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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.
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Wing inertia influences the phase and amplitude relationships between thorax deformation and flapping angle in bumblebees
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.
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- Award ID(s):
- 1942810
- PAR ID:
- 10601267
- Publisher / Repository:
- IOP Publishing
- Date Published:
- Journal Name:
- Bioinspiration & Biomimetics
- Volume:
- 20
- Issue:
- 1
- ISSN:
- 1748-3182
- Page Range / eLocation ID:
- 014001
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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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.more » « less
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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.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript
- Journal Article:
- https://doi.org/10.1088/1748-3190/ada1ba
