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Abstract Flapping Wing Micro Air Vehicles (FWMAVs) are susceptible to destabilization following in-flight wing collisions. Recent efforts to enhance FWMAV collision robustness have introduced bio-inspired buckling mechanisms into the wings to passively mitigate destabilizing effects. However, the physical mechanisms by which these joints influence vehicle stability remain poorly understood. To better understand the role of buckling joints in stability, we designed a test beam comprised of two flexible segments interconnected by a buckling joint. The test beam was subjected to a series of quasi-static torque-displacement and dynamic disturbance tests. Results of the test beam were compared against a homogeneous control beam. In quasi-static torque–displacement tests, the test beam dissipated 3 times more energy compared to the control beam as indicated by hysteresis loops. In dynamic disturbance tests, the test beam exhibited reduced path disturbance as described by the Integral of Squared Error (ISE), which quantifies the cumulative deviation of a signal from a reference trajectory over time. Specifically, the test beam reduced average ISE by over 90% from the control averages for 6 out of 9 input conditions tested. The improved trajectory recovery in the test beam results from lower angular impulse and work imparted by the disturbance. Overall, angular work done by the disturbance was 3 times higher for the control beam than the test beam and the maximal average impulse imparted by the disturbance was approximately 5 times higher for the control beam than the test beam at the same input setting. This study advances the understanding of how bio-inspired buckling joints can improve FWMAV stability following collisions. 

AbstractAbstract The annual westward migration of army cutworm moths, Euxoa auxiliaris (Grote), to the Rocky Mountains plays a crucial role in the diet of grizzly bears, Ursus arctos horribilis (L.), which face considerable variability in food availability throughout the year. During the bears’ hyperphagia period, when they must consume an excess of calories to prepare for hibernation, these migrating moths provide a vital and reliable energy source. Seasonal dispersal of E. auxiliaris has been primarily documented through ground observations. However, advancements in radar technology now offer new opportunities to track high-altitude migrations including direction, speed, and wingbeat frequency (WBF) of flying insects. Atmospheric conditions such as temperature and pressure can influence insect flight dynamics, yet their effects on E. auxiliaris remain poorly understood. Therefore, we characterized the WBF of lab-reared E. auxiliaris under 9 combinations of air temperature (7, 13, 24 °C) and pressure (550, 700, 850 hPa). Using a pressure-controlled altitude chamber, individual moths were systematically subjected to combinations of these conditions, and their WBFs were recorded. Our results show that temperature significantly affected WBF, but barometric pressure did not. These findings provide critical baseline data for understanding the flight dynamics of E. auxiliaris and highlight the importance of integrating biological data into radar-based studies of migration. These results enhance the interpretation and utility of radar-derived datasets and contribute to the development of more accurate monitoring tools, particularly for the study of insect migration. 

Abstract Flapping-wing micro-air vehicles (FWMAVs) are an emerging technology inspired by flying insects that show promise in applications favoring maneuverability and vehicle compactness. However, current designs are limited by inefficient energetics, and current dynamical models of the flight system employ limiting assumptions when considering power demands. Here, we derive a system-level model of the insect flight system including the thorax, wing, and wing hinge that can inform insect-inspired FWMAV design. We applied the model to study the flight system of a hawkmoth, and used a genetic algorithm optimization to tune uncertain model parameters to minimize the power required to hover. Results show that performance is improved by utilizing multimodal excitation to produce favorable flapping kinematics. This is achieved by locating the flapping frequency of the moth between the nonlinear resonant frequencies, resulting in magnified flapping response and aerodynamically advantageous phase. The optimal flapping frequency can be predicted from the system’s underlying linear natural frequencies and is roughly 54% of the system’s mean natural frequency. Furthermore, effective solutions are configured so that the timing of the applied load and thorax responses are matched such that little effort is spent reversing the wing stroke. The optimized model parameters and corresponding kinematics show moderate agreement with those reported for the hawkmoth. To maintain hovering flight, the successful moths in the population expend approximately 58.5 W/kg. The system-level model and the governing principles identified here can inform the design of energy efficient FWMAVs moving forward. 

Abstract Flying insects have a robust flight system that allows them to fly even when their forewings are damaged. The insect must adjust wingbeat kinematics to aerodynamically compensate for the loss of wing area. However, the mechanisms that allow insects with asynchronous flight muscle to adapt to wing damage are not well understood. Here, we investigated the phase and amplitude relationships between thorax deformation and flapping angle in tethered flying bumblebees subject to wing clipping and weighting. We used synchronized laser vibrometry and high-speed videography to measure thorax deformation and flapping angle, respectively. We found that changes in wing inertia did not affect thorax deformation amplitude but did influence wingbeat frequency. Increasing wing inertia increased flapping amplitude and caused a phase lag between thorax deformation and flapping angle, whereas decreasing wing inertia did not affect flapping amplitude and caused the flapping angle to lead thorax deformation. Our findings indicate that bumblebees adapt to wing damage by adjusting their wingbeat frequency rather than altering their wing stroke amplitude. Additionally, our results suggest that bumblebees operate near a wing-hinge-dominated resonant frequency, and that moments generated by steering muscles within the wing hinge influence the phase between thorax deformation and wing stroke nontrivially. These insights can inform the design of resilient, insect-inspired flapping-wing micro air vehicles. 

