Why Are Wings Swept?

If you’re historically inclined, you may be interested to know that the first swept-wing airplane appeared in 1907. It was built by J. W. Dunne, a gifted Irishman who also had some interesting ideas about the nature of Time. It had the distinction of being stable in all axes — uncapsizeable, in the boat-influenced language of the era. Wing sweep played a part in its stability; it provided a powerful dihedral effect, tending to roll the airplane out of a sideslip and consequently to keep it right side up without pilot attention, like a model glider.

Like many aspects of wing shape that designers tried out during the first two or three decades of powered flight, marked sweep — the Dunne biplanes had about 30 degrees — was eventually discarded. By World War II, the “ideal” wing shape was straight, moderately tapered, with an aspect ratio of between five and nine, and rounded tips.

At the end of the war, Operation Paperclip, a massive paper chase through abandoned laboratories that was intended to harvest Germany’s technical and scientific secrets, uncovered documents regarding the application of wing sweep to high-speed aircraft. The information arrived just in time to allow American companies like North American and Boeing to scrap conventional wings and adopt swept ones for airplanes like the F-86 Sabre and the B-47 Stratojet. The swept wing proved manifestly superior for airplanes flying faster than about 70 percent of the speed of sound.

Revolutions often turn out to have been annouced a decade or two in advance by people or events that were promptly forgotten; hence the expression “before his time.” Wing sweep had been proposed in 1935 at an aeronautics conference in Rome by Adolph Busemann, a brilliant character who pops up here and there, Zelig-like, in the history of aerodynamics before settling down as a professor at the University of Colorado at Boulder, where he died in 1986. It was a remark of Busemann’s, too, in 1951 that led Richard Whitcomb, one of NASA’s most productive thinkers, to the idea of the “transonic area rule,” which has been a staple of aerodynamics ever since.

Since the postwar period, we have come to associate swept wings with fast airplanes. They just look right — as though they were being pulled backward by the sheer force of the wind. Through magical thinking, marketing departments have found in swept vertical tails a solution to the problem of making slow airplanes appear fast.

The real function of wing sweep is somewhat more complex — a bit mystifying, perhaps, but not magical.

Below around 400 knots, the drag of a typical clean airplane increases in the expected way, as a function of speed alone. As speed continues to increase, however, shock waves begin to form, notably on wings and canopies. Shock waves are sudden discontinuities in the temperature and pressure of air, and they behave somewhat like large spoilers, greatly increasing the size of the airplane’s disturbed wake. The result is an extremely rapid increase in drag. The speed at which shock waves begin to appear is called the “critical Mach number.” It is not an absolute barrier to further acceleration, but no airplane of the immediate postwar period — engine power was still quite limited — could achieve a top speed much higher than its critical Mach number, because the drag increase was as steep as a cliff.

Efforts to “break the sound barrier” emphasized wing design, because the wing generated the most extensive shock waves. The first airplane to do the trick, the Bell X-1, had a wing that was, for the time, unusually thin. Its thinness delayed the formation of shocks and the consequent drag rise. An airfoil whose thickness is one-sixth of its chord might have a critical Mach number of .72, while the same profile, but with a thickness one-tenth of the chord, would have a critical Mach number of .8.

There are practical limits to how thin wings can be — structural strength and stiffness, fuel capacity and space for internal machinery like retracted landing gear are among the competing considerations — and the German data suggested an alternative to an abnormally thin wing: a wing of normal thickness moving obliquely through the air.

One’s intuitive sense of why this works is that since air is flowing diagonally across the wing, it travels a longer distance from the leading to the trailing edge; so in effect the wing has become thinner and its critical Mach number higher. But this is not in fact the most important effect of sweep, as is apparent from the fact that the speed gains made possible by sweep are much larger than the apparent reduction in section thickness would provide.

Photo: Cessna Aircraft Company The actual point of sweep is somewhat harder to grasp, and it sounds like a sophistry. The reasoning is that the critical Mach number of the wing, before it is swept, is purely a function of its airfoil section — that is, the shape of a cross-section of the wing along a chord line. Now, when you sweep the wing the chord line is no longer parallel to the direction of flight, and so the velocity along the chord line is no longer the same as it was — it is less. To find it, you represent the velocity of the air as two components, in the same way that in ground school you decompose a ground track into airspeed and wind drift. One component is parallel to the wingspan and is ignored, since its chordwise velocity is zero and it has no effect on shock formation. The other component is parallel to the chord, and its size depends on the sweep angle. A sweep angle of 37 degrees produces a chordwise flow that has 80 percent of the free-stream speed; at 45 degrees of sweep, it’s 71 percent.

Let’s look at a practical example. A hypothetical business jet has a wing of 12 percent thickness ratio — its thickness is 12 percent of its chord. The critical Mach number of its airfoil is Mach .8. The designer wants the plane to go faster than that, however, and so he sweeps the wing 35 degrees. The chordwise velocity component is reduced by 18 percent, so that, so far as shock formation is concerned, the wing section now thinks it is flying at Mach .66. If the airplane, which we assume has ample power, continues to accelerate, it would have to gain nearly 130 knots before the wing section would reach its critical Mach number of .80. (Note that the apparent thickness ratio of the swept wing is 10 percent; but its critical Mach number, based on thickness alone, would rise only to .82 — a gain seven times smaller than that due to sweep .)

This reasoning is much over-simplified. Merely sweeping the wing does not add 130 knots to the airplane’s speed — if only! For one thing, fuselage drag is also important, and there is no similarly magical way to reduce the shock-formation propensities of the fuselage. Furthermore, skin friction is a large component of drag, and it continues to increase in proportion to the square of the indicated airspeed. In fact, all that sweep does is push the critical Mach number to a point where speed is limited not by shock waves on the wing but by the same things that limit it on purely subsonic airplanes: skin friction and flow separation. In other words, it moves the cliff.

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