The Whitcomb area rule, named after
NACA
The National Advisory Committee for Aeronautics (NACA) was a United States federal agency founded on March 3, 1915, to undertake, promote, and institutionalize aeronautical research. On October 1, 1958, the agency was dissolved and its assets ...
engineer
Richard Whitcomb and also called the transonic area rule, is a design procedure used to reduce an
aircraft
An aircraft is a vehicle that is able to fly by gaining support from the air. It counters the force of gravity by using either static lift or by using the dynamic lift of an airfoil, or in a few cases the downward thrust from jet engines ...
's
drag at
transonic
Transonic (or transsonic) flow is air flowing around an object at a speed that generates regions of both subsonic and supersonic airflow around that object. The exact range of speeds depends on the object's critical Mach number, but 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
A fixed-wing aircraft is a heavier-than-air flying machine, such as an airplane, which is capable of flight using wings that generate lift caused by the aircraft's forward airspeed and the shape of the wings. Fixed-wing aircraft are distinc ...
today, with transonic acceleration an important performance requirement for combat aircraft and which is improved by reductions in transonic drag.
Description
At high-subsonic flight speeds, the local speed of the airflow can reach the speed of sound where the flow accelerates around the
aircraft
An aircraft is a vehicle that is able to fly by gaining support from the air. It counters the force of gravity by using either static lift or by using the dynamic lift of an airfoil, or in a few cases the downward thrust from jet engines ...
body and
wing
A wing is a type of fin that produces lift while moving through air or some other fluid. Accordingly, wings have streamlined cross-sections that are subject to aerodynamic forces and act as airfoils. A wing's aerodynamic efficiency is expres ...
s. The speed at which this development occurs varies from aircraft to aircraft and is known as the
critical Mach number. The resulting
shock wave
In physics, a shock wave (also spelled shockwave), or shock, is a type of propagating disturbance that moves faster than the local speed of sound in the medium. Like an ordinary wave, a shock wave carries energy and can propagate through a med ...
s formed at these zones of sonic flow cause a sudden increase in
drag, called
wave drag
In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (r ...
. To reduce the number and strength of these shock waves, an
aerodynamic
Aerodynamics, from grc, ἀήρ ''aero'' (air) + grc, δυναμική (dynamics), is the study of the motion of air, particularly when affected by a solid object, such as an airplane wing. It involves topics covered in the field of fluid dyn ...
shape should change in
cross section
Cross section may refer to:
* Cross section (geometry)
** Cross-sectional views in architecture & engineering 3D
*Cross section (geology)
* Cross section (electronics)
* Radar cross section, measure of detectability
* Cross section (physics)
**Abs ...
al 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 and developed by NACA aerodynamicist Robert Jones, "Theory of wing-body drag at supersonic speeds",
is applicable at speeds beyond transonic, but 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
In fluid dynamics, a Mach wave is a pressure wave traveling with the speed of sound caused by a slight change of pressure added to a compressible flow. These weak waves can combine in supersonic flow to become a shock wave if sufficient Mach waves ...
, 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.
[.]
Sears–Haack body
A superficially related concept is the
Sears–Haack body
The Sears–Haack body is the shape with the lowest theoretical wave drag in supersonic flow, for a given body length and given volume. The mathematical derivation assumes small-disturbance (linearized) supersonic flow, which is governed by the P ...
, 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.
History
Germany
![Modellphoto Ju287V1 1](https://upload.wikimedia.org/wikipedia/commons/e/ec/Modellphoto_Ju287V1_1.png)
The area rule was discovered by 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
The Focke-Wulf 1000x1000x1000, also known as Focke-Wulf Fw 239, was a twinjet bomber project for the Luftwaffe, designed by the Focke-Wulf aircraft manufacturing company during the last years of the Third Reich.
Their designation meant that these ...
type A long-range bomber, but also apparent in delta wing designs including the
Henschel Hs 135
Henschel & Son (german: Henschel und Sohn) was a German company, located in Kassel, best known during the 20th century as a maker of transportation equipment, including locomotives, trucks, buses and trolleybuses, and armoured fighting vehicl ...
