Small deviations in kinematics and body form dictate muscle performances in the finely tuned avian downstroke

Avian takeoff requires peak pectoralis muscle power to generate sufficient aerodynamic force during the downstroke. Subsequently, the much smaller supracoracoideus recovers the wing during the upstroke. How the pectoralis work loop is tuned to power flight is unclear. We integrate wingbeat-resolved muscle, kinematic, and aerodynamic recordings in vivo with a new mathematical model to disentangle how the pectoralis muscle overcomes wing inertia and generates aerodynamic force during takeoff in doves. Doves reduce the angle of attack of their wing mid-downstroke to efficiently generate aerodynamic force, resulting in an aerodynamic power dip, that allows transferring excess pectoralis power into tensioning the supracoracoideus tendon to assist the upstroke-improving the pectoralis work loop efficiency simultaneously. Integrating extant bird data, our model shows how the pectoralis of birds with faster wingtip speed need to generate proportionally more power. Finally, birds with disproportionally larger wing inertia need to activate the pectoralis earlier to tune their downstroke.

Birds both avoid and control collisions by harnessing visually guided force vectoring

Birds frequently manoeuvre around plant clutter in complex-structured habitats. To understand how they rapidly negotiate obstacles while flying between branches, we measured how foraging Pacific parrotlets avoid horizontal strings obstructing their preferred flight path. Informed by visual cues, the birds redirect forces with their legs and wings to manoeuvre around the obstacle and make a controlled collision with the goal perch. The birds accomplish aerodynamic force vectoring by adjusting their body pitch, stroke plane angle and lift-to-drag ratios beat-by-beat, resulting in a range of about 100° relative to the horizontal plane. The key role of drag in force vectoring revises earlier ideas on how the avian stroke plane and body angle correspond to aerodynamic force direction-providing new mechanistic insight into avian manoeuvring-and how the evolution of flight may have relied on harnessing drag.

Bird-inspired dynamic grasping and perching in arboreal environments

Birds take off and land on a wide range of complex surfaces. In contrast, current robots are limited in their ability to dynamically grasp irregular objects. Leveraging recent findings on how birds take off, land, and grasp, we developed a biomimetic robot that can dynamically perch on complex surfaces and grasp irregular objects. To accommodate high-speed collisions, the robot’s two legs passively transform impact energy into grasp force, while the underactuated grasping mechanism wraps around irregularly shaped objects in less than 50 milliseconds. To determine the range of hardware design, kinematic, behavior, and perch parameters that are sufficient for perching success, we launched the robot at tree branches. The results corroborate our mathematical model, which shows that larger isometrically scaled animals and robots must accommodate disproportionately larger angular momenta, relative to their mass, to achieve similar landing performance. We find that closed-loop balance control serves an important role in maximizing the range of parameters sufficient for perching. The performance of the robot’s biomimetic features attests to the functionality of their avian counterparts, and the robot enables us to study aspects of bird legs in ways that are infeasible in vivo. Our data show that pronounced differences in modern avian toe arrangements do not yield large changes in perching performance, suggesting that arboreal perching does not represent a strong selection pressure among common bird toe topographies. These findings advance our understanding of the avian perching apparatus and highlight design concepts that enable robots to perch on natural surfaces for environmental monitoring.

Lepidoptera demonstrate the relevance of Murray's Law to circulatory systems with tidal flow

BACKGROUND

Murray's Law, which describes the branching architecture of bifurcating tubes, predicts the morphology of vessels in many amniotes and plants. Here, we use insects to explore the universality of Murray's Law and to evaluate its predictive power for the wing venation of Lepidoptera, one of the most diverse insect orders. Lepidoptera are particularly relevant to the universality of Murray's Law because their wing veins have tidal, or oscillatory, flow of air and hemolymph. We examined over one thousand wings representing 667 species of Lepidoptera.

RESULTS

We found that veins with a diameter above approximately 50 microns conform to Murray's Law, with veins below 50 microns in diameter becoming less and less likely to conform to Murray's Law as they narrow. The minute veins that are most likely to deviate from Murray's Law are also the most likely to have atrophied, which prevents efficient fluid transport regardless of branching architecture. However, the veins of many taxa continue to branch distally to the areas where they atrophied, and these too conform to Murray's Law at larger diameters (e.g., Sesiidae).

CONCLUSIONS

This finding suggests that conformity to Murray's Law in larger taxa may reflect requirements for structural support as much as fluid transport, or may indicate that selective pressures for fluid transport are stronger during the pupal stage-during wing development prior to vein atrophy-than the adult stage. Our results increase the taxonomic scope of Murray's Law and provide greater clarity about the relevance of body size.

How oscillating aerodynamic forces explain the timbre of the hummingbird's hum and other animals in flapping flight

How hummingbirds hum is not fully understood, but its biophysical origin is encoded in the acoustic nearfield. Hence, we studied six freely hovering Anna’s hummingbirds, performing acoustic nearfield holography using a 2176 microphone array in vivo, while also directly measuring the 3D aerodynamic forces using a new aerodynamic force platform. We corroborate the acoustic measurements by developing an idealized acoustic model that integrates the aerodynamic forces with wing kinematics, which shows how the timbre of the hummingbird’s hum arises from the oscillating lift and drag forces on each wing. Comparing birds and insects, we find that the characteristic humming timbre and radiated power of their flapping wings originates from the higher harmonics in the aerodynamic forces that support their bodyweight. Our model analysis across insects and birds shows that allometric deviation makes larger birds quieter and elongated flies louder, while also clarifying complex bioacoustic behavior.

Anyone walking outdoors has heard the whooshing sound of birdwings flapping overhead, the buzzing sound of bees flying by, or the whining of mosquitos seeking blood. All animals with flapping wings make these sounds, but the hummingbird makes perhaps the most delightful sound of all: their namesake hum. Yet, how hummingbirds hum is poorly understood.

Bird wings generate large vortices of air to boost their lift and hover in the air that can generate tones. Further, the airflow over bird wings can be highly turbulent, meaning it can generate loud sounds, like the jets of air coming out of the engines of aircraft. Given all the sound-generating mechanisms at hand, it is difficult to determine why some wings buzz whereas others whoosh or hum.

