The power-speed relationship is U-shaped in two free-flying hawkmoths (Manducasexta)

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.

Trade-off between flight capability and reproduction in Acridoidea (Insecta: Orthoptera)

In many insect taxa, there is a well-established trade-off between flight capability and reproduction. The wing types of Acridoidea exhibit extremely variability from full length to complete loss in many groups, thus, provide a good model for studying the trade-off between flight and reproduction. In this study, we completed the sampling of 63 Acridoidea species, measured the body length, wing length, body weight, flight muscle weight, testis and ovary weight, and the relative wing length (RWL), relative flight muscle weight (RFW), and gonadosomatic index (GSI) of different species were statistically analyzed. The results showed that there were significant differences in RWL, RFW, and GSI among Acridoidea species with different wing types. RFW of long-winged species was significantly higher than that of short-winged and wingless species (p < .01), while GSI of wingless species was higher than that of long-winged and short-winged species. The RWL and RFW had a strong positive correlation in species with different wing types (correlation coefficient r = .8344 for male and .7269 for female, and p < .05), while RFW was strong negatively correlated with GSI (r = -.2649 for male and -.5024 for female, and p < .05). For Acridoidea species with wing dimorphism, males with relatively long wings had higher RFW than that of females with relatively short wings, while females had higher GSI. Phylogenetic comparative analysis showed that RWL, RFW, and GSI all had phylogenetic signals and phylogenetic dependence. These results revealed that long-winged individuals are flight capable at the expense of reproduction, while short-winged and wingless individuals cannot fly, but has greater reproductive output. The results support the trade-off between flight and reproduction in Acridoidea.

Power requirements for the hovering flight of insects with different sizes

Winged insects vary greatly in size, from tiny wasps (0.015 mg) to large moths (1.6 g). Previous studies on the power requirements of insect flight focused on relatively large insects; those of miniature insects remain relatively unknown. In this study the power requirements of a series of miniature insects were calculated, and changes with size across a range of insect sizes were investigated. Aerodynamic power was computed by numerically solving the Navier-Stokes equation, and inertial power was computed analytically. Comparison analysis was then conducted on the power requirements of miniature and large insects. Despite a 100,000-fold weight difference, the required power per unit insect mass, referred to as mass-specific power, was approximately equal for all the insects examined. This finding is explained as follows. Power is approximately proportional to the product of the wing speed and the wing drag per unit weight (i.e., "drag-to-lift ratio"). When insect size decreased, wing speed decreased (due to reduced wing-length), while wing drag increased (due to increased air-viscosity), resulting in an approximately unchanged mass-specific power. For large or small insects, flight power is derived from the same type of muscles (striated). Assuming that the mean power per unit muscle mass is the same under the same type of muscle, the above size/specific-power relation indicates that the ratio of flight-muscle mass to insect mass is the same for different sized insects.

Aerodynamic effects on an emulated hovering passerine with different wing-folding amplitudes

Bird flight involves complicated wing kinematics, especially during hovering flight. The detailed aerodynamic effects of wings with higher degrees of freedom (DOFs) remain to be further investigated. Therefore, we designed a novel multiarticulate flapping-wing robot with five DOFs on each wing. Using this robot we aimed to investigate the more complicated wing kinematics of birds, which are usually difficult to test and analyze. In this study the robot was programmed to mimic the previously observed hovering motion of passerines, and force measurements and particle image velocimetry experiments. We experimented with two different wing-folding amplitudes: one with a larger folding amplitude, similar to that of real passerines, and one with only half the amplitude. The robot kinematics were verified utilizing direct linear transformation, which confirmed that the wing trajectories had an acceptable correlation with the desired motion. According to the lift force measurements, four phases of the wingbeat cycle were characterized and elaborated through camera images and flow visualization. We found that the reduction in folding amplitude caused a higher negative force during upstrokes and also induced a greater positive force at the initial downstroke through 'wake capture'. This could increase the vertical oscillation while hovering despite a minor increase in average force production. This phenomenon was not observed during forward flight in previous studies. Our results provide a critical understanding of the effect of wing folding which is required for designing the wing kinematics of future advanced flapping-wing micro aerial vehicles.

