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REPORT No. 586
AIRFOIL SECTION CHARACTERISTICS AS AFFECTED BY VARIATIONS OF THE
REYNOLDS NUMBER
By EAWIWAN. J ACOBSnd ALBE RTHFIR~ AN
SUMMARY
A n i nved igat i on oj a 8y8t& t i y ch o8en r epr e8en ta--
t ive gr ou p of r el u ted a i zj oi h w as m a th i n t he N . A . C. A .
cu r iabl .e-d .en .d yw in d t un nel over a w i de r an ge oj t he
Reynol ds N um ber & end i ng d i nto t l w y l ight r ange.
Thete8Lswerem udetoprov ideinformat ionj rom which the
variu t ion.soj aiq%i. 8ect ion char aeteri dicswith c?umgtxin
t he Reyno.MsNumber cou l d be i n j er r ed and met lwdaoj
cd l aw i n gj or t h ae ca r ia ti or w i n p r act i ce cou l d be oM er -
mined.
Th ixwork i x oneph iweojan ex tmve andgen.end
ai joi l inv ix t igat ion being conduciedin thevur ia l ie-den.sdy
t un n el a nd ezL 9 ui s t h e p r evi ou s
l y p ubl i d wd T e ea r ch @
conwrn ing a i r joi l charactenk t i csas a$ecied by var iu i i om
in ai r jOi J pr oj i h oktenni ned ai a t i ngl e val ue of the
ReynoldsNumber:
T h e obj ect oj t hi s r ep or t h t o p r ov id e m ea w j or m ak i ng
a va i la bl e a s seci i m ch ar a cf ei %t i a a t a ny j r ee-a i r va l ue
oj theReynolds Num ber thevar iablederwi iy -tunnel a i r jo i l
d at a p r evi ou sl y Pu bl t ibd . A ccor d i ngl y, t he v a r i ow cor -
rect ion-sinvolved in a%ivin g more accur ateai r j oi? seet ion
character i st i .a than those hereiojore employed are j in t
conszderedat length and the corr ect ion jar turbulenceare
eqx?m %wd. An append i x ?k hel uded that w i 3r s the
r esu lt s oj an i nved gat i on oj cer tai n com i st en i er r or s
p re9en t i n t est r esu ti 8 j r om t he var i abh i hw i ty t un nel .
The or i gi n and na tu reoj sca l e e$ect 8 a re d iwu88ed and
the air joi .1wxzle-e~ectdaia are anu.?yzed. Fin uL ly,m etho-
ds areg iven oj dew ing jor 8cu .feef feet8on a i r joi . 1sect ion
churacten8 t i i xn pract i ce w i ih in ord inury l im i ?s oj a .ccw
raq j or t )w app l i ca ti on oj var i ub l e+ i ew i -t y-t unnel a i ~ml
da ta to j l i gh t p rob lenw.
INTRODUCTION
When cln tn fr om n m odel t est n re a pplied t o a fr igh t
pr oblem , t he con &ion t ha t sh ould be m tisiied is t ha t
t he flow s for t he t wo ca ses be simila r. The Reynolds
N um ber , w h ich in dica t es t h e r a t io of t h e m a s s f or ces t o
t h e v is cou s f or ces i n a e r od y na m i c a p pl ica t i on s , i s or d i-
n a r ily u sed a s t h e cr it er ion of
similarity.
The pract ical
n ecess it y for h a vin g t he flow n bou t t he m od el a er od y-
n a m ica l ly s im il nr t o t h e f low a b ou t t h e f ul l-s ca l e ob jeet
in flight becom es a ppa rent from t he fa d t ha t. a ero-
d yn a m ic coeff ici en t s, a s a r ule, va q v w i th ch a ng es i n t h e
R ey n olds Nu m be r .
(scale effect.
Th is ph en om en on i s r efer r ed t o a s
E ar ly invest iga t ions of sca le effect w er e ma de in
s m a ll a t m os ph er ic t u nn el s a t com pa r a t i vel y l ow v a lu es
of t he Reynolds Num ber a nd, for a ir fok, cover ed a
ra nge of t he Reynolds Number t oo lim it ed a nd t oo
r em ot e from t he full-sca le ra nge t o per mit r elia ble
ext ra pola t ions t o flight condit ions. At tem pt s w ere
m a de t o bridge t he ga p bet w een t he t w o Reynolds
Num ber ra nges by m aking full-sca le flight t est s for
com pa r kon w it h m od el t es ts . Th es e in ves tig a tion s of
sca le effect , how ever, proved disa ppoht ing ow ing
pa rt ly t o t he difficult y of obt aining good I light t est s
a nd t o t be d Mcult y of r epr oducin g flight con dit ion s
in t he m odel t est s a nd pa rt ly t o t he la rge unexplored
R ey nold s N um ber r a nge bet w een t he m od el a n d flig ht
t est s w it h conseq uent uncert a int ies rega rding t he
cont inuit y of t he cha ra ct er ist ics over t his ra nge.
