Technicalities: Rules to Fly By

The story of the transonic area rule involves one of those "eureka moments" that we have learned to admire in all great tales of invention and discovery. It happened at the Langley, Virginia, headquarters of the National Advisory Committee for Aeronautics, which would become NASA a few years later. Whitcomb had been ruminating about the rapid increase in drag that airplanes experienced as they approached the speed of sound. He possessed uncommon insight into the behavior of air, a gift that must have been in part a happy congenital mixture of spatial visualization and kinesthetic empathy and in part acquired, as can people who, like Leonardo da Vinci, for some reason or other find rivers and streams, blowing leaves, smoke and clouds worthy of special attention. But a good instinct for subsonic aerodynamics does not serve at supersonic speeds. The supersonic domain, in the phrase a British novelist used about the past, "is a foreign country; they do things differently there."

The legacy of subsonic thinking was that each part of an airplane is responsible for its own drag; you could figure out the contributions of wings, tail, fuselage, antennas and so on separately and then add them up, throwing in a few percent extra for "interference effects." In other words, the details mattered because, after all, each little "packet" of air followed its own path over the surface of the airplane and didn't know what was going on far away. This was such an intuitively obvious proposition that it evidently went unquestioned, at least in the United States, until that day when the burrowing gnomes of Whitcombian thought fortuitously met in mid-mountain.

I say "in the United States" because it appears that the area rule was not really born in 1951 in the brain of Richard Whitcomb, but in Germany during the mid-1940s. Like so many of the insights of German aeronautical engineers working for Hitler — swept and delta wings, for example — this one didn't bear much fruit before the war ended. Its originator, an Austrian-born wind tunnel designer named Otto Frenzl, obtained a 1944 patent on the Flächenregel or "bottle rule," and the theory was presented to a meeting of the German Academy of Flight Research in March of that year. It is difficult to imagine that Adolf Busemann, a German aerodynamicist who came to Langley after the war and who influenced Whitcomb, was not aware of it, and puzzling that it is Whitcomb, and not Busemann or Frenzl, whom we associate with the area rule today.

A familiar staple of transonic theory was the Sears-Haack body, a sort of elongated football characterized by a certain smooth variation of cross-sectional area from one end to the other. This was the shape that generated the least shock-wave resistance, and it was well understood that the reason was the smoothly varying distribution of its volume. What Whitcomb grasped was that the energy lost to shock-wave generation by a supersonic body — the so-called wave drag, which was responsible for the rapid increase in resistance as an airplane approached the "sound barrier" — was a function not of the shapes of individual components but of the volume distribution of the whole.

He conducted a series of wind tunnel tests to confirm this idea, and then presented a modest paper in which he demonstrated that the wave drag of a body with a wing is the same as that of a round wingless body with a midriff bulge whose volume distribution is identical to that of the original wing and body together. Only in the final pages of his paper did Whitcomb toss off his punch line: By locally reducing the diameter of the fuselage, the effects of excrescences such as wings, canopies and engine nacelles could be nullified and an airplane could be made to behave, so far as shock wave formation was concerned, like an ideal Sears-Haack body.

The potential for drag reduction was enormous. In a stroke of career luck for Whitcomb, it happened that, just as he was publishing his idea, Convair was putting the finishing touches on a delta-wing fighter, the F-102, that was supposed to go supersonic in level flight. Because of the unfavorable volume distribution of its barrel-shaped body and delta wing, however, it didn't. Convair, after running out of excuses for keeping the F-102 as it was, invested in a new fuselage with a pinched waist — the so-called "Coke bottle" shape. The F-102A exceeded Mach 1 while climbing.

Area ruling was very important during the 1950s, because engines were just barely able to push airplanes past the transonic drag rise. As engines became more powerful (and supersonic speeds proved to be of little military importance), the conspicuous area ruling visible in Vietnam-era airplanes ceased. It continues to be found, however, in features intended to smooth the volume distribution of airliners and business jets. If material cannot be taken away in the vicinity of, say, a wing, bulges can be added ahead and behind; it's not the total volume that matters so much as the smoothness of its distribution from nose to tail. Long wing-fuselage fairings, the 747's hump, fat flap-track enclosures — these are all manifestations of area ruling, which today is part of every jet designer's tool kit.

The late John Thorp described his decidedly subsonic T-18 homebuilt as embodying a "poor man's area rule," which is not an official rule formulated in mathematical terms, like the Whitcomb area rule, but more of a rough guide for designers. The idea is that you stagger the parts of an airplane so that, for example, the canopy reaches its maximum height before the wing leading edge; the fuselage reaches its maximum width around the trailing edge of the wing; and so on. When items are alongside one another, like a pod on a pylon below a wing, you shape them so that they do not form a narrowing channel.

In subsonic flow, bodies close to one another make more drag than they would separately. The extra resistance, called interference drag, is due to two causes. One is that flow that is pushed aside by a bulging body accelerates, increasing its frictional drag on nearby surfaces. For example, the front upper surface of a low wing, where flow accelerates considerably, causes added "scrubbing drag" on the adjacent fuselage side. The other is that when the pinched, accelerated flow slows down again, turbulence and separation can occur if the deceleration is not sufficiently gradual. Thus, wing-root fairings are usually needed where a fuselage and a wing taper away from one another, as is often the case on low-wing airplanes with rounded fuselages. (That is why the Bonanza has a square bottom.) By the same token, the intersection of a T or cruciform tail almost always requires a "bullet" fairing to prevent separation on the elevator or rudder. The fairing would not be needed if the surfaces were staggered, so that the thickest part of one coincided with the leading or trailing edge of the other; but that arrangement is seldom seen, because it is structurally inconvenient.

On some airplanes we see both the transonic and the poor man's area rules at work. The Mach .92 Citation X is an example. The deep pinching of the fuselage beside the engine nacelles both maintains overall transonic area ruling and also provides a constant-width channel for air to pass through without accelerating. The big fairing between the fin and horizontal tail effectively separates them from one another's influence.

The Whitcomb and the poor man's area rules approach airplanes quite differently. One ignores detail and subjects all the parts of an airplane together to the single criterion of volume distribution. The other catalogs components separately and examines how flow conditions created by each one affect all the others. The Whitcomb rule applies only to the wave drag that appears when flow over parts of an airplane reaches sonic speed, typically at Mach .8 or above. The poor man's rule, on the other hand, applies to all airplanes, because all, at some time or other, need to operate efficiently at subsonic speed.