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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. 

Flying insects are thought to achieve energy-efficient flapping flight by storing and releasing elastic energy in their muscles, tendons, and thorax. However, ‘spring-wing’ flight systems consisting of elastic elements coupled to nonlinear, unsteady aerodynamic forces present possible challenges to generating stable and responsive wing motion. The energetic efficiency from resonance in insect flight is tied to the Weis-Fogh number (N), which is the ratio of peak inertial force to aerodynamic force. In this paper, we present experiments and modeling to study how resonance efficiency (which increases withN) influences the control responsiveness and perturbation resistance of flapping wingbeats. In our first experiments, we provide a step change in the input forcing amplitude to a series-elastic spring-wing system and observe the response time of the wing amplitude increase. In our second experiments we provide an external fluid flow directed at the flapping wing and study the perturbed steady-state wing motion. We evaluate both experiments across Weis-Fogh numbers from 1 < N < 10. The results indicate that spring-wing systems designed for maximum energetic efficiency also experience trade-offs in agility and stability as the Weis-Fogh number increases. Our results demonstrate that energetic efficiency and wing maneuverability are in conflict in resonant spring-wing systems, suggesting that mechanical resonance presents tradeoffs in insect flight control and stability. 

An insect’s wingbeat frequency is a critical determinant of its flight performance and varies by multiple orders of magnitude across Insecta. Despite potential energetic benefits for an insect that matches its wingbeat frequency to its resonant frequency, recent work has shown that moths may operate off their resonant peak. We hypothesized that across species, wingbeat frequency scales with resonance frequency to maintain favourable energetics, but with an offset in species that use frequency modulation as a means of flight control. The moth superfamily Bombycoidea is ideal for testing this hypothesis because their wingbeat frequencies vary across species by an order of magnitude, despite similar morphology and actuation. We used materials testing, high-speed videography and a model of resonant aerodynamics to determine how components of an insect’s flight apparatus (stiffness, wing inertia, muscle strain and aerodynamics) vary with wingbeat frequency. We find that the resonant frequency of a moth correlates with wingbeat frequency, but resonance curve shape (described by the Weis-Fogh number) and peak location vary within the clade in a way that corresponds to frequencydependent biomechanical demands. Our results demonstrate that a suite of adaptations in muscle, exoskeleton and wing drive variation in resonant mechanics, reflecting potential constraints on matching wingbeat and resonant frequencies. 

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. 

An insect’s wingbeat frequency is a critical determinant of its flight performance and varies by multiple orders of magnitude across Insecta. Despite potential energetic benefits for an insect that matches its wingbeat frequency to its resonant frequency, recent work has shown that moths may operate off their resonant peak. We hypothesized that across species, wingbeat frequency scales with resonance frequency to maintain favourable energetics, but with an offset in species that use frequency modulation as a means of flight control. The moth superfamily Bombycoidea is ideal for testing this hypothesis because their wingbeat frequencies vary across species by an order of magnitude, despite similar morphology and actuation. We used materials testing, high-speed videography and a model of resonant aerodynamics to determine how components of an insect’s flight apparatus (stiffness, wing inertia, muscle strain and aerodynamics) vary with wingbeat frequency. We find that the resonant frequency of a moth correlates with wingbeat frequency, but resonance curve shape (described by the Weis-Fogh number) and peak location vary within the clade in a way that corresponds to frequency-dependent biomechanical demands. Our results demonstrate that a suite of adaptations in muscle, exoskeleton and wing drive variation in resonant mechanics, reflecting potential constraints on matching wingbeat and resonant frequencies. 

Abstract Since taking flight, insects have undergone repeated evolutionary transitions between two seemingly distinct flight modes^1–3. Some insects neurally activate their muscles synchronously with each wingstroke. However, many insects have achieved wingbeat frequencies beyond the speed limit of typical neuromuscular systems by evolving flight muscles that are asynchronous with neural activation and activate in response to mechanical stretch^2–8. These modes reflect the two fundamental ways of generating rhythmic movement: time-periodic forcing versus emergent oscillations from self-excitation^8–10. How repeated evolutionary transitions have occurred and what governs the switching between these distinct modes remain unknown. Here we find that, despite widespread asynchronous actuation in insects across the phylogeny^3,6, asynchrony probably evolved only once at the order level, with many reversions to the ancestral, synchronous mode. A synchronous moth species, evolved from an asynchronous ancestor, still preserves the stretch-activated muscle physiology. Numerical and robophysical analyses of a unified biophysical framework reveal that rather than a dichotomy, these two modes are two regimes of the same dynamics. Insects can transition between flight modes across a bridge in physiological parameter space. Finally, we integrate these two actuation modes into an insect-scale robot^11–13that enables transitions between modes and unlocks a new self-excited wingstroke strategy for engineered flight. Together, this framework accounts for repeated transitions in insect flight evolution and shows how flight modes can flip with changes in physiological parameters.