Hovering flight in hummingbird hawkmoths: kinematics, wake dynamics and aerodynamic power

Hovering insects are divided into two categories: 'normal' hoverers that move the wing symmetrically in a horizontal stroke plane, and those with an inclined stroke plane. Normal hoverers have been suggested to support their weight during both downstroke and upstroke, shedding vortex rings each half-stroke. Insects with an inclined stroke plane should, according to theory, produce flight forces only during downstroke, and only generate one set of vortices. The type of hovering is thus linked to the power required to hover. Previous efforts to characterize the wake of hovering insects have used low-resolution experimental techniques or simulated the flow using computational fluid dynamics, and so it remains to be determined whether insect wakes can be represented by any of the suggested models. Here, we used tomographic particle image velocimetry, with a horizontal measurement volume placed below the animals, to show that the wake shed by hovering hawkmoths is best described as a series of bilateral, stacked vortex 'rings'. While the upstroke is aerodynamically active, despite an inclined stroke plane, it produces weaker vortices than the downstroke. In addition, compared with the near wake, the far wake lacks structure and is less concentrated. Both near and far wakes are clearly affected by vortex interactions, suggesting caution is required when interpreting wake topologies. We also estimated induced power (Pind) from downwash velocities in the wake. Standard models predicted a Pind more than double that from our wake measurements. Our results thus question some model assumptions and we propose a reevaluation of the model parameters.

Rapid frequency modulation in a resonant system: aerial perturbation recovery in hawkmoths

Centimetre-scale fliers must contend with the high power requirements of flapping flight. Insects have elastic elements in their thoraxes which may reduce the inertial costs of their flapping wings. Matching wingbeat frequency to a mechanical resonance can be energetically favourable, but also poses control challenges. Many insects use frequency modulation on long timescales, but wingstroke-to-wingstroke modulation of wingbeat frequencies in a resonant spring-wing system is potentially costly because muscles must work against the elastic flight system. Nonetheless, rapid frequency and amplitude modulation may be a useful control modality. The hawkmoth Manduca sexta has an elastic thorax capable of storing and returning significant energy. However, its nervous system also has the potential to modulate the driving frequency of flapping because its flight muscles are synchronous. We tested whether hovering hawkmoths rapidly alter frequency during perturbations with vortex rings. We observed both frequency modulation (32% around mean) and amplitude modulation (37%) occurring over several wingstrokes. Instantaneous phase analysis of wing kinematics revealed that more than 85% of perturbation responses required active changes in neurogenic driving frequency. Unlike their robotic counterparts that abdicate frequency modulation for energy efficiency, synchronous insects use wingstroke-to-wingstroke frequency modulation despite the power demands required for deviating from resonance.

Measuring power input, power output and energy conversion efficiency in un-instrumented flying birds

Cost of flight at various speeds is a crucial determinant of flight behaviour in birds. Aerodynamic models, predicting that mechanical power (Pmech) varies with flight speed in a U-shaped manner, have been used together with an energy conversion factor (efficiency) to estimate metabolic power (Pmet). Despite few empirical studies, efficiency has been assumed constant across flight speeds at 23%. Ideally, efficiency should be estimated from measurements of both Pmech and Pmet in un-instrumented flight. Until recently, progress has been hampered by methodological constraints. The main aim of this study was to evaluate recently developed techniques and estimate flight efficiency across flight speeds. We used the 13C-labelled sodium bicarbonate method (NaBi) and particle image velocimetry (PIV) to measure Pmet and Pmech in blackcaps flying in a wind tunnel. We also cross-validated measurements made by NaBi with quantitative magnetic resonance (QMR) body composition analysis in yellow-rumped warblers. We found that Pmet estimated by NaBi was ∼12% lower than corresponding values estimated by QMR. Pmet varied in a U-shaped manner across flight speeds in blackcaps, but the pattern was not statistically significant. Pmech could only be reliably measured for two intermediate speeds and estimated efficiency ranged between 14% and 22% (combining the two speeds for raw and weight/lift-specific power, with and without correction for the ∼12% difference between NaBi and QMR), which were close to the currently used default value. We conclude that NaBi and PIV are viable techniques, allowing researchers to address some of the outstanding questions regarding bird flight energetics.

