Document
NATIONAL ADVISORY COMMI_EE
FOR AERONAUTICS
REPORT No. 669
AIRFOIL SECTION DATA OBTAINED IN THE N. A. C. A.
VARIABLE-DENSITY TUNNEL AS AFFECTED BY
SUPPORT INTERFERENCE AND OTHER CORRECTIONS
By EASTMAN N. JACOBS and IRA H. ABBOTT l=
CASE FI LE
COPY
For role by the Supedntenden! of Dorumengs, Washington, D.C. " l_lce 10 cents Subscription price, S3 per year AERONAUTIC SYMBOLS 1. FUNDAMENTAL AND DERIVED UNITS Metric English Symbol Abbrevia- Abbrevia- Unit Unit tion tion foot (or mile) ......... ft. (or mi.)
meter ................. m Length ......
sec. (or hr.)
Time ........ second ................ s second (or hour) .......
lb.
Force ........ weight of 1 pound .....
weight of 1 kilogram .... kg horsepower (metric)_ _ .............
Power ....... P horsepower ...........
miles per hour ........
)'kilometers per hour ...... [ k.p.h.
1" Speed .......
feet per second ........
_meters per second ....... [ m.p.s.
I 2. GENERAL SYMBOLS _, Kinematic viscosity l_, Weight=ms p, Density (mass pe'r unit volume) g, Standard acceleration of gravity--9.80665 at Standard density of dry air, 0.12497 kg-m4-s I m/s 2 or 32.1740 ft./see3 W 15 ° C. and 760 ram; or 0.002378 lb.-ft. -4 see2 rn, 51 ass _-- or Specific weight of "standard" air, 1.2255 kg/m 3 g 0.07651 lb./cu, ft.
I, Moment of inertia=m_ "2. (Indicate axis of radius ofgyration k by proper subscript.)
Coefficient of viscosity 3. AERODYNAMIC SYMBOLS @ J Angle of setth-g of wings (relative to thrust S, Area iw, line) S_, Area of wing " j_ Angle of stabilizer setting (relative to thrust .G, Gap _" line) b, Span Resultant moment c, Chord Q, Resultant angular velocity b 2 fl, _,_ Aspect ratio _'l Reynolds Number, where l is a linear dimension V, True air speed P _' (e.g., for a model airfoil 3 in. chord, 100 m.p.h, normal pressure at 15 ° C., the cor- q, Dynamic pressure= _oV"- responding number is 234,000; or for a model of 10 cm chord, 40 m.p.s., the corresponding L, Lift, absolute coefficient C_=_S S number is 274,000) Center-of-pressure coefficient (ratio of distance Cp, D, Drag, absolute coefficient Co=_S of c.p. from leading edge to chord length) T_ Angle of attack Do, Profile drag, absolute coefficient CDO=_ a, Angle of downwash Angle of attack, inflnife aspect ratio D_, Induced drag, absolute coefficient C._=_-_ ao, Anglo of attack, induced Ottj D Angle of attack, absolute (measured from zero- Dp, Parasite drag, absolute coefficient CDp=_ a_, lift position) Flight-path angle C, Cross-wind force, absolute coefficient Ce=_ 7, Resultant force R, J f J
REPORT No. 669
AIRFOIL SECTION DATA OBTAINED IN THE N. A. C. A.
VARiABLE-DENSITY TUNNEL AS AFFECTED BY
SUPPORT INTERFERENCE AND OTHER CORRECTIONS
By EASTMAN N. JACOBS and IRA H. ABBOTT Langley Memorial Aeronautical Laboratory NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS p.
HEADQUARTERS, NAVY BUILDING, WASHINGTON. D. C.
?
LABORATO tIES. LANGLEY FIELD. VA.
Created by act of Congress approved March 3, 1915, for the supervision and direction of the scientific study of the problems of flight (U. 8. Code, Title 50, 8ec. 151). Its membership was increased to 15 by act approved March 2, 1929. The members are appointed by the President, and serve as such without compensation.
ROBERT tI. HINCKLEY, A. B., JOSEPH S. AMES, Ph.D., Chairman, Baltimore, Md. Chairman, Civil Aeronautics Authority.
JEROME C. HUNSAEER, Sc. D., VANNEVAR BUSH, 8C_ D., Vice Chairman, Cambridge, Mass.
Washington, D. C.
SYDNEY _I. KRAVS, Captain, United States Navy, CHARLES G. ASBOT, Se. D., Bureau of Aeronautics, Navy Department.
Secretary, Smithsonian Institution.
CHARLES A. LINDBERGH, LL.D., :HENRY H. ARNOLD, Major General, United States Army, :New York City.
Chief of Air Corps, War Department.
FRANCIS W. REICHELDERFER, A. B., GEORGE iT. BRETT, Brigadier General, United States Army, Chief, United States Weather Bureau.
Chief Mat6riel Division, Air Corps, Wright Field, Dayton, JoHr¢ H. TOWERS, Rear Admiral, United States Navy, Ohio.
Chief, Bureau of Aeronautics, Navy Department.
LY2_IA_ J. BRIGGS, Ph.D., EDWARD WARNER, So. D., Director, National Bureau of Standards. Greenwich, Conn.
ORVILLE WRIGHT, Be. D., Ct,INTON _I. I_ESTER, A. _., LL.B., Dayton, Ohio.
Administrator, Civil Aeronautics Authority, GEORGE W, LEWIS, Director of Aeronautical Research JOHN F. VICTORY, Secretary J HENRY J. E. REID, Engineer-in-Charge, Langley Memorial Aeronautical Laboratory, Langley Field, Va.
JOHN J. IDE, Technical Assistant in Europe, Paris, France TECHNICAL COMMITTEES AERODYNAMICS AIRCRAFT STRUCTURES POWER PLANTS FOR AIRCRAFT AIRCRAFT ACCIDENTs AIRCRAFT MATERIALS INVENTIONS AND DESIGNS Coordination of Research Needs of Military and Civil Aeiation Preparation of Research Programs Allocation of Problems Prevention of Duplication Consideration of Inventions LANGLEY MEMORIAL AERONAUTICAL LABORATORY OFFICE OF AERONAUTICAL INTELLIGENCE LANGLEY FIELD. VA.
WASHINGTON, D. {7.
Unified conduct, for all agencies, of scientific research on the Collection, elass!fication, compilation, and disscminatio6 of scientific and technical information on aeronautics.
fundamental problems of flight.
REPORT No. 669
AIRFOIL SECTION DATA OBTAINED IN THE N. A. C. A. VARIABLE-DENSITY TUNNEL
AS AFFECTED BY SUPPORT INTERFERENCE AND OTHER CORRECTIONS
By EASTMAN N. J'ACOBS and I1tA H. ABBOTT SUMMARY the model tests would largely disappear when tile data so derived were used to predict the characteristics of The results of an investigation oJ the effect of support wings approximating the same plan form and aspect interference on airfoil drag data obtained in the variable- ratio as the models.
density tunnel are presented. As a result of the support The absolute accuracy of the data was, however, inte?ferenee, previously published airfoil data from the improved from time to time by the investigation of eariable-density tunnel have ._'hown too large drag coeffi- consistent errors. An attempt to ewduate the effect cients and too large a rate of increase of drag coefficient of support in t erferen c e on the m ea sured drag co efficien ts with airfoil thickness. Thdpraetieal effect of the correc- was inconclusive (reference 4) and no corrections were tions on the choice q[ the optimum section is briefly applied. The data were further improved by the ap- considered and corrected data for a selected list of airfoils plication of corrections for turbulence and for improve- are presented as a convenience to the designer. 1]Iethods ment of the approximations to section characteristics.
of correcting published data for other airfoils are presented.
