81:
where the numbering system was complemented by an airfoil cross-section, and the complete catalog of 78 airfoils appeared in the NACA's annual report for 1933. Engineers could quickly see the peculiarities of each airfoil shape, and the numerical designator ("NACA 2415", for instance) specified camber lines, maximum thickness, and special nose features. These figures and shapes transmitted the sort of information to engineers that allowed them to select specific airfoils for desired performance characteristics of specific aircraft.
20:
37:
311:= 1 (the trailing edge of the airfoil), the thickness is not quite zero. If a zero-thickness trailing edge is required, for example for computational work, one of the coefficients should be modified such that they sum to zero. Modifying the last coefficient (i.e. to â0.1036) will result in the smallest change to the overall shape of the airfoil. The leading edge approximates a cylinder with a chord-normalized radius of
29:
124:
572:
1170:
813:
2431:
1447:
2196:
1736:
80:
During the late 1920s and into the 1930s, the NACA developed a series of thoroughly tested airfoils and devised a numerical designation for each airfoil â a four digit number that represented the airfoil section's critical geometric properties. By 1929, Langley had developed this system to the point
944:
3512:
For example, the NACA 712A315 has the area of minimum pressure 10% of the chord back on the upper surface and 20% of the chord back on the lower surface, uses the standard "A" profile, has a lift coefficient of 0.3, and has a maximum thickness of 15% of the chord.
1497:
For example, the NACA 23112 profile describes an airfoil with design lift coefficient of 0.3 (0.15 Ă 2), the point of maximum camber located at 15% chord (5 Ă 3), reflex camber (1), and maximum thickness of 12% of chord length (12).
586:
3412:
A new approach to airfoil design was pioneered in the 1930s, in which the airfoil shape was mathematically derived from the desired lift characteristics. Prior to this, airfoil shapes were first created and then had their characteristics measured in a
2207:
1243:
1970:
1507:
579:
The simplest asymmetric foils are the NACA 4-digit series foils, which use the same formula as that used to generate the 00xx symmetric foils, but with the line of mean camber bent. The formula used to calculate the mean camber line is
3488:
Further advancement in maximizing laminar flow achieved by separately identifying the low-pressure zones on upper and lower surfaces of the airfoil. The airfoil is described by seven digits in the following sequence:
23:
Profile geometry â 1: Zero-lift line; 2: Leading edge; 3: Nose circle; 4: Max. thickness; 5: Camber; 6: Upper surface; 7: Trailing edge; 8: Camber mean-line; 9: Lower
558:
3480:-415, has the minimum pressure placed at 50% of the chord, has a maximum thickness of 15% of the chord, design lift coefficient of 0.4 and maintains laminar flow for lift coefficients between 0 and 0.8.
3099:
2844:
1165:{\displaystyle {\begin{aligned}x_{U}&=x-y_{t}\,\sin \theta ,&y_{U}&=y_{c}+y_{t}\,\cos \theta ,\\x_{L}&=x+y_{t}\,\sin \theta ,&y_{L}&=y_{c}-y_{t}\,\cos \theta ,\end{aligned}}}
1235:
3524:
designed to independently maximize laminar flow above and below the wing. The numbering is identical to the 7-series airfoils except that the sequence begins with an "8" to identify the series.
949:
115:
The NACA 0015 airfoil is symmetrical, the 00 indicating that it has no camber. The 15 indicates that the airfoil has a 15% thickness to chord length ratio: it is 15% as thick as it is long.
2886:
843:
For example, a NACA 2412 airfoil uses a 2% camber (first digit) 40% (second digit) along the chord of a 0012 symmetrical airfoil having a thickness 12% (digits 3 and 4) of the chord.
