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.

Flight paths of seabirds soaring over the ocean surface enable measurement of fine-scale wind speed and direction.

Ocean surface winds are an essential factor in understanding the physical interactions between the atmosphere and the ocean. Surface winds measured by satellite scatterometers and buoys cover most of the global ocean; however, there are still spatial and temporal gaps and finer-scale variations of wind that may be overlooked, particularly in coastal areas. Here, we show that flight paths of soaring seabirds can be used to estimate fine-scale (every 5 min, ∼5 km) ocean surface winds. Fine-scale global positioning system (GPS) positional data revealed that soaring seabirds flew tortuously and ground speed fluctuated presumably due to tail winds and head winds. Taking advantage of the ground speed difference in relation to flight direction, we reliably estimated wind speed and direction experienced by the birds. These bird-based wind velocities were significantly correlated with wind velocities estimated by satellite-borne scatterometers. Furthermore, extensive travel distances and flight duration of the seabirds enabled a wide range of high-resolution wind observations, especially in coastal areas. Our study suggests that seabirds provide a platform from which to measure ocean surface winds, potentially complementing conventional wind measurements by covering spatial and temporal measurement gaps.

Oceanic seabirds chase tropical cyclones.

In late summer and autumn, the passage of intense tropical cyclones can profoundly perturb oceanic and coastal ecosystems. Direct negative effects on individuals and marine communities can be dramatic, especially in the coastal zone,1,2,3,4 but cyclones can also enhance pelagic primary and secondary production.5,6,7,8,9 However, cyclone impacts on open ocean marine life remain poorly understood. Here, we investigate their effects on the foraging movements of a wide-ranging higher predator, the Desertas petrel (Pterodroma deserta), in the mid-latitude North Atlantic during hurricane season. Contrary to previously studied pelagic seabirds in tropical and mid-latitude regions,10,11 Desertas petrels did not avoid cyclones by altering course, nor did they seek calmer conditions within the cyclone eye. Approximately one-third of petrels tracked from their breeding colony interacted with approaching cyclones. Upon encountering strong winds, the birds reduced ground speed, likely by spending less time in flight. A quarter of birds followed cyclone wakes for days and over thousands of kilometers, a behavior documented here for the first time. Within these wakes, tailwind support was higher than along alternative routes. Furthermore, at the mesoscale (hours-weeks and hundreds of kilometers), sea surface temperature dropped and surface chlorophyll sharply increased, suggesting direct effects on ocean stratification, primary production, and therefore presumably prey abundance and accessibility for surface-feeding petrels. We therefore hypothesize that cyclone wakes provide both predictably favorable wind conditions and foraging opportunities. As such, cyclones may have positive net effects on the demography of many mid-latitude pelagic seabirds and, likely, other marine top-predators.

A novel approach to seabird posture estimation: finding roll and yaw angles of dynamic soaring albatrosses using tri-axial magnetometers.

With advances in bio-logging technology, the posture of animals is now commonly described by inertial measurement units, which include tri-axial accelerometers to estimate pitch and roll angles. Many large seabirds use dynamic soaring flight to travel long distances, but this low-cost flight mode results in high centripetal acceleration, which obscures posture derived from accelerometers. Tri-axial magnetometers are not influenced by acceleration and might provide a way to estimate the posture of animals that experience high centripetal acceleration. We propose a new method to estimate the posture of dynamic soaring seabirds using tri-axial magnetometer data, with the assumption that they do not have large pitch angles during routine flight. This method was field-tested by deploying a combination of bio-logging devices on three albatross species breeding on Marion Island, using bird-borne video loggers to validate the roll angles. Validated data showed that the method worked well in most instances, but accuracy decreased when the heading was close to magnetic north or south. Accurate, fine-scale posture estimates may provide insight into dynamic soaring flight and allow estimates of fine-scale tracks using dead-reckoning, not only for seabirds, but potentially for other species where centripetal acceleration limits the use of accelerometers to estimate posture.

