SUMMARY

Power output is a unifying theme for bird flight and considerable progress has been accomplished recently in measuring muscular, metabolic and aerodynamic power in birds. The primary flight muscles of birds, the pectoralis and supracoracoideus, are designed for work and power output, with large stress (force per unit cross-sectional area) and strain (relative length change) per contraction. U-shaped curves describe how mechanical power output varies with flight speed, but the specific shapes and characteristic speeds of these curves differ according to morphology and flight style. New measures of induced, profile and parasite power should help to update existing mathematical models of flight. In turn, these improved models may serve to test behavioral and ecological processes. Unlike terrestrial locomotion that is generally characterized by discrete gaits, changes in wing kinematics and aerodynamics across flight speeds are gradual. Take-off flight performance scales with body size, but fully revealing the mechanisms responsible for this pattern awaits new study. Intermittent flight appears to reduce the power cost for flight, as some species flap–glide at slow speeds and flap–bound at fast speeds. It is vital to test the metabolic costs of intermittent flight to understand why some birds use intermittent bounds during slow flight. Maneuvering and stability are critical for flying birds,and design for maneuvering may impinge upon other aspects of flight performance. The tail contributes to lift and drag; it is also integral to maneuvering and stability. Recent studies have revealed that maneuvers are typically initiated during downstroke and involve bilateral asymmetry of force production in the pectoralis. Future study of maneuvering and stability should measure inertial and aerodynamic forces. It is critical for continued progress into the biomechanics of bird flight that experimental designs are developed in an ecological and evolutionary context.

Introduction

Power (work per unit time) is a dominant theme when exploring flapping flight in birds because the power required for flight is greater than for other forms of animal locomotion(Schmidt-Nielsen, 1972). Muscle mass-specific mechanical power output varies from 60–150 W kg–1 during cruising flight(Tobalske et al., 2003; Askew and Ellerby, 2007) to 400 W kg–1 during take-off(Askew and Marsh, 2001; Askew et al., 2001), and metabolic rates during flight are up to 30 times basal metabolic rate(Nudds and Bryant, 2000). As a consequence of high power demands, most studies of bird flight assume that the internal and external wing design in flying birds has been, and continues to be, shaped by natural selection for efficiency in flight, with efficiency defined as mechanical power output from the muscles divided by metabolic power input to the muscles. This assumption, like any hypothesized to be associated with selective pressures, should be explicitly tested more often than is the case (Gould and Lewontin,1979). Nonetheless, from this starting premise, considerable progress has been made into understanding how power output varies with flight speed, mode (level, take-off and ascending, descending), wingbeat kinematics,and flight style (intermittent, maneuvering). Recent research furthering this progress is the focus of this review. As a variety of new technologies have made it more feasible than ever before to measure variables bearing upon flight performance, this is an exciting time to be engaged in studies of the mechanics of bird flight.

Power is measured at three different levels pertinent to flapping flight. The first level is metabolic power input (Pmet) to the muscles, directly of interest to a flying, foraging bird, and generally a realm of study for respiratory, thermal and chemical physiologists. Pmet is the rate the bird expends chemical energy to supply the flight muscles, and it may be measured using double-labeled water(Nudds and Bryant, 2000; Ward et al., 2004; Engel et al., 2006), labeled bicarbonate (Hambly et al.,2002), oxygen consumption and carbon dioxide production(Ward et al., 2001; Ward et al., 2004; Bundle et al., 2007). Pmet equals the sum of mechanical power output from the muscles (Pmus) and the rate of heat loss from the muscles. Thus, Pmet may also be modeled using measures of heat transfer (Ward et al.,2004).

At the next level, still inside the animal, Pmus acts upon the skeleton and feathers. Except for thermal losses in connective tissue, which are presently unknown:
\[\ P_{\mathrm{mus}}=P_{\mathrm{iner}}+P_{\mathrm{aero}},\]
(1)
where Piner is inertial power required to oscillate the wing and Paero is the aerodynamic power required for flight. Biomechanists measure Pmusin vivo using surgically implanted strain-gauges and sonomicrometry crystals(Dial and Biewener, 1993; Tobalske et al., 2003; Hedrick et al., 2003)(Fig. 1A) and in vitrousing isolated muscle fibers and ergometers(Askew and Marsh, 1997; Askew and Marsh, 2001; Askew and Ellerby, 2007). Electromyography (Dial, 1992a)is used to measure neuromuscular control of Pmus, and wing kinematics from high-speed film or video are used to estimate Piner (Hedrick et al.,2004).
External to the animal, Paero is the third level of power output of interest:
\[\ P_{\mathrm{aero}}=P_{\mathrm{ind}}+P_{\mathrm{pro}}+P_{\mathrm{par}}+{\Delta}(E_{\mathrm{p}}+E_{\mathrm{k}}){/}t,\]
(2)
where Pind is induced power, the cost of lift production, Ppro is profile power, used for overcoming drag on the wings, Ppar is parasite power, used for overcoming drag on the body, Ep is potential energy, Ekis kinetic energy, and t is time. Kinematic measurements, coupled with mathematical theory (Pennycuick,1975; Rayner,1979a; Rayner,1979b; Ellington,1984), provide estimates of each of the components of Paero, while empirical measurements involve the use of techniques including accelerometry(Pennycuick et al., 2000; Hedrick et al., 2004),pressure transduction (Usherwood et al.,2003; Usherwood et al.,2005), force balances(Csicsáky, 1977; Pennycuick et al., 1988; Lentink et al., 2007) and digital particle image velocimetry (DPIV)(Spedding et al., 2003; Warrick et al., 2005).

To introduce the biomechanics of bird flight, I will first summarize current understanding about the functional morphology of the avian wing with implications for Pmus. Then, I will evaluate how Paero varies with flight speed and explore some of the wingbeat kinematics, flight modes and styles that covary with Paero. Other variables besides work and power are of great importance to the biology of flying birds, including the ability to maneuver(Warrick et al., 2002) as well as be stable (Thomas and Taylor,2001; Taylor and Thomas,2002; Taylor and Thomas,2003). Compared with the amount of empirical data describing steady hovering and forward flight, less is known about the biomechanics of maneuvering and stability, and these subjects represent a new frontier of study. Thus, I will include a synopsis of current data from maneuvering flight before concluding with reflections on promising avenues for future research.

Primary flight muscles

The pectoralis, the primary depressor and pronator of the wing, is the largest muscle of the wing (Fig. 1A), and the supracoracoideus, the primary elevator and supinator(Poore et al., 1997), is second in mass. Both muscles insert upon the humerus and decelerate and reaccelerate the wing across the transitions between upstroke and downstroke(Dial, 1992a). Because of its size, the pectoralis is perceived to be the `motor' that accounts for the bulk of Pmus for bird flight(Dial and Biewener, 1993). Birds can take-off and fly without use of their supracoracoideus(Sokoloff et al., 2001), which indicates that other flight muscles may contribute to wing elevation. Likewise, birds can fly steadily, but not take-off or land in a controlled manner, without the use of their distal wing muscles(Dial, 1992b). Distal muscles of the wing are activated primarily during non-level modes of flight(Dial, 1992a), and bird species that regularly engage in non-steady modes of flight, including maneuvering, have proportionally bowed forearms. This outward bowing of the radius and ulna is hypothesized to be due to the need to accommodate more muscle mass with an enhanced role of distal wing muscles in these species. The forearm muscles supinate, pronate, flex and extend the distal wing(Dial, 1992b). With the exception of the supracoracoideus (Poore et al., 1997; Tobalske and Biewener, 2007), the mechanical contribution the other muscles of the wing has not yet been measured. Power output in the supracoracoideus closely matches estimated Piner for upstroke (Tobalske and Biewener, in press).

Fig. 1.

In vivo measurements of mechanical work and power output from the pectoralis, the primary downstroke muscle of the avian wing are accomplished using surgically implanted strain gauges calibrated to measure force from bone strain on the deltopectoral crest of the humerus and using sonimicrometry crystals to measure muscle length (A). Similar methods are employed for the primary upstroke muscle, the supracoracoideus (not shown), which is located deep to the pectoralis (Tobalske and Biewener, in press). (From Hedrick et al., 2003.) (B) A`work loop', the area of which represents in vivo mechanical work in the pectoralis of a cockatiel Nymphicus hollandicus during one wingbeat (adapted from Tobalske et al.,2003). Arrows indicate the progression of contractile behavior. Electromyography (EMG) activity in the pectoralis indicates that the muscle functions to decelerate the wing at the end of upstroke and accelerate the wing during the first third of downstroke.

Fig. 1.

In vivo measurements of mechanical work and power output from the pectoralis, the primary downstroke muscle of the avian wing are accomplished using surgically implanted strain gauges calibrated to measure force from bone strain on the deltopectoral crest of the humerus and using sonimicrometry crystals to measure muscle length (A). Similar methods are employed for the primary upstroke muscle, the supracoracoideus (not shown), which is located deep to the pectoralis (Tobalske and Biewener, in press). (From Hedrick et al., 2003.) (B) A`work loop', the area of which represents in vivo mechanical work in the pectoralis of a cockatiel Nymphicus hollandicus during one wingbeat (adapted from Tobalske et al.,2003). Arrows indicate the progression of contractile behavior. Electromyography (EMG) activity in the pectoralis indicates that the muscle functions to decelerate the wing at the end of upstroke and accelerate the wing during the first third of downstroke.