The Aerodynamics and Power Requirements of Forward Flapping Flight in the Mango Stem Borer Beetle (Batocera rufomaculata)

The need for long dispersal flights can drive selection for behavioral, physiological, and biomechanical mechanisms to reduce the energy spent flying. However, some energy loss during the transfer of momentum from the wing to the fluid is inevitable, and inherent to the fluid-wing interaction. Here, we analyzed these losses during the forward flight of the mango stem borer (Batocera rufomaculata). This relatively large beetle can disperse substantial distances in search of new host trees, and laboratory experiments have demonstrated continuous tethered flights that can last for up to an hour. We flew the beetles tethered in a wind tunnel and used high-speed videography to estimate the aerodynamic power from their flapping kinematics and particle image velocimetry (PIV) to evaluate drag and kinetic energy from their unsteady wakes. To account for tethering effects, we measured the forces applied by the beetles on the tether arm holding them in place. The drag of the flying beetle over the flapping cycle, estimated from the flow fields in the unsteady wake, showed good agreement with direct measurement of mean horizontal force. Both measurements showed that total drag during flight is ∼5-fold higher than the parasite drag on the body. The aerodynamic power estimated from both the motion of the wings, using a quasi-steady blade-element model, and the kinetic energy in the wake, gave mean values of flight-muscle mass-specific power of 87 and 65 W kg muscle^-1, respectively. A comparison of the two values suggests that ∼25% of the energy is lost within the fluid due to turbulence and heat. The muscle mass-specific power found here is low relative to the maximal power output reported for insect flight muscles. This can be attributed to reduce weight support during tethered flight or to operation at submaximal output that may ensure a supply of metabolic substrates to the flight muscles, thus delaying their fatigue during long-distance flights.

Kinematics Measurement and Power Requirements of Fruitflies at Various Flight Speeds

Energy expenditure is a critical characteristic in evaluating the flight performance of flying insects. To investigate how the energy cost of small-sized insects varies with flight speed, we measured the detailed wing and body kinematics in the full speed range of fruitflies and computed the aerodynamic forces and power requirements of the flies. As flight speed increases, the body angle decreases and the stroke plane angle increases; the wingbeat frequency only changes slightly; the geometrical angle of attack in the middle upstroke increases; the stroke amplitude first decreases and then increases. The mechanical power of the fruitflies at all flight speeds is dominated by aerodynamic power (inertial power is very small), and the magnitude of aerodynamic power in upstroke increases significantly at high flight speeds due to the increase of the drag and the flapping velocity of the wing. The specific power (power required for flight divided by insect weigh) changes little when the advance ratio is below about 0.45 and afterwards increases sharply. That is, the specific power varies with flight speed according to a J-shaped curve, unlike those of aircrafts, birds and large-sized insects which vary with flight speed according to a U-shaped curve.

Indirect actuation reduces flight power requirements in Manduca sexta via elastic energy exchange

In many insects, wing movements are generated indirectly via exoskeletal deformations. Measurements of inertial and aerodynamic power suggest that elastic recovery of energy between wingstrokes might reduce power requirements of flight. We tested three questions. (1) Can the thorax itself provide significant energy return? (2) Does a simple damped elastic model describe the bulk mechanical behaviour? (3) Are different regions of the thorax specialized for elastic energy exchange? We measured deformation mechanics of the hawkmoth Manduca sexta thorax by recording the force required to sinusoidally deform the thorax over a wide frequency range. Elastic energy storage in the thorax is sufficient to minimize power requirements. However, we find that a structural (frequency-independent) damping model, not a viscoelastic model, best describes the thorax's mechanical properties. We next performed complementary experiments on a structurally damped homogeneous hemisphere. In contrast to the hemispherical shell, we find that mechanical coupling between different regions of the thorax improves energy exchange performance and that local mechanical properties depend on global strain patterns. Specifically, the scutum region provides energy recovery with low dissipation, while the majority of energy loss occurred in the wing hinge region, highlighting the specificity of thorax regions for flight energetics.