Hightower, Wijnings et al. wanted to understand the physical mechanism that causes animal wings to whine, buzz, hum or whoosh in flight. They hypothesized that the aerodynamic forces generated by animal wings are the main source of their characteristic wing sounds. Hummingbird wings have the most features in common with different animals’ wings, while also featuring acoustically complex feathers. This makes them ideal models for deciphering how birds, bats and even insects make wing sounds.

To learn more about wing sounds, Hightower, Wijnings et al. studied how a species of hummingbird called Anna’s hummingbird hums while drinking nectar from a flower. A three-dimensional ‘acoustic hologram’ was generated using 2,176 microphones to measure the humming sound from all directions. In a follow-up experiment, the aerodynamic forces the hummingbird wings generate to hover were also measured. Their wingbeat was filmed simultaneously in slow-motion in both experiments. Hightower, Wijnings et al. then used a mathematical model that governs the wing’s aeroacoustics to confirm that the aerodynamic forces generated by the hummingbirds’ wings cause the humming sound heard when they hover in front of a flower. The model shows that the oscillating aerodynamic forces generate harmonics, which give the wings’ hum the acoustic quality of a musical instrument.

Using this model Hightower, Wijnings et al. found that the differences in the aerodynamic forces generated by bird and insect wings cause the characteristic timbres of their whines, buzzes, hums, or whooshes. They also determined how these sounds scale with body mass and flapping frequency across 170 insect species and 80 bird species. This showed that mosquitos are unusually loud for their body size due to the unusual unsteadiness of the aerodynamic forces they generate in flight.

These results explain why flying animals’ wings sound the way they do – for example, why larger birds are quieter and mosquitos louder. Better understanding of how the complex forces generated by animal wings create sound can advance the study of how animals change their wingbeat to communicate. Further, the model that explains how complex aerodynamic forces cause sound can help make the sounds of aerial robots, drones, and fans not only more silent, but perhaps more pleasing, like the hum of a hummingbird.

The aerodynamic force platform as an ergometer

Animal flight requires aerodynamic power, which is challenging to determine accurately in vivo Existing methods rely on approximate calculations based on wake flow field measurements, inverse dynamics approaches, or invasive muscle physiological recordings. In contrast, the external mechanical work required for terrestrial locomotion can be determined more directly by using a force platform as an ergometer. Based on an extension of the recent invention of the aerodynamic force platform, we now present a more direct method to determine the in vivo aerodynamic power by taking the dot product of the aerodynamic force vector on the wing with the representative wing velocity vector based on kinematics and morphology. We demonstrate this new method by studying a slowly flying dove, but it can be applied more generally across flying and swimming animals as well as animals that locomote over water surfaces. Finally, our mathematical framework also works for power analyses based on flow field measurements.

How flight feathers stick together to form a continuous morphing wing

Variable feather overlap enables birds to morph their wings, unlike aircraft. They accomplish this feat by means of elastic compliance of connective tissue, which passively redistributes the overlapping flight feathers when the skeleton moves to morph the wing planform. Distinctive microstructures form "directional Velcro," such that when adjacent feathers slide apart during extension, thousands of lobate cilia on the underlapping feathers lock probabilistically with hooked rami of overlapping feathers to prevent gaps. These structures unlock automatically during flexion. Using a feathered biohybrid aerial robot, we demonstrate how both passive mechanisms make morphing wings robust to turbulence. We found that the hooked microstructures fasten feathers across bird species except silent fliers, whose feathers also lack the associated Velcro-like noise. These findings could inspire innovative directional fasteners and morphing aircraft.

Birds repurpose the role of drag and lift to take off and land

The lift that animal wings generate to fly is typically considered a vertical force that supports weight, while drag is considered a horizontal force that opposes thrust. To determine how birds use lift and drag, here we report aerodynamic forces and kinematics of Pacific parrotlets (Forpus coelestis) during short, foraging flights. At takeoff they incline their wing stroke plane, which orients lift forward to accelerate and drag upward to support nearly half of their bodyweight. Upon landing, lift is oriented backward to contribute a quarter of the braking force, which reduces the aerodynamic power required to land. Wingbeat power requirements are dominated by downstrokes, while relatively inactive upstrokes cost almost no aerodynamic power. The parrotlets repurpose lift and drag during these flights with lift-to-drag ratios below two. Such low ratios are within range of proto-wings, showing how avian precursors may have relied on drag to take off with flapping wings.

Recent work has suggested that lift and drag may be employed differently in slow, flapping flight compared to classic flight aerodynamics. Here the authors develop a method to measure vertical and horizontal aerodynamic forces simultaneously and use it to quantify lift and drag during slow flight.

Birds land reliably on complex surfaces by adapting their foot-surface interactions upon contact

Birds land on a wide range of complex surfaces, yet it is unclear how they grasp a perch reliably. Here, we show how Pacific parrotlets exhibit stereotyped leg and wing dynamics regardless of perch diameter and texture, but foot, toe, and claw kinematics become surface-specific upon touchdown. A new dynamic grasping model, which integrates our detailed measurements, reveals how birds stabilize their grasp. They combine predictable toe pad friction with probabilistic friction from their claws, which they drag to find surface asperities-dragging further when they can squeeze less. Remarkably, parrotlet claws can undergo superfast movements, within 1-2 ms, on moderately slippery surfaces to find more secure asperities when necessary. With this strategy, they first ramp up safety margins by squeezing before relaxing their grasp. The model further shows it is advantageous to be small for stable perching when high friction relative to normal force is required because claws can find more usable surface, but this trend reverses when required friction shrinks. This explains how many animals and robots may grasp complex surfaces reliably.

A Bird's-Eye View of Regulatory, Animal Care, and Training Considerations Regarding Avian Flight Research

A thorough understanding of how animals fly is a central goal of many scientific disciplines. Birds are a commonly used model organism for flight research. The success of this model requires studying healthy and naturally flying birds in a laboratory setting. This use of a nontraditional laboratory animal species presents unique challenges to animal care staff and researchers alike. Here we review regulatory, animal care, and training considerations associated with avian flight research.

