of leaping gibbons.

The distance that animals leap depends on their take-off angle and velocity. The velocity is generated solely by mechanical work during the push-off phase of standing-start leaps. Gibbons are capable of exceptional leaping performance, crossing gaps in the forest canopy exceeding 10 m, yet possess none of the adaptations possessed by specialist leapers synonymous with maximizing mechanical work. To understand this impressive performance, we recorded leaps of the gibbons exceeding 3.7 m. Gibbons perform more mass-specific work (35.4 J kg(-1)) than reported for any other species to date, accelerating to 8.3 ms(-1) in a single movement and redefining our estimates of work performance by animals. This energy (enough for a 3.5 m vertical leap) is 60 per cent higher than that achieved by galagos, which are renowned for their remarkable leaping performance. The gibbons' unusual morphology facilitates a division of labour among the hind limbs, forelimbs and trunk, resulting in modest power requirements compared with more specialized leapers.

Virtual manipulation of tail postures of a gliding barn owl (Tyto alba) demonstrates drag minimization when gliding.

Aerodynamic functions of the avian tail have been studied previously using observations of bird flight, physical models in wind tunnels, theoretical modelling and flow visualization. However, none of these approaches has provided rigorous, quantitative evidence concerning tail functions because (i) appropriate manipulation and controls cannot be achieved using live animals and (ii) the aerodynamic interplay between the wings and body challenges reductive theoretical or physical modelling approaches. Here, we have developed a comprehensive analytical drag model, calibrated by high-fidelity computational fluid dynamics (CFD), and used it to investigate the aerodynamic action of the tail by virtually manipulating its posture. The bird geometry used for CFD was reconstructed previously using stereo-photogrammetry of a freely gliding barn owl (Tyto alba) and we validated the CFD simulations against wake measurements. Using this CFD-calibrated drag model, we predicted the drag production for 16 gliding flights with a range of tail postures. These observed postures are set in the context of a wider parameter sweep of theoretical postures, where the tail spread and elevation angles were manipulated independently. The observed postures of our gliding bird corresponded to near minimal total drag.

Biomechanics: no force limit on greyhound sprint speed.

Maximum running speed is constrained by the speed at which the limbs can be swung forwards and backwards, and by the force they can withstand while in contact with the ground. Humans sprinting around banked bends change the duration of foot contact to spread the time over which the load is applied, thereby keeping the force on their legs constant. We show here that, on entering a tight bend, greyhounds do not change their foot-contact timings, and so have to withstand a 65% increase in limb forces. This supports the idea that greyhounds power locomotion by torque about the hips, so--just as in cycling humans--the muscles that provide the power are mechanically divorced from the structures that support weight.

Raptor wing morphing with flight speed.

In gliding flight, birds morph their wings and tails to control their flight trajectory and speed. Using high-resolution videogrammetry, we reconstructed accurate and detailed three-dimensional geometries of gliding flights for three raptors (barn owl, Tyto alba; tawny owl, Strix aluco, and goshawk, Accipiter gentilis). Wing shapes were highly repeatable and shoulder actuation was a key component of reconfiguring the overall planform and controlling angle of attack. The three birds shared common spanwise patterns of wing twist, an inverse relationship between twist and peak camber, and held their wings depressed below their shoulder in an anhedral configuration. With increased speed, all three birds tended to reduce camber throughout the wing, and their wings bent in a saddle-shape pattern. A number of morphing features suggest that the coordinated movements of the wing and tail support efficient flight, and that the tail may act to modulate wing camber through indirect aeroelastic control.