Integrating the influence of weather into mechanistic models of butterfly movement

BACKGROUND

Understanding the factors influencing movement is essential to forecasting species persistence in a changing environment. Movement is often studied using mechanistic models, extrapolating short-term observations of individuals to longer-term predictions, but the role of weather variables such as air temperature and solar radiation, key determinants of ectotherm activity, are generally neglected. We aim to show how the effects of weather can be incorporated into individual-based models of butterfly movement thus allowing analysis of their effects.

METHODS

We constructed a mechanistic movement model and calibrated it with high precision movement data on a widely studied species of butterfly, the meadow brown (Maniola jurtina), collected over a 21-week period at four sites in southern England. Day time temperatures during the study ranged from 14.5 to 31.5 °C and solar radiation from heavy cloud to bright sunshine. The effects of weather are integrated into the individual-based model through weather-dependent scaling of parametric distributions representing key behaviours: the durations of flight and periods of inactivity.

RESULTS

Flight speed was unaffected by weather, time between successive flights increased as solar radiation decreased, and flight duration showed a unimodal response to air temperature that peaked between approximately 23 °C and 26 °C. After validation, the model demonstrated that weather alone can produce a more than two-fold difference in predicted weekly displacement.

CONCLUSIONS

Individual Based models provide a useful framework for integrating the effect of weather into movement models. By including weather effects we are able to explain a two-fold difference in movement rate of M. jurtina consistent with inter-annual variation in dispersal measured in population studies. Climate change for the studied populations is expected to decrease activity and dispersal rates since these butterflies already operate close to their thermal optimum.

Mechanical power curve measured in the wake of pied flycatchers indicates modulation of parasite power across flight speeds

How aerodynamic power required for animal flight varies with flight speed determines optimal speeds during foraging and migratory flight. Despite its relevance, aerodynamic power provides an elusive quantity to measure directly in animal flight. Here, we determine the aerodynamic power from wake velocity fields, measured using tomographical particle image velocimetry, of pied flycatchers flying freely in a wind tunnel. We find a shallow U-shaped power curve, which is flatter than expected by theory. Based on how the birds vary body angle with speed, we speculate that the shallow curve results from increased body drag coefficient and body frontal area at lower flight speeds. Including modulation of body drag in the model results in a more reasonable fit with data than the traditional model. From the wake structure, we also find a single starting vortex generated from the two wings during the downstroke across flight speeds (1-9 m s^-1). This is accomplished by the arm wings interacting at the beginning of the downstroke, generating a unified starting vortex above the body of the bird. We interpret this as a mechanism resulting in a rather uniform downwash and low induced power, which can help explain the higher aerodynamic performance in birds compared with bats.

Aerodynamics of manoeuvring flight in brown long-eared bats (Plecotus auritus)

In this study, we explicitly examine the aerodynamics of manoeuvring flight in animals. We studied brown long-eared bats flying in a wind tunnel while performing basic sideways manoeuvres. We used particle image velocimetry in combination with high-speed filming to link aerodynamics and kinematics to understand the mechanistic basis of manoeuvres. We predicted that the bats would primarily use the downstroke to generate the asymmetries for the manoeuvre since it has been shown previously that the majority of forces are generated during this phase of the wingbeat. We found instead that the bats more often used the upstroke than they used the downstroke for this. We also found that the bats used both drag/thrust-based and lift-based asymmetries to perform the manoeuvre and that they even frequently switch between these within the course of a manoeuvre. We conclude that the bats used three main modes: lift asymmetries during downstroke, thrust/drag asymmetries during downstroke and thrust/drag asymmetries during upstroke. For future studies, we hypothesize that lift asymmetries are used for fast turns and thrust/drag for slow turns and that the choice between up- and downstroke depends on the timing of when the bat needs to generate asymmetries.