The corrected coefficients were designated by lower-case symbols, such as ca0, as contrasted to the older CD o.
INTROD UCTION One of the chief effects of these corrections was to re- Airfoil data obtained in the variable-density tunnel duce the profile-drag coefficients, particularly for the thicker airfoils.
(reference 1) have been published (references 2 to 6) in forms that were considered at tlle time of publication As airfoil data at large values of the Reynolds Num- to be most useful to the airplane designer. In the ber became available from the N. A. C. A. full-scale earlier publications (references 1 and 2) no corrections tunnel (reference 7) and from foreign sources (references other than flmse for tunnel-wall effects and to infinite 8 to 13), even the corrected profile-drag coefficients ob- aspect ratio were applied to the data, and emphasis was tained in the variable-density tunnel appeared to be too placed on the pressing problem of obtaining good com- large. The discrepancy increased with airfoil thickness.
parative data for judging the relative merits of airfoils The important practical effect is that the data from the rather than on ol)taining absolute accuracy.
variab].e-density tunnel apparently showed too large It was recognized that certain consistent errors were a variation of drag coefficient with airfoil thickness.
present in the data, but it was tlmught that the effect Correct information regarding this variation may be of of these errors on the comparative value of the data primary importance to the airphme designer in choosing was not of primar 3, importance. Support-strut inter- the optimum airfoil sections for actual wings.
terence, for example, was considered to be a possible Further investigations of this subject were under- source of systematic error, but it was thought that this taken, one of the most important being an investiga- interference would not affect the order of merit of the tion of three symmetrical sections, N. A. C. A. 0009, airfoils tested except possibly in the case of very sensi- 0012, and 0018, under conditions of low turbulence in tive airfoils, which might also be similarly affected by the N. A. C. A. full-scale tunnel. Results from this the wing-strut intersections of biplanes common at the investigation (references 14 and 15) indicate a smaller time. The turbulence of the air stream was thought increase in drag with airfoil thickness than is indicated not seriously to impair the comparative value of the by the results from the N. A. C. A. variable-density data aml, perhaps, even to be desirat)le, because the tunnel. Furthermore, comparative tests were made extensive turbulent t oundary layers occurring on tim in the t_-o tunnels by applying strings to the surface nmdels in the tunnel as a result of the turbulence wotfld of the N. A. C. A. 0012 airfoil to nmve the transition also be found in practice at high values of the Reynolds point to a predetermined position. These tests indi- Numt)er on conventional airfoils with the. usual mod- cated that, for this airfoil, the discrepancies were too erately rough surfaces. It was also considered that large to be ascribed to failure of the effective Reynolds errors arising from failure of the conventional airfoil Number concept to correct approximately for the drag theory to predict sect ion characteristics accurately from as affected by transition.
REPORT NO. 669_NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS strut so located as to be as free as possible from aero- F Another correction, however, was suggested by tile dynanfic interference with the regular supports. The / investigation in the full-scale tunnel. Differences between the results from force and momentum methods sting was symmetrical with respect to the airfoil and was attached near tile trailing edge instead of to the of measurement suggested the presence of increments lower surface, as usual.
of support-interference drag that increased with section The tares due to the special supports were deter- thickness. Further tests, made with additional dummy mined from data obtained from the tests with the models supports, verified the presence of this type of support interference in the full-scale tunnel. Tests were on the regular supports with and without the special therefore started in tile variable-density tunnel to supports. These tares were then applied to the data obtained with the model on the special supports alone; investigate any variation of support interference with the results were then compared with the data obtained airfoil thickness, in spite of the fact that previous in the customary manner to detemnine the unevahmted investigations (see appendix of reference 4) had showqq interference caused by the usual supports. This m_thod no definite corrections for two airfoils, the N. A. C. A.
does not eliminate bahmce deflections arising from 0012 and 4412. Improvements of the balance of the sources other than aerodynamic forces on the model variable-density tunnel were expected to enable greater and the supports. A test was accordingly made with accuracy than was obtainable from tlle previous bal- no motlel nor supports in the tunnel; the result showed ance arrangement. Tile results of this investigation that no such balance deflections were present.
indicate that marked increments of support-interfer- Tlle scope of the present investigation was linfited ence drag, easily measurable, are "present in the drag to tim study of tile profile drag at low and moderate results from the variable-density tmmel, the increment lift coefficients at the highest value of the test Reynolds increasing with airfoil thickness.
Number ordinarily obtained (about 3,000,000). Tests The purpose of this report is to present the cor- were made of the N. A. C. A. 0012, 0018, 0025, 0030, rections for application to published results from tim and 0040 symmetrical airfi)ils to study tlle variation of variable-density tunnel to give more reliable values support interference with airfifil thickness. The N. A.
of section profile-drag coefficient for airfoils of various C. A. 43012, 43018, and 8318 .firfoils were also tested thicknesses. The practical effect of the corrections to obtain an indication of the variation of support inter- on tim choice of tile optimmn section is briefly con- ference witll camber.
sidered. Comparison is made between some corrected drag data fronl the variable-density tunnel and from RESULTS AND DISCUSSION other sere'cos to show tile extent of the existing agree- MINIMUM PROFILE-DRAG COEFFICIENTS meat. Corrected data for a selected list of airfoils are also present,d as a convenience to tile designer. 'The effect of the support interference on the measured section minimum profile-drag coefficients is shown in METHOD figure 1. The increment of the mininmm profile- drag coefficients caused by the support interference is The standard nletllod of testing in the variable- plotted against airfoil thickness for the five symmetrical density tunm'l, the model supports, and the method of and the three cambered airfoils tested. The points deterI_ning the tare forces are described in reference 1.
for the five symmetrical airfoils lie on a fair curve The usual tare tests de_ermine the tare forces on the passting t_rough zero at zero airfoil thickness, the supl)orts including, the interference of the model on scatter of )he points being small when consideration the supports. The c,mventinnal method of dcternfin- is taken of tim_ difficulties inw_lved in these tests.
ing the balance-alinenwnt correction by testing a The points obtaihed for the N. A. C. A. 43012 and symmetrical airfoil through positive and negative 43018 airfoils fall close to but on opposite sides of angles of attack determines the elt'ects of balance and the curve for the symmetrical airfoils. The camber of air-stream misalinement and any interference of the these airfoils (4 percent) is about the upper limit of supports on the model tlmt is equivalent to a change camber for the commonly used airfoils. The point ill ,fir-flow direction.
obtained for tl,e N. A. C. A. 8318 airfoil falls 0.0007 The method selected for investigating the additional above the curve and would seem to indicate an in- interference of the supports on the model was the same crease in support interference for higldy cambered as that described in the appendix of reference 4. Tests airfoils. In this case, however, the point for the were made of each airfifil supported by three ¢lifferent N. A. C. A. 43018 airfoil would be expected to fall nwthods. Besides the method of using tile usual sup- between those for the N. A. C. A. 8318 and 0018 air- port struts, tests were made with tile models mmmted foils; whereas it falls slightly below that for the sym- on the usual supports with the addition of special sup- metrical airfoil. Inasnnieh as each point was obtained ports and with the lnodels mounted only on the special from the results of throe tests, two of which (those supports. The special supports consisted of three wires with the wire supports) were made with very large attached to the quarter-chord point of the model at tare forces, tim (tisplacenwnt of the point for the each wing tip an,I of a sting and nn angle-of-attack AIRFOIL SECTION DATA AS AFFECTED BY SUPPORT INTERFERENCE N_ A. C. A. 8318 airfoil from the fair curve is only of in the appendix (equation (1)), for the support inter- the order of the possible experimental error.