In contrast with the primary muscles of the limbs of terrestrial animals that develop force nearly isometrically during walking and running, the pectoralis in flying birds is designed to produce work and power(Biewener and Roberts, 2000)(Fig. 1B). Sonomicrometry reveals that the pectoralis undergoes proportionally large length change(muscle strain), during contraction (20–40% of muscle resting length)and exhibits a contractile velocity of 4–10 muscle lengths s–1 among species(Biewener et al., 1998; Tobalske and Dial, 2000; Askew and Marsh, 2001; Hedrick et al., 2003; Tobalske et al., 2005). Similar levels of muscle strain and strain rate are exhibited by the supracoracoideus (Tobalske and Biewener, in press). It is important to note that the pectoralis exhibits a bipinnate architecture with regional heterogeneity in contractile behavior, which means that measurements of strain taken at any one location must be evaluated with caution(Soman et al., 2005). Using strain gauges, measurements of bone strain in the humerus adjacent to the insertion of the muscles may be calibrated to measure whole-muscle force, but there are concerns about high variance in calibrations(Tobalske et al., 2003) and some species do not have a humerus shape that is amenable to measurements(Tobalske and Dial, 2000).

Birds may use a variety of methods to modulate Pmus. Among flight speeds, cockatiels Nymphicus hollandicus primarily modulate Pmus by varying the proportion of motor units recruited in the pectoralis and, thereby, varying force(Hedrick et al., 2003). Likewise, pigeons Columba livia vary motor-unit recruitment and pectoralis force among flight modes (Dial,1992a; Dial and Biewener,1993). Other factors may permit modulation in Pmus, including the shortening fraction, trajectory, and timing of muscle activation and deactivation(Askew and Marsh, 1997; Askew and Marsh, 2001). It was formerly hypothesized that small birds were constrained by their muscle physiology to use a narrow range of contractile velocity in their pectoralis(Rayner, 1985), but sonomicrometry and electromyography reveal that they use the same mechanisms as larger birds, the timing and magnitude of neuromuscular activation as well as the contractile velocity of the muscle, for modulating Pmus (Tobalske et al., 2005; Tobalske and Biewener, in press; Askew and Ellerby, 2007). Many birds also regularly use non-flapping phases (brief, extended-wing glides or flexed-wing bounds) to modulate power during intermittent flight (see`Intermittent flight', below).

Variation in Paero with flight speed

U-shaped power curve

A variety of mathematical models may be used to estimate the effects of flight speed upon components of Paero(Norberg, 1990). Models that are mostly widely employed are those of Pennycuick(Pennycuick, 1975; Pennycuick, 1989) and Rayner(Rayner, 1979a) for forward flight and, for hovering, those of Rayner(Rayner, 1979b) and Ellington(Ellington, 1984). Regardless of which model is used, the general prediction that always emerges is that Paero should vary with flight speed according to a U-shaped curve, with greater Paero required during hovering and fast flight and less required during flight at intermediate speeds (Norberg, 1990)(Fig. 2A). As a function of forward flight velocity, the cost of producing lift, Pind,decreases, while power needed to overcome drag on the wings and body, Ppro and Ppar, respectively,increases.

The U-shaped curve for Paero features a characteristic minimum power speed (Vmp) and a maximum range speed(Vmr; Fig. 2A). These characteristic speeds represent one of the most obvious ways in which the biomechanics of flight may be integrated with behavioral ecology. Often, a starting premise for ecological studies of flight is that birds should select Vmp for aerial foraging or searching and select Vmr for long-distance flight such as migration,although specific predictions change when optimal foraging factors such as rate of energy intake or prey-delivery rates are incorporated into the models(Hedenström and Alerstam,1995; Houston,2006).

Consistent with the hypothesis that the pectoralis is the primary muscle supplying the mechanical power output required for flight, measures of Pmusin vivo(Tobalske et al., 2003)(Fig. 2B) and in vitro(Askew and Ellerby, 2007) vary as U-shaped curves in the same manner as Paero. The shape of a Pmus curve is affected by the morphology and flight style of a given species, and this means that there is inter-specific variation in Vmp and Vmr. Some models of Paero may be refined to take into account details of wing shape, wing kinematics and intermittent flight behavior(Rayner, 1979a; Rayner, 1979b; Ellington, 1984; Rayner, 1985). Thus, efforts to better understand both the biomechanics and ecology of flight will benefit from revision of these models as additional empirical evidence emerges.

Small differences in efficiency (i.e. Pmus/Pmet) have the potential to dramatically affect the shape of the Pmet power curve relative to that of Pmus and Paero(Thomas and Hedenström,1998; Rayner,1999). Since Pmet is the rate of energy input by a bird, the shape of the Pmet curve, rather than that of Pmus or Paero, is what is ultimately of importance in governing the Vmp and Vmr of interest to a bird. For many years, it appeared that the curve for Pmet was flat at intermediate flight speeds, which suggested that efficiency is lowest in the range of preferred flight speeds (reviewed in Ellington,1991). Recently, efforts to measure Pmet using a variety of techniques including double-labelled water, heat transfer and gas respirometry, reveal that the curve for Pmet is U-shaped much as that for Pmus and Paero, with muscular efficiency in the range of 20%(Ward et al., 2001; Ward et al., 2004; Engel et al., 2006; Bundle et al., 2007)(Fig. 2C). Comparison of the curves for Pmet and Pmus in cockatiels Nymphicus hollandicus, measured in two different studies, suggests that efficiency is not constant across speeds and that Vmpand Vmr are both faster when measured using Pmet compared with Pmus(Tobalske et al., 2003; Bundle et al., 2007)(Fig. 2). To further clarify this issue, it is vital to measure Pmet and Pmus under similar experimental conditions due to potential differences in Paero when a mask and respirometery cabling is added to an animal(Bundle et al., 2007).

The major difference among models of Paero is the method used to estimate Pind, although different approaches are also employed to estimate Ppro and Ppar. In a relatively simple model that is widely used by ecologists, in part because it is available as a computer program(Pennycuick, 1975; Pennycuick, 1989), Pind is estimated using a steady-state momentum-jet model. This model treats the wings as fixed-length propellers rotating and translating at a steady rate, as in a helicopter, even for the gliding flight of birds. Propellers do not fully represent the complexity of the motions and morphing ability of bird wings (Bilo,1971; Bilo, 1972; Warrick et al., 2005; Lentink et al., 2007). In contrast, alternative models (Rayner,1979a; Rayner,1979b; Ellington,1984) use vortex theory, which is capable of incorporating unsteady motion and long-axis rotation of the wings (e.g. Dickinson et al., 1999).

Fig. 2.

U-shaped curves of power as a function of flight speed in birds. (A)Estimated mechanical power output required for flight in a European kestrel Falco tinnunculu (from Rayner,1999). Paero, total aerodynamic power, Pind, induced power, Ppar, parasite power and Ppro, profile power, Vmp,velocity for minimum power, Vmr, velocity for maximum range. (B) In vivo mechanical power output from wind-tunnel flight across flight speeds as measured using strain gauges, sonomicrometry and wing and body kinematics in dove Zenaida macroura, cockatiel Nymphicus hollandicus, magpie Pica hudsonica (from Tobalske et al., 2003). (C)Oxygen consumption, an index of metabolic power output, measured in cockatiels over a range of flight speeds using gas respirometry (from Bundle et al., 2007).

Fig. 2.

U-shaped curves of power as a function of flight speed in birds. (A)Estimated mechanical power output required for flight in a European kestrel Falco tinnunculu (from Rayner,1999). Paero, total aerodynamic power, Pind, induced power, Ppar, parasite power and Ppro, profile power, Vmp,velocity for minimum power, Vmr, velocity for maximum range. (B) In vivo mechanical power output from wind-tunnel flight across flight speeds as measured using strain gauges, sonomicrometry and wing and body kinematics in dove Zenaida macroura, cockatiel Nymphicus hollandicus, magpie Pica hudsonica (from Tobalske et al., 2003). (C)Oxygen consumption, an index of metabolic power output, measured in cockatiels over a range of flight speeds using gas respirometry (from Bundle et al., 2007).

When a wing produces lift, there is a net circulation of air about the wing that represents a bound vortex on the wing(Rayner, 1979a; Rayner, 1979b; Ellington, 1984). The term`bound' in this instance means attached or close to the wing, and is a definition independent of the flexed-wing bound posture used in intermittent flight. For real-world wings of finite span, the bound vortex is shed into the wake as a `wake' vortex, and the circulation in the wake vortex is equal in magnitude but opposite in sign to that of the bound vortex. Circulation varies with translational and long-axis rotational velocity, angle of attack and camber of the wing. Lift, in turn, is proportional to circulation as well as wing span, translational velocity and air density. One simple way to think of the relationship between wake vortices and lift is that, for a given need for lift, as surface area surrounded by the wake vortices increases, the velocity that the wings induce into the wake and the cost of producing lift, Pind, both decrease.

