### March 20, 2000

## Insect flight obeys aerodynamic rules, Cornell physicist proves

MINNEAPOLIS -- A computer simulation of rapidly oscillating wings and the complex motions of fluids has proved that insect flight conforms to the physical principles of aerodynamics.

The computer-modeling accomplishment - which is expected to aid the future design of tiny insect-like flying machines and should dispel the longstanding myth that "bumblebees cannot fly, according to conventional aerodynamics" - was announced by Cornell University physicist Z. Jane Wang today (March 20) at the Minneapolis meeting of the American Physical Society (APS).

"The old bumblebee myth simply reflected our poor understanding of unsteady viscous fluid dynamics," explained Wang, an assistant professor of theoretical and applied mechanics in Cornell's College of Engineering, in an interview before the APS meeting. "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."

A vortex created by an airplane usually is a minor nuisance that is left behind in the slipstream. But insects depend on vortices to keep them aloft, especially when they are hovering. An important key to solving the mystery of insect flight, Wang said, is the understanding of the vortex "shedding" and how the vortices behave when they separate from the moving surface that created them. Any theory of insect flight has to account for both viscous and inertial effects, Wang said, noting that in a fluid environment like air, inertia is a force due to the motion of the fluid itself as fluid particles are carried along by their own velocity. And viscous force has to do with the differences in velocity, or shear, within the fluid.

"In the earliest studies of insect flight, it was hoped that unsteady effects might be relatively unimportant," Wang noted. "Later, several investigators suggested that unsteady effects might play a significant role. But there was no quantitative theory available because of the difficulties inherent in dealing with unsteady flows coupled to moving boundaries."

Insects aren't the only things affected by the interaction between dynamic boundaries and highly unsteady viscous flows, the engineering professor said. The erratic motion of a falling piece of paper or the wobble of bubbles rising through a glass of soda pop result from vortex wakes, and so did one of civil engineering's greatest design catastrophes - the collapse in 1940 of the Tacoma Narrows Bridge in the state of Washington. Wind blowing across the surface of that newly built structure set up severe vibrations and undulating motions that tore the suspension bridge apart.

"Rapid oscillations pose one of the most difficult questions for fluid dynamics," Wang said. "Things become very messy."

Biologists with high-speed video cameras have been able to document the oscillating motions of insect wings as they move up and down and change pitch by tilting the edges, and the complex motions are beginning to be incorporated in the design of robotic "insect" wings. However, the aerodynamics of hovering insects, such as dragonflies, is still not fully understood. Wang chose the dragonfly as "the worst case for quasi-steady state theory" as the first test of her computer simulation.

The simulation required the development by Wang of some new computational tools - "tricks," she modestly calls them, to resolve unsteady flows and forces, which are governed by a mathematical calculation called the Navier-Stokes Equation - and hundreds of hours of number-crunching by a supercomputer. The result was the first ever proof that dragonflies produce sufficient lift to stay above the ground - at least in a two-dimensional simulation.

The same simulation in three dimensions will require more computational "tricks" and computer time, and Wang currently is working on that. By substituting wing-motion data from other kinds of insects, she says, the simulation will reveal the fluid dynamics of flight by those species - including bumblebees.

The insect aerodynamics studies were funded by the National Science Foundation.

Before joining faculty in 1999 at Cornell, where she teaches applied mathematics and mathematical modeling, Wang conducted postdoctoral research at New York University's Courant Institute of Mathematical Sciences (where she first became interested in insect flight) as well as the University of Oxford. Before that she earned a Ph.D. in physics at the University of Chicago and a bachelor's degree at Fudan University in the People's Republic of China.

Looking ahead to the construction of tiny flying machines for aerial surveillance and other purposes, Wang says the designs need not resemble fixed-wing airplanes or helicopters. Now that the rules for insect flight are quantified, designs for buglike devices of almost any size can be tested in the computer. Various designs can virtually hover, fly backward and perform acrobatic maneuvers in full accordance with the principles of unsteady viscous fluid dynamics. Or crash - virtually - if they don't.

Ever since she heard it, the bumblebee myth has bothered Wang the way yellowjackets pester picnickers, and she has tried to trace its historical source.

"The rumor probably started in the 1930s with students of the noted aerodynamicist Ludwig Prandtl at Gottingen," she said. "That was a time when we were just beginning to think we understood aerodynamic principles, as applied to fixed-wing aircraft, but scientists recognized their limitations in applying the principles to the birds and insects and other creatures in the natural world.

"I'm sure no one, including the bees, seriously doubted that insects can fly," she said. "Now we're beginning to understand why."