Automated calibration of multi-camera-projector structured light systems for volumetric high-speed 3D surface reconstructions

It is challenging to calibrate multiple camera-projector pairs for multi-view 3D surface reconstruction based on structured light. Here, we present a new automated calibration method for high-speed multi-camera-projector systems. The method uses printed and projected dot patterns on a planar calibration target, which is moved by hand in the calibration volume. Calibration is enabled by automated image processing and bundle-adjusted parameter optimization. We determined the performance of our method by 3D reconstructing a sphere. The accuracy is -0.03 ± 0.09 % as a percentage of the diameter of the calibration volume. Applications include quality control, autonomous systems, engineering measurements, and motion capture, such as the preliminary 3D reconstruction of a bird in flight we present here.

How the hummingbird wingbeat is tuned for efficient hovering

Both hummingbirds and insects flap their wings to hover. Some insects, like fruit flies, improve efficiency by lifting their body weight equally over the upstroke and downstroke, while utilizing elastic recoil during stroke reversal. It is unclear whether hummingbirds converged on a similar elastic storage solution, because of asymmetries in their lift generation and specialized flight muscle apparatus. The muscles are activated a quarter of a stroke earlier than in larger birds, and contract superfast, which cannot be explained by previous stroke-averaged analyses. We measured the aerodynamic force and kinematics of Anna's hummingbirds to resolve wing torque and power within the wingbeat. Comparing these wingbeat-resolved aerodynamic weight support measurements with those of fruit flies, hawk moths and a generalist bird, the parrotlet, we found that hummingbirds have about the same low induced power losses as the two insects, lower than that of the generalist bird in slow hovering flight. Previous analyses emphasized how bird flight muscles have to overcome wing drag midstroke. We found that high wing inertia revises this for hummingbirds - the pectoralis has to coordinate upstroke to downstroke reversal while the supracoracoideus coordinates downstroke to upstroke reversal. Our mechanistic analysis aligns with all previous muscle recordings and shows how early activation helps furnish elastic recoil through stroke reversal to stay within the physiological limits of muscles. Our findings thus support Weis-Fogh's hypothesis that flies and hummingbirds have converged on a mechanically efficient wingbeat to meet the high energetic demands of hovering flight. These insights can help improve the efficiency of flapping robots.

Biomechanics of hover performance in Neotropical hummingbirds versus bats

Hummingbirds and nectar bats are the only vertebrates that are specialized for hovering in front of flowers to forage nectar. How their aerodynamic performance compares is, however, unclear. To hover, hummingbirds consistently generate about a quarter of the vertical aerodynamic force required to support their body weight during the upstroke. In contrast, generalist birds in slow hovering flight generate little upstroke weight support. We report that nectar bats also generate elevated weight support during the upstroke compared to generalist bats. Comparing 20 Neotropical species, we show how nectarivorous birds and bats converged on this ability by inverting their respective feathered and membrane wings more than species with other diets. However, while hummingbirds converged on an efficient horizontal wingbeat to mostly generate lift, bats rely on lift and drag during the downstroke to fully support their body weight. Furthermore, whereas the ability of nectar bats to aerodynamically support their body weight during the upstroke is elevated, it is much smaller than that of hummingbirds. Bats compensate by generating more aerodynamic weight support during their extended downstroke. Although, in principle, it requires more aerodynamic power to hover using this method, bats have adapted by evolving much larger wings for their body weight. Therefore, the net aerodynamic induced power required to hover is similar among hummingbirds and bats per unit body mass. This mechanistic insight into how feathered wings and membrane wings ultimately require similar aerodynamic power to hover may inform analogous design trade-offs in aerial robots.

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.

Adaptive control of turbulence intensity is accelerated by frugal flow sampling

The aerodynamic performance of vehicles and animals, as well as the productivity of turbines and energy harvesters, depends on the turbulence intensity of the incoming flow. Previous studies have pointed at the potential benefits of active closed-loop turbulence control. However, it is unclear what the minimal sensory and algorithmic requirements are for realizing this control. Here we show that very low-bandwidth anemometers record sufficient information for an adaptive control algorithm to converge quickly. Our online Newton-Raphson algorithm tunes the turbulence in a recirculating wind tunnel by taking readings from an anemometer in the test section. After starting at 9% turbulence intensity, the algorithm converges on values ranging from 10% to 45% in less than 12 iterations within 1% accuracy. By down-sampling our measurements, we show that very-low-bandwidth anemometers record sufficient information for convergence. Furthermore, down-sampling accelerates convergence by smoothing gradients in turbulence intensity. Our results explain why low-bandwidth anemometers in engineering and mechanoreceptors in biology may be sufficient for adaptive control of turbulence intensity. Finally, our analysis suggests that, if certain turbulent eddy sizes are more important to control than others, frugal adaptive control schemes can be particularly computationally effective for improving performance.

Fruit fly scale robots can hover longer with flapping wings than with spinning wings

Hovering flies generate exceptionally high lift, because their wings generate a stable leading edge vortex. Micro flying robots with a similar wing design can generate similar high lift by either flapping or spinning their wings. While it requires less power to spin a wing, the overall efficiency depends also on the actuator system driving the wing. Here, we present the first holistic analysis to calculate how long a fly-inspired micro robot can hover with flapping versus spinning wings across scales. We integrate aerodynamic data with data-driven scaling laws for actuator, electronics and mechanism performance from fruit fly to hummingbird scales. Our analysis finds that spinning wings driven by rotary actuators are superior for robots with wingspans similar to hummingbirds, yet flapping wings driven by oscillatory actuators are superior at fruit fly scale. This crossover is driven by the reduction in performance of rotary compared with oscillatory actuators at smaller scale. Our calculations emphasize that a systems-level analysis is essential for trading-off flapping versus spinning wings for micro flying robots.

