Kinematic flexibility allows bumblebees to increase energetic efficiency when carrying heavy loads

Efficiency and control trade-offs and work loop characteristics of flapping-wing systems with synchronous and asynchronous muscles

Natural fliers with flapping wings face the dual challenges of energy efficiency and active control of wing motion for achieving diverse modes of flight. It is hypothesized that flapping-wing systems use resonance to improve muscle mechanical output energy efficiency, a principle often followed in bioinspired flapping-wing robots. However, resonance can limit the degree of active control, a trade-off rooted in the dynamics of wing motor systems and can be potentially reflected in muscle work loops. To systematically investigate how energy efficiency trades off with active control of wingbeat frequency and amplitude, here we developed a parsimonious model of the wing motor system with either synchronous or asynchronous power muscles. We then non-dimensionalized the model and performed simulations to examine model characteristics as functions of Weis-Fogh number and dimensionless flapping frequency. For synchronous power muscles, our model predicts that energy efficiency trades off with frequency control rather than amplitude control at high Weis-Fogh numbers; however, no such trade-off was found for models with asynchronous power muscles. The work loops alone are insufficient to fully capture wing motor characteristics, and therefore fail to directly reflect the trade-offs. Finally, using simulation results, we predict that natural fliers function at Weis-Fogh numbers close to 1.

The Weis-Fogh Number Describes Resonant Performance Tradeoffs in Flapping Insects

Dimensionless numbers have long been used in comparative biomechanics to quantify competing scaling relationships and connect morphology to animal performance. While common in aerodynamics, few relate the biomechanics of the organism to the forces produced on the environment during flight. We discuss the Weis-Fogh number, N, as a dimensionless number specific to flapping flight, which describes the resonant properties of an insect and resulting tradeoffs between energetics and control. Originally defined by Torkel Weis-Fogh in his seminal 1973 paper, N measures the ratio of peak inertial to aerodynamic torque generated by an insect over a wingbeat. In this perspectives piece, we define N for comparative biologists and describe its interpretations as a ratio of torques and as the width of an insect's resonance curve. We then discuss the range of N realized by insects and explain the fundamental tradeoffs between an insect's aerodynamic efficiency, stability, and responsiveness that arise as a consequence of variation in N, both across and within species. N is therefore an especially useful quantity for comparative approaches to the role of mechanics and aerodynamics in insect flight.

The Functions of Phasic Wing-Tip Folding on Flapping-Wing Aerodynamics

Insects produce a variety of highly acrobatic maneuvers in flight owing to their ability to achieve various wing-stroke trajectories. Among them, beetles can quickly change their flight velocities and make agile turns. In this work, we report a newly discovered phasic wing-tip-folding phenomenon and its aerodynamic basis in beetles. The wings' flapping trajectories and aerodynamic forces of the tethered flying beetles were recorded simultaneously via motion capture cameras and a force sensor, respectively. The results verified that phasic active spanwise-folding and deployment (PASFD) can exist during flapping flight. The folding of the wing-tips of beetles significantly decreased aerodynamic forces without any changes in flapping frequency. Specifically, compared with no-folding-and-deployment wings, the lift and forward thrust generated by bilateral-folding-and-deployment wings reduced by 52.2% and 63.0%, respectively. Moreover, unilateral-folding-and-deployment flapping flight was found, which produced a lateral force (8.65 mN). Therefore, a micro-flapping-wing mechanism with PASFD was then designed, fabricated, and tested in a motion capture and force measurement system to validate its phasic folding functions and aerodynamic performance under different operating frequencies. The results successfully demonstrated a significant decrease in flight forces. This work provides valuable insights for the development of flapping-wing micro-air-vehicles with high maneuverability.

