Chapter 4: Fluid Mechanics

4.3
Bernoulli’s Principle and Airplanes

Critical Questions:

  • How does an airplane stay up in the air?

You might think that today, more than a century after the Wright brothers flew that first airplane of theirs, most of the people who build and fly airplanes would agree on an explanation for how they stay up there. But just try walking into a room full of pilots and airplane engineers and asking them to explain this to you. The heated arguments and vicious character attacks that will result may well convince you never to step foot on an airplane again.

Upside Down Lynx by Captain Chaos on Flickr

Don't even get me friggin' STARTED on helicopters.

The reason why it’s so hard to pin down one easy explanation for the force that keeps an airplane up in the air – the ‘lift’, as it is called – is that it’s actually pretty complicated. Most simplified explanations of lift leave out some crucial details, or else they add in some incorrect ones.

The most common incorrect explanation of lift involves Bernoulli’s principle, which is interesting enough that we can spend some time getting to know about it before coming back to the problem of airplanes.

Grab a sheet of paper and hold it so that it hangs down. Now put your mouth on one side of the paper, near the top, and blow downwards parallel to the surface of it. In case you can’t be bothered to try this yourself, here’s what happens: the paper will curl, but towards the blowing air rather than away from it.

This is a simple example of Bernoulli’s principle, which says that a moving fluid is (in general) at a lower pressure than a still fluid. In the case of the paper, the moving air above it is at a lower pressure than the still air on the other side, resulting in the unexpected lift.

If you want to make some easy money off of this idea, you should go out and find a drunk college guy who’s just won a game of beer pong.[1] Roll a piece of paper into a cone and drop a ping pong ball into it. Now bet the drunk guy five bucks that he can’t blow upwards into the cone and make the ball pop out. As long as you tell him that he has to blow in a steady stream rather than in short bursts[2], you’ll end up five dollars richer. As the air comes up out of the cone, it’s moving more quickly beneath the ping pong ball than above it. The moving air is at a lower pressure, so the ball will actually be held in place – the harder he blows, the more it’ll be pulled down towards the bottom of the cone.

But aside from gambling opportunities, Bernoulli’s principle really doesn’t show up much in everyday life, unlike most of the things on the rest of this site. The main reason I bring it up is that it is, as I said before, often used to explain the lift provided by airplane wings. You might have heard it yourself: air moves more quickly over the top of the wing than the bottom, resulting in a lower pressure above the wing than below it, which results in an upwards force.

This actually does have some truth to it, but the reasons commonly given for why the air moves more quickly over the top than the bottom are usually far from reality.[3]

Karman trefftz

This animation explains everything! You don't even need to read the rest of the post.

There are a number of things happening as an airplane wing slices through the air. First, the angle of the wing (the “angle of attack”, as it’s called) means that some air hits the bottom of the wing, pushing it upwards. Meanwhile, some other air compresses together as it moves up over the front of the wing; this air then rushes down the far side of the sloping top, pulling some of the air above it downwards as well. Thus, a huge amount of air is moved downwards, and as the wing pulls the air down, the air pushes the wing back up according to Newton’s Third Law. This lift force can also be understood using Bernoulli’s principle and some calculus – the quickly-moving air above the wing does indeed result in a drastically lowered pressure.

There is, of course, quite a bit more to be said about how to keep a plane in the air – the angle of attack must be big enough to generate lift but not so big as to result in stalling, for example, and it has to match up with the plane’s speed and the density of the atmosphere – but that’s the basic story.

Big Ideas:

  • Bernoulli’s principle says that a moving fluid is (in general) at a lower pressure than a still fluid.
  • An airplane stays in the air because of a complex assortment of phenomena, all of which result in the air around a wing being forced downwards.
  1. Note: this is never a good idea.
  2. Grow up.
  3. These reasons include the notorious ‘equal transit time’ explanation, which says that the path over the top of the wing is longer than the one going beneath it, but air going in either direction has to take the same amount of time to reach the other side of the wing. You can see how wrong this is by observing air patterns in a wind tunnel. It also doesn’t explain how airplane wings can be symmetrical (which they are) and how planes could fly upside down (which they can do).
4.3 Bernoulli’s Principle and Airplanes   (from Chapter 4: Fluid Mechanics)


   

4 Responses

  1. So what do you think about the episode of Car Talk that references the Bernoulli Principle (episode #1236, skip to the 4th story, I think…)?

    http://www.cartalk.com/content/1236-bernoulli

  2. byron

    So you’re saying Bernoulli principle is incorrect but Newton’s 3rd Law of motion is…. ?

    • Not at all! Bernoulli’s principle is still an excellent way of explaining a lot of different phenomena. And it is one way to look at what’s happening with an airplane wing, but most explanations that use it to explain lift oversimplify the situation to the point of being incorrect.

      As I said, it’s the combination of air hitting the bottom of the wing and the compression + downwards acceleration of air on top (plus some other crazy fluid-dynamics stuff, probably) that gives the wing its lift.

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