602:
956:
the current state of theoretical knowledge on the leading-edge stall phenomenon. Morris's theory predicts the critical angle of attack for leading-edge stall onset as the condition at which a global separation zone is predicted in the solution for the inner flow. Morris's theory demonstrates that a subsonic flow about a thin airfoil can be described in terms of an outer region, around most of the airfoil chord, and an inner region, around the nose, that asymptotically match each other. As the flow in the outer region is dominated by classical thin airfoil theory, Morris's equations exhibit many components of thin airfoil theory.
354:
will disrupt the laminar flow, making it turbulent. For example, with rain on the wing, the flow will be turbulent. Under certain conditions, insect debris on the wing will cause the loss of small regions of laminar flow as well. Before NASA's research in the 1970s and 1980s the aircraft design community understood from application attempts in the WW II era that laminar flow wing designs were not practical using common manufacturing tolerances and surface imperfections. That belief changed after new manufacturing methods were developed with composite materials (e.g. laminar-flow airfoils developed by
Professor
965:
167:
477:
382:
590:
31:
175:
2038:
485:
43:
2425:
1758:
362:). Machined metal methods were also introduced. NASA's research in the 1980s revealed the practicality and usefulness of laminar flow wing designs and opened the way for laminar-flow applications on modern practical aircraft surfaces, from subsonic general aviation aircraft to transonic large transport aircraft, to supersonic designs.
955:
of the airfoil, which usually occurs at an angle of attack between 10° and 15° for typical airfoils. In the mid-late 2000s, however, a theory predicting the onset of leading-edge stall was proposed by
Wallace J. Morris II in his doctoral thesis. Morris's subsequent refinements contain the details on
353:
in the linear regime shows that a negative pressure gradient along the flow has the same effect as reducing the speed. So with the maximum camber in the middle, maintaining a laminar flow over a larger percentage of the wing at a higher cruising speed is possible. However, some surface contamination
241:
and also an aerodynamic force perpendicular to the wind. This does not mean the object qualifies as an airfoil. Airfoils are highly-efficient lifting shapes, able to generate more lift than similarly sized flat plates of the same area, and able to generate lift with significantly less drag. Airfoils
2213:
2218:
1653:
976:* Laminar flow airfoil for a crewed propeller aircraft * Laminar flow at a jet airliner airfoil * Stable airfoil used for flying wings * Aft loaded airfoil allowing for a large main spar and late stall * Transonic supercritical airfoil * Supersonic leading edge airfoil
45:
2033:{\displaystyle {\begin{aligned}&{\frac {dy}{dx}}=A_{0}+A_{1}\cos(\theta )+A_{2}\cos(2\theta )+\dots \\&\gamma (x)=2(\alpha +A_{0})\left({\frac {\sin \theta }{1+\cos \theta }}\right)+2A_{1}\sin(\theta )+2A_{2}\sin(2\theta )+\dots {\text{.}}\end{aligned}}}
46:
1378:
2050:
3111:
Ramesh, Kiran; Gopalarathnam, Ashok; Granlund, Kenneth; Ol, Michael V.; Edwards, Jack R. (July 2014). "Discrete-vortex method with novel shedding criterion for unsteady aerofoil flows with intermittent leading-edge vortex shedding".
47:
3165:: "A simple solution for general two-dimensional aerofoil sections can be obtained by neglecting thickness effects and using a mean-line only section model.... This also means small changes in position are equivalent so that
2832:
If the body is shaped, moved, or inclined in such a way as to produce a net deflection or turning of the flow, the local velocity is changed in magnitude, direction, or both. Changing the velocity creates a net force on the
2730:
1492:
2805:, p. 378: "The effect of the wing is to give the air stream a downward velocity component. The reaction force of the deflected air mass must then act on the wing to give it an equal and opposite upward component."
537:. For example, an airfoil of the NACA 4-digit series such as the NACA 2415 (to be read as 2 – 4 – 15) describes an airfoil with a camber of 0.02 chord located at 0.40 chord, with 0.15 chord of maximum thickness.
2634:
2420:{\displaystyle C_{M}=-{\frac {\pi }{2}}\left(\alpha +A_{0}+A_{1}-{\frac {A_{2}}{2}}\right)=-{\frac {\pi }{2}}\alpha -\int _{0}^{\pi }{{\frac {dy}{dx}}\cdot \cos(\theta )(1+\cos \theta )\,d\theta }{\text{.}}}
312:
is increased before the wing achieves maximum thickness to minimize the chance of boundary layer separation. This elongates the wing and moves the point of maximum thickness back from the leading edge.
2523:
404:(a.k.a. lower surface) has a comparatively higher static pressure than the suction surface. The pressure gradient between these two surfaces contributes to the lift force generated for a given airfoil.
1721:
1246:
632:
and others in the 1920s. The theory idealizes the flow around an airfoil as two-dimensional flow around a thin airfoil. It can be imagined as addressing an airfoil of zero thickness and infinite
342:, are fitted to airfoils on almost every aircraft. A trailing edge flap acts similarly to an aileron; however, it, as opposed to an aileron, can be retracted partially into the wing if not used.
1763:
3065:: "The equation can only be used for aircraft with medium to large aspect ratio wings and only up to the stall angle, which is usually between 10° and 15° for typical aircraft configurations."
1178:
284:. Various airfoils serve different flight regimes. Asymmetric airfoils can generate lift at zero angle of attack, while a symmetric airfoil may better suit frequent inverted flight as in an
902:
639:
Thin airfoil theory was particularly notable in its day because it provided a sound theoretical basis for the following important properties of airfoils in two-dimensional inviscid flow:
1265:
744:
44:
662:
airfoil, the aerodynamic center lies exactly one quarter of the chord behind the leading edge, but the position of the center of pressure moves when the angle of attack changes.
97:
deflects the oncoming fluid (for fixed-wing aircraft, a downward force), resulting in a force on the airfoil in the direction opposite to the deflection. This force is known as
3664:
139:
The air deflected by an airfoil causes it to generate a lower-pressure "shadow" above and behind itself. This pressure difference is accompanied by a velocity difference, via
34:
Examples of airfoils in nature and in or on various vehicles. The dolphin flipper at bottom left obeys the same principles in a different fluid medium; it is an example of a
941:
257:
of the lift curve. At about 18 degrees this airfoil stalls, and lift falls off quickly beyond that. The drop in lift can be explained by the action of the upper-surface
830:
797:
774:
691:
565:
is momentarily zero. On a cambered airfoil, the center of pressure is not a fixed location as it moves in response to changes in angle of attack and lift coefficient.
1004:
In thin airfoil theory, the width of the (2D) airfoil is assumed negligible, and the airfoil itself replaced with a 1D blade along its camber line, oriented at the
1419:
466:
369:. Various airfoil generation systems are also used. An example of a general purpose airfoil that finds wide application, and pre–dates the NACA system, is the
2656:
308:. Subsonic airfoils have a round leading edge, which is naturally insensitive to the angle of attack. The cross section is not strictly circular, however: the
2208:{\displaystyle C_{L}=2\pi \left(\alpha +A_{0}+{\frac {A_{1}}{2}}\right)=2\pi \alpha +2\int _{0}^{\pi }{{\frac {dy}{dx}}\cdot (1+\cos \theta )\,d\theta }}
323:
has its maximum thickness close to the leading edge to have a lot of length to slowly shock the supersonic flow back to subsonic speeds. Generally such
2539:
143:, so the resulting flowfield about the airfoil has a higher average velocity on the upper surface than on the lower surface. In some situations (e.g.