Flying, nectar-loaded honey bees conserve water and improve heat tolerance by reducing wingbeat frequency and metabolic heat production

Heat waves are becoming increasingly common due to climate change, making it crucial to identify and understand the capacities for insect pollinators, such as honey bees, to avoid overheating. We examined the effects of hot, dry air temperatures on the physiological and behavioral mechanisms that honey bees use to fly when carrying nectar loads, to assess how foraging is limited by overheating or desiccation. We found that flight muscle temperatures increased linearly with load mass at air temperatures of 20 or 30 °C, but, remarkably, there was no change with increasing nectar loads at an air temperature of 40 °C. Flying, nectar-loaded bees were able to avoid overheating at 40 °C by reducing their flight metabolic rates and increasing evaporative cooling. At high body temperatures, bees apparently increase flight efficiency by lowering their wingbeat frequency and increasing stroke amplitude to compensate, reducing the need for evaporative cooling. However, even with reductions in metabolic heat production, desiccation likely limits foraging at temperatures well below bees' critical thermal maxima in hot, dry conditions.

Bumblebees negotiate a trade-off between nectar quality and floral biomechanics

How and why pollinators choose which flowers to visit are fundamental, multifaceted questions in pollination biology, yet most studies of floral traits measure simple relative preferences. Here, we used vertically and horizontally oriented slippery-surfaced artificial flowers to test whether bumblebees could make a trade-off between floral handling difficulty and nectar sucrose concentration. We quantified foraging energetics, thereby resolving the rationale behind the bees' foraging decisions. The bees chose flowers with either a high handling cost or low sucrose concentration, depending on which was the energetically favorable option. Their behavior agreed with the critical currency being the rate of energy return (net energy collected per unit time), not energetic efficiency (net energy collected per unit energy spent). This suggests that bumblebees prioritize immediate carbohydrate flow to the nest rather than energy gain over the working lifespan of each bee. Trade-off paradigms like these are a powerful approach for quantifying pollinator trait preferences.

Flies adaptively control flight to compensate for added inertia

Animal locomotion is highly adaptive, displaying a large degree of flexibility, yet how this flexibility arises from the integration of mechanics and neural control remains elusive. For instance, animals require flexible strategies to maintain performance as changes in mass or inertia impact stability. Compensatory strategies to mechanical loading are especially critical for animals that rely on flight for survival. To shed light on the capacity and flexibility of flight neuromechanics to mechanical loading, we pushed the performance of fruit flies (Drosophila) near its limit and implemented a control theoretic framework. Flies with added inertia were placed inside a virtual reality arena which permitted free rotation about the vertical (yaw) axis. Adding inertia increased the fly's response time yet had little influence on overall gaze stabilization performance. Flies maintained stability following the addition of inertia by adaptively modulating both visuomotor gain and damping. By contrast, mathematical modelling predicted a significant decrease in gaze stabilization performance. Adding inertia altered saccades, however, flies compensated for the added inertia by increasing saccade torque. Taken together, in response to added inertia flies increase reaction time but maintain flight performance through adaptive neural control. Overall, adding inertia decreases closed-loop flight robustness. Our work highlights the flexibility and capacity of motor control in flight.

Nutritional inequalities structure worker division of labor in social insects

Eusocial insect societies are fundamentally non-egalitarian. The reproductive caste 'wins' in terms of resource accumulation, whereas non-reproductive workers 'lose'. Here, we argue that the division of labor among workers is also organized by nutritional inequalities. Across vastly different social systems and a variety of hymenopteran species, there is a recurrent pattern of lean foragers and corpulent nest workers. Experimental manipulations confirm causal associations between nutritional differences, associated molecular pathways, and behavioral roles in insect societies. The comparative and functional genomic data suggest that a conserved toolkit of core metabolic, nutrient storage, and signaling genes has evolved to regulate the social insect division of labor. Thus, the unequal distribution of food resources can be considered a fundamental organizing factor in the social insect division of labor.

The potential underlying mechanisms during learning flights

Hymenopterans, such as bees and wasps, have long fascinated researchers with their sinuous movements at novel locations. These movements, such as loops, arcs, or zigzags, serve to help insects learn their surroundings at important locations. They also allow the insects to explore and orient themselves in their environment. After they gained experience with their environment, the insects fly along optimized paths guided by several guidance strategies, such as path integration, local homing, and route-following, forming a navigational toolkit. Whereas the experienced insects combine these strategies efficiently, the naive insects need to learn about their surroundings and tune the navigational toolkit. We will see that the structure of the movements performed during the learning flights leverages the robustness of certain strategies within a given scale to tune other strategies which are more efficient at a larger scale. Thus, an insect can explore its environment incrementally without risking not finding back essential locations.

