Ascending flight and decelerating vertical glides in Anna's hummingbirds

Ascending flight is commonly used by volant taxa in a diversity of biological contexts, including chases, escapes and mating behavior. Climbing animals must exert sufficient muscle power output to overcome both gravity (i.e. the potential energy gain) and aerodynamic costs, both of which will increase with increasing ascent speed. Thus, near-maximal biomechanical performance can be expected during rapid vertical flight. Although take-off and near- or fully vertical ascent has been well studied for several avian groups (see Tobalske and Dial, 2000; Askew and Marsh, 2001; Berg and Biewener, 2008; Jackson, 2009; Jackson and Dial, 2011) and for some insects (see Marden, 1987; Muijires et al., 2017), it has never been explicitly studied in hummingbirds. Nonetheless, ascending flight is well known in many trochilid taxa. For example, the curving upward trajectory of the display dive in male Anna's hummingbirds is transiently vertical near the end of the behavior (Clark, 2009). Hummingbirds more generally provide an excellent model with which to study vertical flight because, from either perches or while in stationary hovering, they can initiate high accelerations and rapidly ascend distances on the order of tens of meters. Asymptotic load-lifting studies of maximal force production in hummingbirds also indicate that they can generate total vertical forces typically ∼3 times their body weight (Chai et al., 1997; Chai and Millard, 1997; Altshuler et al., 2010), with muscle-mass-specific powers for small and large species that range from 206 to 327 W kg⁻¹, respectively. Hence, we expect that motivated unloaded hummingbirds at a maximal climbing rate should exhibit high levels of power expenditure similar to those during flight with maximal loads.

Hummingbirds in ascent must eventually slow and stop relative to global or local landmarks. When approaching a target in space, or while landing, animal fliers use exteroceptive feedback to decelerate to their final position. The function termed time-to-contact, τ (i.e. the distance-to-contact divided by the approaching speed), can be used to characterize body kinematics relative to control of the approach (see Lee, 1976). If the first derivative of τ is constant and ≤0.5, the trajectory will terminate at the target; if 0.5<τ≤1, then some overshooting will occur. For hummingbirds horizontally approaching a feeder, values for τ are typically 0.75, indicating a controlled but low-speed braking entrance into a simulated flower (Lee et al., 1991). Hummingbirds in ascending flight often target specific objects (e.g. flowers, small insect prey and intruders), and arrival at the target is presumably controlled visually, as in horizontal flight. Here, we analyze flight performance of Anna's hummingbirds [Calypte anna (Lesson 1829)] rapidly traversing a vertical distance of ∼2 m toward a nectar source, and describe their body posture and wingbeat kinematics during this feat, along with their time-to-contact function. We also document a vertical upward glide and associated body and wing orientations immediately prior to reaching their visual target.

This research was conducted in compliance with Animal Use Protocol 2016-02-8338 at the University of California, Berkeley. Live bird trapping was carried out under permits from the United States Fish & Wildlife Service (MB054440-0) and the California Department of Fish and Wildlife (SC-6627). Four adult male Anna's hummingbirds were captured in Berkeley, CA, USA; birds were released into the wild at the capture point following the study's completion. Sample size and bird order during experimentation were based on availability, and were not fixed prior to the study so as to detect pre-specified effects. We trained each bird to perform ascending flights in a vertical chamber (2.4×0.65×0.35 m, height×width×depth) framed with PVC tubing, and covered with tulle fabric. The ceiling of the chamber consisted of white poster board; an artificial feeder filled with a commercial nectar solution (Nektar-Plus) was placed directly beneath the center of the ceiling, and a perch several centimeters above the chamber's floor. Over 2–3 days, birds were individually allowed to fly, for periods of several hours, within the chamber and to freely feed using this perch–feeder configuration.

To initiate flight experiments, the feeder was first physically occluded so as to elicit perching by the bird on an additional perch inserted 30 cm above the flight chamber's floor. An array of 250 W incandescent lights was then turned on to illuminate the chamber background and ceiling, and a visual stimulus, which consisted of one of us (V.M.O.-J.) suddenly turning on the lights in an otherwise darkened room and approaching the cage while rapidly extending his arm as if to contact the bird, was used to elicit a startle response from the bird, which immediately took off and ascended vertically to the feeder. A vertical scale on one wall was used for calibration. A video camera positioned horizontally to the flight chamber, and thus with the optical axis nominally perpendicular to the flight trajectory, was used to film (at 500 frames s⁻¹) the ascent of each bird. Within the camera's field of view was also positioned a mirror (35×45 cm) placed at 45 deg from vertical so as to obtain a simultaneous recording of the trajectory from beneath the ascending bird. A single escape flight was recorded and analyzed per bird (e.g. Movie 1). Body mass m_b, wing area S and wing length R of each bird were measured after filming.

