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• NATIONAL ADVI.$0RY CO_I!:ITTEE FC_R .AErONaUTICS
-TECHNICAL NOTE N0.: 412"
TH_ AERODYNAh_IC CHARACTERISTICS OF _IRFOILS" _ " " . ' ...''7._: ,"
AT L_EGATIVE AI_GLE$ OF A_TACK "_; ': • _•_'"
,- .o
By Raymond F_ Anderson. :-
. o . ".•- • . .- SU_IZARY ."
. . , --." ::
- A number of airfoils, including 14 commonly used air-
foals and I0 N.A.C.A. airfoils, were tested through the:
negative angle-of-attack range in the N.A.C.A. variab.le'-
density wind tunnel at a Reynolds _[umber of approximately
3,000,000. The tests were made to supr_ly data to serve as
a basis for the structural des ig_ ° of airplanes in the in-
verted flight condition. In order to ,_:ake the results im-
:._ediately available for this purpose they are presented
herein in preli:uinary form, together with results of pre-
vious tests of the airfoils at positlve angles of attack."!
An analysis of the results made to find the variatiori
of the ratio of the maximhm negatlve'lift coefficient to
the r,,aximum positive lift coefficient led to the followingconclusions: ....
I. For airfoils of a given thickness, the rati6
-CL max/+OL max tends to decrease as the mean camber is.,
increased. ,.".. : ,
2. For airfoils of a given mean camber, the ratio " _>
-CL max/+CL max tends to increase as the thickness In-
ct'oases.
INTRODUCTION
There is at present little information on the aero-
d_,na_nlc characteristics of airfoils at negative angles ofattac:u. In the few tests which " e een•_av b _nade the Rey-nolds Number has been low.
• o
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ERRATA
NATIONAL ADVISORY C0_i'ITTEE FOR AERONAUTICS
TECHNICAL I_0TE NO. 412
THE A_RODYNA._,:.IC CHAR.iCTERISTICS OF ._IRF01LS AT
_EG.:TIVE A-_-_'.S OF A_:TA3Z
Y i_.ur e i0:
Figure 20 :
The c.p. at -7.9 ° should be 14.9 per cent
instead of 4.9 per cent.
The part of the c.p. curve from-14 o extend-
ing to and beyond -80 should be conc_.ve
upwards. The true form of these and other
c.p. curves ma_- be obtained more accurate-
ly by computing c.p. values from the curvesof C
m c/4'
2 £ .... _A,_..A. Techn}cal,-Note ;!o...4.12 .: .... ,..
. _ . , ....
The need for add._..tlen_l . ds-ta-.,i11.t.hls range was re-
cently experienced by the Bureau of Aeronautics, Navy De-
partment, while they were"f6rn_lhting rationel procedures
to be fo!Ll-owe.d,i.n-d'esigni.ng ..a.ir_-l_.ne_.,.fg.r.:_he Ldiv.e and in-verted flight conditions. Accordingly, a number of air-
foils suggested:'by_._tlh..e Buree.u .o.f.Aeirgnau_ti_s and a number
of N,A,C.A, airfoils were tested at negative angles of at-
tack in the N,A,C.A.: varlab.le.-den..s$_, wlnd tunnel at a
Reynolds Number of approximately S,0O0,000. "_
Pert of the results we r.9..ipubllshed in a preliminarynote (reference l) before the tests were completed, The
present report gives all the results, including those pub-
_l,%-shed_i:_ referenc_..l a_d the re%ult:s .of. l>reviousl, y .un-
pub.lish,ed, t:ests._f the :airf,o il_s'a:t ,loqs.!t_y.eangles of at-
tic/<:: ::...._-,.,.-_.--..:":.if .:" _ : _'r.- ' _ _- I
-"-.=.' ;.,:;_.:.'."': " " " '" .... -'i. :- -" " :: "-C,'. ' . : :_ "_ ._" "..:..:'. , - _. " •:-;'_ t_ "'":: .' _ _" "* :" "' _ " - _ ". , - "" ; "-" " "
..... .;: , :. i_ ,-; • ";'" "i'_." :; ,_"" _ .... T
•,: :" , : .... :-,: .- .'AND. },,ETHOD .:-:., .- , • -, . . .,-. :. . , . ..... _ -. _._ ? "-_............ " "" - " "_: "_-:: .'. . 't _ .',, -. ....