808:{\displaystyle y_{c}={\begin{cases}{\dfrac {m}{p^{2}}}\left(2px-x^{2}\right),&0\leq x\leq p,\\{\dfrac {m}{(1-p)^{2}}}\left((1-2p)+2px-x^{2}\right),&p\leq x\leq 1,\end{cases}}}
2426:{\displaystyle {\frac {dy_{c}}{dx}}={\begin{cases}{\dfrac {k_{1}}{6}}{\big (}3x^{2}-6rx+r^{2}(3-r){\big )},&0<x<r,\\-{\dfrac {k_{1}r^{3}}{6}},&r<x<1.\end{cases}}}
1442:{\displaystyle {\frac {dy_{c}}{dx}}={\begin{cases}{\dfrac {2m}{p^{2}}}\left(p-x\right),&0\leq x\leq p,\\{\dfrac {2m}{(1-p)^{2}}}\left(p-x\right),&p\leq x\leq 1.\end{cases}}}
2654:
3394:
One digit describing the roundness of the leading edge, with 0 being sharp, 6 being the same as the original airfoil, and larger values indicating a more rounded leading edge.
2191:{\displaystyle y_{c}={\begin{cases}{\dfrac {k_{1}}{6}}{\big (}x^{3}-3rx^{2}+r^{2}(3-r)x{\big )},&0<x<r,\\{\dfrac {k_{1}r^{3}}{6}}(1-x),&r<x<1.\end{cases}}}
1731:{\displaystyle y_{c}={\begin{cases}{\dfrac {k_{1}}{6}}{\big (}x^{3}-3rx^{2}+r^{2}(3-r)x{\big )},&0<x<r,\\{\dfrac {k_{1}r^{3}}{6}}(1-x),&r<x<1,\end{cases}}}
351:
248:
936:
890:
446:
400:
3459:
The subscript digit gives the range of lift coefficient in tenths above and below the design lift coefficient in which favorable pressure gradients exist on both surfaces.
2620:
Camber lines such as 231 makes the negative trailing edge camber of the 230 series profile to be positively cambered. This results in a theoretical pitching moment of 0.
1951:
1865:
3310:
3190:
1891:
3267:
3148:
2538:
2461:
1918:
287:
1825:
3239:
3218:
3121:
2510:
2489:
1799:
1779:
1759:
3874:
112:
For example, the NACA 2412 airfoil has a maximum camber of 2% located 40% (0.4 chords) from the leading edge with a maximum thickness of 12% of the chord.
3437:
For example, the NACA 16-123 airfoil has minimum pressure 60% of the chord back with a lift coefficient of 0.1 and maximum thickness of 23% of the chord.
3401:
For example, the NACA 1234-05 is a NACA 1234 airfoil with a sharp leading edge and maximum thickness 50% of the chord (0.5 chords) from the leading edge.
3744:
E. N. Jacobs & R. M. Pinkerton 1936 Test in the variable-density wind tunnel of related airfoils having the maximum camber unusually far forward,
3471:"a=" followed by a decimal number describing the fraction of chord over which laminar flow is maintained. a=1 is the default if no value is given.
60:
airfoil series is a set of standardized airfoil shapes developed by this agency, which became widely used in the design of aircraft wings.
3103:
The following table presents the various camber-line profile coefficients for a theoretical design lift coefficient of 0.3 - the value of
2436:
The following table presents the various camber-line profile coefficients for a theoretical design lift coefficient of 0.3 - the value of
454:
575:
Plot of a NACA 2412 foil. The camber line is shown in red, and the thickness â or the symmetrical airfoil 0012 â is shown in purple.
40:
A: blue line = chord, green line = camber mean-line, B: leading-edge radius, C:
1920:
is determined to give the desired lift coefficient. For a 230 camber-line profile (the first 3 numbers in the 5-digit series),
2892:
2661:
3390:
Four- and five-digit series airfoils can be modified with a two-digit code preceded by a hyphen in the following sequence:
1181:
3658:
3591:
NACA Report No. 460, "The characteristics of 78 related airfoil sections from tests in the variable-density wind tunnel"
3782:
846:
For this cambered airfoil, because the thickness needs to be applied perpendicular to the camber line, the coordinates
3630:
131:
The formula for the shape of a NACA 00xx foil, with "xx" being replaced by the percentage of thickness to chord, is
2852:
563:
Symmetrical 4-digit series airfoils by default have maximum thickness at 30% of the chord from the leading edge.
