Area Rule

At flight speeds close to sound , the local speed of the air stream can reach the speed of sound in places where the stream goes around the structural elements of the aircraft. The value of the speed at which this behavior is observed varies depending on the design of the aircraft and is called the critical Mach number . The shock waves arising in such places have a sudden strong rapidly growing resistance, called wave resistance. To reduce the power of shock waves, the cross-sectional area of ​​the aircraft should vary along the aircraft body as smoothly as possible.

The area rule states that two aircraft with the same longitudinal distribution of the cross-sectional area have the same wave resistance, independent of the distribution of this area in the direction of the transverse fuselage (i.e., on the fuselage itself or on the wings). Moreover, in order to avoid the occurrence of strong shock waves, this distribution must be smooth. An example of the application of this rule is the narrowing of the fuselage of the aircraft at the junction with the wings so that the cross-sectional area does not change.

This rule also applies at speeds greater than the speed of sound, but its application in this case is somewhat more complicated: instead of the cross-sectional area, the sectional areas of the tangent planes of the Mach cone are used. The value of the wave resistance will be equal to the sum of the values ​​of the resistance calculated for cross sections in all directions. ^[1] The design of supersonic aircraft is designed taking into account the Mach cone for the intended speed. For example, for the speed M = 1.3, the angle of the resulting Mach cone will be approximately μ = arcsin (1 / 1.3) = 50.3 °. In this case, the “ideal shape” of the aircraft will be “extended” back. Classical examples of this design are Concord and Tu-144 .

Germany

The area rule was discovered by Otto Frenzl in 1943 while studying the airflow around an arrow - shaped wing and a W-shaped wing, which had an extremely high wave resistance. ^[2] This comparative study was carried out at the Junkers plant in a wind tunnel providing a transonic speed of air flow. Frenzel described his research in Arrangement of Displacement Bodies in High-Speed ​​Flight, dated December 17, 1943, on the basis of which he received a corresponding patent in 1944. ^[3] The results of the Fresnel study were presented to the general public in March 1944 at the German Academy of Aeronautics Research ( Deutsche Akademie der Luftfahrtforschung) at the lecture of Theodor Zobel "Fundamentally new ways to improve the performance of high-speed aircraft" (Fundamentally new ways to increase performance of high speed aircraft). ^[four]

Further design of German aircraft during the war years was carried out taking into account this discovery, as evidenced, for example, by narrowed in the middle part of the fuselages of such aircraft as Messerschmitt P.1112 fighters (developments were used to create the American F7U carrier-based fighter) ^{[5] [6]} , Messerschmitt P.1106 and the Focke-Wulf Fw 239 bomber, which was also known as the Focke-Wulf 1000x1000x1000 (1000 kg bomb load, range of 1000 km, speed of 1000 km / h). In addition, deltoid wing designs such as the Henschel Hs 135 also point to the use of the area rule. Several other researchers, in particular Dietrich Küchemann, who designed the fighter with a cone-shaped fuselage, which the Americans named after its discovery in 1946 by the Küchemann Coke Bottle (approx. - Coca-Cola bottle from Kücheman). Küchemann approached the discovery of the rule of squares, studying the movement of the air flow over the swept wing in its scope. The sweep of the wing, as such, is an indirect application of this rule. "

USA

Wallace D. Hayes, one of the pioneers of supersonic flight, came to formulate the area rule in his publications, the first of which was his dissertation, defended at the California Institute of Technology in 1947. ^[7]

Richard T. Whitcomb, whose name the area rule is called in the West (Whitcomb area rule), independently discovered it in 1952, working at the NASA research center at the Air Force Base. Langley . Carrying out research in a wind tunnel with a flow velocity of 0.95 M , he was impressed by the increase in aerodynamic drag due to the formation of shock waves. Whitcom concluded that the prevention of a sharp increase in resistance would be facilitated by the elimination of unevenness in the cross section, for which the aircraft fuselage - at least in theory - should be close to the streamlined body of rotation of maximum elongation. ^{[8] The} shock waves were clearly visible in photographs taken by the so-called by the schlieren method, but the cause of their occurrence at speeds much less than the speed of sound, sometimes not more than 0.70 M, remained unknown.

