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First published online June 15, 2007
Journal of Experimental Biology 210, 2368-2382 (2007)
Published by The Company of Biologists 2007
doi: 10.1242/jeb.005686
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Three-dimensional kinematics of hummingbird flight

Bret W. Tobalske1,*, Douglas R. Warrick2, Christopher J. Clark3, Donald R. Powers4, Tyson L. Hedrick5, Gabriel A. Hyder1 and Andrew A. Biewener6

1 Department of Biology, University of Portland, 5000 N. Willamette Boulevard, Portland, OR 97203, USA
2 Department of Zoology, Oregon State University, 2002 Cordley Hall, Corvallis, OR 97331, USA
3 Department of Integrative Biology, University of California, Berkeley, 3060 Valley Life Sciences Building # 3140, Berkeley, CA 94720, USA
4 Biology Department, George Fox University, 414 N. Meridian Street, Newberg, OR 97132, USA
5 Department of Biology, University of North Carolina, Chapel Hill, NC 27599 USA
6 Concord Field Station, Department of Organismic and Evolutionary Biology, Harvard University, Old Causeway Road, Bedford, MA 01730, USA


Figure 1
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  		Fig. 1. Angles and areas measured from wing and body motion of rufous hummingbirds (Selasphorus rufus) during flight. Certain measures were bird-centered (A) and those in (B,C) were derived from global coordinates because they incorporated free-stream velocity. Filled-outlines of bird (A,B) illustrate wing at the start of downstroke, and broken-outline of wing illustrates wing position at the end of downstroke. (A) Black cross-section represents a pronated wing at mid-downstroke. {alpha}c=chord angle relative to mid-frontal plane of body with {alpha}c>0 for supination and {alpha}c<0 for pronation. ß=body angle relative to horizontal. {gamma}b=anatomical stroke-plane angle relative to mid-frontal plane of body. {gamma}h=tracking stroke-plane angle relative to horizontal. (B) {Psi}d and {Psi}u=global stroke-plane angle during downstroke and upstroke, respectively. (C) Global stroke-plane area was outlined by the wingtips during downstroke (dark gray areas) and upstroke (light gray areas) for each wingbeat.

 

Figure 2
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  		Fig. 2. Wing motion relative to the body of a rufous hummingbird (Selasphorus rufus) flying at velocities of 0-12 m s-1. (A) Dorsal view with bird silhouette at mid-downstroke. As we measured kinematics only from the right wing, paths for the left-wing are mirror images. (B) Lateral view with bird silhouette at start of downstroke. Black circles indicate position of wingtips, and white circles indicate position of wrists. Paths of wing motion are from 3D measurements, so circles within the paths are synchronized for a given velocity. Circles and arrows indicate sequential position and local direction of movement.

 

Figure 3
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  		Fig. 3. Angles describing bird-centered wing and body kinematics in rufous hummingbirds (Selasphorus rufus, N=5) flying at velocities 0-12 m s-1. (A) Body angle relative to horizontal (ß), tracking stroke-plane angle relative to horizontal ({gamma}h) and anatomical stroke-plane angle relative to mid-frontal plane of body ({gamma}b). (B) Chord angle of wing relative to mid-frontal plane of body ({alpha}c) at mid-downstroke and mid-upstroke. Values are means ± s.d.

 

Figure 4
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  		Fig. 4. Variation in chord angle relative to mid-frontal plane of body ({alpha}c) during wingbeats in rufous hummingbird (Selasphorus rufus, N=5) flying at velocities of 0-12 m s-1. Wingbeat duration is expressed as a percentage of the entire wingbeat. The broken line indicates wrist elevation relative to mid-frontal plane, and the shaded area represents downstroke. Values are means ± s.d.

 

Figure 5
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  		Fig. 5. (A) Wingbeat frequency and amplitude ({phi}), (B) proportion of wingbeat spent in downstroke and (C) average angular velocity of the wing, during downstroke and upstroke during flight in rufous hummingbirds (Selasphorus rufus, N=5) flying at velocities of 0-12 m s-1. Values are means ± s.d.

 

Figure 6
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  		Fig. 6. (A) Wingspan and wristspan during mid-downstroke (black circles) and mid-upstroke (white circles) and (B) span ratio in rufous hummingbirds (Selasphorus rufus, N=5) flying at velocities of 0-12 m s-1. Values are means ± s.d.

 

Figure 7
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  		Fig. 7. Dorsal and lateral views of wingtip and wrist paths with translation due to free-stream velocity (V) and time. These data are from a rufous hummingbird (Selasphorus rufus) flying at velocities of 0-12 m s-1 (same subject as in Fig. 2). All x-axes represent 500 mm along a flight path. Solid line=wingtip, dotted line=wrist. Shaded regions indicate downstroke as defined using wrist motion. For each downstroke, wingtip excursion exceeded wrist excursion in all dimensions, so the shaded regions would be enlarged if downstroke were based on motion of the wingtip.

 

Figure 8
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  		Fig. 8. Kinematic variables derived using free-stream velocity (V) and induced velocity (Vi) for rufous hummingbirds (Selasphorus rufus, N=5) flying at velocities of 0-12 m s-1. (A) Global stroke-plane area for downstroke and upstroke. (B) Global stroke-plane angle for downstroke ({Psi}d) and upstroke ({Psi}u). (C) Angle of attack of the wing ({alpha}) at mid-downstroke and mid-upstroke.

 

Figure 9
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  		Fig. 9. Variation in angle of attack ({alpha}) within wingbeats in rufous hummingbirds (Selasphorus rufus, N=5) flying at velocities of 0-12 m s-1. Wingbeat duration is expressed as a percentage of the entire wingbeat. The broken line indicates wrist elevation relative to mid-frontal plane of body, and the shaded area indicates downstroke. Values are means ± s.d.

 

Figure 10
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  		Fig. 10. Wingspan ratio as a function of flight velocity compared among bird species. Values shown are means. Colors indicate species within the same order: Red=Trochiliformes, rufous hummingbird Selasphorus rufus (this study); blue=Columbiformes, ringed turtle-dove Streptopelia risoria (Tobalske et al., 2003bGo) and rock dove (`pigeon') Columba livia (Tobalske and Dial, 1996Go); green=Psittaciformes, budgerigar Melopsittacus undulatus and cockatiel Nymphicus nymphicus (Tobalske et al., 2003bGo); orange=Passeriformes, barn swallow Hirundo rustica (Park et al., 2001Go), thrush nightingale Luscinia luscinia (Rosén et al., 2004Go), black-billed magpie Pica hudsonica 1Tobalske and Dial (Tobalske and Dial, 1996Go), 2Tobalske et al. (Tobalske et al., 2003bGo) and zebra finch Taeniopygia guttata (Tobalske et al., 1999Go).

 




© The Company of Biologists Ltd 2007