638:
proper turbulence models and transition models should be carefully selected. Furthermore, this method is also sometimes too computationally costly for research purposes as well as the pre-design of a helicopter rotor. On the other hand, to date some semi-empirical models have shown their capability of providing adequate precision, which contains sets of linear and nonlinear equations, based on classical unsteady thin-airfoil theory and parameterized by empirical coefficients. Therefore, a large number of experimental results are demanded to correct the empirical coefficients, and it is foreseeable that these models cannot be generally adapted to a wide range of conditions such as different airfoils, Mach numbers, and so on.
468:
459:
412:
182:
337:
328:
117:
1348:
288:
421:
599:
276:
450:
19:
203:
Although the unsteady mechanism of idealized 2D experiments has already been studied comprehensively, the dynamic stall on a rotor presents strong three-dimensional character differences. According to a well-collected in-flight data by
Bousman, the generation location of the DSV is "tightly grouped",
435:
The effect of airfoil geometry on dynamic stall is quite intricate. As is shown in the figure, for a cambered airfoil, the lift stall is delayed and the maximum nose-down pitch moment is significantly reduced. On the other hand, the inception of stall is more abrupt for a sharp leading-edge airfoil.
624:
During forward flight, the blade element of a rotor will encounter a time-varying incident velocity, leading to additional unsteady aerodynamic characters. Several features have been discovered through experiments, for example, depending on the phasing of the velocity variations with respect to the
615:
Lorber et al. found that at the outermost wing station, the existence of the tip vortex gives both the steady and unsteady lift and pitching moment hysteresis loops a more nonlinear quasi-steady behaviour due to an element of steady vortex-induced lift, while for the rest of the wing stations where
193:
Stage 5: the full flow reattachment is achieved as the AoA gradually decreases until it is fairly smaller than the static stall angle. The reasons for the lag are, firstly, the reorganization of the flow from fully separated to reattached, and secondly, the reverse kinematic "induced camber" effect
637:
method. With regard to the latter method, because of the sophisticated flow field during the process of the dynamic stall, the full Navier-Stokes equations and proper models are adopted, and some promising results have been presented in the literature. However, to utilize this method precisely,
128:
experiments, it has been found that the behavior of an airfoil under unsteady motion is quite different from that under quasi-steady motion. Flow separation is less likely to happen on the upper airfoil surface with a larger value of AoA than the latter, which can increase the maximum lift
589:
Based on experimental data, a sweep angle of 30° is able to delay the onset of stall to a higher AoA thanks to the convection of the leading-edge vortex at a lower velocity and reduce the varying rate of lift, pitch moment, and the scale of hysteresis loops.
606:
As the figure suggests, the effect of
Reynolds numbers seems to be minor, with a low value of reduced frequency k=0.004, stall overshoot is minimal and most of the hysteresis loop is attributable to a delay in reattachment, rather than vortex shedding.
584:
371:
suggests a delay of the onset of flow separation at higher AoA, and a reduction of airloads overshoots and hysteresis is secured because of the increase of the kinematic induced camber effect. But when reduce frequency is rather low, i.e.
103:
The visualization is considered a vivid method to better understand the aerodynamic principle of the dynamic stall on a helicopter rotor, and the investigation generally starts from the analysis of the unsteady motion on 2D airfoil (see
1082:
877:
174:), provides an additional lift for the airfoil so long as it stays over the upper surface, and also noteworthy increases in nose-down pitching moment (moment break, moment stall) while it moves downstream across the chord.
1167:
305:
The increasing of the mean value of AoA leads to more evident flow separation, higher overshoots of lift and pitch moment, and larger airloads hysteresis, which may ultimately result in deep dynamic stall.
712:
482:
The sweep angle of the flow to a blade element for a helicopter in forward flight can be significant. It is defined as the radial component of the velocity relative to the leading edge of the blade:
1899:
Maresca, Christian A.; Favier, Daniel J.; Rebont, Jean M. (1981-04-01). "Unsteady
Aerodynamics of an Aerofoil at High Angle of Incidence Performing Various Linear Oscillations in a Uniform Stream".
65:
so low values of AOA is needed but shock-induced flow separation may happen, while the retreating blade operates at much lower Mach numbers but the high values of AoA result in the stall (also see
1304:
625:
AoA, initiation of LEV shedding and the chordwise convection of LEV appear to be different. However, more works are needed to better understand this problem adopting mathematical models.
