428:
476:
that led to equal upward loadings on the horizontal panels of the box. But the optimum lift distribution is not unique. A constant inward loading (corresponding to a particular constant circulation) can be added to a classical loading like that shown by Durand to obtain a loading like those in the quasi-closed cases below. The two methods of analysis give different-looking versions of the optimum loading that are not fundamentally different. Except for small differences due to the numerical method used for the quasi-closed cases, the two kinds of loading are in principle just shifted versions of each other.
381:
460:
342:
78:
170:
455:
Each of the first three rows in the illustration shows a different C-wing configuration as it is taken through a sequence of theoretical induced-drag calculations in which the wingtips are brought closer together, culminating in the limiting case on the right, where the gap has been taken to zero and
475:
The lift distributions shown here for the quasi-closed cases look different from those typically shown for box wings in the classical literature (see Durand, figure 81, for example). The classical solution in Durand was obtained by a conformal-mapping analysis that happened to be formulated in a way
471:
Note that all of the C-wing configurations have ε greater than 1 and that there is little difference (no difference to the two decimal places shown in two of the cases) between a configuration with a substantial gap (the second entry in each row) and the corresponding closed configuration (the third
451:
The C-wing is a theoretical configuration in which much of the upper centre section of a box wing is removed, creating a wing that folds up and over at the tips but does not rejoin in the centre. A C-wing can achieve very nearly the same induced-drag performance as a corresponding box wing, as shown
124:
For any lifting system (or portion of a lifting system) that forms a closed loop as viewed in the freestream flow direction, the optimum lift (or circulation) distribution that yields the minimum induced drag for a given total vertical lift is not unique, but is defined only to within a constant on
843:
467:
The parameter ε is the optimal aerodynamic efficiency ratio and represents the ratio between the aerodynamic efficiency of a given non-planar wing and the corresponding efficiency of a reference classical cantilevered wing with the same wing span and total lift. Both efficiencies are evaluated for
435:
IDINTOS (IDrovolante INnovativo TOScano) is a research project, co-funded by the regional government of
Tuscany (Italy) in 2011 in order to design and manufacture an amphibious ultralight PrandtlPlane. The research project has been carried out by a consortium of Tuscan public and private partners,
404:
suggested that a box wing, under certain conditions, might provide the minimum induced drag for a given lift and wingspan. In his design, two offset horizontal wings have vertical wings connecting their tips and shaped to provide a linear distribution of side forces. The configuration is said to
360:
Closed wings remain mostly confined to the realms of studies and conceptual designs, as the engineering challenges of developing a strong, self-supporting closed wing for use in the large airliners which would benefit most from increases in efficiency have yet to be overcome.
125:
the closed-loop portion. This is because, regardless of what the circulation distribution is to start with, a constant circulation can be added to the closed-loop portion without changing the total lift of the system or the induced drag. This is the key to explaining how the
116:
is a closed system, i.e. a rectangular box wing with lifting surfaces fully occupying all four boundaries of the allowed rectangular area. However, the induced-drag performance of the ideal closed box wing can be approached very closely by open configurations such as the
443:, must make efficiency trade-offs to keep the wingspan below the 80-meter limit at most airports, but a closed wing with optimal wingspan could be shorter than that of conventional designs, potentially allowing even larger aircraft to use the current infrastructure.
720:
392:'s Aeronautics Research Mission Directorate invited study proposals towards meeting NASA's goal of reducing future aircraft fuel consumption by 50% compared to 1998. Lockheed Martin proposed a box wing design along with other advanced technologies.
133:
The upshot is that although closed systems can produce large induced-drag reductions relative to a conventional planar wing, there is no significant aerodynamic advantage that uniquely accrues to their being closed rather than open.
472:
entry in each row). This is because the optimum lift loading calculated for the quasi-closed cases is very small over the upper centre section, and that part of the wing can be removed with little change in lift or drag.
324:
has since its maiden flight in 2007, been the only manned annular closed wing aircraft to have successfully maintained stable horizontal flight. Flight tests showed that annular closed wing aircraft are less affected by
107:
For a lifting system constrained to fit within a rectangular box of fixed horizontal (spanwise) and vertical dimensions as viewed in the freestream flow direction, the configuration that provides the absolute minimum
282:
continued to develop the idea in the 1980s, claiming it was an efficient structural arrangement in which the horizontal tail provided structural support for the wing as well as acting as a stabilizing surface.
266:
annular wing aircraft. The aircraft proved dangerously unstable despite the development and testing of several prototypes, and the design was abandoned. Later proposals for closed-wing designs included the
62:
which occur at the tips of conventional wings. Although the closed wing has no unique claim on such benefits, many closed wing designs do offer structural advantages over a conventional
220:
in which the fore and aft segments were on the same level. The first was a biplane. It was followed by a series of monoplanes, the last of the line remaining in use until 1914.
