The constraints of body size on aerodynamics and energetics in flying fruit flies: an integrative view

Reynolds number and thus body size may potentially limit aerodynamic force production in flying insects due to relative changes of viscous forces on the beating wings. By comparing four different species of fruit flies similar in shape but with different body mass, we have investigated how small insects cope with changes in fluid mechanical constraints on power requirements for flight and the efficiency with which chemical energy is turned into aerodynamic flight forces. The animals were flown in a flight arena in which stroke kinematics, aerodynamic force production, and carbon dioxide release were measured within the entire working range of the flight motor. The data suggest that during hovering performance mean lift coefficient for flight is higher in smaller animals than in their larger relatives. This result runs counter to predictions based on conventional aerodynamic theory and suggests subtle differences in stroke kinematics between the animals. Estimates in profile power requirements based on high drag coefficient suggest that among all tested species of fruit flies elastic energy storage might not be required to minimize energetic expenditures during flight. Moreover, muscle efficiency significantly increases with increasing body size whereas aerodynamic efficiency tends to decrease with increasing size or Reynolds number. As a consequence of these two opposite trends, total flight efficiency tends to increase only slightly within the 6-fold range of body sizes. Surprisingly, total flight efficiency in fruit flies is broadly independent of different profile power estimates and typically yields mean values between 2–4%.     

Aerial locomotion in flies and robots: kinematic control and aerodynamics of oscillating wings

Flight in flies results from a feedback cascade in which the animal converts mechanical power produced by the flight musculature into aerodynamic forces. A major goal of flight research is to understand the functional significance of the various components in this cascade ranging from the generation of the neural code, the control of muscle mechanical power output, wing kinematics and unsteady aerodynamic mechanisms. Here, I attempted to draw a broad outline on fluid dynamic mechanisms found in flapping insect wings such as leading edge vorticity, rotational circulation and wake capture momentum transfer, as well as on the constraints of flight force control by the neuromuscular system of the fruit fly Drosophila. This system-level perspective on muscle control and aerodynamic mechanisms is thought to be a fundamental bridge in any attempt to link the function and performance of the various flight components with their particular role for wing motion and aerodynamic control in the behaving animal. Eventually, this research might facilitate the development of man-made biomimetic autonomous micro air vehicles using flapping wing motion for propulsion that are currently under construction by engineers.     

Alternative N-terminal regions of Drosophila myosin heavy chain tune muscle kinetics for optimal power output

We assessed the influence of alternative versions of a region near the N-terminus of Drosophila myosin heavy chain on muscle mechanical properties. Previously, we exchanged N-terminal regions (encoded by alternative exon 3s) between an embryonic (EMB) isoform and the indirect flight muscle isoform (IFI) of myosin, and demonstrated that it influences solution ATPase rates and in vitro actin sliding velocity. Because each myosin is expressed in Drosophila indirect flight muscle, in the absence of other myosin isoforms, this allows for muscle mechanical and whole organism locomotion assays. We found that exchanging the flight muscle specific exon 3 region into the embryonic isoform (EMB-3b) increased maximum power generation (P(max)) and optimal frequency of power generation (f(max)) threefold and twofold compared to fibers expressing EMB, whereas exchanging the embryonic exon 3 region into the flight muscle isoform (IFI-3a) decreased P(max) and f(max) to approximately 80% of IFI fiber values. Drosophila expressing IFI-3a exhibited a reduced wing beat frequency compared to flies expressing IFI, which optimized power generation from their kinetically slowed flight muscle. However, the slower wing beat frequency resulted in a substantial loss of aerodynamic power as manifest in decreased flight performance of IFI-3a compared to IFI. Thus the N-terminal region is important in tuning myosin kinetics to match muscle speed for optimal locomotory performance.     