The shape of the curve of figure 1 suggests that the Reynolds Number. Corresponding values obtained interference may be largely of the nature of a buoyancy I terence and for the revised correction for the effective from the support-interference tests are presented in effect., in which case the interference should be primarily the sixth column. The principal result is presented a function of airfoil thickness; and other factors, such in the last cohunn and represents the difference in as camber, should ordinarily be minor variables• Ac- minimum profile-drag coefficients between the data cordingly, because the present tests fail to show sig- published in references 4 to 6 and those presented nificant variations with camber and because it is not herein. Other published data may be corrected by considered practicable to make such tests for a large the methods presented in the appendix.
number of airfoils, the wflues obtained from the faired TABLE I curve of figure 1 will onlinarily be used to correct the measured minimum profile-drag coefficients. These DATA ON CORRECTION OF MINIMUM DRAG OF SYMMETRICAL AIRFOILS values are thought to represent the correction with [Effective Reynolds Number, approximately 8,£D0,000j sufficient accuracy for most applications of commonly :_ (from ] N.A. Ca° r ed° (rote r- ,q q)po t _'0 (eor- i _1 pp rt- It C _rec-ar C, A. (refer- nter inter- tlon I incre- airfoil once 2) once 5', f( rene !
tests) [ ments coted) fcrenex, ] . .
i 0. 0065 0. 0051 (. OOC_ 0009 .0074 .0061 .00fl:
i 1
0012 .0083 .8069 .001( 0015 . (]093 ._77 .(_I_ 0018 .01{}8 .0088 , nOl_ • {RI71 .0017 • o_s :obfi .0oo6 0021 .0120 .0100 .001i 0025 .0143 _. fi119 ,OOZ ] D_2 0027
e_.ooe
• Correction increments are slims of increments resulting from sllplx_rf-interferen(_ correction and change in method of Correcting for effective Reym)hls Number.
Reference 6.
"-.01_ J o q. 0021 .... 0 N.A.C.A. s'ymmefrico/, series_ _r ...... / -- -- a AIA.C,A. 230 series : ... o N A.C.A. 430 ser;es ._ ,010- -- + NA.C.A. 630 series- 0 10 20 30 dO 50 60 Airfoil fhickness percent chord .ooe -- | ----_"*" j_.._ Ft(;URE l.--Variation with airfoil thickness of the increment of minimum profile- drag coefficient caused byffupport interference for the N'. A. C, A. variable-density .......
tunnel, / ,
-
i
used airfoils. The applicability of these values to _2 data obtained at othe.r values of tile Reynolds Number is more doubtful, but such application appears to offer the best approximation possible at tins t lnle and, accordingly, will be made.
The corrected minimum profile-drag coefficients for the symmetrical airfoils from 9 to 25 percent thick are -_ o /o _o 3o given in table I. The second column of this table "_ Airfoil thickness, percent chord gives the C'% vahws originally pul)lished in refcrence 2.
FIGt'RZ 2. Variation of minimum profile-drag coefficient with airfoil tlliekne,¢.s.
E ffectix e Roy nohis Number, 8,2C0,000.
The thirtt column gives tlie c% values taken from reference 5, excel)t for the N. A. C. A. 0025. Some of The application of these corrections results in a these c, 0 values were obtained by correcting the Cs_ 0 greatly decreased variation of drag with airfoil thick- values for the drag increment (0.0011) to correct to ness. This variation is shown for tlle N. A. C. A.
the effective Reynolds Number and for the tip-drag symmetrical, 230,430, and 630 series airfoils in figure 2, increment (reference 4). The rest of the c_ 0 values are wtlich may be considered a correction of figure 53 of reference 5. It is evident that the smaller increase in fl'om the results of more recent measurements similarly corrected. The ftmrttl cohmm gives the support- drag with section thickness will" affect the choice of interference increments taken froln the curve of fig- wing sections. The best simple criterion for the selec- tion of wing sections being consideretl the speed-range tire 1. The finally corrected ca o vahles of the fifth index c_,_,,/C_o,,_,, figure 3 has been prepared from the cohnnn were obtained fr.in the third cohmm by cor- recthtg the data, according to the procedure suggested 'correcte(I data of figure 2 to be used in connection with REPORT NO. 669--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS figure 61 of reference 5 to study the effect of the cor- of figure 3 indicates that the optimum thickness for the rection on the thickness of the optimum Section. The 230 series may then increase to 12.5 or 13 percent and result of the comparison is shown in table II. that the aerodynamic loss associated with thicker sec- tions is considerably smaller than previously indicated.
TABLE II .018 -- EFFECT OF SUPPORT-INTERFERENCE CORRECTION ON OPTIMUM AIRFOIL TttICKNESS .010
, T 'i
Thickne_ of se(,ticn for highest ca_._/c_o_a .N'. A. C. A. airfoils (percent chord) .008 From I Correcte : I referent _i resu]tsL 5 (fig. 3) D06 230 _ries .............. : ......... 9. 5 10 Symmetrical series .............. II.5 lo ]2.5 .004 23fl series with 0.2c split flap ........ 11 I 12.5 Tile change in optimum thickness is evidently small . OO2 for airfoils without flaps. The losses associated with an airfoil that exceeds the optimum thickness, however, I L_ L_ I0 _0 3O A/rfo// fhic/iness, percenf chord FIGURI_: 4. Variation of minimum profile-drag coefficient with thickness fur N. A. C. A. symmetrical airfoils. Effective Reynolds Number, 8,200,000.
Comparison of the corrected data from the variable- density tunnel with the available comparable data from other wind tunnels indicates a generally improved agreement. The close agreement obtained for the .OIZ ._ , .0/0 - _ .oo, _ Woke _urvey 1 5x 7-meter wit t _ *. . 004 x b + Bolonce meosc_emenfJ funnel of the OVL Effective Reynolds I_mber, 2,970,000, .0. 0 A/A.CA. vor_oble-densify tunnel { -- Effechve Reyno/ds A4Jmber. 8/00,000
itt tt tt
0 I0 _0 Airfod fh/chness, percent chord FIGVIIE 5, Variation of profile-drag ct_efflcient with thickness for N. A. C, A. 24 series airfoils.
N. A. C. A. 0009, 0012, and 0018 airfoils in the N. A.
C. A. variable-density and full-scale tunnels (reference 14) is shown in figure 4.
become less marked so that a compromise airfoil will Figure 5 shows a comparison between the profile- drag coefficients at zero lift for the N. A. C. A. 24 series tend to be thicker by a greater amount than is intlicated airfoils as obtained in the varil/1)le-density tunnel and by table ]I. This conclusion is particularly significant in the 5-by 7-meter tunnel of the DVL. The data when full adwmtage can be taken of tim fact that the were not obtainett at the same value of the Reynolds maximum-lift increment produced by a high-lift device may increase _:ith'section thickness. The upper curve Number, but the application of the eprrcction to tile
2S
AIRFOIL SECTION DATA AS AFFECTED BY SUPPORT INTERFERENCE data from the variable-density tunnel has reduced tlle 0025 airfoil (fig. 9) is satisfaetoD-. In tim case of the discrepancies. N. A. C. A. 24 series airfoils (fig. 10), the ctfief discrep- Comparisons of miniature profile drag are made for ancy between the data from the variable-density the N. A. C. A. symmetrical series airfoils in figures 6 to tunnel and those from the 5- by 7-meter tunnel of the 9; comparisons of profile-drag coefficients at zero lift DVL (reference 1I) is that the data from the DVL tunnel show a smaller rate of drag decrease with are made for the N. A. C. A. 24 series airfoils in figure increasing Reynolds Number.