For each video sequence, the beak base, tail tip, tail base, right-wing tip and right shoulder were digitized from the lateral camera view. We also digitized the right-wing tip and right shoulder using the bottom view from the mirror. Vertical position of the bird through time (z) was obtained using the position of the beak base. Vertical body orientation, χ_body, was calculated as the angle from the vector formed by the beak base and tip tail with respect to the horizontal. Similarly, tail orientation (α_tail) was taken as the angle formed by the tail base and tip tail relative to the longitudinal body axis. A quintic spline was applied to smooth all positional data (see Walker, 1998), and the first and second derivatives of the resulting spline function were calculated to obtain the vertical speed (U_z) and acceleration (a_z), respectively. Stroke plane angle (β) relative to horizontal was calculated from the average vector formed by the wing tip at the beginning and the end of both the downstroke and the upstroke, with a correction for average vertical displacement of the body over the same time interval. For each wingbeat cycle, stroke amplitude φ was calculated from the vector formed by the wing tip and shoulder at the top and bottom of the wingbeat; flapping frequency n was obtained from the number of frames required to complete a wingbeat. For each recorded flight, we obtained average and maximum values of stroke amplitude and flapping frequency for all wingbeats of the ascent from the point of take-off until the bird ceased flapping and adopted a ballistic posture (see Results).

Following helicopter theory (Johnson, 1980), we estimated induced power as the product of the body weight and the sum of the bird's vertical speed (U_z) and the induced velocity (V_ind). Profile power was computed using the formula of Ellington (1984) and a drag coefficient equal to 7/(Re)^0.5, where Re is the mean Reynolds number of the wing chord. Although this is a simplified approach to the drag coefficient (see Kruyt et al., 2014), such profile power estimates were up to ∼17% of total power requirements (see Results). Parasite power was estimated using the steady-state drag equation assuming a parasite drag coefficient equal to 2.85×10⁻³m_b^0.75/A (see Norberg, 1990), where A is the frontal projected area of a frozen hummingbird specimen (1.9 cm²). Values for P_kinetic and P_potential were calculated as m_bU_za_z and m_bU_zg, respectively, where a_z is the vertical acceleration of the bird and g is the acceleration of gravity. Because P_potential is included within the estimate of P_ind (see Johnson, 1980), the total aerodynamic power (P_mech) was estimated as the sum of P_kinetic, P_pro, P_par and P_ind, assuming perfect elastic storage of wing inertial energy. All mechanical power calculations were normalized by m_b, and we used the average and maximal values of U_z and a_z to calculate average and maximal values for total power output, respectively. The tau function τ was calculated as the ratio of the approach distance of the beak tip to the feeder at the start of deceleration to its instantaneous vertical speed. Instantaneous speed was estimated from the quintic spline function relating vertical position to time (see Walker, 1998). Linear fits were then determined for the relationship between the tau function and the time of contact; these fits met statistical assumptions for linear regression. A dataset including the raw data from this study is available as supplementary material (Dataset 1).

After take-off, birds accelerated vertically over a distance of ∼1.2 m, and then slowly decelerated (Fig. 1A–C). Mean (maximal) vertical speeds and accelerations among the four birds averaged 2.2±0.1 m s⁻¹ (3.5±0.3 m s⁻¹) and 1.8±0.6 m s⁻² (8.3±1.8 m s⁻²), respectively (Table 1). At a height equal to ∼80% of the total ascent distance, all birds ceased flapping and folded their wings against the body while decelerating, a behavior we term a vertical glide (Fig. 1D,E; Movies 1, 2). Birds maintained this ballistic posture until they attained the approximate height of the feeder (i.e. at 2.0±0.1 m height), and then resumed flapping in hovering flight. Stroke amplitude and wingbeat frequency over the actively powered period of ascent averaged 148±19 deg and 46±2 Hz, respectively, with maxima of 181±14 deg and 53±3 Hz, respectively (Table 1). During the entire ascent (i.e. during both active and passive components), birds maintained a nearly vertical body orientation with the tail nearly parallel to the longitudinal body axis; stroke plane angle was near zero (Table 1, Fig. 1E). Values of P_kinetic, P_pro and P_par were relatively small in all cases (see Table 2). Estimates of total aerodynamic power averaged 50 W kg⁻¹, with an average maximum of 90 W kg⁻¹ (see Table 2). Slopes for the first derivative of the tau function against time-to-contact averaged 0.75±0.1 among the four individual birds (Fig. 2).

