Direct lateral maneuvers in hawkmoths

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.

Downstroke and upstroke conflict during banked turns in butterflies

For all flyers, aeroplanes or animals, making banked turns involve a rolling motion which, due to higher induced drag on the outer than the inner wing, results in a yawing torque opposite to the turn. This adverse yaw torque can be counteracted using a tail, but how animals that lack tail, e.g. all insects, handle this problem is not fully understood. Here, we quantify the performance of turning take-off flights in butterflies and find that they use force vectoring during banked turns without fully compensating for adverse yaw. This lowers their turning performance, increasing turn radius, since thrust becomes misaligned with the flight path. The separation of function between downstroke (lift production) and upstroke (thrust production) in our butterflies, in combination with a more pronounced adverse yaw during the upstroke increases the misalignment of the thrust. This may be a cost the butterflies pay for the efficient thrust-generating upstroke clap, but also other insects fail to rectify adverse yaw during escape manoeuvres, suggesting a general feature in functionally two-winged insect flight. When lacking tail and left with costly approaches to counteract adverse yaw, costs of flying with adverse yaw may be outweighed by the benefits of maintaining thrust and flight speed.

Wing damage affects flight kinematics but not flower tracking performance in hummingbird hawkmoths

Wing integrity is crucial to the many insect species that spend distinct portions of their life in flight. How insects cope with the consequences of wing damage is therefore a central question when studying how robust flight performance is possible with such fragile chitinous wings. It has been shown in a variety of insect species that the loss in lift-force production resulting from wing damage is generally compensated by an increase in wing beat frequency rather than amplitude. The consequences of wing damage for flight performance, however, are less well understood, and vary considerably between species and behavioural tasks. One hypothesis reconciling the varying results is that wing damage might affect fast flight manoeuvres with high acceleration, but not slower ones. To test this hypothesis, we investigated the effect of wing damage on the manoeuvrability of hummingbird hawkmoths (Macroglossum stellatarum) tracking a motorised flower. This assay allowed us to sample a range of movements at different temporal frequencies, and thus assess whether wing damage affected faster or slower flight manoeuvres. We show that hummingbird hawkmoths compensate for the loss in lift force mainly by increasing wing beat amplitude, yet with a significant contribution of wing beat frequency. We did not observe any effects of wing damage on flight manoeuvrability at either high or low temporal frequencies.

Elastic wing deformations mitigate flapping asymmetry during manoeuvres in rose chafers (Protaetia cuprea)

To manoeuvre in air, flying animals produce asymmetric flapping between contralateral wings. Unlike the adjustable vertebrate wings, insect wings lack intrinsic musculature, preventing active control over wing shape during flight. However, the wings elastically deform as a result of aerodynamic and inertial forces generated by the flapping motions. How these elastic deformations vary with flapping kinematics and flight performance in free-flying insects is poorly understood. Using high-speed videography, we measured how contralateral wings elastically deform during free-flight manoeuvring in rose chafer beetles (Protaetia cuprea). We found that asymmetric flapping during aerial turns was associated with contralateral differences in chord-wise wing deformations. The highest instantaneous difference in deformation occurred during stroke reversals, resulting from differences in wing rotation timing. Elastic deformation asymmetry was also evident during mid-strokes, where wing compliance increased the angle of attack of both wings, but reduced the asymmetry in the angle of attack between contralateral wings. A biomechanical model revealed that wing compliance can increase the torques generated by each wing, providing higher potential for manoeuvrability, while concomitantly contributing to flight stability by attenuating steering asymmetry. Such stability may be adaptive for insects such as flower chafers that need to perform delicate low-speed landing manoeuvres among vegetation.

Reconstructing full-field flapping wing dynamics from sparse measurements

Flapping insect wings deform during flight. This deformation benefits the insect's aerodynamic force production as well as energetic efficiency. However, it is challenging to measure wing displacement field in flying insects. Many points must be tracked over the wing's surface to resolve its instantaneous shape. To reduce the number of points one is required to track, we propose a physics-based reconstruction method called system equivalent reduction expansion processes to estimate wing deformation and strain from sparse measurements. Measurement locations are determined using a weighted normalized modal displacement method. We experimentally validate the reconstruction technique by flapping a paper wing from 5-9 Hz with 45° and measuring strain at three locations. Two measurements are used for the reconstruction and the third for validation. Strain reconstructions had a maximal error of 30% in amplitude. We extend this methodology to a more realistic insect wing through numerical simulation. We show that wing displacement can be estimated from sparse displacement or strain measurements, and that additional sensors spatially average measurement noise to improve reconstruction accuracy. This research helps overcome some of the challenges of measuring full-field dynamics in flying insects and provides a framework for strain-based sensing in insect-inspired flapping robots.