3720:
3844:
3869:
3845:
Numerical
Analysis of NACA Airfoil 0012 at Different Attack Angles and Obtaining its Aerodynamic Coefficients
3694:
105:
Second digit describing the distance of maximum camber from the airfoil leading edge in tenths of the chord.
3499:
One digit describing the distance of the minimum pressure area on the lower surface in tenths of the chord.
3496:
One digit describing the distance of the minimum pressure area on the upper surface in tenths of the chord.
2626:
1490:
S: a single digit indicating whether the camber is simple (S = 0) or reflex (S = 1),
3404:
In addition, for a more precise description of the airfoil all numbers can be presented as decimals.
3397:
One digit describing the distance of maximum thickness from the leading edge in tenths of the chord.
2246:
1992:
1529:
1282:
608:
317:
137:
895:
849:
405:
359:
1923:
1830:
1461:
L: a single digit representing the theoretical optimal lift coefficient at ideal angle of attack C
3273:
3153:
73:
69:
3834:
3564:
3774:
1870:
1457:
The NACA five-digit series describes more complex airfoil shapes. Its format is LPSTT, where:
3864:
3521:
95:
3829:
3762:
3645:
3622:
3245:
3126:
2516:
2439:
1896:
265:
3817:
8:
1804:
3770:
3224:
3203:
3106:
2495:
2474:
1784:
1764:
1744:
3802:
NASA Technical
Memorandum 4741, Computer Program To Obtain Ordinates for NACA Airfoils
3456:
One digit describing the distance of the minimum pressure area in tenths of the chord.
68:
NACA initially developed the numbered airfoil system which was further refined by the
3778:
3763:
3626:
3849:
1493:
TT: the maximum thickness in percent of chord, as in a four-digit NACA airfoil code.
108:
Last two digits describing maximum thickness of the airfoil as percent of the chord.
99:
3695:"Tests of N.A.C.A. Airfoils in the Variable-Density Wind Tunnel: Series 43 and 63"
3424:
One digit describing the distance of the minimum-pressure area in tenths of chord.
3616:
1961:
3-digit camber lines provide a very far forward location for the maximum camber.
3417:. The 1-series airfoils are described by five digits in the following sequence:
3664:
32:
Profile lines â 1: Chord, 2: Camber, 3: Length, 4: Midline
3858:
3538:
3533:
3446:
303:
gives the last two digits in the NACA 4-digit denomination divided by 100).
3745:
3590:
3414:
3192:
must be linearly scaled for a different desired design lift coefficient:
2463:
must be linearly scaled for a different desired design lift coefficient:
3602:"Fundamentals of aerodynamics", John D. Anderson, Jr., third ed., ch. 4.
3502:
One letter referring to a standard profile from the earlier NACA series.
1501:
The camber line for the simple case (S = 0) is defined in two sections:
3801:
3449:. The airfoil is described using six digits in the following sequence:
3543:
553:{\displaystyle x_{U}=x_{L}=x,\quad y_{U}=+y_{t},\quad y_{L}=-y_{t}.}
19:
3445:
An improvement over 1-series airfoils with emphasis on maximizing
118:
3589:
E. N. Jacobs, K. E. Ward, & R. M. Pinkerton.
3508:
Two digits describing the maximum thickness as percent of chord.
3468:
Two digits describing the maximum thickness as percent of chord.
3433:
Two digits describing the maximum thickness in percent of chord.