I?urt hennore, t he flight t est s could not ordina rily
include a sufficient ly la rge ra nge of t he Reynolds
N um ber t o es ta blish t he ch a ra ct er of t he s cn le effect s
for cer ta in of t he a ir foil ch a ra ct er is tics over t he fu ll-
s ca l e r a n ge of t h e R ey nold s N um ber , w h ich m a y ext en d
fr om va lues a s low a s a few h un dr ed t housa nd t o t hir ty
m i ll ion or m or e .
Th ese lim it a tion s of t he ea rly in vest iga t ions w er e
@t over com e by t he N. A. C . A. t hrough t he use of
t he va ria bledensit y t unnel, w hich w a s designed t o
fa cilit a t e a er od yn a mic in vest ig a tion s over t he en tir e
r an ge of R ey nolds N um bem bet w een t he w ind t unn el
a nd fligh t VOh.18S .
S ever a l m is cella n eou s a n d com -
m on ly us ed a ir foils w er e in vest ig a ted for s ca le effect
in t he va ria ble-d en sit y t un nel dur ing t he t it y ea rs of
it s oper at ion . Th e r esult s in dicn ted t ha t im por ta nt
m a le effect s for som e a ir foils m ay be expect ed a bove
t h e u su a l w i nd -t un nel r a ng e a n d ev en w i th in t h e f lig ht
ra nge of va lues of t he Reynolds Num ber. La t er ,
w h en t h e N . A. C . A. f ull-s ca l e t un nel w a s con st r uct ed ,
a i rfoi l t es t s t h er ein s er ved t o con ii.r m t h e im por t rm ce
of s ca l e ef fect s occu r ri ng i n t h e f ul l-s ca l e r a n ge a n d a l so
provided va lua ble da ta for t he int erpr et a t ion of t he
va r ia bled en sit y-t un nel r esu lt s, pa r ticu la r ly in con -
n ect ion w i th t h e eff ect s of t h e t ur bu len ce pr es en t in t h e
227
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2%
REP ORT NO. 586-NATIONAL ADVD30RYCOMMITTEE FOR AERONAUTICS
v a ria bled en sit y t u nn el.
The int erpret at ion of t he
v a r ia b led en si t y-t u n nel r es ul t s h a s con seq u en t ly b een
m od ified t o a llow for t he t ur bu len ce on t he ba sis of a n
effect ive Reynolds Number bgher t ha n t he t est
Reynolds Number .
In t he mea nt ime, t he invest iga t ions of a irfoiI s in
t h e va ria bledensit y t unnel ha d been t urned t o a n
ext en sive st udy of a irfoil ch ar act er ist ic a s r dlect ed
by a ir foil sh a pe.
This pha se, w hich result ed in t he
development of t he w ell-know n N. A. 0 A. a ir foils,
involved t he t est ing of a la rge number of rela ted
a ir foils, but t hese t est s w ere la rgely cordin ed t o one
va lue of t he Reyn olds Num ber w it hin t he full-sca le
r an ge. S uch a pr oced ur e exped it ed t he in vest ig at ion
r md pr ovided com pa r able d at a for t he va r iou s a ir foils
w it hin t he full-sca le ra nge of t he Reyn olds Number
bu t , of cou rs e, ga ve n o in for ma t ion a bou t s ca le effect s.
& pr ev iou sly s ta t ed , t h e fu ll+ xd e-t u mel r es ult s h a d
pr ov id ed in for ma t ion r eg a rd in g t h e a pplica t ion of t h e
va ria bldmsit y-t un nel da ta t o flight . Met hods w ere
a ccordin gly developed for corr ec~ t he da t a a nd for
pr esen tin g t hem in for ms t ha t w ould fa cilit a te t heir
use m a pplied t o ~ Wht problems. F ligh t problems,
how ever, req uire a ir foil da ta a t V~ OU S V~ U ~ of t he
Reynolds Number bet w een va lues a s low a s a few
h un dred t housa nd in som e ca ses t o t hir ty million or
m or e in ot he~ .
Obv iou sly t h e r es ult s m a ila b le fr om
t h e t es t s o f r ela t ed a ir foils a t on e v a lu e of t h e R ey nold s
N um ber (ef fect iv e R ey n ol ds N um ber = 8, 000, 000) a r e
i na d eq u a t e f or t h e pu r pos e u n les s t h ey ca n b e cor r ect ed
t o ot her va lu es of t he Rey nold s Nu mber . Th e pr esen t
in vest iga t ion w a s t her efor e u nd er ta ken . t o st ud y t he
s ca l e effect s for t h e r ela t ed a i rfoil s ect ion s pr im a rily
w it h a view t o t he for mula t ion of gen era l met hods for
determining
sca b-effect corr ect ion s for a ny n or ma l
a ir foil sect ion so t ha t t he st anda rd t est rew lt s from
t he vn ria bled en sit y t un nel cou ld be a pplied t o fligh t
a t a ny Reynolds Number. I?or most pmct ic~ U S@it
i s con si der ed d es ir a b le a n d s uf fi ci en t t o pr es en t a i rf oil
t es t r es ult s in t h e for m of t a bu la r v a lu es g iv in g cer t a in
im por t a nt a er od yn a mic ch a r a ct er is tics for ea ch a ~ a i l
8ectwn.