1268:
1350:
456:
the configuration has become a closed box wing (referred to as the "Quasi-closed C-wing" because the calculations were carried out in the limit as the gap went to zero).
436:
led by the
Aerospace Section of the Civil and Industrial Engineering Department of Pisa University, and has resulted in the manufacturing of a 2-seater VLA prototype.
468:
their respective optimal lift distributions. Values of ε greater than 1 indicate lower induced drag than that of a classical cantilevered wing for which ε = 1.
694:
96:, which is a significant contributor to total drag in most regimes. A closed wing avoids the need for wingtips and thus might be expected to reduce wingtip
1073:
817:
866:
431:
Full-scale prototype of an ultralight amphibious
PrandtlPlane, developed during IDINTOS project and presented at Creactivity 2013 (Pontedera, Italy).
1012:
512:
1099:
646:
941:
427:
1366:
1320:
575:
1044:
103:
In addition to potential structural advantages over open cantilevered wings, closed wing surfaces have some unique aerodynamic properties:
838:
1433:
554:. Aerodynamic Theory: a General Review of Progress Under a Grant of the Guggenheim Fund for the Promotion of Aeronautics. Vol. 2.
895:
1304:
858:
439:
The configuration is also claimed to be theoretically efficient for wide-body jet airliners. The largest commercial airliner, the
734:
217:
980:
1454:
294:, is a closed wing surface mounted at the end of a conventional wing. The company announced that the winglets fitted to a
1459:
668:
1164:
841:, Gratzer, Louis B., "Spiroid-tipped wing", issued 1992-04-07, assigned to Aviation Partners Boeing
807:
1136:
673:
539:
129:
produces nearly the same induced-drag reduction as the corresponding fully closed system, as discussed below.
259:
1418:
1395:
600:
291:
206:
503:
1192:
1002:
380:
321:
1213:
Cipolla, Vittorio; Frediani, Aldo; Oliviero, F.; Pinucci, M.; Rizzo, Emanuele; Rossi, R. (2016-07-01).
1107:
715:
638:
1226:
951:
916:
213:
202:
1163:. VKI Lecture Series on Innovative Configurations and Advanced Concepts for Future Civil Aircraft.
946:
739:
511:. VKI Lecture Series on Innovative Configurations and Advanced Concepts for Future Civil Aircraft.
421:
306:
1260:
417:
412:
used this approach. The name "PrandtlPlane" was coined in the 1990s in research by Aldo
Frediani
330:
40:
35:
that effectively has two main planes which merge at their ends so that there are no conventional
1291:
1034:
1437:
1362:
1316:
1252:
1081:
812:
789:
765:
686:
678:
612:
604:
571:
547:
279:
109:
1343:"An Invariant Formulation for the Minimum Induced Drag Conditions of Non-planar Wing Systems"
1354:
1308:
1297:
Variational
Analysis and Aerospace Engineering: Mathematical Challenges for Aerospace Design
1242:
1234:
781:
563:
190:
85:
59:
1039:
620:
559:
459:
272:
89:
63:
1230:
81:
The
Spiroid winglet is a closed wing surface attached to the tip of a conventional wing.
1065:
891:
409:
401:
242:
194:
186:
97:
55:
1448:
1341:
Demasi, Luciano; Dipace, Antonio; Monegato, Giovanni; Cavallaro, Rauno (2014-01-10).
1292:"The PrandtlPlane Configuration: Overview on Possible Applications to Civil Aviation"
1264:
1214:
295:
233:
198:
174:
744:
209:. It was able to leave the ground in small hops before being damaged beyond repair.
310:
229:
113:
93:
1312:
972:
543:
440:
197:. The lifting surfaces comprised two annular wings mounted in tandem. The later
177:
replaced the forward one of its predecessor's annular wings with a conventional
1158:
341:
1085:
690:
567:
369:
326:
1256:
793:
682:
365:
66:
718:, Wolkovitch, Julian, "Joined wing aircraft", issued 1982-12-28
624:
616:
36:
1358:
1247:
1128:
17:
1238:
887:
463:
Nonplanar wings: results for the optimal aerodynamic efficiency ratio ε
317:
302:
287:
268:
178:
169:
1342:
336:
Aircraft wing configuration with a non-planar, continuous surface wing
58:, the closed wing aims to reduce the wasteful effects associated with
1300:
596:
555:
255:
785:
77:
271:
Model 49 Advanced Aerial Fire
Support System (AAFSS) and the 1980s
769:
458:
426:
379:
340:
168:
76:
388:
1410:
1007:
608:
389:
263:
237:
32:
1387:
1188:
201:
replaced the forward annular wing with a biplane and added a
1299:. Springer Optimization and Its Applications. Vol. 66.
