NATIONAL ADVISORY COMMITTEE

_

FOR AERONAUTICS -

WAlr’nm EIIPOIM’ORIGINALLY ISSUEDSeptember 1943 as

IkU.-ameConf’ldentlalReport 31~

EFmcl!sm’-mlm mAmmcnf TEE AEmJJ!mMac

CEWUEKBTtCS OF SCM? ILW4XAG JUXFOIEI

By Milton

Dul@Yy

t

IkwidBon and Wu’old R. !lumer3 Jr.

hkol?id J&’01MUtiC81 “~bo~tory

~ Field,?a.

,,

.

WASHINGTON

NACA WARTIME REPORTS are reprints of papers originally issued to provide rapid distribution ofadvance research results to an authorized group requiring them for the war effort. They were pre-viously held under a security status but are now unclassified. Some of these reports were not tech-d tally edited. All have been reproduced without change in order to expedite general dtstribution.

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https://ntrs.nasa.gov/search.jsp?R=19930092778 2020-04-04T19:07:20+00:00Z

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‘ :$ --.’+ udUMiiilun- ._?.?17601-6862

ENrIcmALAm80RY’Cmidm!3mR AEmAUTIcs—_ ___ 1

AlmEOEamFIlx!mmLmmRl?. .

Immzcsar’MEAmnw$’LoAntmOHmE”A3mmmac-.. .mR@!&6TIf2iC@’“BoldELow-lnw AIm’cms

,Byyilton Dmldsal andma R- TLuwr, Jr.

The effect of variations In the tme of wan llne cm thesection characteristics of mver4 repi%emtative l’W2AI.uw-dragairfoils ‘wasinvestigated● The test results are ooqpered withtheoretical predictions and indloate trends that facilitate theoholce of mean llne in the dhmnce of tests.

Immmclrml

lllievlng *signer, &t& a variety of man llnes at hls dlqmml,is oacfrcnted with the problem of chcos~ the pzmper mean llne fora particular alrfoll application. As an aid In the proper selectionOr meanlines, tests have been made In the IWACAtwo-MmensionaJ.luw-turbulenoe pressure tunnel of some EUM#iluw-drag drfolls to observethe effects of varying the -an line of airfoils of the samefemily.The rolatlve adwntages to be gahd by the use of loading of onetype in preference to mother are dlmmsed, and ~erlmental. twtdata and tiemeticnlly calculated values for the airfoils tested aregiven to Indicate the limltati~ns of the theo~.

TESTMOrHoIsl. .

In orbr to obtain a representative test -p of Wrfoils,membem of the HACA 63-sertes, NACA65-series, end WCA 66-seriee

Wit the tlm this paper was crigjnally p@llehe~ some of thecorrections reguired fcr ccmrwthg the test data to free-a,lrcmdltiaushad not been dete~ed. The meaeured vslues of section lift coeffi-cient Cl (fl@ .1 to U, fi~ , 13 and15) shcu3d be corrected bythe fclloqlng egpatlan

c%ormcta)= 0*$)6*Z + O*O1

The measured aeoticm en@es of sero M% (fig. 12) vIU therefore besli@My differant afterthe aforemmnticned correction is @lledto the llft data●

+’”*, .,-.

9

. . . . .. . . .....’.. . . . . . . . .’, . . .

2

famlli-eawprewere Cadbered

-. .. . . . . ... . . ..

~. ~ .... - *. “. ,.

. . . . .. . . . .

milecrk~ &zfolls ti.tibident$w#. ~asic tklelmess foniw(see reference 1)”for the’same design lift wltb the

uniform-1.wyitiap M.ne, that isf wlt?a a =,1.00, end ~ti ~ l-sother than a = 1 Al;””AM’oIIs of We IUCA $-series were chomn togivO a caniberand a thickness variatlcm,

. . . .“. ,%. ... .

All the altioils, mnetzwtad as described In reference 1,were i3binch-ahordmodels and were tceted in the smooth conditim

at Reynolde nunibexwof approximately 6 x 106 end 9 X 10G; t.models of thickness equalto or greater than 18 perceut of thechcmd (OJ& ) were aleu tested with a standard roughness a@L1.ed

., to.the @uUng edgb .(@ee.reference 2) at..aReynoldsnuniber of

apjroklmately””6“x 1060 Lift @d. “~ values were obtained fnmtuuriel~ and wake-.eurveypreewure meamrements, and ltchln&

7moment values ‘were obtained”from a belance (reference 1 .