Experimental studies suggest differences in the distribution of thorax elasticity between insects with synchronous and asynchronous musculature

Insects have developed diverse flight actuation mechanisms, including synchronous and asynchronous musculature. Indirect actuation, used by insects with both synchronous and asynchronous musculature, transforms thorax exoskeletal deformation into wing rotation. Though thorax deformation is often attributed exclusively to muscle tension, the inertial and aerodynamic forces generated by the flapping wings may also contribute. In this study, a tethered flight experiment was used to simultaneously measure thorax deformation and the inertial/aerodynamic forces acting on the thorax generated by the flapping wing. Compared to insects with synchronous musculature, insects with asynchronous muscle deformed their thorax 60% less relative to their thorax diameter and their wings generated 2.8 times greater forces relative to their body weight. In a second experiment, dorsalventral thorax stiffness was measured across species. Accounting for weight and size, the asynchronous thorax was on average 3.8 times stiffer than the synchronous thorax in the dorsalventral direction. Differences in thorax stiffness and forces acting at the wing hinge led us to hypothesize about differing roles of series and parallel elasticity in the thoraxes of insects with synchronous and asynchronous musculature. Specifically, wing hinge elasticity may contribute more to wing motion in insects with asynchronous musculature than in those with synchronous musculature.

Distinct forms of resonant optimality within insect indirect flight motors

Insect flight motors are extraordinary natural structures that operate efficiently at high frequencies. Structural resonance is thought to play a role in ensuring efficient motor operation, but the details of this role are elusive. While the efficiency benefits associated with resonance may be significant, a range of counterintuitive behaviours are observed. In particular, the relationship between insect wingbeat frequencies and thoracic natural frequencies is uncertain, with insects showing wingbeat frequency modulation over both short and long time scales. Here, we offer new explanations for this modulation. We show how, in linear and nonlinear models of an indirect flight motor, resonance is not a unitary state at a single frequency, but a complex cluster of distinct and mutually exclusive states, each representing a different form of resonant optimality. Additionally, by characterizing the relationship between resonance and the state of negative work absorption within the motor, we demonstrate how near-perfect resonant energetic optimality can be maintained over significant wingbeat frequency ranges. Our analysis leads to a new conceptual model of flight motor operation: one in which insects are not energetically restricted to a precise wingbeat frequency, but instead are robust to changes in thoracic and environmental properties-an illustration of the extraordinary robustness of these natural motors.

How and why do bees buzz? Implications for buzz pollination

Buzz pollination encompasses the evolutionary convergence of specialized floral morphologies and pollinator behaviour in which bees use vibrations (floral buzzes) to remove pollen. Floral buzzes are one of several types of vibrations produced by bees using their thoracic muscles. Here I review how bees can produce these different types of vibrations and discuss the implications of this mechanistic understanding for buzz pollination. I propose that bee buzzes can be categorized according to their mode of production and deployment into: (i) thermogenic, which generate heat with little mechanical vibration; (ii) flight buzzes which, combined with wing deployment and thoracic vibration, power flight; and (iii) non-flight buzzes in which the thorax vibrates but the wings remain mostly folded, and include floral, defence, mating, communication, and nest-building buzzes. I hypothesize that the characteristics of non-flight buzzes, including floral buzzes, can be modulated by bees via modification of the biomechanical properties of the thorax through activity of auxiliary muscles, changing the rate of activation of the indirect flight muscles, and modifying flower handling behaviours. Thus, bees should be able to fine-tune mechanical properties of their floral vibrations, including frequency and amplitude, depending on flower characteristics and pollen availability to optimize energy use and pollen collection.

The function of pitching in Beetle's flight revealed by insect-wearable backpack

The study of insect flight orientation is important for investigating flapping-wing aerodynamics and designing bioinspired micro air vehicles (MAVs). Pitch orientation plays a vital role in flight control, which has been explored less than directional control. In this study, the role of pitching maneuvers in flight was revealed by mounting an insect-wearable backpack on a beetle, which transformed the live insect into a bioelectronic device. The flight status of the cyborg beetle in a large chamber was recorded wirelessly. Accordingly, the pitch angle and forward acceleration showed a strong linear relationship. The coupling of pitch angle and forward acceleration was due to a tilted net aerodynamic force and the induced air drag. Moreover, the left and right subalar muscles of the beetle, a pair of major flight muscles, were electrically stimulated in free flight on demand to pitch up the beetle's body. We demonstrated that the induced nose-up movements were effective for decelerating the beetle in air. The flight orientation findings from the flying cyborgs would inspire a new approach to the study of flapping-wing flight and control of flapping-wing MAVs.

