Peter Garrison
An explanation is a collage in which bits and pieces of the familiar combine to make an image of the unfamiliar. The more obscure the thing being explained, the more numerous and remote the elements that comprise the explanation. It’s a wonder we understand anything at all.
I suppose that Gale Craig, a retired General Motors researcher and engineer, wrote his little book with the indignant title “Stop Abusing Bernoulli!” in the hope that he might, once and for all, dispose of the perennial question, “How do wings produce lift?” If so, he failed, not because of any fault in his own argument, but because the mechanisms involved are sufficiently obscure and remote from everyday experience to defy simple explanation.
All that a pilot really needs to know about lift can be learned by sticking a hand out the window of a moving car. Clambering up to the next level of insight – the one to which Craig hopes to guide us – requires an agility most of us lack, and climbing shoes that we have worn out or lost.
The customary explanation for the production of lift, which Craig contemptuously dubs “hump theory”, has air moving a longer distance over the top of an aerofoil than over the bottom, because of the aerofoil’s camber. Since it is assumed, without evidence, that neighbouring bits of air that part company at the leading edge must, like star-crossed lovers, be reunited at the trailing edge, air passing over the wing’s upper surface must move faster than that passing below the wing.
At this point Daniel Bernoulli (Swiss mathematician and physicist, 1700-1782) is brought in as an expert witness. It was he who first derived, from first principles, the conclusion that as flow through a duct accelerates, pressure within the duct must diminish in proportion to the square of the flow velocity. Applying this principle to wings, the pressure on the upper surface must be less than that on the lower. Ergo, the wing lifts.
In every ground school class, however, there is one pest who raises a hand to inquire how aeroplanes manage to fly upside down, or how aeroplanes with uncambered wings (like many competition acrobatic aeroplanes) or with perfectly flat wings (like paper or balsa gliders) manage to fly at all.
More inventive sceptics might ask why making the upper surface of the wing wavy would not further increase the transit distance, and therefore the flow velocity and the lift. And die-hard agnostics will wonder who it was, exactly, who decreed that the particles of air that pass over the top of the wing have to arrive at the trailing edge at the same time as those that go underneath. (Actually, they don’t – they get there sooner.)
Makeshift answers to all these questions can be concocted, but the truth is that the patented, FAA-approved Bernoulli explanation is just no good. It’s not false – pressure and velocity really are related in the way Bernoulli described, and the variations can be precisely measured on the surface of a wing – but, as Wolfgang Langewiesche put it in his 1944 classic Stick and Rudder, “the explanation is more puzzling than the puzzle!”
Although Craig is not alone in having pointed out the inadequacy of the Bernoulli explanation of lift, it continues to be offered to high school students, would-be pilots, and lay readers aspiring to understand physics. Worse, it is the orthodoxy espoused by the FAA, and so in order to get certain test questions right you have to parrot the Bernoulli explanation. Ironically, Daniel Bernoulli himself would undoubtedly object to his pressure-velocity relation being passed off as the “cause” of wing lift; but dust has stopp’d his mouth.
For the more scientifically sophisticated among his readers, Craig also takes on what he calls the “induction” theory of lift. This is also known as the “circulation” theory, and it is less an explanation than a mathematical convenience. Craig criticises the induction theory as resting upon a useful but incomplete analogy between fluid dynamics and certain electromagnetic phenomena; like “hump theory,” he says, induction theory fails to account for several commonly observed phenomena.
If Craig had his way, we would explain lift by purely Newtonian principles of action and reaction. The lift is the equal and opposite reaction to the force exerted by the wing to accelerate air downward. This is what you experience when you fly your hand out the car window, and it is what we intuitively sense is happening when a plane surface moves through air at a slight positive angle.
If lift could be adequately accounted for by Newtonian principles, however, one would have to wonder why Newton himself could not correctly predict the lift of a flat plate. He tried to, and came up with a formula that grossly underestimated lift and, some say, retarded, by its pessimism and his own godlike authority, the attainment of manned flight. Actually, it’s doubtful that Newton’s sine-squared law had any such effect, since aeronautical experimenters have tended to be practical rather than theoretical sorts, and the fallacy of Newton’s conclusion can be readily demonstrated by the simple experiment of going out on a windy day with an umbrella.
Newton got it wrong, Craig says, because he failed to take into account several different factors that enter into the production of lift. One of these is “flow attachment.” Without this tendency of fluids to follow surfaces over which they are flowing, air might simply peel away from the leading edges of wings, lift would be reduced to the magnitudes predicted by Newton, and we would still be taking the train.
Unfortunately, after disposing of hump theory and induction theory, Craig finds that his own account, which he styles “recirculation theory,” is actually quite complicated. It involves a good many separate phenomena, and by the time he has finished explaining it, one is left reflecting that the virtue of hump theory, whatever its faults, is that it can at least be stated in a single sentence.
Having begun this article with a lecture on explanation, I would like to end it in the same way – this being a common writer’s trick to neatly tie up a package of loosely related ramblings.
We frequently overlook the fact that our understanding of things goes only to a certain point, and that by tacit agreement we do not look any further. For example, all discussions of lift, including Craig’s, contain mention of the word “pressure.” We all know what pressure means, because we have exerted pressure on things and had it exerted on our own skin. If we have read popular scientific texts we know that the pressure of air arises from the impacts of air molecules on a surface in the course of their random flights (which, by the way, occur, on average, at the speed of sound). The surface of a wing is also a network of molecules, but unlike those of a fluid they are held in place, vibrating but not, by and large, escaping. But what is a surface, really, and what are these molecules? They aren’t baseballs. They are strange, almost immaterial things.
If we could shrink ourselves to atomic dimensions (while acquiring a suitable new sensory apparatus), we would find a very unfamiliar world indeed.
For one thing, it would be largely empty. An atom is to an apple as an apple is to the Earth. Atoms themselves, however, are not closely-packed solids. They consist of a tiny nucleus whose radius is only one ten-thousandth of that of the weird, indescribable, but decidedly un-matter-like electron cloud surrounding it. In this world, mass is unrelated to size. Matter is mostly empty space, like the universe itself, and so the collisions that produce pressure are really advances and retreats of fields of force, similar to magnetic or gravitational fields.
An aeroplane is “really” a cloud of forces barely differentiable from the surrounding electromagnetic haze. In this alien world, which is arguably the most “real” world we can try to imagine, our common ideas of weight, pressure, solidity and flow mean nothing, and the terms we use to “explain” phenomena like lift turn out to be just as mystifying and incomprehensible as the things themselves.
And that is why, when it comes to understanding lift, feeling your hand respond to the wind can be just as good as reading a book.