Wake patterns of the wings and tail of hovering hummingbirds
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The flow fields of slowly flying bats and faster-flying birds differ in that bats produce two vortex loops during each stroke, one per wing, and birds produce a single vortex loop per stroke. In addition, the circulation at stroke transition approaches zero in bats but remains strong in birds. It is unknown if these difference derive from fundamental differences in wing morphology or are a consequence of flight speed. Here, we present an analysis of the horizontal flow field underneath hovering Anna’s hummingbirds (Calypte anna) to describe the wake of a bird flying at zero forward velocity. We also consider how the hummingbird tail interacts with the wake generated by the wings. High-speed image recording and analysis from three orthogonal perspectives revealed that the wing tips reach peak velocities in the middle of each stroke and approach zero velocity at stroke transition. Hummingbirds use complex tail kinematic patterns ranging from in phase to antiphase cycling with respect to the wings, covering several phase shifted patterns. We employed particle image velocimetry to attain detailed horizontal flow measurements at three levels with respect to the tail: in the tail, at the tail tip, and just below the tail. The velocity patterns underneath the wings indicate that flow oscillates along the ventral–dorsal axis in response to the down- and up-strokes and that the sideways flows with respect to the bird are consistently from the lateral to medial. The region around the tail is dominated by axial flows in dorsal to ventral direction. We propose that these flows are generated by interaction between the wakes of the two wings at the end of the upstroke, and that the tail actively defects flows to generate moments that contribute to pitch stability. The flow fields images also revealed distinct vortex loops underneath each wing, which were generated during each stroke. From these data, we propose a model for the primary flow structures of hummingbirds that more strongly resembles the bat model. Thus, pairs of unconnected vortex loops may be shared features of different animals during hovering and slow forward flight.
KeywordsParticle Image Velocimetry Particle Image Velocimetry Measurement Particle Tracking Velocimetry Instantaneous Velocity Field Vortex Loop
Since Kokshaysky (1979) first photographed birds flying through wood and paper dust clouds, flight biologists have been working to attain higher resolution views and quantifiable features of the wakes of flying animals. Experiments have focused on vertical measurement planes with one view or two orthogonal views to characterize the momentum imparted behind and below the animal (Spedding 1986, 1987a, b; Spedding et al. 1984). Recent efforts have yielded high-resolution, three-dimensional descriptions of the wakes produced during moderate and fast forward flight in passerine birds (Hedenström et al. 2006; Rosén et al. 2007; Spedding et al. 2003), and also during slow and moderate forward flight in bats, the only other extant vertebrate lineage that has powered, flapping flight (Hedenström et al. 2007; Muijres et al. 2008). In birds, the two wings together produce a single vortex loop, whereas in bats each wing produces a separate vortex loop. In addition, birds generate considerable circulation during stroke transitions whereas circulation during bat flapping approaches zero at stroke transition. It is unknown to what extent these alternative wake structures derive from differences in flight speed versus lineage-specific differences in the morphology and neuromuscular control of the wings.
The hovering flight of hummingbirds provides an excellent opportunity to examine the wake structure produced by birds during hovering and thus with no forward velocity. The flow fields generated by hovering rufous hummingbirds (Selasphorus rufus) have been described from two orthogonal, vertical perspectives with the results that the wings generate a powerful wake oriented directly below the animal, which is dominated by the much stronger downstroke (Warrick et al. 2005). A horizontal view of the wakes underneath hovering hummingbirds has not been described, but this perspective should provide unique information about the wing wake structures. A horizontal perspective has the additional advantage of providing pertinent information concerning how the hummingbird tail interacts with the very strong downwards wing wakes.
Three aerodynamic functions for bird tails are known. During forward flight tails (1) function in maneuverability and stability, (2) can help control the angle of attack of the wings, and (3) during slow forward flight can produce lift (Thomas 1997; Thomas and Balmford 1995). However, the elaborated tails of some species are elongated in response to sexual selection and increase costs of parasitic drag (Balmford et al. 1993; Evans and Hatchwell 1992; Møller 1989; Norberg 1995). The aerodynamic function of the tail in hovering flight is not clear given the absence of a translational flow velocity, but it has been suggested that the tail may be generally involved in pitch control (references in Warrick et al. 2002), which should be important for maintaining stability during hovering.
