Search for: All records

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. 

Muscles act through elastic and dissipative elements to mediate movement, which can introduce dissipation and filtering which are important for energetics and control. The high power requirements of flapping flight can be reduced by an insect's exoskeleton, which acts as a spring with frequency-independent material properties under purely sinusoidal deformation. However, this purely sinusoidal dynamic regime does not encompass the asymmetric wing strokes of many insects or non-periodic deformations induced by external perturbations. As such, it remains unknown whether a frequency-independent model applies broadly and what implications it has for control. We used a vibration testing system to measure the mechanical properties of isolated Manduca sexta thoraces under symmetric, asymmetric and band-limited white noise deformations. The asymmetric and white noise conditions represent two types of generalized, multi-frequency deformations that may be encountered during steady-state and perturbed flight. Power savings and dissipation were indistinguishable between symmetric and asymmetric conditions, demonstrating that no additional energy is required to deform the thorax non-sinusoidally. Under white noise conditions, stiffness and damping were invariant with frequency, suggesting that the thorax has no frequency-dependent filtering properties. A simple flat frequency response function fits our measured frequency response. This work demonstrates the potential of materials with frequency-independent damping to simplify motor control by eliminating any velocity-dependent filtering that viscoelastic elements usually impose between muscle and wing.