Whitcomb area rule

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The F-106 Delta Dart, a development of the F-102, clearly shows the "wasp-waisted" shaping due to area rule considerations.
The F-106 Delta Dart, a development of the F-102, clearly shows the "wasp-waisted" shaping due to area rule considerations.

The Whitcomb area rule (sometimes just called the area rule) is a design technique used to reduce an aircraft's drag at transonic speeds, speeds between about Mach 0.8 and 1.2. This is the operating speed range of the vast majority of all commercial and military fixed-wing aircraft today.

Even at high subsonic speeds, local supersonic flow can develop in areas where the flow accelerates around the aircraft body and wings due to the Bernoulli effect. The resulting shock waves formed at these points of supersonic flow radiate away a considerable amount of power, which is seen to the aircraft as a sudden and very powerful form of drag, called wave drag.

In order to reduce the number and power of these shock waves, the body should change in shape as slowly as possible. That is, the cross section of the body should get larger or smaller in a smooth manner. This leads to a "perfect" aerodynamic shape known as the Sears-Haack body, roughly shaped like a cigar but pointed at both ends.

Richard Whitcomb, after an extensive series of wind tunnel tests at NASA's (then still NACA) Langley Research Center, realized that the Sears-Haack shaping had to apply to the aircraft as a whole, as opposed to the fuselage itself. That meant that the extra cross sectional area of the wings and tail had to be accounted for in the overall shaping, and that the fuselage should actually be narrowed where they meet to more closely match the ideal.

The area rule was immediately applied to a number of current development efforts. One of the most famous was Whitcomb's personal work on the re-design of the F-102 Delta Dagger, which was demonstrating performance considerably worse than expected. By indenting the fuselage beside the wings, and (paradoxically) adding more volume to the rear of the plane, transonic drag was considerably reduced and the original Mach 1.2 design speeds were reached.

Missing image
Antishock body on the trailing edge of a Convair 990 wing.

Numerous designs of the era were likewise modified in this fashion, or by adding new fuel tanks or tail extensions to smooth out the profile. The Tupolev Tu-95, a Soviet-era bomber, was modified by adding large bulged nacelles behind its four engines, instead of decreasing the cross section of the fuselage next to the wing root. It remains the highest speed propeller aircraft in the world. The Convair 990 used a similar solution, adding bumps called antishock bodies to the trailing edge of the upper wing. The 990 remains the fastest US airliner in history, cruising at up to Mach 0.89, beating even much newer designs like the Boeing 747. Designers at Armstrong-Whitworth took the concept a step further in their proposed M-Wing, in which the wing was first swept forward and then to the rear. This allowed the fuselage to narrowed on either side of the root instead of just behind it, leading to a smoother fuselage that remained wider on average than one using a classic swept wing.

Missing image
Oilflow visualization of flow separation without and with antishock bodies.

Aircraft designed according to Whitcomb's area rule looked odd at the time they were first tested, and were dubbed "flying Coke bottles," but the area rule is indubitably effective and came to be an expected part of the appearance of any transonic vehicle. Later designs started with the area rule in mind, and came to look much more pleasing. Although the rule still applies, the visible fuselage "waisting" is no longer common — the same effect is now achieved by careful positioning of aircraft components. For instance, this image (http://news.bbc.co.uk/1/shared/spl/hi/pop_ups/05/business_a380_makes_air_show_debut/html/3.stm) of the Airbus A380 in flight shows obvious area rule shaping at the wing root, but these modifications are practically invisible from any other angle.

Although it was not publicized at the time, it was later re-discovered that a German WWII design, the Küchemann Coke Bottle included a fuselage shaping basically identical to the area rule. In this case Dietrich Küchemann arrived at the solution by studying airflow, notably spanwise flow, over a swept wing. It is unclear if the dramatic drag reduction was known to him at the time, but even he later commented (now working at the British RAE at Farnborough) that Whitcomb's statement of the problem, and solution, was considerably more clear and decisive than his own. A Messerschmitt project using the area rule appears to have been designed specifically with drag reduction in mind, but their complex double-boom design was never built even to the extent of a model.

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