Insect and insect-inspired aerodynamics: unsteadiness, structural mechanics and flight control

Flying insects impress by their versatility and have been a recurrent source of inspiration for engineering devices. A large body of literature has focused on various aspects of insect flight, with an essential part dedicated to the dynamics of flapping wings and their intrinsically unsteady aerodynamic mechanisms. Insect wings flex during flight and a better understanding of structural mechanics and aeroelasticity is emerging. Most recently, insights from solid and fluid mechanics have been integrated with physiological measurements from visual and mechanosensors in the context of flight control in steady airs and through turbulent conditions. We review the key recent advances concerning flight in unsteady environments and how the multi-body mechanics of the insect structure-wings and body-are at the core of the flight control question. The issues herein should be considered when applying bio-informed design principles to robotic flapping wings.

Bees with attitude: the effects of directed gusts on flight trajectories

Flight is a complicated task at the centimetre scale particularly due to unsteady air fluctuations which are ubiquitous in outdoor flight environments. Flying organisms deal with these difficulties using active and passive control mechanisms to steer their body motion. Body attitudes of flapping organisms are linked with their resultant flight trajectories and performance, yet little is understood about how isolated unsteady aerodynamic phenomena affect the interlaced dynamics of such systems. In this study, we examined freely flying bumblebees subject to a single isolated gust to emulate aerodynamic disturbances encountered in nature. Bumblebees are expert commanders of the aerial domain as they persistently forage within complex terrain elements. By tracking the three-dimensional dynamics of bees flying through gusts, we determined the sequences of motion that permit flight in three disturbance conditions: sideward, upward and downward gusts. Bees executed a series of passive impulsive maneuvers followed by active recovery maneuvers. Impulsive motion was unique in each gust direction, maintaining control by passive manipulation of the body. Bees pitched up and slowed down at the beginning of recovery in every disturbance, followed by corrective maneuvers which brought body attitudes back to their original state. Bees were displaced the most by the sideward gust, displaying large lateral translations and roll deviations. Upward gusts were easier for bees to fly through, causing only minor flight changes and minimal recovery times. Downward gusts severely impaired the control response of bees, inflicting strong adverse forces which sharply upset trajectories. Bees used a variety of control strategies when flying in each disturbance, offering new insights into insect-scale flapping flight and bio-inspired robotic systems.This article has an associated First Person interview with the first author of the paper.

Role of side-slip flight in target pursuit: blue-tailed damselflies (Ischnura elegans) avoid body rotation while approaching a moving perch

Visually guided flight control requires processing changes in the visual panorama (optic-flow) resulting from self-movement relative to stationary objects, as well as from moving objects passing through the field of view. We studied the ability of the blue-tailed damselfly, Ischnura elegans, to successfully land on a perch moving unpredictably. We tracked the insects landing on a vertical pole moved linearly 6 cm back and forth with sinusoidal changes in velocity. When the moving perch changed direction at frequencies higher than 1 Hz, the damselflies engaged in manoeuvres that typically involved sideways flight, with minimal changes in body orientation relative to the stationary environment. We show that these flight manoeuvres attempted to fix the target in the centre of the field of view when flying in any direction while keeping body rotation changes about the yaw axis to the minimum. We propose that this pursuit strategy allows the insect to obtain reliable information on self and target motion relative to the stationary environment from the translational optic-flow, while minimizing interference from the rotational optic-flow. The ability of damselflies to fly in any direction, irrespective of body orientation, underlines the superb flight control of these aerial predators.

Allometry of wing twist and camber in a flower chafer during free flight: How do wing deformations scale with body size?

Intraspecific variation in adult body mass can be particularly high in some insect species, mandating adjustment of the wing's structural properties to support the weight of the larger body mass in air. Insect wings elastically deform during flapping, dynamically changing the twist and camber of the relatively thin and flat aerofoil. We examined how wing deformations during free flight scale with body mass within a species of rose chafers (Coleoptera: Protaetia cuprea) in which individuals varied more than threefold in body mass (0.38-1.29 g). Beetles taking off voluntarily were filmed using three high-speed cameras and the instantaneous deformation of their wings during the flapping cycle was analysed. Flapping frequency decreased in larger beetles but, otherwise, flapping kinematics remained similar in both small and large beetles. Deflection of the wing chord-wise varied along the span, with average deflections at the proximal trailing edge higher by 0.2 and 0.197 wing lengths compared to the distal trailing edge in the downstroke and the upstroke, respectively. These deflections scaled with wing chord to the power of 1.0, implying a constant twist and camber despite the variations in wing and body size. This suggests that the allometric growth in wing size includes adjustment of the flexural stiffness of the wing structure to preserve wing twist and camber during flapping.

