# How does a wing work?

27 January 2018

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Flying has become a vital part of our lives. In the one hundred years since the Wright Brothers first took to the air, the aviation industry has grown meteorically. Now, routinely, planes loaded with over 800 passengers and tonnes of cargo are cruising long-haul. But what keeps these metal tubes in the sky?

The physics of how an aeroplane wing works is an essential - if not frequently misunderstood topic - in school science lessons. For the curious reader, who carefully paid attention to the teacher, the answer to the aforementioned question seems easy. The specific shape of the wing, we are told, is the reason for the uplift. The air on the curved top surface needs to travel faster than the stream along the straight bottom. And because there is a physical relationship between air velocity and pressure, described by the famous Bernoulli equation named after mathematician Daniel Bernoulli, a rise in fluid velocity decreases its pressure.

For the wing this means that, on the top surface, the pressure is lower than on the bottom surface. This difference in pressure creates the lift force. Et voilà, we fly! Problem solved, let’s get some tea! But, hold on a second: how can a paper aeroplane generate such a force with equal distances on both sides of the wing? How are acrobatic, upside-down flights possible with this explanation?

How can we go about identifying the issues in a theory? Firstly, we can analyse the formulas used and hope for some transposed digits or variables that could explain the issues. Secondly, we could check the assumptions and ideas the formulas are based on and question, if they are appropriate in a given case. As an example, the statement “water boils at 100°C” is true. But only with the assumption that the kettle is at sea level and with a pressure of one atmosphere (bar). Making tea on Mount Everest would prove the given comment wrong and challenge the argument.

In terms of the physics of the wing, we were assuming that the two air streams (the one above and the other below the surface of the wing) need to catch up and reunite at the trailing edge of the wing; hence the upper one needs to speed up because it has farther to travel. And that’s the crux of the matter. There is no lifelong bonding between two particles of air that compels them to find their mate again when they get separated by the leading edge of a wing. It’s air, not penguins. Some research has even proved that the stream from the upper surface reaches the back edge of the wing long before the lower one. So we need to find another way to explain how the uplift is generated.

When a wing – or aerofoil to give it its proper name – is moving through air, the air splits and the pressure changes on both sides of the wing as the air flows around it. The change in pressure comes from the fact that the passing air cannot flow in a straight line but, instead, needs to bend. This is because the wing's upper surface is curved. With this bending, the same amount of air now needs to spread out to occupy a bigger volume, and this is what leads to a drop in pressure. On the bottom side of the wing, the whole situation is turned upside down and the approaching amount of air is compressed into a smaller volume. This pressure slows down the stream over the lower surface and speeds up the air passing over the upper wing surface. And the more the wing is tilted downwards at the back, the stronger the effect. This is because, in addition to the lift generated by the pressure difference around the wing, the air stream will also be deflected downwards at the wing's trailing edge. And Newton’s 3rd Law says that, for every action, there is an equal and opposite reaction. So if the wing pushes the air downwards, the air pushes back up on the wing.

What the interpretation with the Bernoulli equation is still lacking is the reason as to why the stream follows the aerofoil. This can be explained by another theory: the Coandă effect. Romanian scientist Henri Coandă discovered that flowing fluids stick to and follow curved surfaces. In our problem with the wing, the stream creates a downward force at the end of the wing because it extrapolates the curvature it was following. But like the Bernoulli equation explanation, the Coandă phenomenon also suffers from limitations and some assumptions. The reason why air “sticks” to the surface of the wing is often attributed to its viscosity. If this was the case, the stream would hold better if the surface was rough and would stay straight if it was greased. As with the Bernoulli explanation, this is a misconception. The viscosity does not play a significant role at all. Rather, it is the incompressible nature of air, together with a slipping boundary of the wing, that is responsible for the generation of lift.

So it appears that neither Bernoulli nor Coandă can provide an airtight answer. Digging deeper into literature, even more names and theories surface, such as Kutta-Zhukovsky, or the Prandtl Drag Theory to name but a few. Aerodynamics of wings is an active field of research perfectly represented by the colourful jungle of theories. Scientists love to give the unknown a fancy name and, usually, the more they use it, the less they understand!

In a nutshell, researchers still don’t know why planes fly. But no need to worry on your next flight. It’s not a scientist, who designed the plane: it is the product of a bunch of crafty engineers who just make things work.

If you'd not guessed, I'm a scientist by profession but an engineer at heart!