10. Ill all cases, the data have been corrected to the These discrepancies in the rate of decrease of the drag proper effective Reynolds Number and for tip effects when necessary to make these data comparable with with increasing Reynolds Numbers as shown for the those from the variable-density tunnel. The a_ee- N. A. C. A. 0012 airfoil in figure 7 and for the N. A. C. A.
meat of the data for tile N. A. C. A. 0009, 0012, and 24 series airfoils in figure l0 are particularly important because, for large airplanes, the drag data must be extrapolated. The differences in the data are such as o lu_ i_I, ,i L -?: to cast some doubt on the applicability of the recom- '.020 -- ' J L o._ Vorio/Dte-def_sity #unnel _ _ , ,
I VFII ----Fu//-_°:_ t:neX I
mended extrapolation formula (reference 4), although
_, ....... ri- - i! _ -
no better formula can be suggested at this time. The need for additional data obtained at large Reynolds Numbers in tunnels of low turbulence is obvious.
l : I 'i -- [
.oo4_--_IILI_ _ III :J, , i
--_ I'%,LH _ I i ', -L tl _ I i .046 i I _t _ : _l ! '+t _ _-j_ II _ i [ I ; n_n L"_ L_o-- Vor:oble- densi/y tunnel_
-r-r i lilt __I_,.L!I ILI 1
I .... F _ ----Zull-sco/e funnel L
II Iltll 1 JLi'<_] I
: __ I1 iltllllltV
• .. o.; •
i O/OL_ i i L __LL2£1 IiT[_t J 2' .4 .6..8 / 2 d 6 810 .20 40 Effeeh:ve /?eymo/ds Number, re;f/funs
'oosp r--,¢.! lH41_41 _LHT ,,:_4-.-._L
FIGURE £.- Minimum profile-drag coefficients of N. A. C. A. 0e09 airfoil as measured in the N. A. C. A, vafiable-densil y and frill-stifle ttlnnels.
•/00
t li i i --J i:Ltlt
._.080 o-- Vqrioble-demsity tunnel 3r_] r 1 _. 0_0 -- -- -- Full-sccz/e tunnel -H4
: oil IHHIttil ? Iktlltt °°"
-- × Compressed-o/r tunnel, hond-finished mode/ ,,2 ,0#0 --+ ,, . chromJum-p/oted model .t ._ .4 .6 .8 I _ 4 6 8 I0 _0 40 ,, # , /5-foot-chord model, e Effective fPeyno/ds Number, millions
i i II _i *1_:"q ve,=_:t
FI6UR:E S, Minimum profile-drag coefficienls of the N. A. C. A. 001S air/oil as
i
, 020 measured in "O_e N. A. C. A. variable-density and full-scale tunnels.
ttNI -Jilt i-
i.OlO _. 008
:_o ': _illl!l;illll !! !!!l:lfl!!lll
!"-4._!
_ . 006 ____ .LqL"_ ---1_| ] I-o--Var:obie-denmfy Yunne, i l .020 _| i l x Compressed-o/r tunnel g .oo4 ! _1 I 1 ill I _9 ._.ooz .....
I
oo,,_._Li -iiili_7__i_iI7-t<I ri
006 "-.J , II1['[1.111 l L I _il]3"_-.]--4-M_ 1 ]
• _ _tlHHtlt tt tJ_IFtTItttt--V_
°/ .b '
.4 .6.8 I 2 ,¢ 6 810 ZO ;J EffecHve Reynolds Number, mJ/fions FInURE 7.--Mininlllm profile-drag coefficients of lhe N, A. C, A, 0012 airfoil as -- i ,_ 121_, illllP't..l. II 11 I i_lil. Hlilll t , I ineastlred in _veral wind ttlnlle]m
oU -oo_ L i
1tlI!tt ![2 i
0018 airfoils as obtained in the variable-density and the
./ ._ ._ ._._ / _ , _ _ o _ 40
Effective /geynolds Number, m/7/ions full-scale tunnels is seen to be generally satisfactory.
FIG[RE _.). .".Iinimlim profile-drag coefficients of the N. A. C. A. 0025 airfoil as The agreement of tile data for the N. A, C. A. 0012 measure,! in the N. A. C. A. var|al le- lens y lure el and in the British compressed- airfoil (fig. 7) as obtained in the variable-deusity tunnel air hmneL and in the British compressed-air tmmel (references VARIATION OF SECTION PRO_'ILE-DRAG COEFFICIENT V*ITH LIFT 12 and t3) cannot be considered satisfactory, in COEFFICIENT particular, the results from the compressed-air tunnel do not indicate a decrease of the minimum profile-drag Curves of section profile-drag coefficient plotted coefficient with increasing Reynolds Numbers at. the against section lift coefficient with the model mounted higher Reynolds Numbers. The agreement of the on the wire supports and on the usual supports are presented in figures 11 to 17 for seven of the airfoils data obtained ill the variable-density and the com- tested. Tile data obtained with the models on the pressed-air tunnels (reference 12) for the N. A. C. A.
REPORT NO. 669---N.ATION'AL ADVISORY COMMITTEE FOR AERON.AUTICS V,,lO0 . _÷_ -- I./SL,x:_I supporfS ] A/A.C.A __ - D A/A CA, 2409 alrfodlMAC_ vorlable- z o-- " Z412 " t dens#y funnel -_
1: _ ,, 242! " ] -H ._.o/_ I x_ -- wi,-¢ . I vet I
X ........ 2 09 " i S×7-meter tunnel .
b ,,.,: _. 0OG (3 _.oae
g
}
u 0 Z .d G .8 g 4 _ 810 20 40 -.8 -.4 O .4 .8 /.,2 [/fechve R_ _f)olds Number, mdllom5 Section /if/" co_ff_Ciemf, cz FIGUP,I_ 10.--Profile-drag coefficient of N'. A. C. A, 24 series airfoils as mea-_ured at FIGURE I2.--Variation of profile-drag eoemeient with lift coefficient. N-. A. C. A.
zero lift in the N'. A. C. A, variable-density tunnel and in the 5- by 7-meier hmnel 0018 airfoil. Effective Reynolds Number, 8,200,000.
of the DVL.
o.0,_0 - -- -- ] ÷ Usual _upporfs _ AZA. C. A.
•_.016_-- x_ Wire " ] V.O.T. -- ._ _ ...... /Vfomen_u m meos(wremenf$, f. 5. T,
.... --=+/7 - -
-.8 -.4 0 .4 : _8 -- L2 Secfion l_ff coefflciez_f. ¢_ F]c.t-_ ll.--Vari_tlon el pn_file-drag coefficient with lift coefficient. N', ,4,. C. ,4,.
0012 airfoil. E Tect _e R ,_uo, s N'uml_er, $,,-:_0,g00.
wire supports include all corrections and represent the best available approximation to the actual airfoil
' t-5-
section characteristics. The two curves of eaclt figure g -_._'_-.4 0 .4 .8 L2 " are comparable except for the presence of support Secfion Elf coefficiemf, e_ interference in tl,e data obtained with the model on Fluuill_: 13.-- Variation of profile-drag coefficient with lift coefficient. N. A. C. k.