Here we describe the relative motion of the hummingbird wings and tail, and the horizontal wake pattern in a two-dimensional plane. We separately considered three elevations of perspective: a plane centered within the tail, a plane at the tail tip, and a plane located just below the tail. We present velocity profiles based upon temporal sequences of wing positions. These measurements provide information about the wake structure, the tail-wake interaction, and the horizontal orientation of the velocity vectors. We use these data to propose a model of the dominant flow structures produced during hovering flight in hummingbirds.
2 Phase relationships between hummingbird wings and tail
The wing and tail kinematics of hovering hummingbirds were studied using five male Anna’s hummingbirds (Calypte anna), which were captured in Berkeley (three birds) and Pasadena (two birds), California. These hummingbirds were housed in institutional vivaria and trained to feed from artificial feeders made from 10 ml syringes. For filming trials, the hummingbirds were moved from the vivaria to an acrylic chamber (1 m × 1 m × 1 m) constructed with three clear sides and three opaque sides. The chamber contained a single perch and a single artificial feeder, also made from a 10-ml syringe. Hovering bouts were filmed from three perspectives (top and two sides) using three digital high-speed cameras filming at 1,000 frames per second. The Institutional Animal Care and Use Committees at the University of California Berkeley and the California Institute of Technology approved these vertebrate animal procedures.
3 Methods for recording flow features in hovering hummingbirds
We measured the flow characteristics of three male Anna’s hummingbirds (C. anna), captured in Riverside, CA, USA and housed in the vivarium at the University of California Riverside (UCR). The Institutional Animal Care and Use Committee at UCR approved these vertebrate animal procedures.
Experiments began the day after training and involved the same feeding protocol. A particle image velocimetry (PIV) system was used to measure the instantaneous velocity field in the horizontal plane. The PIV technique measures the velocity in a fluid by correlating images of the particle-seeded flow (Adrian 1988). For these experiments, atomized food grade olive oil was utilized as the seeding particles. In the minute prior to providing feeder access, we filled the chamber with olive oil mist created using a pressurized oil container equipped with a perforated tube to enable oil–air mixing for adequate atomization.
As the bird approached the feeder, the olive oil particles were illuminated in a plane below the feeder using a horizontal laser sheet with a wavelength of 532 nm (with energy of 388 mJ/pulse) generated by a double-pulsed Nd:YAG laser (Big Sky Laser Technologies, Inc, model CFR400) located 0.5 m from the feeder. The Q-switch was set to 100 μs corresponding to approximately medium laser power. The laser beam was expanded into a 20° diverging light sheet using sheet-forming optics, which included a cylindrical lens (−15 mm focal length) and a spherical lens (200 mm focal length). In this way, the beam was transformed into a 200-mm wide and 0.212 mm thick sheet to illuminate seed particles in a horizontal plane close to the bird. In separate experiments, we illuminated three planes: (1) 1 cm above the middle plane, i.e., within the tail, (2) at the tail tip during its cyclical oscillation, and (3) just underneath the tail. A LASERPULSE Synchronizer (TSI Inc.) was utilized to trigger the laser pulse and the camera with correct sequences and timing through a 2.66-GHz dual-processor workstation (Intel® Xeon™). The laser sheet was synchronized with a high-resolution (1,600 × 1,192 pixel) POWERVIEW 2M CCD camera (TSI Inc., model 630157) with a 50-mm f/1.8 Nikkor lens and an exposure time of 260 μs. Camera aperture was set to 5.6. A total of 15 image pairs per second (15 Hz) were captured. Time difference between the two images in a pair was optimized for the best PIV quality to Δt = 100 μs. A grid for the PIV processing was formed using the Nyquist Grid Engine over 64 × 64 pixels interrogation regions. Fast Fourier transform correlation was used with the Gaussian peak engine.
