How did extinct giant birds and pterosaurs fly? A comprehensive modeling approach to evaluate soaring performance

Albatrosses employ orientation and routing strategies similar to yacht racers

The way goal-oriented birds adjust their travel direction and route in response to wind significantly affects their travel costs. This is expected to be particularly pronounced in pelagic seabirds, which utilize a wind-dependent flight style called dynamic soaring. Dynamic soaring seabirds in situations without a definite goal, e.g. searching for prey, are known to preferentially fly with crosswinds or quartering-tailwinds to increase the speed and search area, and reduce travel costs. However, little is known about their reaction to wind when heading to a definite goal, such as homing. Homing tracks of wandering albatrosses (Diomedea exulans) vary from beelines to zigzags, which are similar to those of sailboats. Here, given that both albatrosses and sailboats travel slower in headwinds and tailwinds, we tested whether the time-minimizing strategies used by yacht racers can be compared to the locomotion patterns of wandering albatrosses. We predicted that when the goal is located upwind or downwind, albatrosses should deviate their travel directions from the goal on the mesoscale and increase the number of turns on the macroscale. Both hypotheses were supported by track data from albatrosses and racing yachts in the Southern Ocean confirming that albatrosses qualitatively employ the same strategy as yacht racers. Nevertheless, albatrosses did not strictly minimize their travel time, likely making their flight robust against wind fluctuations to reduce flight costs. Our study provides empirical evidence of tacking in albatrosses and demonstrates that man-made movement strategies provide a new perspective on the laws underlying wildlife movement.

Coracoid strength as an indicator of wing-beat propulsion in birds

Birds generate a propulsive force by flapping their wings. They use this propulsive force for various locomotion styles, such as aerodynamic flight, wing-paddle swimming and wing-assisted incline running. It is therefore important to reveal the origin of flapping ability in the evolution from theropod dinosaurs to birds. However, there are no quantitative indices to reconstruct the flapping abilities of extinct forms based on their skeletal morphology. This study compares the section modulus of the coracoid relative to body mass among various extant birds to test whether the index is correlated with flapping ability. According to a survey of 220 historical bird specimens representing 209 species, 180 genera, 83 families and 30 orders, the section modulus of the coracoid relative to body mass in non-flapping birds was significantly smaller than that of flapping birds. This indicates that coracoid strength in non-flapping birds is deemphasised, whereas in flapping birds the strength is emphasised to withstand the contractile force produced by powerful flapping muscles, such as the m. pectoralis and m. supracoracoideus. Therefore, the section modulus of the coracoid is expected to be a powerful tool to reveal the origin of powered flight in birds.

A novel hypothesis for how albatrosses optimize their flight physics in real-time: an extremum seeking model and control for dynamic soaring

The albatross optimized flight maneuver-known as dynamic soaring-is nothing but a wonder of biology, physics, and engineering. By utilizing dynamic soaring, this fascinating bird can travel in the desired flight direction almost for free by harvesting energy from the wind. This phenomenon has been observed for centuries as evidenced by the writings of Leonardo da Vinci and Lord Rayleigh. Moreover, dynamic soaring biological inspiration has triggered a momentous interest among many communities of science and engineering, particularly aeronautical, control, and robotic engineering communities. That is, if dynamic soaring is mimicked, we will have arrived at a new class of unmanned aerial vehicles that are very energy-efficient during part (or the full) duration of their flight. Studying, modeling, and simulating dynamic soaring have been conducted in literature by mostly configuring dynamic soaring as an optimal control problem. Said configuration requires accurate dynamic system modeling of the albatross/mimicking-object, accurate wind profile models, and a defined mathematical formula of an objective function that aims at conserving energy and minimizing its dissipation; the solution then of such optimal control problem is the dynamic soaring trajectory taken-or to be taken-by the bird/mimicking-object. Furthermore, the decades-long optimal control configuration of the dynamic soaring problem resulted in non-real-time algorithms and control solutions, which may not be aligned well with the biological phenomenon itself; experimental observations of albatrosses indicate their ability to conduct dynamic soaring in real-time. Indeed, a functioning modeling and control framework for dynamic soaring that allows for a meaningful bio-mimicry of the albatross needs to be autonomous, real-time, stable, and capable of tolerating the absence of mathematical expressions of the wind profiles and the objective function-hypothetically similar to what the bird does. The qualifications of such modeling and control framework are the very same characteristics of the so-called extremum seeking systems. In this paper, we show that extremum seeking systems existing in control literature for decades are a natural characterization of the dynamic soaring problem. We propose an extremum seeking modeling and control framework for the dynamic soaring problem hypothesizing that the introduced framework captures more features of the biological phenomenon itself and allows for possible bio-mimicking of it. We provide and discuss the problem setup, design, and stability of the introduced framework. Our results, supported by simulations and comparison with optimal control methods of the literature, provide a proof of concept that the dynamic soaring phenomenon can be a natural expression of extremum seeking. Hence, dynamic soaring has the potential to be performed autonomously and in real-time with stability guarantees.