During the 1980s there was an earnest attempt to test vortex theory for flying birds using particle image velocimetry (PIV). Although the geometry of the vortices shed into the wake during slow flight matched expectations, the researchers were frustrated by measurements of momentum in the wake that were insufficient to support the weight of the bird(Spedding et al., 1984). This`momentum deficit paradox' was resolved using modern DPIV(Spedding et al., 2003), which offers finer resolution of flow patterns in the wake. Significant new observations about wake structure will undoubtedly improve models of Pind.

For example, based on wake samples in the European kestrel Falco tinnunculus engaged in moderate-speed forward flight(Spedding, 1987), it was formerly thought that birds varied lift primarily using wing flexion, and not by changing circulation in the bound vortex on their wings viachanges in wing velocity, camber or angle of attack(Rayner, 1988). Instantaneous changes in circulation on the wings initiate the shedding into the wake of`cross-stream' vortices that are parallel to long-axis of the wings. These cross-stream vortices traverse the wake, they reveal a reduction in the effective area for lift production that is swept by the wings, and this reduction in effective area is predicted to increase the cost of producing lift, Pind (Rayner,1988). Assuming a lack of significant cross-stream vortices, the kinematics of faster flight in birds such as kestrels or pigeons (Columba livia) emerge as an optimal pattern of wing motion(Rayner, 1999)(Fig. 3A). Modern DPIV reveals that cross-stream vortices are typical of forward flight(Spedding et al., 2003; Hedenström et al., 2006)(Fig. 4), and this should serve to revise models of Pind during fast flight.

Fig. 3.

Wing kinematics differ depending upon a bird's wing design and flight speed. (A) Birds with pointed, high-aspect ratio wings such as the pigeon Columba livia transition from tip-reversal upstrokes during slow flight to feathered upstrokes at intermediate speeds and a swept-wing upstroke during fast flight. (B) Birds with rounded, low-aspect ratio wings such as the black-billed magpie Pica hudsonica use a flexed upstroke at all flight speeds. Shown are wingtip (filled circles) and wrist (open circles)paths in dorsal and lateral view (from Tobalske and Dial, 1996).

Fig. 3.

Wing kinematics differ depending upon a bird's wing design and flight speed. (A) Birds with pointed, high-aspect ratio wings such as the pigeon Columba livia transition from tip-reversal upstrokes during slow flight to feathered upstrokes at intermediate speeds and a swept-wing upstroke during fast flight. (B) Birds with rounded, low-aspect ratio wings such as the black-billed magpie Pica hudsonica use a flexed upstroke at all flight speeds. Shown are wingtip (filled circles) and wrist (open circles)paths in dorsal and lateral view (from Tobalske and Dial, 1996).

Likewise, DPIV has recently revised our understanding of the mechanics of hovering (Warrick et al.,2005). Hummingbirds are the only birds that can sustain hovering in still air, and formerly it was thought that they supported their weight during hovering using symmetrical down and upstrokes with equal Pind during each half of the wingbeat. This assumption lead to a proportionally lower estimate for Pind compared with all other bird species, in which it appears that only the downstroke helps to support weight during hovering and slow flight(Rayner, 1979a). DPIV instead reveals that approximately 75% of the weight support during a wingbeat is provided by downstroke, and 25% is provided by upstroke, in hovering rufous hummingbirds Selasphorus rufus(Warrick et al., 2005).

Fig. 4.

Representations of vortex wakes shed from the wings of a thrush nightingale Luscinia luscinia at slow (A), medium (B) and fast (C) flight speeds in a wind tunnel, measured using digital particle image velocimetry [DPIV(from Spedding et al., 2003)]. Red and blue indicate the wake from upstroke and downstroke, respectively. Both phases of the wingbeat are aerodynamically active at each speed, and there are prominent cross-stream vortices apparent at the ends of half-strokes during slower flight (A,B) and throughout the wingbeat cycle during faster flight (C).

Fig. 4.

Representations of vortex wakes shed from the wings of a thrush nightingale Luscinia luscinia at slow (A), medium (B) and fast (C) flight speeds in a wind tunnel, measured using digital particle image velocimetry [DPIV(from Spedding et al., 2003)]. Red and blue indicate the wake from upstroke and downstroke, respectively. Both phases of the wingbeat are aerodynamically active at each speed, and there are prominent cross-stream vortices apparent at the ends of half-strokes during slower flight (A,B) and throughout the wingbeat cycle during faster flight (C).

Reasonable measurements of Ppro are largely lacking for birds engaged in flapping flight, and this highlights a clear need for new research. Models presently either assume that profile drag is constant during intermediate flight speeds (Pennycuick,1975; Pennycuick,1989) or apply a coefficient of drag for the wing that is obtained from fixed-wing measurements and modeled according to blade-element theory,which treats the wing as set of fixed-width strips each moving at their own velocity, due to the flight velocity of the bird as well as the angular velocity of the wing (Rayner,1979b). Unfortunately, drag on fixed wings(Withers, 1981; Lentink et al., 2007) or during gliding in live birds (Pennycuick et al., 1992) is probably quite different from unsteady drag forces operating on the flapping wings during slow flight(Spedding, 1993; Dickinson, 1996). Promising methods for more accurate models of Ppro during flapping include measuring force using transducers at the base of mounted, revolving wings (Usherwood and Ellington,2002) or robotic flapping wings(Sane and Dickinson, 2001),perhaps coupled with computational fluid dynamics(Wang et al., 2004).

Caution is always merited when interpreting the measurements from revolving wings because propeller motion does not fully emulate the complex motion of the bird wing. Bearing this in mind, it may be that drag is higher during rotational motion of the wings compared with gliding. Maximal drag coefficients for the wings of galliform birds (Phasianidae) during rotation(Usherwood and Ellington,2002) are approximately double the value measured for translating wings (Drovetski, 1996).

To date, dynamically scaled robotic models have only been developed for insects (Willmott et al.,1997; Sane and Dickinson,2001), and these models have wings designed as flat plates that do not morph like bird wings (Bilo,1971; Bilo, 1972; Warrick et al., 2005). Ideally, efforts to physically model Ppro will incorporate detailed 3D kinematics of the wing (Askew et al., 2001; Hedrick et al.,2002; Tobalske et al.,2007) to program robotic motion and use materials for the robotic wing that morph in a realistic manner.

As for Ppro, estimates of Ppar are subject to considerable uncertainty because drag coefficients obtained from isolated bird bodies vary over 400%, from ∼0.1 in varnished, footless,starling carcasses (Maybury,2000) to ∼0.4 in frozen waterfowl(Pennycuick et al., 1988). One might expect values from live birds to be lower than frozen carcasses, but a parasite drag coefficient of ∼0.37 was measured from dive rates in passerines during migration(Hedenström and Liechti,2001). Coefficients from 0.24–0.34 may be representative of live starlings in flight, and drag coefficients decrease as a function of forward flight speed (Maybury,2000). There is some debate over the manner in which body area scales with body mass among species, and frontal projected area is necessary for a computation of coefficient of drag(Norberg, 1990). Hedenström and Rosén suggest that the frontal area of the body scales differently in passerines and non-passerines(Hedenström and Rosén,2003), whereas Nudds and Rayner argue that scaling is similar between the two groups, and that reported differences in other studies are caused by comparing live birds with frozen specimens(Nudds and Rayner, 2006).

To further understanding of the aerodynamics of the bird body, it will be useful to take a broader view of the body to include the tail(Thomas, 1993). Treating the body as a `parasite' upon the wings is a leftover from early aerodynamics research and is misleading, because the body is capable of producing lift even with the wings completely folded, as during intermittent bounds, which are flexed-wing pauses in between flapping phases(Csicsáky, 1977; Tobalske et al., 1999). The tail functions to reduce parasite drag(Maybury and Rayner, 2001); it contributes to the production of lift both when the wings are not present on a carcass (Maybury, 2000; Maybury et al., 2001) as well as during flight in live birds (Usherwood et al., 2005). Incorporating body lift (and, by extension, tail lift) into a model of Paero reduces the estimated power required for relatively fast flight in flap–bounding birds(Rayner, 1985; Tobalske et al., 1999).

A model that is useful for describing the aerodynamics of the tail considers the tail as delta wing (Thomas,1993). This model indicates that the tail morphology that produces the optimum lift-to-drag ratio is slightly forked when folded and triangular in shape when fanned, and that the area of the tail in front of the maximum span contributes to lift and drag, whereas the area behind the maximum span contributes only to drag. These properties of the tail serve as a foundation for testing, with vigorously debated conclusions, whether the evolution of ornamentation, such as an elongated tail or streamers on a forked tail,represent a handicap that resulted from sexual selection or an aerodynamic benefit for activities such as maneuvering(Thomas, 1993; Møller et al., 1995; Park et al., 2000; Evans, 2004). Aspects of the model do not appear to be well supported by the use of the tail during flight in barn swallows Hirundo rustica(Evans et al., 2002), so new efforts are needed to modify the delta-wing model or develop alternative models.

