Inertial coupling of the hummingbird body in the flight mechanics of an escape manoeuvre

When a hovering hummingbird performs a rapid escape manoeuvre in response to a perceived threat from the front side, its body may go through simultaneous pitch, yaw and roll rotations. In this study, we examined the inertial coupling of the three-axis body rotations and its effect on the flight mechanics of the manoeuvre using analyses of high-speed videos as well as high-fidelity computational modelling of the aerodynamics and inertial forces. We found that while a bird's pitch-up was occurring, inertial coupling between yaw and roll helped slow down and terminate the pitch, thus serving as a passive control mechanism for the manoeuvre. Furthermore, an inertial coupling between pitch-up and roll can help accelerate yaw before the roll-yaw coupling. Different from the aerodynamic mechanisms that aircraft and animal flyers typically rely on for flight control, we hypothesize that inertial coupling is a built-in mechanism in the flight mechanics of hummingbirds that helps them achieve superb aerial agility.

Wing deformation improves aerodynamic performance of forward flight of bluebottle flies flying in a flight mill

Insect wings are flexible structures that exhibit deformations of complex spatiotemporal patterns. Existing studies on wing deformation underscore the indispensable role of wing deformation in enhancing aerodynamic performance. Here, we investigated forward flight in bluebottle flies, flying semi-freely in a magnetic flight mill; we quantified wing surface deformation using high-speed videography and marker-less surface reconstruction and studied the effects on aerodynamic forces, power and efficiency using computational fluid dynamics. The results showed that flies' wings exhibited substantial camber near the wing root and twisted along the wingspan, as they were coupled effects of deflection primarily about the claval flexion line. Such deflection was more substantial for supination during the upstroke when most thrust was produced. Compared with deformed wings, the undeformed wings generated 59-98% of thrust and 54-87% of thrust efficiency (i.e. ratio of thrust and power). Wing twist moved the aerodynamic centre of pressure proximally and posteriorly, likely improving aerodynamic efficiency.

Sideways maneuvers enable narrow aperture negotiation by free-flying hummingbirds

Many birds routinely fly fast through dense vegetation characterized by variably sized structures and voids. Successfully negotiating these cluttered environments requires maneuvering through narrow constrictions between obstacles. We show that Anna's hummingbirds (Calypte anna) can negotiate apertures less than one wingspan in diameter using a novel sideways maneuver that incorporates continuous, bilaterally asymmetric wing motions. Crucially, this maneuver allows hummingbirds to continue flapping as they negotiate the constriction. Even smaller openings are negotiated via a faster ballistic trajectory characterized by tucked and thus non-flapping wings, which reduces force production and increases descent rate relative to the asymmetric technique. Hummingbirds progressively shift to the swept method as they perform hundreds of consecutive transits, suggesting increased locomotor performance with task familiarity. Initial use of the slower asymmetric transit technique may allow birds to better assess upcoming obstacles and voids, thereby reducing the likelihood of subsequent collisions. Repeated disruptions of normal wing kinematics as birds negotiate tight apertures may determine the limits of flight performance in structurally complex environments. These strategies for aperture transit and associated flight trajectories can inform designs and algorithms for small aerial vehicles flying within cluttered environments.

Hummingbirds use wing inertial effects to improve manoeuvrability

Hummingbirds outperform other birds in terms of aerial agility at low flight speeds. To reveal the key mechanisms that enable such unparalleled agility, we reconstructed body and wing motion of hummingbird escape manoeuvres from high-speed videos; then, we performed computational fluid dynamics modelling and flight mechanics analysis, in which the time-dependent forces within each wingbeat were resolved. We found that the birds may use the inertia of their wings to achieve peak body rotational acceleration around wing reversal when the aerodynamic forces were small. The aerodynamic forces instead counteracted the reversed inertial forces at a different wingbeat phase, thereby stabilizing the body from inertial oscillations, or they could become dominant and provide additional rotational acceleration. Our results suggest such an inertial steering mechanism was present for all four hummingbird species considered, and it was used by the birds for both pitch-up and roll accelerations. The combined inertial steering and aerodynamic mechanisms made it possible for the hummingbirds to generate instantaneous body acceleration at any phase of a wingbeat, and this feature is probably the key to understanding the unique dexterity distinguishing hummingbirds from other small-size flyers that solely rely on aerodynamics for manoeuvering.