-.-.: A brl.e_f de soript!o.n.'of the _.edeslgned variable-den-
s.lty,wind tunnel :and :Its. z.ethod .of operat, ion wil!_ be found
in reference 2. The custo'mery 5 by 30 inch polished du-
.ralumin airfoil, s wez.e used:i.n _he tests, In reference 2
wil_l _be found a descrlpti_n qf.the .meth9 d of constructing
_t.he a:.i,rfoils. The._spe.cif!e& or dina. t.ea.wi.!l be found in
Table I. : ..
The.alrfoi.!s were t:ested in the._._suel ,manner (.as de-
sc_:i,bed in.reference 2)exoept for the method 0.f.,mounting.
on the support struts, When airfoils are _ested at posi-.
tire angles of attack they are mounted on the support
struts of the balance .with the sting and .str.uts attached
on the flat s'ide, F.or these tests,, however, the ai'rfoils.o
wereinv'erted and t,he sting was _leced on the curved sur-face to leave the flat surface free from obstructions that
might affect the value of the maximum nega-tive lift coef-ficient,
The measurements of "ift, drag, end pitching moment
were n:ade at a pressu, re cf approxi'_:ately 20 atmospheres
and an air speed Of ap_rcxlzatel 7 7C' feet For second,which corres ....nd to a Re_,:n_ds "'-,,-". cf. _-- . ......... oer ._,I00,000 Thetests at l_ositive angles cf at_ac_ were reade under.'thesame conditions. ' .......
N.A.C,A. TechnicS/ N_te I_o. 412 3
After" the tests were complb'ted, Ch'eck t'e's'tswere
za•de on some" Of 'the N',A.C.A.airfoils'. 'The"max-'Imhm lift_
coeff'Icients°'_were found to" be of the .order of •3 per cent
1_er than the v.alues obtained in thee flrst_.te_ts . Itwas suspected" _hat the' difference-mi'ght :have _been _ue to .... -_-
roughening of the noses of the airfoils by pa.r ticles in -
t11_ "airs_ream, Se_zeral of-the N.A.Q,A.°aiyfoils we_T.e ....!_ thebefo_e "repolished" on the. nos_e_nd on" retcst gave.vDl-
il ues ofmaXimum lift coefficients approximately equal to " ___i those obtained in the first tests. It was therefore _p-" ......• parent that in order to make accura'te com'_a'rison Of the
: maximum lift. coefficients possible, specio, l care, wa_sn_c -essary in finishing .the _.oses of the airfoils. The dif-
ferences betreen the s_rfaoes of the alrfoils used in the
tests described in this report are no_ known, b'at it is
estimated that the uncertainty in the maximum lift coef-
ficients resulti_g from possible variations of" the sur-
-_!_"_/ face textur.e does not eXceud +__ per ce_t. In_smuch.. a_ _
_' other sources of error may amount to +I per .cent, the v._.l_ues of the maximum lift coefficients may be considered
accurate to."wit1_in +4 per cent. ' ....-
- : °
•If the results of the prezent tests f.0r the Clark Y,
the M-6, the U.S.A. 27, and the U,S.A, 35B airfoils are"compared with the results for these airfoils from .the
tests made in the original tunnel, the r_:aximum lift Coef-ficients from the earlier tests will be found to be lower.
(Reference 3,) Although the original tunnel differed in
some respects from the l_resent one, .most of the differe_:cebetween the maximum lift coefficients is ettrib_,ted to the
use of unpolished airfoils In the original tunnel.