Optimal trajectories for the short-distance foraging flights of swans

Optimal flight theory relates body measurements (wing span, body cross-section, body mass) and aerodynamic variables (air density, drag, profile and induced power ratios) to the most energy-efficient velocity for long distance migration. For short-range (2-10 km) foraging flights the theory is expanded to include non-negligible costs for take-off and energy savings/losses for climbing to altitude (drag decreases with air density and therefore with altitude). The theory predicts clear differences between Tundra and Trumpeter swans. Generally speaking, for flights between 2 and 10 km Trumpeter swans can be expected to fly approximately 5-10 m lower in altitude and 1-2 ms(-1)more slowly than Tundra swans. Moreover, the total energy required for these foraging flights is approximately 150% larger for a Trumpeter than a Tundra swan (80 vs. 120 kJ of direct mechanical energy for a 5 km flight), suggesting that Trumpeter swans may be less inclined to take-off than Tundra swans. These factors indicate that even Trumpeters native to the area (as opposed to recently translocated) would be more vulnerable to hunting than native Tundra swans. The expanded theory is compared to observations made in Utah's Bear River Migratory Bird Refuge.     

Ambient temperature affects free-flight performance in the fruit fly Drosophila melanogaster

To gain insight into how temperature affects locomotor performance in insects, the limits of flight performance have been estimated in freely flying fruit flies Drosophila melanogaster by determining the maximum load that a fly could carry following take-off. At a low ambient temperature of 15 °C, muscle mechanical power output matches the minimum power requirements for hovering flight. Aerodynamic force production rises with increasing temperature and eventually saturates at a flight force that is roughly equal to 2.1 times the body mass. Within the two-fold range of different body sizes, maximum flight force production during free flight does not decrease with decreasing body size as suggested by standard aerodynamic theories. Estimations of flight muscle mechanical power output yields a peak performance of 110 W kg⁻¹ muscle tissue for short-burst flight that was measured at an ambient temperature of 30 °C. With respect to the uncertainties in estimating muscle mechanical power during free flight, the estimated values are similar to those that were published for flight under tethered flight conditions. Accepted: 5 January 1999     

Vortexlet models of flapping flexible wings show tuning for force production and control

Insect wings are compliant structures that experience deformations during flight. Such deformations have recently been shown to substantially affect induced flows, with appreciable consequences to flight forces. However, there are open questions related to the aerodynamic mechanisms underlying the performance benefits of wing deformation, as well as the extent to which such deformations are determined by the boundary conditions governing wing actuation together with mechanical properties of the wing itself. Here we explore aerodynamic performance parameters of compliant wings under periodic oscillations, subject to changes in phase between wing elevation and pitch, and magnitude and spatial pattern of wing flexural stiffness. We use a combination of computational structural mechanics models and a 2D computational fluid dynamics approach to ask how aerodynamic force production and control potential are affected by pitch/elevation phase and variations in wing flexural stiffness. Our results show that lift and thrust forces are highly sensitive to flexural stiffness distributions, with performance optima that lie in different phase regions. These results suggest a control strategy for both flying animals and engineering applications of micro-air vehicles.     

Maximal horizontal flight performance of hummingbirds: effects of body mass and molt

Hovering and fast forward flapping represent two strenuous types of flight that differ in aerodynamic power requirement. Maximal capabilities of ruby-throated hummingbirds (Archilochus colubris) in hovering and forward flight were compared under varying body mass and wing area. The capability to hover in low-density gas mixtures was adversely affected by body mass, whereas the capability to fly in a wind tunnel did not show any adverse mass effect. Molting birds that lost primary flight feathers and reduced wing area also displayed mass loss and loss of aerodynamic power and flight speed. This suggests that maximal flight speed is insensitive to short-term perturbations of body mass but that molting is stressful and reduces the birds' speed and capacity for chase and escape. Hummingbirds' flight behavior in confined space was also investigated. Birds reduced their speeds flying through a narrow tube to approximately one-fifth of that in the wind tunnel and did not display differences under varying body mass and wing area. Hence, performance in the flight tube was submaximal and did not correlate with performance variation in the wind tunnel. For ruby-throated hummingbirds, both maximal mass-specific aerodynamic power derived from hovering performance in low-density air media and maximal flight velocity measured in the wind tunnel were invariant with body mass.     

Morphological and kinematic basis of the hummingbird flight stroke: scaling of flight muscle transmission ratio

Hummingbirds (Trochilidae) are widely known for their insect-like flight strokes characterized by high wing beat frequency, small muscle strains and a highly supinated wing orientation during upstroke that allows for lift production in both halves of the stroke cycle. Here, we show that hummingbirds achieve these functional traits within the limits imposed by a vertebrate endoskeleton and muscle physiology by accentuating a wing inversion mechanism found in other birds and using long-axis rotational movement of the humerus. In hummingbirds, long-axis rotation of the humerus creates additional wing translational movement, supplementing that produced by the humeral elevation and depression movements of a typical avian flight stroke. This adaptation increases the wing-to-muscle-transmission ratio, and is emblematic of a widespread scaling trend among flying animals whereby wing-to-muscle-transmission ratio varies inversely with mass, allowing animals of vastly different sizes to accommodate aerodynamic, biomechanical and physiological constraints on muscle-powered flapping flight.     