331:. Modern aircraft wings may have different airfoil sections along the wing span, each one optimized for the conditions in each section of the wing.
3621:
3680:
2844:“It has been known from the very beginning of flight that wings with a sharp trailing edge must be used in order to obtain a well-defined lift.”
2430:
124:
airfoils can generate lift at zero angle of attack. Airfoils can be designed for use at different speeds by modifying their geometry: those for
150:) the lift force can be related directly to the average top/bottom velocity difference without computing the pressure by using the concept of
1664:
1187:
253:
so some lift is produced at zero angle of attack. With increased angle of attack, lift increases in a roughly linear relation, called the
427:
is the point on the airfoil most remote from the leading edge. The angle between the upper and lower surfaces at the trailing edge is the
1648:{\displaystyle \left(\alpha -{\frac {dy}{dx}}\right)V=-w(x)=-{\frac {1}{2\pi }}\int _{0}^{c}{\frac {\gamma (x')}{x-x'}}\,dx'{\text{,}}}
1126:
3578:
3310:
214:, are similar in cross-section and operate on the same principles as airfoils. Swimming and flying creatures and even many plants and
508:
is the locus of points midway between the upper and lower surfaces. Its shape depends on the thickness distribution along the chord;
2820:
550:, which is the chord-wise location about which the pitching moment is independent of the lift coefficient and the angle of attack.
242:
are used in the design of aircraft, propellers, rotor blades, wind turbines and other applications of aeronautical engineering.
237:
When the wind is obstructed by an object such as a flat plate, a building, or the deck of a bridge, the object will experience
2926:. U.S. Government Printing Office, Washington, D.C.: U.S. Navy, Aviation Training Division. pp. 21–22. NAVWEPS 00-80T-80.
3523:
3440:
3389:
3299:
3467:
Morris, Wallace J.; Rusak, Zvi (October 2013). "Stall onset on aerofoils at low to moderately high
Reynolds number flows".
2732:
Thin-airfoil theory shows that, in two-dimensional inviscid flow, the aerodynamic center is at the quarter-chord position.
2526:
644:
555:
261:, which separates and greatly thickens over the upper surface at and past the stall angle. The thickened boundary layer's
3233:. Oxford Applied Mathematics and Computing Science. Oxford: Clarendon Press (published 2009). pp. 140–141, 143–145.
3712:
581:
of the wing also significantly influences the slope of the curve. As aspect ratio decreases, the slope also decreases.
3408:
319:
are much more angular in shape and can have a very sharp leading edge, which is very sensitive to angle of attack. A
309:
845:
577:. The slope is greatest if the angle is zero; and decreases as the angle increases. For a wing of finite span, the
4094:
3921:
3630:
Numerical
Analysis of NACA Airfoil 0012 at Different Attack Angles and Obtaining its Aerodynamic Coefficients.
3629:
601:
518:
Thickness measured perpendicular to the camber line. This is sometimes described as the "American convention";
4161:
218:
organisms employ airfoils/hydrofoils: common examples being bird wings, the bodies of fish, and the shape of
570:
521:
Thickness measured perpendicular to the chord line. This is sometimes described as the "British convention".
3669:
270:
151:
839:
Also as a consequence of (3), the section lift coefficient of a cambered airfoil of infinite wingspan is:
707:
3636:
Bearman, Matt (2019). "Going with the Flow? Britain's
Contribution to Laminar-Flow Research, 1930–1947".
2876:, pp. 497–503: "If a streamline is curved, there must be a pressure gradient across the streamline."
1116:
350:
328:
155:
3875:
3852:
2751:
578:
540:
Finally, important concepts used to describe the airfoil's behaviour when moving through a fluid are:
3757:
1426:
2741:
359:
190:
rotor blades, are built with airfoil-shaped cross sections. Airfoils are also found in propellers,
140:
17:
3325:
909:
3534:
1046:
The flow across the airfoil generates a circulation around the blade, which can be modeled as a
3752:
3705:
1389:
814:
781:
262:
231:
83:
1373:{\displaystyle w(x)={\frac {1}{2\pi }}\int _{0}^{c}{\frac {\gamma (x')}{x-x'}}\,dx'{\text{,}}}
397:(a.k.a. upper surface) is generally associated with higher velocity and lower static pressure.
4156:
4099:
3513:
3430:
751:
672:
659:
529:
320:
266:
250:
121:
4007:
3908:
3898:
3888:
3817:
3582:
3555:
3476:
3455:
3452:
A universal prediction of stall onset for airfoils at a wide range of
Reynolds number flows
3340:
3121:
355:
3659:
1395:
373:. Today, airfoils can be designed for specific functions by the use of computer programs.
8:
1659:
1251:
316:
215:
183:
133:
110:
106:
3559:
3480:
3459:
3344:
3125:
2816:
3785:
3615:
3500:
3356:
3145:
2766:
2637:
648:
546:
451:
339:
4119:
3698:
3641:
3519:
3504:
3492:
3436:
3404:
3385:
3352:
3295:
3149:
3137:
2991:. Reports and Memoranda of the Aeronautical Research Council of Great Britain No 2308
2889:
Flight evaluation of an insect contamination protection system for laminar flow wings
2845:
1487:
1381:
964:
418:
is the point at the front of the airfoil that has maximum curvature (minimum radius).
98:
2947:
2945:
2756:
3563:
3484:
3429:
Houghton, E. L.; Carpenter, P. W.; Collicott, Steven H.; Valentine, Daniel (2012).
3368:
3360:
3348:
3129:
2044:
804:
698:
652:
436:
296:
a symmetric airfoil can be used to increase the range of angles of attack to avoid
195:
191:
63:
4135:
4104:
4002:
3865:
3419:
3289:
2942:
2930:
2904:
2887:
2040:
The resulting lift and moment depend on only the first few terms of this series.
1059:
1005:
800:
629:
617:
569:
In two-dimensional flow around a uniform wing of infinite span, the slope of the
561:
335:
305:
202:. Sails are also airfoils, and the underwater surfaces of sailboats, such as the
166:
125:
117:
71:
27:
Cross-sectional shape of a wing, blade of a propeller, rotor, or turbine, or sail
515:
of an airfoil varies along the chord. It may be measured in either of two ways:
496:
The shape of the airfoil is defined using the following geometrical parameters:
3964:
3805:
3790:
3762:
3737:
3729:
1748:
952:
948:
833:
489:
476:
301:
258:
249:
testing is shown on the right. The curve represents an airfoil with a positive
238:
147:
79:
265:
changes the airfoil's effective shape, in particular it reduces its effective
136:
tend to be slimmer with a sharp leading edge. All have a sharp trailing edge.
4150:
4114:
3959:
3954:
3893:
3827:
3645:
3568:
3543:
3496:
3285:
3141:
621:
594:
423:
297:
274:
102:
3685:
381:
277:, so that the overall drag increases sharply near and past the stall point.