RESULTS AND DISCUSSION
The method used in obtaining the f_nal results, in.-
cluding the correctlon for the influence of the tunnel ..
walls, is given in reference S, Values of CL, CD, CDo,
Cmc/4" and c.p. are plotted against angle of attack• in
Figures i to 24. These curves, together ,Nith the indi-
cated velues of Cmo (C:_.c/4 when CL = 0), present the data
in preliminary form with sufflcient, accurac,v for use in
r
4 N.A.C.A. Technicel Note _'o. 412
• ' _ - : , ,
structural design. A technical report will be published
later which will give these and other results in a more
complete form, including tables of the,r data.
To indicate the scale effect on the;negative range
of the lift curve, data on the CYH airs'oil are compared
in _Ig-a.re 25. The curve from.the test at low Reynolds
Numb_r_shows a burble at a_comparatively low Ang1"e of at" .....
tack followed by a gradual increase in lift • -
° An effort' has been made to find t_=e_varlation of the
maximum negative lift .co.efficlents of these airfoils wi_h
the shapes of the profi!es. For this purpose "the ratio- C_
max has been t{eed. The'd'eterminat. ion of the' variation+CL"max "_--_ " '-_ ..... ' - -
of this ratio w lth the shape of the profile is difficult
beck.use Of the Yarge n'imber of variables which determine
the shape. However, a reasonably consistent variation of
-c Lthe ratio max,. has been found with two shape "charac-
•+CL max
teri'stlcs of the profiles the thickness (maximum) and
the mean camber. . • "• - _ _. _b._-._:U
For th_ purpose of this analysis the' mean camber isdefined as the maximum dep-arture of the mean ilne of the
profile from the chord, where the chord is taken as the
line joining the extremities Of the mean line. The mean
line is defined as a line midway between the upper andlo-,er surfaces of the profile, where the thickness is
measured l_erpendicular to the mean line.
-C LIn Figure 26 'max has been plotted •against the
+CL max
me_.n camber and a line has been draw= in to represent
-CL max with the mean camber for pro-the varia'tion of _C L max
files of 12 per cent thickness. The values for profiles
of a_roximately 12 per cent thicl:nesz lie near this
line; whereas the values for th_c!:er and thinner pro-
files lie above and below it, respectively. The ratios
for the 2512, the 4512, and the 6512 (_hich have the
mean camber at 0.5 of the chord and a thickness of 12
per cent) have the same trend as the general.trend of the
ratios; that is, -CL max decreases as the mean camber in-
"_CL max
cr_._.s-_. The Clark Y, th-_ Clark Y !-15, and the
N_C,A_ Technlcal.Note No. 412 5
Clark Y _'-18 profiles, whlch have a_proximately the same
ease of CL .max .... _as the thicknessmean c_mber, sho_ an incr +CL max _
is increased. (The designation: M _me_ns: that the pro-'- •
files -ere thickened from the mean'ordinates of the orl-gi.nal Cl'ark Y.) " "" " .. . .:i, .. " . . : -
The plot may be used for ma]'-ing an estimate of the
val-ue of uC L max for "any airfoil fur whlch data "a_4'ava'li- _
able from a varY[able-density [tunhel test a-t p0sltlve an- ........
glee of attack. The airfoil should be located "on the plot_il _according to its mean camber (found as described above) i_and.thic_:.ness', If" the airfoil -is s'imilar to one of" tho'se
on;the ;plot', the loca_i'ng of It wi'll be easler.
•The error in the estimate i.e.l'ilzely[to be "large if
the profile has peculiarities of shape such_es a shgrpcurvature of the _lea.cling or" trailing sec-t'ion_; -b_/t for '
profi.les o.f co-nventiohal shape, the error in %he:_estlmate
of -C L max should not e-xceed.l.2 per cent of the _ true value.
CONCLUSIONS
• I. For airfoils of a given thickness, the ratio
-CL max tends to decrease as the n:ean c_mber is increased.
+CL max
2. For airfoils of a given mean camber, the ratio
-CL max tends to increase as the thickness is increased.