Calcium and stretch activation modulate power generation in Drosophila flight muscle

Many animals regulate power generation for locomotion by varying the number of muscle fibers used for movement. However, insects with asynchronous flight muscles may regulate the power required for flight by varying the calcium concentration ([Ca²⁺]). In vivo myoplasmic calcium levels in Drosophila flight muscle have been found to vary twofold during flight and to correlate with aerodynamic power generation and wing beat frequency. This mechanism can only be possible if [Ca²⁺] also modulates the flight muscle power output and muscle kinetics to match the aerodynamic requirements. We found that the in vitro power produced by skinned Drosophila asynchronous flight muscle fibers increased with increasing [Ca²⁺]. Positive muscle power generation started at pCa = 5.8 and reached its maximum at pCa = 5.25. A twofold variation in [Ca²⁺] over the steepest portion of this curve resulted in a two- to threefold variation in power generation and a 1.2-fold variation in speed, matching the aerodynamic requirements. To determine the mechanism behind the variation in power, we analyzed the tension response to muscle fiber-lengthening steps at varying levels of [Ca²⁺]. Both calcium-activated and stretch-activated tensions increased with increasing [Ca²⁺]. However, calcium tension saturated at slightly lower [Ca²⁺] than stretch-activated tension, such that as [Ca²⁺] increased from pCa = 5.7 to pCa = 5.4 (the range likely used during flight), stretch- and calcium-activated tension contributed 80% and 20%, respectively, to the total tension increase. This suggests that the response of stretch activation to [Ca²⁺] is the main mechanism by which power is varied during flight.     

Artificial evolution of the morphology and kinematics in a flapping-wing mini-UAV

Birds demonstrate that flapping-wing flight (FWF) is a versatile flight mode, compatible with hovering, forward flight and gliding to save energy. This extended flight domain would be especially useful on mini-UAVs. However, design is challenging because aerodynamic efficiency is conditioned by complex movements of the wings, and because many interactions exist between morphological (wing area, aspect ratio) and kinematic parameters (flapping frequency, stroke amplitude, wing unfolding). Here we used artificial evolution to optimize these morpho-kinematic features on a simulated 1 kg UAV, equipped with wings articulated at the shoulder and wrist. Flight tests were conducted in a dedicated steady aerodynamics simulator. Parameters generating horizontal flight for minimal mechanical power were retained. Results showed that flight at medium speed (10-12 m s(-1)) can be obtained for reasonable mechanical power (20 W kg(-1)), while flight at higher speed (16-20 m s(-1)) implied increased power (30-50 W kg(-1)). Flight at low speed (6-8 m s(-1)) necessitated unrealistic power levels (70-500 W kg(-1)), probably because our simulator neglected unsteady aerodynamics. The underlying adaptation of morphology and kinematics to varying flight speed were compared to available biological data on the flight of birds.     

The Control of Mechanical Power in Insect Flight

SYNOPSIS. The cost of locomotion is rarely constant, but rathervaries as an animal changes speed and direction. Ultimately,the locomotory muscles of an animal must compensate for thesechanging requirements by varying the amount of mechanical powerthat they produce. In this paper, we consider the mechanismsby which the mechanical power generated by the asynchronousflight muscles of the fruit fly, Drosophila melanogaster, isregulated to match the changing requirements during flight controlbehaviors. Our data come from individual flies flown in a flightarena under conditions in which stroke kinematics, total metaboliccost, and flight force are simultaneously measured. In orderto increase force production, flies must increase wing beatfrequency and wing stroke amplitude. Theory predicts that thesekinematics changes should result in a roughly cubic increasein the mechanical power requirements for flight. However, themechanical energy generated by muscle should increase only linearlywith stroke amplitude and frequency. This discrepancy impliesthat flight muscles must either recruit myofibrils or increaseactivation in order to generate sufficient mechanical powerto sustain elevated force production. By comparing respirometricallymeasured total metabolic power with kinematically estimatedmechanical power, we have calculated that the stress in theflight muscles of Drosophila must increase by 50% to accommodatea doubling of flight force. Electrophysiological evidence suggeststhat this change in stress may be accomplished by an increasedneural drive to the asynchronous muscles, which in turn mayact to recruit additional cross bridges through an increasein cytosolic calcium.     