36:
28:
566:
3839:
938:, of respectively the upper and lower airfoil surface, become
3823:
3618:
An introduction to theoretical and computational aerodynamics
123:
3765:
Theory of Wing
Sections: Including a Summary of Airfoil Data
571:
3702:
National
Advisory Committee for Aeronautics, Technical Note
3465:
One digit describing the design lift coefficient in tenths.
2419:
2184:
1724:
1435:
801:
260:
is the position along the chord from 0 to 1.00 (0 to 100%),
57:
1483:
coordinate of the point of maximum camber (max. camber at
90:
The NACA four-digit wing sections define the profile by:
3824:
John Dreese's NACA airfoil coordinate generation program
299:
is the maximum thickness as a fraction of the chord (so
3094:{\displaystyle {\frac {y}{c}}={\frac {k_{1}}{6}}\left.}
2839:{\displaystyle {\frac {y}{c}}={\frac {k_{1}}{6}}\left.}
3692:
3276:
3248:
3227:
3206:
3156:
3129:
3109:
2895:
2855:
2664:
2629:
2519:
2498:
2477:
2442:
2366:
2250:
2210:
2116:
1996:
1973:
1926:
1899:
1873:
1833:
1807:
1787:
1767:
1747:
1653:
1533:
1510:
1356:
1286:
1246:
1230:{\displaystyle \theta =\arctan {\frac {dy_{c}}{dx}},}
1184:
947:
898:
852:
690:
612:
589:
457:
408:
362:
320:
268:
140:
3505:
One digit describing the lift coefficient in tenths.
3430:
One digit describing the lift coefficient in tenths.
1956:
3850:NACA 4 & 5 digits, 16 series airfoil generator
3796:
3794:
3760:
3304:
3261:
3233:
3212:
3184:
3142:
3115:
3093:
2880:
2838:
2648:
2532:
2504:
2483:
2455:
2425:
2190:
1945:
1912:
1885:
1859:
1819:
1793:
1773:
1753:
1730:
1441:
1229:
1164:
930:
884:
839:is the second digit in the NACA xxxx description).
807:
552:
440:
394:
345:
281:
242:
3693:Eastman N., Jacobs; M. Pinkerton, Robert (1931).
1781:have been normalized by the chord. The constant
3856:
2615:
3791:
3646:Aerospaceweb.org | Ask Us - NACA Airfoil Series
1801:is chosen so that the maximum camber occurs at
127:Plot of a NACA 0015 foil generated from formula
119:Equation for a symmetrical 4-digit NACA airfoil
3677:
44:coordinates for the profile geometry (chord =
2330:
2270:
2083:
2016:
1620:
1553:
567:Equation for a cambered 4-digit NACA airfoil
3875:National Advisory Committee for Aeronautics
3800:C. L. Ladson, C.W. Brooks Jr., A. S. Hill.
2881:{\displaystyle r<{\frac {x}{c}}\leq 1.0}
3761:Abbott, Ira; von Doenhoff, Albert (1959).
289:is the half thickness at a given value of
3756:
3754:
3610:
3608:
1145:
1090:
1040:
985:
1827:; for example, for the 230 camber line,
570:
122:
35:
27:
18:
3857:
3751:
3605:
835:is the location of maximum camber (10
3835:NASA website feature on NACA airfoils
3820:coordinates for nearly 1,600 airfoils
3680:Principles of Helicopter Aerodynamics
3656:
3614:
3562:
3493:The number "7" indicating the series.
3453:The number "6" indicating the series.
3421:The number "1" indicating the series.
3718:
2649:{\displaystyle {\frac {x}{c}}\leq r}
1452:
85:
13:
14:
3886:
3811:
1957:Non-reflexed 3 digit camber lines
1469:the same as the lift coefficient
829:is the first of the four digits),
448:of the lower airfoil surface are
402:of the upper airfoil surface and
76:. According to the NASA website:
3818:UIUC Airfoil Coordinate Database
3385:
3738:
520:
490:
94:First digit describing maximum
52:axis line on that leading edge)
3712:
3686:
3671:
3650:
3639:
3596:
3583:
3563:Allen, Bob (31 January 2017).
