Lift calculations based on accepted wake models for animal flight are inconsistent and sensitive to vortex dynamics

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

Experimental characterization of bird flight without instrumenting the animal requires measuring the flow behind the bird in a wind tunnel. Models are used to link the measured velocities to the corresponding aerodynamic forces. Widely-used models can, however, prove inconsistent when evaluating the instantaneous lift. Yet, accurately estimating variations of lift is critical in order to reverse-engineer flapping flight. In this work, we revisit mathematical models of lift based on the conservation of momentum in a control volume around a bird. Using a numerical framework to represent a flapping bird wing and compute the flow around it, we mimic the conditions of a wind tunnel and produce realistic wakes, which we compare to experimental data. Providing ground truth measurements of the flow everywhere around the simulated bird, we assess the validity of several lift estimation techniques. We observe that the circulation-based component of the instantaneous lift can be retrieved from measurements of velocity in a single plane behind a bird, with a latency that is found to depend directly on the free-stream velocity. We further show that the lift contribution of the added-mass effect cannot be retrieved from such measurements and quantify the level of approximation due to ignoring this contribution in instantaneous lift estimation.

Model coupling biomechanics and fluid dynamics for the simulation of controlled flapping flight

This paper proposes a multiphysics computational framework coupling biomechanics and aerodynamics for the simulation of bird flight. It features a biomechanical model based on the anatomy of a bird, which models the bones and feathers of the wing. The aerodynamic solver relies on a vortex particle-mesh method and represents the wing through an immersed lifting line, acting as a source of vorticity in the flow. An application of the numerical tool is presented in the modeling of the flight of a northern bald ibis (Geronticus eremita). The wing kinematics are imposed based on biological observations and controllers are developed to enable stable flight in a closed loop. Their design is based on a linearized model of flapping flight dynamics. The controller solves an underdetermination in the control parameters through minimization. The tool and the controllers are used in two simulations: one where the bird has to trim itself at a given flight speed, and another where it has to accelerate from a trimmed state to another at a higher speed. The bird wake is accurately represented. It is analyzed and compared to the widespread frozen-wake assumption, highlighting phenomena that the latter cannot capture. The method also allows the computation of the aerodynamic forces experienced by the flier, either through the lifting line method or through control-volume analysis. The computed power requirements at several flight speeds exhibit an order of magnitude and dependency on velocity in agreement with the literature.

Analysis of a 180-degree U-turn maneuver executed by a hipposiderid bat

Bats possess wings comprised of a flexible membrane and a jointed skeletal structure allowing them to execute complex flight maneuvers such as rapid tight turns. The extent of a bat's tight turning capability can be explored by analyzing a 180-degree U-turn. Prior studies have investigated more subtle flight maneuvers, but the kinematic and aerodynamic mechanisms of a U-turn have not been characterized. In this work, we use 3D optical motion capture and aerodynamic simulations to investigate a U-turn maneuver executed by a great roundleaf bat (Hipposideros armiger: mass = 55 g, span = 51 cm). The bat was observed to decrease its flight velocity and gain approximately 20 cm of altitude entering the U-turn. By lowering its velocity from 2.0 m/s to 0.5 m/s, the centripetal force requirement to execute a tight turn was substantially reduced. Centripetal force was generated by tilting the lift force vector laterally through banking. During the initiation of the U-turn, the bank angle increased from 20 degrees to 40 degrees. During the initiation and persisting throughout the U-turn, the flap amplitude of the right wing (inside of the turn) increased relative to the left wing. In addition, the right wing moved more laterally closer to the centerline of the body during the end of the downstroke and the beginning of the upstroke compared to the left wing. Reorientation of the body into the turn happened prior to a change in the flight path of the bat. Once the bat entered the U-turn and the bank angle increased, the change in flight path of the bat began to change rapidly as the bat negotiated the apex of the turn. During this phase of the turn, the minimum radius of curvature of the bat was 5.5 cm. During the egress of the turn, the bat accelerated and expended stored potential energy by descending. The cycle averaged total power expenditure by the bat during the six wingbeat cycle U-turn maneuver was 0.51 W which was approximately 40% above the power expenditure calculated for a nominally straight flight by the same bat. Future work on the topic of bat maneuverability may investigate a broader array of maneuvering flights characterizing the commonalities and differences across flights. In addition, the interplay between aerodynamic moments and inertial moments are of interest in order to more robustly characterize maneuvering mechanisms.

