725:
379:. The choice of the reference surface should be specified since it is arbitrary. For example, for cylindric profiles (the 3D extrusion of an airfoil in the spanwise direction), the first axis generating the surface is always in the spanwise direction. In aerodynamics and thin airfoil theory, the second axis is commonly in the chordwise direction:
251:
941:
with a gradient known as the lift slope. For a thin airfoil of any shape the lift slope is π/90 ≃ 0.11 per degree. At higher angles a maximum point is reached, after which the lift coefficient reduces. The angle at which maximum lift coefficient occurs is the
949:
The stall angle for a given profile is also increasing with increasing values of the
Reynolds number, at higher speeds indeed the flow tends to stay attached to the profile for longer delaying the stall condition. For this reason sometimes
703:
497:
617:
861:
777:
The section lift coefficient is based on two-dimensional flow over a wing of infinite span and non-varying cross-section so the lift is independent of spanwise effects and is defined in terms of
136:
423:
926:, calculated numerically or determined from wind tunnel tests on a finite-length test piece, with end-plates designed to ameliorate the three-dimensional effects. Plots of
764:
546:
802:
353:
910:
885:
377:
322:
301:
276:
972:, i.e. asymmetrical, convex from above, there is still a small but positive lift coefficient with angles of attack less than zero. That is, the angle at which
954:
testing performed at lower
Reynolds numbers than the simulated real life condition can sometimes give conservative feedback overestimating the profiles stall.
628:
1208:
434:
557:
912:
is chosen. Note this is directly analogous to the drag coefficient since the chord can be interpreted as the "area per unit span".
979:= 0 is negative. On such airfoils at zero angle of attack the pressures on the upper surface are lower than on the lower surface.
810:
246:{\displaystyle C_{\mathrm {L} }\equiv {\frac {L}{q\,S}}={\frac {L}{{\frac {1}{2}}\rho u^{2}\,S}}={\frac {2L}{\rho u^{2}S}}}
17:
1172:
1127:
937:, but the particular numbers will vary. They show an almost linear increase in lift coefficient with increasing
887:
is the reference length that should always be specified: in aerodynamics and airfoil theory usually the airfoil
766:. It is common to show, for a particular airfoil section, the relationship between section lift coefficient and
502:
While in marine dynamics and for thick airfoils, the second axis is sometimes taken in the thickness direction:
1203:
385:
732:
Lift coefficient may also be used as a characteristic of a particular shape (or cross-section) of an
1008:
742:
508:
780:
998:
70:
50:
728:
A typical curve showing section lift coefficient versus angle of attack for a cambered airfoil
1198:
969:
337:
8:
923:
894:
869:
709:
361:
306:
285:
260:
74:
1182:
988:
1168:
1123:
946:
angle of the airfoil, which is approximately 10 to 15 degrees on a typical airfoil.
993:
888:
771:
325:
112:
770:. It is also useful to show the relationship between section lift coefficient and
1003:
938:
767:
698:{\displaystyle C_{\mathrm {L} ,\,mar}\equiv {\frac {c}{t}}C_{\mathrm {L} ,\,aer}}
108:
91:
87:
1013:
943:
66:
31:
27:
Dimensionless quantity relating lift to fluid density and velocity over an area
1192:
1049:
62:
1160:
279:
58:
54:
951:
891:
is chosen, while in marine dynamics and for struts usually the thickness
713:
95:
356:
804:, the lift force per unit span of the wing. The definition becomes
492:{\displaystyle C_{\mathrm {L} ,\,aer}\equiv {\frac {L}{q\,c\,s}},}
934:
733:
622:
The ratio between these two coefficients is the thickness ratio:
612:{\displaystyle C_{\mathrm {L} ,\,mar}\equiv {\frac {L}{q\,t\,s}}}
332:
724:
329:
933:
versus angle of attack show the same general shape for all
1036:. New York: John Wiley & Sons. Sections 4.15 & 5.4.
111:
foil section, with the reference area replaced by the foil
1145:
856:{\displaystyle c_{\text{l}}={\frac {L^{\prime }}{q\,c}},}
69:
and an associated reference area. A lifting body is a
897:
872:
813:
783:
745:
631:
560:
511:
437:
388:
364:
340:
309:
288:
263:
139:
1177:
Abbott, Ira H., and
Doenhoff, Albert E. von (1959):
708:The lift coefficient can be approximated using the
904:
879:
855:
796:
758:
697:
611:
540:
491:
417:
371:
347:
316:
295:
270:
245:
1122:. Cambridge, MA: Bentley Publishers. p. 93.
1190:
107:refers to the dynamic lift characteristics of a
957:Symmetric airfoils necessarily have plots of c
1091:Abbott, Ira H., and Von Doenhoff, Albert E.:
1142:
961:versus angle of attack symmetric about the
719:
716:test of a complete aircraft configuration.
712:, numerically calculated or measured in a
1147:. Cambridge University Press. p. 525.