During ascent from rest, Anna's hummingbirds reached speeds up to ∼4 m s⁻¹ and accelerations against gravity as high as 1 g. Flight performance for this behavior was comparable to that observed in studies of hummingbirds sustaining external loads of approximately one body weight, during which they hover via compensatory increases of ∼20% in both flapping frequency and wingbeat amplitude (see Chai et al., 1997; Chai and Millard, 1997). Similarly, Anna's hummingbirds during ascent showed average (maximal) increases in n and φ of 13% (29%) and 17% (44%), respectively (see Table 1), relative to typical values in hovering flight (i.e. 41 Hz and 126 deg, respectively; Ortega-Jimenez and Dudley, 2012). Body-mass-specific power P_per (i.e. P_pro+P_par+P_ind) of these ascending hummingbirds averaged 48 W kg⁻¹, which corresponds to ∼185 W kg⁻¹ of muscle-mass-specific power output assuming a flight muscle to body mass fraction of 26% (the average value from 14 species of hummingbirds obtained by Altshuler et al., 2010). This latter power estimate is 41% greater than that estimated for comparably sized ruby-throated hummingbirds hovering in a demanding low-density atmosphere (∼131 W kg⁻¹; Chai and Dudley, 1996). By contrast, the average muscle-mass-specific power value of ascending hummingbirds was up to 24% lower than that of small hummingbird species (<4 g) lifting maximum loads over a shorter time period (i.e. 206–230 W kg⁻¹ of muscle; Chai et al., 1997; Chai and Millard, 1997). However, direct comparison of load-lifting studies and the vertical ascent described here is confounded, as hummingbirds in the present study exhibited variable accelerations and changes in potential energy during the behavior, and power estimates will thus strongly depend on the time interval of estimation. Our calculations do suggest, however, that the total maximum muscle-mass-specific power of Anna's hummingbirds, which includes P_kinetic and P_potential, can be as high as 354 W kg⁻¹ (see Table 2); this value is ∼10% higher than that achieved by large hummingbirds (∼8 g) lifting three times their body mass (∼327 W kg⁻¹; Chai and Millard, 1997). Black-chinned hummingbirds during much more rapid transient maneuvers can reach values of ∼480 W kg⁻¹ of muscle mass (see Cheng et al., 2016). Here, the motivated vertical ascent in question occurs over 40–45 wingbeats, and is thus behaviorally very different than sustained hovering in low-density gas mixtures (Chai and Dudley, 1996), but more similar (albeit still of longer duration) to those during territorial bouts (e.g. Sholtis et al., 2015). Thus, physiological limits to hummingbird flight performance in different kinds of challenging scenarios (e.g. flight in reduced atmospheres, maneuvers or accelerating ascent) may reflect time-dependent aerobic performance of the flight muscle under such conditions (see Butler, 2016). During vertical escape, songbirds of mass <10 g are characterized by average mass-specific power outputs ranging from 90 to 100 W kg⁻¹ (see fig. 7 in Jackson, 2009), values that are similar to those obtained here for hummingbirds in vertical ascent (Table 2).

Power production during vertical flight has also been studied in larger birds. For example, various phasianid species (e.g. chukar and bobwhite quail) can produce a muscle power output of ∼150 W kg⁻¹ in vertical ascent (Tobalske and Dial, 2000), roughly half that of the hummingbirds studied here. Similarly, corvids and quail during vertical burst escape reach high and likely maximal muscle-specific powers ranging from 200 to 471 W kg⁻¹ of muscle (Jackson and Dial, 2011; Askew and Marsh, 2001). Hummingbirds in the present study in vertical ascent reached power outputs comparable to the average values reached by the aforementioned larger birds, in part because of high stroke amplitudes and flapping frequencies (see Table 1); these power estimates suggests a vertical speed limit for male Anna's hummingbirds of approximately ∼4 m s⁻¹ in still air. However, the maximal muscle power output of hummingbirds as estimated here may also reflect the absence of anaerobic contributions, which will be present in the larger avian taxa. Additional studies of ascending flight over short distances can potentially demonstrate limiting kinematics and the mechanical costs of maximum performance for a variety of volant taxa, including insects and bats, and without the use of external weight loading, altered flight media or other such experimental manipulations.

Ascending hummingbirds accelerate maximally during the initial portion of the ascent, and then progressively slow (Fig. 1C). As observed in horizontal deceleration to feeders (Lee et al., 1991), the rate of slowing is consistent with use of the tau function, although in this case target approach occurs during passive upward gliding with folded wings. Substantial wing folding and bending (also known as wing morphing) is known from swifts in gliding maneuvers (Lentink et al., 2007), during intermittent flights in some avian taxa (Tobalske et al., 2009) and during passage through apertures (Schiffner et al., 2014), although the timing of wing folding relative to body trajectories has not been examined in these cases. Particularly impressive here is the calculated ballistic approach to the top of the flight chamber, with wing folding occurring approximately 150 ms prior to the end of the trajectory (Fig. 1). Control of body pitch (either passively or actively) is also required to maintain vertical posture; corrective torque could be applied either aerodynamically or inertially through tail motions (see Movies 1, 2). Comparable use of the tail, apparently for stability, occurs in Anna's hummingbirds during horizontal flight in von Kármán vortex streets (Ortega-Jimenez et al., 2014). Impressively, hummingbirds in vertical ascent are also capable of controlled high-speed shaking (Movie 3), a behavior otherwise only known during hovering in rain (Ortega-Jimenez and Dudley, 2012; this aerial shaking sequence was not included in either the data tables or power estimates). Such precise positional control during rapid ascent, as well as the vertical glide, further extend the range of novel maneuvers (see also Dakin et al., 2018) that have been recently described for this amazing lineage of birds.

We thank Sarahi Arriaga-Ramirez for programming help in MATLAB.