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Area rule
The Whitcomb area rule, named after a US National Advisory Committee for Aeronautics (NACA) engineer Richard Whitcomb and also called the transonic area rule, is a design procedure used to reduce an aircraft's drag at transonic speeds which occur between about Mach 0.75 and 1.2. For supersonic speeds a different procedure called the supersonic area rule, developed by NACA aerodynamicist Robert Jones, is used.
Transonic is one of the most important speed ranges for commercial and military fixed-wing aircraft today, with transonic acceleration an important performance requirement for combat aircraft and which is improved by reductions in transonic drag.
At high-subsonic flight speeds, the local speed of the airflow can reach the speed of sound where the flow accelerates around the aircraft body and wings. The speed at which this development occurs varies from aircraft to aircraft and is known as the critical Mach number. The resulting shock waves formed at these zones of sonic flow cause a sudden increase in drag, called wave drag. To reduce the number and strength of these shock waves, an aerodynamic shape should change in cross sectional area as smoothly as possible from front to rear.
The area rule says that two airplanes with the same longitudinal cross-sectional area distribution have the same wave drag, independent of how the area is distributed laterally (i.e. in the fuselage or in the wing). Furthermore, to avoid the formation of strong shock waves the external shape of the aircraft has to be carefully arranged so that the cross-sectional area changes as smoothly as possible going from nose to tail. At the location of the wing, the fuselage is narrowed or "waisted". Fuselage cross-sectional area may need to be reduced by flattening the sides of the fuselage below a bubble canopy and at the tail surfaces to compensate for their presence, both of which were done on the Hawker Siddeley Buccaneer.
A different area rule, known as the supersonic area rule, developed by NACA aerodynamicist Robert Jones in "Theory of wing-body drag at supersonic speeds", is applicable at speeds beyond transonic, and in this case, the cross-sectional area requirement is established with relation to the angle of the Mach cone for the design speed. For example, consider that at Mach 1.3 the angle of the Mach cone generated by the nose of the aircraft will be at an angle μ = arcsin(1/M) = 50.3° (where μ is the angle of the Mach cone, also known as Mach angle, and M is the Mach number). In this case the "perfect shape" is biased rearward; therefore, aircraft designed for lower wave drag at supersonic speed usually have wings towards the rear.
A superficially related concept is the Sears–Haack body, the shape of which allows minimum wave drag for a given length and a given volume. However, the Sears–Haack body shape is derived starting with the Prandtl–Glauert equation which approximately governs small-disturbance subsonic flows, as well as Ackeret Theory, which closely describes supersonic flow. Both methods lose validity for transonic flows where the area rule applies, due to assumptions made in their derivations. So although the Sears–Haack body shape, being smooth, will have favorable wave drag properties according to the area rule, it is not theoretically optimum.
The area rule was discovered by Otto Frenzl when comparing a swept wing with a w-wing with extreme high wave drag while working on a transonic wind tunnel at Junkers works in Germany between 1943 and 1945. He wrote a description on 17 December 1943, with the title Anordnung von Verdrängungskörpern beim Hochgeschwindigkeitsflug ("Arrangement of Displacement Bodies in High-Speed Flight"); this was used in a patent filed in 1944. The results of this research were presented to a wide circle in March 1944 by Theodor Zobel at the Deutsche Akademie der Luftfahrtforschung (German Academy of Aeronautics Research) in the lecture "Fundamentally new ways to increase performance of high speed aircraft."
Subsequent German wartime aircraft design took account of the discovery, evident in slim mid-fuselage of aircraft including the Messerschmitt P.1112, P.1106 and Focke-Wulf 1000x1000x1000 type A long-range bomber, but also apparent in delta wing designs including the Henschel Hs 135. 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 theory by studying airflow, notably the interference, or local flow streamlines, at the junction between a fuselage and swept wing. The fuselage was contoured, or waisted, to match the flow. The shaping requirement of this "near field" approach would also result from Whitcomb's later "far field" approach to drag reduction using his Sonic area rule.