120:. Most foil shapes require a positive angle of attack to generate lift, but
3949:
3860:
3795:
3780:
1047:
589:
414:
366:
281:
129:
75:
4109:
4025:
4017:
3939:
3883:
3842:
3488:
3133:
2725:{\displaystyle {\frac {\partial (C_{M'})}{\partial (C_{L})}}=0{\text{.}}}
1484:
606:
273:
and the lift. The thicker boundary layer also causes a large increase in
246:
219:
203:
74:) is a streamlined body that is capable of generating significantly more
52:
3314:
408:
The geometry of the airfoil is described with a variety of terms :
86:
of similar function designed with water as the working fluid are called
4068:
4030:
3944:
3916:
1102:
973:
969:
227:
187:
30:
1039:, is assumed sufficiently small that one need not distinguish between
327:
airfoils and also the supersonic airfoils have a low camber to reduce
4045:
2746:
811:(The above expression is also applicable to a cambered airfoil where
324:
285:
223:
87:
35:
4050:
4040:
3969:
3822:
3428:
2951:
2936:
2855:
2852:, Section VIII.2, p.179, Dover Publications Inc. ISBN 0-486-60541-8
2761:
633:
625:
289:
199:
144:
3032:
3020:
174:
170:
Streamlines around a NACA 0012 airfoil at moderate angle of attack
4060:
3931:
3721:
1109:
943:
is the section lift coefficient when the angle of attack is zero.
527:
Some important parameters to describe an airfoil's shape are its
370:
365:
Schemes have been devised to define airfoils – an example is the
349:
has a maximum thickness in the middle camber line. Analyzing the
293:
93:
When oriented at a suitable angle, a solid body moving through a
2989:
An analysis of the lift slope of aerofoils of small aspect ratio
2629:{\displaystyle \Delta x/c=\pi /4((A_{1}-A_{2})/C_{L}){\text{.}}}
440:
is the straight line connecting leading and trailing edges. The
3997:
3837:
3747:
207:
3675:
3080:
3044:
2905:"Natural laminar flow experiments on modern airplane surfaces"
82:. Wings, sails and propeller blades are examples of airfoils.
4089:
4084:
4035:
3772:
3742:
3195:
3193:
3110:
2969:
484:
94:
3291:
Theory of Wing
Sections, Including a Summary of Airfoil Data
3249:
3237:
269:, which modifies the overall flow field so as to reduce the
3992:
3987:
3832:
3809:
3690:
3535:"Question #136: Lift Coefficient & Thin Airfoil Theory"
3212:
3210:
3208:
1655:
which uniquely determines it in terms of known quantities.
211:
3632:
Journal of
Mechatronics and Automation. 2019; 6(3): 8–16p.
3190:
2518:{\displaystyle C_{M}(1/4c)=-\pi /4(A_{1}-A_{2}){\text{.}}}
3537:. Ask a Rocket Scientist: Aerodynamics. Aerospaceweb.org.
389:
The various terms related to airfoils are defined below:
3576:
3261:
3205:
3178:
2861:
1658:
An explicit solution can be obtained through first the
1070:, but the strength is singular at the bladefront, with
2957:
2903:
Holmes, B. J.; Obara, C. J.; Yip, L. P. (1984-06-01).
1716:{\displaystyle x=c\cdot {\frac {1+\cos(\theta )}{2}},}
116:
The lift on an airfoil is primarily the result of its
2784:
2659:
2542:
2433:
2221:
2053:
1761:
1667:
1495:
1398:
1268:
1241:{\displaystyle \rho V\int _{0}^{c}x\;\gamma (x)\,dx.}
1190:
1129:
912:
848:
817:
784:
754:
710:
701:
of a thin symmetric airfoil of infinite wingspan is:
675:
454:
968:
From top to bottom: * Laminar flow airfoil for a RC
593:An airfoil section is displayed at the tip of this
559:, which is the chord-wise location about which the
304:. Thus a large range of angles can be used without
3577:Weltner, Klaus; Ingelman-Sundberg, Martin (1999).
3284:
3092:
3068:
3038:
3026:
2724:
2628:
2517:
2427:The moment about the 1/4 chord point will thus be
2419:
2207:
2032:
1715:
1647:
1413:
1372:
1240:
1172:
935:
896:
824:
791:
768:
738:
685:
651:are coincident and lie exactly one quarter of the
460:
51:Streamlines on an airfoil visualised with a smoke
3544:"Semi-Empirical Prediction of Airfoil Hysteresis"
1173:{\displaystyle \rho V\int _{0}^{c}\gamma (x)\,dx}
1023:at the trailing edge; the camber of the airfoil,
821:
788:
765:
682:
4148:
832:is the angle of attack measured relative to the
3686:Airflow across a wing (University of Cambridge)
3417:
2802:
468:, is the length of the chord line. That is the
101:and can be resolved into two components: lift (
3379:
2975:
2902:
1454:, and the normal component is correspondingly
897:{\displaystyle \ c_{l}=c_{l_{0}}+2\pi \alpha }
628:and further refined by British aerodynamicist
3706:
3665:Airfoil & Hydrofoil Reference Application
3380:Bertin, John J.; Cummings, Russel M. (2009).
2640:is the position at which the pitching moment
3620:: CS1 maint: multiple names: authors list (
3308:
3216:
3162:
3013:Abbott, I.H., and Von Doenhoff, A.E. (1949)
3000:Abbott, I.H., and Von Doenhoff, A.E. (1949)
2987:Lyons, D.J., and Bisgood, P.L., (Jan 1945).
616:is a simple theory of airfoils that relates
3466:
3086:
2885:
3713:
3699:
2886:Croom, C. C.; Holmes, B. J. (1985-04-01).
1215:
947:Thin airfoil theory assumes the air is an
480:Different definitions of airfoil thickness
178:Lift and drag curves for a typical airfoil
3567:
3418:Halliday, David; Resnick, Robert (1988).
3367:
3267:
3255:
3243:
3199:
3184:
2404:
2197:
1628:
1353:
1228:
1163:
624:. It was devised by German mathematician
3605:
3511:
3323:
2963:
2873:
963:
600:
588:
483:
475:
380:
173:
165:
41:
29:
3676:Airfoil Playground - Interactive WebApp
3635:
3384:(5th ed.). Pearson Prentice Hall.
3228:
1184:about the leading edge proportional to
1043:and position relative to the fuselage.
1011:. Let the position along the blade be
667:lift coefficient versus angle of attack
14:
4149:
3449:
3424:(3rd ed.). John Wiley & Sons.
3398:
3288:; Von Doenhoff, Albert Edward (1959).
3074:
3050:
2790:
584:
376:
3694:
3541:
3532:
3432:Aerodynamics for Engineering Students
3098:
3062:
803:in radians, measured relative to the
697:As a consequence of (3), the section
2921:
2862:Weltner & Ingelman-Sundberg 1999
2529:is aft of the 'quarter-chord' point
739:{\displaystyle \ c_{l}=2\pi \alpha }
222:. An airfoil-shaped wing can create
2653:with a change in lift coefficient:
280:Airfoil design is a major facet of
24:
3628:Ali Kamranpay, Alireza Mehrabadi.
3599:
3324:Babinsky, Holger (November 2003).
3277:
2689:
2663:
2543:
1450:relative to the blade at position
1421:must balance an inverse flow from
245:A lift and drag curve obtained in
230:or other motor vehicle, improving
25:
4173:
3660:UIUC Airfoil Coordinates Database
3653:
3542:Traub, Lance W. (24 March 2016).
3375:. Cambridge UP. pp. 467–471.
3373:An Introduction to Fluid Dynamics
3309:Auld, Douglass; Srinivas (1995).
2922:Hurt, H. H. Jr. (January 1965) .
2823:from the original on 5 July 2011
2814:
1119:gives that the total lift force
972:* Laminar flow airfoil for a RC
776:is the section lift coefficient,
3579:"Physics of flight - revisited"
3222:
3156:
3104:
3056:
3007:
2994:
2981:
2924:Aerodynamics for Naval Aviators
573:is determined primarily by the
288:airplane. In the region of the
3672:An airfoil simulator from NASA
3533:Scott, Jeff (10 August 2003).
