Distributed elasticity: a high-reward, moderate-risk strategy for efficient control modulation in insect flight

The environments inhabited by flying insects demand a balance between flight efficiency and flight manoeuvrability. In structural oscillators such as the insect indirect flight motor, efficiency (arising from resonance) and manoeuvrability (arising from kinematic modulation) are typically quid pro quo, with modulation incurring penalties to efficiency. Band-type resonance is a phenomenon that offers, in theory, a strategy to lessen these penalties via careful navigation through a band of efficient kinematic states. However, identifying this band is challenging: no methods exist to identify the complete band in realistic motor models, involving elasticity distributed across thorax and wing. Nor are the effects of elasticity distribution on the band known. In this work, we address both open topics. We present a suite of numerical methods for identifying the complete resonance band in general systems. Applying them to models of the insect flight motor with distributed elasticity-thoracic and wing flexion-reveals that distributed elasticity is moderate-risk, but high-reward, morphological feature. Well-tuned distributions expand the resonance band over fourfold, whereas poorly tuned distributions completely extinguish the resonance band. These results indicate that distributing elasticity across the insect flight motor can have an adaptive value, and they motivate broader work identifying distributions across species.