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Area rule
The Whitcomb area rule, named after a US National Advisory Committee for Aeronautics (NACA) engineer Richard Whitcomb and also called the transonic area rule, is a design procedure used to reduce an aircraft's drag at transonic speeds which occur between about Mach 0.75 and 1.2. For supersonic speeds a different procedure called the supersonic area rule, developed by NACA aerodynamicist Robert Jones, is used.
Transonic is one of the most important speed ranges for commercial and military fixed-wing aircraft today, with transonic acceleration an important performance requirement for combat aircraft and which is improved by reductions in transonic drag.
At high-subsonic flight speeds, the local speed of the airflow can reach the speed of sound where the flow accelerates around the aircraft body and wings. The speed at which this development occurs varies from aircraft to aircraft and is known as the critical Mach number. The resulting shock waves formed at these zones of sonic flow cause a sudden increase in drag, called wave drag. To reduce the number and strength of these shock waves, an aerodynamic shape should change in cross sectional area as smoothly as possible from front to rear.
The area rule says that two airplanes with the same longitudinal cross-sectional area distribution have the same wave drag, independent of how the area is distributed laterally (i.e. in the fuselage or in the wing). Furthermore, to avoid the formation of strong shock waves the external shape of the aircraft has to be carefully arranged so that the cross-sectional area changes as smoothly as possible going from nose to tail. At the location of the wing, the fuselage is narrowed or "waisted". Fuselage cross-sectional area may need to be reduced by flattening the sides of the fuselage below a bubble canopy and at the tail surfaces to compensate for their presence, both of which were done on the Hawker Siddeley Buccaneer.
A different area rule, known as the supersonic area rule, developed by NACA aerodynamicist Robert Jones in "Theory of wing-body drag at supersonic speeds", is applicable at speeds beyond transonic, and in this case, the cross-sectional area requirement is established with relation to the angle of the Mach cone for the design speed. For example, consider that at Mach 1.3 the angle of the Mach cone generated by the nose of the aircraft will be at an angle μ = arcsin(1/M) = 50.3° (where μ is the angle of the Mach cone, also known as Mach angle, and M is the Mach number). In this case the "perfect shape" is biased rearward; therefore, aircraft designed for lower wave drag at supersonic speed usually have wings towards the rear.
A superficially related concept is the Sears–Haack body, the shape of which allows minimum wave drag for a given length and a given volume. However, the Sears–Haack body shape is derived starting with the Prandtl–Glauert equation which approximately governs small-disturbance subsonic flows, as well as Ackeret Theory, which closely describes supersonic flow. Both methods lose validity for transonic flows where the area rule applies, due to assumptions made in their derivations. So although the Sears–Haack body shape, being smooth, will have favorable wave drag properties according to the area rule, it is not theoretically optimum.
The area rule was discovered by Otto Frenzl when comparing a swept wing with a w-wing with extreme high wave drag while working on a transonic wind tunnel at Junkers works in Germany between 1943 and 1945. He wrote a description on 17 December 1943, with the title Anordnung von Verdrängungskörpern beim Hochgeschwindigkeitsflug ("Arrangement of Displacement Bodies in High-Speed Flight"); this was used in a patent filed in 1944. The results of this research were presented to a wide circle in March 1944 by Theodor Zobel at the Deutsche Akademie der Luftfahrtforschung (German Academy of Aeronautics Research) in the lecture "Fundamentally new ways to increase performance of high speed aircraft."
Subsequent German wartime aircraft design took account of the discovery, evident in slim mid-fuselage of aircraft including the Messerschmitt P.1112, P.1106 and Focke-Wulf 1000x1000x1000 type A long-range bomber, but also apparent in delta wing designs including the Henschel Hs 135. 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 theory by studying airflow, notably the interference, or local flow streamlines, at the junction between a fuselage and swept wing. The fuselage was contoured, or waisted, to match the flow. The shaping requirement of this "near field" approach would also result from Whitcomb's later "far field" approach to drag reduction using his Sonic area rule.