Design and analysis of aerodynamic force platforms for free flight studies

We describe and explain new advancements in the design of the aerodynamic force platform, a novel instrument that can directly measure the aerodynamic forces generated by freely flying animals and robots. Such in vivo recordings are essential to better understand the precise aerodynamic function of flapping wings in nature, which can critically inform the design of new bioinspired robots. By designing the aerodynamic force platform to be stiff yet lightweight, the natural frequencies of all structural components can be made over five times greater than the frequencies of interest. The associated high-frequency noise can then be filtered out during post-processing to obtain accurate and precise force recordings. We illustrate these abilities by measuring the aerodynamic forces generated by a freely flying bird. The design principles can also be translated to other fluid media. This offers an opportunity to perform high-throughput, real-time, non-intrusive, and in vivo comparative biomechanical measurements of force generation by locomoting animals and robots. These recordings can include complex bimodal terrestrial, aquatic, and aerial behaviors, which will help advance the fields of experimental biology and bioinspired design.

Inspiration for wing design: how forelimb specialization enables active flight in modern vertebrates

Harnessing flight strategies refined by millions of years of evolution can help expedite the design of more efficient, manoeuvrable and robust flying robots. This review synthesizes recent advances and highlights remaining gaps in our understanding of how bird and bat wing adaptations enable effective flight. Included in this discussion is an evaluation of how current robotic analogues measure up to their biological sources of inspiration. Studies of vertebrate wings have revealed skeletal systems well suited for enduring the loads required during flight, but the mechanisms that drive coordinated motions between bones and connected integuments remain ill-described. Similarly, vertebrate flight muscles have adapted to sustain increased wing loading, but a lack of in vivo studies limits our understanding of specific muscular functions. Forelimb adaptations diverge at the integument level, but both bird feathers and bat membranes yield aerodynamic surfaces with a level of robustness unparalleled by engineered wings. These morphological adaptations enable a diverse range of kinematics tuned for different flight speeds and manoeuvres. By integrating vertebrate flight specializations-particularly those that enable greater robustness and adaptability-into the design and control of robotic wings, engineers can begin narrowing the wide margin that currently exists between flying robots and vertebrates. In turn, these robotic wings can help biologists create experiments that would be impossible in vivo.

How birds direct impulse to minimize the energetic cost of foraging flight

Birds frequently hop and fly between tree branches to forage. To determine the mechanical energy trade-offs of their bimodal locomotion, we rewarded four Pacific parrotlets with a seed for flying voluntarily between instrumented perches inside a new aerodynamic force platform. By integrating direct measurements of both leg and wing forces with kinematics in a bimodal long jump and flight model, we discovered that parrotlets direct their leg impulse to minimize the mechanical energy needed to forage over different distances and inclinations. The bimodal locomotion model further shows how even a small lift contribution from a single proto-wingbeat would have significantly lengthened the long jump of foraging arboreal dinosaurs. These avian bimodal locomotion strategies can also help robots traverse cluttered environments more effectively.

High-speed surface reconstruction of a flying bird using structured light

Birds fly effectively and maneuver nimbly by dynamically changing the shape of their wings during each wingbeat. These shape changes have yet to be quantified automatically at high temporal and spatial resolution. Therefore, we developed a custom 3D surface reconstruction method, which uses a high-speed camera to identify spatially encoded binary striped patterns that are projected on a flying bird. This non-invasive structured-light method allows automated 3D reconstruction of each stand-alone frame and can be extended to multiple views. We demonstrate this new technique by automatically reconstructing the dorsal surface of a parrotlet wing at 3200 frames s^-1 during flapping flight. From this shape we analyze key parameters such as wing twist and angle of attack distribution. While our binary 'single-shot' algorithm is demonstrated by quantifying dynamic shape changes of a flying bird, it is generally applicable to moving animals, plants and deforming objects.

A new low-turbulence wind tunnel for animal and small vehicle flight experiments

Our understanding of animal flight benefits greatly from specialized wind tunnels designed for flying animals. Existing facilities can simulate laminar flow during straight, ascending and descending flight, as well as at different altitudes. However, the atmosphere in which animals fly is even more complex. Flow can be laminar and quiet at high altitudes but highly turbulent near the ground, and gusts can rapidly change wind speed. To study flight in both laminar and turbulent environments, a multi-purpose wind tunnel for studying animal and small vehicle flight was built at Stanford University. The tunnel is closed-circuit and can produce airspeeds up to 50 m s^-1 in a rectangular test section that is 1.0 m wide, 0.82 m tall and 1.73 m long. Seamless honeycomb and screens in the airline together with a carefully designed contraction reduce centreline turbulence intensities to less than or equal to 0.030% at all operating speeds. A large diameter fan and specialized acoustic treatment allow the tunnel to operate at low noise levels of 76.4 dB at 20 m s^-1. To simulate high turbulence, an active turbulence grid can increase turbulence intensities up to 45%. Finally, an open jet configuration enables stereo high-speed fluoroscopy for studying musculoskeletal control in turbulent flow.

Coevolving advances in animal flight and aerial robotics

Our understanding of animal flight has inspired the design of new aerial robots with more effective flight capacities through the process of biomimetics and bioinspiration. The aerodynamic origin of the elevated performance of flying animals remains, however, poorly understood. In this themed issue, animal flight research and aerial robot development coalesce to offer a broader perspective on the current advances and future directions in these coevolving fields of research. Together, four reviews summarize and 14 reports contribute to our understanding of low Reynolds number flight. This area of applied aerodynamics research is challenging to dissect due to the complicated flow phenomena that include laminar–turbulent flow transition, laminar separation bubbles, delayed stall and nonlinear vortex dynamics. Our mechanistic understanding of low Reynolds number flight has perhaps been advanced most by the development of dynamically scaled robot models and new specialized wind tunnel facilities: in particular, the tiltable Lund flight tunnel for animal migration research and the recently developed AFAR hypobaric wind tunnel for high-altitude animal flight studies. These world-class facilities are now complemented with a specialized low Reynolds number wind tunnel for studying the effect of turbulence on animal and robot flight in much greater detail than previously possible. This is particular timely, because the study of flight in extremely laminar versus turbulent flow opens a new frontier in our understanding of animal flight. Advancing this new area will offer inspiration for developing more efficient high-altitude aerial robots and removes roadblocks for aerial robots operating in turbulent urban environments.

