Articles

The Flight of the Bumblebee

by Matthew Vanhorn

“Ladies and gentlemen, please take your seats, and fasten your safety belts. We are ready for take off,” the flight attendant says pleasantly over the intercom. Jet engines begin to roar. You feel a subtle jolt, and the plane begins to rumble down the runway. You grab your seat in nervous anticipation of the unprecedented experience you are about to undertake. Once on track, the plane quickly gains speed. Your stomach drops in awkward exhilaration as the plane lifts from the ground, and you watch the landscape grow smaller and smaller as you float above the earth into a white sea of clouds.

Sound familiar? Unless you are prone to motion sickness or terrified of flying, the aforementioned account is probably reminiscent of your first experience aboard an airplane. Did you ever wonder what makes the airplane’s flight possible? Physicists and engineers understand this phenomenon very well. They have studied the plane’s sophisticated airfoil design. The wing’s round leading edge and sharp trailing edge, powered by 63,300+ pounds of engine thrust, produce an effective lift for the plane.

Now, imagine that there were no engines with which to power the airplane. What would it take for the plane to fly? For an Airplane to fly on its own without engines is impossible. And that brings us to the case of the humble bumblebee. Theoretically, scientists say, the bumblebee should remain grounded, just like the engineless jumbo jet. Considering that the basic equation governing the aerodynamics of flying insects and airplanes is supposed to be the same, there is no apparent explanation as to how bumblebees can fly. Bumblebee wings produce more lift than predicted by conventional aerodynamic analyses. The reciprocating motion of the wings makes the aerodynamics incredibly unsteady and difficult to analyze.

Bumblebees are hairy, robust bees, ranging from ½ inch to 1 inch in size. Bumblebee wings are very small in relation to their bodies. An airplane built with the same proportions of a bumblebee would never get off the ground, but bumblebees are not like airplanes. Rather, they are more like helicopters with flexible blades. A moving airfoil generates much more lift than a rigid one. However, the ostrich can create a moving airfoil and, yet, never lift from the ground. Thus, scientists have been in a quandary as to how the bees generate lift.

Theoretical physicists applied to the bumblebee the theories that are effective in the flight of 747s, and determined that the bees should not be able to take flight. This does not “prove” that bumblebees cannot fly; it simply means that physicists have the equation wrong. Ivars Peterson attempted to defend scientists by saying: “The real issue is not that scientists are wrong, but that there’s a crucial difference between a thing and a mathematical model of the thing.” This seemingly ambiguous statement, however, was followed by a valid reason: “A certain simple mathematical model wasn’t adequate or appropriate for describing the flight of a bumblebee” (1997). Indeed, there is nothing simple about the flight of the bumblebee.

Insect flight in general has been a mystery to scientists for many years. This difficulty traces back as far as a 1934 book by French entomologist Antoine Magnan, who referred to a calculation made by engineer André Sainte-Lague. His conclusion was based on the fact that “the maximum possible lift produced by air craft wings as small as a bumblebee’s and traveling as slowly as a bee in flight would be much less than the weight of a bee” (Dickinson, 2001).

Since 1934, engineers have employed aerodynamic theory to design Boeing 747s and stealth fighters. These aircraft are quite complex, yet their function is based upon steady-state principles. Insects disrupt this principle because they flap and rotate their wings at a rate of 300 to 400 beats per second—over ten times faster than the firing rate of the nervous system! The bumblebee achieves such fast wing speeds by simply contracting and relaxing muscles in its abdomen. Additionally, variations in stroke patterns cause differing aerodynamic forces that disconcert mathematical analyses. Insect wings do not flap like doors on simple hinges. Rather, the tip of each wing traces a thin oval at a steep angle. Also, the wings “flip” during each beat: The topside of the wing faces up during the down stroke, and down during the upstroke.

Animal mechanics specialist Charlie Ellington, from the University of Cambridge in England, discovered something that seemed to solve the puzzle. He learned that the extra lift was generated by a vortex traveling along the leading edge of the insect’s wing. Researchers Michael Dickinson and James Birch, from the University of California at Berkeley, had contrary findings. In the science journal Nature, they shared their research concerning the extra aerodynamic lift created by bumblebees. They built a largely scaled model of a fruit fly, and observed its flight in a tank of mineral oil. They simulated a tiny, real fruit fly flying in air—a much thinner medium. Professor Dickinson said: “Based on these experiments, we concluded that the [ Cambridge] hypothesis cannot explain the attachment of the vortex through the stroke” (Macphee, 2001).