. Several other researchers came close to developing a similar theory, notably
Dietrich Küchemann
Dietrich Küchemann CBE FRS FRAeS (11 September 1911 – 23 February 1976) was a German aerodynamicist who made several important contributions to the advancement of high-speed flight. He spent most of his career in the UK, where he is ...
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
A swept wing is a wing that angles either backward or occasionally forward from its root rather than in a straight sideways direction.
Swept wings have been flown since the pioneer days of aviation. Wing sweep at high speeds was first investigate ...
. 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.
United States
Wallace D. Hayes, a pioneer of
supersonic
Supersonic speed is the speed of an object that exceeds the speed of sound ( Mach 1). For objects traveling in dry air of a temperature of 20 °C (68 °F) at sea level, this speed is approximately . Speeds greater than five times ...
flight, developed the transonic area rule in publications beginning in 1947 with his Ph.D. thesis at the
California Institute of Technology
The California Institute of Technology (branded as Caltech or CIT)The university itself only spells its short form as "Caltech"; the institution considers other spellings such a"Cal Tech" and "CalTech" incorrect. The institute is also occasional ...
.
[.]
Richard T. Whitcomb, after whom the rule is named, independently discovered this rule in 1952, while working at the
National Advisory Committee for Aeronautics
The National Advisory Committee for Aeronautics (NACA) was a United States federal agency founded on March 3, 1915, to undertake, promote, and institutionalize aeronautical research. On October 1, 1958, the agency was dissolved and its assets ...
(NACA). While using the new Eight-Foot High-Speed Tunnel, a
wind tunnel
Wind tunnels are large tubes with air blowing through them which are used to replicate the interaction between air and an object flying through the air or moving along the ground. Researchers use wind tunnels to learn more about how an aircraft ...
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. Whitcomb realized that, for analytical purposes, an airplane could be reduced to a streamlined body of revolution, elongated as much as possible to mitigate abrupt discontinuities and, hence, equally abrupt drag rise.
The shocks could be seen using
Schlieren photography
Schlieren photography is a process for photographing fluid flow. Invented by the German physicist August Toepler in 1864 to study supersonic motion, it is widely used in aeronautical engineering to photograph the flow of air around objects.
C ...
, 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
Adolf Busemann (20 April 1901 – 3 November 1986) was a German aerospace engineer and influential Nazi-era pioneer in aerodynamics, specialising in supersonic airflows. He introduced the concept of swept wings and, after emigrating in 1947 to t ...
, a famous German aerodynamicist who had moved to Langley after
World War II
World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...
. He talked about the behavior of airflow around an airplane as its speed approached the critical Mach number, when air no longer behaved as a compressible 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
Eureka (often abbreviated as E!, or Σ!) is an intergovernmental organisation for research and development funding and coordination. Eureka is an open platform for international cooperation in innovation. Organisations and companies applying th ...
" moment. The reason for the high drag was that the "pipes" of air were interfering with each other in three dimensions. One does 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 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 first aircraft where the area rule was consequently implemented was the German bomber
testbed
A testbed (also spelled test bed) is a platform for conducting rigorous, transparent, and replicable testing of scientific theories, computational tools, and new technologies.
The term is used across many disciplines to describe experimental rese ...
Junkers Ju-287 (1944). Other corresponding German designs were not completed due to the end of the war or even remained in the planning stage.
When the area rule was re-discovered by Whitcomb, it was made available to the U.S. aircraft industry on a secret basis for military programs from 1952 and it was reported in 1957 for civilian programs.
Convair and Grumman, with Whitcomb's help, used it concurrently to design the
Grumman F-11 Tiger
The Grumman F11F/F-11 Tiger is a supersonic, single-seat carrier-based United States Navy fighter aircraft in operation during the 1950s and 1960s. Originally designated the F11F Tiger in April 1955 under the pre-1962 Navy designation system, i ...
and to redesign the
Convair F-102.