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.

Lift calculations based on accepted wake models for animal flight are inconsistent and sensitive to vortex dynamics

There are three common methods for calculating the lift generated by a flying animal based on the measured airflow in the wake. However, these methods might not be accurate according to computational and robot-based studies of flapping wings. Here we test this hypothesis for the first time for a slowly flying Pacific parrotlet in still air using stereo particle image velocimetry recorded at 1000 Hz. The bird was trained to fly between two perches through a laser sheet wearing laser safety goggles. We found that the wingtip vortices generated during mid-downstroke advected down and broke up quickly, contradicting the frozen turbulence hypothesis typically assumed in animal flight experiments. The quasi-steady lift at mid-downstroke was estimated based on the velocity field by applying the widely used Kutta-Joukowski theorem, vortex ring model, and actuator disk model. The calculated lift was found to be sensitive to the applied model and its different parameters, including vortex span and distance between the bird and laser sheet-rendering these three accepted ways of calculating weight support inconsistent. The three models predict different aerodynamic force values mid-downstroke compared to independent direct measurements with an aerodynamic force platform that we had available for the same species flying over a similar distance. Whereas the lift predictions of the Kutta-Joukowski theorem and the vortex ring model stayed relatively constant despite vortex breakdown, their values were too low. In contrast, the actuator disk model predicted lift reasonably accurately before vortex breakdown, but predicted almost no lift during and after vortex breakdown. Some of these limitations might be better understood, and partially reconciled, if future animal flight studies report lift calculations based on all three quasi-steady lift models instead. This would also enable much needed meta studies of animal flight to derive bioinspired design principles for quasi-steady lift generation with flapping wings.

The role of passive avian head stabilization in flapping flight

Birds improve vision by stabilizing head position relative to their surroundings, while their body is forced up and down during flapping flight. Stabilization is facilitated by compensatory motion of the sophisticated avian head-neck system. While relative head motion has been studied in stationary and walking birds, little is known about how birds accomplish head stabilization during flapping flight. To unravel this, we approximate the avian neck with a linear mass-spring-damper system for vertical displacements, analogous to proven head stabilization models for walking humans. We corroborate the model's dimensionless natural frequency and damping ratios from high-speed video recordings of whooper swans (Cygnus cygnus) flying over a lake. The data show that flap-induced body oscillations can be passively attenuated through the neck. We find that the passive model robustly attenuates large body oscillations, even in response to head mass and gust perturbations. Our proof of principle shows that bird-inspired drones with flapping wings could record better images with a swan-inspired passive camera suspension.

Flapping wing aerodynamics: from insects to vertebrates

More than a million insects and approximately 11,000 vertebrates utilize flapping wings to fly. However, flapping flight has only been studied in a few of these species, so many challenges remain in understanding this form of locomotion. Five key aerodynamic mechanisms have been identified for insect flight. Among these is the leading edge vortex, which is a convergent solution to avoid stall for insects, bats and birds. The roles of the other mechanisms – added mass, clap and fling, rotational circulation and wing–wake interactions – have not yet been thoroughly studied in the context of vertebrate flight. Further challenges to understanding bat and bird flight are posed by the complex, dynamic wing morphologies of these species and the more turbulent airflow generated by their wings compared with that observed during insect flight. Nevertheless, three dimensionless numbers that combine key flow, morphological and kinematic parameters – the Reynolds number, Rossby number and advance ratio – govern flapping wing aerodynamics for both insects and vertebrates. These numbers can thus be used to organize an integrative framework for studying and comparing animal flapping flight. Here, we provide a roadmap for developing such a framework, highlighting the aerodynamic mechanisms that remain to be quantified and compared across species. Ultimately, incorporating complex flight maneuvers, environmental effects and developmental stages into this framework will also be essential to advancing our understanding of the biomechanics, movement ecology and evolution of animal flight.

The biophysics of bird flight: functional relationships integrate aerodynamics, morphology, kinematics, muscles, and sensors

Bird flight is a remarkable adaptation that has allowed the approximately 10 000 extant species to colonize all terrestrial habitats on earth including high elevations, polar regions, distant islands, arid deserts, and many others. Birds exhibit numerous physiological and biomechanical adaptations for flight. Although bird flight is often studied at the level of aerodynamics, morphology, wingbeat kinematics, muscle activity, or sensory guidance independently, in reality these systems are naturally integrated. There has been an abundance of new studies in these mechanistic aspects of avian biology but comparatively less recent work on the physiological ecology of avian flight. Here we review research at the interface of the systems used in flight control and discuss several common themes. Modulation of aerodynamic forces to respond to different challenges is driven by three primary mechanisms: wing velocity about the shoulder, shape within the wing, and angle of attack. For birds that flap, the distinction between velocity and shape modulation synthesizes diverse studies in morphology, wing motion, and motor control. Recently developed tools for studying bird flight are influencing multiple areas of investigation, and in particular the role of sensory systems in flight control. How sensory information is transformed into motor commands in the avian brain remains, however, a largely unexplored frontier.

Power reduction and the radial limit of stall delay in revolving wings of different aspect ratio

Airplanes and helicopters use high aspect ratio wings to reduce the power required to fly, but must operate at low angle of attack to prevent flow separation and stall. Animals capable of slow sustained flight, such as hummingbirds, have low aspect ratio wings and flap their wings at high angle of attack without stalling. Instead, they generate an attached vortex along the leading edge of the wing that elevates lift. Previous studies have demonstrated that this vortex and high lift can be reproduced by revolving the animal wing at the same angle of attack. How do flapping and revolving animal wings delay stall and reduce power? It has been hypothesized that stall delay derives from having a short radial distance between the shoulder joint and wing tip, measured in chord lengths. This non-dimensional measure of wing length represents the relative magnitude of inertial forces versus rotational accelerations operating in the boundary layer of revolving and flapping wings. Here we show for a suite of aspect ratios, which represent both animal and aircraft wings, that the attachment of the leading edge vortex on a revolving wing is determined by wing aspect ratio, defined with respect to the centre of revolution. At high angle of attack, the vortex remains attached when the local radius is shorter than four chord lengths and separates outboard on higher aspect ratio wings. This radial stall limit explains why revolving high aspect ratio wings (of helicopters) require less power compared with low aspect ratio wings (of hummingbirds) at low angle of attack and vice versa at high angle of attack.