An evaluation of common methods for comparing the scaling of vertical force production in flying insects

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Two methods to measure max vertical force production give similar values in bees

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Interspecific differences in force-scaling depend on the body size metric used

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Only dry mass shows interspecific differences in relative force (% of mass lifted)

Maximum vertical force production (F_vert) is an integral measure of flight performance that generally scales with size. Numerous methods of measuring F_vert and body size are accessible to entomologists, but we do not know whether method selection affects inter- and intraspecific comparisons of F_vert-size scaling. We compared two common techniques for measuring F_vert in bumblebees (Bombus impatiens) and mason bees (Osmia lignaria), and examined F_vert scaling using five size metrics. F_vert results were similar with incremental or asymptotic load-lifting, but scaling analyses were sensitive to the size metric used. Analyses based on some size metrics indicated similar scaling exponents and coefficients between species, whereas other metrics indicated coefficients that differed by up to 18%. Furthermore, F_vert showed isometry with body lengths and fed and starved masses, but negative allometry with dry mass. We conclude that F_vert can be measured using either incremental or asymptotic loading but choosing a size metric for scaling studies requires careful consideration.

Size constrains oxygen delivery capacity within but not between bumble bee castes

Bumble bees are eusocial, with distinct worker and queen castes that vary strikingly in size and life-history. The smaller workers rely on energetically-demanding foraging flights to collect resources for rearing brood. Queens can be 3 to 4 times larger than workers, flying only for short periods in fall and again in spring after overwintering underground. These differences between castes in size and life history may be reflected in hypoxia tolerance. When oxygen demand exceeds supply, oxygen delivery to the tissues can be compromised. Previous work revealed hypermetric scaling of tracheal system volume of worker bumble bees (Bombus impatiens); larger workers had much larger tracheal volumes, likely to facilitate oxygen delivery over longer distances. Despite their much larger size, queens had relatively small tracheal volumes, potentially limiting their ability to deliver oxygen and reducing their ability to respond to hypoxia. However, these morphological measurements only indirectly point to differences in respiratory capacity. To directly assess size- and caste-related differences in tolerance to low oxygen, we measured critical PO₂ (P_crit; the ambient oxygen level below which metabolism cannot be maintained) during both rest and flight of worker and queen bumble bees. Queens and workers had similar P_crit values during both rest and flight. However, during flight in oxygen levels near the P_crit, mass-specific metabolic rates declined precipitously with mass both across and within castes, suggesting strong size limitations on oxygen delivery, but only during extreme conditions, when demand is high and supply is low. Together, these data suggest that the comparatively small tracheal systems of queen bumble bees do not limit their ability to deliver oxygen except in extreme conditions; they pay little cost for filling body space with eggs rather than tracheal structures.

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.

Effects of abdomen undulation in energy consumption and stability for monarch butterfly

The flight of monarch butterflies is characterized by a relatively large wing, flapping at a relatively low frequency coupled with abdomen undulation. This paper presents the dynamics of a flapping wing flyer that can be applied to the coupled motion of the wing, body, and abdomen at the monarch butterfly scale, which is formulated directly on the configuration manifold. The resulting thorax and abdomen motion as well as the resultant forces are consistent with the flight of a live monarch butterfly. Based on these, beneficial effects of the abdomen undulation in the flight of monarch butterflies are illustrated. For both hover and forward-climbing trajectories, the abdomen undulation results in a reduction of the energy and power consumption. Furthermore, the Floquet stability analysis shows that the periodic orbits associated with both flight modes are stable. In particular, the abdomen undulation improves the stability. Compared to the dynamics of hawkmoth, bumblebee, and fruitfly models, the monarch possesses superior stability properties.