At the end of 1951, Adolf Busemann , a famous German specialist in aerodynamics, who moved to the USA after the war, delivered a lecture at the NASA research center. The topic of the lecture was the behavior of the air flow around the aircraft at speeds approaching the critical Mach number, when the air ceases to behave like an incompressible fluid. Engineers are accustomed to imagine the air flow smoothly flowing around the airplane’s hull, but at high speeds the air “had no time” for a smooth flow, and therefore the air moved like a stream consisting of pipes ( you can also use the analogy with a continuous stream of logs fused along the river ) In expounding his concept of high-speed air movement around an airplane, Buseman spoke not of generally accepted “flow lines,” but of “airflow pipes,” and jokingly suggested that engineers consider themselves pipelines.

A few days after this lecture, Whitky came up with an insight - the cause of the high aerodynamic drag was the mutual interference of the air "tubes" in three-dimensional space. In contrast to the previously accepted concept of airflow around a two-dimensional cross-section of an airplane, now it was necessary to take into account air at a certain distance from the airplane, also interacting with these "pipes". Whitcom realized that now it becomes important not so much the shape of the fuselage as the shape of the entire aircraft, as a whole. This meant that when developing the general shape of the aircraft, it was necessary to take into account the additional cross section of the wings and the tail, and that for the best fit the ideal shape, the fuselage should have a narrowing at the point of docking with them.

Immediately after its discovery, the area rule was applied in the design of aircraft developed at that time. One of the most famous cases was Whitcom's personal alteration of the design of the American F-102 fighter, whose characteristics were significantly worse than expected. ^[9] After “pushing” the fuselage behind the wings and, despite the apparent paradox, the increase in the volume of the rear of the aircraft, the aerodynamic drag at transonic speeds was significantly reduced, and the design speed of 1.2 M was reached. The area rule was fully taken into account when designing the F-106 , for many years remained the main all-weather interceptor of the US Air Force. ^[ten]

In the same way, the designs of many aircraft of that time were changed: to ensure a smoother profile, additional fuel tanks were added or the tail unit was increased in size. The Soviet Tu-95 bomber received more protruding fairings of the landing gear compartment behind both internal engines, which increased the overall cross-section of the aircraft behind the root of the wings. The civilian version of this aircraft from 1960 to the present remains the fastest propeller aircraft in the world. A similar solution was used in the design of the Convair 990 , where bulges were added to the trailing edge of the wing to prevent the formation of shock waves. This aircraft with a cruising speed of up to 0.89 M is still the fastest American airliner. Engineers from Armstrong-Whitworth proposed the further development of this concept in the form of an M-shaped wing, which had a reverse sweep in its root part. Such a wing made it possible to narrow the fuselage on both sides of the root part of the wing, and not only after it, which gave a more streamlined and at the same time wider, on average, fuselage compared to the classic swept wing.

An interesting example of applying the area rule is the shape of the top of the fuselage of a Boeing 747 . ^[11] This aircraft was designed to transport standard transport containers located on the main deck in two stacks of two in a row, which in the event of an accident could pose a serious danger to the crew when it was normally placed in the pilot's cabin in the nose of the fuselage. Therefore, the cockpit was moved to a small "hillock" above the deck, the size of which - based on the streamlining primacy at that time - was initially minimized. However, later it was understood that lengthening this “tubercle” would give a much greater decrease in aerodynamic drag than minimizing it, since the wave impedance of the elongated pilot's cabin “neutralized” the wave impedance of the tail stabilizer. A new form of the cabin began to be used on this aircraft, starting with the 747-300 series, which allowed to increase cruising speed and reduce aerodynamic drag, as well as slightly increase the capacity of the passenger version of the aircraft.

Airplanes designed to comply with the area rules (such as the Blackburn Buccaneer and Northrop F-5 ) looked odd by the standards of their first trials and were called "Coca-Cola flying bottles." However, the area rule proved to be effective, and subsequently - when it was not so much taken into account in the design as it was originally laid in the design of the aircraft - their fuselages began to take on a more familiar shape again. Despite the continued application of this rule, a clear “waist” is present in only a few aircraft, such as the B-1B Lancer , Learjet 60 and Tu-160 . Currently, the same effect is achieved by layout solutions: a combination of the shape and relative position of the accelerators and the cargo compartment on the launch vehicles; the position of the engines in front of the wing of the Airbus A-380 , and not directly below it; the position of the engines behind the Cessna Citation X fuselage, and not on the sides of it; the shape and location of the pilot light on the F-22 , etc.

• Discovery story
• Rule explanation and application