Kinematics and upstroke aerodynamics

Unlike some forms of terrestrial locomotion in which gait selection may be identified using discrete changes in duty factor (the proportion of time a limb is in contact with the substrate, producing force) and patterns of sequential limb motion (Alexander,1989), wing kinematics and associated aerodynamics, vary in a continuous manner with flight speed in birds.

Although downstroke kinematics are relatively invariant, upstroke kinematics differ among species and according to flight speed(Brown, 1963; Scholey, 1983; Tobalske, 2000; Park et al., 2001; Hedrick et al., 2002). Birds with wings that are relatively pointed, or of high-aspect ratio (long and thin), transition among flight speeds using tip-reversal upstrokes at slow speeds, feathered upstrokes at intermediate speeds, and swept-wing upstrokes at fast flight speeds (Fig. 3B). Birds that have rounded distal wings or wings of low aspect ratio (short and broad) tend to flex their wings regardless of flight speed. Some exceptions to this pattern exist. For example, galliform birds with rounded wings use a tip-reversal upstroke during take-off(Brown, 1963; Tobalske and Dial, 2000), and birds with rounded wings such as the black-billed magpie Pica hudsonica will alter upstroke postures according to acceleration and deceleration (Tobalske and Dial,1996). Regardless of wing shape, the span ratio (mid-upstroke span divided by mid-downstroke span) generally decreases as a function of flight speed in birds, although it may increase with increasing speed in some passerines (Tobalske and Dial,1996; Tobalske et al.,1999; Rosén et al.,2004; Tobalske et al.,2007).

Formerly, it was thought that there were two wingbeat gaits in birds because early PIV experiments revealed one of two patterns. One vortex ring was shed per downstroke during slow flight(Spedding et al., 1984), and the upstroke appeared aerodynamically inactive. This was identified as a`vortex-ring' gait (Rayner,1988; Rayner,1999). During faster flight(Spedding, 1987), tip-vortices were shed into the wake during the entire wingbeat, indicating a`continuous-vortex' gait (Rayner,1988; Rayner,1999). Because the wake area for a continuous-vortex wake would be greater than for a vortex ring, Pind was predicted to be lower for the continous-vortex gait.

Several problems are, nevertheless, apparent with a simple two-gait scheme for classifying avian flight (Tobalske,2000), and new data reveal that continuous, rather than discrete,variation is characteristic of wing kinematics and aerodynamics(Spedding et al., 2003; Rosén et al., 2004; Tobalske et al., 2007). Although a two-gait system is intuitively acceptable to humans, given our use of walking and running, a two-gait system does not advance our understanding of obvious differences in wing kinematics during the presumptive vortex-ring gait of slow flight (Tobalske,2000) (Fig. 3). All measured wing kinematics, as well as patterns of muscle activity, change in a gradual way across flight speeds (Tobalske and Dial, 1996; Tobalske,2000; Park et al.,2001; Tobalske et al.,2007). Furthermore, DPIV measurements of wake vortices across a range of speeds (Spedding et al.,2003; Hedenström et al.,2006) reveal that upstrokes are aerodynamically active during slow flight and that upstroke function varies gradually rather than categorically(Fig. 4).

Thus, the use of modern DPIV has highlighted a need for new comparative study of the aerodynamics of bird flight. For the limited number of species studied to date using DPIV, there does not appear to be significant variation in wake geometry during forward flight(Spedding et al., 2003; Hedenström et al., 2006). Also, the magnitude of normalized circulation (a dimensionless form, equal to circulation divided by wing chord and flight velocity) in the wake is similar among species (Hedenström et al.,2006). This may indicate that wing chord and flight speed are adequate predictors of circulation upon the wing, which would be highly useful for modeling efforts (Hedrick et al.,2002), since lift is proportional to circulation. More pessimistically, it may indicate that current DPIV measurements of time-averaged wake structures lack sufficient temporal resolution to reveal important details of wing aerodynamics(Dabiri, 2005).

Instead of a gait-based system of classification, a fascinating alternative that may serve to unify comparisons of kinematics and aerodynamics among birds is that they seek to maintain their Strouhal number (frequency times amplitude, divided by forward flight speed) during cruising flight in an effort to optimize the frequency of vortex shedding(Taylor et al., 2003). A diverse array of birds, as well as flying insects and swimming fish, exhibit Strouhal numbers in the range of 0.2–0.4 during cruising locomotion. Coordinated kinematic and DPIV studies will help test how these kinematics compare with rates of vortex shedding.

Maximum effort in slow flight

One way to elicit maximal performance from a bird is to get it to fly under conditions characteristic of the left side of the U-shaped power curve for flight (Fig. 2). Efforts to measure maximal performance may involve load-lifting(Marden, 1994; Chai and Millard, 1997; Altshuler et al., 2004),hovering in air of reduced density (Chai and Dudley, 1995; Altshuler et al., 2004), allowing the animal to escape to a refuge or freedom(DeJong, 1983; Warrick, 1998; Tobalske and Dial, 2000; Earls, 2000; Askew et al., 2001), or fostering competitive interaction(Tobalske et al., 2004).

Birds are already moving with significant velocity when their feet leave the ground at the end of take-off, and the majority of their initial flight velocity is due to hindlimb thrust (Earls,2000; Tobalske et al.,2004). Initial flight velocity increases with body size among birds (Tobalske et al., 2004)from 0.8 m s–1 in the rufous hummingbird (weighing 3 g) to 6 m s–1 in wild turkey (Meleagris gallopavo; 6 kg). Since they are already moving, Paero required immediately after take-off is lower than it would be from a standing start at 0 m s–1 (Fig. 2). This may represent a significant saving in power for birds that regularly take-off and land, so it would be worthwhile if measurements could be made in the same species for power during leg thrust(Henry et al., 2005) and Pmus of the wings during take-off(Dial and Biewener, 1993).

It is widely recognized that mass-specific whole-body power (W kg–1; theΔ(Ep+Ek)/t term in Eqn 2, divided by body mass),declines as body size increases among bird species(Pennycuick, 1975; DeJong, 1983; Ellington, 1991; Warrick, 1998; Tobalske and Dial, 2000). However, the mechanical explanations for this trend are not fully understood. Since whole-body power is directly relevant to escape from predation(Kullberg et al., 1998; Hedenström and Rosén,2001), new research is needed to better understand what factors limit performance. A potential explanation is that available mass-specific power from the flight muscles declines as a function of increasing body mass(Pennycuick, 1975; Ellington, 1991). If muscle stress and strain are invariant with body mass, then mass-specific work is invariant as well, and mass-specific power should scale with wingbeat frequency, approximately with mass to the –1/3 power(Hill, 1950; Pennycuick, 1975; Ellington, 1991).

As expected from this line of reasoning, mass-specific whole-body power scales with wingbeat frequency in galliforms during escape flight(Tobalske and Dial, 2000). However, when wing kinematics are input to an aerodynamic model(Askew et al., 2001), it is estimated that mass-specific Pmus actually increases,rather than decreases, with body mass. The estimated positive scaling of Pmus may be due to an increase in pectoralis strain(proportional to body mass raised to the 0.26 power)(Tobalske and Dial, 2000) or pectoralis stress (proportional to body mass raised to the 0.33 power)(Askew et al., 2001). Ideally these alternatives should be tested using in vivo strain-gauge recording, but the humerus of galliform birds is not suited for such measurements (Tobalske and Dial,2000). Other groups of species, such as doves [Columbidae(Dial and Biewener, 1993; Soman et al., 2005)] may prove useful for such a test. Lacking in vivo force data, the conclusion(Askew et al., 2001) that muscle strain scales positively with body mass during escape flight relies on the accuracy of models used for Paero. As outlined above(see `U-shaped power curve'), a variety of new methods including DPIV(Spedding et al., 2003; Warrick et al., 2005) and pressure-transducer measurements(Usherwood et al., 2003; Usherwood et al., 2005) show promise for helping to revise estimates of the cost of producing lift.

Additional evidence also indicates that flight performance in take-off or ascending flight should not necessarily be limited by a negative scaling of muscle-mass-specific power. In a broad comparison of take-off in insects and some birds, all of which had their legs immobilized, proportional load-lifting ability is reported to increase with increasing body mass(Marden, 1994). Also, larger hummingbirds exhibit greater ability to climb with added load or support their weight in reduced-density air compared with smaller hummingbirds(Chai and Millard, 1997; Altshuler et al., 2004). For hummingbirds, the positive scaling of flight performance is accounted for by departures from geometric and dynamic similarity among species. Larger hummingbirds have proportionally larger wings and use greater wingbeat amplitudes (Chai and Millard,1997; Altshuler et al.,2004); both attributes should reduce proportional Pind costs.

Fig. 5.

