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322:. He talked about the behavior of airflow around an airplane as its speed approached the critical Mach number, when air 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
503:
333:" 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
134:
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
373:
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.
307:, 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
372:
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
393:
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
376:
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
133:
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
146:
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
385:
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
171:
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
355:
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
257:
who designed a tapered fighter that was dubbed the "KĂĽchemann Coke Bottle" when it was discovered by US forces in 1946. In this case KĂĽchemann arrived at the theory by studying airflow, notably the interference, or local flow streamlines, at the junction between a fuselage and
450:
337:, 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.
147:
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
420:", 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
262:. 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.
710:
230:("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
34:
Cross-sectional area distribution along the complete airframe determines wave drag, largely independent of the actual shape. The blue and light green shapes are roughly equal in area.
547:
728:
976:
The World's
Fighting Planes Fourth and completely revised edition, William Green 1964, MacDonald & Co.(Publishers) Ltd., Gulf House,2 Portman Street, London W.1, p.136
490:
155:). 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.
532:
470:
1083:
167:, 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
250:
643:
85:
today, with transonic acceleration an important performance requirement for combat aircraft and which is improved by reductions in transonic drag.
428:. 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
1009:
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
212:
296:
563:
311:, 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.
93:
At high-subsonic flight speeds, the local speed of the airflow can reach the speed of sound where the flow accelerates around the
323:
234:(German Academy of Aeronautics Research) in the lecture "Fundamentally new ways to increase performance of high speed aircraft."
352:(1944). Other corresponding German designs were not completed due to the end of the war or even remained in the planning stage.
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Subsequent German wartime aircraft design took account of the discovery, evident in slim mid-fuselage of aircraft including the
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810:
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when comparing a swept wing with a w-wing with extreme high wave drag while working on a transonic wind tunnel at
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368:
was the first of the two aircraft to fly and had been designed using the area rule from the outset. The
Convair
1151:
639:
75:
172:
smooth, will have favorable wave drag properties according to the area rule, it is not theoretically optimum.
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1080:
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flight, developed the transonic area rule in publications beginning in 1947 with his Ph.D. thesis at the
1135:
681:
656:
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538:
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246:
135:
1119:
A Study of the Zero-Lift Drag-Rise
Characteristics of Wing-Body Combinations Near the Speed of Sound
1054:
439:. The rear fuselage was extended by 3.73m on the production aircraft and reduced wave drag by 1.8%.
284:
599:
226:
works in
Germany between 1943 and 1945. He wrote a description on 17 December 1943, with the title
122:
101:. The speed at which this development occurs varies from aircraft to aircraft and is known as the
304:
295:, after whom the rule is named, independently discovered this rule in 1952, while working at the
1074:
1068:
308:
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254:
1024:
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Flügelpfeilung und Flächenregel, zwei grundlegende deutsche
Patente der Flugzeugaerodynamik
242:
238:
164:
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The first aircraft where the area rule was consequently implemented was the German bomber
8:
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April 1955: Whitcomb examines a model aircraft designed in accordance with his area rule.
82:
47:
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916:
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was added to improve the cross-sectional area distribution according to the area rule.
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speed before the shock, which weakened it and reduced the drag associated with it. The
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326:, and jokingly suggested that engineers had to consider themselves "pipefitters".
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type A long-range bomber, but also apparent in delta wing designs including the
81:
Transonic is one of the most important speed ranges for commercial and military
652:
349:
315:
253:. Several other researchers came close to developing a similar theory, notably
217:
192:
110:
59:
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594:
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30:
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424:, and rear fuselage thinning on business jets with rear engines such as the
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Wing sweep and area rule, two basic German patents of aircraft aerodynamics
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508:
421:
413:
319:
618:
From
Spitfire To Eurofighter 45 Years of Combat Aircraft Design, Roy Boot,
496:
Oilflow visualization of flow separation without and with antishock bodies
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429:
417:
378:
300:
152:
118:
67:
416:) looked odd when they first appeared and were sometimes dubbed "flying
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2004: Overuse increases drag but still reduces boom heard on the ground
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114:
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0.75 and 1.2. For supersonic speeds a different procedure called the
63:
570:
554:
464:, shows the "wasp-waisted" shaping due to area rule considerations
436:
94:
55:
435:
The supersonic area rule was applied, at Mach 2, to the prototype
1121:(Technical report). National Advisory Committee for Aeronautics.
