The Whitcomb area rule, also called the transonic area rule, is a design technique used to reduce an aircraft's drag at transonic and supersonic speeds, particularly between Mach 0. In Fluid dynamics, drag (sometimes called fluid resistance) is the force that resists the movement of a Solid object through a Fluid (a Transonic is an Aeronautics term referring to a range of velocities just below and above the Speed of sound (about mach 0 For other uses see Supersonic. The term supersonic is used to define a speed that is over the Speed of sound ( Mach 1 Mach number (\mathrm{Ma} or M (generally ˈmɑːk sometimes /ˈmɑːx/ or /ˈmæk/ is the speed of an object moving through air or any Fluid 8 and 1. 2. This is the operating speed range of the vast majority of commercial and military fixed-wing aircraft today.

Contents 1 Description 2 History 2.1 Germany 2.2 United States 3 Applications 4 Images 5 See also 6 References 7 External links

Description

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. For other uses see Supersonic. The term supersonic is used to define a speed that is over the Speed of sound ( Mach 1 In Fluid dynamics, Bernoulli's principle states that for an Inviscid flow, an increase in the speed of the fluid occurs simultaneously with a decrease in The speed at which this occurs varies from aircraft to aircraft, and is known as the critical Mach number. The Critical Mach number (Mcr of an aircraft is the slowest Mach number at which the airflow over a small region of the wing reaches the speed of sound The resulting shock waves formed at these points of supersonic flow can 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. For the music album by Converter see Shock Front For the 1977 horror film see Shock Waves A shock wave (also called For other uses see Supersonic. The term supersonic is used to define a speed that is over the Speed of sound ( Mach 1 Wave drag is an Aerodynamics term that refers to a sudden and very powerful form of drag that appears on aircraft and blade tips moving at high-subsonic and supersonic In order to reduce the number and power of these shock waves, an aerodynamic shape should change in cross-sectional area as smoothly as possible. For the music album by Converter see Shock Front For the 1977 horror film see Shock Waves A shock wave (also called This leads to a "perfect" aerodynamic shape known as the Sears-Haack body, roughly shaped like a cigar but pointed at both ends. The Sears-Haack body is generally speaking the body least susceptible to Wave drag. A cigar is a tightly rolled bundle of dried and fermented Tobacco which is ignited so that its smoke may be drawn into the smoker's mouth

The area rule says that an airplane designed with the same cross-sectional area as the Sears-Haack body generates the same wave drag as this body, largely independent of the actual shape. As a result, aircraft have to be carefully arranged so that large volumes like wings are positioned at the widest area of the Sears-Haack body, and that the cockpit, tailplane, intakes and other "bumps" be spread out along the fuselage.

The area rule also holds true at speeds higher than the speed of sound, but in this case the body arrangement is in respect to the Mach line for the design speed. Sound is a vibration that travels through an elastic medium as a Wave. For instance, at Mach 1. 3 the angle of the Mach cone formed off the body of the aircraft will be at about sinμ = 1/M (μ is the sweep angle of the Mach cone). In this case the "perfect shape" is biased rearward, which is why aircraft designed for high speed cruise tend to be arranged with the wings at the rear. A classic example of such a design is the Concorde. WikipediaWikiProject Aircraft. Please see WikipediaWikiProject Aircraft/page content for recommended layout

History

Germany

The area rule was first discovered by Otto Frenzl when comparing a swept wing with a w-wing with extreme high wave drag ^[1] working on a transonic wind tunnel at Junkers works in Germany between 1943 and 1945. Germany, officially the Federal Republic of Germany ( ˈbʊndəsʁepuˌbliːk ˈdɔʏtʃlant is a Country in Central Europe. Year 1943 ( MCMXLIII) was a Common year starting on Friday (the link will display full 1943 calendar of the Gregorian calendar. Year 1945 ( MCMXLV) was a Common year starting on Monday (link will display the full calendar He wrote an inventor message on 17 December 1943, with the title “Arrangement of Displacement Bodies in High-Speed Flight”; this was used in a patent filed in 1944. Year 1944 ( MCMXLIV) was a Leap year starting on Saturday (link will display full calendar of the Gregorian calendar. ^[2] 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 “Basically new ways to increase performance of high speed aircraft. ” ^[3] 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. Messerschmitt AG was a famous German Aircraft manufacturer known primarily for its World War II Fighter aircraft, notably the Bf 109 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. Dr Dietrich Küchemann CBE FRS FRAeS (1911&ndash1976 was a German Aerodynamicist who made several important contributions to S. forces in 1946. Year 1946 ( MCMXLVI) was a Common year starting on Tuesday (link will display full 1946 calendar of the Gregorian calendar. In this case Küchemann arrived at the solution by studying airflow, notably spanwise flow, over a swept wing. A swept-wing is a wing Planform common on high-speed Aircraft, with the wing swept back instead of being set at right angles to the Fuselage.