In Vivo Time-Resolved Microtomography Reveals the Mechanics of the Blowfly Flight Motor

Dipteran flies are amongst the smallest and most agile of flying animals. Their wings are driven indirectly by large power muscles, which cause cyclical deformations of the thorax that are amplified through the intricate wing hinge. Asymmetric flight manoeuvres are controlled by 13 pairs of steering muscles acting directly on the wing articulations. Collectively the steering muscles account for <3% of total flight muscle mass, raising the question of how they can modulate the vastly greater output of the power muscles during manoeuvres. Here we present the results of a synchrotron-based study performing micrometre-resolution, time-resolved microtomography on the 145 Hz wingbeat of blowflies. These data represent the first four-dimensional visualizations of an organism''s internal movements on sub-millisecond and micrometre scales. This technique allows us to visualize and measure the three-dimensional movements of five of the largest steering muscles, and to place these in the context of the deforming thoracic mechanism that the muscles actuate. Our visualizations show that the steering muscles operate through a diverse range of nonlinear mechanisms, revealing several unexpected features that could not have been identified using any other technique. The tendons of some steering muscles buckle on every wingbeat to accommodate high amplitude movements of the wing hinge. Other steering muscles absorb kinetic energy from an oscillating control linkage, which rotates at low wingbeat amplitude but translates at high wingbeat amplitude. Kinetic energy is distributed differently in these two modes of oscillation, which may play a role in asymmetric power management during flight control. Structural flexibility is known to be important to the aerodynamic efficiency of insect wings, and to the function of their indirect power muscles. We show that it is integral also to the operation of the steering muscles, and so to the functional flexibility of the insect flight motor.     

Aerodynamic performance of a hovering hawkmoth with flexible wings: a computational approach

Insect wings are deformable structures that change shape passively and dynamically owing to inertial and aerodynamic forces during flight. It is still unclear how the three-dimensional and passive change of wing kinematics owing to inherent wing flexibility contributes to unsteady aerodynamics and energetics in insect flapping flight. Here, we perform a systematic fluid-structure interaction based analysis on the aerodynamic performance of a hovering hawkmoth, Manduca, with an integrated computational model of a hovering insect with rigid and flexible wings. Aerodynamic performance of flapping wings with passive deformation or prescribed deformation is evaluated in terms of aerodynamic force, power and efficiency. Our results reveal that wing flexibility can increase downwash in wake and hence aerodynamic force: first, a dynamic wing bending is observed, which delays the breakdown of leading edge vortex near the wing tip, responsible for augmenting the aerodynamic force-production; second, a combination of the dynamic change of wing bending and twist favourably modifies the wing kinematics in the distal area, which leads to the aerodynamic force enhancement immediately before stroke reversal. Moreover, an increase in hovering efficiency of the flexible wing is achieved as a result of the wing twist. An extensive study of wing stiffness effect on aerodynamic performance is further conducted through a tuning of Young's modulus and thickness, indicating that insect wing structures may be optimized not only in terms of aerodynamic performance but also dependent on many factors, such as the wing strength, the circulation capability of wing veins and the control of wing movements.     

A Quasi-Steady Lifting Line Theory for Insect-Like Hovering Flight

A novel lifting line formulation is presented for the quasi-steady aerodynamic evaluation of insect-like wings in hovering flight. The approach allows accurate estimation of aerodynamic forces from geometry and kinematic information alone and provides for the first time quantitative information on the relative contribution of induced and profile drag associated with lift production for insect-like wings in hover. The main adaptation to the existing lifting line theory is the use of an equivalent angle of attack, which enables capture of the steady non-linear aerodynamics at high angles of attack. A simple methodology to include non-ideal induced effects due to wake periodicity and effective actuator disc area within the lifting line theory is included in the model. Low Reynolds number effects as well as the edge velocity correction required to account for different wing planform shapes are incorporated through appropriate modification of the wing section lift curve slope. The model has been successfully validated against measurements from revolving wing experiments and high order computational fluid dynamics simulations. Model predicted mean lift to weight ratio results have an average error of 4% compared to values from computational fluid dynamics for eight different insect cases. Application of an unmodified linear lifting line approach leads on average to a 60% overestimation in the mean lift force required for weight support, with most of the discrepancy due to use of linear aerodynamics. It is shown that on average for the eight insects considered, the induced drag contributes 22% of the total drag based on the mean cycle values and 29% of the total drag based on the mid half-stroke values.     