+CL max
Langley Memorial Aeronautical Laboratory,
National Advisory Coumittee for Aeronautics,
Langley Field, Va., February 26, 1982.
i,
6 N A C.A, Technical Note N0._412 "', - :. ; - , . . .' • .
REFE_.ENCES " :
i. Anderson, Raymond F.: The Aerodynamic Character-
istics, of Six Commonly Used Airfoils over a Large. ....'; Range _f Pos'itlve and Negative Angles of Attack, •
"'-'- " T'.N.'N'o..'397, N.A.C.A.,. 1931. • :,/._ ;;:_ %
2. Jacobs, Eastmaln N,: Tests of Six Symmetr{cal Air-_ , _foils in tlhe Variable-Density Wind Tunnel. • T.N,
;" " ,_1'o." 385, N,A.C.A.,.1931-., , -"
3. Jacobs, Eastman N., and Anderson, Raymond. F.' Large
" scale Aerodynamic Characteristics of Airfoils as
..... T'ested in the Variable-Density Wind Tunnel. T.R.
• ":: No, 352",.N,A.C,A., 1.930..• . . : . • - .. . .÷ •
4. Clark. j Z,: W;, and Lockspelser. B.: Wind Tunnel Tests
on Aerofoils at Negative Incidences. R. & M. No.
' 1383, British A.R.0..,.-1930.
. , ,'.. " ,'':.2 <; :.'_
: .. : .. t
.. : . - ._ ..... ." ; . . ; •
_'. _.
• '%
N.A.C.A. Techn_:_al Note No. 412
Ordinates of the Airfoils in Bar Cent of the Chord
t_
%irfollL.E.
R_ ius
o 3.5o
5._5
2-_./2 6.5o
5 ?.9o
7-112 8.85
IO 9.6o
15 lO.6S
20 l! .3b
30 11.7o
4o 11._o
50 i0.52
60 9.15i
70 7.351
gO 5.221
90 2.gOl
95 1.49
I00 .12I
i Clark Y
I 1.50
Lower
3.50
!..93
1.47
.93
.63
.15
.03
0
0
0
0
0
0
0
0
0
Clark Y-I_ Clark Y M-I 5 Cl_k Y k-l_
Upper Lower Upper Lower Upper Lower
5.3_
8.3S
I0.00
12.15
13.61
lh.76
16._5
17.47
18.00
17.53
16.19
1_.o7
n .30
.03
.31
2.29
.!g
5.3 •I3.5o]i3.502.97 5.951 1.43t
I '2.26 7.21 : .76
1._3 s._ i .o5I -
•97 i0.01 - .53
•65 10._9 - .87
•23 12.17 -1.3_
•05 12.96 -1.56
0 13.35 -1.65
0 13.01 -1.61
0 12.00 -l.bS
o lO._4 -1.29
0 8.39 -i.0_
3.50
6.40
7.s6
9.7s
11.06
1_.o7
13.52
lh.41
lb.8 5
14._7
13.35
n.61
9.33
0
C
0
0
5.95
3.20
1.7o
.i_
.7_
.40
.__i
.02
'.•o?.
3.56
!.90
.15
3.50
.98
.Ii
- .9_
-I .5_
-2.05
-2.$9
-3 •02
-3.15
-3.o7
-2._3
-2.46
-l.9g
-!.401
- .75
- ._0
- .03
U.S.A. 27
Ui_per Lower
1.77 _.77
3._o .5oi
5.07 .361
_.5_ ._91
g.22 .I0
9.19 .o2
lO.5O .IC
"In'.37 .3oI
_i.97 .93
ii.6_ l.ih
io._6 .75
9.5_ ._g
S.O@ ._
6.10 .0i
3.-_ .12i
_.26 .33!
• 67 .651
!
p
N._.C.A. Toenn_ca] Note No. 412 8
T_LE r - COL'TI!U_ED
OrS iit%t_s of the Airfoils in Per Cent of the Chord - Continued
4"
Air:foil U.S.A. 37_B Boeing 103 Boeing 10JA NACA M6
L.E.