1111:
The
Whitcomb Area Rule: NACA Aerodynamics Research and Innovation
1026:
The Whitcomb Area Rule: NACA Aerodynamics Research and Innovation
724:
408:
Aircraft designed according to Whitcomb's area rule (such as the
318:, a famous German aerodynamicist who had moved to Langley after
679:
386:
area-ruling, was applied to achieve the required cruise speed.
228:
Anordnung von Verdrängungskörpern beim Hochgeschwindigkeitsflug
204:
109:
formed at these zones of sonic flow cause a sudden increase in
557:
before tail was modified using Mach 2 application of area rule
117:. To reduce the number and strength of these shock waves, an
1092:
299:(NACA). While using the new Eight-Foot High-Speed Tunnel, a
98:
43:
1105:
See Image 4 for an extreme example: fuselage before wing
842:"The NACA, NASA, and the Supersonic-Hypersonic Frontier"
1023:
Wallace, Lane E (1998). "5". In Mack, Pamela E (ed.).
991:
979:
682:"Studies of optimum body shapes at hypersonic speeds"
1136:
Contemporary reporting and explanation of area rule
872:Die PfeilflĂĽgelentwicklung in Deutschland bis 1945
779:Die PfeilflĂĽgelentwicklung in Deutschland bis 1945
680:Spencer, B. Jr; Stivers, L. S. Jr (October 1967).
1095:– look for Patent DE 932410 filed March 21, 1944.
125:area as smoothly as possible from front to rear.
1143:
911:
909:
876:The swept-wing development in Germany until 1945
783:The swept-wing development in Germany until 1945
805:Design For Combat Aircraft, Ray Whitford 1987,
541:showing rear fuselage thinning between engines
931:
906:
645:Theory of wing-body drag at Supersonic speeds
941:. McGraw-Hill. 12 September 1955. p. 12
816:
397:The extension behind the flight deck on the
303:with performance up to Mach 0.95 at NACA's
297:National Advisory Committee for Aeronautics
1131:– via NASA Technical Reports Server.
54:, is a design procedure used to reduce an
1126:
919:. McGraw-Hill. 12 August 1957. p. 29
634:
632:
1116:
1075:Whitcomb Area Rule and KĂĽchemann Carrots
283:
232:Deutsche Akademie der Luftfahrtforschung
198:
184:
29:
1022:
997:
985:
708:
314:In late 1951, the lab hosted a talk by
163:A superficially related concept is the
141:
14:
1144:
629:
128:
1117:Whitcomb, Richard T. (January 1956).
869:
776:
638:
959:Design For Air Combat, Ray Whitford,
878:] (in German), pp. 166–99,
785:] (in German), pp. 166–99,
207:jet engines is due to the area rule.