Hummingbird wing efficacy depends on aspect ratio and compares with helicopter rotors

Hummingbirds are the only birds that can sustain hovering. This unique flight behaviour comes, however, at high energetic cost. Based on helicopter and aeroplane design theory, we expect that hummingbird wing aspect ratio (AR), which ranges from about 3.0 to 4.5, determines aerodynamic efficacy. Previous quasi-steady experiments with a wing spinner set-up provide no support for this prediction. To test this more carefully, we compare the quasi-steady hover performance of 26 wings, from 12 hummingbird taxa. We spun the wings at angular velocities and angles of attack that are representative for every species and measured lift and torque more precisely. The power (aerodynamic torque × angular velocity) required to lift weight depends on aerodynamic efficacy, which is measured by the power factor. Our comparative analysis shows that AR has a modest influence on lift and drag forces, as reported earlier, but interspecific differences in power factor are large. During the downstroke, the power required to hover decreases for larger AR wings at the angles of attack at which hummingbirds flap their wings (p < 0.05). Quantitative flow visualization demonstrates that variation in hover power among hummingbird wings is driven by similar stable leading edge vortices that delay stall during the down- and upstroke. A side-by-side aerodynamic performance comparison of hummingbird wings and an advanced micro helicopter rotor shows that they are remarkably similar.

How Lovebirds Maneuver Rapidly Using Super-Fast Head Saccades and Image Feature Stabilization

Diurnal flying animals such as birds depend primarily on vision to coordinate their flight path during goal-directed flight tasks. To extract the spatial structure of the surrounding environment, birds are thought to use retinal image motion (optical flow) that is primarily induced by motion of their head. It is unclear what gaze behaviors birds perform to support visuomotor control during rapid maneuvering flight in which they continuously switch between flight modes. To analyze this, we measured the gaze behavior of rapidly turning lovebirds in a goal-directed task: take-off and fly away from a perch, turn on a dime, and fly back and land on the same perch. High-speed flight recordings revealed that rapidly turning lovebirds perform a remarkable stereotypical gaze behavior with peak saccadic head turns up to 2700 degrees per second, as fast as insects, enabled by fast neck muscles. In between saccades, gaze orientation is held constant. By comparing saccade and wingbeat phase, we find that these super-fast saccades are coordinated with the downstroke when the lateral visual field is occluded by the wings. Lovebirds thus maximize visual perception by overlying behaviors that impair vision, which helps coordinate maneuvers. Before the turn, lovebirds keep a high contrast edge in their visual midline. Similarly, before landing, the lovebirds stabilize the center of the perch in their visual midline. The perch on which the birds land swings, like a branch in the wind, and we find that retinal size of the perch is the most parsimonious visual cue to initiate landing. Our observations show that rapidly maneuvering birds use precisely timed stereotypic gaze behaviors consisting of rapid head turns and frontal feature stabilization, which facilitates optical flow based flight control. Similar gaze behaviors have been reported for visually navigating humans. This finding can inspire more effective vision-based autopilots for drones.

Folding in and out: passive morphing in flapping wings

We present a new mechanism for passive wing morphing of flapping wings inspired by bat and bird wing morphology. The mechanism consists of an unactuated hand wing connected to the arm wing with a wrist joint. Flapping motion generates centrifugal accelerations in the hand wing, forcing it to unfold passively. Using a robotic model in hover, we made kinematic measurements of unfolding kinematics as functions of the non-dimensional wingspan fold ratio (2-2.5) and flapping frequency (5-17 Hz) using stereo high-speed cameras. We find that the wings unfold passively within one to two flaps and remain unfolded with only small amplitude oscillations. To better understand the passive dynamics, we constructed a computer model of the unfolding process based on rigid body dynamics, contact models, and aerodynamic correlations. This model predicts the measured passive unfolding within about one flap and shows that unfolding is driven by centrifugal acceleration induced by flapping. The simulations also predict that relative unfolding time only weakly depends on flapping frequency and can be reduced to less than half a wingbeat by increasing flapping amplitude. Subsequent dimensional analysis shows that the time required to unfold passively is of the same order of magnitude as the flapping period. This suggests that centrifugal acceleration can drive passive unfolding within approximately one wingbeat in small and large wings. Finally, we show experimentally that passive unfolding wings can withstand impact with a branch, by first folding and then unfolding passively. This mechanism enables flapping robots to squeeze through clutter without sophisticated control. Passive unfolding also provides a new avenue in morphing wing design that makes future flapping morphing wings possibly more energy efficient and light-weight. Simultaneously these results point to possible inertia driven, and therefore metabolically efficient, control strategies in bats and birds to morph or recover within a beat.

In vivo recording of aerodynamic force with an aerodynamic force platform: from drones to birds

Flapping wings enable flying animals and biomimetic robots to generate elevated aerodynamic forces. Measurements that demonstrate this capability are based on experiments with tethered robots and animals, and indirect force calculations based on measured kinematics or airflow during free flight. Remarkably, there exists no method to measure these forces directly during free flight. Such in vivo recordings in freely behaving animals are essential to better understand the precise aerodynamic function of their flapping wings, in particular during the downstroke versus upstroke. Here, we demonstrate a new aerodynamic force platform (AFP) for non-intrusive aerodynamic force measurement in freely flying animals and robots. The platform encloses the animal or object that generates fluid force with a physical control surface, which mechanically integrates the net aerodynamic force that is transferred to the earth. Using a straightforward analytical solution of the Navier-Stokes equation, we verified that the method is accurate. We subsequently validated the method with a quadcopter that is suspended in the AFP and generates unsteady thrust profiles. These independent measurements confirm that the AFP is indeed accurate. We demonstrate the effectiveness of the AFP by studying aerodynamic weight support of a freely flying bird in vivo. These measurements confirm earlier findings based on kinematics and flow measurements, which suggest that the avian downstroke, not the upstroke, is primarily responsible for body weight support during take-off and landing.