4 PIV flow field analysis
We further narrowed our analysis to the velocity measurements (i.e., image pairs) that could be grouped into one of eight wing positions within a complete wingbeat cycle (see Fig. 2b, c). This was accomplished by visual assignment of wing positions based upon each raw image. Arranging the measurements by wing position allowed us to compile a stroke sequence of velocity and vorticity profiles even though the images came from separate wingbeats. It is important to note that the wing tip velocity is greatest during mid-stroke and slowest during stroke transition (Fig. 1). Therefore the time difference between wing positions (average ~3 ms) was not constant.
The different experiments yielded different perspectives of the bird and wake both due to design and behavioral variability. In the former case, we moved the camera either closer to the feeder thereby focusing on the front (ventral) half of the stroke cycle or ~10 cm further away from the feeder to focus on the back (dorsal) half of the stroke cycle. In the latter case, the bird fed at different angles relative to the feeder in the horizontal plane providing either a left or right bias. To facilitate comparisons among these multiple views, we calculated velocity over specific regions of interest (ROI) and along bird-centered axes. The ROIs were constrained to one of three positions: (1) underneath either the left or right wing on the front (ventral) side of the bird, including wing positions 3–7; (2) underneath either the left or the right wing on the back (dorsal) side of the bird, including wing positions 1–3 and 7–8; (3) underneath the tail in a narrow region that covered the full range of tail movement. The original velocity vector components in the x and y axes, u and v, respectively, were rotated to along the bird component, V s (positive from ventral to dorsal) and to a component that is perpendicular to the ventral–dorsal axis, V n (positive when moving from the bird’s lateral right to lateral left).
Within a filmed hovering bout, the velocities were averaged over all frames corresponding to the same wing position and the same ROIs were used for all frames. Because the area of the ROIs differed across experiments, we restricted our analysis to within experiment results rather than combining experiments to generate average values.
On average, the measured flow field was 5 cm below the wing stroke plane. We assumed the vertical velocity to be U vert ~2 m/s based upon measurements from similarly sized rufous hummingbirds, S. rufus (Warrick et al. 2005). Thus, it is estimated to require an average of 25 ms for the flow structures to be advected from the wing to the measuring plane. Because the wingbeat frequency is ~40 Hz (corresponding to a wingbeat period of 25 ms), the measured flow field should be lagging by the full cycle behind the actual wing stroke visible on the raw PIV image.
Another important reason why we avoided combining experiments for analytical purposes is that the vertical distance between the wings and the measuring plane—and thus the time lag—differed across experiments. Within each experiment, the hummingbirds maintained a constant body orientation and the time lag between wake generation and measurement is invariant. However, across experiments, hummingbirds used slightly different body angles, which should produce slight phase shifts in the wingbeat and PIV measurement cycles. Accordingly, we present results for individual experiments and then focus on the common features among experiments to develop a model of the wake of hovering hummingbirds.
5 Results of flow measurements
Measurements of the hovering hummingbird wake in the horizontal plane near the tail revealed three general patterns of flow velocity: (1) Along the ventral–dorsal axis underneath the wings, air flow switches direction more or less sinusoidally indicating the influence of forwards (downstroke) and backwards (upstroke) movement of the wings (Fig. 4); (2) Perpendicular to this axis, underneath the wings, air flows from the periphery (lateral) in toward to the region underneath the hummingbird’s body (medial) but with varying intensity (Fig. 5); (3) In a small region around the tail, the air flow is consistently oriented along the head–tail axis and away from the body (Fig. 7). In addition, we see clear evidence for separate vortex loops that are shed underneath each wing, and separate loops that are shed during down- and up-strokes.
As is the case for other PIV measurements from real flying animals, these flow fields reveal a complex wake that contains many disrupted structures and secondary flows. Furthermore, the patterns of flow reversal do not fit perfect sinusoids as might be expected. However, it is unrealistic to expect invariant flow fields with perfect sinusoids because real hummingbirds exhibit differences in angle of attack, airfoil shape and stroke period between down- and up-strokes (Tobalske et al. 2007; Warrick et al. 2005; D.L. Altshuler, unpublished data). Additionally, we expect that the animals make rapid adjustments to these and other kinematic features to control stability, which will produce flow fields that vary across wingbeats.