Intermittent flight postures exhibited by budgerigar Melopsittacus undulatus as a function of flight speed in a wind tunnel. Black, glide;grey, partial bound; white, bound (from Tobalske and Dial, 1994). As flight speed increases, the proportion of non-flapping phases consisting of glides decreases, and the proportion consisting of bounds increases.

Fig. 5.

Intermittent flight postures exhibited by budgerigar Melopsittacus undulatus as a function of flight speed in a wind tunnel. Black, glide;grey, partial bound; white, bound (from Tobalske and Dial, 1994). As flight speed increases, the proportion of non-flapping phases consisting of glides decreases, and the proportion consisting of bounds increases.

Intermittent flight

Many species of birds use intermittent flight, and the interruption of flapping phases with extended-wing glides or flexed-wing bounds has the potential to reduce Paero(Rayner, 1985; Rayner et al., 2001; Tobalske, 2001). Compared with continuous flapping, flap–gliding is estimated to require less Paero, at most flight speeds and in particular during slow flight, and flap–bounding is estimated to save Paeroin fast flight, more rapid than Vmr(Rayner, 1985). Generally consistent with the assumption that intermittent flight is useful for reducing Paero required for flight, a variety of bird species use intermittent glides at slow speeds and switch to intermittent bounds or partial bounds at faster speeds (Tobalske,2001; Bruderer et al.,2001) (Fig. 5). The pectoralis and supracoracoideus are inactive during bounds, and exhibit isometric contractions with reduced levels of muscle activation during glides(Tobalske, 2001; Tobalske et al., 2005).

There are profound effects of body size upon the use of intermittent flight. Species that use both flap–gliding and flap–bounding either have a body mass less than 300 g or have pointed wings of relatively high aspect ratio (Tobalske,1996; Tobalske,2001; Bruderer et al.,2001). Species larger than 300 g, for example pigeons, use intermittent glides but do not exhibit bounds. The scaling in passerines(Passeriformes) and woodpeckers (Piciformes) reveals that the percentage of time spent flapping increases with body mass(Tobalske, 1996; Tobalske, 2001). These patterns may be explained by an adverse scaling of sustainable mass-specific power in the flight muscles as body size increases, but this hypothesis must be tested exactly as outlined above (see `Maximum effort in slow flight')

Although they can glide, small birds, less than 30 g, with rounded,low-aspect ratio wings, appear to almost exclusively use bounds during intermittent flight (Tobalske et al.,1999; Tobalske et al.,2005; Askew and Ellerby,2007). This behavior is puzzling in light of the estimated higher Paero for flap–bounding during slow flight compared with continuous flapping (Rayner,1985; Rayner et al.,2001). Testing the underlying variables responsible for this behavior should prove challenging but, nevertheless, worthwhile, as flap–bounding is extremely common in the most diverse birds, the passerines.

An important hypothesis is that intermittent bounds are the sole mechanism available to small birds to enable them to modulate power output(Rayner, 1985), but the zebra finch Taeniopygia guttata (13 g) appears to be able to modulate contractile behavior in its muscles in the same manner as larger birds(Tobalske et al., 2005; Askew and Ellerby, 2007). An argument that such modulation may nevertheless be inefficient requires measurement of Pmet during continuous flight and flap–bounding. Likewise, any argument about the functional significance of flap–bounding would be strengthened if Paero was measured empirically rather than estimated from modeling and if Pmus could be measured in vivo. Unfortunately,the added weight and drag associated with masks and tubing used in gas respirometry causes small birds to stop using intermittent pauses(Bundle et al., 2007), and their bones are too small to permit strain-gauge recordings. For investigating the energetics of flap–bounding, it is feasible to use techniques other than gas respirometry for measuring metabolic rate including double-labelled water (Nudds and Bryant, 2000; Ward et al., 2001; Engel et al., 2006) or labeled bicarbonate (Hambly et al.,2002). Efficiency was estimated at 11% using labeled bicarbonate during slow flight in zebra finch Taeniopygia guttata(Hambly et al., 2002), and this is intriguing because this estimate is lower than a ∼20% estimate for efficiency during fast flight in starlings that was obtained using double-labelled water (Ward et al.,2001). It may be possible to measure thermal efficiency of contractions in isolated muscle preparations(Barclay, 1996).

Another hypothesis is that, regardless of efficiency, variation in flap–bounding flight patterns could be constrained by neural control of limb motion. This control could be in the form of a central pattern generator such as has already been reported for the flapping motion and respiration of birds (Funk et al., 1992). Aspects of flap–bounding do not appear consistent with this hypothesis,however, as the duration of bounds and the number of wingbeats between bounds vary significantly with flight speed(Tobalske et al., 1999).

Maneuvering and stability

The ability to maneuver (Warrick et al., 2002) and the converse, controlling position to be stable in the air (Thomas and Taylor,2001; Taylor and Thomas,2002; Taylor and Thomas,2003), are of great importance to flying animals. Highly maneuverable animals may respond more quickly to perturbations, thus they are expected to be better able to maintain their path during flight in turbulent conditions (Thomas and Taylor,2001). Certainly the ability to maneuver has implications for aerial foraging (Warrick,1998; Lentink et al.,2007). Wing morphology that is specialized for maneuvering may compromise other forms of performance such as acceleration ability during take-off (Warrick, 1998), so new research is needed to better understand how maneuvering ability may be related to escape performance.

Flapping motions may affect both maneuvering and stability. Downstroke is predicted to be a stabilizing influence about the longitudinal axis, whereas a lift-producing upstroke may be used to lower stability and thereby enhance maneuverability (Taylor and Thomas,2002). Depending upon their posture, the wings alone may provide longitudinal stability during gliding(Taylor and Thomas, 2002; Thomas and Taylor, 2001).

Lift and drag from the tail may also enhance stability, and the contribution of the tail is affected by morphology and posture(Hummel, 1992; Thomas and Taylor, 2001). For example, greater drag associated with a long tail contributes to longitudinal stability (Hummel, 1992),whereas pitching the tail with the trailing edge down will decrease stability(Thomas and Taylor, 2001). Kinematics from aerial insectivores indicates that the tail is used to vary total lift in concert with the wings rather than as an independent mechanism for controlling body pitch (Warrick,1998), and this hypothesis merits new comparative study.

Because the intrinsic three-dimensionality of maneuvering presents special challenges for study, relatively few data are available at present, and a general pattern does not yet emerge for describing the mechanics with which birds accomplish maneuvers. One pattern that is shared by pigeons and two species of parrots (Psittaciformes) during slow flight is that the birds initiate rolls during downstroke (Warrick and Dial, 1998; Hedrick and Biewener, 2007a; Hedrick and Biewener, 2007b). Pigeons effect their turns using subtle,bilateral force asymmetries in their pectoralis that are maintained throughout a turn (Warrick et al.,1998). Electromyographic patterns suggest that asymmetries in pectoralis force are also used in cockatiels during turns, but the side that exhibits greater activation switches midway through a turn(Hedrick and Biewener, 2007a). In contrast with these two species, in rose-breasted cockatoos Eolophus roseicapillus, electromyography indicates that bilateral asymmetries of force in distal wing muscles are more important for turning than minor asymmetries in the pectoralis (Hedrick and Biewener, 2007a; Hedrick and Biewener, 2007b).

Fig. 6.

Representation of a left turn during slow flight in a pigeon Columba livia, as seen in caudal view (from Warrick and Dial, 1998). (A)Roll is initiated using greater velocity on the outside (right) wing during the first part of downstroke. (B) Roll is arrested using greater velocity on the inside (left) wing during the latter half of downstroke.

Fig. 6.

Representation of a left turn during slow flight in a pigeon Columba livia, as seen in caudal view (from Warrick and Dial, 1998). (A)Roll is initiated using greater velocity on the outside (right) wing during the first part of downstroke. (B) Roll is arrested using greater velocity on the inside (left) wing during the latter half of downstroke.

In pigeons, roll is initiated in early downstroke with a higher velocity on the outer wing, and this roll is arrested with higher velocity on the inner wing during late downstroke or during the subsequent upstroke(Warrick and Dial, 1998)(Fig. 6). Cockatiels use asymmetric wingbeat amplitudes whereas cockatoos exhibit less significant asymmetry in amplitude, and they integrate this minor asymmetry with asymmetry in feathering angle (the angle wing chord relative to midline of the body)(Hedrick and Biewener, 2007a). Aerodynamic models suggest that velocity, amplitude and feathering-angle asymmetries cause lift asymmetries(Warrick and Dial, 1998; Hedrick and Biewener, 2007a). However, asymmetry in wing inertia may also contribute significantly(Hedrick and Biewener, 2007a; Hedrick and Biewener, 2007b; Hedrick et al., 2007). For example, in cockatoos, within-wingbeat rolling is accomplished primarily using asymmetries in wing inertia. Thus, future research would do well to measure wing inertia along with aerodynamic forces(Hedrick et al., 2007).