The
Grumman F-11 Tiger
The Grumman F11F/F-11 Tiger is a supersonic, single-seat carrier-based United States Navy fighter aircraft in operation during the 1950s and 1960s. Originally designated the F11F Tiger in April 1955 under the pre-1962 Navy designation system, i ...
was the first of the two aircraft to fly and had been designed using the area rule from the outset. The Convair
F-102 Delta Dagger had to be redesigned as it had been unable to reach Mach 1 although its design speed was Mach 1.2. The expectation that it would reach design speed had been based on optimistic wind-tunnel drag predictions. Modifications which included indenting the fuselage beside the wings and adding more volume to the rear of the aircraft, reduced the transonic drag significantly and the Mach 1.2 design speed was reached. The reason for using the area rule on these fighter aircraft was to reduce the peak value of the drag which occurs at Mach 1 and so enable supersonic speeds with less thrust than would otherwise have been necessary.
In 1957 a modified area rule was available for raising the subsonic cruise speed of transport aircraft by 50 mph.
The cruise speed is limited by the sudden increase in drag which indicates the presence of local supersonic flow on top of the wing. Whitcomb's modified rule reduced the supersonic speed before the shock, which weakened it and reduced the drag associated with it. The
Convair 990 had bumps called
antishock bodies added to the top surface of the wing with the intent of achieving the required cruise speed. However, the area distribution in the channels formed by the nacelle/pylon/wing surfaces also caused supersonic velocities and was the source of significant drag. An area-rule technique, so-called channel area-ruling, was applied to achieve the required cruise speed.
Designers at
Armstrong-Whitworth
Sir W G Armstrong Whitworth & Co Ltd was a major British manufacturing company of the early years of the 20th century. With headquarters in Elswick, Newcastle upon Tyne, Armstrong Whitworth built armaments, ships, locomotives, automobiles and a ...
took the sonic area rule a step further in their proposed M-Wing, in which the wing was first swept forward and then to the rear. This allowed the fuselage to be narrowed in front of the root as well as behind it, leading to a smoother fuselage that remained wider on average than one using a classic swept wing.
The extension behind the flight deck on the
Rockwell B-1 Lancer
The Rockwell B-1 Lancer is a supersonic variable-sweep wing, heavy bomber used by the United States Air Force. It is commonly called the "Bone" (from "B-One"). It is one of three strategic bombers serving in the U.S. Air Force fleet along with ...
and
Boeing 747
The Boeing 747 is a large, long-range wide-body airliner designed and manufactured by Boeing Commercial Airplanes in the United States between 1968 and 2022.
After introducing the 707 in October 1958, Pan Am wanted a jet times its size, t ...
was added to improve the cross-sectional area distribution according to the area rule.
Aircraft designed according to Whitcomb's area rule (such as the
F-102 Delta Dagger and the
Northrop F-5
The Northrop F-5 is a family of supersonic light fighter aircraft initially designed as a privately funded project in the late 1950s by Northrop Corporation. There are two main models, the original F-5A and F-5B Freedom Fighter variants and t ...
) looked odd when they first appeared and were sometimes dubbed "flying
Coke bottle
Coca-Cola, or Coke, is a carbonated soft drink manufactured by the Coca-Cola Company. Originally marketed as a temperance drink and intended as a patent medicine, it was invented in the late 19th century by John Stith Pemberton in Atlant ...
s", but this became an expected part of the appearance of some transonic aircraft. Visually-apparent indications that the area rule has defined the shape of an aircraft are fuselage "waisting" and tip-tank shaping as on the
Northrop F-5
The Northrop F-5 is a family of supersonic light fighter aircraft initially designed as a privately funded project in the late 1950s by Northrop Corporation. There are two main models, the original F-5A and F-5B Freedom Fighter variants and t ...
, and rear fuselage thinning on business jets with rear engines such as the
Bombardier Global Express
The Bombardier Global Express is a large cabin, 6,000 nmi / 11,100 km range business jet designed and manufactured by Bombardier Aviation (formerly Bombardier Aerospace).
Announced in October 1991, it first flew on 13 October 1996, receiv ...
. The rule also requires careful positioning of parts, like the boosters and cargo bay on rockets and the shape and location of the canopy on the
F-22 Raptor
The Lockheed Martin F-22 Raptor is an American single-seat, twin-engine, all-weather stealth tactical fighter aircraft developed for the United States Air Force (USAF). As the result of the USAF's Advanced Tactical Fighter (ATF) program, th ...
.
