Wing-pitch modulation in maneuvering fruit flies is explained by an interplay between aerodynamics and a torsional spring

Abstract

While the wing kinematics of many flapping insects have been well characterized, understanding the underlying sensory, neural, and physiological mechanisms that determine these kinematics is still a challenge. Two main difficulties in understanding the physiological mechanisms arise from the complexity of the interaction between a flapping wing and its own unsteady flow, as well as the intricate mechanics of the insect wing hinge, which is among the most complicated joints in the animal kingdom. These difficulties call for the application of reduced-order approaches. Here this strategy is used to model the torques exerted by the wing hinge along the wing-pitch axis of maneuvering fruit flies as a damped torsional spring with elastic and damping coefficients as well as a rest angle. Furthermore, we model the air flows using simplified quasistatic aerodynamics. Our findings suggest that flies take advantage of the passive coupling between aerodynamics and the damped torsional spring to indirectly control their wing-pitch kinematics by modulating the spring parameters. The damped torsional-spring model explains the changes measured in wing-pitch kinematics during roll correction maneuvers through modulation of the spring damping and elastic coefficients. These results, in conjunction with the previous literature, indicate that flies can accurately control their wing-pitch kinematics on a sub-wing-beat time scale by modulating all three effective spring parameters on longer time scales.

Aerodynamics, sensing and control of insect-scale flapping-wing flight

“…Overall, the wing motion is significantly affected by the spanwise bending and torsional twist [139]. Recent experiment on the fruit fly dynamics suggests that fruit fly muscles may affect the structural properties, such as the damping and elastic modulus, to modulate the wing-pitch [76]. The wing deformation can also lead to a rapid stroke reversal, which can lead to greater force magnitudes [139,140].…”

“…These coefficients are empirically determined from various experiments [26,27,73,76]. Such a need for empirically fitted coefficients can be partially mitigated by considering an unsteady model that captures the nonlinear effect of the LEV on the lift [77] or a hybrid model of high-fidelity Navier-Stokes equation solutions and low-order quasi-steady models [78].…”

Genetic Algorithm Based Optimization of Wing Rotation in Hover

“…From an aeromechanics point of view, the wing hinge acts as a torsional spring that allows for a wing rotation with minimal active actuation in response to the aerodynamic and inertial forces [37,38]. Mechanical wing models that mimic the passive rotational mechanisms of insects can be designed using artificial wings with torsional compliance [39] or wing hinges equipped with damped torsional springs [40]. These passive rotational dynamics have the potential to increase the pitching efficiency even further and decrease the mechanical complexity and mass of the system [37,39].…”

Flight of the fruit fly

“…This achievement opened the door to a number of interesting studies. Once access became available to the kinematic data, we were able to understand how insects are able to take advantage of drag forces to achieve sideways flight [4], forward flight [5], and yaw turns [6][7][8]. Using an ingenious apparatus developed by my student (now Professor Ristroph at NYU), where in-flight perturbations could be induced using magnetic fields that torqued tiny magnets we glued onto the backs of flies, we were able to show that such wing manipulations are also crucial for stabilizing flapping flight [9].…”