Ammage tunnel conctant3 for these tests m

Tunnel texlk“. . R@ldF~ number, R “ pressure -c pres~ n%;r

.“ (atm) (lb/sq ffi)

6 x 106t

89: 0.1376 ,103

.,”. 9 k ti8 ,153

RI!sum3

Routine-test remits giving section characteristicsfor airfoilstested in a c3moth oontition are presenteflh figures 1 to 7. Thereeul.taare @.vem In standard chart form, with two alrfcdia to eachchart, for the folhwlng airfollo:

. .

NAOA 63,4-4a), a = 1.0

W-W 63,4-4=, a = o.3

I’?ACA65a-415# a =“1.0 .

-,

NAY65a-4158“a = O *5

.mm “~ -%18, ‘a=l.O. .. ..

. . .-. . “m.-

E40A---...- ..---- -.

RAti... .......

E&u

. SU04. ..m. . . . .

mu

\ 19AOA

.. *. ISA*

N4CA

u (!A● .

65s-418., a..E.-0.5., .......... .

.6S442i, al= .i,o “ ... . .. -.

66,3-418, a m 1.9 .,. ...-.

66,3-418, s .= 0,8. ” “

-6.6,3-6.18i a E 190. ..

6S$~618, a =..06$- . . ..

66,2416,:.a== 1.0

‘Charts of the air follfi “w$th “a.standard roughness” qre“ given in figures 8 to. llj the .llft r.nd drag characteristicsaxe preyented in thqsd charts” for all of the afore-mentionedalrfoile , 0.180 Ishiok or thiokep , “with the exception Qf theITACA 66,3-418, a = 1.0 an-d the HA(IA 66,%418, a = 0.8 air-foila; “The oharacteristios for the corresponding smoothairfoil with ha = 1.0 are also shown on each chart for com-parleon. ..

Measured values and theoretical mean-lice values ofangle of 5er~ lift, design eection lift ooefflcient, andsection pitching-moment coef’fioient are given in figures12 to 14, reOpect Lvely. The theoretloal mean-line va~~eshave been computed by using the valuee aad methods of ref-erences 1 and 3.

Figure 15 shows”the variation of design seotion liftcoefficslent and seotion pitching-moment coefficient wi$hairfoil thiakness for.several airfoils of ttie MAW 66Aserias. The results ~lven were obtalnod from tunnel meas-urements: from mean-line (thin+airfoll-theory) Wloula.ttons:from integratlag of tbo oom%ined theoretical pressure dis~tributions due to basic form thiokness and to camber

‘=(+’~)’(see .refeaence 1); and from a 9!heodorsen

calculation (see reference 4) on the HA(!A 6%-418, a = 1-Oalrfotlm !Che symbols in”the=formula for “S are defined as

...

. .

s pressure coefficient. ..,. . . .

v velocity on surface of basic thickness form,.

v free-e tream ;eloctty

Au velocity in~;eaent due to mean-line load distr~-l)ution . .. . . .

,Dt$CUSSIGN

Soct20n Chara~teristics Applicable to Ylng Design

●

Aerodynamically, wing design u8ually Conststs of theselection of suitable root agd tip airfoil eections~ Theselection of sultqble roGt and tip sections Involves thepropor choics of noan line: h~aco, the aerodynamicist mustevaluate available .nean.-llne data. Yhe advantages cf choos-ing one me~n line in preference to another for a particularapplication can tsst bo shown By the effect~ of differentmean linss on the airfoil sect-ion characteristics The mostl~portant of theoe cha.raoterietlca qre

“.

at “ angle of aero lifto

.,

a. slope of section lift curve, per d.egreo..

cl . optimum lift coefficient, & 09ctlon lift coef-Opt ficiemt selected as middle of lo~-drag ra~ge

C;=x maximum sectloa lift coefficient

c~-ran~o angular rango corresponding to dlfferonce betweenangle of attack at c2&= and at Cz=cl

. . .

Cd.-range extent of minimum section profilq-drag coefficient

. .

cmc/4 section pitching-moment coefficient about section... . . quarter-chord point . ..

.

Vc section critical speed

6

Seleqtlon -of Ifean Itlnes .,... . . . .

Rdferenae 1, ‘which presen{s ““mean llnes with values “}

of a ranging from 0-3 to 1.0.,recommends that a valueof & be seleeted which 3s” eqUal to or g~eater than the

b’.iextent of the falltng pressure for the associated basltithiqknee-s fobm. & large variety ~fc loadinga may be ob-tained by com’binatlons of the varidue mean. llaes: however.

.’ the pr~ent paper ts uonceraed with only the values of a“as reoomminded in reference 1. “ .

