Area rule

Lore & Background

The area rule was discovered by Otto Frenzl at Junkers works in Germany between 1943 and 1945, who wrote a description on 17 December 1943 titled 'Arrangement of Displacement Bodies in High-Speed Flight'. This was presented in March 1944 by Theodor Zobel at the Deutsche Akademie der Luftfahrtforschung. Subsequent German wartime designs, such as the Messerschmitt P.1112 and Henschel Hs 135, took account of the discovery. Dietrich Küchemann also arrived at a similar theory by studying airflow at the junction between a fuselage and swept wing, leading to the 'Küchemann Coke Bottle' shape.

In the United States, Wallace D. Hayes developed the transonic area rule in publications beginning in 1947. Richard T. Whitcomb independently discovered the rule in 1952 while working at NACA's Langley Research Center, after a talk by Adolf Busemann about 'streampipes' of airflow. Whitcomb realized that the shaping had to apply to the aircraft as a whole, meaning the fuselage should be narrowed where wings and tail meet to match an ideal cross-sectional area distribution.

The area rule states that two airplanes with the same longitudinal cross-sectional area distribution have the same wave drag, independent of lateral distribution. To avoid strong shock waves, the external shape must change cross-sectional area as smoothly as possible from nose to tail. At the location of the wing, the fuselage is narrowed or 'waisted'. This was done on the Hawker Siddeley Buccaneer by flattening the fuselage sides below a bubble canopy and at the tail surfaces.

Reader's Guide

The area rule's significance lies in its ability to reduce wave drag at transonic speeds, which is critical for both commercial and military fixed-wing aircraft. The rule was made available to the US aircraft industry on a secret basis for military programs from 1952 and was reported in 1957 for civilian programs. Convair and Grumman used it concurrently to design the Grumman F-11 Tiger and to redesign the Convair F-102. The F-102 had been unable to reach Mach 1 despite a design speed of Mach 1.2, but modifications including indenting the fuselage beside the wings and adding volume to the rear reduced transonic drag significantly, allowing the design speed to be reached. The rule was used on these fighters to reduce the peak drag at Mach 1, enabling supersonic speeds with less thrust. In 1957 a modified area rule was available for raising the subsonic cruise speed of transport aircraft by 50 mph (80 km/h). The Sears–Haack body, though superficially related, is not theoretically optimum for transonic flows where the area rule applies, as its derivation assumes small-disturbance subsonic or supersonic flows, not transonic.

Did You Know?

• The area rule was independently discovered by Richard Whitcomb in 1952 after a talk by Adolf Busemann about 'streampipes' of airflow.
• The first aircraft to implement the area rule was the German bomber testbed Junkers Ju-287 in 1944.
• The Convair F-102 Delta Dagger had to be redesigned using the area rule because it could not reach Mach 1 despite a design speed of Mach 1.2.
• For supersonic speeds, a different procedure called the supersonic area rule was developed by NACA aerodynamicist Robert Jones.