Abstract Flapping insect wings frequently collide with vegetation and other obstacles during flight. Repeated collisions may irreversibly damage the insect wing, thereby compromising the insect’s ability to fly. Further, reaction torques caused by the collision may destabilize the insect and hinder its ability to maneuver. To mitigate the adverse effects of impact, some insect wings are equipped with a flexible joint called a “costal break.” The costal break buckles once it exceeds a critical angle, which is believed to improve flight stability and prevent irreversible wing damage. However, to our knowledge, there are no models to predict the dynamics of the costal break. Through this research, we develop a simple model of an insect wing with a costal break. The wing was modeled as two beams interconnected by a torsional spring, where the stiffness of the torsional spring instantaneously decreases once it has exceeded a critical angle. We conducted a series of static tests to approximate model parameters. Then, we used numerical simulation to estimate the peak stresses and reaction moments experienced by the wing during a collision. We found that costal break increased the wing’s natural frequency by about 50% compared to a homogeneous wing and thus reduced the stress associated with normal flapping. Buckling did not significantly affect peak stresses during collision. Joint buckling reduced the peak reaction moment by about 32%, suggesting that the costal break enhances flight stability. 

Flapping wing insects leverage the dynamics of their compliant flight systems to reduce the energetic costs of flying. However, the extent to which the wing hinge dynamics contribute to the overall system dynamics remains unknown. Therefore, we developed an approach to (i) quantify the passive dynamic properties of the wing hinge and (ii) identify the resonant frequency of the isolated wing/wing hinge system. First, we measured the frequency response relating thorax deformation to wing stroke angle in sacrificed honeybees and army cutworm moths. Using these data, we developed a linear model of the flight system, which we then extended to incorporate nonlinear effects associated with large wing stroke angles. Our findings revealed that both species flap below the linear resonance of the wing hinge. At larger angles, nonlinear aerodynamic damping reduces the resonant frequency, causing both species to flap above wing hinge resonance. We discuss how wing–thorax coupling and muscle dynamics may cause the resonant frequency of the entire flight system to deviate from that of the wing/wing hinge system. Our estimates of wing hinge stiffness and damping provide quantitative parameters that can be incorporated into models of the insect flight system to enable more accurate predictions of resonance behaviour. 

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. 

Abstract Approximately 10% of flowering plant species conceal their pollen within tube-like poricidal anthers. Bees extract pollen from poricidal anthers via floral buzzing, a behavior during which they apply cyclic forces by biting the anther and rapidly contracting their flight muscles. The success of pollen extraction during floral buzzing relies on the direction and magnitude of the forces applied by the bees, yet these forces and forcing directions have not been previously quantified. In this work, we developed an experiment to simultaneously measure the directional forces and thorax kinematics produced by carpenter bees ( Xylocopa californica) during defensive buzzing, a behavior regulated by similar physiological mechanisms as floral buzzing. We found that the buzzing frequencies averaged about 130 Hz and were highly variable within individuals. Force amplitudes were on average 170 mN, but at times reached nearly 500 mN. These forces were 30–80 times greater than the weight of the bees tested. The two largest forces occurred within a plane formed by the bees’ flight muscles. Force amplitudes were moderately correlated with thorax displacement, velocity and acceleration amplitudes but only weakly correlated with buzzing frequency. Linear models developed through this work provide a mechanism to estimate forces produced during non-flight behaviors based on thorax kinematic measurements in carpenter bees. Based on the buzzing frequencies, individual bee’s capacity to vary buzz frequency and predominant forcing directions, we hypothesize that carpenter bees leverage vibration amplification to increase the deformation of poricidal anthers, and hence the amount of pollen ejected. 

Small-scale flapping-wing micro air vehicles (FWMAVs) are an emerging robotic technology with many applications in areas including infrastructure monitoring and remote sensing. However, challenges such as inefficient energetics and decreased payload capacity preclude the useful implementation of FWMAVs. Insects serve as inspiration to FWMAV design owing to their energy efficiency, maneuverability, and capacity to hover. Still, the biomechanics of insects remain challenging to model, thereby limiting the translational design insights we can gather from their flight. In particular, it is not well-understood how wing flexibility impacts the energy requirements of flapping flight. In this work, we developed a simple model of an insect drive train consisting of a compliant thorax coupled to a flexible wing flapping with single-degree-of-freedom rotation in a fluid environment. We applied this model to quantify the energy required to actuate a flapping wing system with parameters based off a hawkmoth Manduca sexta. Despite its simplifications, the model predicts thorax displacement, wingtip deflection and peak aerodynamic force in proximity to what has been measured experimentally in flying moths. We found a flapping system with flexible wings requires 20% less energy than a flapping system with rigid wings while maintaining similar aerodynamic performance. Passive wing deformation increases the effective angle of rotation of the flexible wing, thereby reducing the maximum rotation angle at the base of the wing. We investigated the sensitivity of these results to parameter deviations and found that the energetic savings conferred by the flexible wing are robust over a wide range of parameters. 

Abstract Flapping insect wings collide with vegetation and other obstacles during flight. Repeated collisions may irreversibly damage the insect wing, thereby compromising the insect's ability to fly. Further, reaction torques caused by the collision may destabilize the insect and hinder its ability to maneuver. To mitigate the adverse effects of impact, some insect wings are equipped with a flexible joint called a “costal break.” The costal break buckles once it exceeds a critical angle, which is believed to improve flight stability and prevent irreversible wing damage. However, to our knowledge, there are no models to predict the dynamics of the costal break. Through this research, we develop a simple model of an insect wing with a costal break. The wing was modeled as two beams interconnected by a torsional spring, where the stiffness of the torsional spring instantaneously decreases once it has exceeded a critical angle. We conducted a series of static tests to approximate model parameters. Then, we used numerical simulation to estimate the reaction moments, angular impulse, and peak stresses experienced by the wing during a collision. When evaluated over the duration of an external load, we found that buckling could reduce reaction moments and angular impulse up to 82% and 99%, respectively, compared to a homogeneous wing. This suggests the costal break can enhance flight stability. On the other hand, buckling maximally increased peak stresses two times compared to a homogeneous wing, indicating the costal break does not reduce likelihood of damage under the simplified loading considered.