Whecq the loading of an alrf.oll is changed, th”e lnher-“ent characterist#.ce of *he basic thickaess form may be re-tained and yet the airfoil seotion character’ie~lcs may be

“ “greatly varied. For example, by employing one type of.cam-ber in preference to another, K higher section critical

‘- speed, a hi,gher maximum sect,ion lift coefficient, and ahigher sectic~ pitch.ing+n?ment coefficient may be obtainedwithout any bhango In seotton ]fllnlmumprofile-drag coeffl-c$onto “ .

The trend of section,characterlstics can %e shownp&tly by thaory end pertly b~ gonorallmtion~ from testresults, Thin-airfoil theory Indicates that a higher ‘critical speed, a greatc~ section pitchinemonent cooffl-cimnt, and a lowor valuo of section angle of.soro lift areobtained as the mean line progresses in the direction froma= o.? to a = 1.0: howevor, Indications of what happensto tha maximum seotion lift coofficieat nust be obtalnod

‘ from test results..

. .Test results giving the section characteristics of

airfoils with a uniform-load meaq line and-airfoils withloadings othor than a E. 1.0 are presented. in figures 1,to”ll. The charts for the airfOilS In the smooth cond-

ition (figk. 1 to 7) indicate a higher ~a~~s a greater

ao, and a narrower c~-range for the airfo$ls with. a = 100. .‘.than~with a < 1.0, .The plots of . cd Qgalnst . ~Z show no

significant difference la Cd. alt@ough_ at the highermih -

values of c $, the drag Is conefderably less for the air-. foil with ‘a = 1.0 than with other mean-line loadtngs. ItIs noted that the cdo-range for the airfoile with .a ~ l.o

shifts toward higher lift coefficients as compared to theairfoil with the a = 1.0 loading, and also the cloptIs greater in almost every. ln~tance. The section pitchin~

—-

6

moment ooeffioient, .as is expected, Is greater (more nega-tive) for the airfoil with the a =. 1.0 lo~ding, “

With regard. to rloughn~ss, ai~folls with a = 1.0appear to be more oontaervative than airfoils with a < 3*00!Che charts of the airfoils with roughne66 (flgsp 8 to 11)show tlkt the a = 1,0 airfoll~ havo higher values ofcl an-d lower values of Od throughout the al-range

maxthan the a < l.O airfoils,

..

Oom~arison of measured values and theoretical mean-line values are shown 86 an aid in predicting airfoil.seotlo~ characteristics from mean+llne ~.ta based on “thin- “airfoil theory. Beaause thin-airfoil theory does not takeInto account ‘alrfotl-thiakness and boundary-layer con~id~r-Stlo”na, .meav-line. data and .meaeured results might be 6x-poctod to. diverge considerably, A compari60u of moaeuredvalues acd theoretical man-line values (figc. 12.150 15.)‘ .shows that, for tha a < l*G airfoils, the theorettoalangles of zero lift and the theoretical pitahing-mbmentooeffleients are In fair agreement with *hoOe measured:,the measured desi~n section lift ooeffioientfj, however, areusuall,v higher than the theoretical values ks indicated inthe”airfoll designation mumbers. Although, for the airfoilswith a = lmO, the theoretical.and measured design lift co-efficients are in fair agreement, thq measured angles ofzero lift and the measured pitching-moment coefficients aroconsiderably less than t~ose indicated by theory. The de-viation of values of measured pitching-moment coeffici~ntfrom the theoretical values results because In Gxperimanta uniform load was not naintalned over the airfoil to thetrailing adge. This fact Buggosts that a reducing ‘factormight ba applied In order that tho thoorotical values ofpitching-moment coafficlant might conform ~ore closely totho measured values.

.

. Ifith increasing airfoil thickness, thoro Is an acco=panylng Inorease In soctlon design lift and seotlon pitchin~moment coeffi.oient. (See fig. 15. ) Although thin-kirfoiltheory obviousl~ gives no evidence of th16. increase, it Isapparent from integrated theoretical pressure-distributioncalculations and is substantiated by test results.

00NCLUSIOE,

.

.“ The general affecte of variation In the type of maanline on the seotion characteristics of several representa- “

—..— . .

7

tive low-drag airfoils are shown.. Zhe aonelatenay of

. ,,rseults I,ndicatea that these general trends are aultable ofor uae in the seloatlori of-mean lines f?or applloatton toairfoils for wttioh teat reaulta are not available?

Langley Memo~lal Aeronautical Labbrstory,l?at~onal Advlwory Ooaumlttee for A.eroaautias,

Langley Field. Pa.

1. Jacoba, Eaatman ~., Abbott, $ra E,, and Davidaon,Mlltons Preliminary Zow-Pra#irfoll and ~lapData from Tests at Large Reynolds Humbera.and LowTurbulence, and Supplement. NACA A.C.R., March1942.