1223:
66:
805:
488:
61:, the advancing and retreating blades almost reach their operation limits whereas flows are still attached to the blade surfaces. That is, the advancing blades operate at high
909:
163:
Stage 1: the AoA exceeds the static stall angle but the flow separation is delayed due to the reduction of adverse pressure gradients produced by the kinematics of pitch rate.
1372:
One significant advantage of the model is that it uses relatively few empirical coefficients, with all but four at each Mach number being derived from static airfoil data.
129:
coefficient to a certain extent. Three primary unsteady phenomena have been identified to contribute to the delay in the onset of flow separation under unsteady condition:
1009:
775:
745:
50:(AOA) of blade elements varies intensively due to time-dependent blade flapping, cyclic pitch and wake inflow. For example, during forward flight at the velocity close to
956:
396:
314:
The amplitude of oscillation is also an important parameter for the stall behaviour of an airfoil. With a larger oscillating angle, deep dynamic stall tends to occur.
976:
1334:
166:
Stage 2: flow separation and the formation of a vortex disturbance is cast-off from the leading edge region of the airfoil. This vortex, called leading edge vortex (
144:
By virtue of a kinematic induced camber effect, a positive pitch rate further decreases the leading edge pressure and pressure gradients for a given value of lift;
133:
During the condition where the AoA is increasing with respect to time, the unsteadiness of the flow resulting from circulation that is shed into the wake at the
929:
369:
42:
occurs at relatively low flight speed, the dynamic stall on a helicopter rotor emerges at high airspeeds or/and during manoeuvres with high load factors of
1014:
1842:
Pierce, G. Alvin; Kunz, Donald L.; Malone, John B. (1978-04-01). "The Effect of
Varying Freestream Velocity on Airfoil Dynamic Stall Characteristics".
812:
1819:
Lorber, Peter; Covino, Jr., Alfred; Carta, Franklin (1991-06-24). "Dynamic stall experiments on a swept three-dimensional wing incompressible flow".
1661:
Khalifa, Nabil M.; Rezaei, Amir S.; Taha, Haithem E. (2021). "Comparing the performance of different turbulence models in predicting dynamic stall".
1362:
Attached flow model for the unsteady (linear) airloads (with compressibility effects included) using the compressible indicial response functions;
1089:
1869:
Favier, D.; Agnes, A.; Barbi, C.; Maresca, C. (September 1988). "Combined translation/pitch motion - A new airfoil dynamic stall simulation".
190:
Stage 4: full separation of the flow on the upper surface of the airfoil can be observed, accompanied by the peak of nose-down pitch moment.
1463:
McCroskey, W. J.; Fisher, Richard K. (1972-01-01). "Detailed
Aerodynamic Measurements on a Model Rotor in the Blade Stall Regime".
2047:
1787:
655:
1942:
1978:
1678:
1506:
1228:
2020:
2118:
Tyler, Joseph C.; Leishman, J. Gordon (1992-07-01). "Analysis of Pitch and Plunge
Effects on Unsteady Airfoil Behavior".
1702:
Green, R. B.; Galbraith, R. A. McD. (August 1995). "Dynamic recovery to fully attached aerofoil flow from deep stall".
1355:
The model was initially developed by
Beddoes and Leishman&Beddoes and refined by Leishman and Tyler&Leishman.
633:
There are mainly two types of mathematical models to predict the dynamic stall behaviour: semi-empirical models and
2151:
177:
Stage 3: a steep decrease of the lift coefficient (lift break, lift stall) occurs as the DSV passes into the wake.
1806:
The influence of sweep on the aerodynamic loading of an oscillating NACA 0012 airfoil. Volume 1: Technical report
204:
where lift overshoots and large nose-down pitching moments are featured and can be classified into three groups.
147:
In response to the external pressure gradients, there are also additional unsteady effects that occur within the
467:
1172:
458:
411:
641:
Here, two typical semi-empirical methods are presented to give insights into the modelling of dynamic stall.
1788:
An experimental investigation of the influence of a range of aerofoil design features on dynamic stall onset
1549:
Carta, Franklin O. (October 1971). "Effect of
Unsteady Pressure Gradient Reduction on Dynamic Stall Delay".
