Sunday, March 4th, 2012 10:42 am GMT -7 Sunday, March 4th, 2012 10:42 am GMT -7Sunday, March 4th, 2012 10:42 am GMT -7
Airliner Wing in Flight

I take a stab at a clear and simple explanation of how an airplane stays up. Do I succeed?





This is the type of article where I invariably get emails from guys telling me to try cracking open an aerodynamics book for a change. News flash: not only did I write one of those myself, but I crack open other’s aerodynamics books on a regular basis. Scout’s honor!

A full explanation of how lift on a wing (bird or airplane) really works is very complicated. The only way an explanation can be understandable by mere humans is by making major simplifying assumptions. If you find an explanation and it does not include pages full of equations, I can guarantee you that simplifications were made.

In fact, two explanations of how lift works can both be correct yet appear to be totally incompatible with each other. That is because the authors chose to make different sets of simplifications. Unfortunately, other different looking explanations of lift floating around are also dead wrong. No wonder there is so much confusion on this topic!

Momentum, Energy and Mass

Any correct calculation of air flowing around an object has to account for the momentum, energy, and mass of the air particles. These are simply fundamental laws of nature.

A set of equations that can do this are called the Euler equations for fluid dynamics. They are scary looking, and we are still ignoring the effects of the viscosity of the air, which are very important. If we include those, then we end up with the Navier-Stokes (NS) equations.

If the Euler equations are scary looking, the NS equations are downright terrifying. I would include a picture of what they look like, but I don’t like scaring people if I don’t really have to.

Even with today’s computing technology and advanced knowledge of how they work, solving the NS equations to exactly compute the lift around a wing is not possible. It is just too hard to do. In practice simplifying assumptions are made, which is where this discussion started.

Airliner wing in flight

Conservation of Energy

One set of simplifying assumptions only looks at the conservation of energy. In an airplane, we are used to trading off altitude (potential energy) for speed (kinetic energy). It’s the same principle that applies to the flow of air around a wing.

These equations say that when flowing air speeds up (gaining kinetic energy), it has to decrease in pressure (losing potential energy). But why does the air going over a wing speed up?

This is where many explanations of lift stumble. There are several kooky ones floating around. Watch out for those. Instead, here’s an explanation you can trust.

The leading edge of a wing has to push the air around it. It is more curved on top, so the air going over the wing gets squeezed more. When air gets squeezed into a smaller space, to maintain its energy, it has to speed up.

When the air going over the wing speeds up, its pressure drops. I just finished explaining why that happens. This lower pressure acts like a partial vacuum and literally sucks the wing up. We call that lift, and we call the equations that explain the conservation of energy the Bernoulli equations.

Although not as strong, there is a similar but opposite effect occurring on the bottom of the wing. When the air hits it, it slows down a little. That leads to a pressure increase below the wing, pushing it up.

Henri Coanda 1910 airplane - replica

Coanda Effect

Another set of simplifying equations looks at conserving the momentum of the air. Before I can talk about those, though, I need to explain the Coanda Effect.

Henri Coanda was an early aviation pioneer from Romania. In 1910 he designed an airplane that included a very primitive type of jet engine. The air coming from the engines traveled in between two wings, the airplane being a biplane. Coanda noticed that the air from the engines was pulled and made to flow around the top of the bottom wing. It is hard to describe exactly why this happens, but it is related to the viscosity of air.

Anyway, this effect of air being pulled to flow around an object is now called the Coanda effect.

As an aside, if the curve of the upper surface of the wing is so much that the air cannot follow it around, that is when we say that a wing is stalled.

Conservation of Momentum

When air is forced to flow over a wing, the Coanda effect makes the air follow the contour of the wing as its surface curves up and then down. This contour can be virtual. For example, a flat plate tilted up in relation to the air stream will act effectively as if it had a contour on its upper surface.

If the back of the wing is tilted even slightly down (as it is usually), then the air coming out the back will be pushed down. Newton’s laws of motion state that every force must have an equal and opposite reaction. In our case, the reaction is the wing being pushed up. We call that lift, too.

Air hitting the bottom of the wing is also pushed down and helps create lift. But most of the lift on a wing is from the Coanda effect on the upper surface.

Conservation of Mass

The third simplified approach, using just conservation of mass, is not normally used. The equations for the conservation of mass in a fluid are very counter-intuitive.

Comparing the Approaches

The two explanations of lift we covered here, conservation of energy and conservation of momentum, could not be more different. However, they are both correct yet incomplete explanations of how lift really works.

What is really interesting is that the two approaches for explaining lift can be used to come up with very similar resulting numbers under most circumstances that we are interested in. I think this is amazing, but is not as odd as it sounds once you dig into it.

You see, Bernoulli derived his equations partly based on his knowledge of Newton’s laws of motion. It would take many pages to explain, but they are just two ways of looking at the same physical phenomenon. Like they say, sometimes truth is stranger than fiction!

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