Flap, flip, back, flip... that's (roughly) how insects beat their wings– the `flap' and `back' are the down- and upstroke, and the `flip' is when they flip their wings over at the end of each stroke. The flips set the wing at the correct angle to produce lift force during the strokes, but the rotational motion during the flip also generates substantial lift itself.

Insects' proficiency at wing flipping sets them apart from birds and helps to make them such agile flyers. Now, recent computational simulations from researchers at Cornell University suggest that insects may get the flip for free – fluid dynamic forces naturally flip the wing over at the end of a wingbeat, without the need for any muscular forces.

It's not a new idea that fluid dynamic forces may help the wing flip (the correct tongue-twisting terms are `pronation' for the flip at the beginning of downstroke and `supination' for the flip at the beginning of upstroke). But without today's powerful computers, no one had been able to test the idea.

So Attila Bergou, Sheng Xu and Jane Wang developed a computer simulation of a flapping insect wing. They measured the kinematics of both the fore- and hindwings of a tethered dragonfly. Then they used code they had developed previously to calculate the fluid motion around a two-dimensional slice through each wing, about halfway along their length. The team estimated the mechanical power required to flip the wing over, including fluid and inertial forces. Negative power values indicate that fluid forces tend to flip the wing over.

Sure enough, the researchers found negative power at the ends of the up-and downstrokes. As the wing starts to slow down, fluid forces tend to flip the wing over. But this observation didn't explain the mechanism. Fluid forces take many forms – forces due to acceleration, or to pressure, or to friction – but which effect was responsible for the flip?

To answer this question, they used a different mathematical model, a much simpler one, called a `quasi-steady' model. After tuning several parameters in the simple model, they found that it matched up fairly well with the much fancier simulation. Not only that, but it conveniently allowed them to separate different types of fluid dynamic forces.

The dominant effect turned out to be acceleration. As the wing begins to slow down at the end of a wing beat, the air around it must also slow down. Since air has mass, it resists that deceleration, applying a force that pushes primarily on the center of the wing. Since the wings are attached to the insect's body near the front edge, not at the center, the fluid's`acceleration reaction' causes a torque that tends to flips the wing over.

Does this fluid-assisted wing flip occur in reality? To find out, the researchers realized they could exploit the asymmetry of fluid and muscular forces. Fluid dynamic forces are strongest at the tip of the wing, while muscular forces are applied at the base. If fluid forces cause the flip, then the wing should start twisting at the tip. Inspecting the high-speed movies in detail, Bergou saw a distinct twisting wave, starting at the tip and propagating towards the base.

It seems that insects really can flip their wings for free.

Bergou, A. J., Xu, S. and Wang, Z. J. (
). Passive wing pitch reversal in insect flight.
J. Fluid Mech.