2. Jaooba, Eaatman H., Abbott, Ira H., and Davidson,Mtlton: Invoatigation of ~xtreme Leadin@dgeEoughneSa on Thiok Low-Drag Airfoils to Indicatethose Oritlcal to Separation. XACA CP3$, June 1942.

3. Jaooba, E. M., and Abbott, I. H.: Angles of zeroLift for Some HACA Low-Drag Airfoils. HACACJ3.,Teb. 1942.

4. Theodoraen, T., and Garrlokp I. 3,; General Potential “Theory of Arbitrary Wing Sections. Eep, No. 452, INACA, 1933.

2.8

2.4

2.0

6.3,f-420,a=’LO/.6 \\

d \

$“,2“% “ \g t r

1\

5 .8 rQ /“*

.& .4~/

j~

o

-.4Airhils:NACA#,4420

-.8 )‘ .R:9x I06Chod: 24in.Tesfs:Z?T 24/,402

.4‘ 408,421,und42dI I i I I I I 1 1 I

““2 -16 -8 01 I I

/6 24Sectionungk of o%ck, ~, u’eg

-J.2 -.8 -.4 0 .4 .8 k2 1.6 20Sec+im /if+ coeffikkwt, ct.

Figure 1.- Section characteristics of two NACA63,4-420 airfoils.●

+

>

,032

/ ~— — —

\ \.028— — — — — —- .— -- v

1/ -

-1.2- -A -.4 0 4 .8 L2 1.6 2.0Sedim Ii#coeffkientc1

Fipyre 2.- Section characteristics of two NACA652-415 airfoils.

I

2.8

2.4

2.0‘

65.3-4 /8,a= /.0/.6 T \

(7

j’,2

:$ “ +’ \#4 I

k \U~ .8

65,,-4/8,a= 0.5

% /\.

g .4 f* /u 1‘u% -0 b’

-.4Airfoils: NACA653-4/8

\

-.&R:9XI06

d Chord:24 in.Teds: TDT 3/4, 320,

406 und411

‘/”2 -/6 -8 01 [

8 /6 24Sec+ion angle of utiack, a., iieg

.032.__.,. .— _-

.028

,

(f/

Figure 3.- Section characteristics of two NACA653-418 airfoils. w

Seciim lift coeffiutit. c1%1_l-J.09

Figure 4.-” Section characteristics of two NACA654-421 airfoils.0

IP

Secfbn angle of o+tuck, do, deg

+-H-H-F+

) -.8 -.4 0 .4 .8 /.2 “/.6 2.0Sectiw lift coefficient cl

w.m

●

Figure 5.- Section characteristics of two NACA65,3-418 airfoils. m

28

2.4

2065 3;618 a=LO

t‘1

1.6 / / ‘%+ ,_! ,+’ ‘+\

c YY) ~

$ /.2:Qtwg .8 /)4

t*

g .4~

$

0 ‘

i#

-.4 ~ /I+

A)+fai’s: NAOl 653-&’8_

+/ and 65J -6/8

-.8R: 9x/OeChar-a! 24 IFI.Tes+s: TDT 19522240Z.

and 420-1.2 1 1 I I 1 1

-/6 -8 0 8 16 24Sec+im anqle of u++ock, d, deg

Figure 6.- Section characters653-618, a = 0.5 ai

t

r

.03?

-/.2 -.8 -.4 0 .4 8 /.2 /.6 2.0Sec+ion Iif+ coefflcknt, c1

ics of an NACA65,3-618, a = 1.0 and an NACAfoil. m

_-

2.8

2.4 ‘

2,0 r

66, 2-2 ’16, a= /.0/.6

c\

~-,2\\

\:G “

b

st)~ .8.

k;.

$ .42u$0

I

-.4 Ly

I Airfoi/s: IVACA66,2-216 _

-.8 }{ .R:9x I06Chord: 24in. “Tesfs: TDT 2/5,247,

4 and 249-/.2~4LJ

O 8 16 24Sec+ionongleof ffffock, aj, deg Secfion lift coefffcien~ ~ “-- “--

Figure 7.- Section characteristics of two NACA66,2-216 airfoils.

NACA Figs. 8,s

Figure 9.- Lift and-drag characteristics of two NACA 653-418 air-foilswith a standard roughness applied to the leading edges.

.