Feather roughness reduces flow separation during low Reynolds number glides of swifts

Swifts are aerodynamically sophisticated birds with a small arm and large hand wing that provides them with exquisite control over their glide performance. However, their hand wings have a seemingly unsophisticated surface roughness that is poised to disturb flow. This roughness of about 2% chord length is formed by the valleys and ridges of overlapping primary feathers with thick protruding rachides, which make the wing stiffer. An earlier flow study of laminar–turbulent boundary layer transition over prepared swift wings suggests that swifts can attain laminar flow at low angle-of-attack. In contrast, aerodynamic design theory suggests that airfoils must be extremely smooth to attain such laminar flow. In hummingbirds, which have similarly rough wings, flow measurements on a 3D printed model suggests that the flow separates at the leading edge and becomes turbulent well above the rachis bumps in a detached shear layer. The aerodynamic function of wing roughness in small birds is, therefore, not fully understood. Here we perform particle image velocimetry and force measurements to compare smooth versus rough 3D-printed models of the swift hand wing. The high-resolution boundary layer measurements show that the flow over rough wings is indeed laminar at low angle-of-attack and Reynolds number, but becomes turbulent at higher values. In contrast, the boundary layer over the smooth wing forms open laminar separation bubbles that extend beyond the trailing edge. The boundary layer dynamics of the smooth surface varies nonlinear as a function of angle-of-attack and Reynolds number, whereas the rough surface boasts more consistent turbulent boundary layer dynamics. Comparison of the corresponding drag values, lift values, and glide ratios suggests, however, that glide performance is equivalent. The increased structural performance, boundary layer robustness, and equivalent aerodynamic performance of rough wings might have provided small (proto) birds with an evolutionary window to high glide performance.

Gliding swifts attain laminar flow over rough wings

Swifts are among the most aerodynamically refined gliding birds. However, the overlapping vanes and protruding shafts of their primary feathers make swift wings remarkably rough for their size. Wing roughness height is 1-2% of chord length on the upper surface--10,000 times rougher than sailplane wings. Sailplanes depend on extreme wing smoothness to increase the area of laminar flow on the wing surface and minimize drag for extended glides. To understand why the swift does not rely on smooth wings, we used a stethoscope to map laminar flow over preserved wings in a low-turbulence wind tunnel. By combining laminar area, lift, and drag measurements, we show that average area of laminar flow on swift wings is 69% (n = 3; std 13%) of their total area during glides that maximize flight distance and duration--similar to high-performance sailplanes. Our aerodynamic analysis indicates that swifts attain laminar flow over their rough wings because their wing size is comparable to the distance the air travels (after a roughness-induced perturbation) before it transitions from laminar to turbulent. To interpret the function of swift wing roughness, we simulated its effect on smooth model wings using physical models. This manipulation shows that laminar flow is reduced and drag increased at high speeds. At the speeds at which swifts cruise, however, swift-like roughness prolongs laminar flow and reduces drag. This feature gives small birds with rudimentary wings an edge during the evolution of glide performance.

Vortex interactions with flapping wings and fins can be unpredictable

As they fly or swim, many animals generate a wake of vortices with their flapping fins and wings that reveals the dynamics of their locomotion. Previous studies have shown that the dynamic interaction of vortices in the wake with fins and wings can increase propulsive force. Here, we explore whether the dynamics of the vortex interactions could affect the predictability of propulsive forces. We studied the dynamics of the interactions between a symmetrically and periodically pitching and heaving foil and the vortices in its wake, in a soap-film tunnel. The phase-locked movie sequences reveal that abundant chaotic vortex-wake interactions occur at high Strouhal numbers. These high numbers are representative for the fins and wings of near-hovering animals. The chaotic wake limits the forecast horizon of the corresponding force and moment integrals. By contrast, we find periodic vortex wakes with an unlimited forecast horizon for the lower Strouhal numbers (0.2-0.4) at which many animals cruise. These findings suggest that swimming and flying animals could control the predictability of vortex-wake interactions, and the corresponding propulsive forces with their fins and wings.

Rotational accelerations stabilize leading edge vortices on revolving fly wings

The aerodynamic performance of hovering insects is largely explained by the presence of a stably attached leading edge vortex (LEV) on top of their wings. Although LEVs have been visualized on real, physically modeled, and simulated insects, the physical mechanisms responsible for their stability are poorly understood. To gain fundamental insight into LEV stability on flapping fly wings we expressed the Navier-Stokes equations in a rotating frame of reference attached to the wing's surface. Using these equations we show that LEV dynamics on flapping wings are governed by three terms: angular, centripetal and Coriolis acceleration. Our analysis for hovering conditions shows that angular acceleration is proportional to the inverse of dimensionless stroke amplitude, whereas Coriolis and centripetal acceleration are proportional to the inverse of the Rossby number. Using a dynamically scaled robot model of a flapping fruit fly wing to systematically vary these dimensionless numbers, we determined which of the three accelerations mediate LEV stability. Our force measurements and flow visualizations indicate that the LEV is stabilized by the ;quasi-steady' centripetal and Coriolis accelerations that are present at low Rossby number and result from the propeller-like sweep of the wing. In contrast, the unsteady angular acceleration that results from the back and forth motion of a flapping wing does not appear to play a role in the stable attachment of the LEV. Angular acceleration is, however, critical for LEV integrity as we found it can mediate LEV spiral bursting, a high Reynolds number effect. Our analysis and experiments further suggest that the mechanism responsible for LEV stability is not dependent on Reynolds number, at least over the range most relevant for insect flight (100<Re<14,000). LEVs are stable and continue to augment force even when they burst. These and similar findings for propellers and wind turbines at much higher Reynolds numbers suggest that even large flying animals could potentially exploit LEV-based force augmentation during slow hovering flight, take-offs or landing. We calculated the Rossby number from single-wing aspect ratios of over 300 insects, birds, bats, autorotating seeds, and pectoral fins of fish. We found that, on average, wings and fins have a Rossby number close to that of flies (Ro=3). Theoretically, many of these animals should therefore be able to generate a stable LEV, a prediction that is supported by recent findings for several insects, one bat, one bird and one fish. This suggests that force augmentation through stably attached (leading edge) vortices could represent a convergent solution for the generation of high fluid forces over a quite large range in size.