Active wing-pitching mechanism in hummingbird escape maneuvers

Previous studies suggested that wing pitching, i.e. the wing rotation around its long axis, of insects and hummingbirds is primarily driven by an inertial effect associated with stroke deceleration and acceleration of the wings and is thus passive. Here we considered the rapid escape maneuver of hummingbirds who were initially hovering but then startled by the frontal approach of a looming object. During the maneuver, the hummingbirds substantially changed their wingbeat frequency, wing trajectory, and other kinematic parameters. Using wing kinematics reconstructed from high-speed videos and computational fluid dynamics modeling, we found that although the same inertial effect drove the wing flipping at stroke reversal as in hovering, significant power input was required to pitch up the wings during downstroke to enhance aerodynamic force production; furthermore, the net power input could be positive for wing pitching in a complete wingbeat cycle. Therefore, our study suggests that an active mechanism was present during the maneuver to drive wing pitching. In addition to the powered pitching, wing deviation during upstroke required twice as much power as hovering to move the wings caudally when the birds redirected the aerodynamic force vector for escaping. These findings were consistent with our hypothesis that enhanced muscle recruitment is essential for hummingbirds' escape maneuvers.

Musculoskeletal wing-actuation model of hummingbirds predicts diverse effects of primary flight muscles in hovering flight

Hummingbirds have evolved to hover and manoeuvre with exceptional flight control. This is enabled by their musculoskeletal system that successfully exploits the agile motion of flapping wings. Here, we synthesize existing empirical and modelling data to generate novel hypotheses for principles of hummingbird wing actuation. These may help guide future experimental work and provide insights into the evolution and robotic emulation of hummingbird flight. We develop a functional model of the hummingbird musculoskeletal system, which predicts instantaneous, three-dimensional torque produced by primary (pectoralis and supracoracoideus) and combined secondary muscles. The model also predicts primary muscle contractile behaviour, including stress, strain, elasticity and work. Results suggest that the primary muscles (i.e. the flight 'engine') function as diverse effectors, as they do not simply power the stroke, but also actively deviate and pitch the wing with comparable actuation torque. The results also suggest that the secondary muscles produce controlled-tightening effects by acting against primary muscles in deviation and pitching. The diverse effects of the pectoralis are associated with the evolution of a comparatively enormous bicipital crest on the humerus.

Wing Kinematics and Unsteady Aerodynamics of a Hummingbird Pure Yawing Maneuver

As one of few animals with the capability to execute agile yawing maneuvers, it is quite desirable to take inspiration from hummingbird flight aerodynamics. To understand the wing and body kinematics and associated aerodynamics of a hummingbird performing a free yawing maneuver, a crucial step in mimicking the biological motion in robotic systems, we paired accurate digital reconstruction techniques with high-fidelity computational fluid dynamics (CFD) simulations. Results of the body and wing kinematics reveal that to achieve the pure yaw maneuver, the hummingbird utilizes very little body pitching, rolling, vertical, or horizontal motion. Wing angle of incidence, stroke, and twist angles are found to be higher for the inner wing (IW) than the outer wing (OW). Unsteady aerodynamic calculations reveal that drag-based asymmetric force generation during the downstroke (DS) and upstroke (US) serves to control the speed of the turn, a characteristic that allows for great maneuvering precision. A dual-loop vortex formation during each half-stroke is found to contribute to asymmetric drag production. Wake analysis revealed that asymmetric wing kinematics led to leading-edge vortex strength differences of around 59% between the IW and OW. Finally, analysis of the role of wing flexibility revealed that flexibility is essential for generating the large torque necessary for completing the turn as well as producing sufficient lift for weight support.

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.

The evolution of two distinct strategies of moth flight

Across insects, wing shape and size have undergone dramatic divergence even in closely related sister groups. However, we do not know how morphology changes in tandem with kinematics to support body weight within available power and how the specific force production patterns are linked to differences in behaviour. Hawkmoths and wild silkmoths are diverse sister families with divergent wing morphology. Using three-dimensional kinematics and quasi-steady aerodynamic modelling, we compare the aerodynamics and the contributions of wing shape, size and kinematics in 10 moth species. We find that wing movement also diverges between the clades and underlies two distinct strategies for flight. Hawkmoths use wing kinematics, especially high frequencies, to enhance force and wing morphologies that reduce power. Silkmoths use wing morphology to enhance force, and slow, high-amplitude wingstrokes to reduce power. Both strategies converge on similar aerodynamic power and can support similar body weight ranges. However, inter-clade within-wingstroke force profiles are quite different and linked to the hovering flight of hawkmoths and the bobbing flight of silkmoths. These two moth groups fly more like other, distantly related insects than they do each other, demonstrating the diversity of flapping flight evolution and a rich bioinspired design space for robotic flappers.

