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., energetic 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 analysed. 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.

Numerical assessment of wake-based estimation of instantaneous lift in flapping flight of large birds

“…higher) velocities, which is consistent with the observations of [ 23 ], who observed that birds tend to furl their tails in fast flight. Finally, it is shown in [ 24 ] that the cost of transport of large flapping birds increases with the opening angle of their tails, and that reducing tail lift thus improves flight efficiency. Since our scenario concerns steady flapping flight at a high forward velocity, for a large bird with a high aspect ratio, we consider that the assumption of low tail lift is reasonable.…”

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

“…Modeling wing pitch independent of body pitch has plausible biological footing, as the wing pitch is presumed to emanate from the rotation of the humerus at the shoulder joint. Adding this degree of freedom at the shoulder is a departure from common avian flight dynamics modeling frameworks premised on a wing with its root fixed to the body [42,49,50]. However, the latter frameworks are typically applied to rhythmic flapping and steady-state gliding conditions where the dynamics of the wing root may not significantly impact averaged or longer time-scale dynamics.…”

“…Harvey et al elucidates how control over the elbow and wrist joints in concert with the aerodynamic and inertial properties allows birds to actively transition between regimes of static and dynamic stability [4,37,41]. 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.…”