Biomechanics and biomimetics in insect-inspired flight systems

Insect- and bird-size drones—micro air vehicles (MAV) that can perform autonomous flight in natural and man-made environments are now an active and well-integrated research area. MAVs normally operate at a low speed in a Reynolds number regime of 10⁴–10⁵ or lower, in which most flying animals of insects, birds and bats fly, and encounter unconventional challenges in generating sufficient aerodynamic forces to stay airborne and in controlling flight autonomy to achieve complex manoeuvres. Flying insects that power and control flight by flapping wings are capable of sophisticated aerodynamic force production and precise, agile manoeuvring, through an integrated system consisting of wings to generate aerodynamic force, muscles to move the wings and a control system to modulate power output from the muscles. In this article, we give a selective review on the state of the art of biomechanics in bioinspired flight systems in terms of flapping and flexible wing aerodynamics, flight dynamics and stability, passive and active mechanisms in stabilization and control, as well as flapping flight in unsteady environments. We further highlight recent advances in biomimetics of flapping-wing MAVs with a specific focus on insect-inspired wing design and fabrication, as well as sensing systems.This article is part of the themed issue ‘Moving in a moving medium: new perspectives on flight’.     

Genetic Variability of Flight Metabolism in DROSOPHILA MELANOGASTER . II. Relationship between Power Output and Enzyme Activity Levels

The major goal of the studies reported here was to determine the extent to which genetic variation in the activities of the enzymes participating in flight metabolism contributes to variation in the mechanical power output of the flight muscles in Drosophila melanogaster. Isogenic chromosome substitution lines were used to partition the variance of both types of quantitative trait into genetic and environmental components. The mechanical power output was estimated from the wingbeat frequency, wing amplitude and wing morphology of tethered flies by applying the aerodynamic models of Weis-Fogh and Ellington. There were three major results. (1) Chromosomes sampled from natural populations provide a large and repeatable genetic component to the variation in the activities of most of the 15 flight metabolism enzymes investigated and to the variation in the mechanical power output of the flight muscles. (2) The mechanical power output is a sensitive indicator of the rate of flight metabolism (i.e., rate of oxygen consumption during tethered flight). (3) In spite of (1) and (2), no convincing cases of individual enzyme effects on power output were detected, although the number and sign of the significant enzyme-power correlations suggests that such effects are not totally lacking.     

Time-Varying Wing-Twist Improves Aerodynamic Efficiency of Forward Flight in Butterflies

Insect wings can undergo significant chordwise (camber) as well as spanwise (twist) deformation during flapping flight but the effect of these deformations is not well understood. The shape and size of butterfly wings leads to particularly large wing deformations, making them an ideal test case for investigation of these effects. Here we use computational models derived from experiments on free-flying butterflies to understand the effect of time-varying twist and camber on the aerodynamic performance of these insects. High-speed videogrammetry is used to capture the wing kinematics, including deformation, of a Painted Lady butterfly (Vanessa cardui) in untethered, forward flight. These experimental results are then analyzed computationally using a high-fidelity, three-dimensional, unsteady Navier-Stokes flow solver. For comparison to this case, a set of non-deforming, flat-plate wing (FPW) models of wing motion are synthesized and subjected to the same analysis along with a wing model that matches the time-varying wing-twist observed for the butterfly, but has no deformation in camber. The simulations show that the observed butterfly wing (OBW) outperforms all the flat-plate wings in terms of usable force production as well as the ratio of lift to power by at least 29% and 46%, respectively. This increase in efficiency of lift production is at least three-fold greater than reported for other insects. Interestingly, we also find that the twist-only-wing (TOW) model recovers much of the performance of the OBW, demonstrating that wing-twist, and not camber is key to forward flight in these insects. The implications of this on the design of flapping wing micro-aerial vehicles are discussed.     

