Ходжа Н. (hojja_nusreddin) wrote,
Ходжа Н.

наконец математики тоже поняли, как летают пчёлы :)

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,
- called 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 8 different experiments with 8 different species
- Nabawy and his colleagues have shown that LEVs don’t actually give any extra lift at all

By creating 3 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.

Tiny tornadoes

- 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”
- 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”

Timothy Revell: Journal of the Royal Society Interface, DOI: 10.1098/rsif.2017.0159
Tags: математика, насекомое, наука, полёт

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