922:can be calculated approximately using the
73:or a complete foil-bearing body such as a
901:
876:
843:
683:
645:
602:
598:
574:
534:
479:
475:
451:
411:
368:
344:
313:
292:
267:
203:
164:
1209:Dimensionless numbers of fluid mechanics
1045:
1043:
968:axis, but for any airfoil with positive
736:. In this application it is called the
723:
14:
1191:
1031:
551:resulting in a different coefficient:
1167:. Pitman Publishing Limited, London,
1040:
1025:
1117:
24:
834:
789:
676:
638:
567:
444:
418:{\displaystyle S_{aer}\equiv c\,s}
146:
25:
1220:
303:is the relevant surface area and
1052:, and Doenhoff, Albert E. von:
98:. The section lift coefficient
1136:
1111:
1098:
1085:
1072:
1059:
118:
13:
1:
1154:
915:For a given angle of attack,
90:of the body to the flow, its
1143:Katz, J; Plotkin, A (2001).
759:{\displaystyle c_{\text{l}}}
541:{\displaystyle S_{mar}=t\,s}
428:resulting in a coefficient:
7:
982:
797:{\displaystyle L^{\prime }}
10:
1225:
1019:
1009:Circulation control wing
738:section lift coefficient
720:Section lift coefficient
328:, in turn linked to the
1185:New York, # 486-60586-8
1179:Theory of Wing Sections
1093:Theory of Wing Sections
1054:Theory of Wing Sections
348:{\displaystyle \rho \,}
1032:Clancy, L. J. (1975).
999:Foil (fluid mechanics)
906:
881:
857:
798:
760:
729:
699:
613:
542:
493:
419:
373:
349:
318:
297:
272:
247:
51:dimensionless quantity
1120:Race Car Aerodynamics
907:
882:
858:
799:
761:
727:
700:
614:
543:
494:
420:
374:
350:
319:
298:
273:
248:
123:The lift coefficient
86:is a function of the
65:around the body, the
1204:Aircraft wing design
895:
870:
811:
781:
743:
629:
558:
509:
435:
386:
362:
338:
307:
286:
261:
137:
924:thin airfoil theory
905:{\displaystyle t\,}
880:{\displaystyle c\,}
710:lifting-line theory
372:{\displaystyle u\,}
317:{\displaystyle q\,}
296:{\displaystyle S\,}
271:{\displaystyle L\,}
75:fixed-wing aircraft
18:Coefficient of lift
1183:Dover Publications
989:Lift-to-drag ratio
902:
877:
853:
794:
756:
730:
695:
609:
538:
489:
415:
369:
345:
314:
293:
268:
243:
1118:Katz, J. (2004).
848:
821:
753:
668:
607:
484:
241:
208:
188:
169:
53:that relates the
16:(Redirected from
1216:
1149:
1148:
1140:
1134:
1133:
1115:
1109:
1102:
1096:
1089:
1083:
1076:
1070:
1063:
1057:
1047:
1038:
1037:
1029:
994:Drag coefficient
911:
909:
908:
903:
886:
884:
883:
878:
862:
860:
859:
854:
849:
847:
838:
837:
828:
823:
822:
819:
803:
801:
800:
795:
793:
792:
772:drag coefficient
765:
763:
762:
757:
755:
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704:
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696:
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679:
669:
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641:
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570:
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326:dynamic pressure
323:
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202:
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189:
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175:
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168:
156:
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106:
85:
48:
36:lift coefficient
21:
1224:
1223:
1219:
1218:
1217:
1215:
1214:
1213:
1189:
1188:
1157:
1152:
1141:
1137:
1130:
1116:
1112:
1104:Clancy, L. J.:
1103:
1099:
1090:
1086:
1078:Clancy, L. J.:
1077:
1073:
1065:Clancy, L. J.:
1064:
1060:
1048:
1041:
1030:
1026:
1022:
1004:Pitching moment
985:
978:
967:
960:
939:angle of attack
932:
921:
896:
893:
892:
871:
868:
867:
839:
833:
829:
827:
818:
814:
812:
809:
808:
788:
784:
782:
779:
778:
768:angle of attack
750:
746:
744:
741:
740:
722:
675:
674:
670:
660:
637:
636:
632:
630:
627:
626:
594:
589:
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556:
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516:
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510:
507:
506:
471:
466:
443:
442:
438:
436:
433:
432:
393:
389:
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384:
383:
363:
360:
359:
339:
336:
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308:
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304:
287:
284:
283:
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231:
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197:
193:
180:
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155:
145:
144:
140:
138:
135:
134:
129:
121:
109:two-dimensional
105:
99:
92:Reynolds number
84:
78:
57:generated by a
46:
39:
28:
23:
22:
15:
12:
11:
5:
1222:
1212:
1211:
1206:
1201:
1187:
1186:
1175:
1156:
1153:
1151:
1150:
1135:
1128:
1110:
1097:
1084:
1082:. Section 8.11
1071:
1069:. Section 4.15
1058:
1050:Abbott, Ira H.