0025 airfoil. Effective Reynolds Number, 8,200,01_.
the usual suppvrts. The displacement l)etween the two curves of each figure thus represents the support s3anmetrical airfoils. The data obtained were thought interference.
not to justify the application of a valTing correction The data of figures 11 tltrovgtt 17 show a tendency to the profile drag, and it was decided to apply the for the support interference to decrease with increasing support-interference correction for the minimum profile- lift coefficients, this tendency being m6re marked for drag coefficient to all measured profile-drag coefficients.
the cambered tltan for the symmetrical airfoils. This Tlte effect of applying this constant correction may be x-ariation, however, is _ot consistent. The determina- to indicate an optimum lift coefficient that is somewhat tion of the profile-drag coefticient at other than small too high and to reduce the profile-drag coefficients at lift coefficients from the _upport-intcrference tests was high positive lift coefficients more than is generally complicated by tile fact that the air-stream direction at justified by these tests. Moreover, the effect of apply- the airfoil was apparently dr:pendent upon the support lug a proportional correction instead of a constant in- system used, necessitating tile determination of the bal- crement (o the profile-drag coefficients to correct them ance and the air-stream alinement from the tests of the AIRFOIL SECTI01_ DATA AS AFFECTED BY SUPPORT INTERFERENCE • 0_0 - .016 / (012 • 004 --- -.8 -.4 O .4 .8 /.2 Sechon lift coeffzcient, ('z Ei(}urtE 16,--Variation of profile-drag coefficient with lift coefficient. IT. A. C. A.
43018 airfoil. Effective Reynolds Number. g,200,0_.
-- Wlre I 1 , LS__. 2 , -.4 0 .4 .8 /.2 Gechon lift coefficient, et
I/_
:4t fit
FIGURE l_--Variation of profile-drag coefficient with liftcoel_eient._. A. C. A.
I .020 ....
0030 airfoil. Effective Reynolds Number, 8,21_,000.
e , I -- I _.00 ! -- USuo/ SvpportSIAIA.C.A. i
11L 11 ,:/
-.8 -.4 0 .4 .8 /._ $echon bft coefficient, c_ FIGURIg 17.--Variation of profile-drag coefficient with lift coefficient. N. A, C. A.
8318 airfoil. Effective Reynolds Number, 8,200,000.
corrected to tile effective Reynolds Number to be com- parable with the variable-density-tunnel data. It will FIGtrar 15--X,_ariation 0f profile-drag coefficient with lift coefficient N. A. C, A be seen that the profile-drag coefficients as obtained in 43012 airfoil• Effective Reynolds Number, _,'200,01_.
the full-scale tunnel at the higher lift coefficients are lower than those obtained in the variable-density to tile effective Rcynohls Number is to reduce still tunnel, indicating that the application of a constant fnrther the profile-(Irag coefficients at large lift coeffi- support-interference correction probably does not result cients. Figure 11 shows a curve of profile-drag coeffi- cients for tile N. A. C. A. 0012 airfoil as obtained from in too low profile-drag coefficients at moderate lift coefficients.
wake surveys in the full-scale tunnel (reference 15) and REPORT NO. 669 --NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS DATA FOR COMMONLY USED AIRFOILS airfoil thickness. The effects of these increments As a convenience to designers, corrected data for a were to make airfoil drag data from the variable-density number of commonly used airf(_ils are presented in tunnel appear high aml to show too large a rate of figures 18 to 59 and in table III. The left-hand side drag increase with airfoil thickness. Tlwse increments ,)f each figure presents the data for rectangular airfoils have been evaluated and the corrected data are recom- corrected to an aspect ratio of 6 in free air but uncor- mended for immediate use. A large amount of recent rected for turb_dence effects. The right-hand side of data, however, tins suggested that these, or other cor- each figure presents the best al)proximz_tion to the sec- rections, to airfoil data obtained in the variable-density tion clmracteristics, which are corrected as summarized tunnel will not produce ultimately satisfactory results.
in the appendix. These data supersede previous data It is planned, therefore, to obtain further airfoil section published fl)r these airfoils and are recommended for data under test conditions more favorable than those design use until more reliable data are ava_able.
in the variable-density tunnel.
CONCLUDING REMARKS An investig_ltion of the effect of support interference on airf¢)il (lr_tg data from the N. A. C. A. variable- LANGLEY ._IEMORIAL _I':RONAUTICAL LABORATORY, density tunnel showed the presence in these data of _ATIONAL ADVISORY COMMITTEE FOR AEBONAUTICS_ large support-interference increments, increasing with LANGI,EY FIELD, VA., Febr_la_y 18, 193.9.
f AIRFOIL SECTION DATA AS AFFECTED BY SUPPORT INTERFERENC_ -- - - 028 i i ] 56 Sfalcp'rlL'_'z!_.'_, 20_TT'-- I _ i/
__, ..... 0-20 ....... ,-. II ii !i -il-_ k i-1,8
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,,,,o:,,_ ,,, Pero._, o, c.o_ I i _ I : _ _ L ]
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.028 :l_r I 5to.l ?_01 1._5l _ 9SI
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ill1 8.881 - .05 I .02z
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,-I .-I o_, o__-_%1 i-t t_ o_.-'_
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I"ii
A J J i '7_ol 745__1._ I,LL_ 1 1 ./t_l _ -I .'_ ._o ].1._ I '_ N e5 .1_ -- _ ...... _ i
. .,LLJ-:_, i_t_-l;t t t/_.o +o _o,_
[J I 1 1 1 l Lmz, ._'._51 °_ __1 [ I 1 I IA 11 LL_t " " _" i-IS
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i l I LLj l i \LJ _ e_
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..4 LI oil .<-1 ILLS.{ I/ i l l _,.,_.,4_.ooo_"
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o u _YIG_ i I I I I I I i 7"f"4- I _66m'_en 387. R..s.mo, oool _._ " Iq __Where tested: L JKAL V.D.T.8_- []Press.(_/'nd. otto.): 21.0 ] _ I_ Corrected for- tunnel- wo//e/fec/ _ I • - INc_ ........ _ - 4,_
-8 _ -8 -_o"-"_W °°_ ._ VY""-'f-7"-,_
0 8 I6 24 32 " "-,4 Sechbn lift coefh'c/em#, c_ Anqle of o#tock, c_ o (deq_ees) FlGrlal_ 22.--G6ttingen 387 airfoil.
st, o L£ 2.
Z_ 2_ 3( 4£
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3S
AIRFOIL SECTION DATA AS AFFECTED BY SUPPORT INTERFERENCE
_I i.o
qllJ];r_-i: t* _-_:.<
i
I 0 .4 .8 1.2 IG Ang/e of ot/acH, d(de{Irees] Sechon /if/ coeff/c/en/, C,o FItiURE .'_i. N.X.C. At 'A'I8 airh,il.
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t_._1
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[Pt-ess.($Knd. aim.)." 20.8 { (3 Whet-# tested: L.M.A.L. _D.E6.gS -8 _ -8 ' " 0 8 I_ 24 3Z -.4 0 .4 :8 I.Z 1.8 J Ample of attack, d (degrees) Sechon hft coeffic/en& eta FIGL',_I_ 29.--U. S. A. 3._-B airfoil.