A minimal longitudinal dynamic model of a tailless flapping wing robot for control design

Recently, several insect- and hummingbird-inspired tailless flapping wing robots have been introduced. However, their flight dynamics, which are likely to be similar to that of their biological counterparts, remain yet to be fully understood. We propose a minimal dynamic model that is not only validated with experimental data, but also able to predict the consequences of various important design changes. Specifically, the model captures the flapping-cycle-averaged longitudinal dynamics, considering the main aerodynamic effects. We validated the model with flight data captured with a tailless flapping wing robot, the DelFly Nimble, for air speeds from near-hover flight up to 3.5 m s^-1. Moreover, the model succeeds in predicting the effects of changes to the center of mass location, and to the control system gains. Hence, the model is suitable even for the initial control design phase. To demonstrate this, we have used the simulation model to tune the robot's control system for higher speeds. Using the new control parameters on the real robot improved its maximal stable speed from 4 m s^-1 to 7 m s^-1.

Avoiding topsy-turvy: how Anna's hummingbirds (Calypte anna) fly through upward gusts

Flying organisms frequently confront the challenge of maintaining stability when moving within highly dynamic airflows near the Earth's surface. Either aerodynamic or inertial forces generated by appendages and other structures, such as the tail, may be used to offset aerial perturbations, but these responses have not been well characterized. To better understand how hummingbirds modify wing and tail motions in response to individual gusts, we filmed Anna's hummingbirds as they negotiated an upward jet of fast-moving air. Birds exhibited large variation in wing elevation, tail pitch and tail fan angles among transits as they repeatedly negotiated the same gust, and often exhibited a dramatic decrease in body angle (29±6 deg) post-transit. After extracting three-dimensional kinematic features, we identified a spectrum of control strategies for gust transit, with one extreme involving continuous flapping, no tail fanning and little disruption to body posture (23±3 deg downward pitch), and the other extreme characterized by dorsal wing pausing, tail fanning and greater downward body pitch (38±4 deg). The use of a deflectable tail on a glider model transiting the same gust resulted in enhanced stability and can easily be implemented in the design of aerial robots.

Ascending flight and decelerating vertical glides in Anna's hummingbirds

Hummingbirds are observationally well known for their capacity to vertically ascend whilst hovering, but the underlying mechanics and possible energetic limits to ascent rates are unclear. Decelerations during vertical ascent to a fixed target may also be associated with specific visual responses to regulate the body's trajectory. Here, we studied climbing flight and subsequent deceleration in male Anna's hummingbirds (Calypte anna) over an approximately 2 m vertical distance. Birds reached vertical speeds and accelerations up to ∼4 m s^-1 and 10 m s^-2, respectively, through the use of flapping frequencies as high as 56 Hz and stroke amplitudes slightly greater than 180 deg. Total mass-specific power at maximal ascent speed was up to 92 W kg^-1 body mass. Near the end of the ascending trajectory, all individuals decelerated ballistically via cessation of flapping and folding of wings over the body without losing control, a behavior termed here a vertical glide. Visual modulation of the deceleration trajectory during ascent was indicated by a constant value (∼0.75) for the first derivative of the time-to-contact to target. Our results indicate that hummingbirds in rapid vertical ascent expended near-maximal power output during flight, but also tightly controlled their subsequent deceleration during the vertical glide.

Biomechanics of omnidirectional strikes in flat spiders

Many ambush predators attack prey using rapid strikes, but these strikes are typically only anteriorly directed. However, a predator may attack laterally and posteriorly oriented prey if it can couple the strikes with rapid body reorientation. Here, we examined omnidirectional strikes in flattie spiders (Selenopidae), a group of sit-and-wait ambush predators found on open surfaces. These spiders attack prey throughout their entire peripheral range using rapid strikes that consist of rapid translation and rotation toward the prey. These spiders ambush with radially oriented, long, laterigrade legs in a ready-to-fire status. Once prey is detected, the spider maneuvers toward it using a single flexion of the legs closest to the prey, which is assisted by 0-3 extension strides by the contralateral legs. The within-stance joint actions by a few legs generate a large resultant force directed toward the prey and a large turning moment. Furthermore, the turning speed is enhanced by rapid midair leg adductions, which effectively reduce the spider's moment of inertia during angular acceleration. Our results demonstrate a novel hunting behavior with high maneuverability that is generated with effectively controlled reconfigurations of long, laterigrade legs. These results provide insights for understanding the diversity of animal legs and developing highly maneuverable multi-legged robots.