United States

Wallace D. Hayes, a pioneer of supersonic flight, developed the supersonic area rule in a series of publications beginning in 1947 with his Ph. Wallace D Hayes (c 1919 - 2001 was a professor of mechanical and aerospace engineering who made numerous fundamental contributions to the understanding of Supersonic flight For other uses see Supersonic. The term supersonic is used to define a speed that is over the Speed of sound ( Mach 1 For other uses see Supersonic. The term supersonic is used to define a speed that is over the Speed of sound ( Mach 1 D. thesis at the California Institute of Technology. The California Institute of Technology (commonly referred to as Caltech) is a private, Coeducational research university located in Pasadena

Richard T. Whitcomb, after whom the rule is named, independently discovered this rule in 1952, while working at NACA. Richard T Whitcomb (1921 Evanston Illinois) is an aeronautical engineer who spent most of his career at the Langley Laboratory of the NACA and its successor Year 1952 ( MCMLII) was a Leap year starting on Tuesday (link will display full calendar of the Gregorian calendar. While using the new Eight-Foot High-Speed Tunnel, a wind tunnel with performance up to Mach 0. A wind tunnel is a research tool developed to assist with studying the effects of air moving over or around solid objects 95 at NACA's Langley Research Center, he was surprised by the increase in drag due to shock wave formation. Langley Research Center (LaRC is the oldest of NASA 's field centers located in Hampton, Virginia, United States. 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. Schlieren photography is a visual process that is used to photograph the flow of fluids of varying density 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. Year 1951 ( MCMLI) was a Common year starting on Monday. Events of 1951 January Adolph Busemann ( 20 April 1901 - 3 November 1986) was a German aerospace engineer and influential early pioneer in World War II, or the Second World War, (often abbreviated WWII) was a global military conflict which involved a majority of the world's nations, including He talked about the difference in the behavior of airflow at speeds approaching the supersonic, where it no longer behaved as an incompressible fluid. Fluid mechanics is the study of how Fluids move and the Forces on them 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. Eureka ( Greek "I have found it" is an exclamation used as an Interjection to celebrate a discovery 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.

Applications

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 Convair F-102 Delta Dagger, a U. WikipediaWikiProject Aircraft. Please see WikipediaWikiProject Aircraft/page content for recommended layout S. Air Force jet fighter that 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. The culminating design of this research was the Convair F-106 Delta Dart, an aircraft which for many years was the USAF's primary all-weather interceptor. WikipediaWikiProject Aircraft. Please see WikipediaWikiProject Aircraft/page content for recommended layout

