origin of bird flight

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Origin of Bird Flight:

A Physics ViewpointBernard J. Feldman andThomas F. George,University of MissouriSt. Louis, St. Louis, MOCharles A. Long andClaudine F. Long,University of WisconsinStevens Point, Stevens Point, WIGuoping Zhang,Indiana State University, Terre Haute, IN

The debate over the origin of bird flight datesback over 100 years. Over the last centurytwo opposing viewpoints have emerged. The

first claims that flight originated by running alongthe ground and then leaping and flappingthis iscalled the ground-up theory.1 The second claimsthat flight originated from the treesfrom jumpingout of trees and glidingand is called the tree-down theory.2 Recently, Long et al. proposed a newtheoryflutter-glidingthat combines featuresfrom both of these previous theories.35 This paperwill discuss all three of these theories of the originof bird flight in terms of Newtons second law ofmotion and provides a simplified version of a seriesof articles published by Long et al.35 We believethis material is a wonderful application of Newtonssecond law of motion that is appropriate for bothhigh school and college introductory physics courses,and leads naturally into a discussion of the physics ofgliding, flying, and sprinting.

Let us consider the forces acting on a bird in flight

when the wings execute a down stroke; the forces dur-ing an upstroke are significantly smaller and will beneglected in this analysis. The force diagrams of a birdtraveling with speed V, but at angles above and be-low the horizontal, are shown in Fig. 1. The followingforces are acting on the bird. The force of gravitymg,where m is the mass of the bird and gis the free-fall ac-celeration, is always straight down. The aerodynamicforce Rcomes directly from Bernoullis equationwhere the aerodynamic shape of the birds camberedwing causes the air on the top of the wing to travel

faster than the air on the bottom of the wing. Thisforce is proportional to the square of the velocityVrelof the moving wing with respect to the air (which isassumed to be at rest with respect to the Earth).Vrel isthe vector sum of the velocity of the bird with respectto the Earth (V) and the velocity of the downward

moving wing with respect to the birds body.6

The dragforce D is due to the air resistance slowing down thebird. It is always opposite to the direction ofVand is astrong function of bothVand the shape of the bird.

By Newtons second law of motion, the sum of allthey-components of the forces is equal to the mass ofthe bird times they-component of the acceleration ay.Let us first consider Fig. 1(a), where the bird is flyingupward after a running jump from the ground. Then

Rcos Dsin mg= may. (1)

Fig. 1. (a) Force diagram for a proto-bird flying upward

with wings on a down stroke after a running jump from the

ground. (b) Force diagram for a proto-bird flying downwardwith wings on a down stroke after leaping from a tree limb.

The forces acting on the bird are gravity mg, the aerodynamic

force R, and drag due to air resistance D.

THE PHYSICS TEACHER Vol. 44, September 2006 DOI: 10.1119/1.2336135 351


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352 THE PHYSICS TEACHER Vol. 44, September 2006

They-component of the acceleration must be greater

than zero for the bird to leave the ground, whichmeans that the vertical component ofRhas to beable to overcome both gravity and a component ofthe drag force. Given that the birds initial velocityis limited by its terminal running speed (see below)and given that Ris proportional to Vrel

2, as well asthe fact that the underdeveloped wings of a proto-bird are not designed for lift, its unlikely that aywillbe positive.

By contrast, let us consider Fig. 1(b), where thebird is moving downward after leaping from a treelimb. In they-direction:

Rcos + Dsin mg= may. (2)

For the tree-down gliding theory, first notice that thedrag force is helping the bird to counteract gravity.Second, because the bird is falling it has no troublegaining velocity, and thus Rcan make a significantpositive contribution. In this scenario, it is very plau-sible that ayis close to zero.

There is a potential problem with this glidingtheory. By jumping from greater heights, the proto-bird can generate greater velocities, greater R, and thustravel significantly greater distances, but it also in-creases its chances of fatally crashing into the ground.This danger of crashing is an important negative fac-tor not only for survival of the animal but over longperiods of geological time to the evolution of flight.

We now consider the third theory, flutter-gliding,where the proto-bird jumps out of a tree and flaps itspoorly developed wings as it glides. Now the vertical

component ofRis increased due to the increase in theair velocity with respect to the moving wing, and themagnitude ofD is increased due to the disturbanceof the air and its flow by the flapping wings.6 Both

of these contribute toward a zero or positive ayandto minimizing the odds of fatally crashing into theground. The flapping of the wings during flutter-glid-ing can then easily evolve into muscle-powered flight.

Let us return to the ground-up theory. A similarforce analysis as in Fig. 1 can be applied to a bird orhuman being running on a horizontal surface. A forcein the horizontal direction, due to the ground pushingback on the running legs of the animal, and a normalforce in the vertical direction, due to the ground, mustnow be added to R, mg, and D. The leg force precipi-

tously decreases to almost zero with increasing run-ning speed. In the case of world-class 100-m sprinters,the leg force at the very beginning of the race is about854 N and after three seconds 27 N.7 After 3 s, therunner reaches terminal velocity where the 27 N arejust sufficient to balance the drag force. The dramaticreduction in leg thrust is due to the fact that almostall the power the leg muscles can generate is used justto rapidly move the runners legs. The best strategy forthe proto-bird is to start flapping its poorly developedwings after it runs and reaches its terminal velocity.At that moment of take-off, the question is whetherenough Rhas been generated so that the bird canovercome gravity in the vertical direction and fric-tional drag in the horizontal direction. One biologi-cal calculation of the birds maximum leg thrust andstriding rate strongly suggests a terminal velocity ofabout 7 m/s and insufficient Rfor flight.3 A differentcalculation where the proto-bird flaps its wings fromthe beginning of its run generates a velocity of 8 m/sand sufficient Rfor flight.8 For most modern birds,

their wings generate sufficient Rneeded to fly withoutany running or falling starts.