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

The largest extinct volant birds (Pelagornis sandersi and Argentavis magnificens) and pterosaurs (Pteranodon and Quetzalcoatlus) are thought to have used wind-dependent soaring flight, similar to modern large birds. There are 2 types of soaring: thermal soaring, used by condors and frigatebirds, which involves the use of updrafts to ascend and then glide horizontally; and dynamic soaring, used by albatrosses, which involves the use of wind speed differences with height above the sea surface. Previous studies have suggested that P. sandersi used dynamic soaring, while A. magnificens and Quetzalcoatlus used thermal soaring. For Pteranodon, there is debate over whether they used dynamic or thermal soaring. However, the performance and wind speed requirements of dynamic and thermal soaring for these species have not yet been quantified comprehensively. We quantified these values using aerodynamic models and compared them with that of extant birds. For dynamic soaring, we quantified maximum travel speeds and maximum upwind speeds. For thermal soaring, we quantified the animal's sinking speed circling at a given radius and how far it could glide losing a given height. Our results confirmed those from previous studies that A. magnificens and Pteranodon used thermal soaring. Conversely, the results for P. sandersi and Quetzalcoatlus were contrary to those from previous studies. P. sandersi used thermal soaring, and Quetzalcoatlus had a poor ability both in dynamic and thermal soaring. Our results demonstrate the need for comprehensive assessments of performance and required wind conditions when estimating soaring styles of extinct flying species.

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.

Observations and models of across-wind flight speed of the wandering albatross.

Wandering albatrosses exploit wind shear by dynamic soaring (DS), enabling rapid, efficient, long-range flight. We compared the ability of a theoretical nonlinear DS model and a linear empirical model to explain the observed variation of mean across-wind airspeeds of GPS-tracked wandering albatrosses. Assuming a flight trajectory of linked, 137° turns, a DS cycle of 10 s and a cruise airspeed of 16 m s-1, the theoretical model predicted that the minimum wind speed necessary to support DS is greater than 3 m s-1. Despite this, tracked albatrosses were observed in flight at wind speeds as low as 2 m s-1. We hypothesize at these very low wind speeds, wandering albatrosses fly by obtaining additional energy from updrafts over water waves. In fast winds (greater than 8 m s-1), assuming the same 10 s cycle period and a turn angle (TA) of 90°, the DS model predicts mean across-wind airspeeds of up to around 50 m s-1. In contrast, the maximum observed across-wind mean airspeed of our tracked albatrosses reached an asymptote at approximately 20 m s-1. We hypothesize that this is due to birds actively limiting airspeed by making fine-scale adjustments to TAs and soaring heights in order to limit aerodynamic force on their wings.

Bioinspired dynamic soaring simulation system with distributed pressure sensors.

Inspired by the albatross, this paper presents the construction of a dynamic soaring simulation system with distributed pressure sensors. The advantage of our system lies in harvesting energy from the wind shear layer and estimating the wind information using a pressure-based sensor system. Specifically, the dynamic soaring simulation system contains an offline training stage and an online estimation and control stage. In the offline training stage, computational fluid dynamics simulations are conducted and used as the data source. A surrogate model is established to correlate the local flow conditions and the surface pressure at optimal sensor positions. In the online estimation and control stage, through sensing the pressure information, the real-time wind velocity and wind gradient are estimated by the surrogate model trained in the offline stage. Moreover, wind information is adopted in the simulation of dynamic soaring control. In this study, the simulation system was applied to linear and circular path-following tasks. It was found that the dynamic soaring simulation system with distributed pressure sensors provides an acceptable estimation of wind velocity and wind gradient with a certain time delay caused by numerical differentiation.

Opportunistic soaring by birds suggests new opportunities for atmospheric energy harvesting by flying robots.

The use of flying robots (drones) is increasing rapidly, but their utility is limited by high power demand, low specific energy storage and poor gust tolerance. By contrast, birds demonstrate long endurance, harvesting atmospheric energy in environments ranging from cluttered cityscapes to open landscapes, coasts and oceans. Here, we identify new opportunities for flying robots, drawing upon the soaring flight of birds. We evaluate mechanical energy transfer in soaring from first principles and review soaring strategies encompassing the use of updrafts (thermal or orographic) and wind gradients (spatial or temporal). We examine the extent to which state-of-the-art flying robots currently use each strategy and identify several untapped opportunities including slope soaring over built environments, thermal soaring over oceans and opportunistic gust soaring. In principle, the energetic benefits of soaring are accessible to flying robots of all kinds, given atmospherically aware sensor systems, guidance strategies and gust tolerance. Hence, while there is clear scope for specialist robots that soar like albatrosses, or which use persistent thermals like vultures, the greatest untapped potential may lie in non-specialist vehicles that make flexible use of atmospheric energy through path planning and flight control, as demonstrated by generalist flyers such as gulls, kites and crows.

A stability perspective of bioinspired unmanned aerial vehicles performing optimal dynamic soaring.