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. WikipediaWikiProject Aircraft. Please see WikipediaWikiProject Aircraft/page content for recommended layout The Union of Soviet Socialist Republics (USSR was a constitutionally Socialist state that existed in Eurasia from 1922 to 1991 A bomber is a Military aircraft designed to attack ground and sea targets primarily by dropping Bombs on them It remains the highest speed propeller aircraft in the world. A propeller is essentially a type of fan which transmits power by converting Rotational motion into Thrust for propulsion of a vehicle such as an The Convair 990 used a similar solution, adding bumps called antishock bodies to the trailing edge of the upper wing. WikipediaWikiProject Aircraft. Please see WikipediaWikiProject Aircraft/page content for recommended layout Anti-shock bodies or Küchemann carrots are pods placed at the Trailing edge of a Subsonic Aircraft 's wings in order to reduce The trailing edge of a Wing is the rear edge of the wing where the airflow separated by the Leading edge rejoins after passing over and under the top and bottom surfaces The 990 remains the fastest U. S. airliner in history, cruising at up to Mach 0. An airliner is a large Fixed-wing aircraft with the primary function of transporting paying passengers Mach number (\mathrm{Ma} or M (generally ˈmɑːk sometimes /ˈmɑːx/ or /ˈmæk/ is the speed of an object moving through air or any Fluid 89. 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. Sir W G Armstrong Whitworth & Co Ltd was a major British manufacturing company of the early years of the 20th century 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. WikipediaWikiProject Aircraft. Please see WikipediaWikiProject Aircraft/page content for recommended layout 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 "hump", 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 hump, 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, (eg. 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. WikipediaWikiProject Aircraft. Please see WikipediaWikiProject Aircraft/page content for recommended layout 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 on rockets; the jet engines in front of (and not directly below) the wings of the Airbus A380; the jet engines behind (and not purely at the side of) the fuselage of a Cessna Citation X; the shape and location of canopy on the F-22 Raptor; and this image of the Airbus A380 in flight showing obvious area rule shaping at the wing root, but these modifications are practically invisible from any other angle. WikipediaWikiProject Aircraft. Please see WikipediaWikiProject Aircraft/page content for recommended layout WikipediaWikiProject Aircraft. Please see WikipediaWikiProject Aircraft/page content for recommended layout specific --->A jet engine is a Reaction engine that discharges a fast moving jet of Fluid to WikipediaWikiProject Aircraft. Please see WikipediaWikiProject Aircraft/page content for recommended layout WikipediaWikiProject Aircraft. Please see WikipediaWikiProject Aircraft/page content for recommended layout WikipediaWikiProject Aircraft. Please see WikipediaWikiProject Aircraft/page content for recommended layout Aftershock bodies are likewise "invisible" today, serving double-duty as flap actuators, which are also visible in the A380 image above.

Images

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 Demonstration, 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. WikipediaWikiProject Aircraft. Please see WikipediaWikiProject Aircraft/page content for recommended layout WikipediaWikiProject Aircraft. Please see WikipediaWikiProject Aircraft/page content for recommended layout WikipediaWikiProject Aircraft. Please see WikipediaWikiProject Aircraft/page content for recommended layout WikipediaWikiProject Aircraft. Please see WikipediaWikiProject Aircraft/page content for recommended layout The NASA Shaped Sonic Boom Demonstration, also known as the Shaped Sonic Boom Experiment, was a two-year program that used a Northrop F-5E with a modified 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 therefore travels faster. In Aerodynamics, compression lift refers to an Aircraft that uses Shock waves generated by its own Supersonic flight to generate lift
Overhead view of a Tu-95. Two large bulged nacelles can be seen behind its engines.

See also

• Anti-shock body
• Mach number
• Shock wave
• Sonic boom
• Sound barrier
• Supersonic aerodynamics

References

External links

• Aerospaceweb.org: Area rule explained
• Aerospaceweb.org: Whitcomb Area Rule and Küchemann Carrots
• DGLR document
• German patent search system - look for Patent DE 932410 filed March 21, 1944
• NASA 2004: Overuse increases drag but still reduces boom heard on the ground
• PBS.org - See Image 4 for an extreme example: fuselage before wing
• The Whitcomb Area Rule: NACA Aerodynamics Research and Innovation
• Whitcomb, Richard T.: A Study of the Zero-Lift Drag-Rise Characteristics of Wing-Body Combinations Near the Speed of Sound. NACA Report 1273, 1956. Events 630 - Byzantine emperor Heraclius restores the True Cross to Jerusalem. Year 1944 ( MCMXLIV) was a Leap year starting on Saturday (link will display full calendar of the Gregorian calendar.
• Wallace D. Hayes developed the Supersonic area rule

Wallace D Hayes (c 1919 - 2001 was a professor of mechanical and aerospace engineering who made numerous fundamental contributions to the understanding of Supersonic flight The Whitcomb area rule, also called the transonic area rule, is a design technique used to reduce an Aircraft 's drag at Transonic and Supersonic

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