3556:
3028:
3015:
2773:
2760:
2325:
2313:
2201:with the camber line gradient
2158:
2146:
2075:
2063:
1964:The camber line is defined as
1695:
1683:
1612:
1600:
1380:
1367:
925:
899:
879:
853:
742:
727:
709:
696:
435:
409:
389:
363:
346:{\displaystyle r=1.1019t^{2}.}
243:{\displaystyle y_{t}=5t\left,}
1:
3826:Works on Windows XP, 7 and 8.
3549:
2616:Reflexed 3-digit camber lines
1741:where the chordwise location
931:{\displaystyle (x_{L},y_{L})}
885:{\displaystyle (x_{U},y_{U})}
441:{\displaystyle (x_{L},y_{L})}
395:{\displaystyle (x_{U},y_{U})}
1946:{\displaystyle k_{1}=15.957}
1860:{\displaystyle p=0.3/2=0.15}
7:
3708:: 3 – via NTRS, NASA.
3527:
3516:
3483:
3440:
3407:
3305:{\displaystyle k_{2}/k_{1}}
3185:{\displaystyle k_{2}/k_{1}}
825:is the maximum camber (100
10:
3891:
3840:Airfoil Interactive WebApp
3657:Payne, Greg (8 Jul 1994),
1479:P: a single digit for the
63:
3721:"The NACA airfoil series"
3476:For example, the NACA 65
1886:{\displaystyle r=0.2025}
293:(centerline to surface),
3660:NACA 6, 7, and 8 series
74:Langley Research Center
70:United States Air Force
3522:Supercritical airfoils
3306:
3263:
3235:
3214:
3186:
3144:
3117:
3095:
2882:
2840:
2650:
2534:
2506:
2485:
2457:
2427:
2192:
1947:
1914:
1887:
1861:
1821:
1795:
1775:
1755:
1732:
1443:
1231:
1166:
932:
886:
809:
576:
554:
442:
396:
347:
283:
244:
128:
83:
53:
33:
25:
3804:. Page 7. NASA, 1996.
3726:. Clarkson University
3307:
3264:
3262:{\displaystyle k_{1}}
3236:
3215:
3187:
3145:
3143:{\displaystyle k_{1}}
3118:
3096:
2883:
2841:
2651:
2535:
2533:{\displaystyle k_{1}}
2507:
2486:
2458:
2456:{\displaystyle k_{1}}
2428:
2193:
1948:
1915:
1913:{\displaystyle k_{1}}
1888:
1862:
1822:
1796:
1776:
1756:
1733:
1444:
1232:
1167:
933:
887:
810:
574:
555:
443:
397:
348:
307:In this equation, at
284:
282:{\displaystyle y_{t}}
245:
126:
98:as percentage of the
78:
39:
31:
22:
3870:Aircraft wing design
3678:Gordon J. Leishman.
3615:Moran, Jack (2003).
3274:
3246:
3225:
3204:
3154:
3127:
3107:
2893:
2853:
2662:
2627:
2517:
2496:
2475:
2440:
2208:
1971:
1924:
1897:
1893:. Finally, constant
1871:
1831:
1805:
1785:
1765:
1745:
1508:
1244:
1182:
945:
896:
850:
587:
455:
406:
360:
356:Now the coordinates
318:
266:
138:
3830:NACA Airfoil Series
3746:NACA Report No. 537
3198:Camber-line profile
2469:Camber-line profile
1820:{\displaystyle x=p}
3771:Dover Publications
3302:
3259:
3231:
3210:
3182:
3140:
3113:
3091:
2878:
2836:
2646:
2530:
2502:
2481:
2453:
2423:
2418:
2394:
2266:
2188:
2183:
2144:
2012:
1943:
1910:
1883:
1857:
1817:
1791:
1771:
1751:
1728:
1723:
1681:
1549:
1465:= 0.15âŻL (this is
1439:
1434:
1391:
1307:
1227:
1162:
1160:
928:
882:
805:
800:
720:
628:
577:
550:
438:
392:
343:
279:
240:
129:
54:
34:
26:
3667:on April 27, 2009
3621:. Dover. p.
