On the role of tail in stability and energetic cost of bird flapping flight

Abstract

Migratory birds travel over impressively long distances. Consequently, they have to adopt flight regimes being both efficient - in order to spare their metabolic resources - and robust to perturbations. This paper investigates the relationship between both aspects, i.e. mechanical performance and stability in flapping flight of migratory birds. Relying on a poly-articulated wing morphing model and a tail-like surface, several families of steady flight regime have been identified and analyzed. These families differ by their wing kinematics and tail opening. A systematic parametric search analysis has been carried out, in order to evaluate power consumption and cost of transport. A framework tailored for assessing limit cycles, namely Floquet theory, is used to numerically study flight stability. Our results show that under certain conditions, an inherent passive stability of steady and level flight can be achieved. In particular, we find that progressively opening the tail leads to passively stable flight regimes. Within these passively stable regimes, the tail can produce either upward or downward lift. However, these configurations entail an increase of cost of transport at high velocities penalizing fast forward flight regimes. Our model-based predictions suggest that long range flights require a furled tail configuration, as confirmed by field observations, and consequently need to rely on alternative mechanisms to stabilize the flight.

Shoulder viscoelasticity in a raptor-inspired model alleviates instability and enhances passive gust rejection

“…Surprisingly, while series-elastic actuation, which involves combining a motor with a passive spring element, is a well-known strategy for improving force and torque control in legged robotics, exoskeletons, and human-machine interaction, it is not widely investigated in bio-inspired flight dynamics [71][72][73][74]. A notable exception may be found in chapter 8 of Ducci's dissertation, where the effect of shoulder flexibility on driven wing flapping is studied via a torsional series-viscoelastic actuator [43]. Therein, the author finds beneficial effects of shoulder flexibility on the overall stability of flapping flight as well as preliminary discussion on how a compliant joint can reduce the effect of external perturbations on the wing angle of attack.…”

“…Control over the wing flap degree of freedom is not investigated in this paper, as gust experiments with both a barn owl and a tawny eagle seem to favor pitch control before flap control. To include control of the flap degree of freedom for future investigations, model complexity would likely evolve to include a third control input emulating the approach by Ducci [43].…”

“…Empirical alignment was only achieved as stiffness of the spring governing wing elevation reduced to zero. Viscous dissipation at the shoulder for wing elevation, however, was not investigated and would constitute a compelling future direction in view of Ducci's preliminary findings that torsional viscoelasticity may be beneficial for stability for gust resilience when birds are in powered, flapping flight [43].…”

“…Ducci et al identifies how passively stable flight regimes can be accessed in steady flapping flight with a high-fidelity multi-body model featuring both tail and wing morphing [42]. Strong precedent for the current investigation may be found in chapter 8 of Ducci's dissertation [43], where the author obtains preliminary results indicative of enhanced flapping flight stability by modeling the effect of the powerful pectoralis and supracoracoideus muscles acting on the shoulder as a viscoelastic driven element. This is distinct from the current investigation, which models torsional coupling between the wing pitch and body pitch; Ducci models torsional coupling with respect to the frontal plane (i.e.…”