1011:
derived from
Theodorsen's theory at the appropriate reduced frequency of the forcing and a reference angle
634:
1961:
Dumlupinar, Ercan; Murthy, V (2011-06-27). "Investigation of
Dynamic Stall of Airfoils and Wings by CFD".
978:
function is empirical, depends on geometry and Mach number and is different for lift and pitching moment.
579:{\displaystyle \Lambda =\arctan {\frac {U_{R}}{U_{T}}}=\arctan {\frac {\mu \cos {\psi }}{r+\sin {\psi }}}}
181:
780:
1737:
Bousman, William G. (1998-10-01). "A Qualitative Examination of Dynamic Stall from Flight Test Data".
885:
116:
1347:
34:, which can cause the onset of large torsional airloads and vibrations on the rotor blades. Unlike
2014:
A Mathematical Model of Unsteady Aerodynamics and Radial Flow for Application to Helicopter Rotors
984:
750:
720:
336:
327:
88:
High blade structural loads, which may result in excessive vibrations and blade structural damage;
2156:
934:
649:
The model was initially developed by Gross&Harris and Gormont, the basic idea is as follows:
1401:
1396:
1339:
A comprehensive analysis of a helicopter rotor using this model is presented in the reference.
981:
The airloads coefficients are constructed from static data using an equivalent angle of attack
375:
287:
70:
39:
420:
961:
598:
1603:
McAlister, K. W.; Carr, L. W. (1979-09-01). "Water Tunnel Visualizations of Dynamic Stall".
1309:
159:
The development process of dynamic stall on 2D airfoil can be summarized in several stages:
1711:
1358:
The model consists of three distinct sub-systems for describing the dynamic stall physics:
105:
2064:
Leishman, J. G.; Beddoes, T. S. (1989-07-01). "A Semi-Empirical Model for Dynamic Stall".
398:, the vortex-shedding phenomenon is not likely to happen, so does the deep dynamic stall.
8:
35:
1715:
1576:
Ericsson, Lars E.; Reding, J. Peter (1972-01-01). "Dynamic Stall of Helicopter Blades".
81:
The effect of dynamic stall limits the helicopter performance in several ways such as:
2038:
1684:
914:
354:
275:
1974:
1688:
1674:
1641:
Analysis of the development of dynamic stall based on oscillating airfoil experiments
1502:
1406:
1077:{\displaystyle \alpha _{r}=\alpha \pm \gamma {\sqrt {{\dot {\alpha }}c/V_{\infty }}}}
255:
232:
2127:
2100:
2073:
1998:. Proceedings of the 25th annual national forum of the American Helicopter Society.
1966:
1908:
1878:
1851:
1824:
1746:
1719:
1666:
1612:
1585:
1558:
1531:
1472:
1445:
1411:
1391:
31:
1416:
872:{\displaystyle \Delta \alpha _{D}=\gamma {\sqrt {{\dot {\alpha }}c/V_{\infty }}}}
152:
47:
1436:
Tarzanin, F. J. (1972-04-01). "Prediction of Control Loads Due to Blade Stall".
449:
2013:
148:
1927:
1805:
1765:
1764:
Mcalister, Kenneth W.; Carr, Lawremce W.; Mccroskey, William J. (1978-01-01).
1640:
1639:
Carr, Lawremce W.; Mcalister, Kenneth W.; Mccroskey, William J. (1977-01-01).
151:, including the existence of flow reversals in the absence of any significant
2145:
1928:
Dynamic stall of an oscillating wing. Part 1: Evaluation of turbulence models
1365:
Separated flow model for the nonlinear airloads (Kirchhoff-Helmholtz theory);
134:
616:
oscillations below stall, there is no particular difference from 2-D cases.
1522:
Ericsson, Lars Eric (September 1967). "Comment on unsteady airfoil stall".
1162:{\displaystyle C_{L}={\frac {\alpha _{eq}}{\alpha _{r}}}C_{L}(\alpha _{r})}
141:
and adverse pressure gradients compared to the steady case at the same AoA;
138:
2104:
2091:
Leishman, J. G. (1989-07-01). "Modeling Sweep Effects on Dynamic Stall".