The prima ry object of t his invest iga tion,
t h er efor e, is t o g iv e in for ma t ion a bou t t h e v a ria t ion of
t hese im por ta n t a ir foil sect ion ch a ra ct er ist ics w it h
Reynolds Number .
I n r eg a rd t o t h e s cope of t h e exper im en t a l in veAg a -
t ion, t he Reyn olds Number ra nge w as chosen a s t he
la r ges t pos sib le in t h e v mia ble-d en sit y t u nn el a n d t h e
a ir foil s ect ion s w er e ch osen t o cover a s fa r a s possible
t he ra nge of sha pes commonly employed. Accord-
in gly, gr ou ps of r ela t ed a ir foils (@g. 1) w er e t est ed t o
invest iga te t he follow i.qg va ria bles rela ted t o t he
airfoil-section shape:
Thickness.
Camber.
.
Thickness and camber .
Thicknem shape.
C a m b er s h a pe.
Sect ions with high-l if t devices.
The t est ing progra m w as begun in Ma y 1934 a nd
ext ended severa l t imes a s it beca me a ppa rent t ha t
a ddit iona l t est s w ould be des~ ble, The @a l t est s
in t h e v a ria b l+ d en sit y t un nel w er e m a de in S ept em ber
1935.
TESTS AND MODELS
D escr ipt ions of t he va ria bl~ deusit y w ind t unnel
a n d of t he m et hod s of t est in g a r e g iven in r efer en ce 1.
Th e t ea t s h erein r epor ted w er e ma de for t he m ost
pa r t for ea ch a ir foil a t t a nk pr essu res of 1/4, 1/2, 1, 2,
4, 8,
15,
a nd 20 a t m os ph er es , cov er in g a r a ng e of t es t
Reyn olds Number s from 40,000 t o 3,100,000. Th e
1/4- a n d l/2-a t m os ph er e r un s w er e om it t ed for m a ny
of t h e a ir foils a n d, in s ev er a l ca s es , on ly t h e lift -cu rv e
pea ks w er e obt a in ed a t t he low er R ey nolds Nu mber s.
R un s a t r ed uced s peed s (1/5 a n d 1/2 t h e s t a n da r d v a lu e
of t he dyna mic pressure q) a t 20 a tmosph eres w ere
som et im es su bst it ut ed for t he t es ts a t 8 a nd 15 a t mos-
ph er es. S evera l ch eck t est s a t 8 a nd 16 a t mosph er es
a n d r es u lt s f r om s om e ea r l ie r i nv es t ig a t i on s h a v e s h ow n
t ha t t he specific ma nner of va rying t he Reynolds
N um ber w i t h r es pect t o s peed or d en si t y i s u n im por t a n t
w h en t h e ef fect s of com pr es si bi li t y a r e n eg li gi bl e. l ?or
a l l t h e a ir foils , t h e a ir in t h e t u nn el w a s d ecom pr es sed
a nd t he
air fo i l
repolished before
Reyn olds Num ber t est s.
r un nin g t he h igh er
Ta res obt ained ~ t corre-
spon din g R ey nold s N um ber s w er e u sed in w or kin g u p
t h e r es u lt s .
Th e a i r foi l m od el s a r e of m et a l , u su a lly of d ur a lu min
a nd of st a nda rd 5- by 30-in ch pla n for m; t he sect ion s
employed (see @. 1), except for t he slot ted C la rk Y,
m e m em ber s of N . A. C . A. a i rf oil f a milies (r efer en ces
2 a n d.3). Th e slot t ed C la r k Y m od el is of 36-in ch spa n
a nd 6-inch ch or d (w it h t he slot closed) a nd w a s ma de
t o t he or din a tes given in r efer en ce 4. F or t his a ir foil,
t h e coef ficien t s a r e g iven a s b a sed on t h e c hor d a n d a r ea
corr espon din g t o t he sloixlosed con dit ion . Th e sla t
w as ma de of st a inless st eel a nd fa st ened t o t he ma in
w in g in t h e pos it ion r epor t ed (r efer cu ce 4) t o r es ult in
t he h igh est va lue of ma ximum lift coei%cien t. Th is
m od el w a s t es t ed a t a m uch ea r lier d a t e t h a n t h e ot h er s,
a nd t he t est da ta a re somew h a t less a ccura te, The
m a in w in g of t h e N . A. C . A. 23012 a i rfoil w it h ext er na l-
a ir foil fla p is of 30-in ch spa n a nd 4.167-in ch ch or d.
The fla p is of st a inless st eel a nd is a lso of N. A. C . A.