One conclusion that is clear from this recent work is that flapping dynamics must be incorporated into existing models of maneuvering(Taylor and Thomas, 2002; Warrick et al., 2002). Given a lack of kinematics, early attempts to model the comparative maneuvering ability of birds have treated these activities as fixed-wing events(Norberg, 1990). Moreover,even fixed-wing maneuvering predictions may need revision, given the recent observation that the distal portions of the wings of common swifts Apus apus may exhibit leading-edge vorticity when in a glide posture(Videler et al., 2004). Leading-edge vorticity on physical models of swift wings is of sufficient magnitude to increase lift, hence torque for maneuvering, above that predicted using blade-element wing theory. It has been hypothesized that the magnitude of this lift may help explain tight-turning maneuvers during high-speed gliding in swifts (Videler et al.,2004), but experiments with wings of varying posture indicates that it is drag reduction, rather than enhanced lift, that is the primary benefit derived from the swept-wing posture during high-speed glides(Lentink et al., 2007).

There are empirical measures of stability during flight in tethered insects(Taylor and Thomas, 2003), but no data are yet available from flying birds. Results from desert locusts Schistocerca gregaria indicate that they can correct for perturbations within one wingbeat. It is hypothesized that a key element to this ability to quickly react to disturbance is the tuning of their neuromuscular control to an observed pitching oscillation that occurs near the rate of the wingbeat. In the case of the locust, the pitching oscillation is at one half the rate of the wingbeat frequency. If the neuromuscular control of stability is tuned at this frequency of oscillation, the timing of neuromuscular control should scale among similarly shaped insects proportional to square root of the length of the insect(Taylor and Thomas, 2003). The tuning of the neural system for control in birds is predicted to be less constrained by a need to approximate the timing of the wingbeat because the tail of birds can also control stability(Taylor and Thomas, 2003).

Reflections on future research

As recent technological developments have opened new opportunities to test hypotheses about function in bird flight, the key to enhancing development in this area of science is twofold. First, it is vital to update existing mathematical theory pertaining to bird flight by incorporating new empirical observations, and then enter into a healthy process of iteration in which empirical measures are used to test new theory and models are used to inform new experiments.

Secondly, it is imperative that biomechanical studies be integrated in an ecological, evolutionary context. A recent example of how this may be accomplished is a comparative study of flight performance in hummingbirds(Altshuler et al., 2004) that helps explain morphology, flight performance and ecological distribution in a broad array of species. Scanning the literature, there is a general trend for biomechanical studies to explore mechanisms in one representative species without explicit tests of how these mechanisms relate to the behavior and ecology of species in nature. A reductionist approach to designing experiments is a necessary first step, of course, but if it becomes a defining characteristic, it will lead to a plethora of studies that spin only in their own small domain and fail to demonstrate how flight mechanics fit into the larger reality of the biology of birds. Studying closely related species may help to reveal patterns that would be otherwise be obscured in a two-species approach (Tobalske, 1996), and a phylogenetic approach to experimental design is always mandatory for supporting an argument of adaptive significance for a trait(Garland and Adolph,1994).

List of symbols

     
  • DPIV

    digital particle image velocimetry

  •  
  • Ek

    kinetic energy

  •  
  • Ep

    potential energy

  •  
  • Paero

    aerodynamic power

  •  
  • Pind

    induced power

  •  
  • Piner

    inertial power associated with wing movement

  •  
  • Pmet

    metabolic power

  •  
  • Pmus

    mechanical power output of flight muscles

  •  
  • Ppar

    parasite power

  •  
  • Ppro

    profile power

  •  
  • t

    time

  •  
  • Vmp

    minimum power velocity

  •  
  • Vmr

    maximum range velocity

Acknowledgements

I thank two anonymous referees for their helpful comments on an earlier draft of the manuscript. Supported by NSF Grant IOB-0615648.