ITACA Figs . 10,11

2.0 ,&o

[

6S4 -421,a =/. O1.6 ~+.. .040- /

‘. J‘. ‘. ~— x%. . /“”” 7 r

‘.\, ;>.~

‘y Jd

/

~.I.2*’X, D

$ .Cm ,

i

/ Y/ ~- ~,, Q)\\/

\s. .

z / /k

+

j8 / I

L

2 , ., 654-421, a = c25.< /8

,f

.= 4 N %. -b & ‘> ‘04 I

4“ J.010 ~ m

// ‘Wx-E -_~ X-Xq

o +/

o-4irfof7s: 654+21

1~ R: 6 x foeChcmd: 24 in.Test: TOT 3/6 M 434

-.4-8 0 8. f6 24 -.4 0 .4 .8 1.2 i.6Section anqle of ottock,~, O@ S= fionItft coefftinf. cz

Figure 10.- Lift and drag characteristics of two NACA 654-421 airfoi-lswith a standard roughness applied to the leading edge~.

r

2.0 .050

i~v

x66,3618, a =1.01:8 r Smooth.. I /

l?oL@, . . . . /$, >& s

G ‘. ;? / I /

i‘. x?’./

“;/2 f /

I~ /

/f x

ic cc .$

‘8~“ /

~.a?o“, +-‘,,653-6M a = 0.5 w /

j/?oq?h x

/

+\

_ & /

.4 .010- x

%x-

- x-x a

x x- — /

0A/rfods:85,3-6B and

653- 6/8- R: 6xIOE

*’ ChordZWin.Tes+:1950nd 407

-.4-8 0 8 16 24 -.4 0 .4 .8 1.2 1.6

S~tim angle of otfock$ a& deg Sec+iOn lift coeff!ciknt. c1

Figure 11.- Lift and dra~ characteristics of an NACA 65,3-618, a = 1.0 and an NACA653-6U3, a = 0.5 airfOil with a standard roughness applied to the leading edge.

-8

~-7

*

$’-6

[

:-50qm+8 654-42/,u =0.5-;g — 652-4/5, a =0.51~ t I 1 [ I

$-3653 -4/8, u=, O.5:: “653-6/6 u =0.5

,‘. ~------~65)3-418,‘u=0.8

8 654-421,u=1.O-—‘;>’.~65~-415,u= 1.0b

>..-?-~ ?,,“;’653-418,U=i.0-—>

:‘~,:6%3-418,u= l.O__

, , “63,4-420,u=1.0i 6~4-420,u =0.3-

‘...‘--6G2-216ju= 1.0..66,2-2/6,u= 0.6-

0 -1 -2 -3 -4 -5 -6 -7 o7heoreiiml seqtion angle of zem /ift for 7%e

owfoil meon line, deg

I I, I r 1

I /1 I IW+t+--t+--l=””’’’‘ ‘/

654- +21, u = O./j., “.

65,3- 4/8,u -0.8--.:;

r-

./ .2 .3 .4 .5 .6, .7 .87heorefico/ section design W coefficid tbr +he

uirfoi/ meon line, Cli

Figure 12. - Comparison of theoretical Figure 13. - Comparison of theoretical ~and measured section and measured section design ~

angles of zero lift for some NACA lift coefficients for some NACAlow-drag airfoils. low-drag airfoils.

+N“+w

.6

~ -.18.$ #4 --- ---- ---- --= ---- -— ---------- --- ---0 “\-+s.

‘t&/6 Cl!

,0.b Curve{ <c Source

UL.2 —— — Meosun?d – “ “Ex@erimnfol test dm% —

L -./4$$ II ‘ Meun I/he Mean hne from fhi~1 1

J

airfoi/ +heory I 1

0 - --- -!--- i-Pressure Jnfegrdd fheorei&ol_& dkfrlbuiio~ pressure didrihuhon

.+. -. /2 -. /2 ~ S= (v/V *Au/V);1

v Theodorsen cu/cuA7fion8%

-. /0 653-618, 0 = 0.5---? <+-------------------------------------------m..$ -.10“

*,65,3-418, u= /.0 -) =/. o.2Q 654-42/, u’=0.’5--7 ‘---w /

& -.W —653 -4/8,o =0.5,:2

$Q-.06$ 634-4Za 0= 0.3

/“

c b%u -.04 ‘~ X 654 -&/, O= /.0

8$-.02

A 653-41.8$ u= 0.5

0 -.02 -.04 -.06 708 7/0 -./2 714Theoretic/ momen+ coefficied for +he uirfoi/ Airfoil fhickness, t/c

mean line obou+ quorfer- chord poin+

Figure 14. - Comparison of theoretical Figure 15. - Variation of moment coeffi -and measured moment cient cmc/4 and section lift

coefficients for some NACAlow-drag coefficient CL with airfoil thicknessairfoils. for some NACAlow-drag airfoils.

9

6$●

K.t--0

I

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