Biofluiddynamic scaling of flapping, spinning and translating fins and wings

Organisms that swim or fly with fins or wings physically interact with the surrounding water and air. The interactions are governed by the morphology and kinematics of the locomotory system that form boundary conditions to the Navier–Stokes (NS) equations. These equations represent Newton's law of motion for the fluid surrounding the organism. Several dimensionless numbers,such as the Reynolds number and Strouhal number, measure the influence of morphology and kinematics on the fluid dynamics of swimming and flight. There exists, however, no coherent theoretical framework that shows how such dimensionless numbers of organisms are linked to the NS equation. Here we present an integrated approach to scale the biological fluid dynamics of a wing that flaps, spins or translates. Both the morphology and kinematics of the locomotory system are coupled to the NS equation through which we find dimensionless numbers that represent rotational accelerations in the flow due to wing kinematics and morphology. The three corresponding dimensionless numbers are (1) the angular acceleration number, (2) the centripetal acceleration number, and (3) the Rossby number, which measures Coriolis acceleration. These dimensionless numbers consist of length scale ratios,which facilitate their geometric interpretation. This approach gives fundamental insight into the physical mechanisms that explain the differences in performance among flapping, spinning and translating wings. Although we derived this new framework for the special case of a model fly wing, the method is general enough to make it applicable to other organisms that fly or swim using wings or fins.

Automated visual tracking for studying the ontogeny of zebrafish swimming

The zebrafish Danio rerio is a widely used model organism in studies of genetics, developmental biology, and recently, biomechanics. In order to quantify changes in swimming during all stages of development, we have developed a visual tracking system that estimates the posture of fish. Our current approach assumes planar motion of the fish, given image sequences taken from a top view. An accurate geometric fish model is automatically designed and fit to the images at each time frame. Our approach works across a range of fish shapes and sizes and is therefore well suited for studying the ontogeny of fish swimming, while also being robust to common environmental occlusions. Our current analysis focuses on measuring the influence of vertebra development on the swimming capabilities of zebrafish. We examine wild-type zebrafish and mutants with stiff vertebrae (stocksteif) and quantify their body kinematics as a function of their development from larvae to adult (mutants made available by the Hubrecht laboratory, The Netherlands). By tracking the fish, we are able to measure the curvature and net acceleration along the body that result from the fish's body wave. Here, we demonstrate the capabilities of the tracking system for the escape response of wild-type zebrafish and stocksteif mutant zebrafish. The response was filmed with a digital high-speed camera at 1500 frames s–1. Our approach enables biomechanists and ethologists to process much larger datasets than possible at present. Our automated tracking scheme can therefore accelerate insight in the swimming behavior of many species of (developing)fish.

Vortex-wake interactions of a flapping foil that models animal swimming and flight

The fluid dynamics of many swimming and flying animals involves the generation and shedding of vortices into the wake. Here we studied the dynamics of similar vortices shed by a simple two-dimensional flapping foil in a soap-film tunnel. The flapping foil models an animal wing, fin or tail in forward locomotion. The vortical flow induced by the foil is correlated to(the resulting) thickness variations in the soap film. We visualized these thickness variations through light diffraction and recorded it with a digital high speed camera. This set-up enabled us to study the influence of foil kinematics on vortex-wake interactions. We varied the dimensionless wavelength of the foil (λ*=4–24) at a constant dimensionless flapping amplitude (A*=1.5) and geometric angle of attack amplitude (Aα,geo=15°). The corresponding Reynolds number was of the order of 1000. Such values are relevant for animal swimming and flight.

We found that a significant leading edge vortex (LEV) was generated by the foil at low dimensionless wavelengths (λ*&lt;10). The LEV separated from the foil for all dimensionless wavelengths. The relative time(compared with the flapping period) that the unstable LEV stayed above the flapping foil increased for decreasing dimensionless wavelengths. As the dimensionless wavelength decreased, the wake dynamics evolved from a wavy von Kármán-like vortex wake shed along the sinusoidal path of the foil into a wake densely packed with large interacting vortices. We found that strongly interacting vortices could change the wake topology abruptly. This occured when vortices were close enough to merge or tear each other apart. Our experiments show that relatively small changes in the kinematics of a flapping foil can alter the topology of the vortex wake drastically.

How swifts control their glide performance with morphing wings

Gliding birds continually change the shape and size of their wings, presumably to exploit the profound effect of wing morphology on aerodynamic performance. That birds should adjust wing sweep to suit glide speed has been predicted qualitatively by analytical glide models, which extrapolated the wing's performance envelope from aerodynamic theory. Here we describe the aerodynamic and structural performance of actual swift wings, as measured in a wind tunnel, and on this basis build a semi-empirical glide model. By measuring inside and outside swifts' behavioural envelope, we show that choosing the most suitable sweep can halve sink speed or triple turning rate. Extended wings are superior for slow glides and turns; swept wings are superior for fast glides and turns. This superiority is due to better aerodynamic performance-with the exception of fast turns. Swept wings are less effective at generating lift while turning at high speeds, but can bear the extreme loads. Finally, our glide model predicts that cost-effective gliding occurs at speeds of 8-10 m s(-1), whereas agility-related figures of merit peak at 15-25 m s(-1). In fact, swifts spend the night ('roost') in flight at 8-10 m s(-1) (ref. 11), thus our model can explain this choice for a resting behaviour. Morphing not only adjusts birds' wing performance to the task at hand, but could also control the flight of future aircraft.