References

Alexander, R. McN. (
1989
). Optimization and gaits in the locomotion of vertebrates.
Physiol. Rev.
69
,
1199
-1227.
Altshuler, D. L., Dudley, R. and McGuire, J. A.(
2004
). Resolution of a paradox: hummingbird flight at high elevation does not come without a cost.
Proc. Natl. Acad. Sci. USA
101
,
17731
-17736.
Askew, G. N. and Ellerby, D. J. (
2007
). The mechanical power requirements of avian flight.
Biol. Lett.
3
,
445
-448.
Askew, G. N. and Marsh, R. L. (
1997
). The effects of length trajectory on the mechanical power output of mouse skeletal muscles.
J. Exp. Biol.
200
,
3119
-3131.
Askew, G. N. and Marsh, R. L. (
2001
). The mechanical power output of the pectoralis muscle of blue-breasted quail(Coturnix chinensis): in vivo length cycle and its implications for muscle performance.
J. Exp. Biol.
204
,
3587
-3600.
Askew, G. N., Marsh, R. L. and Ellington, C. P.(
2001
). The mechanical power output of the flight muscles of blue-breasted quail (Coturnix chinensis) during take-off.
J. Exp. Biol.
204
,
3601
-3619.
Barclay, C. J. (
1996
). Mechanical efficiency and fatigue of fast and slow muscles of the mouse.
J. Physiol. Lond.
497
,
781
-794.
Biewener, A. A. and Roberts, T. J. (
2000
). Muscle and tendon contributions to force, work, and elastic energy savings: a comparative perspective.
Exerc. Sport Sci. Rev.
28
,
99
-107.
Biewener, A. A., Corning, W. R. and Tobalske, B. W.(
1998
). In vivo pectoralis muscle force-length behavior during level flight in pigeons (Columba livia).
J. Exp. Biol.
201
,
3293
-3307.
Bilo, D. (
1971
). Flugbiophysik von Kleinvögeln. I. Kinematik und Aerodynamik des Flügelabschlages beim Haussperling (Passer domesticus L.).
Z. Vergl. Physiol.
71
,
382
-454.
Bilo, D. (
1972
). Flugbiophysik von Kleinvögeln. II. Kinematik und Aerodynamik des Flügelaufschlages beim Haussperling (Passer domesticus L.).
Z. Vergl. Physiol.
76
,
426
-437.
Brown, R. H. J. (
1963
). The flight of birds.
Biol. Rev.
38
,
460
-489.
Bruderer, L., Liechti, F. and Bilo, D. (
2001
). Flexibility in flight behaviour of barn swallows (Hirundo rustica)and house martins (Delichon urbica) tested in a wind tunnel.
J. Exp. Biol.
204
,
1473
-1484.
Bundle, M. W., Hansen, K. S. and Dial, K. P.(
2007
). Does the metabolic rate-flight speed relationship vary among geometrically similar birds of different mass?
J. Exp. Biol.
210
,
1075
-1083.
Chai, P. and Dudley, R. (
1995
). Limits to vertebrate locomotor energetics suggested by hummingbirds hovering in heliox.
Nature
377
,
722
-725.
Chai, P. and Millard, D. (
1997
). Flight and size constraints: hovering performance of large hummingbirds under maximal loading.
J. Exp. Biol.
200
,
2757
-2763.
Csicsáky, M. J. (
1977
). Body-gliding in the zebra finch.
Fortschr. Zool.
24
,
275
-286.
Dabiri, J. O. (
2005
). On the estimation of swimming and flying forces from wake measurements.
J. Exp. Biol.
208
,
3519
-3532.
Dejong, M. J. (
1983
).
Bounding flight in birds
. PhD thesis, University of Wisconsin, Madison, USA.
Dial, K. P. (
1992a
). Activity patterns of the wing muscles of the pigeon (Columba livia) during different modes of flight.
J. Exp. Zool.
262
,
357
-373.
Dial, K. P. (
1992b
). Avian forelimb muscles and nonsteady flight: can birds fly without using the muscles of their wings?
Auk
109
,
874
-885.
Dial, K. P. and Biewener, A. A. (
1993
). Pectoralis muscle force and power output during different modes of flight in pigeons (Columba livia).
J. Exp. Biol.
176
,
31
-54.
Dickinson, M. H. (
1996
). Unsteady mechanisms of force generation in aquatic and aerial locomotion.
Am. Zool.
36
,
537
-554.
Dickinson, M. H., Lehman, F. O. and Sane, S. P.(
1999
). Wing rotation and the aerodynamic basis of insect flight.
Science
284
,
1954
-1960.
Drovetski, S. V. (
1996
). Influence of the trailing-edge notch on flight performance in galliforms.
Auk
113
,
802
-810.
Earls, K. D. (
2000
). Kinematics and mechanics of ground take-off in the starling Sturnus vulgaris and the quail Coturnix coturnix.
J. Exp. Biol.
203
,
725
-739.
Ellington, C. P. (
1984
). The aerodynamics of hovering insect flight I–V.
Philos. Trans. R. Soc. Lond. B Biol. Sci.
305
,
1
-181.
Ellington, C. P. (
1991
). Limitations on animal flight performance.
J. Exp. Biol.
160
,
71
-91.
Engel, S., Biebach, H. and Visser, G. H.(
2006
). Metabolic costs of avian flight in relation to flight velocity: a study in Rose Coloured Starlings (Sturnus roseus,Linnaeus).
J. Comp. Physiol. B
176
,
415
-427.
Evans, M. R. (
2004
). Limits on the evolution of tail ornamentation in birds.
Am. Nat.
163
,
341
-357.
Evans, M. R., Rosén, M., Park, K. and Hedenström,A. (
2002
). How do birds' tails work? Delta-wing theory fails to predict tail shape during flight.
Proc. Biol. Sci.
269
,
1053
-1057.
Funk, G. D., Steeves, J. D. and Milsom, W. K.(
1992
). Coordination of wingbeat and respiration in birds. II.`Fictive' flight.
J. Appl. Physiol.
73
,
1025
-1033.
Garland, T., Jr and Adolph, S. C. (
1994
). Why not to do two species comparative studies: limitations on inferring adaptation.
Physiol. Zool.
67
,
797
-828.
Gould, S. J. and Lewontin, R. C. (
1979
). The spandrels of San Marco and the panglossian paradigm: a critique of the adaptationist programme
Proc. R. Soc. Lond. B Biol. Sci.
205
,
581
-598.
Hambly, C., Harper, E. and Speakman, J. (
2002
). Cost of flight in the zebra finch (Taenopygia guttata): a novel approach based on elimination of 13C labelled bicarbonate.
J. Comp. Physiol. B
172
,
529
-539.
Hedenström, A. and Alerstam, T. (
1995
). Optimal flight speed of birds.
Philos. Trans. R. Soc. Lond. B Biol. Sci.
348
,
471
-487.
Hedenström, A. and Liechti, L. (
2001
). Field estimates of body drag coefficient on the basis of dives in passerine birds.
J. Exp. Biol.
204
,
1167
-1175.
Hedenström, A. and Rosén, M.(
2001
). Predator versus prey: on aerial hunting and escape strategies in birds.
Behav. Ecol.
12
,
150
-156.
Hedenström, A. and Rosén, M.(
2003
). Body frontal area in passerine birds.
J. Avian Biol.
34
,
159
-162.
Hedenström, A., Griethuijsen, L. V., Rosén, M. and Spedding, G. R. (
2006
). Vortex wakes of birds: recent developments using digital particle image velocimetry in a wind tunnel.
Anim. Biol.
56
,
535
-549.
Hedrick, T. L. and Biewener, A. A. (
2007a
).
Experimental study of low speed turning flight in cockatoos and cockatiels
. 45th AIAA Aerospace Sciences Meeting and Exhibit 8-11 January 2007, Reno, Nevada. AIAA Paper, 2007-0044.
Hedrick, T. L. and Biewener, A. A. (
2007b
). Low speed maneuvering flight of the rose-breasted cockatoo (Eolophus roseicapillus). I. Kinematic and neuromuscular control of turning.
J. Exp. Biol.
210
,
1897
-1911.
Hedrick, T. L., Tobalske, B. W. and Biewener, A. A.(
2002
). Estimates of circulation and gait change based on a three-dimensional kinematic analysis of flight in cockatiels (Nymphicus hollandicus) and ringed turtle doves (Streptopelia risoria).
J. Exp. Biol.
205
,
1389
-1409.
Hedrick, T. L., Tobalske, B. W. and Biewener, A. A.(
2003
). How cockatiels (Nymphicus hollandicus) modulate pectoralis power output across flight speeds.
J. Exp. Biol.
206
,
1363
-1378.
Hedrick, T. L., Usherwood, J. R. and Biewener, A. A.(
2004
). Wing inertia and whole-body acceleration: an analysis of instantaneous aerodynamic force production in cockatiels (Nymphicus hollandicus) flying across a range of speeds.
J. Exp. Biol.
207
,
1689
-1702.
Hedrick, T. L., Usherwood, J. R. and Biewener, A. A.(
2007
). Low speed maneuvering flight of the rose-breasted cockatoo (Eolophus roseicapillus). II. Inertial and aerodynamic reorientation.
J. Exp. Biol.
210
,
1912
-1924.
Henry, H. T., Ellerby, D. J. and Marsh, R. L.(
2005
). Performance of guinea fowl Numida meleagrisduring jumping requires storage and release of elastic energy.
J. Exp. Biol.
208
,
3293
-3302.
Hill, A. V. (
1950
). The dimensions of animals and their muscular dynamics.
Sci. Prog.
38
,
209
-230.
Houston, A. I. (
2006
). The flight speed of parent birds feeding young.
J. Avian Biol.
37
,
545
-554.
Hummel, D. (
1992
). Aerodynamic investigations on tail effects in birds.
Z. Flugwiss. Weltraumforsch.
16
,
159
-168.
Kullberg, C., Jakobsson, S. and Fransson, T.(
1998
). Predator-induced take-off strategy in Great Tits(Parus major).
Proc. R. Soc. Lond. B Biol. Sci.
265
,
1659
-1664.
Lentink, D., Müller, U. K., Stamhuis, E. J., de Kat, R.,van Gestel, W., Veldhuis, L. L. M., Henningsson, P., Hedenström, A.,Videler, J. J. and van Leeuwen, J. L. (
2007
). How swifts control their glide performance with morphing wings.
Nature
446
,
1082
-1085.
Marden, J. H. (
1994
). From damselflies to pterosaurs: how burst and sustainable flight performance scale with size.
Am. J. Physiol.
266
,
R1077
-R1084.
Maybury, W. J. (
2000
).
The aerodynamics of bird bodies
. PhD thesis, University of Bristol, UK.
Maybury, W. J. and Rayner, J. M. V. (
2001
). The avian tail reduces body parasite drag by controlling flow separation and vortex shedding.
Proc. R. Soc. Lond. B Biol. Sci.
268
,
1405
-1410.
Maybury, W. J., Rayner, J. M. V. and Couldrick, L. B.(
2001
). Lift generation by the avian tail.
Proc. R. Soc. Lond. B Biol. Sci.
268
,
1443
-1448.
Møller, A.P., de Lope, F. and Saino, N.(
1995
). Sexual selection in the barn swallow Hirundo rustica VI. aerodynamic adaptations.
J. Evol. Biol.
8
,
671
-687.
Norberg, U. M. (
1990
).
Vertebrate Flight: Mechanics, Physiology, Morphology, Ecology and Evolution
. New York: Springer-Verlag.
Nudds, R. L. and Bryant, D. M. (
2000
). The energetic cost of short flights in birds.
J. Exp. Biol.
203
,