23012 s ect ion h a vin g a ch or d of 20 per cen t t ha t of t he
ma in a irfoil. I t w as fa st ened t o t he ma in w ing m t he
opt &m m h in ge pos it ion r epor t ed in r efer en ce 6. D a t ~
for t his a irfoil combin at ion a re given h er ein for t w o
a n g ula r f la p s et t i ng s:
3 , w hich corresponds t o t he
m in im um dr a g con dit ion ; a n d 30 , w h ich cor res pon ds
t o t he m axim um -lift con dit ion . Th e coefficien ts a r e
given a s ba sed on t he sums of t he ma in w ing a nd fla p
ch or ds a n d a r ea s .
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AIRFOIL SE CTION CHARACTERIS TICSAS AFFE CTED BY
7hickness
N.A.CM.
0012
00/ 5
0018
Cbmber
~
242c====
VAR I ATI ON S O F TH E R E YN OL D S N U M B E R 229
Canb er shape
N A . C .A .
CU12
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c====
230/2
iRa
12
4412
430/2
64/.2
67/2
Hi gh-l i f f de vic es
83/8
T hi ck ne ss s ha pe
00/2
23012
23015
43012
cJu ld
23012
6
=?$
.
< 75*
75
=$
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Clark Y
{~y
Wi t h Hond/ey-Puge slof
FIGURE LAlrfiil sectfors emplopwi for the @e-eff@t lnvedgatIorL.
The SEUIIXB. exmpt for the dotted Clerk Y. are mwnbra of N. A. O. A. alrfoll fmnilleb.
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230 REP ORTNO. 586-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
ACCURACY
Th e a ccu r a cy of t h e e xp er im en t a l d a t a of t h is i nv es t i-
ga t ion a t t he h ig hest R ey nold s N um ber is com pa r a ble
w it h t ha t of t he st mda d a ir foil t est da ta a s discuss.ed
in r ef er en ce 2. Th e s ys t em a t ic er r or s of m ea s ur em en t
t h er ein m en t ion ed , h ow ever , h a ve s in ce been in ves ti -
g a ted a n d t he r es ult s a r e pr esen ted in t ho a ppen dix t o
t h is r epor t . Th e s ys t em a t ic er r or s o f velocit y m ea s ur e-
m en t h a ve h en ce b een el im in a t ed , t h e er r or s a s s oci a t ed
w it h s uppor t d eflcd ion h a ve b een la r gely r em ov ed , a n d
t h e er r or s a s socia t ed w i th m od el r ou gh nes s h a ve been
minim ized by giving ca reful a t t ent ion t o t he model
surfaces
Th e r em ain in g sy st em a tic er ror s a re m a in ly t hose
a s socia t ed w it h t he in ter pr et a t ion of t he w in d-t un nel
r es ult s r a th er t ha n t he d ir ect er ror s of m ea s ur em en t.
Th es e er r or s a r e a s socia t ed , f ir st , w i th t h e ca l cu la t ion
of a i r foi l
seciion
ch a r a ct er is t ics f rom t h e t es t s of i in it e-
r mpecb ra t io a ir foils a n d, secon d, w it h t he cor rect ion
of t h e t es t r es ul ts t o z er o t ur bu len ce or f ree-a i r con di-
t ions. S uch err or s w ill be more fully t rea ted in t he
d is cu ss ion w h er e t h e m et h od s of cor r ect i on , i ncl ud in g
t h e in t er pr et a t ion of t h e r es ult s a s in volvin g t h e eff ec-
t i ve R ey n ol ds N um ber , a r e con s id er ed .
Th e m agnit ud e of t he d ir ect exper im en ta l er ror s,
pa r ticu la r ly of t he a ccid en ta l er ror s, in cr ea s es a s t he
Reynolds Num ber is reduced. by va ria tion of t he
suppor t in ter fer en ce w it h t he R ey nolds Num ber w a s
n ot t a ken in to a ccoun t in spit e of t he fa ct t ha t t he t est
r esu lt s t en d t o in dica t e t ha t t he u ncor rect ed pa r t (see
a ppen dix) of t he su ppor t in ter fer en ce m a y cea s e t o be
n eg lig ib le a t low t es t R ey nold s N um bem . Th es e er r or s
ma y be judged by a st udy of t he dissym met r y of t he
t es t r es ult s for posit ive a n d n eg at ive a n gles of a t t a ck
f or t h e s ym m et r ica l a i rf oil s a n d by t h e s ca t t er in g of t h e
poin ts r epr es en tin g t he exper im en ta l d a ta . (S ee figs .
2 t o 24.) S uch a st udy indica tea t ha t t he r esult s b m
t est s a t t a nk pr essures a t a nd a bove 4 a tm ospheres
(ef fect iv e R ey nold s N um bem a b ove 1,700,000) a r e of
t he sa m e or der of a ccur acy a s t hose fr om t he h ighest
R ey nolds Num ber t est s.
