Predicting power-optimal kinematics of avian wings

On the role of tail in stability and energetic cost of bird flapping flight

Migratory birds travel over impressively long distances. Consequently, they have to adopt flight regimes being both efficient-in order to spare their metabolic resources-and robust to perturbations. This paper investigates the relationship between both aspects, i.e., energetic performance and stability, in flapping flight of migratory birds. Relying on a poly-articulated wing morphing model and a tail-like surface, several families of steady flight regime have been identified and analysed. These families differ by their wing kinematics and tail opening. A systematic parametric search analysis has been carried out, in order to evaluate power consumption and cost of transport. A framework tailored for assessing limit cycles, namely Floquet theory, is used to numerically study flight stability. Our results show that under certain conditions, an inherent passive stability of steady and level flight can be achieved. In particular, we find that progressively opening the tail leads to passively stable flight regimes. Within these passively stable regimes, the tail can produce either upward or downward lift. However, these configurations entail an increase of cost of transport at high velocities penalizing fast forward flight regimes. Our model-based predictions suggest that long range flights require a furled tail configuration, as confirmed by field observations, and consequently need to rely on alternative mechanisms to stabilize the flight.

Role of wing inertia in maneuvering bat flights

The role of aerodynamics and wing inertia on the motion dynamics for the maneuvering flight of two bats from two species of roundleaf bats,H. armigerandH. prattiare investigated. Comparative studies among a straight flight, two ascending sweeping right turns, and a U-turn reveal that inertial forces play an essential and sometimes crucial role in the maneuvers. The translational trajectory of the bat is mostly driven by aerodynamic forces generated by the wings along the flight path, whereas inertial forces for the most part drive the intra-cycle fluctuations. However, inertial forces are found to contribute non-trivially to the ascending motion of theH. armigerduring the sweeping turn and the U-turn. The roll maneuver is found to be primarily driven by aerodynamic asymmetries during flight, whereas the yaw maneuver is primarily driven by imbalances in wing inertial moments. Inertial moments resulting from Coriolis and centrifugal forces are found to play an important role in accurate yaw prediction. The moment due to Coriolis force plays a very prominent role in predicting the correct yaw angle during the extreme 180° U-turn.

Power requirements for bat-inspired flapping flight with heavy, highly articulated and cambered wings

Bats fly with highly articulated and heavy wings. To understand their power requirements, we develop a three-dimensional reduced-order model, and apply it to flights of Cynopterus brachyotis, the lesser dog-faced fruit bat. Using previously measured wing kinematics, the model computes aerodynamic forces using blade element momentum theory, and incorporates inertial forces of the flapping wing using the measured mass distribution of the membrane wing and body. The two are combined into a Lagrangian equation of motion, and we performed Monte Carlo simulations to address uncertainties in measurement errors and modelling assumptions. We find that the camber of the armwing decreases with flight speed whereas the handwing camber is more independent of speed. Wing camber disproportionately impacts energetics, mainly during the downstroke, and increases the power requirement from 8% to 22% over flight speed U = 3.2-7.4 m s-1. We separate total power into aerodynamic and inertial components, and aerodynamic power into parasitic, profile and induced power, and find strong agreement with previous theoretical and experimental studies. We find that inertia of wings help to balance aerodynamic forces, alleviating the muscle power required for weight support and thrust generation. Furthermore, the model suggests aerodynamic forces assist in lifting the heavy wing during upstroke.

Model coupling biomechanics and fluid dynamics for the simulation of controlled flapping flight

This paper proposes a multiphysics computational framework coupling biomechanics and aerodynamics for the simulation of bird flight. It features a biomechanical model based on the anatomy of a bird, which models the bones and feathers of the wing. The aerodynamic solver relies on a vortex particle-mesh method and represents the wing through an immersed lifting line, acting as a source of vorticity in the flow. An application of the numerical tool is presented in the modeling of the flight of a northern bald ibis (Geronticus eremita). The wing kinematics are imposed based on biological observations and controllers are developed to enable stable flight in a closed loop. Their design is based on a linearized model of flapping flight dynamics. The controller solves an underdetermination in the control parameters through minimization. The tool and the controllers are used in two simulations: one where the bird has to trim itself at a given flight speed, and another where it has to accelerate from a trimmed state to another at a higher speed. The bird wake is accurately represented. It is analyzed and compared to the widespread frozen-wake assumption, highlighting phenomena that the latter cannot capture. The method also allows the computation of the aerodynamic forces experienced by the flier, either through the lifting line method or through control-volume analysis. The computed power requirements at several flight speeds exhibit an order of magnitude and dependency on velocity in agreement with the literature.