1912:
1476:
125:
62:
2077:
1970:
1828:
1750:
1670:
2131:
1926:
Srinivasan, G. R.; Ekaterinaris, J. A.; Mccroskey, W. J. (1993-08-09).
1855:
1589:
1449:
1386:
1381:
222:
43:
18:
1804:
St.hilaire, A.O.; Carta, F.O.; Fink, M.R.; Jepson, W.D. (1979-05-01).
1616:
228:
The same order of the viscous zone thickness as the airfoil thickness;
1996:
Prediction of inflight stalled airloads from oscillating airfoil data
1944:
CFD study of three-dimensional dynamic stall various planform shapes
1882:
1723:
1562:
1535:
91:
Control system loads, manoeuvre capability, and handling qualities;
1368:
Dynamic stall model for the leading edge vortex-induced airloads.
194:
on the leading edge pressure gradient by the negative pitch rate.
1925:
1634:
1632:
1630:
1628:
1626:
707:{\displaystyle \alpha _{DS}=\alpha _{SS}+\Delta \alpha _{D}}
251:
Extension of the viscous zone to the order of airfoil chord;
1941:
Spentzos, A.; Barakos, G.N.; Badcock, K.J.; Richards, B.E.
1940:
1894:
1892:
1821:
22nd Fluid Dynamics, Plasma Dynamics and Lasers Conference
1757:
1803:
1623:
198:
51:
1889:
1868:
1501:(2nd ed.). Cambridge: Cambridge University Press.
185:
Rotor map of dynamic stall locations for all conditions
1818:
1763:
1638:
644:
1312:
1299:{\displaystyle C_{M}=(0.25-x_{CP})C_{L}(\alpha _{r})}
1231:
1175:
1092:
1017:
987:
964:
937:
917:
888:
815:
783:
753:
723:
658:
491:
378:
357:
1954:
2057:
1898:
120:
The events of dynamic stall on the NACA0012 airfoil
1766:Dynamic stall experiments on the NACA 0012 airfoil
1456:
1328:
1298:
1217:
1161:
1076:
1003:
970:
950:
923:
903:
871:
799:
769:
739:
706:
652:The onset of dynamic stall is assumed to occur at
578:
390:
363:
2111:
2046:. Prediction of Aerodynamic Loads on Rotorcraft.
1660:
1569:
1351:Flowchart of Leishman-Beddoes dynamic stall model
248:High deviations of airloads and large hysteresis;
2143:
1960:
1841:
1596:
111:
2063:
1862:
1462:
85:The maximum forward flight velocity and thrust;
2007:
2005:
1919:
1797:
1701:
1575:
1492:
1490:
1488:
1486:
2117:
1602:
245:Domination of the vortex-shedding phenomenon;
2084:
1934:
1835:
610:
345:Effect of reduced frequency on dynamic stall
293:Effect of oscillating angle on dynamic stall
2030:
2002:
1515:
1483:
1429:
602:Effect of Reynolds numbers on dynamic stall
429:Effect of airfoil geometry on dynamic stall
2120:Journal of the American Helicopter Society
2093:Journal of the American Helicopter Society
2066:Journal of the American Helicopter Society
1901:Journal of the American Helicopter Society
1844:Journal of the American Helicopter Society
1812:
1739:Journal of the American Helicopter Society
1578:Journal of the American Helicopter Society
1465:Journal of the American Helicopter Society
1438:Journal of the American Helicopter Society
1342:
1993:
1987:
1963:29th AIAA Applied Aerodynamics Conference
1779:
261:Rapid overshoots of airloads after stall.
137:of the airfoil causes a reduction in the
2090:
1542:
1521:
1496:
1435:
1346:
1218:{\displaystyle C_{D}=C_{D}(\alpha _{r})}
619:
597:
180:
115:
17:
2011:
1736:
2144:
1994:Gross, David W.; Franklin, D. Harris.
747:is the critical AoA of dynamic stall,
476:Effect of sweep angle on dynamic stall
254:Less sensitivity to airfoil geometry,
212:
199:Dynamic stall in the rotor environment
1785:
1548:
1499:Principles of helicopter aerodynamics
239:
221:Low deviations of airloads and small
76:
30:is one of the hazardous phenomena on
436:More information is available here.