1039:
1023:
1021:
1018:
1017:
1016:
1014:Zero lift axis
1011:
1006:
1001:
996:
991:
984:
981:
976:
965:
958:
930:
919:
900:
875:
864:
863:
852:
846:
842:
836:
832:
826:
817:
791:
787:
749:
721:
718:
706:
705:
692:
689:
686:
682:
678:
673:
667:
664:
659:
654:
651:
648:
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640:
635:
620:
619:
605:
601:
597:
593:
588:
583:
580:
577:
573:
569:
564:
549:
548:
537:
533:
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519:
515:
500:
499:
488:
482:
478:
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460:
457:
454:
450:
446:
441:
426:
425:
414:
410:
407:
402:
399:
396:
392:
367:
343:
312:
291:
266:
255:
254:
239:
234:
230:
226:
221:
218:
212:
206:
200:
196:
192:
187:
184:
178:
173:
167:
163:
159:
154:
148:
143:
130:is defined by
127:
120:
117:
103:
82:
67:fluid velocity
44:
32:fluid dynamics
26:
9:
6:
4:
3:
2:
1221:
1210:
1207:
1205:
1202:
1200:
1197:
1196:
1194:
1184:
1180:
1176:
1174:
1173:0-273-01120-0
1170:
1166:
1162:
1159:
1158:
1146:
1139:
1131:
1129:0-8376-0142-8
1125:
1121:
1114:
1108:. Section 8.2
1107:
1101:
1095:. Appendix IV
1094:
1088:
1081:
1075:
1068:
1062:
1056:. Section 1.2
1055:
1051:
1046:
1044:
1035:
1028:
1024:
1015:
1012:
1010:
1007:
1005:
1002:
1000:
997:
995:
992:
990:
987:
986:
980:
975:
971:
964:
955:
953:
947:
945:
940:
936:
929:
925:
918:
913:
898:
890:
873:
850:
844:
840:
830:
824:
815:
807:
806:
805:
785:
775:
773:
769:
747:
739:
735:
726:
717:
715:
711:
690:
687:
684:
680:
671:
665:
662:
657:
652:
649:
646:
642:
633:
625:
624:
623:
603:
599:
595:
591:
586:
581:
578:
575:
571:
562:
554:
553:
552:
535:
531:
528:
523:
520:
517:
513:
505:
504:
503:
486:
480:
476:
472:
468:
463:
458:
455:
452:
448:
439:
431:
430:
429:
412:
408:
405:
400:
397:
394:
390:
382:
381:
380:
365:
358:
355:, and to the
341:
334:
331:
327:
324:is the fluid
310:
289:
281:
264:
237:
232:
228:
224:
219:
216:
210:
204:
198:
194:
190:
185:
182:
176:
171:
165:
161:
157:
152:
141:
133:
132:
131:
126:
116:
114:
110:
102:
97:
93:
89:
81:
76:
72:
68:
64:
63:fluid density
60:
56:
52:
47:
43:
37:
33:
19:
1199:Aerodynamics
1178:
1165:Aerodynamics
1164:
1161:L. J. Clancy
1144:
1138:
1119:
1113:
1106:Aerodynamics
1105:
1100:
1092:
1087:
1080:Aerodynamics
1079:
1074:
1067:Aerodynamics
1066:
1061:
1053:
1034:Aerodynamics
1033:
1027:
973:
962:
956:
948:
927:
916:
914:
865:
776:
737:
731:
707:
621:
550:
501:
427:
256:
124:
122:
100:
79:
59:lifting body
41:
40:
35:
29:
952:wind tunnel
714:wind tunnel
119:Definitions
96:Mach number
1193:Categories
1155:References
357:flow speed
280:lift force
835:′
790:′
658:≡
587:≡
464:≡
406:≡
342:ρ
225:ρ
191:ρ
153:≡
1163:(1975):
983:See also
935:airfoils
94:and its
734:airfoil
333:density
278:is the
257:where
61:to the
49:) is a
1171:
1126:
970:camber
866:where
34:, the
1020:Notes
944:stall
889:chord
330:fluid
113:chord
88:angle
1169:ISBN
1124:ISBN
71:foil
55:lift
30:In
1195::
1181:,
1042:^
774:.
282:,
115:.
77:.
1132:.
977:l
974:c
966:l
963:c
959:l
931:l
928:c
920:l
917:c
899:t
874:c
851:,
845:c
841:q
831:L
825:=
820:l
816:c
786:L
752:l
748:c
691:r
688:e
685:a
681:,
677:L
672:C
666:t
663:c
653:r
650:a
647:m
643:,
639:L
634:C
604:s
600:t
596:q
592:L
582:r
579:a
576:m
572:,
568:L
563:C
536:s
532:t
529:=
524:r
521:a
518:m
514:S
487:,
481:s
477:c
473:q
469:L
459:r
456:e
453:a
449:,
445:L
440:C
413:s
409:c
401:r
398:e
395:a
391:S
366:u
311:q
290:S
265:L
253:,
238:S
233:2
229:u
220:L
217:2
211:=
205:S
199:2
195:u
186:2
183:1
177:L
172:=
166:S
162:q
158:L
147:L
142:C
128:L
125:C
104:l
101:c
83:L
80:C
45:L
42:C
38:(
20:)
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