The supersonic area rule was applied, at Mach 2, to the prototype
Concorde
The Aérospatiale/BAC Concorde () is a retired Franco-British supersonic airliner jointly developed and manufactured by Sud Aviation (later Aérospatiale) and the British Aircraft Corporation (BAC).
Studies started in 1954, and France an ...
. The rear fuselage was extended by 3.73m on the production aircraft and reduced wave drag by 1.8%.
[A Case Study By Aerospatiale And British Aerospace On The Concorde By Jean Rech and Clive S. Leyman,AIAA Professional Study Series, Fig. 3.6]
Images
Image:Eclipse_program_QF-106_aircraft_in_flight,_view_from_tanker.jpg, The F-106 Delta Dart
The Convair F-106 Delta Dart was the primary all-weather interceptor aircraft of the United States Air Force from the 1960s through to the 1980s. Designed as the so-called "Ultimate Interceptor", it proved to be the last specialist interceptor ...
, a development of the F-102 Delta Dagger, shows the "wasp-waisted" shaping due to area rule considerations
Image:Convair 990 on ramp EC92-05275-30.jpg, NASA Convair 990 with antishock bodies on the rear of the wings
Image:Antishock_Bodies_Visualization.jpg, Oilflow visualization of flow separation without and with antishock bodies
File:J-3005.jpg, Northrop F-5
The Northrop F-5 is a family of supersonic light fighter aircraft initially designed as a privately funded project in the late 1950s by Northrop Corporation. There are two main models, the original F-5A and F-5B Freedom Fighter variants and t ...
showing fuselage waisting
File:IIAF F-5A 3-417.jpg, Northrop F-5
The Northrop F-5 is a family of supersonic light fighter aircraft initially designed as a privately funded project in the late 1950s by Northrop Corporation. There are two main models, the original F-5A and F-5B Freedom Fighter variants and t ...
showing tip-tank shaping
File:Bombardier Global Express 91.jpg, Bombardier Global Express
The Bombardier Global Express is a large cabin, 6,000 nmi / 11,100 km range business jet designed and manufactured by Bombardier Aviation (formerly Bombardier Aerospace).
Announced in October 1991, it first flew on 13 October 1996, receiv ...
showing rear fuselage thinning between engines
File:Concorde first visit Heathrow Fitzgerald.jpg, Prototype Concorde
The Aérospatiale/BAC Concorde () is a retired Franco-British supersonic airliner jointly developed and manufactured by Sud Aviation (later Aérospatiale) and the British Aircraft Corporation (BAC).
Studies started in 1954, and France an ...
before tail was modified using Mach 2 application of area rule
File:Aerospatial Concorde (6018513515).jpg, Production Concorde
The Aérospatiale/BAC Concorde () is a retired Franco-British supersonic airliner jointly developed and manufactured by Sud Aviation (later Aérospatiale) and the British Aircraft Corporation (BAC).
Studies started in 1954, and France an ...
with area ruled tail
See also
*
Anti-shock body
Anti-shock body is the name given by Richard T. Whitcomb to a pod positioned on the upper surface of a wing. Its purpose is to reduce wave drag while travelling at transonic speeds ( Mach 0.8–1.0), which includes the typical cruising range of co ...
*
Sonic boom
A sonic boom is a sound associated with shock waves created when an object travels through the air faster than the speed of sound. Sonic booms generate enormous amounts of sound energy, sounding similar to an explosion or a thunderclap to t ...
*
Sound barrier
The sound barrier or sonic barrier is the large increase in aerodynamic drag and other undesirable effects experienced by an aircraft or other object when it approaches the speed of sound. When aircraft first approached the speed of sound, th ...
*
Supersonic aerodynamics
Notes
Bibliography
*
External links
Area rule explained Aerospace Web.
Whitcomb Area Rule and Küchemann Carrots Aerospace Web.
DGLR document
German patent search system– look for Patent DE 932410 filed March 21, 1944.
NASA
*
ttps://www.pbs.org/wgbh/nova/concorde/shock.html See Image 4 for an extreme example: fuselage before wing PBS.
The Whitcomb Area Rule: NACA Aerodynamics Research and Innovation History Nasa.
* , Whitcomb, Richard T, NACA Report 1273, 1956.
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