351:A higher value of reduced frequency
317:
309:
2053:from the original on June 24, 2021.
2036:
2026:from the original on June 24, 2021.
645:Boeing-Vertol Gamma Function Method
401:
281:Effect of mean AoA on dynamic stall
13:
2040:Representation of airfoil behavior
1067:
943:
862:
816:
800:{\displaystyle \Delta \alpha _{D}}
784:
691:
593:
492:
14:
2168:
2012:Gormont, Ronald E. (1973-05-01).
1950:. 30th European Rotorcraft Forum.
1336:is the center point of rotation.
958:is the free-stream velocity. The
231:Sensitivity to airfoil geometry,
904:{\displaystyle {\dot {\alpha }}}
466:
457:
448:
419:
410:
335:
326:
286:
274:
98:
1730:
1695:
911:is the time derivative of AoA,
94:Helicopter dynamic performance.
67:advancing blade compressibility
1654:
1293:
1280:
1267:
1245:
1212:
1199:
1156:
1143:
439:
1:
1605:Journal of Fluids Engineering
1422:
112:Dynamic stall for 2D airfoils
1497:Leishman, J. Gordon (2006).
1004:{\displaystyle \alpha _{eq}}
770:{\displaystyle \alpha _{SS}}
740:{\displaystyle \alpha _{DS}}
635:computational fluid dynamics
628:
7:
1375:
951:{\displaystyle V_{\infty }}
300:
170:) or dynamic stall vortex (
10:
2173:
1786:Wilby, P.G. (1984-08-28).
265:
611:Three-dimensional effects
391:{\displaystyle k<0.05}
931:is the blade chord, and
777:is static stall AoA and
207:
2152:Helicopter aerodynamics
1663:AIAA Scitech 2021 Forum
1343:Leishman-Beddoes Method
971:{\displaystyle \gamma }
1402:retreating blade stall
1397:Stall (fluid dynamics)
1352:
1330:
1329:{\displaystyle x_{CP}}
1300:
1219:
1163:
1078:
1005:
972:
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905:
873:
801:
771:
741:
708:
603:
580:
392:
365:
218:Minor flow separation;
186:
121:
71:retreating blade stall
59:velocity, never exceed
23:
1350:
1331:
1301:
1220:
1164:
1079:
1006:
973:
953:
926:
906:
874:
802:
772:
742:
709:
620:Time-varying velocity
601:
581:
393:
366:
184:
119:
21:
2105:10.4050/JAHS.34.3.18
1913:10.4050/JAHS.26.2.40
1477:10.4050/JAHS.17.1.20
1310:
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1173:
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985:
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489:
376:
355:
106:Blade element theory
22:Dynamic stall region
2078:10.4050/JAHS.34.3.3
1971:10.2514/6.2011-3511
1871:Journal of Aircraft
1829:10.2514/6.1991-1795
1751:10.4050/JAHS.43.279
1716:1995AIAAJ..33.1433G
1671:10.2514/6.2021-1651
1551:Journal of Aircraft
1524:Journal of Aircraft
213:Light dynamic stall
36:fixed-wing aircraft
2132:10.4050/JAHS.37.69
1856:10.4050/JAHS.23.27
1590:10.4050/JAHS.17.11
1450:10.4050/JAHS.17.33
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576:
388:
361:
240:Deep dynamic stall
187:
122:
77:Performance limits
24:
1980:978-1-62410-145-8
1680:978-1-62410-609-5
1617:10.1115/1.3448981
1508:978-0-521-85860-1
1407:Reduced frequency
1131:
1072:
1051:
924:{\displaystyle c}
898:
867:
846:
574:
526:
364:{\displaystyle k}
318:Reduced frequency
310:Oscillating angle
256:reduced frequency
233:reduced frequency
32:helicopter rotors
2164:
2136:
2135:
2115:
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1710:(8): 1433–1440.
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1412:Lift coefficient
1392:Helicopter rotor
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402:Airfoil geometry
397:
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389:
370:
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339:
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290:
278:
258:and Mach number;
235:and Mach number.
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2165:
2163:
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2161:
2142:
2141:
2140:
2139:
2116:
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2062:
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2043:
2037:Beddoes, T. S.
