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'.

Wing tucks are a response to atmospheric turbulence in the soaring flight of the steppe eagle Aquila nipalensis.

Turbulent atmospheric conditions represent a challenge to stable flight in soaring birds, which are often seen to drop their wings in a transient motion that we call a tuck. Here, we investigate the mechanics, occurrence and causation of wing tucking in a captive steppe eagle Aquila nipalensis, using ground-based video and onboard inertial instrumentation. Statistical analysis of 2594 tucks, identified automatically from 45 flights, reveals that wing tucks occur more frequently under conditions of higher atmospheric turbulence. Furthermore, wing tucks are usually preceded by transient increases in airspeed, load factor and pitch rate, consistent with the bird encountering a headwind gust. The tuck itself immediately follows a rapid drop in angle of attack, caused by a downdraft or nose-down pitch motion, which produces a rapid drop in load factor. Positive aerodynamic loading acts to elevate the wings, and the resulting aerodynamic moment must therefore be balanced in soaring by an opposing musculoskeletal moment. Wing tucking presumably occurs when the reduction in the aerodynamic moment caused by a drop in load factor is not met by an equivalent reduction in the applied musculoskeletal moment. We conclude that wing tucks represent a gust response precipitated by a transient drop in aerodynamic loading.