3450:Morris, Wallace J. II (2009).
3039:Abbott & Von Doenhoff 1959
3027:Abbott & Von Doenhoff 1959
2915:
2896:
2879:
2867:
2838:
2819:. NASA Glenn Research Center.
2808:
2796:
2705:
2692:
2684:
2666:
2618:
2600:
2574:
2571:
2525:From this it follows that the
2507:
2481:
2461:
2444:
2401:
2383:
2380:
2374:
2194:
2176:
2012:
2003:
1978:
1972:
1907:
1888:
1879:
1873:
1856:
1847:
1825:
1819:
1701:
1695:
1606:
1595:
1550:
1544:
1408:
1402:
1331:
1320:
1278:
1272:
1225:
1219:
1160:
1154:
609:helicopter's lower rotor blade
13:
1:
2772:
1050:of position-varying strength
959:
182:The wings and stabilizers of
113:to the freestream velocity).
3720:
3608:Fundamentals of Aerodynamics
3512:Phillips, Warren F. (2004).
3229:Acheson, D. J. (1990).
2777:
2215:and the moment coefficient
999: supersonic flow volume
951:so does not account for the
836:instead of the chord line.)
643:on a symmetric airfoil, the
620:to lift for incompressible,
7:
3876:Internal combustion engines
3853:External combustion engines
3454:(PhD). Harvard University.
2803:Halliday & Resnick 1988
2735:
1388:. Since the airfoil is an
936:{\displaystyle \ c_{l_{0}}}
358:for use with wings made of
334:Movable high-lift devices,
161:
132:, while those designed for
10:
4178:
3606:Anderson, John, D (2007).
3469:Journal of Fluid Mechanics
3435:(6th ed.). Elsevier.
3382:Aerodynamics for Engineers
3353:10.1088/0031-9120/38/6/001
3311:"2-D Thin Aerofoil Theory"
3114:Journal of Fluid Mechanics
2976:Bertin & Cummings 2009
1755:with a modified lead term:
4128:
4077:
4059:
4016:
3978:
3930:
3907:
3874:
3851:
3804:
3771:
3730:Classical simple machines
3728:
3518:. John Wiley & Sons.
3316:Aerodynamics for Students
3231:Elementary Fluid Dynamics
1427:small-angle approximation
825:{\displaystyle \alpha \!}
792:{\displaystyle \alpha \!}
306:boundary layer separation
128:generally have a rounded
3569:10.3390/aerospace3020009
3217:Auld & Srinivas 1995
3163:Auld & Srinivas 1995
2817:"Lift from Flow Turning"
2742:Circulation control wing
1747:as a nondimensionalized
1723:and then expanding both
655:behind the leading edge.
597:aircraft, built in 1991.
488:An airfoil designed for
360:fibre-reinforced plastic
4115:Check weighing machines
3421:Fundamentals of Physics
3319:. University of Sydney.
3087:Morris & Rusak 2013
3015:Theory of Wing Sections
3002:Theory of Wing Sections
1117:Kutta–Joukowski theorem
1019:at the wing's front to
769:{\displaystyle c_{l}\!}
686:{\displaystyle 2\pi \!}
472:of the airfoil section.
351:Navier–Stokes equations
156:Kutta–Joukowski theorem
3638:The Aviation Historian
2909:NASA Technical Reports
2752:Kline–Fogleman airfoil
2726:
2630:
2519:
2421:
2209:
2034:
1717:
1649:
1415:
1374:
1262:produces a flow field
1242:
1174:
1001:
937:
898:
826:
793:
770:
740:
687:
610:
598:
493:
481:
462:
386:
263:displacement thickness
179:
171:
55:
39:
4100:Seed-counting machine
3399:Clancy, L.J. (1975).
2727:
2631:
2520:
2422:
2210:
2035:
1718:
1650:
1433:is inclined at angle
1416:
1375:
1243:
1175:
993: subsonic stream
967:
938:
899:
827:
794:
771:
741:
688:
604:
592:
487:
479:
463:
384:
321:supercritical airfoil
177:
169:
141:Bernoulli's principle
50:
33:
4162:Aircraft wing design
3899:Nutating disc engine
3889:Reciprocating engine
3585:on 29 September 2011
3489:10.1017/jfm.2013.440
3369:Batchelor, George. K
3326:"How do wings work?"
3134:10.1017/jfm.2014.297
2952:Houghton et al. 2012
2937:Houghton et al. 2012
2815:Hall, Nancy R.
2657:
2540:
2431:
2219:
2051:
1759:
1665:
1493:
1414:{\displaystyle w(x)}
1396:
1266:
1188:
1127:
987: turbulent flow
910:
846:
815:
782:
752:
708:
673:
452:
385:Airfoil nomenclature
3560:2016Aeros...3....9T
3515:Mechanics of Flight
3481:2013JFM...733..439M
3460:2009PhDT.......146M
3345:2003PhyEd..38..497B
3286:Abbott, Ira Herbert
3126:2014JFM...751..500R
3089:, pp. 439–472.
2343:
2151:
1660:change of variables
1588:
1390:impermeable surface
1313:
1211:
1150:
1123:is proportional to
614:Thin airfoil theory
585:Thin airfoil theory
575:trailing edge angle
470:reference dimension
429:trailing edge angle
377:Airfoil terminology
317:Supersonic airfoils
310:radius of curvature
184:fixed-wing aircraft
107:freestream velocity
3922:Peaucellier-Lipkin
3403:. London: Pitman.
3258:, p. 469-470.
3246:, p. 467-468.
2846:von Mises, Richard
2767:Wing configuration
2722:
2638:aerodynamic center
2626:
2527:center of pressure
2515:
2417:
2329:
2205:
2137:
2030:
2028:
1713:
1645:
1574:
1411:
1384:to the airfoil at
1370:
1299:
1238:
1197:
1170:
1136:
1002:
981: laminar flow
933:
894:
822:
789:
766:
736:
683:
649:aerodynamic center
645:center of pressure
611:
599:
556:center of pressure
547:aerodynamic center
494:
482:
458:
387:
180:
172:
56:
40:
4144:
4143:
4120:Riveting machines
3818:Archimedes' screw
3525:978-0-471-33458-3
3442:978-0-08-096633-5
3391:978-0-13-227268-1
3333:Physics Education
3301:978-0-486-60586-9
2720:
2709:
2624:
2513:
2415:
2363:
2321:
2300:
2246:
2171:
2112:
2024:
1944:
1785:
1708:
1643:
1626:
1572:
1525:
1483:must satisfy the
1368:
1351:
1297:
915:
851:
713:
693:units per radian.
665:the slope of the
461:{\displaystyle c}
347:laminar flow wing
134:supersonic flight
99:aerodynamic force
48:
16:(Redirected from
4169:
3823:Eductor-jet pump
3715:
3708:
3701:
3692:
3691:
3649:
3625:
3619:
3611:
3594:
3592:
3590:
3581:. Archived from
3573:
3571:
3538:
3529:
3508:
3463:
3446:
3425:
3414:
3395:
3376:
3364:
3330:
3320:
3305:
3271:
3265:
3259:
3253:
3247:
3241:
3235:
3234:
3226:
3220:
3214:
3203:
3202:, p. 467-9.