The phenomenon of dynamic soaring, as exhibited by soaring birds, has long been a biological inspiration for aerospace and control engineers. If this fascinating phenomenon, which allows soaring birds to perform almost unpowered flight using wind shear, can be mimicked by unmanned aerial vehicles (UAVs), then there is substantial potential for technological and economic enhancement of UAV performance. Although there has been a considerable amount of research covering the modeling, optimization, control and simulation aspects of different UAVs performing dynamic soaring, there is little to no conclusive work analyzing the stability of such UAVs in soaring orbits. In this paper we present a comprehensive framework for determining the stability of soaring UAVs utilizing both linear (Floquet-based) and nonlinear (contraction theory-based) techniques. Floquet stability analysis was inconclusive, which led to the use of a nonlinear contraction formulation to reach a conclusive stability assessment for an actual nonlinear fixed-wing UAV performing dynamic soaring. Furthermore, parametric variation along with numerical simulations were conducted to ascertain the response of the actual nonlinear system when perturbed from the nominal motion studied in this paper. The analysis and simulations revealed that the system possesses instability as the UAV motion diverges from its nominal trajectory and follows an undesirable path. From this result we conclude, for the first time in the literature as far as we are aware, that UAVs performing dynamic soaring in an optimal way to reduce wind shear requirements are inherently unstable. The results of this work suggest that mimicking of dynamic soaring by UAVs will require careful investigation of tracking and regulatory controls that need to be implemented.

Hidden Markov models identify major movement modes in accelerometer and magnetometer data from four albatross species.

BACKGROUND: Inertial measurement units (IMUs) with high-resolution sensors such as accelerometers are now used extensively to study fine-scale behavior in a wide range of marine and terrestrial animals. Robust and practical methods are required for the computationally-demanding analysis of the resulting large datasets, particularly for automating classification routines that construct behavioral time series and time-activity budgets. Magnetometers are used increasingly to study behavior, but it is not clear how these sensors contribute to the accuracy of behavioral classification methods. Development of effective  classification methodology is key to understanding energetic and life-history implications of foraging and other behaviors. METHODS: We deployed accelerometers and magnetometers on four species of free-ranging albatrosses and evaluated the ability of unsupervised hidden Markov models (HMMs) to identify three major modalities in their behavior: 'flapping flight', 'soaring flight', and 'on-water'. The relative contribution of each sensor to classification accuracy was measured by comparing HMM-inferred states with expert classifications identified from stereotypic patterns observed in sensor data. RESULTS: HMMs provided a flexible and easily interpretable means of classifying behavior from sensor data. Model accuracy was high overall (92%), but varied across behavioral states (87.6, 93.1 and 91.7% for 'flapping flight', 'soaring flight' and 'on-water', respectively). Models built on accelerometer data alone were as accurate as those that also included magnetometer data; however, the latter were useful for investigating slow and periodic behaviors such as dynamic soaring at a fine scale. CONCLUSIONS: The use of IMUs in behavioral studies produces large data sets, necessitating the development of computationally-efficient methods to automate behavioral classification in order to synthesize and interpret underlying patterns. HMMs provide an accessible and robust framework for analyzing complex IMU datasets and comparing behavioral variation among taxa across habitats, time and space.

Wave-slope soaring of the brown pelican.

BACKGROUND: From the laboratory at Scripps Institution of Oceanography, it is common to see the brown pelican (Pelecanus occidentalis) traveling along the crests of ocean waves just offshore of the surf-zone. When flying in this manner, the birds can travel long distances without flapping, centimeters above the ocean's surface. Here we derive a theoretical framework for assessing the energetic savings related to this behavior, 'wave-slope soaring,' in which an organism in flight takes advantage of localized updrafts caused by traveling ocean surface gravity waves. METHODS: The energy cost of steady, constant altitude flight in and out of ground effect are analyzed as controls. Potential flow theory is used to quantify the ocean wave-induced wind associated with near-shoaling, weakly nonlinear, shallow water ocean surface gravity waves moving through an atmosphere initially at rest. Using perturbation theory and the Green's function for Laplace's equation in 2D with Dirichlet boundary conditions, we obtain integrals for the horizontal and vertical components of the wave-induced wind in a frame of reference moving with the wave. Wave-slope soaring flight is then analyzed using an energetics-based approach for waves under a range of ocean conditions and the body plan of P. occidentalis. RESULTS: For ground effect flight, we calculate a ∼15 - 25% reduction in cost of transport as compared with steady, level flight out of ground effect. When wave-slope soaring is employed at flight heights ∼2m in typical ocean conditions (2m wave height, 15s period), we calculate 60-70% reduction in cost of transport as compared with flight in ground effect. A relatively small increase in swell amplitude or decrease in flight height allows up to 100% of the cost of transport to be offset by wave-slope soaring behavior. CONCLUSIONS: The theoretical development presented here suggests there are energy savings associated with wave-slope soaring. Individual brown pelicans may significantly decrease their cost of transport utilizing this mode of flight under typical ocean conditions. Thus wave-slope soaring may provide fitness benefit to these highly mobile organisms that depend on patchy prey distribution over large home ranges.