376:
1289:
Frediani, Aldo; Cipolla, Vittorio; Rizzo, Emanuele (2012).
51:), the joined wing, the box wing, and spiroid tip devices.
298:
reduced fuel consumption in the cruise phase by over 10%.
505:
Nonplanar Wing
Concepts For Increased Aircraft Efficiency
859:"FlyNano Goes Electric, Starts "Airborne Test Flights""
1336:
1334:
1332:
1215:"Ultralight amphibious PrandtlPlane: the final design"
552:
Division E: General Aerodynamic Theory-Perfect Fluids
212:
Based on the work of G.J.A. Kitchen, Cedric Lee and
405:offer improved efficiency for a range of aircraft.
1351:American Institute of Aeronautics and Astronautics
1290:
917:"ЭКСПЕРИМЕНТАЛЬНЫЙ САМОЛЕТ С ОВАЛЬНЫМ КРЫЛОМ OW-1"
808:"Types of Blended Winglets and Spiroid Technology"
142:Various types of closed wing have been described:
43:include the annular wing (commonly known as the
1033:Rosenblum, Andrew; Pastore, Rose (2012-05-01).
185:An early example of the closed wing was on the
1003:"New Ideas Sharpen Focus for Greener Aircraft"
8:
1074:National Advisory Committee for Aeronautics
364:The closed wing is also used in water, for
1295:. In Buttazzo, G.; Frediani, Aldo (eds.).
1183:
1181:
290:, a design currently under development by
1246:
534:
532:
1068:(1924). "Induced Drag of Multiplanes".
485:
452:by the calculations illustrated below.
349:Miscellaneous modern examples include:
735:"Future Technology and Aircraft Types"
497:
495:
493:
491:
489:
246:, but the project was soon abandoned.
1386:Filippone, Antonio (September 2006).
923:. Belarus Aerospace Museum - Borovaya
254:During the 1950s, the French company
7:
420:. It is currently also used in some
400:In 1924, the German aerodynamicist
384:AOK Spacejet at Paris Air Show 2013
368:fins of the type also known as the
240:multirole single-seater called the
305:flew a prototype of a closed wing
25:
1411:"Advanced Aircraft Configuration"
942:"Nonplanar Wings: Closed Systems"
236:began working on an annular-wing
1219:Aerotecnica Missili & Spazio
1011:. NASA Langley Research Center.
1001:Barnstorff, Kathy (2012-01-27).
1421:from the original on 2021-06-12
1415:Advanced Aircraft Configuration
1398:from the original on 2021-04-11
1392:Advanced Topics in Aerodynamics
1347:52nd Aerospace Sciences Meeting
1271:from the original on 2022-04-07
1195:from the original on 2021-05-06
1167:from the original on 2022-04-07
1139:from the original on 2022-01-02
1047:from the original on 2021-12-08
1015:from the original on 2022-03-25
983:from the original on 2021-06-12
898:from the original on 2022-03-16
869:from the original on 2022-04-07
820:from the original on 2021-05-18
770:"The joined wing - An overview"
697:from the original on 2022-04-07
649:from the original on 2021-12-28
518:from the original on 2022-03-07
1:
1157:Frediani, Aldo (June 2005).
1106:. 2010-09-20. Archived from
155:Concentric wing and fuselage
1313:10.1007/978-1-4614-2435-2_8
674:Air & Space/Smithsonian
669:"Cancelled: Vertical Flyer"
667:Davis, Jeremy (July 2012).
591:Lewis, Peter M. H. (1962).
189:aircraft, built in 1906 by
126:
118:
112:for a given total vertical
1476:
857:Grady, Mary (2012-06-12).
593:British Aircraft 1809–1914
88:form a major component of
1388:"Non-Planar Wing systems"
568:10.1007/978-3-642-91485-0
1434:"Convair Model 49 image"
1100:"Ligeti Stratos History"
1076:Technical note No. 182.
1035:"The Jets of the Future"
502:Kroo, Ilan (June 2005).
92:and are associated with
921:Белорусский авиадневник
639:"Heinkel Lerche (Lark)"
329:then planes with other
218:annular-wing aeroplanes
216:built and flew several
205:foreplane to make it a
1349:. AIAA SciTech Forum.
464:
432:
385:
346:
345:An annular closed wing
207:three-surface aircraft
182:
82:
839:US patent 5102068
716:US patent 4365773
462:
430:
383:
344:
322:experimental aircraft
275:"Ring Wing" concept.
172:
80:
1455:Aircraft wing design
1307:. pp. 179–210.
603:. pp. 340–343.
301:The Finnish company
214:G. Tilghman Richards
1460:Wing configurations
1359:10.2514/6.2014-0901
1231:2016AeMiS..95..125C
1070:Technische Berichte
947:Stanford University
774:Journal of Aircraft
740:Stanford University
422:ultralight aircraft
331:wing configurations
307:ultralight aircraft
1239:10.1007/BF03404721
973:"Turbo Tunnel Fin"
766:Wolkovitch, Julian
548:Durand, William F.