3197:
3188:
3182:
3176:
3174:
3160:
3154:
3153:
3108:
3102:
3096:
3090:
3084:
3078:
3072:
3066:
3060:
3054:
3048:
3042:
3036:
3030:
3024:
3018:
3011:
3005:
3004:, section 7.4(b)
2998:
2992:
2985:
2979:
2973:
2967:
2961:
2955:
2949:
2940:
2934:
2928:
2927:
2919:
2913:
2912:
2900:
2894:
2893:
2883:
2877:
2871:
2865:
2859:
2853:
2850:Theory of Flight
2842:
2836:
2835:
2829:
2828:
2812:
2806:
2800:
2794:
2788:
2731:
2729:
2728:
2723:
2721:
2718:
2710:
2708:
2704:
2703:
2687:
2683:
2682:
2681:
2661:
2648:
2647:
2635:
2633:
2632:
2627:
2625:
2622:
2617:
2616:
2607:
2599:
2598:
2586:
2585:
2567:
2553:
2535:
2524:
2522:
2521:
2516:
2514:
2511:
2506:
2505:
2493:
2492:
2477:
2454:
2443:
2442:
2426:
2424:
2423:
2418:
2416:
2413:
2411:
2364:
2362:
2354:
2346:
2342:
2337:
2322:
2314:
2306:
2302:
2301:
2296:
2295:
2286:
2281:
2280:
2268:
2267:
2247:
2239:
2231:
2230:
2214:
2212:
2211:
2206:
2204:
2172:
2170:
2162:
2154:
2150:
2145:
2118:
2114:
2113:
2108:
2107:
2098:
2093:
2092:
2063:
2062:
2045:lift coefficient
2039:
2037:
2036:
2031:
2029:
2025:
2022:
1996:
1995:
1965:
1964:
1949:
1945:
1943:
1926:
1915:
1906:
1905:
1868:
1840:
1839:
1812:
1811:
1799:
1798:
1786:
1784:
1776:
1768:
1765:
1754:
1746:
1738:
1737:
1736:
1730:
1722:
1720:
1719:
1714:
1709:
1704:
1681:
1654:
1652:
1651:
1646:
1644:
1641:
1639:
1627:
1625:
1624:
1609:
1605:
1590:
1587:
1582:
1573:
1571:
1560:
1531:
1527:
1526:
1524:
1516:
1508:
1482:
1474:
1469:
1468:
1462:
1453:
1449:
1448:
1447:
1441:
1432:
1424:
1420:
1418:
1417:
1412:
1387:
1379:
1377:
1376:
1371:
1369:
1366:
1364:
1352:
1350:
1349:
1334:
1330:
1315:
1312:
1307:
1298:
1296:
1285:
1261:
1254:, the vorticity
1247:
1245:
1244:
1239:
1210:
1205:
1183:
1179:
1177:
1176:
1171:
1149:
1144:
1122:
1114:
1107:
1100:
1093:
1092:
1091:
1090:
1089:
1080:
1069:
1057:
1042:
1038:
1037:
1036:
1030:
1022:
1018:
1014:
1010:
998:
992:
986:
980:
942:
940:
939:
934:
932:
931:
930:
929:
913:
903:
901:
900:
895:
881:
880:
879:
878:
861:
860:
849:
831:
829:
828:
823:
798:
796:
795:
790:
775:
773:
772:
767:
764:
763:
745:
743:
742:
737:
723:
722:
711:
699:lift coefficient
692:
690:
689:
684:
502:mean camber line
467:
465:
464:
459:
402:pressure surface
64:American English
49:
21:
4177:
4176:
4172:
4171:
4170:
4168:
4167:
4166:
4147:
4146:
4145:
4140:
4136:Spring (device)
4124:
4105:Vending machine
4073:
4055:
4012:
3974:
3926:
3903:
3870:
3866:Stirling engine
3847:
3800:
3767:
3724:
3719:
3656:
3613:
3612:
3602:
3600:Further reading
3597:
3588:
3586:
3526:
3443:
3411:
3392:
3328:
3302:
3280:
3278:General Sources
3275:
3274:
3266:
3262:
3254:
3250:
3242:
3238:
3227:
3223:
3215:
3206:
3198:
3191:
3183:
3179:
3166:
3161:
3157:
3109:
3105:
3097:
3093:
3085:
3081:
3073:
3069:
3061:
3057:
3053:, §8.1 to §8.8.
3049:
3045:
3037:
3033:
3025:
3021:
3012:
3008:
2999:
2995:
2986:
2982:
2974:
2970:
2962:
2958:
2950:
2943:
2935:
2931:
2920:
2916:
2901:
2897:
2884:
2880:
2872:
2868:
2860:
2856:
2843:
2839:
2826:
2824:
2813:
2809:
2801:
2797:
2789:
2785:
2780:
2775:
2738:
2717:
2699:
2695:
2688:
2674:
2673:
2669:
2662:
2660:
2658:
2655:
2654:
2645:
2641:
2621:
2612:
2608:
2603:
2594:
2590:
2581:
2577:
2563:
2549:
2541:
2538:
2537:
2530:
2510:
2501:
2497:
2488:
2484:
2473:
2450:
2438:
2434:
2432:
2429:
2428:
2412:
2355:
2347:
2345:
2344:
2338:
2333:
2313:
2291:
2287:
2285:
2276:
2272:
2263:
2259:
2252:
2248:
2238:
2226:
2222:
2220:
2217:
2216:
2163:
2155:
2153:
2152:
2146:
2141:
2103:
2099:
2097:
2088:
2084:
2077:
2073:
2058:
2054:
2052:
2049:
2048:
2027:
2026:
2021:
1991:
1987:
1960:
1956:
1927:
1916:
1914:
1910:
1901:
1897:
1866:
1865:
1835:
1831:
1807:
1803:
1794:
1790:
1777:
1769:
1767:
1762:
1760:
1757:
1756:
1752:
1740:
1732:
1726:
1725:
1724:
1682:
1680:
1666:
1663:
1662:
1640:
1632:
1617:
1610:
1598:
1591:
1589:
1583:
1578:
1564:
1559:
1517:
1509:
1507:
1500:
1496:
1494:
1491:
1490:
1476:
1464:
1458:
1457:
1455:
1451:
1443:
1437:
1436:
1434:
1430:
1422:
1397:
1394:
1393:
1385:
1365:
1357:
1342:
1335:
1323:
1316:
1314:
1308:
1303:
1289:
1284:
1267:
1264:
1263:
1255:
1252:Biot–Savart law
1206:
1201:
1189:
1186:
1185:
1181:
1180:and its moment
1145:
1140:
1128:
1125:
1124:
1120:
1112:
1105:
1095:
1085:
1083:
1082:
1078:
1077:
1071:
1063:
1060:Kutta condition
1051:
1040:
1032:
1026:
1025:
1024:
1020:
1016:
1015:, ranging from
1012:
1008:
1006:angle of attack
1000:
996:
994:
990:
988:
984:
982:
978:
962:
925:
921:
920:
916:
911:
908:
907:
874:
870:
869:
865:
856:
852:
847:
844:
843:
816:
813:
812:
801:angle of attack
783:
780:
779:
759:
755:
753:
750:
749:
718:
714:
709:
706:
705:
674:
671:
670:
630:Hermann Glauert
618:angle of attack
587:
562:pitching moment
453:
450:
449:
395:suction surface
379:
329:drag divergence
164:
126:subsonic flight
118:angle of attack
72:British English
42:
28:
23:
22:
15:
12:
11:
5:
4175:
4165:
4164:
4159:
4142:
4141:
4139:
4138:
4132:
4130:
4126:
4125:
4123:
4122:
4117:
4112:
4107:
4102:
4097:
4092:
4087:
4081:
4079:
4075:
4074:
4072:
4071:
4065:
4063:
4057:
4056:
4054:
4053:
4048:
4043:
4038:
4033:
4028:
4022:
4020:
4014:
4013:
4011:
4010:
4005:
4000:
3995:
3990:
3984:
3982:
3976:
3975:
3973:
3972:
3967:
3965:Wind generator
3962:
3957:
3952:
3947:
3942:
3936:
3934:
3928:
3927:
3925:
3924:
3919:
3913:
3911:
3905:
3904:
3902:
3901:
3896:
3891:
3886:
3880:
3878:
3872:
3871:
3869:
3868:
3863:
3857:
3855:
3849:
3848:
3846:
3845:
3840:
3835:
3830:
3825:
3820:
3814:
3812:
3802:
3801:
3799:
3798:
3793:
3791:Pendulum clock
3788:
3783:
3777:
3775:
3769:
3768:
3766:
3765:
3763:Wheel and axle
3760:
3755:
3750:
3745:
3740:
3738:Inclined plane
3734:
3732:
3726:
3725:
3718:
3717:
3710:
3703:
3695:
3689:
3688:
3683:
3678:
3673:
3667:
3662:
3655:
3654:External links
3652:
3651:
3650:
3633:
3626:
3610:. McGraw-Hill.