The dra g a nd pit ching-
m om en t r es ul t s f or ef fect iv e R ey n ol ds N um b er s b el ow
800,000, h ow e ver , b ecom e r el a t iv el y i na ccu r a t e ow i ng
t o li mit a t ion s i mpos ed b y t h e s en si tiv it y of t h e m ea s ur -
ing e q uipm en t .
In fa ct , it a ppea rs t ha t t he a ccura cy
b ecom es i ns uf fi ci en t t o d ef in e w i t h cer t a i nt y t h e s h a pes
of cu rves r epr esen tin g va r ia t ion s of t hes e q ua n tit ies
w it h a ngle of a t t ack or lift coet licient . H ence a ir foil
ch a r a ct er is ti cs d epen den t on t h e s ha pe of s uch cu rv es ,
e. g ., t h e op ti m um l if t coe ff ici en t a n d t h e a e rod y na m i c-
ccn t er pos it ion , a r e con sid er ed u nr el ia b le a n d in m os t
ca ses a re n ot pr esen ted below a n effect ive R ey nolds
Nu m be r of 800, 000.
RESULTS
F ig ur es 2 t o 24 p re sen t t h e t e st r es ul t s c or r ect ed a f t er
t he m et hods given in r efer ence 1 for a ppr oxim a tin g
i .n ii ni t e-a s pect -r a t i o ch a r a ct m is t ics . C u rv es a r e g iv en
(f or ea ch a i r foi l f or d ii ler en t t es t R ey n ol ds N u mb er s ) of
lift coefficien t C L a g a in st effect ive a n gle of a t t a ck a oj
a n d of pr ofile-d ra g C od icien t 6 Do ~d of P i~ ~ %
moment coefficient a bout t he a erodyna mic cent er
c
.=-C.gainstift
coefficient CL. The x a nd y coordi-
n a t es of t h e a e rod y na m i c cen t er f rom t h e a i r foi l q u a r t er -
chord point a re a lso given w here t he da ta per m it .
Al th ou gh n ot pr eci se ly g ect i on ch ur u ci di cs , ch a r a ct er -
i st i cs s o cor r ect ed h a ve b een u sed h er et of or e a s s ect i on
ch a ra ct er ist ics beca use of t he la ck of a nyt hin g m or e
exact.
F u rt h er cor r ect i on s, h ow e ver , t o a l low f or t h e ef fect s
of w i nd -t u nn el t u rb ul en ce, a i r foi l-t i p s h a pe, a n d s om e
of t h e li mit a t ion s of t h e pr ev iou s cor r ect ion s b a sed on
a i rfoil t h eor y w er e d ev eloped d ur in g t h e cou rs e of t h is
in vest iga t ion a nd, w hen a pplied, give r esu lt s r epr e-
sen tin g t he m ost r elia ble sect ion da t a n ow m -a ilfible
from t he va ria bledensi~ w ind t unnel. These a ddi-
t ion al cor rect ion s a nd t heir der iva t ion a re fully d is-
cussed la ter in t his report . The more e--a ct
gec t im
ch a r a ct er is t ics h a ve b een d is t in g ui sh ed b y l ow e r-ca s e
s ym bols , e. g ., s ect ion l if t cot icien t cl, s ect ion pr ofle-
d ra g coefficien t c%
s ect ion opt im um l if t coeff icien t
czo, ,, a n d s ect ion p it ch ing -m om en t coe ff icien t a bou t t h e
a er od yn a m ic cen t er % .C ..
Th es e v a lu es a r e t h en con -
sid er ed a pplica ble t o flig ht a t t he effect ive R ey nold s
Number, R..
Ta b le I pr es en t s, for v a riou s R ey nold s N um bem j t h e
pr in cipa l a er od yn a mic ch a ra ct er ist ics , in t he for m of
t h es e f ul ly cor r ect ed s ect i on ch a r a ct er is t ics , of t h e &-
foils t est ed. C ross plot s of cer t a in of t hese sect ion
ch a r a ct er is t ics a g a i ns t R ey n ol ds N um b er a r e a l s o g iv en
for We w it h t he discussion. (S ee fig. 28 a nd @s. 32
t o 43 .)
D I SC U SSI O N
S ca l e ef fect s, or t h e v a ria t ion s of a er od yn a m ic coef -
f icien t s w i th R ey nold s N um ber , h a ve pr ev iou sly b een
con sid er ed of pr im a ry im por ta n ce on ly in r ela t ion t o
t h e in t er pr et a t ion of low -s t ile t es t r es ult s f r om r Lt m os
ph er ic w in d t un nels . I t now a ppea rs from va ria ble-
densit y a nd full-sca le-t unnel da ta t hnt im port ant
v a r ia t i on s of t h e coef fi ci en t s m u st b e r ecog n iz ed w i t hi n
t he flight ra nge of va lues of t he Reynolds Number ,
pa r ticula rly in view of t he fa ct t ha t t he fligh t r ange is
cont inual ly being increased.
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AIRFOIL SEC TION CHARACTERISTIC-SAS AFFECTED BY VARIATIONSOF THE REYNOLDS NUMB ER 231
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FIGURE 2N. A. O. A. tWE3.