Flight in Ground Effect Dramatically Reduces Aerodynamic Costs in Bats

Most flying animals, from insects to seabirds [1], perform flights close to ground or water when taking off or landing [2], drinking, and feeding [3-5] or when traveling near water surfaces [1, 6, 7]. When flying close to a surface within approximately one wingspan, the surface acts as an aerodynamic mirror, interrupting the downwash [8, 9], resulting in increased pressure underneath the wing and suppression of wingtip vortex development [10]. This aerodynamic interaction lowers the energy added to the air by the animal, reducing the cost of flying. Modeling suggests that flapping wings in ground effect can affect the expected power savings compared to gliding flight, either positively or negatively, depending on the wing motion [11-13]. Although aerodynamic theory predicts substantial power reductions when animals fly in ground effect [4-6, 9, 11, 12], quantitative measurements of savings are lacking. Here, we show, through wake-based power measurements, that Daubenton's bats utilize 29% less aerodynamic power when flying in compared to out of ground effect, which is twice the predicted savings. Contrary to theoretical predictions [4-6, 9, 11, 12] we find no variation in savings with distance above ground when in ground effect. Given alterations in kinematics with ground proximity, we hypothesize that modulation of wing kinematics raises the achievable benefit from ground effect relative to current model predictions. The savings from ground effect are comparable to formation flight [14, 15] but are not limited to large bird species. Instead, ground effect is experienced by most flying animals and may have facilitated the evolution of powered animal flight.

Lift and power in fruitflies in vertically-ascending flight

We measured the wing kinematics of fruitflies in both vertically-ascending and hovering flights and studied the aerodynamic forces and power in the two flight modes. The average ascending velocity is 0.45 m s^-1; the stroke plane angle and the stroke frequency are the same as that in hovering flight, whilst the stroke amplitude is increased by 12% and the wing angle of attack in the latter half of a down- and upstroke both increased by 10%. Flow analysis shows that during ascending, the flies experience a downward inflow which reduces the effective angle of attack considerably. This problem is overcome by the increases in the stroke amplitude and the angle of attack, which result in a larger wing drag. As a result, the power at ascending is increased by 36% over that at hovering. Two very interesting observations were made. (1) Using the same power, level-forward flight can be about four times as fast as ascending flight. (2) Power for ascending flight is the same as that for carrying a load about 27% of the insect's weight at hovering.

Body lift, drag and power are relatively higher in large-eared than in small-eared bat species

Bats navigate the dark using echolocation. Echolocation is enhanced by external ears, but external ears increase the projected frontal area and reduce the streamlining of the animal. External ears are thus expected to compromise flight efficiency, but research suggests that very large ears may mitigate the cost by producing aerodynamic lift. Here we compare quantitative aerodynamic measures of flight efficiency of two bat species, one large-eared (Plecotus auritus) and one small-eared (Glossophaga soricina), flying freely in a wind tunnel. We find that the body drag of both species is higher than previously assumed and that the large-eared species has a higher body drag coefficient, but also produces relatively more ear/body lift than the small-eared species, in line with prior studies on model bats. The measured aerodynamic power of P. auritus was higher than predicted from the aerodynamic model, while the small-eared species aligned with predictions. The relatively higher power of the large-eared species results in lower optimal flight speeds and our findings support the notion of a trade-off between the acoustic benefits of large external ears and aerodynamic performance. The result of this trade-off would be the eco-morphological correlation in bat flight, with large-eared bats generally adopting slow-flight feeding strategies.

Flight capacities of yellow-legged hornet (Vespa velutina nigrithorax, Hymenoptera: Vespidae) workers from an invasive population in Europe

The invasive yellow-legged hornet, Vespa velutina nigrithorax Lepeletier, 1836 (Hymenoptera: Vespidae), is native to Southeast Asia. It was first detected in France (in the southwest) in 2005. It has since expanded throughout Europe and has caused significant harm to honeybee populations. We must better characterize the hornet’s flight capacity to understand the species’ success and develop improved control strategies. Here, we carried out a study in which we quantified the flight capacities of V. velutina workers using computerized flight mills. We observed that workers were able to spend around 40% of the daily 7-hour flight tests flying. On average, they flew 10km to 30km during each flight test, although there was a large amount of variation. Workers sampled in early summer had lower flight capacities than workers sampled later in the season. Flight capacity decreased as workers aged. However, in the field, workers probably often die before this decrease becomes significant. During each flight test, workers performed several continuous flight phases of variable length that were separated by rest phases. Based on the length of those continuous flight phases and certain key assumptions, we estimated that V. velutina colony foraging radius is at least 700 m (half that in early summer); however, some workers are able to forage much farther. While these laboratory findings remain to be confirmed by field studies, our results can nonetheless help inform V. velutina biology and control efforts.