Area rule

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Junkers patent drawing from March 1944.

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

NASA Convair 990 with antishock bodies on the rear of the wings.

Oilflow visualization of flow separation without and with antishock bodies.

This F-5E Tiger II, the Shaped Sonic Boom Demonstraton, was modified by NASA applying the area rule at the fuselage below the wing to decrease the shock by the wings and produce negative lift. Note that the wings still produce a shock due to compression lift, so the nose-cone is widened to produce an even stronger shock, which therefor travels faster.

To generate lift a supersonic airplane has to produce at least two shock waves: One over-pressure downwards wave, and one under-pressure upwards wave. Whitcomb’s area rule states that air displacement can be reused without generating additional shock waves. In this case the fuselage reuses some displacement of the wings.

The Whitcomb area rule (sometimes just called the area rule) is a design technique used to reduce an aircraft's drag at transonic and supersonic speeds, particularly between 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 Bernoulli's principle. The speed at which this occurs varies from aircraft to aircraft, and is known as critical mach. The resulting shock waves formed at these points of supersonic flow bleed away a considerable amount of power, which is experienced by 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 aircraft's shape should change in cross-sectional area as smoothly as possible. The design implications for standard "tube and wing" aircraft are that the body narrows beside the wings. This leads to a "perfect" aerodynamic shape known as the Sears-Haack body, roughly shaped like a cigar but pointed at both ends.

The area rule was first discovered by a team including Heinrich Hertel and Otto Frenzl working on a transonic wind tunnel at Junkers works in Germany between 1943 and 1945; it is used in a patent filed in 1944. The design concept was applied to a variety of German wartime aircraft, including a rather odd Messerschmitt project, but their complex double-boom design was never built even to the extent of a model. Several other researchers came close to developing a similar theory, notably Dietrich Küchemann who designed a tapered fighter that was dubbed the Küchemann Coke Bottle when it was discovered by US forces in 1946. In this case Küchemann arrived at the solution by studying airflow, notably spanwise flow, over a swept wing.

Richard T. Whitcomb, after whom the rule is named, independently discovered this rule in 1952, while working at NACA. While using the new Eight-Foot High-Speed Tunnel, a wind tunnel with performance up to Mach 0.95 at NACA's Langley Research Center, he was surprised by the increase in drag due to shock wave formation. The shocks could be seen using Schlieren photography, but the reason they were being created at speeds far below the speed of sound, sometimes as low as Mach 0.70, remained something of a mystery.

In late 1951 the lab hosted a talk by Adolf Busemann, a world-famous German aerodynamicist who had moved to Langley after World War II. He talked about the difference in the behaviour of airflow at speeds approaching the supersonic, where it no longer behaved as an incompressible fluid. Whereas engineers were used to thinking of air flowing smoothly around the body of the aircraft, at high speeds it simply didn't have time to "get out of the way", and instead started to flow as if it were rigid pipes of flow, a concept Busemann referred to as "streampipes", as opposed to streamlines, and jokingly suggested that engineers had to consider themselves "pipefitters".

Several days later Whitcomb had a "Eureka" moment. The reason for the high drag was that the "pipes" of air were interfering with each other in three dimensions. You could not simply consider the air flowing over a 2D cross-section of the aircraft as you could in the past; now you also had to consider the air to the "sides" of the aircraft which would also interact with these streampipes. Whitcomb realized that the Sears-Haack shaping had to apply to the aircraft as a whole, rather than just the fuselage. 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 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.

Numerous designs of the era were likewise modified in this fashion, either by adding new fuel tanks or tail extensions to smooth out the profile. The Tupolev Tu-95 'Bear', 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 0.89 Mach. 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 be 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.

One interesting outcome of the area rule is the current shaping of the Boeing 747's upper deck. The aircraft was originally designed to carry standard cargo containers in a two-wide, two-high stack on the main deck, which was considered a serious accident risk for the pilots if they were located in a cockpit at the front of the aircraft. They were instead moved above the deck in a small "pod", which was deliberately designed to be as small as possible given normal streamlining principles. It was later realized that the drag could be reduced much more by lengthening the pod, using it to reduce wave drag offsetting the tail surface's contribution. The new design was introduced on the 747-300, improving its cruise speed and lowering drag.

Aircraft designed according to Whitcomb's area rule looked odd at the time they were first tested, (e.g. the Blackburn Buccaneer), and were dubbed "flying Coke bottles," but the area rule is 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" can only be seen on the B-1B Lancer and the Tupolev Tu-160 'Blackjack' — the same effect is now achieved by careful positioning of aircraft components, like the boosters and cargo bay of rockets, the jet engines in front (and not below) the wings of a Airbus A380, the jet engines behind (and not purely at the side) the fuselage of a Cessna Citation X , the canopy of the F-22 Raptor, and this image 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. Aftershock bodies are likewise "invisible" today, serving double duty as flap actuators, which also visible in the A380 image above.