465:
433:
418:University of Pisa
408:In the 1980s, the
386:
356:Lockheed ring-wing
347:
262:, a single-person
183:
83:
1368:978-1-62410-256-1
1322:978-1-4614-2434-5
813:Aviation Partners
577:978-3-642-89628-6
313:on 11 June 2012.
292:Aviation Partners
280:Julian Wolkovitch
152:Flat annular wing
16:(Redirected from
1467:
1441:
1436:. Archived from
1429:
1427:
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1160:The Prandtl Wing
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1148:
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1129:"Ligeti Stratos"
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950:. Archived from
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743:. Archived from
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396:Prandtl Box Wing
121:discussed below.
86:Wingtip vortices
60:wingtip vortices
21:
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1040:Popular Science
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560:Julius Springer
540:von Kármán, Th.
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149:Rhomboidal wing
140:
90:wake turbulence
75:
73:Characteristics
56:wingtip devices
23:
22:
15:
12:
11:
5:
1473:
1471:
1463:
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1457:
1447:
1446:
1443:
1442:
1440:on 2007-10-29.
1430:
1407:
1381:
1380:External links
1378:
1375:
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1328:
1321:
1281:
1225:(3): 125–135.
1205:
1177:
1149:
1133:Projet Plaisir
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1091:
1080:(7): 309–315.
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1025:
993:
964:
933:
908:
890:(2012-06-12).
879:
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799:
780:(3): 161–178.
768:(1986-03-01).
757:
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659:
645:. 2020-10-27.
630:
583:
576:
544:Burgers, J. M.
528:
484:
483:
481:
478:
448:
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410:Ligeti Stratos
402:Ludwig Prandtl
397:
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377:
374:
358:
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354:
353:Stanford study
335:
258:developed the
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195:Gabriel Voisin
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138:Configurations
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1135:(in French).
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1110:on 2013-09-17
1109:
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1104:LGT Aerospace
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954:on 2011-08-11
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234:Ernst Heinkel
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228:In 1944, the
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191:Louis Blériot
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165:Pioneer years
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19:
1438:the original
1423:. Retrieved
1414:
1400:. Retrieved
1391:
1346:
1296:
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1273:. Retrieved
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211:
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110:induced drag
102:
94:induced drag
84:
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44:
41:wing designs
28:
26:
1066:Prandtl, L.
977:TurboTunnel
441:Airbus A380
320:built OW-1
187:Blériot III
45:cylindrical
29:closed wing
1449:Categories
1425:2022-04-07
1402:2022-04-07
1275:2022-04-07
1199:2022-04-07
1171:2022-04-07
1143:2022-04-07
1114:2022-04-07
1086:1121049802
1051:2012-12-17
1019:2012-12-17
987:2022-04-13
958:2012-07-04
927:2024-05-16
902:2012-07-07
892:"Airborne"
873:2012-07-07
824:2022-04-07
751:2012-07-04
701:2022-04-07
691:1054386888
653:2022-04-07
522:2022-04-07
480:References
370:tunnel fin
327:cross wind
318:Belarusian
260:Coléoptère
199:Blériot IV
175:Blériot IV
64:cantilever
54:Like many
1265:195242441
1257:0365-7442
1189:"IDINTOS"
794:0021-8669
683:0886-2257
366:surfboard
232:designer
100:effects.
67:monoplane
49:ring wing
39:. Closed
37:wing tips
1419:Archived
1396:Archived
1305:Springer
1269:Archived
1193:Archived
1165:Archived
1137:Archived
1045:Archived
1013:Archived
981:Archived
896:Archived
867:Archived
818:Archived
695:Archived
647:Archived
625:5924340M
609:64035723
546:(1935).
513:Archived
273:Lockheed
146:Box wing
18:Box wing
1227:Bibcode
888:FlyNano
617:1301968
550:(ed.).
416:of the
303:FlyNano
288:winglet
269:Convair
250:Postwar
179:biplane
160:History
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597:London
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556:Berlin
447:C-wing
414:et al.
309:, the
256:SNECMA
243:Lerche
230:German
203:canard
127:C-wing
119:C-wing
1261:S2CID
863:AVweb
516:(PDF)
509:(PDF)
31:is a
1363:ISBN
1317:ISBN
1253:ISSN
1082:OCLC
1008:NASA
790:ISSN
687:OCLC
679:ISSN
613:OCLC
605:LCCN
572:ISBN
390:NASA
316:The
278:Dr.
264:VTOL
238:VTOL
193:and
181:wing
173:The
114:lift
98:drag
33:wing
1355:doi
1309:doi
1243:hdl
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