The Sears–Haack body is the aerodynamic body shape with the lowest theoretical wave drag. Aircraft designed to operate at high subsonic or supersonic speeds have their cross-sectional areas designed to match as closely as possible the proportions of Sears-Haack body.
By Whitcomb's area rule, the derivative of cross-sectional area gives wave drag. Thus, the Sears–Haack body is pointed at two ends and grows to a maximum and then decreases toward the second point.
Under the area rule, shapes with the same cross-sectional area at each point along their length as this shape have the minimal amount of wave drag, and the overall shape of many aircraft designed with transonic flight considerations have cross-sectional areas that approach this form (despite appearances).
The area rule was discovered by Otto Frenzl when comparing a swept wing with a w-wing with extreme high wave drag 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 “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 the slim mid-fuselage of aircraft such as the Messerschmitt Me P.1112, P.1106, and the indisputably wasp-waisted Focke-Wulf Fw 1000x3 type A long range bomber, but also apparent in delta wing designs like 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 U.S. forces in 1946. In this case Küchemann arrived at the solution by studying airflow, notably spanwise flow, over a swept wing. The swept wing is already an indirect application of the area rule.
The derivation and shape were published independently by two separate researchers: Wolfgang Haack in 1941 and later by William Sears in 1947.
Wallace D. Hayes, a pioneer of supersonic flight, developed the supersonic area rule in publications beginning in 1947 with his Ph.D. thesis at the California Institute of Technology.
Richard T. Whitcomb, after whom the rule is named, independently discovered this rule in 1952, while working at the 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 a mystery.
In late 1951, the lab hosted a talk by Adolf Busemann, a famous German aerodynamicist who had moved to Langley after World War II. He talked about the difference in the behavior of airflow at speeds approaching 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 did not 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. One could not simply consider the air flowing over a 2D cross-section of the aircraft as others could in the past; now they 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 to 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.