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Tuesday, May 22, 2018

Why airplanes stay in the sky: an epistemological window

Growing up, I was told by several science teachers that airplanes obtained lift via the "equal transit-time" phenomenon (from Wikipedia's "Airplane" entry):
...the "equal transit-time"... states that the parcels of air which are divided by an airfoil must rejoin again; because of the greater curvature (and hence longer path) of the upper surface of an aerofoil, the air going over the top must go faster in order to "catch up" with the air flowing around the bottom. Therefore, because of its higher speed the pressure of the air above the airfoil must be lower.
Turns out this is basically false. See these pictures for evidence that air does not need to rejoin at the same place at all, though of course that doesn't mean that no air acceleration occurs at all.

As Wikipedia points out in its article on lift:
Such an explanation would predict that an aircraft could not fly inverted, which is demonstrably not the case. When an aircraft is flying inverted, the air moving over the bottom (in the aircraft reference frame) surface of the airfoil is moving faster. The explanation also fails to account for airfoils which are fully symmetrical yet still develop significant lift.
It is unclear why this explanation has gained such currency, except by repetition by authors of populist (rather than rigorously scientific) books, and perhaps the fact that the explanation is easiest to grasp intuitively without mathematics.

For my money, the best explanation is from "See How it Flies", an online book about airplane physics. Here's the crucial part, which gets into circulation and vortexes (OK, "vortices") as not just byproducts of airplane lift, but an indispensable aspect of it. I highly recommend following the author's suggestion to explore how a curveball (or a tennis ball hit with backspin) uses circulation to move laterally through the air; you can demonstrate this using any ordinary business card:

Drop the card from shoulder height, with its long axis horizontal. As you release it, give it a little bit of backspin around the long axis. It will fly surprisingly well...
Jef Raskin, who started the Macintosh project within Apple, has a great page about what makes airplanes fly, which gets into curveball aerodynamics, upside-down flight, and the wing Albert Einstein designed for the Luftwaffe in WWI.
...the most common explanation of lift seen in elementary texts and popular articles today... is based on the Bernoulli effect, which correctly correlates the increased speed with which air moves over a surface and the lowered air pressure measured at that surface.

In fact, most airplane wings do have considerably more curvature on the top than the bottom, lending credence to this explanation. But, even as a child, I found that it presented me with a puzzle: how can a plane fly inverted (upside down). When I pressed my 6th grade science teacher on this question, he just got mad, denied that planes could fly inverted and tried to continue his lecture. I was very frustrated and argued until he said, "Shut up, Raskin!" I will relate what happened next later in this essay. A few years later I carried out a calculation according to a naive interpretation of the common explanation of how a wing works. Using data from a model airplane I found that the calculated lift was only 2% of that needed to fly the model.

Jef, you had me at pissing off your 6th grade science teacher!

So, why does the equal transit-time myth persist, to the detriment of the much simpler explanation of angle of attack? I think part of the explanation must be that it makes a good story; another part is that a full understanding of all the dynamics at play is quite out of reach of the typical grade school science teacher, at least in the know-nothing United States. Incidentally, the question of airplane lift makes for a good shibboleth for distinguishing between those who think through scientific questions from first principles, and those who just go by What they assume to be conventional wisdom. I'm not claiming I understood this before I encountered the dispute recently, but as soon as someone pointed out the problem of an airplane flying upside down, I realized my understanding was at least incomplete.

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