3601:
3598:
3596:
3595:
3574:
3539:
3530:
3524:
3509:
3464:
3447:
3441:
3426:
3415:
3409:
3396:
3390:
3377:
3365:
3339:(6): 497–503.
3321:
3306:
3300:
3281:
3279:
3276:
3273:
3272:
3270:, p. 470.
3268:Batchelor 1967
3260:
3256:Batchelor 1967
3248:
3244:Batchelor 1967
3236:
3221:
3204:
3200:Batchelor 1967
3189:
3187:, p. 467.
3185:Batchelor 1967
3177:
3155:
3103:
3091:
3079:
3067:
3055:
3043:
3031:
3019:
3006:
2993:
2980:
2978:, p. 199.
2968:
2956:
2941:
2929:
2914:
2895:
2878:
2866:
2854:
2837:
2807:
2795:
2782:
2781:
2779:
2776:
2774:
2771:
2770:
2769:
2764:
2759:
2757:KĂĽssner effect
2754:
2749:
2744:
2737:
2734:
2716:
2713:
2707:
2702:
2698:
2694:
2691:
2686:
2680:
2677:
2672:
2668:
2665:
2620:
2615:
2611:
2606:
2602:
2597:
2593:
2589:
2584:
2580:
2576:
2573:
2570:
2566:
2562:
2559:
2556:
2552:
2548:
2545:
2509:
2504:
2500:
2496:
2491:
2487:
2483:
2480:
2476:
2472:
2469:
2466:
2463:
2460:
2457:
2453:
2449:
2446:
2441:
2437:
2410:
2407:
2403:
2400:
2397:
2394:
2391:
2388:
2385:
2382:
2379:
2376:
2373:
2370:
2367:
2361:
2358:
2353:
2350:
2341:
2336:
2332:
2328:
2325:
2320:
2317:
2312:
2309:
2305:
2299:
2294:
2290:
2284:
2279:
2275:
2271:
2266:
2262:
2258:
2255:
2251:
2245:
2242:
2237:
2234:
2229:
2225:
2203:
2200:
2196:
2193:
2190:
2187:
2184:
2181:
2178:
2175:
2169:
2166:
2161:
2158:
2149:
2144:
2140:
2136:
2133:
2130:
2127:
2124:
2121:
2117:
2111:
2106:
2102:
2096:
2091:
2087:
2083:
2080:
2076:
2072:
2069:
2066:
2061:
2057:
2020:
2017:
2014:
2011:
2008:
2005:
2002:
1999:
1994:
1990:
1986:
1983:
1980:
1977:
1974:
1971:
1968:
1963:
1959:
1955:
1952:
1948:
1942:
1939:
1936:
1933:
1930:
1925:
1922:
1919:
1913:
1909:
1904:
1900:
1896:
1893:
1890:
1887:
1884:
1881:
1878:
1875:
1872:
1869:
1867:
1864:
1861:
1858:
1855:
1852:
1849:
1846:
1843:
1838:
1834:
1830:
1827:
1824:
1821:
1818:
1815:
1810:
1806:
1802:
1797:
1793:
1789:
1783:
1780:
1775:
1772:
1766:
1764:
1749:Fourier series
1712:
1707:
1703:
1700:
1697:
1694:
1691:
1688:
1685:
1679:
1676:
1673:
1670:
1638:
1635:
1631:
1623:
1620:
1616:
1613:
1608:
1604:
1601:
1597:
1594:
1586:
1581:
1577:
1570:
1567:
1563:
1558:
1555:
1552:
1549:
1546:
1543:
1540:
1537:
1534:
1530:
1523:
1520:
1515:
1512:
1506:
1503:
1499:
1410:
1407:
1404:
1401:
1363:
1360:
1356:
1348:
1345:
1341:
1338:
1333:
1329:
1326:
1322:
1319:
1311:
1306:
1302:
1295:
1292:
1288:
1283:
1280:
1277:
1274:
1271:
1237:
1234:
1231:
1227:
1224:
1221:
1218:
1214:
1209:
1204:
1200:
1196:
1193:
1169:
1166:
1162:
1159:
1156:
1153:
1148:
1143:
1139:
1135:
1132:
995:
989:
983:
977:
961:
958:
949:inviscid fluid
945:
944:
928:
924:
919:
904:
893:
890:
887:
884:
877:
873:
868:
864:
859:
855:
834:zero-lift line
820:
809:
808:
787:
777:
762:
758:
746:
735:
732:
729:
726:
721:
717:
695:
694:
681:
678:
663:
656:
622:inviscid flows
586:
583:
567:
566:
551:
525:
524:
523:
522:
519:
509:
492:(PSU 90-125WL)
474:
473:
457:
432:
419:
406:
405:
398:
378:
375:
356:Franz Wortmann
338:and sometimes
259:boundary layer
163:
160:
148:potential flow
105:to the remote
26:
9:
6:
4:
3:
2:
4174:
4163:
4160:
4158:
4155:
4154:
4152:
4137:
4134:
4133:
4131:
4127:
4121:
4118:
4116:
4113:
4111:
4108:
4106:
4103:
4101:
4098:
4096:
4093:
4091:
4088:
4086:
4083:
4082:
4080:
4078:Miscellaneous
4076:
4070:
4067:
4066:
4064:
4062:
4058:
4052:
4049:
4047:
4044:
4042:
4039:
4037:
4034:
4032:
4029:
4027:
4024:
4023:
4021:
4019:
4015:
4009:
4006:
4004:
4001:
3999:
3996:
3994:
3991:
3989:
3986:
3985:
3983:
3981:
3977:
3971:
3968:
3966:
3963:
3961:
3960:Water turbine
3958:
3956:
3955:Steam turbine
3953:
3951:
3948:
3946:
3943:
3941:
3938:
3937:
3935:
3933:
3929:
3923:
3920:
3918:
3915:
3914:
3912:
3910:
3906:
3900:
3897:
3895:
3894:Rotary engine
3892:
3890:
3887:
3885:
3882:
3881:
3879:
3877:
3873:
3867:
3864:
3862:
3859:
3858:
3856:
3854:
3850:
3844:
3841:
3839:
3836:
3834:
3831:
3829:
3828:Hydraulic ram
3826:
3824:
3821:
3819:
3816:
3815:
3813:
3811:
3807:
3803:
3797:
3794:
3792:
3789:
3787:
3784:
3782:
3779:
3778:
3776:
3774:
3770:
3764:
3761:
3759:
3756:
3754:
3751:
3749:
3746:
3744:
3741:
3739:
3736:
3735:
3733:
3731:
3727:
3723:
3716:
3711:
3709:
3704:
3702:
3697:
3696:
3693:
3687:
3684:
3682:
3679:
3677:
3674:
3671:
3668:
3666:
3663:
3661:
3658:
3657:
3647:
3643:
3640:(29): 74–87.