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. IJ
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s)
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gree
FIGUEE 6.N. A. O. A. 24Lz
-.4 -.2 0 .2 .4 .6
.8 1.0 L2 1.4 /.6 1.8
H-H+H+.o
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L i f f c oe f ic ien~ C.
FIGUEB 7.-N. A. O. A. 4-W?.
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.
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.,. ...
234
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o
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.t i rf oi l: N .A .CA . 6 412
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235
ITT
Upc LwF.
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236
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AI R F OI L S E C TI O N C H A R AC TE R I S TI C SAS AF F E C TE D B Y VAR I ATI O NS O F TH E R E Y NO L D S N U M B E R
237
I
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0
A ir fo il : M A. C.A . 2 Rz 1 2
..5 28 : 5 x3 0
I
V ei (f 7/s ec ):6 8 ..2
? re s.(s fh a. a fm .) : I f o~
Tesf : K D. Z /239
O of e :3 -3 5
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I
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8 12 16 20 24 28 32
~gle of of f oc k fo r in finife aspecf rafio, h (degrees)
L i f f C08f t iCi~( G
FIQURE 14.-N. L O. A. 21M2
4
2
0
8
6
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4~ -
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z%
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&
8
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. .. .. .1. J.. .
APPENDIX
INVESTIG A~ ONOF CE RTAINCONSIS TENTERRORS P RES ENTIN TES TRE SU LTSFROM THE
VARIABLE-DENSITYUNNEL
B y I RAH . AB B C P P
JNTEODUGTION
An in vest iga t ion ha s been m ade t o eva lua t e t hr ee
cor r ect ion s t h a t w er e n ot a pplied t o t he d a t a , ob ~ ed
in t he va r ia bled en sit y w in d t un nel, a nd pu blis hed in
r efer en ce 2 a n d ea r lier r epor t s. Th e n eed for t h es e c or -
r ect i on s h a d b een r ecog ni zed , a n d p os si bl e er r om i n t h e
d at a r esu lt in g fr om t he la ck of t hese cor rect ion s h ave
b een l is t ed a s con si st en t er r or s (r ef er en ce 2) d ue t o t h e
following effects:
1. Aer od yn a mic in ter fer a uce of t h e m od el s uppor t s
on t h e m od el.
2. E f fect of t h e com pr es sed a i r on t h e ef fect iv e w e ig ht
of ma nomet er liq uids used t o mea sure t he dyna mic
pressure. .
3. C om bin ed ef fect s on t he m ea s ur ed d yn a mic pr es -
s ur e o f b lock in g d ue t o t he m od el a n d t o er ror s in pit ot -
t ube ca l ib ra t ion a r is in g fiw m d ilTer en ces i n d yn a mic
sca le a nd t ur bu len ce bet w een con dit ion s of u se in t he
va r ia b led en sit y t un nel a n d con di tion s of ca l ib ra t ion .
Th ese effect s r es ult in er ror s in t he ca libr a tion of t he
s t a t ic-pr es su r e or if ices u sed t o d et er m in e t h e d y na m i c
preswre.
INTllEP13EENCERMODELUPPOliTs
Th e m od el s uppor t s u sed in t h e v a r kbled en sit y t un -
nel a nd t he m et hod of det er minin g t he t a re for ces a re
descr ibed in r efer en ce 1. Th e usua l t a re t ea t s det er -
m in e t h e t a r e f or ces on t h e s uppor t s i ncl ud in g t h e i nt er -
ference of t he model on t he support s. In a ddit ion,
t h e u su a l m et h od of d et er m in in g
t h e ba la n ce a l ine me nt
w it h r espect t o t he a ir -flow d ir ect ion by t est in g a n a ir -
f oil er ect a n d in ver t ed in clu des a n y in t er fer en ce of t he
suppor ts on t he m odel t ha t is eq uiva lent t o a ch ~ ~ e in
a i r-flow d ir ect ion . E a r lier a t t em pt s t o d et er min e a n y
a d d i t ion a l in t er f er en ce of t h e s u pp or t s on t h e m o d el w e r e
i ncon cl us iv e except t o s how t h a t s uch i nt er fer en ce w a s
small.
Tw o a i r foi ls of m od er a t e t h ick nes s w e re ch os en t o b e
u sed i n t h e p res en t i nv es t ig a t ion , on e b ei ng a s ym m et r i-
ca l a ir foil (N . A. C . A. 0012) a nd t he ot her a m a ir foil of
modera te ca mber ~ . A. C . A. 4412). Teds w ere ma de
of ea ch a ir foil u sin g t hr ee m et hod s of s uppor tin g t he
m odel. B esides t he m et hod usin g t he usua l suppor t
s tr ut s, t es t s w e re m a de w i th t h e m od els m ou nt ed on t he
usua l suppor ts w it h t he a ddit ion of specia l w ir e snp-
port s a nd w it h t he m odels mount ed only on t he w ire
s uppor ts . Th e w ir e su ppor ts ecm sis ted of t hr ee w ir es
a tt a ched t o t he q ua rt a r+ h ord point of t he model a t
260
ea ch w ing t ip a nd of a st in g a nd a ngle-of-a t ta ck st rut
s o l oca t ed a s t o be fr ee fr om a er od yn mn ic in t er fer en ce
w it h t he usua l suppor t s. The st ing used w as sym-
m et r ica l w i t h r es pect t o t h e a i r foi l a n d w a s a t t a ch ed n ea r
t he t miling edge inst ea d of t o t he low er surfa ce, a s
i s u su a l.
