What is the best way to flap a wing? Engineers would love to use the millions of years of evolution of insect flight to help them design the best possible miniature flying vehicles. But even though insects clearly fly well,it's not clear that they've arrived at the `best' way, nor is it obvious what`best' would mean from an evolutionary standpoint. Deriving concrete physical principles from the complex evolutionary pressures that produced insect flight turns out to be quite challenging.
Instead, the engineers Michele Milano and Morteza Gharib of the California Institute of Technology decided to take evolution into their own hands. They built a simple model of a flapping wing – a 5 cm-wide rectangular plate that can rotate and move from side to side in a tank of water – and connected it to a computerised simulation of natural selection. The simulation, called a genetic algorithm, adjusts four components of the flapping motion – the amplitude, velocity, angle of attack and rotational speed as the wing changes direction – and calculates a`fitness' for each motion. But unlike the many competing selective pressures in natural evolution, Milano and Gharib selected only for high average lift force. Motions that produced high forces thrived and produced `offspring' with similar motions, while those with low forces died.
In this way, they evolved a population of optimal flappers, all with about the same high lift forces but different flapping motions. They looked for tradeoffs between flapping parameters, which could illuminate the fundamental physics of the best flapping motion. For example, if high-angle, low-velocity motions and low-angle, high-velocity motions produce about the same force,then perhaps angle of attack and velocity aren't individually very important,but some combination of them is. They hoped that their simple model would make such tradeoffs obvious. It didn't. All four parameters seemed equally important and covered fairly substantial ranges.
So, the researchers had to look harder to find commonalities between all of their optimal flappers. All of them used high angles of attack – around 62° – which would make the flow peel off the top edge of the wing,rolling up into a vortex. This vortex, called a leading edge vortex, is known to increase lift – as long as it stays attached to the top of the wing. When it peels off completely, the wing stalls and the lift force drops precipitously.
Maybe, the researchers thought, the optimal flappers were tuning their vortex production. Gharib had previously found that vortex generators can make vortices up to a maximum strength, or circulation; trying to make a vortex above that maximum circulation doesn't make a stronger vortex, just lots of little vortices. The maximum circulation occurs when a parameter called the`formation number' is about 4. When he calculated a formation number for the flapping wings, he found that the optimal flappers had peak formation numbers ranging from 3.6 to 4.6.
The last thing to check was whether less optimal flapping motions didn't reach a formation number of 4, and were therefore underutilising their leading-edge vortices, or exceeded 4, causing the vortices to peel off entirely. Examining the flow around a low-lift steady motion and one of the optimal motions, Milano and Gharib found that the leading edge vortex in the low-lift motion reached maximum circulation and peeled off early in the stroke. But in the optimal motion, the wing started rotating when the vortex hit maximum circulation, allowing the wing to hang on to the vortex for as long as possible.
At least for their simple evolutionary scenario, the researchers ultimately did find an answer to the question, `how best to flap?' The answer, it seems,is 4.