Radius
St_tlons U_per Lower
2-i/2 6.n
5 7.52
7-1/2 _.S5
io 9._5
i5 io.56
20 ll.2g
25
•63 7
.2S S
.I_ 9
.07 io
.00 Ii
.05 i2
Upp,? r
3.56
6.10
.17
.56
.55
.35
.53
.28
3o
be
50
So
65
70
_o
90
95
I00
-E• O
li.7S
il.b_
io.33
_._i
7.08
5.02
2.72
1.50
.25
.i5
.2_
.39
.u5
.35
.20
.12
.OO
12.70
12.h2
!i _.pO
_0._i
1.23
Lower
3.56
2.20
1.73
1.22
.6_
.32
.15
.02
0
.02
.ll
._S
6.26
3.s_ .7i
2.5o i .s5i.II 1.00
0.05
._-5
._6
o.97
UDDer Lower_ , , -
2.92 2.92
5.00 l.SO
5-_7 I._2
7.oi I.OO
7.s2 .72
_-._s .52
9._ .26
I0.00 .12
io._o .02
io.i7 o
9._7 .o2
.36 .os
6._% .]7
3.i3 .3o
3.i_ ._5
2.i_ .53
._7 ._7
i, ii.._)
Upper
o ii
i.97i
2. iI
5.71!
Lower
NACA CYH
1.50
ii.70
Ii .)40
io.52
9.i5
.30
7 ._i
5.62
3._
£.A.$.A. T_chn_,_a_ Note ilo. 412
TABLE _, , CONTIIU_'ED
Ordinates of the Airfoils in Per Cent of the Chord - Continued
/
Airfoil _, 22 C 72 Boeing 106 GStt. 398
--- 1.40 ---
Stations
0
1-1/_
2-1/2
5
7-1/2
I0
15
2o
3o
_o
5o
6o
70
so
90
95
ICC
Upper Lo_er
5.37 3.37
5.5s 1.7o
6.66 1.15
8.25 .62
9.33 .32
I0.13 .16
11.28 .03
12.C1 0
12._2 .05
12.01 .15
Upper Lov;cr
Ii.04
9.57
7.6s
5.51
3.c6
1.73
.4t[
.2_
•30
.32
.2_
.12
.C5
0
3.49
5.55
6.51
7._9
S.85
9.60
1C.69
n.36
l_.73
11. hl
3._9
1.92
x.h7
.93
.h3
.16
.03
O
.21
lO.
9.
7.
5"
2.
1.
i
53 •59
15 .85
36 .91
23 •72
GO ._o
52 .21
lO 0
o.70
Upper iLo_Teri
i 2.981.5 b,
i.O_
-I .iS
-I •28
-1.30
-i. 22
Upper
6.20
7._o
._2 9.
.0_ i0.
.28 ll.
.04 12.
.9o 13.
2.98
5.2b
6.1_
7.5_
s.56
9._
10.62
1!.3_
II.83
11.54
lO.5_
9.os
13.
13.
12.
It.
•9S S.
• 72 6.
.h2 3.
•23 I.
.C_
17
37
7.18 -
5.96 -
2.5_ -
1.29 -
.04 -
Lower
3.74
1.89
25
53
3_
80
3_
27
$3
53
12
qo
(].'_
_o
1.2g
.69
.35
.ig
.03
0
.05
.17
.27
.33
.35
.27
.._-3
.O,S
C
N.A._._ A. Technical Note No. 412 i0
T__._LEI - C_._TIh_JED i
Ordinates cf the Airfoiis_n Per Cent of the Chord - Continued
Airfoil
0
i-i/b
2-1/2
5
7-1/2
10
i5
20
25
30
50
60
70
SO
90i 2.CS! ._;2 2.t+5-i.i7 2.7i- 22 i 93- 971.72 '- ._7i , ....