3639:
3634:
3631:
3627:
3623:
3617:
3609:
3604:
3603:
3584:
3580:
3575:
3570:
3565:
3561:
3557:
3553:
3549:
3545:
3540:
3536:
3531:
3527:
3521:
3517:
3516:
3510:
3506:
3502:
3498:
3494:
3490:
3486:
3482:
3478:
3474:
3470:
3465:
3461:
3457:
3453:
3448:
3444:
3438:
3434:
3433:
3427:
3423:
3422:
3416:
3412:
3410:0-273-01120-0
3406:
3402:
3397:
3393:
3387:
3383:
3378:
3374:
3370:
3366:
3362:
3358:
3354:
3350:
3346:
3342:
3338:
3334:
3327:
3322:
3318:
3317:
3312:
3307:
3303:
3297:
3293:
3292:
3287:
3283:
3282:
3269:
3264:
3257:
3252:
3245:
3240:
3232:
3225:
3218:
3213:
3211:
3209:
3201:
3196:
3194:
3186:
3181:
3173:
3169:
3164:
3159:
3151:
3147:
3143:
3139:
3135:
3131:
3127:
3123:
3119:
3115:
3107:
3100:
3095:
3088:
3083:
3076:
3071:
3064:
3059:
3052:
3047:
3040:
3035:
3028:
3023:
3017:, section 1.3
3016:
3010:
3003:
2997:
2990:
2984:
2977:
2972:
2966:, p. 27.
2965:
2964:Phillips 2004
2960:
2954:, p. 17.
2953:
2948:
2946:
2939:, p. 18.
2938:
2933:
2925:
2918:
2910:
2906:
2899:
2891:
2890:
2882:
2875:
2874:Babinsky 2003
2870:
2863:
2858:
2851:
2847:
2841:
2834:
2822:
2818:
2811:
2804:
2799:
2792:
2787:
2783:
2768:
2765:
2763:
2760:
2758:
2755:
2753:
2750:
2748:
2745:
2743:
2740:
2739:
2733:
2714:
2711:
2700:
2696:
2678:
2675:
2670:
2652:
2644:
2639:
2613:
2609:
2604:
2595:
2591:
2587:
2582:
2578:
2568:
2564:
2560:
2557:
2554:
2550:
2546:
2534:
2528:
2502:
2498:
2494:
2489:
2485:
2478:
2474:
2470:
2467:
2464:
2458:
2455:
2451:
2447:
2439:
2435:
2408:
2405:
2398:
2395:
2392:
2389:
2386:
2377:
2371:
2368:
2365:
2359:
2356:
2351:
2348:
2339:
2334:
2330:
2326:
2323:
2318:
2315:
2310:
2307:
2303:
2297:
2292:
2288:
2282:
2277:
2273:
2269:
2264:
2260:
2256:
2253:
2249:
2243:
2240:
2235:
2232:
2227:
2223:
2201:
2198:
2191:
2188:
2185:
2182:
2179:
2173:
2167:
2164:
2159:
2156:
2147:
2142:
2138:
2134:
2131:
2128:
2125:
2122:
2119:
2115:
2109:
2104:
2100:
2094:
2089:
2085:
2081:
2078:
2074:
2070:
2067:
2064:
2059:
2055:
2046:
2041:
2018:
2015:
2009:
2006:
2000:
1997:
1992:
1988:
1984:
1981:
1975:
1969:
1966:
1961:
1957:
1953:
1950:
1946:
1940:
1937:
1934:
1931:
1928:
1923:
1920:
1917:
1911:
1902:
1898:
1894:
1891:
1885:
1882:
1876:
1870:
1862:
1859:
1853:
1850:
1844:
1841:
1836:
1832:
1828:
1822:
1816:
1813:
1808:
1804:
1800:
1795:
1791:
1787:
1781:
1778:
1773:
1770:
1750:
1744:
1735:
1729:
1710:
1705:
1698:
1692:
1689:
1686:
1683:
1677:
1674:
1671:
1668:
1661:
1656:
1636:
1633:
1629:
1621:
1618:
1614:
1611:
1602:
1599:
1592:
1584:
1579:
1575:
1568:
1565:
1561:
1556:
1553:
1547:
1541:
1538:
1535:
1532:
1528:
1521:
1518:
1513:
1510:
1504:
1501:
1497:
1489:
1486:
1480:
1473:
1467:
1461:
1446:
1440:
1428:
1405:
1399:
1391:
1383:
1361:
1358:
1354:
1346:
1343:
1339:
1336:
1327:
1324:
1317:
1309:
1304:
1300:
1293:
1290:
1286:
1281:
1275:
1269:
1259:
1253:
1248:
1235:
1232:
1229:
1222:
1216:
1212:
1207:
1202:
1198:
1194:
1191:
1167:
1164:
1157:
1151:
1146:
1141:
1137:
1133:
1130:
1118:
1111:
1104:
1098:
1088:
1075:
1067:
1062:implies that
1061:
1055:
1049:
1044:
1035:
1029:
1007:
975:
971:
966:
957:
954:
950:
926:
922:
917:
905:
891:
888:
885:
882:
875:
871:
866:
862:
857:
853:
842:
841:
840:
837:
835:
818:
806:
802:
785:
778:
760:
756:
747:
733:
730:
727:
724:
719:
715:
704:
703:
702:
700:
679:
676:
668:
664:
661:
657:
654:
650:
646:
642:
641:
640:
637:
635:
631:
627:
623:
619:
615:
608:
605:Airfoil of a
603:
596:
595:Denney Kitfox
591:
582:
580:
576:
572:
564:
563:
558:
557:
552:
549:
548:
543:
542:
541:
538:
536:
532:
531:
520:
517:
516:
514:
510:
507:
503:
499:
498:
497:
491:
486:
478:
471:
455:
447:
443:
439:
438:
433:
430:
426:
425:
424:trailing edge
420:
417:
416:
411:
410:
409:
403:
399:
396:
392:
391:
390:
383:
374:
372:
368:
363:
361:
357:
352:
348:
343:
341:
337:
332:
330:
326:
322:
318:
314:
311:
307:
303:
299:
295:
291:
287:
283:
278:
276:
275:pressure drag
272:
268:
264:
260:
256:
252:
248:
243:
240:
235:
233:
229:
225:
221:
217:
213:
209:
205:
201:
197:
193:
189:
186:, as well as
185:
176:
168:
159:
157:
153:
149:
146:
142:
137:
135:
131:
127:
123:
119:
114:
112:
108:
104:
103:perpendicular
100:
96:
91:
89:
85:
81:
77:
73:
69:
65:
61:
54:
37:
32:
19:
4157:Aerodynamics
4095:Agricultural
3979:
3950:Quasiturbine
3861:Steam engine
3796:Quartz clock
3781:Atomic clock
3637:
3607:
3587:. Retrieved
3583:the original
3551:
3547:
3514:
3472:
3468:
3451:
3431:
3420:
3401:Aerodynamics
3400:
3381:
3372:
3336:
3332:
3315:
3290:
3263:
3251:
3239:
3230:
3224:
3180:
3171:
3167:
3158:
3117:
3113:
3106:
3101:, p. 9.
