803: Airfoil

Explain xkcd: It's 'cause you're dumb.
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This is a fun explanation to prepare your kids for; it's common and totally wrong. Good lines include "why does the air have to travel on both sides at the same time?" and "I saw the Wright brothers plane and those wings were curved the same on the top and bottom!"
Title text: This is a fun explanation to prepare your kids for; it's common and totally wrong. Good lines include "why does the air have to travel on both sides at the same time?" and "I saw the Wright brothers plane and those wings were curved the same on the top and bottom!"


This comic is about the common teaching that an airfoil works because the air on top of the wing must travel faster to "keep up" with the air flowing across the bottom of the wing. The theory goes that, because the air on top of the wing is traveling faster, it must, as a result of Bernoulli's Principle, create an area of lower pressure above the wing; this causes lift (that is, the wing rises) because the higher pressure below the wing (symbolized thick "up" arrow arrow) pushes it up more than the low pressure above the wing. As it turns, out this is, to put it mildly, a vast oversimplification of how lift is truly created.

In the next panel, a student asks a particularly insightful question: Why, if the theory is true, can planes fly upside down? (If the simple airfoil theory is all that permits planes to stay up in the air, then flying upside down should reverse the pressures — pushing the plane down and causing it to crash.) The teacher thinks about it and clearly has no answer.

The final set of panels posit three potential responses from the teacher, upon realizing her theory has been disproved. In the "right" one, the teacher realizes that perhaps the model she's been using to explain how an airfoil is wrong (or, at a minimum, too simple). She is curious about it and suggests that this is an area for further exploration, and encourages additional study — in effect, rewarding the student for his insight. In the "wrong" panel, the teacher, out of apparent embarrassment, avoids the question entirely, saying simply that it's complicated (and implying that such questions are outside the student's understanding). In the "very wrong" panel, not only does the teacher avoid answering the question, she attempts to distract them (or even punish them for asking such an insightful question) by telling the kids that Santa Claus isn't real and that Santa Claus is really their parents — something that would obviously distress them (in addition to distracting them from the question they've asked) and constitute harsh punishment for pointing out the teacher's ignorance.

The alt-text suggests additional reasons for re-thinking the common theory as to how airfoils create lift. It points out that (1) it is absurd to believe the air has to get across the airfoil's two sides in the same amount of time, and (2) the Wright brothers plane's wings were curved the same amount on both sides of the airfoil, meaning that the distance that the air needs to travel to get across the wing is not the dispositive factor in creating lift.

The strip is correct in noting that lift is a far more complicated process than the simple theory posited by the teacher. While the role of Bernoulli's Principle (that is, the difference in pressures) cannot be entirely discounted, the theory here is vastly too simple. As an initial matter, as suggested by the alt-text, there is no reason that the air on top of the wing should be compelled to "keep up" with the air on the bottom of the wing. Indeed, as demonstrated by the illustration below, in the time that the air below the wing travels across, the air on top of the wing has not only traveled the length of the entire top of the wing (a distance that may be farther than the distance under the wing, due to its shape), but often additional distance.

Karman trefftz.gif

Lift may be more usefully described as resulting from the deflection of air, although this explanation still does not explain how symmetrical wings will work (at least, absent effects caused by a change in the "angle of attack") nor how a plane may fly upside down. The Wikipedia article on lift provides a more detailed explanation. It in fact gives an explanation as to these two issues. It explains that with zero angle of attack, a symmetrical wing will not generate lift (though it is possible that other factors may generate other slight upward force, such as updrafts, the shape of the plane, and the angle of the engine relative to the wings. It also explains that an asymmetrical (or "cambered") wing may adjust angle of attack to compensate and still generate lift.


Handling a student who challenges your expertise with an insightful question:
[There's a picture of the cross section of an airfoil, with an arrow above and below, pointing from right to left. Layered on top of these arrows, pointing up and down at the cross section, are a larger arrow below and a smaller arrow above.]
(This panel just contains text, and has a speech curlique hanging towards the person in the next panel.)
Teacher: So, kids, the air above the wing travels a longer distance, so it has to go faster to keep up. Faster air exerts less pressure, so :the wing is lifted upward.
Student: But then why can planes fly upside down?
(The teacher is standing, pondering the question. Three arrows point out of this panel, leading to each of the next three panels which are :arranged vertically.)
(This is a label at the top of the panel, not a character speaking.)
(This is the character speaking.)
Teacher: Wow, good question! Maybe this picture is simplified -- or wrong! We should learn more.
Teacher: It's... complicated.
Teacher: And we need to move on.
Very wrong:

(Fists are clenched.)

Teacher: Santa Claus is your parents.

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Since gases are unique in the way they convert pressure change to heat or cold, none of the above can be true. The schema shows more columns of air under the wing than pass above. How come? We know that an actual wing pulls air down from the layers above rather than bludgeon the air in front of it.

What happens is that vortices are engendered. Wing design is all about getting them past the control sections (the major problem to aircraft design in the 1940's.)

I used Google News BEFORE it was clickbait (talk) 01:15, 26 January 2015 (UTC)

It is a convention in fluid dynamics that the flow always comes from the left. Nobody working in this field would ever draw a picture with the flow coming from the right side. So this is a hint by its own that the image may be wrong.

Regarding the last comment: The image is from wikipedia. The original comment tells us that the wing influences the flow even at a great distance. The flow at the top is still a lot faster than below the wing. 21:01, 3 June 2015 (UTC)

My high school math teacher said there were three ways for a teacher to say "I don't know" -- "I don't know", "It's beyond the scope of the course", and "You wouldn't understand it if I told you." So, whenever we asked a question like the one in the comic, he'd say "It's beyond the scope of the course, and you wouldn't understand it if I told you anyway! Dumb kids!" We loved that guy. 17:01, 5 July 2018 (UTC)

This airfoil problem is a 2D problem and the classical Bernoulli's equation is a 1D equation. If you use velocity vector(speed and direction) instead speed the equation works.