The Straw Man of "Equal Transit Time" (Lift Part 1)

Over the years, I've had the misfortune of hearing far too many arguments about where lift on a wing comes from. The whole debate has become something of a pet peeve of mine, because it's all nonsense. I can't stand listening to people try to present themselves as experts, and supporting the position by making false (and often outright ridiculous!) statements. Does this make me a negative person?

Some of the silliness out there includes things like:

1. "Equal Transit Time" is wrong, therefore Bernoulli is wrong,
2. "Equal Transit Time" is right,
3. Bernoulli is "just a theory" and has never been proven,
4. If Bernoulli were right, it wouldn't be possible to fly inverted, and
5. 80% of lift comes from Bernoulli, 20% comes from Newton.

For number 5, the numbers vary, but the wrongness is all the same. Is "wrongness" a word? According to spellchecker it is, but I'm not so sure...

The "Equal Transit Time" of points 1 and 2 is a fallacy that has (fortunately!) fallen into disrepute over the years. But it still gets set up as a straw-man to "disprove" Bernoulli. According to the equal-transit-time principle, the air particles that separate at the leading edge of the wing must meet up again at the trailing edge. So, because of the wing's curvature (the top surface is longer than the bottom surface), the over-top flow must travel faster than the under-bottom flow.

Unfortunately, there is no physical principle that requires air parcels to meet up again once they are separated. In fact, wind tunnel testing (among other methods available) can and has demonstrated conclusively that the equal-transit-time requirement is not met by a lift-producing airfoil—the over-top air travels significantly faster than the under-bottom flow and reaches the trailing edge first (see a useful NASA applet here).

Ok. So equal-transit-time is wrong. So far so good. But here's the problem: Several authors and educators have taken the position that since equal-transit-time is wrong, Bernoulli must also be wrong. The "reasoning" (and I use the term in the loosest possible way) is that equal-transit-time leads into Bernoulli by supplying a source of velocity difference, which is then converted into a pressure difference using Bernoulli (higher velocity over-top means lower pressure over-top). So if the source of the velocity difference is wrong, the pressure conversion must also be wrong. Right? Wrong!

The change in velocity and the change in pressure are two different phenomena that require two separate explanations. There is in fact a velocity difference above and below a wing. And that velocity difference does in fact result in a pressure difference a-la Daniel Bernoulli. It's just that the velocity difference is not explained by the equal-transit-time concept—instead, it must be explained by the principle of continuity, or circulation (which, in turn, is rooted in continuity anyway).

More on Mr. Bernoulli and Sir Isaac in my next post. And for those of you who insist on discussing Circulation, don't fret! I haven't forgotten you!

Happy Flying!