AIRFOIL SECTION DATA AS AFFECTED BY SUPPORTINTERFERENCE
s_l,_'______ _._2° IlL I 1 11 1 .oz8
LJ "1.31 •
'_II,.,:_,_ .,.,e,_,__2o ° .oz4 48
_l aJO 20 40 60 80 I00 ltl I _Srl' 2.J_l /_ -'6_1" Z$7 Pefgenf of C/70rd 4O k, t_ _,,__ 3'1. ,'.85 / | | 1 t I I I I I ._
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o 4 8 12 18 Angle of ¢//ec/_. of (decZrees} "_ Sech_)m liH coeff/c/en/. Cto F1G'(.:F,E _0. N.A.C.A. 0006 airfoil, _T' ',;_Z_-ZOlrllJl la,.c,, - | I "OZ81 Ij
o '._,1-_ _a oI_k_ _ _ k t
}'i [:i_ q's_'/_5_'_" _- 0 20 40 60 80 /00 " "=t I_
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l!l! -i li'l !i
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16 REPORT NO. 669---NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
50 35_4-_56, _lad ',_. JJ.2.J E oea
z5 _.zo1-4zo q /0 4.68]-46a 0 20 40 60 80 100 " 15 5.34-5.34 Percent of chord t ZO 5.74-5.74- I Z.4 .'48 C.020 3.66]-3.6s- ..t: so /.45]-/.45 2.0 .40 .016 35 .811- .01 ,,j
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-.4 - _ 8 /6 24 3Z -4 i I Corrected for tunnel- wall effect.
_,g/e of o#ack, d (degrees] FIGURE 32.--,'_. A. C. A, 0012 airfoil.
...... _6 20 _ .02,9
I
7! ='7 t. ' ":" _ _ --" J
]
l,t 5_ /; _.09 _8[ Percent of c/_ord
_,; ;:il i_[tilitlll![l _ o
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AIRFOIL SECTION DATA AS AFFECTED BY SUPPORT INTERFERENCE Ste.I
-_-_ --_ -
_2512._ 2,513J.
5,015._
_ __._-_°[Jlllllll I I H ,oze-
-_sj. o_._;ol_Hl_l['-c. IL I] o_,_-
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iE._. o o _._-e -_
" _ _ • z_ _z -._ -44 _
_0°
_gle of attack, _ (degrees) .See/ion l/f/ coeffic/enl, tto F]G_Rg 34.- -N. A. C. A. 0O]_ _irfoff.
E6 A_51 x_
_-_o
_:, - ,[-[ [ !T
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Re: 8,340,000
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-16
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0 .4 .8 12 1.6 9/e of offock, d (degrees) Sechon lift coef//c/_nl, c,o FIGUR_ &5.--N. A. C, A. 002.1 _r|oil. , REPORT NO. 669---NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS 1.
%-
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L.M.A.L .
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o -ill ,"-
,=_',°c,V',,:%:_ ; I ! I H f_ 7l I4-1:.s .3z_>o_.o:a-hL! i :\
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:_ _ " -_ /_ z_ _<'- " "- " _z-'4 -:_d'''o ""'._ ..... ;_ Zz _._ ---
.L 4ng/e of" a/tocJ, d (degrees) Seth'on HI'# coeff/cien#. £t_ FIe, URE 3_.--N. A. C. A. T2t2 airfoil.
4.o1_.:'°,1z..31#,,,__olll1111 _U oz4 7 1 ! _ : 4a
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L ILl
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22 REPORT NO. 669---NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS zs _¢_. - .7_ ,,,. o-_v 0 gO 40 60 80 /00 " _ ,o iz, . ._i _ _ . Z4 48 _, OgO - ZO 40 "_0/6 95 /g_ .C_| " " " ttt Ft t t t P/i t t4 ..... t-.
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_ 8 -o -8 " 0 " 8 16 2,# 2,Z" "-.d 0 d 8 /2 6 AngM of o//oc/'_, d (degrees) ,Sec//on lift coeff/'c/ent, ct.
FIOV_ 44.--_. A. C. A. 4409 airfoil.
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24 REPORT NO. 669--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
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AIRFOIL SECTION DATA AS AFFECTED BY SUPPORT INTERFERENCE -- 5G 5to. u/ L 'w'r I. "_5 5,0 _ -45= Z5 "5.5Z -- 48
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REPORT NO. 669 NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS 20 c OZ81 q _ I-
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AIRFOIL SECTION DATA AS AFFECTED BY SUPPORT INTERFERENCE tfLi: tIll t!", -.5C
; ; -2.. '<_
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Aee=tqle of aHack, _ (degrees) Se¢#1Ot't /iH coetrf,,cie,"-,/; c_, Fmt'x_ _.--N. A. C. A. &_lll airfoil.
APPENDIX SUMMARY OF CORRECTIONS TO AIRFOIL DATA FROM curve of profile-drag coefficient against lift coefficien_ THE N. A. C. A. VARIABLE-DENSITY TUNNEL is modified at high lift coefficients (usually above about CL=I) owing to the change of c_,,a: and the variation As a convenience to designers in correcting prex_iously of ca0 along the span, resulting in final values of cdo lower published data to be comparable with the data published than those given by tim formula in this range of lift in this repor.t, a brief summary of the corrections now coefficients (reference 4).
applied to airfoil section data is presented. These Turbulence.--The corrections for turbulence are corrections apply to data obtained after January 1931 made by use of the concept of an effective Reynolds and most of them have been discussed in greater de- Number. The scale effects that appear in the tunnel tail in reference 4. The corrections are presented in tend to correspond, in general, with those that would the order in which they are applied. Information is appear in flight at a higher Reynolds Number, which is also given to aid in correcting previously published data.
therefore referred to as the "effect'ire" Reynolds Corrections for tunnel-wall effects and to infinite Number. The effective Reynolds Number is obtained aspect ratio. The formulas for correcting the data for by multiplying the test Reynolds Number by the tunnel-wall effects and to infinite aspect ratio are given turbulence factor, which is taken as 2.64 for the variable- in reference 1. Second-order effects not allowed for in density tunnel. This correction to the effective these formulas have been investigated and found to be Reynolds Number necessitates a correction to the drag negligible for the usual tunnel tests. These corrections coefficient; this correction is applied by multiplying the have been applied to all published data.
profile-drag coefficient, after the foregoing corrections Support-interference correction.--The support-inter- have been applied, by the ratio of the turbulent skin- ference increment as obtained from figure 1 for the friction coefficient of a flat plate at the effective Reyn- proper airfoil tllicknes.s is deducted from the drag or olds Number to that at the test Reynolds Number.
the profile-drag coefficients. A support-interference This factor is taken as 0.85 for the usual test Reynolds increment of the pitching-moment coefficient of 0.002 Number of about 3,000,000. Because of the presence (see appendix of reference 4) is subtracted from the of induced velocities over the airfoil surface, this measured pitching moment. This second correction method is considered more justifiable than the method has already been applied to all published data.
formerly used of subtracting a constant increment Corrections to section characteristics.--The first- from the drag coefficients (see pp. 19-22, reference 4) approximation section characteristics as obtained by but is obviously not applicable when large form drags correcting to irffinite aspect ratio are unsatisfactory, are involved. For flapped airfoils, an approximate first, because the airfoil theory does not represent with correction may t)e applied by subtracting the incre- sufficient accuracy the flow about the tip portions of ments determined for the plain airfoil.
rectangular airfoils and, second, because the measured Correction of previously published data. The im- coefficients represent average values for all the sections portant previously published airfoil data from the along the span; whereas each section actually operates variable-density tunnel may be placed in five groups as at a section lift coefficient that may differ markedly regards the corrections needed to make the data com- from the wing lift coefficient. The following corrections parable with those published herein. The five groups, are therefore applied as a second approximation to the and the corrections necessary, are as follows: section characteristics, f 1. The data of group 1 are uncorrected except for those corrections described herein as having been c,,,,_ = 1.07CL,_,.
ao--- 0.96ao' applied to all published data. The other corrections ao= O_o' q-O.39CL (deg.)
should be applied in the order listed. These data are subject to a correction arising from a consistent error in measuring the dynamic pressure. If considered of c_o= CDo+O.OO16CL:--l (t--6)O.O002 (t _ 6) sufficient importance, these data may be corrected by where t is the maximum thickness of the airfoil in changing the coefficients to correspond to a reduction of measured dynamic pressure of 0.5 percent. (See percent of its chord and the primed values are those obtained from the first approximation. For _ome appendix of reference 4.)