1561
-1572.
Nudds, R. L. and Rayner, J. M. V. (
2006
). Scaling of body frontal area and body width in birds.
J. Morphol.
327
,
341
-346.
Park, K. J., Evans, R. M. and Buchanan, K. L.(
2000
). Assessing the aerodynamic effects of tail elongations in the house martin (Delichon urbica): implications for the initial selection pressures in hirundines.
Behav. Ecol. Sociobiol.
48
,
364
-372.
Park, K. J., Rosén, M. and Hedenström, A.(
2001
). Flight kinematics of the barn swallow Hirundo rustica over a wide range of speeds in a wind tunnel.
J. Exp. Biol.
204
,
2741
-2750.
Pennycuick, C. J. (
1975
). Mechanics of flight. In
Avian Biology
. Vol.
5
(ed. D. S. Farner and J. R. King), pp.
1
-75. New York:Academic Press.
Pennycuick, C. J. (
1989
).
Bird Flight Performance: A Practical Calculation Manual
. Oxford:Oxford University Press.
Pennycuick, C. J., Obrecht, H. H., III and Fuller, M. R.(
1988
). Empirical estimates of body drag of large waterfowl and raptors.
J. Exp. Biol.
135
,
253
-264.
Pennycuick, C. J., Heine, C. E., Kirkpatrick, S. J. and Fuller,M. R. (
1992
). The profile drag of a hawk's wing, measured by wake sampling in a wind tunnel.
J. Exp. Biol.
165
,
1
-19.
Pennycuick, C. J., Hedenström, A. and Rosén, M.(
2000
). Horizontal flight of a swallow (Hirundo rustica)observed in a wind tunnel, with a new method for directly measuring mechanical power.
J. Exp. Biol.
203
,
1755
-1765.
Poore, S. O., Ashcroft, A., Sanchez-Haiman, A. and Goslow, G. E., Jr (
1997
). The contractile properties of the M. supracoracoideus in the pigeon and starling: a case for long-axis rotation of the humerus.
J. Exp. Biol.
200
,
2987
-3002.
Rayner, J. M. V. (
1979a
). A vortex theory of animal flight. Part I. The vortex wake of a hovering animal.
J. Fluid Mech.
91
,
697
-730.
Rayner, J. M. V. (
1979b
). A vortex theory of animal flight. Part II. The forward flight of birds.
J. Fluid Mech.
91
,
731
-763.
Rayner, J. M. V. (
1985
). Bounding and undulating flight in birds.
J. Theor. Biol.
117
,
47
-77.
Rayner, J. M. V. (
1988
). Form and function in avian flight.
Curr. Ornithol.
5
,
1
-66.
Rayner, J. M. V. (
1999
). Estimating power curve of flying vertebrates.
J. Exp. Biol.
202
,
3449
-3461.
Rayner, J. M. V., Viscardi, P. W., Ward, S. and Speakman, J. R. (
2001
). Aerodynamics and energetics of intermittent flight in birds.
Am. Zool.
41
,
188
-204.
Rosén, M. W., Spedding, G. R. and Hedenström, A.(
2004
). The relationship between wingbeat kinematics and vortex wake of a thrush nightingale.
J. Exp. Biol.
207
,
4255
-4268.
Sane, S. and Dickinson, M. H. (
2001
). The control of flight force by a flapping wing: lift and drag production.
J. Exp. Biol.
204
,
2607
-2626.
Schmidt-Nielsen, K. (
1972
). Locomotion: energy cost of swimming, running and flying.
Science
177
,
222
-228.
Scholey, K. D. (
1983
).
Developments in vertebrate flight: climbing and gliding of mammals and reptiles, and the flapping flight of birds
. PhD thesis, University of Bristol,UK.
Sokoloff, A. J., Gray-Chickering, J., Harry, J. D., Poore, S. O. and Goslow, G. E., Jr (
2001
). The function of the supracoracoideus muscle during takeoff in the European starling (Sternus vulgaris): Maxheinz Sy revisited. In
New Perspectives on the Origin and Early Evolution of Birds: Proceedings of the International Symposium in Honor of John H. Ostrom
(ed. J. Gauthier and L. F. Gall), pp.
319
-332. New Haven: Peabody Museum of Natural History, Yale University.
Soman, A., Hedrick, T. L. and Biewener, A. A.(
2005
). Regional patterns of pectoralis fascicle strain in the pigeon Columba livia during level flight.
J. Exp. Biol.
208
,
771
-786.
Spedding, G. R. (
1987
). The wake of a kestrel(Falco tinnunculus) in flapping flight.
J. Exp. Biol.
127
,
59
-78.
Spedding, G. R. (
1993
). On the significance of unsteady effects in the aerodynamic performance of flying animals.
Contemp. Math.
141
,
401
-419.
Spedding, G. R., Rayner, J. M. V. and Pennycuick, C. J.(
1984
). Momentum and energy in the wake of a pigeon (Columba livia) in slow flight.
J. Exp. Biol.
111
,
81
-102.
Spedding, G. R., Rosén, M. and Hedenström, A.(
2003
). A family of vortex wakes generated by a thrush nightingale in free flight in a wind tunnel over its entire natural range of flight speeds.
J. Exp. Biol.
206
,
2313
-2344.
Taylor, G. K. and Thomas, A. L. R. (
2002
). Animal flight dynamics. II. Longitudinal stability in flapping flight.
J. Theor. Biol.
214
,
351
-370.
Taylor, G. K. and Thomas, A. L. R. (
2003
). Dynamic flight stability in the desert locust Schistocerca gregaria.
J. Exp. Biol.
206
,
2803
-2829.
Taylor, G. K., Nudds, R. L. and Thomas, A. L.(
2003
). Flying and swimming animals cruise at a Strouhal number tuned for high power efficiency.
Nature
425
,
707
-711.
Thomas, A. L. R. (
1993
). On the aerodynamics of birds' tails.
Philos. Trans. R. Soc. Lond. B Biol. Sci.
340
,
361
-380.
Thomas, A. L. R. and Hedenström, A.(
1998
). The optimum flight speeds of animals.
J. Avian Biol.
29
,
469
-477.
Thomas, A. L. R. and Taylor, G. K. (
2001
). Animal flight dynamics. I. Stability in gliding fight.
J. Theor. Biol.
212
,
399
-424.
Tobalske, B. W. (
1996
). Scaling of muscle composition, wing morphology, and intermittent flight behavior in woodpeckers.
Auk
113
,
151
-177.
Tobalske, B. W. (
2000
). Biomechanics and physiology of gait selection in flying birds.
Physiol. Biochem. Zool.
73
,
736
-750.
Tobalske, B. W. (
2001
). Morphology, velocity,and intermittent flight in birds.
Am. Zool.
41
,
177
-187.
Tobalske, B. W. and Biewener, A. A. (
2008
). Contractile properties of the pigeon supracoracoideus during different modes of flight.
J. Exp. Biol.
In press.
Tobalske, B.W. and Dial, K.P. (
1994
). Neuromuscular control and kinematics of intermittent flight in budgerigars(Melopsittacus undulatus).
J. Exp. Biol.
187
,
1
-18.
Tobalske, B. W. and Dial, K. P. (
1996
). Flight kinematics of black-billed magpies and pigeons over a wide range of speeds.
J. Exp. Biol.
199
,
263
-280.
Tobalske, B. W. and Dial, K. P. (
2000
). Effects of body size on take-off flight performance in the Phasianidae (Aves).
J. Exp. Biol.
203
,
3319
-3332.
Tobalske, B. W., Peacock, W. L. and Dial, K. P.(
1999
). Kinematics of flap-bounding flight in the zebra finch over a wide range of speeds.
J. Exp. Biol.
202
,
1725
-1739.
Tobalske, B. W., Hedrick, T. L., Dial, K. P. and Biewener, A. A. (
2003
). Comparative power curves in bird flight.
Nature
421
,
363
-366.
Tobalske, B. W., Altshuler, D. L. and Powers, D. A.(
2004
). Take-off mechanics in hummingbirds (Trochilidae).
J. Exp. Biol.
207
,
1345
-1352.
Tobalske, B. W., Puccinelli, L. A. and Sheridan, D. C.(
2005
). Contractile activity of the pectoralis in the zebra finch according to mode and velocity of flap-bounding flight.
J. Exp. Biol.
208
,
2895
-2901.
Tobalske, B. W., Warrick, D. R., Clark, C. J., Powers, D. R.,Hedrick, T. L., Hyder, G. A. and Biewener, A. A. (
2007
). Three-dimensional kinematics of hummingbird flight.
J. Exp. Biol.
210
,
2368
-2382.
Usherwood, J. R. and Ellington, C. P. (
2002
). The aerodynamics of revolving wings. II. Propeller force coefficients from mayfly to quail.
J. Exp. Biol.
205
,
1565
-1576.
Usherwood, J. R., Hedrick, T. L. and Biewener, A. A.(
2003
). The aerodynamics of avian take-off from direct pressure measurements in Canada geese (Branta canadensis).
J. Exp. Biol.
206
,
4051
-4056.
Usherwood, J. R., Hedrick, T. L., McGowan, C. P. and Biewener,A. A. (
2005
). Dynamic pressure maps for wings and tails of pigeons in slow, flapping flight, and their energetic implications.
J. Exp. Biol.
208
,
355
-369.
Videler, J. J., Stamhuis, E. J. and Povel, G. D. E.(
2004
). Leading-edge vortex lifts swifts.
Science
306
,
1960
-1962.
Wang, Z. J., Birch, J. and Dickinson, M. H.(
2004
). Unsteady forces and flows in low Reynolds number hovering flight: two-dimensional computations vs robotic wing experiments.
J. Exp. Biol.
207
,
449
-460.
Ward, S., Möller, U., Rayner, J. M. V., Jackson, D. M.,Bilo, D., Nachtigall, W. and Speakman, J. R. (
2001
). Metabolic power, mechanical power and efficiency during wind tunnel flight by European starlings Sturnus vulgaris.
J. Exp. Biol.
204
,
3311
-3322.
Ward, S., Möller, U., Rayner, J. M. V., Jackson, D. M.,Nachtigall, W. and Speakman, J. R. (
2004
). Metabolic power of European starlings Sturnus vulgaris during flight in a wind tunnel,estimated from heat transfer modelling, doubly labelled water and mask respirometry.
J. Exp. Biol.
207
,
4291
-4298.
Warrick, D. R. (
1998
). The turning and linear manervering performance of birds: the cost of efficiency for coursing insectivores.
Can. J. Zool.
7
,
1063
-1079.
Warrick, D. R. and Dial, K. P. (
1998
). Kinematic, aerodynamic and anatomical mechanisms in the slow, maneuvering flight of pigeons.
J. Exp. Biol.
201
,
655
-672.
Warrick, D. R., Dial, K. P. and Biewener, A. A.(
1998
). Asymmetrical force production in the slow maneuvering flight of birds.
Auk
115
,
916
-928.
Warrick, D. R., Bundle, M. W. and Dial, K. P.(
2002
). Bird maneuvering flight: blurred bodies, clear heads.
Integr. Comp. Biol.
42
,
141
-148.
Warrick, D. R., Tobalske, B. W. and Powers, D. P.(
2005
). Aerodynamics of the hovering hummingbird.
Nature
435
,
1094
-1097.
Willmott, A. P., Ellington, C. P. and Thomas, A. L. R.(
1997
). Flow visualization and unsteady aerodynamics in the flight of the hawkmoth, Manduca sexta.
Philos. Trans. R. Soc. Lond. B Biol. Sci.
352
,
303
-316.
Withers, P. C. (
1981
). An aerodynamic analysis of bird wings as fixed aerofoils.
J. Exp. Biol.
90
,
143
-162.