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2016:
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2003:
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1883:10.2514/3.45663
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1762:
1758:
1735:
1731:
1724:10.2514/3.12565
1700:
1696:
1681:
1659:
1655:
1646:
1644:
1637:
1624:
1601:
1597:
1574:
1570:
1563:10.2514/3.59179
1557:(10): 839–841.
1547:
1543:
1536:10.2514/3.43872
1520:
1516:
1509:
1495:
1484:
1461:
1457:
1434:
1430:
1425:
1417:Angle of attack
1378:
1345:
1317:
1313:
1311:
1308:
1307:
1287:
1283:
1274:
1270:
1258:
1254:
1236:
1232:
1230:
1227:
1226:
1206:
1202:
1193:
1189:
1180:
1176:
1174:
1171:
1170:
1150:
1146:
1137:
1133:
1125:
1121:
1112:
1108:
1106:
1097:
1093:
1091:
1088:
1087:
1066:
1062:
1057:
1043:
1042:
1040:
1022:
1018:
1016:
1013:
1012:
992:
988:
986:
983:
982:
963:
960:
959:
942:
938:
936:
933:
932:
916:
913:
912:
890:
889:
887:
884:
883:
861:
857:
852:
838:
837:
835:
823:
819:
814:
811:
810:
791:
787:
782:
779:
778:
758:
754:
752:
749:
748:
728:
724:
722:
719:
718:
698:
694:
679:
675:
663:
659:
657:
654:
653:
647:
631:
622:
613:
596:
594:Reynolds number
568:
555:
549:
539:
537:
520:
516:
510:
506:
504:
490:
487:
486:
480:
479:
478:
477:
473:
472:
471:
463:
462:
454:
453:
442:
433:
432:
431:
430:
426:
425:
424:
416:
415:
404:
377:
374:
373:
356:
353:
352:
349:
348:
347:
346:
342:
341:
340:
332:
331:
320:
312:
303:
298:
297:
296:
295:
294:
291:
283:
282:
279:
268:
242:
215:
210:
201:
153:flow separation
114:
101:
79:
55:
48:angle of attack
38:, of which the
12:
11:
5:
2170:
2160:
2159:
2157:Fluid dynamics
2154:
2138:
2137:
2110:
2083:
2056:
2029:
2001:
1986:
1979:
1953:
1933:
1918:
1888:
1877:(9): 805–814.
1861:
1834:
1811:
1796:
1778:
1768:(Report). NASA
1756:
1745:(4): 279–295.
1729:
1694:
1679:
1653:
1643:(Report). NASA
1622:
1611:(3): 376–380.
1595:
1568:
1541:
1530:(5): 478–480.
1514:
1507:
1482:
1455:
1427:
1426:
1424:
1421:
1420:
1419:
1414:
1409:
1404:
1399:
1394:
1389:
1384:
1377:
1374:
1370:
1369:
1366:
1363:
1344:
1341:
1323:
1320:
1316:
1295:
1290:
1286:
1282:
1277:
1273:
1269:
1264:
1261:
1257:
1253:
1250:
1247:
1244:
1239:
1235:
1214:
1209:
1205:
1201:
1196:
1192:
1188:
1183:
1179:
1158:
1153:
1149:
1145:
1140:
1136:
1128:
1124:
1118:
1115:
1111:
1105:
1100:
1096:
1069:
1065:
1060:
1056:
1050:
1047:
1039:
1036:
1033:
1030:
1025:
1021:
998:
995:
991:
967:
945:
941:
920:
897:
894:
864:
860:
855:
851:
845:
842:
834:
831:
826:
822:
818:
794:
790:
786:
764:
761:
757:
734:
731:
727:
701:
697:
693:
690:
685:
682:
678:
674:
669:
666:
662:
646:
643:
630:
627:
621:
618:
612:
609:
595:
592:
587:
586:
571:
567:
564:
561:
558:
552:
548:
545:
542:
536:
533:
530:
523:
519:
513:
509:
503:
500:
497:
494:
475:
474:
465:
464:
456:
455:
447:
446:
445:
444:
443:
441:
438:
428:
427:
418:
417:
409:
408:
407:
406:
405:
403:
400:
387:
384:
381:
360:
344:
343:
334:
333:
325:
324:
323:
322:
321:
319:
316:
311:
308:
302:
299:
292:
285:
284:
280:
273:
272:
271:
270:
269:
267:
264:
263:
262:
259:
252:
249:
246:
241:
238:
237:
236:
229:
226:
219:
214:
211:
209:
206:
200:
197:
196:
195:
191:
179:
178:
175:
164:
157:
156:
149:boundary layer
145:
142:
113:
110:
100:
97:
96:
95:
92:
89:
86:
78:
75:
53:
9:
6:
4:
3:
2:
2169:
2158:
2155:
2153:
2150:
2149:
2147:
2133:
2129:
2125:
2121:
2114:
2106:
2102:
2098:
2094:
2087:
2079:
2075:
2071:
2067:
2060:
2049:
2042:
2041:
2033:
2022:
2015:
2008:
2006:
1997:
1990:
1982:
1976:
1972:
1968:
1964:
1957:
1946:
1945:
1937:
1929:
1922:
1914:
1910:
1906:
1902:
1895:
1893:
1884:
1880:
1876:
1872:
1865:
1857:
1853:
1849:
1845:
1838:
1830:
1826:
1822:
1815:
1807:
1800:
1789:
1782:
1767:
1760:
1752:
1748:
1744:
1740:
1733:
1725:
1721:
1717:
1713:
1709:
1705:
1698:
1690:
1686:
1682:
1676:
1672:
1668:
1664:
1657:
1642:
1635:
1633:
1631:
1629:
1627:
1618:
1614:
1610:
1606:
1599:
1591:
1587:
1583:
1579:
1572:
1564:
1560:
1556:
1552:
1545:
1537:
1533:
1529:
1525:
1518:
1510:
1504:
1500:
1493:
1491:
1489:
1487:
1478:
1474:
1470:
1466:
1459:
1451:
1447:
1443:
1439:
1432:
1428:
1418:
1415:
1413:
1410:
1408:
1405:
1403:
1400:
1398:
1395:
1393:
1390:
1388:
1385:
1383:
1380:
1379:
1373:
1367:
1364:
1361:
1360:
1359:
1356:
1349:
1340:
1337:
1321:
1318:
1314:
1288:
1284:
1275:
1271:
1262:
1259:
1255:
1251:
1248:
1242:
1237:
1233:
1207:
1203:
1194:
1190:
1186:
1181:
1177:
1151:
1147:
1138:
1134:
1126:
1122:
1116:
1113:
1109:
1103:
1098:
1094:
1085:
1063:
1058:
1054:
1048:
1045:
1037:
1034:
1031:
1028:
1023:
1019:
996:
993:
989:
979:
965:
939:
918:
895:
892:
880:
858:
853:
849:
843:
840:
832:
829:
824:
820:
808:
792:
788:
762:
759:
755:
732:
729:
725:
715:
699:
695:
688:
683:
680:
676:
672:
667:
664:
660:
650:
642:
639:
636:
626:
617:
608:
600:
591:
569:
565:
562:
559:
556:
550:
546:
543:
540:
534:
531:
528:
521:
517:
511:
507:
501:
498:
495:
485:
484:
483:
469:
460:
451:
437:
422:
413:
399:
385:
382:
379:
358:
338:
329:
315:
307:
289:
277:
260:
257:
253:
250:
247:
244:
243:
234:
230:
227:
224:
220:
217:
216:
205:
192:
189:
188:
183:
176:
173:
169:
165:
162:
161:
160:
154:
150:
146:
143:
140:
136:
135:trailing edge
132:
131:
130:
127:
118:
109:
107:
99:Flow topology
93:
90:
87:
84:
83:
82:
74:
72:
68:
64:
60:
56:
49:
45:
41:
37:
33:
29:
28:dynamic stall
20:
16:
2126:(3): 69–82.
2123:
2119:
2113:
2099:(3): 18–29.
2096:
2092:
2086:
2069:
2065:
2059:
2039:
2032:
1995:
1989:
1962:
1956:
1943:
1936:
1921:
1907:(2): 40–45.
1904:
1900:
1874:
1870:
1864:
1850:(2): 27–33.
1847:
1843:
1837:
1820:
1814:
1799:
1781:
1770:. Retrieved
1759:
1742:
1738:
1732:
1707:
1704:AIAA Journal
1703:
1697:
1662:
1656:
1645:. Retrieved
1608:
1604:
1598:
1584:(1): 11–19.