Th e t a ms d ue t o t he w ir e su ppor ts w er e d et er min ed
fr om t he da t a obt ain ed fr om t he t est s w it h t he m od els
on t he usua l support s w it h a nd w it hout t ha w ire
s u pp or t s . Som e d if ii cu l~ v m .se xp er ie nced in obt a ining
sufficien tly a ccur at e t a res beca use of t he r ela t ively
la rge dng of t he w ires a s compa red w it h t he dra g of
t he model. S ticient a ccura cy w a s obt aina ble only a t
t he h ig hes t va l ue of t h e t es t R ey nold s N um ber or din a r-
i ly obt a ine d (a bou t 3, 000, 000). Th e p rof ile-d r a g coef fi -
cien ts obt a in ed for t he t w o a ir foils a r e plot ted a s s olid
lin es in fig ur es 46 a n d 47, t og et h er w i th d a t a ob toin ed
t im severa l t est s ma de w it h t he usua l support s over
a considera ble period of t ime. The sca tt er ing of t ho
poin t s ob ta i ned f rom t h e t a s ta w it h t he u su a l s uppor t s
a b ou t t h e s olid lin e i s w it h in t h e l i mi ts of t he a m id en t a l
er ror s list ed in r efer ence 2, show ing t ha t t her e is no
s uppor t i nt er fer en ce w i t hi n t h e a ccu ra oy of t h e r es ul t s
r utl@h va lu es of t h e R ey nold s N um ber .
I t is evident t ha t t he da t a obt a in ed ca n be a na lyzed
in difler en t w a ys.
F or exa mple, t he da ta obt ained
w it h t he m odels m oun ted on bot h t he usua l suppor ts
a n d t h e w i re s uppor t s ca n b e cor r ect ed f or t h e u s ua l s up-
por t t a res a nd com pa red w it h t he da t a fr om t est s w it h
t he models mount ed only on t he w ire suppor ts, The
com pa r i son w a s m a d e cor r ect i ng t h e d a t a f or t h e ch a n ge
i n a i r-f low d ir ect i on d ue t o t h e u su a l s upp or t s a n d f a il ed
t o show a ny support int erference w it hin t he t est
accuracy.
An alysis of t he da t a t o det er mine t he effect s of t he
support interference on the measured pitching-moment
coef%cient a w a s m or e dii%cult . The suppor t w ir es
s tr et ch ed u nd er t he lift a n d d ra g loa ds , n ecessit a tin g
a cor rect ion t o t he m ea s ur ed pit ch in g-m om en t coeffi-
cient s, m d t he m et hod of suppor tin g t he m od el a t t he
w in g t ips r dlow ed t he m od el it self t o d eflect un der t he
lift loa ds m uch m or e t ha n w hen m oun ted on t he usua l
s uppor ts . Th e cor rect ion d ue t o t he d eflect ion of t he
m od el i s d ii licu lt t o eva l ua t e w it h cer t a in t y b eca u se i t
in volve s in t eg r a t ion s a lon g t h e s pa n a f t er d et e rm ina t ion
D f t he spa n loa d d ish ibu tion . Accor din gly , t he effect
of t he su ppor t in ter fer en ce for t he pit din g m om en ts
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AI R F OI L SE C TI O NC H A RAC TE R I STI C SAS AF F E C TE D B Y VAR I ATI O NSO F TH E R E Y NO L D SNU M B E R 261
w as det er mined only a t zero lilt w here it w as foond
t h a t t h e m ea s u red pi tch in g -m om en t coef fi ci en t w a s t oo
la r ge (a lg ebr a ica lly ) by 0.002. Th is s a me cor rect ion
h a d b een f ou nd pr ev iou sl y f rom t es t s w i t h s y mm et r ica l
An gles V.D.T.
Do+e
Condi t ion
PosNeg Test
TestR,
millions
; 1~~-6 IO-26-33 Wire supporf
3.07
0
/2-30-3I USUO1 = struis 3.24
+ x 1120 4-17-34 . $ 3.20
?06
V 1233 2- 6-35 * * :
3.17
::05
c
w
:;04
k
al
Q
Q.03
g)
+ D2
.s?
?
,4ngIe of of fac k, a, degrees
I UBE49.Calfbmtfon
of pitot M mmmti on the FC-2W2 afrplann fn ilfght and on the FC-2W2 ah-plane mcdel fn the varfabkhnsftg wind tunnel. RW JMS
mrmclexf fo r tnnne l-w fdl e ff ec t.