Quantifying the dynamic wing morphing of hovering hummingbird

Animal wings are lightweight and flexible; hence, during flapping flight their shapes change. It has been known that such dynamic wing morphing reduces aerodynamic cost in insects, but the consequences in vertebrate flyers, particularly birds, are not well understood. We have developed a method to reconstruct a three-dimensional wing model of a bird from the wing outline and the feather shafts (rachides). The morphological and kinematic parameters can be obtained using the wing model, and the numerical or mechanical simulations may also be carried out. To test the effectiveness of the method, we recorded the hovering flight of a hummingbird (Amazilia amazilia) using high-speed cameras and reconstructed the right wing. The wing shape varied substantially within a stroke cycle. Specifically, the maximum and minimum wing areas differed by 18%, presumably due to feather sliding; the wing was bent near the wrist joint, towards the upward direction and opposite to the stroke direction; positive upward camber and the 'washout' twist (monotonic decrease in the angle of incidence from the proximal to distal wing) were observed during both half-strokes; the spanwise distribution of the twist was uniform during downstroke, but an abrupt increase near the wrist joint was found during upstroke.

Asymmetry costs: effects of wing damage on hovering flight performance in the hawkmoth Manduca sexta

Flight performance is fundamental to the fitness of flying organisms. Whilst airborne, flying organisms face unavoidable wing wear and wing area loss. Many studies have tried to quantify the consequences of wing area loss to flight performance with varied results, suggesting that not all types of damage are equal and different species may have different means to compensate for some forms of wing damage with little to no cost. Here, we investigated the cost of control during hovering flight with damaged wings, specifically wings with asymmetric and symmetric reductions in area, by measuring maximum load lifting capacity and the metabolic power of hovering flight in hawkmoths (Manduca sexta). We found that while asymmetric and symmetric reductions are both costly in terms of maximum load lifting and hovering efficiency, asymmetric reductions are approximately twice as costly in terms of wing area lost. The moths also did not modulate flapping frequency and amplitude as predicted by a hovering flight model, suggesting that the ability to do so, possibly tied to asynchronous versus synchronous flight muscles, underlies the varied responses found in different wing clipping experiments.

Limitations of rotational manoeuvrability in insects and hummingbirds: evaluating the effects of neuro-biomechanical delays and muscle mechanical power

Flying animals ranging in size from fruit flies to hummingbirds are nimble fliers with remarkable rotational manoeuvrability. The degrees of manoeuvrability among these animals, however, are noticeably diverse and do not simply follow scaling rules of flight dynamics or muscle power capacity. As all manoeuvres emerge from the complex interactions of neural, physiological and biomechanical processes of an animal's flight control system, these processes give rise to multiple limiting factors that dictate the maximal manoeuvrability attainable by an animal. Here using functional models of an animal's flight control system, we investigate the effects of three such limiting factors, including neural and biomechanical (from limited flapping frequency) delays and muscle mechanical power, for two insect species and two hummingbird species, undergoing roll, pitch and yaw rotations. The results show that for animals with similar degree of manoeuvrability, for example, fruit flies and hummingbirds, the underlying limiting factors are different, as the manoeuvrability of fruit flies is only limited by neural delays and that of hummingbirds could be limited by all three factors. In addition, the manoeuvrability also appears to be the highest about the roll axis as it requires the least muscle mechanical power and can tolerate the largest neural delays.

Flight mechanics and control of escape manoeuvres in hummingbirds I. Flight kinematics

Hummingbirds are nature‘s masters of aerobatic manoeuvres. Previous research shows hummingbirds and insects converged evolutionarily upon similar aerodynamic mechanisms and kinematics in hovering. Herein, we use three-dimensional kinematic data to begin to test for similar convergence of kinematics used for escape flight and to explore the effects of body size upon manoeuvring. We studied four hummingbird species in North America including two large species (magnificent hummingbird, Eugenes fulgens, 7.8 g and blue-throated hummingbird, Lampornis clemenciae, 8.0 g) and two smaller species (broad-billed hummingbird, Cynanthus latirostris, 3.4 g and black-chinned hummingbirds Archilochus alexandri, 3.1 g). Starting from a steady hover, hummingbirds consistently manoeuvred away from perceived threats using a drastic escape response that featured body pitch and roll rotations coupled with a large linear acceleration. Hummingbirds changed their flapping frequency and wing trajectory in all three degrees-of-freedom on stroke-by-stroke basis, likely causing rapid and significant alteration of the magnitude and direction of aerodynamic forces. Thus it appears that the flight control of hummingbirds does not obey the “helicopter model” that is valid for similar escape manoeuvres in fruit flies. Except for broad-billed hummingbirds, the hummingbirds had faster reaction times than those reported for visual feedback control in insects. The two larger hummingbird species performed pitch rotations and global-yaw turns with considerably larger magnitude than the smaller species, but roll rates and cumulative roll angles were similar among the four species.