The dynamics of hovering flight in hummingbirds, insects and bats with implications for aerial robotics

We analyze the effects of morphology and wing kinematics on the performance of hovering flight. We present a simplified dynamical model with body translational and rotational degrees of freedom that incorporates the flapping, long-axis wing rotation and folding of the wing. To validate our simulation, we compare our results with direct measurements from hovering insects, hummingbirds and bats. Results show that long-axis wing rotation angle (a proxy for pronation) has a significant effect on energy efficiency. For a given wing rotation amplitude, the hovering system has a power-optimal flapping frequency for each stroke-plane orientation, and that frequency closely corresponds to the wingbeat frequencies observed in a diverse range of hummingbird species. We find that larger animals (with larger total mass and wing size), such as bats, require more power to maintain a stable hovering orbit and that hovering with a constant wingspan becomes increasingly impractical with increasing body size. We show, as an exemplar, that for a system of the size of a hovering bat, e.g. Glossophaga soricina, hovering with constant wingspan is dynamically possible, but is implausible and inefficient. For these conditions, hovering with varying wingspan, retracting the wing on the upstroke, is a more realistic hovering modality.

A dynamics and stability framework for avian jumping take-off

Jumping take-off in birds is an explosive behaviour with the goal of providing a rapid transition from ground to airborne locomotion. An effective jump is predicated on the need to maintain dynamic stability through the acceleration phase. The present study concerns understanding how birds retain control of body attitude and trajectory during take-off. Cursory observation suggests that stability is achieved with relatively little cost. However, analysis of the problem shows that the stability margins during jumping are actually very small and that stability considerations play a significant role in the selection of appropriate jumping kinematics. We use theoretical models to understand stability in prehensile take-off (from a perch) and also in non-prehensile take-off (from the ground). The primary instability is tipping, defined as rotation of the centre of gravity about the ground contact point. Tipping occurs when the centre of pressure falls outside the functional foot. A contribution of the paper is the development of graphical tipping stability margins for both centre of gravity location and acceleration angle. We show that the nose-up angular acceleration extends stability bounds forward and is hence helpful in achieving shallow take-offs. The stability margins are used to interrogate simulated take-offs of real birds using published experimental kinematic data from a guinea fowl (ground take-off) and a diamond dove (perch take-off). For the guinea fowl, the initial part of the jump is stable; however, simulations exhibit a stuttering instability not observed experimentally that is probably due to the absence of compliance in the idealized joints. The diamond dove model confirms that the foot provides an active torque reaction during take-off, extending the range of stable jump angles by around 45°.

How pigeons couple three-dimensional elbow and wrist motion to morph their wings

Birds change the shape and area of their wings to an exceptional degree, surpassing insects, bats and aircraft in their ability to morph their wings for a variety of tasks. This morphing is governed by a musculoskeletal system, which couples elbow and wrist motion. Since the discovery of this effect in 1839, the planar 'drawing parallels' mechanism has been used to explain the coupling. Remarkably, this mechanism has never been corroborated from quantitative motion data. Therefore, we measured how the wing skeleton of a pigeon (Columba livia) moves during morphing. Despite earlier planar assumptions, we found that the skeletal motion paths are highly three-dimensional and do not lie in the anatomical plane, ruling out the 'drawing parallels' mechanism. Furthermore, micro-computed tomography scans in seven consecutive poses show how the two wrist bones contribute to morphing, particularly the sliding ulnare. From these data, we infer the joint types for all six bones that form the wing morphing mechanism and corroborate the most parsimonious mechanism based on least-squares error minimization. Remarkably, the algorithm shows that all optimal four-bar mechanisms either lock, are unable to track the highly three-dimensional bone motion paths, or require the radius and ulna to cross for accuracy, which is anatomically unrealistic. In contrast, the algorithm finds that a six-bar mechanism recreates the measured motion accurately with a parallel radius and ulna and a sliding ulnare. This revises our mechanistic understanding of how birds morph their wings, and offers quantitative inspiration for engineering morphing wings.