3383:
3382:
3234:{\displaystyle r}
3213:{\displaystyle p}
3116:{\displaystyle r}
3068:
3045:
3013:
2969:
2953:
2924:
2904:
2870:
2813:
2790:
2758:
2714:
2693:
2673:
2638:
2613:
2612:
2505:{\displaystyle r}
2484:{\displaystyle p}
2393:
2265:
2236:
2143:
2011:
1794:{\displaystyle r}
1774:{\displaystyle y}
1761:and the ordinate
1754:{\displaystyle x}
1680:
1548:
1453:Five-digit series
1390:
1306:
1272:
1222:
719:
627:
173:
86:Four-digit series
3882:
3805:
3798:
3789:
3788:
3768:
3758:
3749:
3742:
3736:
3735:
3733:
3731:
3725:
3719:Marzocca, Pier.
3716:
3710:
3709:
3699:
3690:
3684:
3683:
3675:
3669:
3668:
3663:, archived from
3654:
3648:
3643:
3637:
3636:
3612:
3603:
3600:
3594:
3587:
3581:
3580:
3578:
3576:
3560:
3311:
3309:
3308:
3303:
3301:
3300:
3291:
3286:
3285:
3268:
3266:
3265:
3260:
3258:
3257:
3240:
3238:
3237:
3232:
3219:
3217:
3216:
3211:
3195:
3194:
3191:
3189:
3188:
3183:
3181:
3180:
3171:
3166:
3165:
3149:
3147:
3146:
3141:
3139:
3138:
3122:
3120:
3119:
3114:
3100:
3098:
3097:
3092:
3087:
3083:
3082:
3081:
3069:
3061:
3059:
3058:
3046:
3038:
3036:
3035:
3014:
3012:
3011:
3002:
3001:
2992:
2987:
2986:
2981:
2977:
2970:
2962:
2954:
2952:
2951:
2942:
2941:
2932:
2925:
2920:
2919:
2910:
2905:
2897:
2887:
2885:
2884:
2879:
2871:
2863:
2845:
2843:
2842:
2837:
2832:
2828:
2827:
2826:
2814:
2806:
2804:
2803:
2791:
2783:
2781:
2780:
2759:
2757:
2756:
2747:
2746:
2737:
2732:
2731:
2726:
2722:
2715:
2707:
2694:
2689:
2688:
2679:
2674:
2666:
2655:
2653:
2652:
2647:
2639:
2631:
2539:
2537:
2536:
2531:
2529:
2528:
2511:
2509:
2508:
2503:
2490:
2488:
2487:
2482:
2466:
2465:
2462:
2460:
2459:
2454:
2452:
2451:
2432:
2430:
2429:
2424:
2422:
2421:
2395:
2389:
2388:
2387:
2378:
2377:
2367:
2334:
2333:
2312:
2311:
2287:
2286:
2274:
2273:
2267:
2261:
2260:
2251:
2237:
2235:
2227:
2226:
2225:
2212:
2197:
2195:
2194:
2189:
2187:
2186:
2145:
2139:
2138:
2137:
2128:
2127:
2117:
2087:
2086:
2062:
2061:
2049:
2048:
2030:
2029:
2020:
2019:
2013:
2007:
2006:
1997:
1983:
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3812:External links
3810:
3807:
3806:
3790:
3784:978-0486605869
3783:
3750:
3737:
3711:
3685:
3682:. p. 361.
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3632:0-486-42879-6
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3609:
3599:
3593:. NACA, 1933.