3094:
3082:
3070:
3058:
3046:
3034:
3022:
3014:
3009:
3001:
2996:
2988:
2983:
2971:
2959:
2932:
2923:
2917:
2908:
2898:
2888:
2881:
2869:
2857:
2849:
2840:
2831:
2825:. Retrieved
2810:
2798:
2786:
2650:
2642:
2532:
2042:
1742:
1733:
1727:
1657:
1478:
1471:
1465:
1459:
1444:
1438:
1257:
1249:
1096:
1086:
1073:
1065:
1053:
1048:vortex sheet
1045:
1033:
1027:
1003:
946:
838:
810:
696:
666:
638:
613:
612:
579:aspect ratio
574:
568:
560:
554:
545:
539:
534:
528:
526:
512:
505:
501:
495:
469:
445:
444:, or simply
442:chord length
441:
435:
428:
422:
415:leading edge
413:
407:
401:
394:
388:
364:
346:
344:
333:
315:
282:aerodynamics
279:
254:
244:
236:
220:sand dollars
181:
138:
130:leading edge
115:
109:) and drag (
92:
67:
59:
57:
4110:Wind tunnel
4026:Vacuum tube
4018:Electronics
3940:Gas turbine
3884:Gas turbine
3843:Vacuum pump
3806:Compressors
3786:Chronometer
3681:Desktopaero
3475:: 439–472.
3120:: 500–538.
3075:Morris 2009
3051:Clancy 1975
2791:Clancy 1975
1485:convolution
1392:, the flow
1115:, then the
974:pylon racer
607:Kamov Ka-26
367:NACA system
292:and near a
271:circulation
247:wind tunnel
204:centerboard
196:compressors
152:circulation
53:wind tunnel
4151:Categories
4069:Automobile
4031:Transistor
3945:Jet engine
3917:Pantograph
3099:Traub 2016
3063:Scott 2003
2827:2011-06-29
2773:References
2047:satisfies
1425:. By the
1101:. If the
970:park flyer
960:Derivation
571:lift curve
437:chord line
228:automobile
188:helicopter
88:hydrofoils
4046:Capacitor
4008:Propeller
3646:2051-1930
3616:cite book
3548:Aerospace
3505:122817884
3497:0022-1120
3294:. Dover.
3150:121962230
3142:0022-1120
2778:Citations
2747:Hydrofoil
2690:∂
2664:∂
2649:does not
2588:−
2561:π
2544:Δ
2495:−
2471:π
2468:−
2409:θ
2399:θ
2396:
2378:θ
2372:
2366:⋅
2340:π
2331:∫
2327:−
2324:α
2316:π
2311:−
2283:−
2254:α
2241:π
2236:−
2202:θ
2192:θ
2189:
2174:⋅
2148:π
2139:∫
2129:α
2126:π
2079:α
2071:π
2019:…
2010:θ
2001:
1976:θ
1970:
1941:θ
1938:
1924:θ
1921:
1892:α
1871:γ
1863:…
1854:θ
1845:
1823:θ
1817:
1699:θ
1693:
1678:⋅
1615:−
1593:γ
1576:∫
1569:π
1557:−
1539:−
1505:−
1502:α
1475:. Thus,
1380:oriented
1340:−
1318:γ
1301:∫
1294:π
1250:From the
1217:γ
1199:∫
1192:ρ
1152:γ
1138:∫
1131:ρ
1103:main flow
1099:≈ 0
892:α
889:π
819:α
786:α
734:α
731:π
680:π
535:thickness
513:thickness
506:mean line
325:transonic
286:aerobatic
224:downforce
36:hydrofoil
4061:Vehicles
4051:Inductor
4041:Resistor
3980:Aerofoil
3970:Windmill
3909:Linkages
3722:Machines
3589:25 April
3554:(2): 9.
3371:(1967).
3170:≈
2848:(1945),
2821:Archived
2762:Parafoil
2736:See also
2679:′
1637:′
1622:′
1603:′
1488:equation
1456:(α-
1362:′
1347:′
1328:′
1076:)∝
669:line is
660:cambered
634:wingspan
626:Max Munk
533:and its
490:winglets
290:ailerons
232:traction
200:turbines
162:Overview
154:and the
145:inviscid
122:cambered
111:parallel
68:aerofoil
18:Airfoils
4129:Springs
3932:Turbine
3670:FoilSim
3556:Bibcode
3477:Bibcode
3456:Bibcode
3361:1657792
3341:Bibcode
3122:Bibcode
3041:, §4.3.
3029:, §4.2.
2793:, §5.2.
1741:γ(
1731:⁄
1477:γ(
1463:⁄
1442:⁄
1435:α-
1256:γ(
1110:density
1084:√
1081:⁄
1072:γ(
1064:γ(
1058:. The
1052:γ(
1031:⁄
799:is the
371:Clark-Y
294:wingtip
216:sessile
60:airfoil
3998:Rudder
3838:Trompe
3773:Clocks
3748:Pulley
3644:
3522:
3503:
3495:
3439:
3407:
3388:
3359:
3298:
3148:
3140:
1753:θ
1382:normal
1113:ρ
1009:α
997:
991:
985:
979:
914:
906:where
850:
748:where
712:
530:camber
267:camber
251:camber
226:on an
210:, and
208:rudder
4090:Robot
4085:Mecha
4036:Diode
3810:pumps
3758:Wedge
3753:Screw
3743:Lever
3501:S2CID
3357:S2CID
3329:(PDF)
3146:S2CID
2833:body.
2536:, by
953:stall
807:line.
805:chord
658:on a
653:chord
446:chord
340:slats
336:flaps
302:stall
255:slope
95:fluid
84:Foils
78:than
66:) or
4003:Flap
3993:Wing
3988:Sail
3833:Pump
3808:and
3642:ISSN
3622:link
3591:2021
3520:ISBN
3493:ISSN
3437:ISBN
3405:ISBN
3386:ISBN
3296:ISBN
3138:ISSN
2651:vary
2636:The
2531:0.25
2043:The
1739:and
1108:has
1094:for
647:and
553:The
544:The
511:The
500:The
434:The
421:The
412:The
400:The
393:The
298:spin
239:drag
212:keel
198:and
192:fans
80:drag
76:lift
3564:doi
3485:doi
3473:733
3349:doi
3130:doi
3118:751
2393:cos
2369:cos
2186:cos
1998:sin
1967:sin
1935:cos
1918:sin
1842:cos
1814:cos
1751:in
1690:cos
1068:)=0
504:or
58:An
4153::
3618:}}
3614:{{
3562:.
3550:.
3546:.
3499:.
3491:.
3483:.
3471:.
3355:.
3347:.
3337:38
3335:.
3331:.
3313:.
3207:^
3192:^
3175:."
3172:dx
3168:ds
3144:.
3136:.
3128:.
3116:.
2944:^
2907:.
2830:.
1734:dx
1728:dy
1466:dx
1460:dy
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