2. The data of group 2 are uncorrected except for unusual cases, where the lift-curve peaks are very those corrections described herein as having been graduaUy rounding with little loss of lift beyond the applied to all published data. The other corrections stMI, the maximum lift coefficients for the sections are should be applied in the order listed.
increa_d by 4 percent instead of by 7 percent. The AIRFOIL SECTION DATA AS AFFECTED BY SUPPORT INTERFERENCE Sections from Tests in the Variable-Density Wind Tunnel.
3. The data of group 3 are partly corrected. The T. R. No. 460, N. A. C. A., 1933.
corrections to section characteristics axe satisfactory 3. Jacobs, Eastman N., and Pinkerton, Robert M.: Tests in except for the maximum lift coefficient, which should the Variable-Density Wind Tunnel of Related Airfoils be increased an additional 4 percent. A correction, no Having the Maximum Camber Unusually Far Forward.
longer considered justifiable, has been applied to the T. R. No. 537, N. A. C. A., 1935.
4. Jacobs, Eastman N., and Sherman, Albert: Airfoil Section aerodynamic-center position and may be removed by Characteristics as Affected by Variations of the Reynolds shifting the published positions back from the leading Number. T.R. No. 586, N. A. C. A., 1937.
edge by 0.005c and by doubling the vertical distance 5. Jacobs, Eastman N., Pinkerton, Robert M., and Greenberg, between the aerodynamic-center position and the chord Harry: Tests of Related Forward-Camber Airfoils in the line. The profile-drag coefficients may be corrected Variable-Density Wind Tunnel. T.R. No. 610, N. A. (3. A., 1937.
for the support interference and the revised correction 6. Pinkerton, Robert M., and Greenberg, Harry: Aerodynamic to the effective Reynolds Number by the following Characteristics of a Large Number of Airfoils Tested in formula: the Variable-Density Wind Tunnel. T. R. No. 628, N. A. C. A., 1938.
C,_O--0.85(Cdop_bnLO.OO11--ACDo,,,,,,) (1) 7. Jacobs, Eastman N., and Clay, William C.: Characteristics of the N. A. C. A. 23012 Airfoil from Tests in the Full- where ACD0_ is the proper support-interference incre- Scale and Variable-Density Tunnels. T. R. No. 530, N. A. C. A., 1935.
ment obtained from figure I.
8. Relf, E. F., Jones, R., and Bell, A. H.: Tests of Six Aerofoil 4. The only correction needed for the data of group 4 Sections at Various Reynolds Numbers in the Compressed is the correction to the profile-drag coefficients given Air Tunnel. R. & M. No. 1706, British A. R. C., 1936.
in equation (1). 9. Williams, D. H., Brown, A. F., and Smyth, E.: Tests of Aerofoils R. A. F. 69 and R. A. F. 89, with and without 5. Tile data of group 5 need no corrections.
Split Flaps, in the Compressed Air Tunnel. R. & M.
The data of the more important publications are No. 1717, British A. R. C., 1936.
classified in the following table 10. Do$tsch, H., and Kramer, M.: Systematic Airfoil Tests in the Large Wind Tunnel of the DVL. T. M. No. 852, CLASSIFICATION OF PUBLISHED AIRFOIL DATA N. A. C. A., 1938.
FROM THE N. A. C. A. VARIABLE-DENSITY WIND 11. Doetsch, H.: Profilwiderstandsmessungen im grossen Wind- TUNNEL kanal der DVL. Luftfahrtforschung, Bd. 14, Lfg. 4/5, 20. April 1937, S. 173-178.
Published source 12. Jones, R., and Williams, D. H.: The Profile Drag of Aero- _rollp foils at High Reynolds Numbers in the Compressed Air No. of N. A, Figure or table C. A. Report Tunnel. R. & M. No. 1804, British A. R. C., 1937.
13. Jones, R., and Williams, D. H.: The Effect of Surface 40) All material.
Roughness on the Characteristics of the Aerofoils N. A.
,537 ll figures.
igure_ 2-24.
C. A. 0012 and R. A. F. 34. R. & M. No. 1708, British Table n.
N A. R. C., I936.
All but figures 2-24.
4 610 AI1 material.
14. Goett, ttarry J., and Bullivant, W. :Kenneth: Tests of no.
5 Table I.
N. A. C. A. 0009, 0012, 0018 Airfoils in the Full-Scale Tunnel. T.R. No. 647, N. A. C. A., 1938.
15. Goett, Harry J.: Experimental Investigation of the Mo- REFERENCES mcntum Method of Determining Profile Drag. T.R.
No. 660, N. A. C. A., 1939.
I. Jacobs, Eastman N., and Abbott, Ira H.: The N. A. C. A.
Variable-Density Wind Tunnel. T.R. No. 416, N. A. C. A., 16. Jaeobs, Eastman N., and Rhode, R. V.: Airfoil Section 1932.
Characteristics as Applied to the Prediction of Air Forces 2. Jacobs, Eastman N., Ward, Kenneth E., a_d Pinkerton, and Their Distribution on Wings. T.R. No. 631, N. A.
Robert M.: The Characteristics of 78 Related Airfoil C. A., 1938.
32 REPORT NO. 669---NATIONAL ADVISORY COMMITTEE FOR AERONAI,_ICS
TABLE III AIRFOIL SECTION CHARACTERISTICS Derived and additional characteristics that may be used for structural design Wing char- I actcristics I Thickness (percent A=6; round e) at-- fron tips [ r . I 3.9 1, I 237 _.,_1 o._z_ io._3 . .
I. I T24 • . , 13.51 10•63 ' 13. OO 4.0 4.0 I, 4 18q 404 OOq_ 16.21 12.72 ] 18.00 i 5.9 4.0 I, 0 245 4, 8 IMI7S ! 10._3 7.39 ] 11.73 ] •7 224 4.24 I .oo81 i 13.40 9.69 i 14.85 i 4.9 ,4 221 4.14 .o079 12.50 9,27 13.75 i 4,20 I_07a 11.25 8.36 12.37 .6 229 4.5 3.1 4•18 .0066 I 10.53 8.?0 i 11.70 i -.4 229 2._ i 4.18 [ oor_ 10.29 I g.oo 12.01 [ ],0 228 4.14 [ .[H)N4 10.40 I 8.70 11.12 [ 5.0 F, 6 • 8 1_2 4,18 [ _ 16.60 11.90 18.18 [ 7.3 I R 628 _ B E 10 U. S. A. 35-A - --5.2 .099 .35 .5 257 C5 B 0.3 1.81 U, S. A. 35-B ...