939:"Aviation Week: September 12, 1955"
839:
833:
329:Several days later Whitcomb had a "
158:
74:, developed by NACA aerodynamicist
24:
727:: Deutsches Museum, archived from
279:California Institute of Technology
25:
1168:
1062:
66:speeds which occur between about
917:"Aviation Week: August 12, 1957"
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531:
516:
501:
489:
469:
449:
265:
211:The area rule was discovered by
1016:
1003:
970:
953:
892:
863:
851:. NASA Technical Reports Server
340:
203:The unusual arrangement of the
799:
770:
754:Patentschrift zur Flächenregel
745:
702:
673:
612:
88:
13:
1:
689:NASA Technical Reports Server
655:: NACA, 1284, archived from
7:
1093:German patent search system
870:Meier, Hans-Ulrich (2006),
777:Meier, Hans-Ulrich (2006),
578:
10:
1173:
900:"Aviation Week 1955-09-12"
180:
175:
539:Bombardier Global Express
511:showing fuselage waisting
442:
426:Bombardier Global Express
247:Focke-Wulf 1000x1000x1000
136:Hawker Siddeley Buccaneer
1138:, Flight global archives
765:(in German), 21 Mar 1944
759:Patent for the area rule
605:
526:showing tip-tank shaping
484:on the rear of the wings
169:Prandtl–Glauert equation
1029:. NASA. pp. 144–47
600:Supersonic aerodynamics
460:, a development of the
305:Langley Research Center
121:shape should change in
723:(in German), MĂĽnchen,
289:
208:
196:
35:
1152:Aircraft aerodynamics
828:(obituary), Princeton
709:Heinzerling, Werner,
309:Schlieren photography
287:
202:
188:
33:
1157:Aircraft wing design
902:. 12 September 1955.
840:Hallion, Richard P.
573:with area ruled tail
360:and to redesign the
239:Messerschmitt P.1112
142:Supersonic area rule
103:critical Mach number
72:supersonic area rule
50:and also called the
1069:Area rule explained
399:Rockwell B-1 Lancer
391:Armstrong-Whitworth
293:Richard T. Whitcomb
129:Transonic area rule
83:fixed-wing aircraft
52:transonic area rule
27:Aerodynamic concept
1086:2016-08-06 at the
462:F-102 Delta Dagger
410:F-102 Delta Dagger
370:F-102 Delta Dagger
366:Grumman F-11 Tiger
358:Grumman F-11 Tiger
290:
255:Dietrich KĂĽchemann
209:
197:
40:Whitcomb area rule
36:
381:had bumps called
18:Coke bottle shape
16:(Redirected from
1164:
1132:
1130:
1128:2060/19930092271
1077:, Aerospace Web.
1071:, Aerospace Web.
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383:antishock bodies
271:Wallace D. Hayes
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165:Sears–Haack body
159:Sears–Haack body
105:. The resulting
48:Richard Whitcomb
21:
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1113:, History Nasa.
1088:Wayback Machine
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1063:External links
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792:3-7637-6130-6
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734:on 2011-07-19
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1031:. Retrieved
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1017:Bibliography
1005:
998:Wallace 1998
993:
986:Wallace 1998
981:
972:
955:
943:. Retrieved
933:
921:. Retrieved
894:
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865:
853:. Retrieved
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782:
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758:
753:
747:
736:, retrieved
729:the original
716:
711:
704:
692:. Retrieved
688:
675:
664:, retrieved
657:the original
644:
614:
524:Northrop F-5
509:Northrop F-5
434:
422:Northrop F-5
418:Coke bottles
414:Northrop F-5
407:
396:
394:swept wing.
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341:Applications
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320:World War II
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76:Robert Jones
71:
51:
39:
37:
1051:|work=
855:8 September
569:Production
478:Convair 990
430:F-22 Raptor
379:Convair 990
324:streamlines
301:wind tunnel
216: [
213:Otto Frenzl
153:Mach number
119:aerodynamic
107:shock waves
89:Description
78:, is used.
1146:Categories
1033:August 29,
945:4 November
923:4 November
738:2010-11-06
694:4 November
666:2008-09-12
651:(report),
590:Sonic boom
553:Prototype
403:Boeing 747
335:as a whole
275:supersonic
260:swept wing
149:Mach angle
1053:ignored (
1043:cite book
813:, Fig.161
115:wave drag
113:, called
97:body and
64:transonic
46:engineer
1084:Archived
642:(1956),
579:See also
571:Concorde
555:Concorde
437:Concorde
412:and the
95:aircraft
56:aircraft
967:, p.156
347:testbed
224:Junkers
190:Junkers
181:Germany
176:History
1107:, PBS.
963:
882:
809:
789:
761:]
719:]
626:, p.93
622:
443:Images
364:. The
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