1581:
1577:
1571:
1554:
1550:
1544:
1527:
1523:
1517:
1498:
1471:(1): 20–30.
1468:
1464:
1458:
1444:(2): 33–46.
1441:
1437:
1431:
1371:
1357:
1354:
1338:
1086:
1084:as follows:
980:
881:
809:
807:is given by
716:
651:
648:
640:
632:
623:
614:
605:
588:
481:
434:
350:
313:
304:
202:
171:
167:
158:
123:
102:
80:
63:Mach numbers
58:
27:
25:
15:
2072:(3): 3–17.
440:Sweep angle
126:wind tunnel
46:, when the
44:helicopters
2146:Categories
2019:(Report).
1772:2013-09-03
1647:2013-09-03
1423:References
1387:Rotorcraft
1382:helicopter
223:hysteresis
1930:(Report).
1808:(Report).
1793:(Report).
1689:234321807
1285:α
1252:−
1204:α
1148:α
1123:α
1110:α
1068:∞
1049:˙
1046:α
1038:γ
1035:±
1032:α
1020:α
990:α
966:γ
944:∞
896:˙
893:α
863:∞
844:˙
841:α
833:γ
821:α
817:Δ
789:α
785:Δ
756:α
726:α
696:α
692:Δ
677:α
661:α
629:Modelling
570:ψ
566:
551:ψ
547:
541:μ
535:
502:
493:Λ
2048:Archived
2021:Archived
1665:: 1651.
1376:See also
1306:, where
301:Mean AoA
1712:Bibcode
266:Factors
1977:
1687:
1677:
1505:
882:where
717:where
532:arctan
499:arctan
2051:(PDF)
2044:(PDF)
2024:(PDF)
2017:(PDF)
1948:(PDF)
1791:(PDF)
1685:S2CID
208:Types
40:stall
1975:ISBN
1675:ISBN
1503:ISBN
1249:0.25
386:0.05
383:<
139:lift
69:and
26:The
2128:doi
2101:doi
2074:doi
1967:doi
1909:doi
1879:doi
1852:doi
1825:doi
1747:doi
1720:doi
1667:doi
1613:doi
1609:101
1586:doi
1559:doi
1532:doi
1473:doi
1446:doi
563:sin
544:cos
172:DSV
168:LEV
124:By
108:).
73:).
2148::
2124:37
2122:.
2097:34
2095:.
2070:34
2068:.
2004:^
1973:.
1965:.
1905:26
1903:.
1891:^
1875:25
1873:.
1848:23
1846:.
1823:.
1743:43
1741:.
1718:.
1708:33
1706:.
1683:.
1673:.
1625:^
1607:.
1582:17
1580:.
1553:.
1526:.
1485:^
1469:17
1467:.
1442:17
1440:.
1225:,
1169:,
879:,
714:,
57:,
54:NE
2134:.
2130::
2107:.
2103::
2080:.
2076::
1983:.
1969::
1915:.
1911::
1885:.
1881::
1858:.
1854::
1831:.
1827::
1775:.
1753:.
1749::
1726:.
1722::
1714::
1691:.
1669::
1650:.
1619:.
1615::
1592:.
1588::
1565:.
1561::
1555:8
1538:.
1534::
1528:4
1511:.
1479:.
1475::
1452:.
1448::
1322:P
1319:C
1315:x
1294:)
1289:r
1281:(
1276:L
1272:C
1268:)
1263:P
1260:C
1256:x
1246:(
1243:=
1238:M
1234:C
1213:)
1208:r
1200:(
1195:D
1191:C
1187:=
1182:D
1178:C
1157:)
1152:r
1144:(
1139:L
1135:C
1127:r
1117:q
1114:e
1104:=
1099:L
1095:C
1064:V
1059:/
1055:c
1029:=
1024:r
997:q
994:e
940:V
919:c
859:V
854:/
850:c
830:=
825:D
793:D
763:S
760:S
733:S
730:D
700:D
689:+
684:S
681:S
673:=
668:S
665:D
560:+
557:r
529:=
522:T
518:U
512:R
508:U
496:=
380:k
359:k
225:;
155:.
52:V
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
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