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3386:Modifications
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2178:
2175:
2172:
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2155:
2152:
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2140:
2134:
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2124:
2120:
2108:
2105:
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2099:
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2069:
2066:
2058:
2054:
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2045:
2041:
2037:
2034:
2031:
2026:
2022:
2008:
2003:
1999:
1989:
1984:
1979:
1975:
1967:
1966:
1965:
1962:
1954:
1940:
1937:
1932:
1928:
1905:
1901:
1880:
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1574:
1571:
1568:
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1545:
1540:
1536:
1526:
1521:
1516:
1512:
1504:
1503:
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1499:
1492:
1489:
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1482:
1478:
1475:
1468:
1460:
1459:
1458:
1429:
1426:
1423:
1420:
1417:
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1408:
1404:
1401:
1398:
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1301:
1297:
1292:
1289:
1279:
1274:
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1258:
1254:
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1240:
1239:
1224:
1218:
1215:
1208:
1204:
1200:
1194:
1191:
1188:
1185:
1178:
1177:
1176:
1155:
1152:
1149:
1146:
1140:
1136:
1132:
1127:
1123:
1119:
1117:
1110:
1106:
1100:
1097:
1094:
1091:
1085:
1081:
1077:
1074:
1071:
1069:
1062:
1058:
1050:
1047:
1044:
1041:
1035:
1031:
1027:
1022:
1018:
1014:
1012:
1005:
1001:
995:
992:
989:
986:
980:
976:
972:
969:
966:
964:
957:
953:
941:
940:
939:
920:
916:
912:
907:
903:
874:
870:
866:
861:
857:
844:
838:
834:
831:
828:
824:
821:
820:
819:
795:
792:
789:
786:
783:
780:
775:
771:
765:
761:
757:
754:
751:
748:
745:
739:
736:
733:
730:
723:
713:
705:
702:
699:
692:
682:
679:
676:
673:
670:
667:
662:
658:
652:
648:
644:
641:
638:
635:
631:
622:
618:
614:
605:
600:
595:
591:
583:
582:
581:
573:
564:
547:
542:
538:
534:
531:
526:
522:
517:
512:
508:
504:
501:
496:
492:
487:
484:
481:
476:
472:
468:
463:
459:
451:
450:
449:
430:
426:
422:
417:
413:
384:
380:
376:
371:
367:
340:
335:
331:
327:
324:
321:
314:
313:
312:
310:
302:
298:
295:
292:
274:
270:
262:
259:
256:
255:
254:
237:
233:
227:
223:
219:
216:
211:
207:
203:
200:
195:
191:
187:
184:
181:
178:
175:
170:
165:
161:
157:
154:
151:
146:
142:
134:
133:
132:
125:
116:
113:
107:
104:
101:
97:
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82:
77:
75:
71:
61:
59:
51:
47:
43:
38:
30:
21:
3865:Aerodynamics
3769:. New York:
3764:
3740:
3728:. Retrieved
3714:
3705:
3701:
3688:
3679:
3673:
3665:the original
3659:
3652:
3641:
3617:
3598:
3585:
3573:. Retrieved
3568:
3558:
3539:NACA cowling
3534:Vought V-173
3520:
3511:
3487:
3474:
3447:laminar flow
3444:
3436:
3411:
3403:
3400:
3389:
3102:
2889:
2848:
2622:
2619:
2435:
2200:
1963:
1960:
1740:
1500:
1496:
1484:
1480:
1470:
1466:
1456:
1174:
845:
842:
836:
832:
826:
822:
817:
578:
562:
355:
308:
306:
300:
296:
290:
257:
252:
130:
114:
111:
89:
79:
67:
55:
49:
45:
41:
3415:wind tunnel
3859:Categories
3773:. p.
3550:References
1487:= 0.05âŻP),
16:Wing shape
3544:NACA duct
3462:A hyphen.
3427:A hyphen.