Functional Morphology of Gliding Flight I: Modeling Reveals Distinct Performance Landscapes Based on Soaring Strategies

The physics of flight influences the morphology of bird wings through natural selection on flight performance. The connection between wing morphology and performance is unclear due to the complex relationships between various parameters of flight. In order to better understand this connection, we present a holistic analysis of gliding flight that preserves complex relationships between parameters. We use a computational model of gliding flight, along with analysis by uncertainty quantification, to (1) create performance landscapes of gliding based on output metrics (maximum lift-to-drag ratio, minimum gliding angle, minimum sinking speed, and lift coefficient at minimum sinking speed) and (2) predict what parameters of flight (chordwise camber, wing aspect ratio [AR], and Reynolds number) would differ between gliding and nongliding species of birds. We also examine performance based on the soaring strategy for possible differences in morphology within gliding birds. Gliding birds likely have greater ARs than non-gliding birds, due to the high sensitivity of AR on most metrics of gliding performance. Furthermore, gliding birds can use two distinct soaring strategies based on performance landscapes. First, maximizing distance traveled (maximizing lift-to-drag ratio and minimizing gliding angle) should result in wings with high ARs and middling-to-low wing chordwise camber. Second, maximizing lift extracted from updrafts should result in wings with middling ARs and high wing chordwise camber. Following studies can test these hypotheses using morphological measurements.

Determination of spatial fidelity required to accurately mimic the flight dynamics of a bat

Bats possess unique flight capabilities enabled by their wing morphology. While the articulated bone structure and flexible membrane constituting the wing are known to play a critical role in aerodynamic performance, the relationship has never been robustly quantified. Characterization of the sensitivity between precise wing contour and aerodynamic performance is important when designing a biomimetic flight vehicle based on experimentally measured wing kinematics. 3D optical motion capture, a standard method for obtaining wing kinematic measurements, discretely samples the smooth surface of a bat wing during flight. If the constellation of tracked 3D points is too sparse, a loss of critical information occurs. Here, we have explored the relationship between the density of wing surface points and several aerodynamic metrics, specifically, wing surface area variation, aerodynamic loads, and power expenditure. Loads and power were calculated using an incompressible Navier-Stokes solver. Of the metrics examined, aerodynamic power was found to be most sensitive to the spatial fidelity of the wing-the normalized root mean squared difference (NRMSD) between the 10- and 238-point cases was 35%. Load calculations varied slightly less with a peak NRMSD of 24% between the highest and lowest fidelity cases. Lastly, the wing surface area was least sensitive to the spatial fidelity of the wing kinematics, with a maximum NRMSD surface area of 8%. Close similarity in aerodynamic behavior was observed when using either a 120- and 238-point surface representation, establishing a bound to the sensitivity between wing shape and aerodynamics. The results from the 10- and 22-point configurations demonstrate that sparse representation of a wing surface can lead to a loss of information. The characterization of kinematic complexity of the wings both informs how many degrees of freedom are important to measure and also informs how many degrees of freedom are required to robotically reproduce the flapping flight.

How lovebirds maneuver through lateral gusts with minimal visual information

Flying birds maneuver effectively through lateral gusts, even when gust speeds are as high as flight speeds. What information birds use to sense gusts and how they compensate is largely unknown. We found that lovebirds can maneuver through 45° lateral gusts similarly well in forest-, lake-, and cave-like visual environments. Despite being diurnal and raised in captivity, the birds fly to their goal perch with only a dim point light source as a beacon, showing that they do not need optic flow or a visual horizon to maneuver. To accomplish this feat, lovebirds primarily yaw their bodies into the gust while fixating their head on the goal using neck angles of up to 30°. Our corroborated model for proportional yaw reorientation and speed control shows how lovebirds can compensate for lateral gusts informed by muscle proprioceptive cues from neck twist. The neck muscles not only stabilize the lovebirds' visual and inertial head orientations by compensating low-frequency body maneuvers, but also attenuate faster 3D wingbeat-induced perturbations. This head stabilization enables the vestibular system to sense the direction of gravity. Apparently, the visual horizon can be replaced by a gravitational horizon to inform the observed horizontal gust compensation maneuvers in the dark. Our scaling analysis shows how this minimal sensorimotor solution scales favorably for bigger birds, offering local wind angle feedback within a wingbeat. The way lovebirds glean wind orientation may thus inform minimal control algorithms that enable aerial robots to maneuver in similar windy and dark environments.