Effect of hindlimb unweighting on anaerobic metabolism in rat skeletal muscle.

Female Sprague-Dawley rats (250 g) were hindlimb suspended for 14 days, and the effects of hindlimb unweighting (HU) on skeletal muscle anaerobic metabolism were investigated and compared with nonsuspended controls (C). Soleus (SOL), plantaris (PL), and red and white portions of the gastrocnemius (RG, WG) were sampled from resting and stimulated limbs. Muscle atrophy after HU was 46% in SOL, 22% in PL, and 24% in the gastrocnemius compared with nonsuspended C animals. The muscles innervated by the sciatic nerve were stimulated to contract with an occluded circulation for 60 s with trains of supramaximal impulses (100 ms, 80 Hz) at a train rate of 1.0 Hz. Peak tension development by the gastrocnemius-PL-SOL muscle group was similar in HU and C animals (13.0 +/- 1.2, 12.2 +/- 0.8 N/g wet muscle). Occlusion of the circulation before stimulation created a predominantly anaerobic environment, and in situ glycogenolysis and glycolysis were estimated from accumulations of glycolytic intermediates. Total glycogenolysis and glycolysis were higher in the RG muscle of HU animals (74.6 +/- 3.3, 58.1 +/- 1.1) relative to C (57.1 +/- 4.6, 46.1 +/- 2.9 mumol glucosyl units/g dry muscle). Consequently, total anaerobic ATP production was also increased (HU, 251.3 +/- 1.1; C, 204.6 +/- 8.9 mumol ATP/g dry muscle). Total ATP production, glycogenolysis, and glycolysis were unaffected by HU in SOL, PL, and WG muscles. The enhanced glycolytic activity in RG after HU may be attributed to a shift in the metabolic profile from oxidative to glycolytic in the fast oxidative-glycolytic fiber population.     

Comparing aerodynamic efficiency in birds and bats suggests better flight performance in birds

Flight is one of the energetically most costly activities in the animal kingdom, suggesting that natural selection should work to optimize flight performance. The similar size and flight speed of birds and bats may therefore suggest convergent aerodynamic performance; alternatively, flight performance could be restricted by phylogenetic constraints. We test which of these scenarios fit to two measures of aerodynamic flight efficiency in two passerine bird species and two New World leaf-nosed bat species. Using time-resolved particle image velocimetry measurements of the wake of the animals flying in a wind tunnel, we derived the span efficiency, a metric for the efficiency of generating lift, and the lift-to-drag ratio, a metric for mechanical energetic flight efficiency. We show that the birds significantly outperform the bats in both metrics, which we ascribe to variation in aerodynamic function of body and wing upstroke: Bird bodies generated relatively more lift than bat bodies, resulting in a more uniform spanwise lift distribution and higher span efficiency. A likely explanation would be that the bat ears and nose leaf, associated with echolocation, disturb the flow over the body. During the upstroke, the birds retract their wings to make them aerodynamically inactive, while the membranous bat wings generate thrust and negative lift. Despite the differences in performance, the wake morphology of both birds and bats resemble the optimal wake for their respective lift-to-drag ratio regimes. This suggests that evolution has optimized performance relative to the respective conditions of birds and bats, but that maximum performance is possibly limited by phylogenetic constraints. Although ecological differences between birds and bats are subjected to many conspiring variables, the different aerodynamic flight efficiency for the bird and bat species studied here may help explain why birds typically fly faster, migrate more frequently and migrate longer distances than bats.     

Wing flexibility enhances load-lifting capacity in bumblebees

The effect of wing flexibility on aerodynamic force production has emerged as a central question in insect flight research. However, physical and computational models have yielded conflicting results regarding whether wing deformations enhance or diminish flight forces. By experimentally stiffening the wings of live bumblebees, we demonstrate that wing flexibility affects aerodynamic force production in a natural behavioural context. Bumblebee wings were artificially stiffened in vivo by applying a micro-splint to a single flexible vein joint, and the bees were subjected to load-lifting tests. Bees with stiffened wings showed an 8.6 per cent reduction in maximum vertical aerodynamic force production, which cannot be accounted for by changes in gross wing kinematics, as stroke amplitude and flapping frequency were unchanged. Our results reveal that flexible wing design and the resulting passive deformations enhance vertical force production and load-lifting capacity in bumblebees, locomotory traits with important ecological implications.