3328:0.000764
3048:−
3022:−
2989:−
2972:−
2873:≤
2793:−
2767:−
2734:−
2717:−
2641:≤
2363:−
2320:−
2289:−
2153:−
2070:−
2032:−
1953:is used.
1690:−
1607:−
1569:−
1427:≤
1421:≤
1402:−
1374:−
1343:≤
1337:≤
1318:−
1195:
1186:θ
1153:θ
1150:
1133:−
1098:θ
1095:
1048:θ
1045:
993:θ
990:
973:−
790:≤
784:≤
758:−
734:−
703:−
677:≤
671:≤
645:−
535:−
217:−
185:−
176:−
3569:nasa.gov
3528:See also
3517:8-series
3484:7-series
3441:6-series
3408:1-series
3345:0.00677
3730:July 5,
3575:27 July
3379:0.1355
3362:0.0303
3342:15.793
3325:51.990
2581:15.957
2578:0.2025
2567:51.640
2553:361.40
2550:0.0580
253:where:
64:Origins
24:surface
3781:
3629:
3571:. NASA
3376:3.191
3373:0.441
3359:6.520
3356:0.318
3339:0.217
3322:0.130
2609:3.230
2606:0.391
2595:6.643
2592:0.290
2564:0.126
1941:15.957
1881:0.2025
1192:arctan
1175:where
818:where
328:1.1019
220:0.1015
204:0.2843
188:0.3516
179:0.1260
166:0.2969
96:camber
48:axis;
3724:(PDF)
3698:(PDF)
3370:0.25
3353:0.20
3336:0.15
3319:0.10
2849:From
2623:From
2603:0.25
2589:0.20
2575:0.15
2561:0.10
2547:0.05
100:chord
3779:ISBN
3732:2016
3627:ISBN
3577:2020
3367:251
3350:241
3333:231
3316:221
3150:and
2860:<
2600:250
2586:240
2572:230
2558:220
2544:210
2411:<
2405:<
2350:<
2344:<
2176:<
2170:<
2103:<
2097:<
1867:and
1855:0.15
1713:<
1707:<
1640:<
1634:<
892:and
58:NACA
56:The
3775:115
3706:391
2876:1.0
1841:0.3
1467:not
1147:cos
1092:sin
1042:cos
987:sin
72:at
3861::
3793:^
3777:.
3753:^
3704:.
3700:.
3625:.
3607:^
3567:.
3123:,
2414:1.
2179:1.
1476:),
1463:LI
1430:1.
42:xy
3787:.
3748:.
3734:.
3635:.
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3579:.
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2958:(
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2907:=
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2697:[
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2676:=
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2215:d
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2027:3
2023:x
2017:(
2009:6
2004:1
2000:k
1990:{
1985:=
1980:c
1976:y
1938:=
1933:1
1929:k
1906:1
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1878:=
1875:r
1852:=
1849:2
1845:/
1838:=
1835:p
1815:p
1812:=
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1554:(
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1527:{
1522:=
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1266:d
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1255:y
1251:d
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1201:d
1189:=
1156:,
1141:t
1137:y
1128:c
1124:y
1120:=
1111:L
1107:y
1101:,
1086:t
1082:y
1078:+
1075:x
1072:=
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1059:x
1051:,
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1028:+
1023:c
1019:y
1015:=
1006:U
1002:y
996:,
981:t
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970:x
967:=
958:U
954:x
926:)
921:L
917:y
913:,
908:L
904:x
900:(
880:)
875:U
871:y
867:,
862:U
858:x
854:(
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615:m
606:{
601:=
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548:.
543:t
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497:U
493:y
488:,
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482:=
477:L
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469:=
464:U
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423:,
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410:(
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364:(
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336:2
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325:=
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238:,
234:]
228:4
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192:x
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162:[
158:t
155:5
152:=
147:t
143:y
102:.
50:y
46:x
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
