Circulation is hinted at by a computer-
generated map of velocities imparted to the
surrounding
air by a passing wing.
You will never understand lift. Forget it. You haven’t got a chance.
So I muttered to myself as I closed a fascinating book called The Enigma of the Aerofoil. The author, David Bloor, is an emeritus professor of the University of Edinburgh whose field is the sociology of science: how cultural and personal factors shape the acquisition and use of scientific knowledge.
Bloor’s story, which unfolds like a genial Foyle’s War-style slow-motion whodunit from the BBC, concerns the efforts of scientists and mathematicians in the ivory towers of England and Germany between 1909 and 1930 to understand how wings produce lift. Their work went on parallel to, and largely insulated from, that of manufacturers and aeronautical engineers, who built tens of thousands of airplanes without worrying about why wings worked. They did — that was all that mattered.
The sense in which scientists understand something is not the sense in which you and I do. We know what it feels like to stick a hand out the window of a moving car, to sail a boat or to carry an umbrella on a windy day. These are direct, elemental experiences, familiar since childhood, and we have no difficulty extrapolating them to the wings of airplanes. We understand lift by empathy: We feel it.
But that is not the kind of understanding that exercised the giant brains of Cambridge and Göttingen. They were not Impressionists. To them, understanding wings meant finding the mathematical laws that govern them and that would allow accurate prediction of their behavior. These laws were elusive. Not that much of the grunt work hadn’t already been done: Mathematical descriptions of the behavior of frictionless “ideal fluids” under highly prescribed conditions had been developed in the 18th century by Leonhard Euler and our old pal Daniel Bernoulli. But real air is not a frictionless fluid; there, so to speak, is the rub.
The basic difference is that an ideal fluid lacks viscosity, and air has it. In viscosity-free air there would be no drag and no lift. Any force produced as the wing pushed the air aside would be exactly neutralized as the air sprang back into place. Obviously, this was not what was happening, since real wings produce real lift and real drag. Where were they coming from?
In Bloor’s narrative, the British and the Germans approached the riddle from different angles. It was not just a matter of national character, however. Rather, it was that the British brains who worked on the problem were pure mathematicians in the last degree, mostly drawn from among the highest-performing survivors of Cambridge University’s merciless tripos examinations, while the Germans came from their country’s system of technical upper schools, in which it was not considered uncouth to take an interest in practical aspects of a problem.
The great difficulty concerned something called circulation theory. This is an approach that emerges from the readily observed fact that an airfoil slows the air passing below it and accelerates the air above it. The difference in speed bends the airflow behind the airfoil, angling it slightly downward. This small downward (or backward, in the case of a propeller) movement of a large amount of air — because the rapidly moving wing influences thousands of cubic feet of air per second — produces the reaction that we call lift or, in the case of a propeller, thrust.
It was possible, if you made the right set of assumptions, to get the circulation model to predict real lift quite accurately. The trick was to think of the flow of air past an airfoil as a circular motion superimposed upon a horizontal one. This was mathematically convenient, because methods existed for computing rotary and straight-line flows, and they could be combined. It was actually an Englishman, a plebeian polymath named Frederick Lanchester, who originally proposed a circulation theory of lift in the 1890s and connected the circulation to the rotation of the tip vortices. In modern terms, Lanchester pretty much had it right. But the tripos set looked down its collective nose at him; after all, Lanchester had gone to a technical school.
