Animal flight is a bit of an enigma. On the one hand, a fruit fly—with its millimeter-sized wings sweeping intricate trajectories several hundred times each second—represents a complex system far beyond our present technological capabilities. On the other hand, flapping flight should be dictated by rather simple principles. It is, after all, accomplished by critters as lowly as the fruit fly.
These seemingly contradictory perspectives have inspired a flurry of research into the aerodynamics of flapping-wing flight. A common approach focuses on how the wing shape and motions of a particular organism produce the aerodynamic forces needed for flying. The state of the art involves using high-speed videography to extract wing motions and replaying these kinematics on dynamically scaled motorized wings or in computational flow simulations. These techniques are invaluable for understanding how, for example, an insect adjusts its wing motions to perform an aerial maneuver.
Flying animals of all shapes and sizes seem to share some common mechanisms. To distill these general principles, we have conducted a series of flight experiments using the simplest conceivable wing geometries and flapping motions. In particular, our investigations typically involve free-moving bodies: given a shape and flapping motion, a wing is allowed to locomote under its self-generated fluid forces.
Figure 1. A flapping wing spontaneously flies forward, leaving a staggered array of counter-rotating vortices in its wake.
In work inspired by the forward flight of birds, we considered the motion of a rigid, rectangular wing that is driven to heave up and down in water.1–4 We mounted the wing on an axle that allows for rotation, which in this system is analogous to forward flight. The wing is symmetric—there is no difference between its leading and trailing edges—and thus it seems that there is no reason for it to fly forward at all. To our surprise, we found that if flapped appreciably fast, the symmetry of the system is spontaneously broken and the wing takes off.
This robust flight is associated with a unique flow pattern behind the traveling wing. To reveal this flow, we applied a voltage to the metallic wing, inducing tiny bubbles to form in the water that can be illuminated with a sheet of light. Figure 1 shows a photograph of the staggered array of vortices or swirls trailing the body. Pairs of vortices are shed per oscillation, arranged such that puffs of fluid are ejected into the wake. This backward flow is associated with a forward reaction force on the wing. Interestingly, this so-called inverted von Kármán flow pattern has also been observed in the wakes of swimming and flying animals.
Figure 2. A Λ-shaped, asymmetric structure in a vertically oscillating flow produces lift by ejecting vortex pairs downward. The vortices are redirected to counteract any tilts of the body, ensuring flight stability. Photographs are captured when the flow moves up (time t=0) and down (t=T/2) within one period (T) of oscillation.
In a second set of studies, we investigated how flapping structures generate upward force and remain stable during hovering flight.5–7 Here, we abstracted the flight of insects using a unique experimental system in which ‘bugs’—upward-pointing pyramid shapes made of paper—are placed in a vertically oscillating airflow. Although the flow is symmetrical, the asymmetric body shape enables hovering against gravity: qualitatively speaking, the pyramid experiences a stronger force for the upward than for the downward flow.
Flow visualization, however, reveals that the actual force-generation mechanism of these bugs is far more intriguing. In an analogous 2D system, we used a Λ-shaped body that is fixed in an oscillating layer of water and illuminated from below, casting a shadow on a screen. Vortical flows cause slight depressions of the fluid surface, lensing light away and yielding a shadow on the screen. As shown in Figure 2, this method reveals that a vortex pair is shed from each side of the bug during an oscillation. These ‘vortex dipoles’ carry fluid momentum downward, thus generating lift. Further, if the Λ-shape is tilted, one pair is strongly redirected, automatically providing an inward force that tends to restore the upright orientation of the body. This rearrangement of the unsteady flow explains the surprisingly robust flight stability of our hovering pyramids.
As natural scientists, we derive deep satisfaction from the discovery that efficient and stable flight is associated with orderly arrays of vortices. In engineering applications, this connection suggests that propulsion systems might be designed and evaluated based on the flow patterns produced in flapping flight. For these flying, swimming, and hovering animals, the key to their successful locomotion and maneuverability lies in the production and subtle manipulation of the swirling fluid flows. We are currently designing free-flying devices that will not exactly mimic animal motions but do take advantage of the principles learned from these studies.
Leif Ristroph, Stephen Childress, Jun Zhang
Courant Institute New York University (NYU)
New York, NY
Leif Ristroph studied insect flight while earning his PhD in physics at Cornell University. As a National Science Foundation postdoctoral fellow at NYU's Applied Math Lab (AML), he is continuing his work on biolocomotion and also exploring geophysical fluid dynamics.
Stephen Childress came to the Courant Institute in 1964 from the California Institute of Technology, where he studied aeronautics and mathematics. His research is in theoretical fluid mechanics, including studies of the mechanisms of locomotion in nature.
Jun Zhang is professor of physics and mathematics at NYU. He earned his PhD in physics from the University of Copenhagen and completed postdoctoral fellowships at Rockefeller University and NYU. His research interests include biolocomotion, geophysical flows, and the dynamics of complex systems.
School of Engineering Brown University
Bin Liu graduated from NYU with a PhD in physics. After a postdoctoral term at AML, Bin is continuing research in fluid dynamics, animal locomotion, and complex fluids as a research scientist at Brown University.
N. Vandenberghe, J. Zhang, S. Childress, Symmetry breaking leads to forward flapping flight,
J. Fluid Mech.
506, p. 147-155, 2004.
S. Alben, M. Shelley, Coherent locomotion as an attracting state for a free flapping body,
Proc. Nat'l Acad. Sci. USA
102(32), p. 11163-11166, 2005.
N. Vandenberghe, S. Childress, J. Zhang, On unidirectional flight of a free flapping wing,
18, p. 014102, 2006.
S. E. Spagnolie, L. Moret, M. J. Shelley, J. Zhang, Surprising behaviors in flapping locomotion with passive pitching,
22, p. 041903, 2010.
S. Childress, N. Vandenberghe, J. Zhang, Hovering of a passive body in an oscillating airflow,
18, p. 117103, 2006.
A. Weathers, B. Folie, B. Liu, S. Childress, J. Zhang, Hovering of a rigid pyramid in an oscillatory airflow,
J. Fluid Mech.
650, p. 415-425, 2010.
B. Liu, L. Ristroph, A. Weathers, S. Childress, J. Zhang, Intrinsic stability of a body hovering in an oscillating airflow,
Phys. Rev. Lett.
108, p. 068103, 2012.