" 95 .9_,- .2,: ! i.i_i- .ts i._+.- .63 i._7 - .i6 1.o5 - .56
i J. ,._, _.,-_;'-._++_(.'.,,:,(-,,;I _:,.6>!(-.,6: _._.:+I_-.:,.3_<.:,3_.:,-3_' , i
p
N.A.C.A. Technical IJote Yo. 412 II
T_ .... I CONT!I__:D
Ordinates of the A_rfoils in Per Ccnt of the Chord - C.:,ntinued
' Li i....., ....Airfoil NAOA 2512 :TAC" 6:_12 ""_"..._v.,I"0aL, . _,"""-.-_A 12 ,._-._._4_].o
L.E. 1.576 1.576 O.g:J7 1,776 i_.adius - I 3.547_
Slope of Iradius .oass- 2/25 o/22"- 4/25 h/25;_ ,.,.,I_,ing thr,r,tsh I
end o£ chord _- . , ! i
Staticns U_.,ocrlLower Upper!Lower L'pper]Lo':ler Lr._4:eriI;ov.erl:k_P'_":";%cwer" _'1_ I [
o - I o.cc - i c.°° - i o.oo - [o.oo - o.co
i i ' I ii-i/14 P.ogl -1.7o 2.57-i. _, 1.751 -i . i2 2.33- i • r_l. ...._5r,- - _. _'-,
i I ' i '....... .. " ' '.o7 ,;.7 c' .__62-1/2 2.91 -2.33 3.50 I-I._2 2.'*t'-i.5 O Z._21-'.-_- " , _1-3
5
i ! i ! , I , ._,.
7-1/2 _._3-3 :,_ 6.13!-2._3 _.3<-_.99 i .._!-2._ 7..... I .... 7_ l-_:..o
• I
lO 5.46. -3.92 7.o6', --2._45 5.o41-2.c5 i 6.25 -3.1s z.7:- ' -"-._l
' 15 ;_._cI ,, . I '-,,.% _.58!-2.27 6.1_-1.26 7.46-3.2,1 lO.25-5.g9i
25 7.14q-'4.14h 10.50-1.47 7.4_.;-I.1+7 8.'."5-2._5 iil.9:-" ::._1
1 : 66 I ,30 7.69-k.33 11.07' .9 g 7 _=! -i.16 o x-,I , _i2._7- - "" "" "" "';i -e. ., -5. >.8! t
40 7.7 -'_.90.. 11.%6. .oE 8.1_ .52 9. _:_:.-1 97 1:2. ='_'-:1 _'_
50 7,2S' 2q '1,29 .71 7.9_ .c3 q._91-1 e9 "_,:t. "'I I
70 5.35,'-_.97 s.7g-. 1.39 " ' 62 c6 - .,..'< ."
- o._, -._.3480 3- -1.33 6.5L_ 1.24 _ nd .6o , p._31 .d+ 7 " :
90 . _. - .72 i 3._8 .72 1 _2.5 .35 i 2.93 .CO ).,, - .T1
! ,1oc (.13)li ,[(_13 ] ( _ [ _ _ .' ' _c].1 , ._ 2)!¢.c9)(-.",>) I ( _,)_- ie) (.__')),-.
i I i _ I
' - - i " ,' - " ,: - ° " ,: - , " - li .
.?,
"T'
"-'.A. g '0 ,¢-o mZccP.nicrl "_o_e Fo :I:.. ".'-_
..%,"
'-20 ' C0'%u_T_;A;_oo 2e.:(_
i l • •
.9/°_D
:,_,soo %u_,,Jo:;.,'
•_', CO
r-l, H ' • " 0 O
i _" | • I! , I I ./ ,i / i " . 'I l.... .... ....J-.......... I...... ....... ........ I
I //! i I I II, i i.,L _/ tl I I ; ! '_'_ I .I I-..,
--'_;"_'.,___'--.L"'_..... _ ..................i ' t ........-_ 1- / ,_I_-"'?-"-' ---)I ......... " I""CQ
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