4,31 i OOT_ 10.56 7.54 11.61 N412 ]BI C10 4 28 I 5._5 4.13 6.00 0 .098 0 . .7 178 R460 A' A10 A D 8 5 91 N. A. C. A. OOOO 240 4[ 28 ] _•_ 6. 20 no A 8:3!t;39 0 .0980 ._58[ 1.0 H_so:: x ! Bt0 N. A. C. A 0OO9 4.32 ] otw, n 10.69 I 8.27 12.00 CO A 8.4166 0 .099 0 00COl .6 277 It 58%_ A [ C l0 r _. A.C. A 0012 ooy_ 8, 02 10. 33 0. O0 o .o_7 o _ooo+1 i.2 D0 AI 8.6',1._ 259 4.24 ] .oo64 13,36 15. OO N. A.. C. A. 0015 R586 I A i DI0 o o_ o . oo7o ' ir 21o 4 2fl : .0070 16.04 12.40 18. OO E0 A 7.8 .53 R38O A i El0[ N,A C A._Ig-- 0 .093 0 .OOg0 , 3.0 E 1 A 8.3 I 1.48 185 4.11 ! .0080 18.71 14.40 I 21.OO R 460_fl A I l_lOi N. A. C A. 0021 0 _ E 2 D 8,8 1.28 0 .085 0 .0094 [ 2.7 134 3.82 [ Pa_14 22.27 17.'2"2 25.00 N.A.C A. 0025 21:2:_. x _._ N+ A. C. A. OO30 0 ,074 ]0 .0117 I 0.9 91 3.48 m_7 t 26.72 ', 20.66 30. OO 0
Dt 84iioo
t __tA 1 -1.8 .o_1.12 . .0 _7 4 31 C3 B1 8.4il.72 R 400 A C 12 N. A. C. A. 2212 ooll, 1 8.02 --1.7 .099 l .08 .7 270 4131 1
B2 ]_ 8.1 : 1. fl2 N
N+ A. C, A. 240_ R 460 -I A B 10 .0062 [ I0.71 ; i !
C2 B 8.21172 -2,0 ,o_81.14 -i .5 282 4.28 ont'l'_ ; 10.69 ii _ i!0_ _ 2 R'556 . A C 10 N. A. C. A. _2412 4.24 244 1.4 on"o ', 13 39 1 D2 C'I 8.0 P 1.66 -t._ .o0r .to.oo581 R460 A[ Dr0 ¢ N. .k, C. ,k. 2415 ._Te,_loos 12:_o! 18:oo! 2 --1.9 .094 I .06 .0076 _ 1.1 _01 4.14 R 400 A ', E 10 1'4,A. C. A. 2118 I E 2 C I 8.0 1:53 R460 A I AI0 A D 8.1 1,32 -30 09_i l _ .oo82 .4 213 4.34 •_72_ 8o7 6;21 o;oo: -3.9 1 i .00_ .0 268 4.20 _. A. C. A. 4405 R 586 A _ B 10 B4 A I 8.1 1.77 . A.C A.4409 .
.0073 1 10.77 [ g. 28 12.00 4.0 .o98 1 .32 .0o71 ! .8 246 4.28 R ,_86 A C 10 C4 D [ 7.9 1.74 N. A. C A. 4412 .
oo7_ i 13,45 [ 10.34 15.00 D 4 C [ 7.9 1.72 -4.0 ,097[.2"2 .OO76] 1.0 _ 4.24 14 586_ A D 10 N. A. C, A. 4415 --3.7 .092[ .13 .OOV9 1.4 199 4.07 .=,, 5.4o, 416t 6ool i t R 460 A E 10 E4 D 8.1 1.57 nn_ : 16. I,5 [ 12.40 11S. oo N.A.C A.4 'tl_ oo89 I 18.79 i 14.48 21,00 N. A, C. A. 4421 -3.4 .089 { ,08 .oo88 1.9 160 396 R 460__ A t F l0 E5 D[ 8.211.41 I --I.2 .leo[.15 .oo57 1,0 205 4,34 N. A. C. A. 2,'gx_ .oo_ol : 6.21 9.ool i.8 ("2 --I.1 .099[.08 .0050 .9 281 4.32 N. A+ C, A. 23009 D2 --1.2 leo _ 08 .00_ 1.2 _0 4.34 _ .0061 I I 8.25 [ 12.00 i 1.8 R 610 A [ C 12 N. A. C. k. 23012 .oo_s_ 1,130 ! 10.38 l 15.00I 1.8 --1.1 .098 _ .t0 .oo67 1.1 258 4.28 !
R610 A ! D 12 N. A. C. A. 23015 1.8 --1.2 ,097 .08 .oo74 1.7 214 4.24 ] 16.04112.39 18. OO E2 R 610 I A E 12 N.A.C &.23018 oo74 18.70 ] 1.8 R610 A ! FI2 E2 N. A. C. A. 23021 --t.2 .092 .07 2.3 188 4.07 ] .oo8_ 14.44t21.00 i I D4 [ A 8.4 1.84 .OO71 10.60 8. 26 112. OO ] 3,7 R610 ]A] C12 --2.3 .100 [ .20 .0068 1.0 271 4.,_4 ] N, A. C. A. 43012 .OOT1 13.36 10.32 I I5. OO [ 3.7 --2.3 .101 .18 .ooT0 1,2 231 4.37 I D4 A[ r 8.3 [ 1.76 It, 010 ] A D 12 N, A. C. A.43015
+ ++++ .OO79 10.03 j 12.40 18, OO 3.7
E4 C: 8.311.63 --2. 4 .096 .16 ,0078 1.8 299 4.20 R 610 A F, 12 N, A: C. A.43018 --3.5 .IOO .40 .oo75 2,7 245 4.34 .OO87 II.03 8.27 12. OO 55 R 610 A C 12 D6 A '+ 8.3 i t.84 N. A. C. A.63012 --3.4 .097 _ .15 .flO_O 2.1 204 4,24 .ooSl 16.04 5:5 N. A. C. A.63018 12. 44 I 18. OO t
i 821103
| R 610__ A E 12 _+ I Type of chord. See reference 16.
I Type of pressure distribution. See reference lfl.
see reference 4.
t Type of scale effect on maximum lift. A signifies practically no scale effect. For other designations, Type of liR-curve peak as shown in the sket_'hes: t Turbulence factor Is 2.64.
_S
Z Positive directions of axes and angles _forces and moments) are shown by arrows Velocities Axis, Moment about axis Angle Force Linear (parallel Sym- Positive Designa- Sym-i (compo- to axis) Angular Designation Sym- Designation tion bol bol direction bol nent along symbol axis) L Y---_Z Roll .....
x _b U Longitudinal ..... X Rolling .....
0 v Lateral .......... Y Y M Z----)X Pitch ....
Pitching ....
Normal .......... Z g N X-----* Y Yaw .....
Yawing ....
Absolu_e coefficients of moment Angle .of set of control surface (relative to neutral
N
position), & (Indicate surface by proper subscript.)
(yawing) (rolling) (pitching) 4. PROPELLER SYMBOLS D, Diameter
C_ P
P, Power, absolute coefficient " =pn-'_"_ p, Geometric pitch p/D, Pitch ratio C,, Speed-power coefficient= _]_-_ V', Inflow velocity _, Efficiency _, Slipstream velocity n, Revolutions per second, r.p.s.
T T, Thrust, absolute coefficient Cr=pn-_-D_ Effective helix angle=tan-'(, v _ ¢, \za, rn/ Q, Torque, absolute coefficient C_=p_D5 5. NUMERICAL RELATIONS 1 hp.=76.04 kg-m/s=550 ft-lb./sec. 1 lb.=0.4536 kg.
1 metric horsepower= 1.0132 hp. 1 kg=2.2046 lb.
1 mi.=1,609.35 m=5,280 ft.
1 m.p.h.----0.4470 m.p.s.
1 m=3.2808 ft.
1 m.p.s.=2.2369 m.p.h.
NACA - Langley Field, Va.