Mechanical power curve measured in the wake of pied flycatchers indicates modulation of parasite power across flight speeds

How aerodynamic power required for animal flight varies with flight speed determines optimal speeds during foraging and migratory flight. Despite its relevance, aerodynamic power provides an elusive quantity to measure directly in animal flight. Here, we determine the aerodynamic power from wake velocity fields, measured using tomographical particle image velocimetry, of pied flycatchers flying freely in a wind tunnel. We find a shallow U-shaped power curve, which is flatter than expected by theory. Based on how the birds vary body angle with speed, we speculate that the shallow curve results from increased body drag coefficient and body frontal area at lower flight speeds. Including modulation of body drag in the model results in a more reasonable fit with data than the traditional model. From the wake structure, we also find a single starting vortex generated from the two wings during the downstroke across flight speeds (1-9 m s^-1). This is accomplished by the arm wings interacting at the beginning of the downstroke, generating a unified starting vortex above the body of the bird. We interpret this as a mechanism resulting in a rather uniform downwash and low induced power, which can help explain the higher aerodynamic performance in birds compared with bats.

A computational investigation of lift generation and power expenditure of Pratt's roundleaf bat (Hipposideros pratti) in forward flight

The aerodynamic mechanisms of bat flight have been studied using a numerical approach. Kinematic data acquired using a high resolution motion capture system was employed to simulate the unsteady air flow around a bat’s wings. A flapping bat wing contains many degrees of freedom, which make 3D motion tracking challenging. In order to overcome this challenge, an optical motion capture system of 21 cameras was used to reduce wing self-occlusion. Over the course of a meter-long flight, 108 discrete marker points on the bat’s wings (Pratt’s roundleaf bat, Hipposideros pratti) were tracked. The time evolution of the surface of each wing was computationally reconstructed in 3D space. The resulting kinematic model was interfaced with an unsteady incompressible flow solver using the immersed boundary method (IBM) and large eddy simulation (LES). Verification and validation of the flow simulation were conducted to establish accuracy. The aerodynamic forces calculated from the simulation compared well to the forces theoretically needed to sustain the observed flight trajectory. The transient flow field generated by the simulation allowed for the direct calculation of lift, drag, and power output of the bat during flight. The mean lift coefficient was found to be 3.21, and the flap cycle averaged aerodynamic power output was 1.05 W. Throughout the flap cycle, the planform area of the wings varied up to 46% between the largest and smallest values. During the upstroke, wing rotation was found to mitigate negative lift thereby improving overall flight efficiency. The high resolution motion capture and flow simulation framework presented here has the potential to facilitate the understanding of complex bat flight aerodynamics for both straight and maneuvering flight modes.

Design and analysis of aerodynamic force platforms for free flight studies

We describe and explain new advancements in the design of the aerodynamic force platform, a novel instrument that can directly measure the aerodynamic forces generated by freely flying animals and robots. Such in vivo recordings are essential to better understand the precise aerodynamic function of flapping wings in nature, which can critically inform the design of new bioinspired robots. By designing the aerodynamic force platform to be stiff yet lightweight, the natural frequencies of all structural components can be made over five times greater than the frequencies of interest. The associated high-frequency noise can then be filtered out during post-processing to obtain accurate and precise force recordings. We illustrate these abilities by measuring the aerodynamic forces generated by a freely flying bird. The design principles can also be translated to other fluid media. This offers an opportunity to perform high-throughput, real-time, non-intrusive, and in vivo comparative biomechanical measurements of force generation by locomoting animals and robots. These recordings can include complex bimodal terrestrial, aquatic, and aerial behaviors, which will help advance the fields of experimental biology and bioinspired design.