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Abstract Powering small-scale flapping flight is challenging, yet insects sustain exceptionally fast wingbeats with ease. Since insects act as tiny biomechanical resonators, tuning their wingbeat frequency to the resonant frequency of their springy thorax and wings could make them more efficient fliers. But operating at resonance poses control problems and potentially constrains wingbeat frequencies within and across species. Resonance may be particularly limiting for the many orders of insects that power flight with specialized muscles that activate in response to mechanical stretch. Here, we test whether insects operate at their resonant frequency. First, we extensively characterize bumblebees and find that they surprisingly flap well above their resonant frequency via interactions between stretch-activation and mechanical resonance. Modeling and robophysical experiments then show that resonance is actually a lower bound for rapid wingbeats in most insects because muscles only pull, not push. Supra-resonance emerges as a general principle of high-frequency flight across five orders of insects from moths to flies. 

Legged animals still outperform many terrestrial robots due to the complex interplay of various component subsystems. Centralization is a potential integrated design axis to help improve the performance of legged robots in variable terrain environments. Centralization arises from the coupling of multiple limbs and joints through mechanics or feedback control. Strong couplings contribute to a whole-body coordinated response (centralized) and weak couplings result in localized responses (decentralized). Rarely are both mechanical and neural couplings considered together in designing centralization. In this study, we use an empirical information theory-based approach to evaluate the emergent centralization of a hexapod robot. We independently vary the mechanical and neural coupling through adjustable joint stiffness and variable coupling of leg controllers, respectively. We found an increase in centralization as neural coupling increased. Changes in mechanical coupling did not significantly affect centralization during walking, but did change the total information processing of the neuromechanical control architecture. Information-based centralization increased with robotic performance in terms of cost of transport and speed, implying that this may be a useful metric in robotic design. 

Synopsis 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.