Finally, it is informative to end this paper with abrief mention of the fossil record. The most relevantfossil to this discussion is Archaeopteryx, which isbelieved to be the earliest bird fossil found (from theJurassic period about 150 million years ago).9 Anartists sketch of Archaeopteryx is shown in Fig. 2. Thereader may also want to learn about the recent fossilfind (from the Cretaceous Age, 125 million years ago)of a four-winged gliding dinosaur, Microraptor gui. It

Fig. 2. Artists sketch of Archaeopteryx.

(courtesy of Patricia J. Wynne)9


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THE PHYSICS TEACHER Vol. 44, September 2006 353

is believed that this fossil is not a direct descendent ofbirds but from a nearby extinct branch.10Archaeopter-yxis about the size of a pigeon and has well-developedfeathered wings consistent with flapping. It has clawed

fingers, suggesting tree clambering. It has a long tailuseful for gliding but a hindrance for running. On theother hand, it has a bipedal stance in support of theground-up theory and small pectoral muscles in sup-port of the tree-down gliding theory. When combiningthe physics and biological information, we believe theflutter-glide theory makes the strongest case, but this isstill not a settled question in the scientific community.

Acknowledgment

The authors wish to acknowledge the valuable assis-

tance of the reviewer, Charles Eastlake.

References1. See, for example, K. Padian and L. M. Chiappe, The

origin of birds and their flight, Sci. Am. 278, 3847(Feb. 1998).

2. See, for example, U.M. Norberg, Evolution of verte-brate flight: An aerodynamic model for the transitionfrom gliding to active flight,Am. Nat. 126, 303327(1985).

3. C.A. Long, G.P. Zhang, and T.F. George, Physical

and evolutionary problems in take-off runs of bipedalwinged vertebrates,Archaeopteryx20, 6371 (2002).

4. C.A. Long, G.P. Zhang, T.F. George, and C.F. Long, Airresistance and the origin of vertebrate flight, World Sci.Eng. Acad. Soc. T. Bio. Biomed. 1, 305-310 (2004).

5. C.A. Long, G.P. Zhang, T.F. George, and C.F. Long,Physical theory, origin of flight, and a synthesis pro-posed for birds,J. Theor. Bio. 224, 926 (2003).

6. U. Norberg, Vertebrate Flight(Springer-Verlag, Berlin,1990).

7. W.G. Pritchard and J.K. Pritchard, Mathematicalmodels for running,Am. Sci. 82, 546553 (1994).

For a more mathematical treatment, see A.J. Ward-Smith, A mathematical theory of running, based onthe first law of thermodynamics, and its application tothe performance of world-class athletes,J. Biomech.18, 337349 (1985).

8. P. Burgers and L.M. Chiappe, The wing of Archaeop-teryx as a primary thrust generator, Nature399, 6062(1999).

9. P. Wellnhofer, Archaeopteryx, Sci. Am. 262, 7077(May 1990).

10. X. Xu, Z. Zhou, X. Wang, X. Kuang, F. Zhang, and X.Du, Four-winged dinosaurs from china, Nature421,335340 (2003). For a less technical discussion, see

R.O. Prum, Dinosaurs take to the air, Nature421,323324 (2003).

PACS codes: 87.00.00, 45.20.da, 45.40.Aa

Bernard J. Feldman is professor of physics and associate

dean of the Undergraduate Engineering Program at the

University of Missouri-St. Louis. His research interests are

in amorphous materials and, recently, physics education.

Department of Physics & Astronomy, University

of Missouri-St. Louis, St. Louis, MO 63121;

[email protected]

Thomas F. George is chancellor and professor of chem-

istry and physics at the University of Missouri-St. Louis.

In addition to research on the flight of birds, he is involved

in theoretical studies of chemical/materials/laser physics,

including polymers, clusters, and nanoscience/technology.

Center for Molecular Electronics, Departments of

Chemistry & Biochemistry and Physics & Astronomy,

University of Missouri-St. Louis, St. Louis, MO 63121;

[email protected]

Charles A. Long is professor emeritus of biology at the

University of WisconsinStevens Point. His research inter-

ests are in bio-mathematics and natural history of wild

mammals and birds.

Department of Biology and Museum of NaturalHistory, University of WisconsinStevens Point,

Stevens Point, WI 54481; [email protected]

Claudine F. Longhas taught biology and chemistry at

the University of WisconsinStevens Point. Her research

interests are in studied flight of parrots with clipped wings.

Department of Biology and Museum of Natural

History, University of WisconsinStevens Point,

Stevens Point, WI 54481; [email protected]

Guoping Zhangis on the physics faculty at Indiana State

University. His research interests include the flight of

birds, ultrafast phenomena, strongly correlated systems,

nonlinear optics, x-ray spectroscopy, fast magnetization,

and nanoscience.

Department of Physics, Indiana State University, Terre

Haute, IN 47809; [email protected]

origin of bird flight

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