Flight speed and performance of the wandering albatross with respect to wind.

BACKGROUND: Albatrosses and other large seabirds use dynamic soaring to gain sufficient energy from the wind to travel large distances rapidly and with little apparent effort. The recent development of miniature bird-borne tracking devices now makes it possible to explore the physical and biological implications of this means of locomotion in detail. Here we use GPS tracking and concurrent reanalyzed wind speed data to model the flight performance of wandering albatrosses Diomedea exulans soaring over the Southern Ocean. We investigate the extent to which flight speed and performance of albatrosses is facilitated or constrained by wind conditions encountered during foraging trips. RESULTS: We derived simple equations to model observed albatross ground speed as a function of wind speed and relative wind direction. Ground speeds of the tracked birds in the along-wind direction varied primarily by wind-induced leeway, which averaged 0.51 (± 0.02) times the wind speed at a reference height of 5 m. By subtracting leeway velocity from ground velocity, we were able to estimate airspeed (the magnitude of the bird's velocity through the air). As wind speeds increased from 3 to 18 m/s, the airspeed of wandering albatrosses flying in an across-wind direction increased by 0.42 (± 0.04) times the wind speed (i.e. ~ 6 m/s). At low wind speeds, tracked birds increased their airspeed in upwind flight relative to that in downwind flight. At higher wind speeds they apparently limited their airspeeds to a maximum of around 20 m/s, probably to keep the forces on their wings in dynamic soaring well within tolerable limits. Upwind airspeeds were nearly constant and downwind leeway increased with wind speed. Birds therefore achieved their fastest upwind ground speeds (~ 9 m/s) at low wind speeds (~ 3 m/s). CONCLUSIONS: This study provides insights into which flight strategies are optimal for dynamic soaring. Our results are consistent with the prediction that the optimal range speed of albatrosses is higher in headwind than tailwind flight but only in wind speeds of up to ~ 7 m/s. Our models predict that wandering albatrosses have oval-shaped airspeed polars, with the fastest airspeeds ~ 20 m/s centered in the across-wind direction. This suggests that in upwind flight in high winds, albatrosses can increase their ground speed by tacking like sailboats.

Optimal dynamic soaring consists of successive shallow arcs.

Albatrosses can travel a thousand kilometres daily over the oceans. They extract their propulsive energy from horizontal wind shears with a flight strategy called dynamic soaring. While thermal soaring, exploited by birds of prey and sports gliders, consists of simply remaining in updrafts, extracting energy from horizontal winds necessitates redistributing momentum across the wind shear layer, by means of an intricate and dynamic flight manoeuvre. Dynamic soaring has been described as a sequence of half-turns connecting upwind climbs and downwind dives through the surface shear layer. Here, we investigate the optimal (minimum-wind) flight trajectory, with a combined numerical and analytic methodology. We show that contrary to current thinking, but consistent with GPS recordings of albatrosses, when the shear layer is thin the optimal trajectory is composed of small-angle, large-radius arcs. Essentially, the albatross is a flying sailboat, sequentially acting as sail and keel, and is most efficient when remaining crosswind at all times. Our analysis constitutes a general framework for dynamic soaring and more broadly energy extraction in complex winds. It is geared to improve the characterization of pelagic birds flight dynamics and habitat, and could enable the development of a robotic albatross that could travel with a virtually infinite range.

Soaring energetics and glide performance in a moving atmosphere.

Here, we analyse the energetics, performance and optimization of flight in a moving atmosphere. We begin by deriving a succinct expression describing all of the mechanical energy flows associated with gliding, dynamic soaring and thermal soaring, which we use to explore the optimization of gliding in an arbitrary wind. We use this optimization to revisit the classical theory of the glide polar, which we expand upon in two significant ways. First, we compare the predictions of the glide polar for different species under the various published models. Second, we derive a glide optimization chart that maps every combination of headwind and updraft speed to the unique combination of airspeed and inertial sink rate at which the aerodynamic cost of transport is expected to be minimized. With these theoretical tools in hand, we test their predictions using empirical data collected from a captive steppe eagle (Aquila nipalensis) carrying an inertial measurement unit, global positioning system, barometer and pitot tube. We show that the bird adjusts airspeed in relation to headwind speed as expected if it were seeking to minimize its aerodynamic cost of transport, but find only weak evidence to suggest that it adjusts airspeed similarly in response to updrafts during straight and interthermal glides.This article is part of the themed issue 'Moving in a moving medium: new perspectives on flight'.