Allometry of wing twist and camber in a flower chafer during free flight: How do wing deformations scale with body size?

Intraspecific variation in adult body mass can be particularly high in some insect species, mandating adjustment of the wing's structural properties to support the weight of the larger body mass in air. Insect wings elastically deform during flapping, dynamically changing the twist and camber of the relatively thin and flat aerofoil. We examined how wing deformations during free flight scale with body mass within a species of rose chafers (Coleoptera: Protaetia cuprea) in which individuals varied more than threefold in body mass (0.38-1.29 g). Beetles taking off voluntarily were filmed using three high-speed cameras and the instantaneous deformation of their wings during the flapping cycle was analysed. Flapping frequency decreased in larger beetles but, otherwise, flapping kinematics remained similar in both small and large beetles. Deflection of the wing chord-wise varied along the span, with average deflections at the proximal trailing edge higher by 0.2 and 0.197 wing lengths compared to the distal trailing edge in the downstroke and the upstroke, respectively. These deflections scaled with wing chord to the power of 1.0, implying a constant twist and camber despite the variations in wing and body size. This suggests that the allometric growth in wing size includes adjustment of the flexural stiffness of the wing structure to preserve wing twist and camber during flapping.

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.

Generation of the pitch moment during the controlled flight after takeoff of fruitflies

In the present paper, the controlled flight of fruitflies after voluntary takeoff is studied. Wing and body kinematics of the insects after takeoff are measured using high-speed video techniques, and the aerodynamic force and moment are calculated by the computational fluid dynamics method based on the measured data. How the control moments are generated is analyzed by correlating the computed moments with the wing kinematics. A fruit-fly has a large pitch-up angular velocity owing to the takeoff jump and the fly controls its body attitude by producing pitching moments. It is found that the pitching moment is produced by changes in both the aerodynamic force and the moment arm. The change in the aerodynamic force is mainly due to the change in angle of attack. The change in the moment arm is mainly due to the change in the mean stroke angle and deviation angle, and the deviation angle plays a more important role than the mean stroke angle in changing the moment arm (note that change in deviation angle implies variation in the position of the aerodynamic stroke plane with respect to the anatomical stroke plane). This is unlike the case of fruitflies correcting pitch perturbations in steady free flight, where they produce pitching moment mainly by changes in mean stroke angle.

Flight mechanics and control of escape manoeuvres in hummingbirds II. Aerodynamic force production, flight control and performance limitations

The superior manoeuvrability of hummingbirds emerges from complex interactions of specialized neural and physiological processes with the unique flight dynamics of flapping wings. Escape manoeuvring is an ecologically relevant, natural behaviour of hummingbirds, from which we can gain understanding into the functional limits of vertebrate locomotor capacity. Here, we extend our kinematic analysis of escape manoeuvres from a companion paper to assess two potential limiting factors of manoeuvring performance of hummingbirds 1) muscle mechanical power output and 2) delays in the neural sensing and control system. We focused on the magnificent hummingbird, (Eugenes fulgens, 7.8g) and black-chinned hummingbird (Archilochus alexandri, 3.1 g), which represent large and small species, respectively. We first estimated the aerodynamic forces, moments and the mechanical power of escape manoeuvres using measured wing kinematics. Comparing active-manoeuvring and passive-damping aerodynamic moments, we found that pitch dynamics were lightly damped and dominated by effect of inertia while roll dynamics were highly damped. To achieve observed closed-loop performance, pitch manoeuvres required faster sensorimotor transduction, as hummingbirds can only tolerate half the delay allowed in roll manoeuvres. Accordingly, our results suggested that pitch control may require a more sophisticated control strategy, such as those based on prediction. For the magnificent hummingbird, we estimated escape manoeuvres required muscle mass-specific power 4.5 times that during hovering. Therefore, in addition to the limitation imposed by sensorimotor delays, muscle power could also limit the performance of escape manoeuvres.