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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. 

Synopsis The evolution of flight in an early winged insect ancestral lineage is recognized as a key adaptation explaining the unparalleled success and diversification of insects. Subsequent transitions and modifications to flight machinery, including secondary reductions and losses, also play a central role in shaping the impacts of insects on broadscale geographic and ecological processes and patterns in the present and future. Given the importance of insect flight, there has been a centuries-long history of research and debate on the evolutionary origins and biological mechanisms of flight. Here, we revisit this history from an interdisciplinary perspective, discussing recent discoveries regarding the developmental origins, physiology, biomechanics, and neurobiology and sensory control of flight in a diverse set of insect models. We also identify major outstanding questions yet to be addressed and provide recommendations for overcoming current methodological challenges faced when studying insect flight, which will allow the field to continue to move forward in new and exciting directions. By integrating mechanistic work into ecological and evolutionary contexts, we hope that this synthesis promotes and stimulates new interdisciplinary research efforts necessary to close the many existing gaps about the causes and consequences of insect flight evolution.