Speed-dependent modulation of wing muscle recruitment intensity and kinematics in two bat species

Animals respond to changes in power requirements during locomotion by modulating the intensity of recruitment of their propulsive musculature, but many questions concerning how muscle recruitment varies with speed across modes of locomotion remain unanswered. We measured normalized average burst EMG (aEMG) for pectoralis major and biceps brachii at different flight speeds in two relatively distantly related bat species: the aerial insectivore Eptesicus fuscus, and the primarily fruit-eating Carollia perspicillata These ecologically distinct species employ different flight behaviors but possess similar wing aspect ratio, wing loading and body mass. Because propulsive requirements usually correlate with body size, and aEMG likely reflects force, we hypothesized that these species would deploy similar speed-dependent aEMG modulation. Instead, we found that aEMG was speed independent in E. fuscus and modulated in a U-shaped or linearly increasing relationship with speed in C. perspicillata This interspecific difference may be related to differences in muscle fiber type composition and/or overall patterns of recruitment of the large ensemble of muscles that participate in actuating the highly articulated bat wing. We also found interspecific differences in the speed dependence of 3D wing kinematics: E. fuscus modulates wing flexion during upstroke significantly more than C. perspicillata Overall, we observed two different strategies to increase flight speed: C. perspicillata tends to modulate aEMG, and E. fuscus tends to modulate wing kinematics. These strategies may reflect different requirements for avoiding negative lift and overcoming drag during slow and fast flight, respectively, a subject we suggest merits further study.

Flight feather attachment in rock pigeons (Columba livia): covert feathers and smooth muscle coordinate a morphing wing

Mechanisms for passively coordinating forelimb movements and flight feather abduction and adduction have been described separately from both in vivo and ex vivo studies. Skeletal coordination has been identified as a way for birds to simplify the neuromotor task of controlling flight stroke, but an understanding of the relationship between skeletal coordination and the coordination of the aerodynamic control surface (the flight feathers) has been slow to materialize. This break between the biomechanical and aerodynamic approaches - between skeletal kinematics and airfoil shape - has hindered the study of dynamic flight behaviors. Here I use dissection and histology to identify previously overlooked interconnections between musculoskeletal elements and flight feathers. Many of these structures are well-placed to directly link elements of the passive musculoskeletal coordination system with flight feather movements. Small bundles of smooth muscle form prominent connections between upper forearm coverts (deck feathers) and the ulna, as well as the majority of interconnections between major flight feathers of the hand. Abundant smooth muscle may play a role in efficient maintenance of folded wing posture, and may also provide an autonomically regulated means of tuning wing shape and aeroelastic behavior in flight. The pattern of muscular and ligamentous linkages of flight feathers to underlying muscle and bone may provide predictable passive guidance for the shape of the airfoil during flight stroke. The structures described here provide an anatomical touchstone for in vivo experimental tests of wing surface coordination in an extensively researched avian model species.

Three-dimensional simulation for fast forward flight of a calliope hummingbird

We present a computational study of flapping-wing aerodynamics of a calliope hummingbird (Selasphorus calliope) during fast forward flight. Three-dimensional wing kinematics were incorporated into the model by extracting time-dependent wing position from high-speed videos of the bird flying in a wind tunnel at 8.3 m s(-1). The advance ratio, i.e. the ratio between flight speed and average wingtip speed, is around one. An immersed-boundary method was used to simulate flow around the wings and bird body. The result shows that both downstroke and upstroke in a wingbeat cycle produce significant thrust for the bird to overcome drag on the body, and such thrust production comes at price of negative lift induced during upstroke. This feature might be shared with bats, while being distinct from insects and other birds, including closely related swifts.