Ellington’s conclusion nevertheless triggered a quest for an “unsteady function” equation that could explain the superior performance of flapping wings. Distribution of velocities and pressures within a fluid is governed by what are known as the Navier-Stokes equations, which were formulated in the early nineteenth century. Ellington’s findings revealed that the flight of the bumblebee could not be solved through virtue of the Navier-Stokes equations alone. The motions of the bumblebee’s wings are too complex to formulate an exact equation to characterize the aerodynamics of its flight.

In attempts to solve the mysteries of insect flight, scientists made enlarged scale models of bumblebee wings. These models produced viable results by combining the two essential forces in a fluid—a pressure force produced by fluid inertia, and a shear force caused by fluid viscosity. Professor Dickinson reported new findings of his own in 2001 as a result of building upon the theories of Ellington that he previously had attempted to refute. In his study published in Scientific American (“Solving the Mystery of Insect Flight”), Dickinson attributed the flight of the bumblebee to the phenomena of delayed stall, wake capture, and rotational circulation.

Delayed stall occurs when an aircraft’s wing cuts through the air at too steep of an angle. Vortices created by airplanes usually leave behind a pestering turbulence in the slipstream. However, insects require these vortices to remain in flight. A vortex is a rotating flow of fluid, such as occurs in a draining bathtub. When proceeding at shallow angles, the air splits at the front of the wing and flows smoothly in two streams along the upper and lower surfaces. The upper flow travels faster, resulting in a lower pressure above the wing. This draws the wing upward, producing lift. The first stage of stall initially increases the lift because of a brief flow structure called a leading-edge vortex. This type of vortex forms directly above and behind the wing’s leading edge. Airflow in the vortex is extremely fast, and the resulting low pressure adds substantial lift.

Dickinson’s findings seem to be in harmony with the experimental data recorded by physicist Jane Wang of Cornell University, who wrote:

The old bumblebee myth simply reflected our poor understanding of unsteady viscous fluid dynamics. Unlike fixed-wing aircraft with their steady, almost inviscid (without viscosity) flow dynamics, insects fly in a sea of vortices, surrounded by tiny eddies and whirlwinds that are created when they move their wings (as quoted in Segelken, 2000, parenthetical item in orig.).

In addition to delayed stall, Dickinson discovered that the wings generated short-lived strong forces at the beginning and end of each stroke that could not be explained by the stall. These force peaks occurred during stroke reversal, when the wing decelerates and rapidly rotates, suggesting that the rotation itself might be responsible. Dickinson illustrated the idea of rotational circulation by using a tennis ball. A tennis ball hit with backspin pulls air faster over the top, causing the ball to rise, whereas a topspin will pull air faster underneath, causing the ball to sink. Dickinson concluded that flapping wings develop significant lift by rotational circulation.

Finally, Dickinson discovered that wake capture—the collision of the wing with the swirling wake of the previous wing stroke—assists in the flight of insects. Each stroke of the wing leaves behind a complex of vortices. When the wing reverses direction, it passes back through this churning air. A wake contains energy lost from the insect to the air, so wake capture provides a way for the insect to recover energy.

Scientists still do not know every intricacy involved in the flight of bumblebees and other insects. Scientists hope to learn more from the complex wings of the bumblebee in order to apply the knowledge to aircraft. Engineers can design great aircraft by patterning their work after the Great Architect—He who builds all (Hebrews 3:4). God put so much obvious and careful planning into the tiny wing of the bumblebee—and that is only a minute fraction of the awesome Universe He decisively designed.

REFERENCES

Dickinson, Michael (2001), “Solving the Mystery of Insect Flight,” [On-line], URL: http://www.sciam.com/article.cfm?articleID=000EE5B1-DCA8-1C6F-84A9809EC588EF21.

Macphee, Kona (2001) “The Buzz on Bumblebees,” [On-line], URL: http://pass.maths.org.uk/issue17/news/bumble.

Peterson, Ivars (1997), “Flight of the Bumblebee,” [On-line], URL: http://www.maa.org/mathland/mathland_3_31.html.

Segelken, Roger (2000), “Bumblebees Finally Cleared for Takeoff,” [On-line], URL: http://www.news.cornell.edu/releases/March00/APS_Wang.hrs.html.

http://www.apologeticspress.org/articles/2528