It is not possible to infer the complete three-dimensional structure of the hummingbird’s wake from the single perspective described here. Although there are relatively few measurements of the flow fields of different flying animals, we can compare our results with previous studies of forward flight in pigeons (Spedding et al. 1984), passerines (Hedenström et al. 2006; Rosén et al. 2007; Spedding et al. 2003) and bats (Hedenström et al. 2007; Muijres et al. 2008). In addition to these vertebrate fliers, the flow fields of numerous insect taxa have been measured during hovering and forward flight (Bomphrey et al. 2005, 2006; Brodsky 1991; Grodnitsky and Dudley 1996; Grodnitsky and Morozov 1992, 1993; Srygley and Thomas 2002; Willmott et al. 1997). Most of these invertebrate studies concerned single vertical perspectives oriented along the body axis and therefore do not provide information about the contributions of bilateral wings to overall flow field structures. However, Bomphrey et al. (2006) constructed a composite view from serial sections and concluded that the Tobacco Hawkmoth (Manduca sexta) uses its wings to produce a single vortex loop during downstroke in forward flight.
Wake descriptions from slow-flying bats and faster-flying birds differ in two fundamental aspects: (1) bat wings produce two vortex loops whereas birds produce a single vortex loop per stroke, and (2) bats do not exhibit strong circulation during stroke transitions unlike birds. Our data indicate that during hovering flight, hummingbirds more strongly resemble the bat pattern. First, we see clear evidence for separate vortex loops for each wing (Fig. 8). Second, our kinematic results indicate that wingtip velocities approach 0 at stroke transition whereas for other birds during forward flight, airstream velocity at the wing tips remains high. Because aerodynamic forces are proportional to the square of velocity, vortex generation should cease as the wings decelerate near stroke transition for hovering hummingbirds. It would be highly informative to consider the flow field patterns of hummingbirds across a wide range of flight speeds.
With this model in mind, we can now consider the how the tail interacts with the wing wake. Although the tail oscillates with an approximately sinusoidal motion, the velocities around the actual tail are either 0 or positive, indicating net flow along the body axis but away from the bird. These velocities have high magnitudes and are almost certainly not a consequence of the wake imparted by the tail motion. Instead, these flows are likely the result of wake encounter by the two wings coming toward each other during the end of the upstroke. We hypothesize that the tail is deflecting these larger flows, although the magnitude of interference with the wake will depend upon the degree of tail spreading and the precise phasing of tail oscillation. Because the magnitude of the pressure force will be proportional to the square of the velocity, the hummingbird should have the capability of generating tail moments of sufficient size to use this structure in maintaining pitch stability.
In this communication, we focus on the analysis of the mean flow patterns for different wing and tail positions. This was done using measured horizontal velocity components in the horizontal plane. Although it is our eventual goal, at this stage we are not attempting to explain the force balance of the hovering bird through momentum or vorticity analysis because such computations would have to involve doubtful assumptions pertaining to the full three-dimensional flow field surrounding the bird. Dabiri (2005) demonstrated that the spatial velocity distribution in the wake is not sufficient for determination of locomotive forces but has to be combined with the pressure distribution. He proposed a method for accounting for the pressure contribution via wake vortex added-mass in analogy with the added-mass of fluid surrounding solid bodies.
At the present state, computational fluid dynamics and direct numerical simulation cannot be applied with confidence to bird flight. To develop and validate numerical models and to obtain information needed for analytical models (e.g., information to quantify added-mass tensor component proposed by Dabiri 2005) more detailed measurements are required. New technologies for real three-dimensional flow measurements should provide the necessary information, and can be combined with a numerical model to extract the pressure fields needed for full force balance analysis. In addition, such pressure estimates can be validated against existing, limited, pressure measurements (e.g., as in Usherwood et al. 2005). Particle tracking velocimetry can be applied directly to determine the Lagrangian properties of the flow, which can be used to determine the added-mass contributions (Dabiri 2005; Darwin 1953).
We thank David Lentink for comments on an earlier version of the manuscript, and Bret Tobalske and Paolo Segre for suggestions for experimental procedures. We also gratefully acknowledge Christian Bartolome, Brian Cho, Sirish Makan, Elsa Quicazán, James Soh, and Kenneth Welch for assistance with data collection and analysis. This research was supported by a Regents Faculty Fellowship to Douglas L. Altshuler.
This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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