# Maths Explains How Bees Can Stay Airborne With Such Tiny Wings

We first realised that bees seem to flout the laws of mathematics in the 1930s. Calculations showed that their wings could not provide enough lift to get their bodies off the ground, but that didn’t stop them.

“The bee, of course, flies anyway because bees don’t care what humans think is impossible,” says the narrator at the beginning of 2007’s Bee Movie.

Now a new mathematical analysis has put together a complete picture of how bees, as well as other insects and small birds, actually manage to fly.

Up until the 1990s it was assumed that bees used a continuous flow of air over their wing to generate lift, similar to how commercial planes fly. But in 1996 it was discovered that bees also have tiny tornado-like airflows that form on the leading edges of their wings, known as leading edge vortices (LEVs).

“Initially, everyone thought this was the magical solution we’d been looking for. People worshipped vortices and assumed they must be responsible for the extra lift,” says Mostafa Nabawy at University of Manchester.

But after reanalysing eight different experiments with eight different species Nabawy and his colleagues have shown that LEVs don’t actually give any extra lift at all. By creating three mathematical models each with a different mechanism for generating lift and then comparing the models to the original experiments, they were able to work out how the creatures stay in the air.

Surprisingly, they found that LEVs don’t directly generate the lift as was previously thought. “Instead we found that LEVs mean the wing can fly at a much higher angle of attack without stalling,” says Nabawy.

The swirls of air at the edge of a bee’s wing enable the insect to angle its wing more sharply toward the sky, improving the flow of air over the wing. It’s this higher wing angle that gives bees, fruit flies and even humming birds enough lift to fly.

If a bee was mid-flight and the LEVs just stopped spinning the bee would stall, meaning that the pressure difference between the top and the underside of the wing responsible for lift would drop. They would then fall out of the air and bounce along the floor before finally skidding to a halt with a sore behind.

“By testing these mathematical ideas against measured data from real wings, the authors have shown convincingly that the best explanation is that the leading-edge vortex prevents stall,” says Richard Bomphrey at Royal Veterinary College.

Understanding how a bee flies and having the last word on the so-called bee paradox is a worthy goal in itself. But the new work could also “have an important impact on the development of fans, turbines, or miniature flying vehicles for deliveries, surveillance or search-and-rescue tasks,” says Bomphrey.

Journal reference: Journal of the Royal Society Interface, DOI: 10.1098/rsif.2017.0159