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AI R F OI L SE C TI O NC H AR AC TE R I STI C SAS AF F E C TE D B Y VAR I ATI O NSO F TH E R E Y NO L D SNU M B E R 263
wall
effect. Force teats made in t he t unnel a nd in
flight show t ha t t h is met hod of compa rison is very
n ea r ly eq uiva len t t o m a kin g t he com pa r is on s a t eq ua l
li ft coeff icien t s. A v a lu e of t h e r a t io g /q Ow a s s elect ed
fr om t he t un nel d~ t a t o cor respon d M w ell a s pot ible
t o flig ht con dit ion s of t rim a n d R ey nold s N um ber for
ea ch pit ot -t ube posit ion a t ea ch a ngle of a t ta ck. The
va lu es ob ta in ed w er e, in g en er a l, h ig her t ha n t h e flig ht
va luea a t sm a ll a nglea of a tt a ck. Accordingly , t he
va lu es obt a in ed w er e r ed uced by in cr ea s kg t he va lu e
of go b y 1.5 percent , w hich is eq uiva lent t o a cha nge
in t h e s ta t ic-pr es su re-or if ice ca l ib ra t ion fa ct or f rom
1.172 t o 1.190. The va luea of t he ra t io so obt ained
m e plot ted on t he figure a s solid lin es, a nd t he va lues
a gree rea sona bly w ell w it h t he t light da ta a t sma ll
1.6
..32
/4
.28
1.2
.24
--
g/e
of af fac k, d, degrees
k I OUEE
J .-Compu fsm of data obta in ed In CJght and in the variabledem$ity wind
tonml for tbe FC-2W2 akplane and model.
a ngles of a tt a ck. A compa rison of t he t unnel a nd
I light da t a in dica t es t ha t a fur ther cor rect ion, w hich
ma y be due t o blocking effect s, ma y be desira ble a t
h igh a n glea of a t ta ck.
Th e a i r pl a ne m od el , h ow e ver ,
ha d la rge dra gs a t high a ngles of a t t ack a s compa red
w it h m od els n or mr illy used in t he t un nel, m a kin g t he
a pplica t ion of t h is a d dit ion a l cor rect ion q ues tion a ble
f or t h e u su a l a i rfoil t es t s.
Th e r esu lt s of t he for ce t ea t s of t he m od el a r e sh ow n
by mea ns of composit e curv~ dra w n a s solid lines in
figure 50, The curves w ere obt a ined from t he t est
r es ult s by s elect in g, a t ea ch a n gle of a t t a ck, t es t r es uM s
t o cor res pon d a s w ell a s pos sib le w it h flig ht con di tion s
of t r im a nd Reynolds Number. The t unnel result s
h ove been fu lly cor rect ed in clu din g cor rect ion s t o t he
effect ive R eynolds Num ber . D a ta obt a ined in fligh t
t est s (r efer en ce 20) a r e sh ow n on t he figur e.
Alt hough t he model w as much more det a iled a nd
a ccur at e t ha n is usua l in w ind-t un nel m odels, it w a s
not considered before t he t eds t o represent t he a ir-
pla ne w it h suiiicient a ccura cy a nd det a il t o give
r elia ble dra g r esult s. Ther efor e t oo much em ph asis
hould not be given t o t he good a greement of dra g
coefficien ts obt a ined in fligh t a nd in t he t unn el. At
lift coefficien ts lea s t ha n 1.0 t he a gr eem en t bet w een
fligh t a nd t un nel da t a is con sider ed sa t isfa ct or y. At
higher lift cdlicien ts som e divergen ce of t he t unn el
md i3ight da ta is indica ted. As previously st at ed,
t he r esult s obt a ined fr om t he pit obt ube ca libr at ion
s how ed t h a t a n a d dit ion a l cor r ect ion t o t h e ca l ib ra t ion
f a ct or of t h e s t a t ic-pr es su r e or i.i ice m i gh t b e d es ir a b le
~ t high a ngles of a t ta ck.
S uch a cor rect ion h a s been
det ermined from figure 49 a nd a pplied t o t he da ta .
Th e r es ult s a r e plot t ed a s d ot t ed lin es in fig ur e 50 a n d
show a n im pr oved a gr eem en t of t he lift coefficien ts
obt ained in flight a nd in t he t unnel a t high a ngles of
wt tack.
Th is a d d it ion a l cor r ect i on i s n ot or d in a r il y a p pl ied t o
t he da ta obt ained in t he va ria bl-densit y t unnel be-
ca u se i t i s d ou bt fu l w h et h er t h e cor r ect ion i n m os t ca s es
w ou ld g ive a b et t er a ppr oxim a t ion t o t h e a ct ua l con di-
t ion s t ha n n o cor rect ion . Th e pit ot + t u be ca libr a tion
t es ts w er e les s a ccu ra t e a t h igh m gles of a t t a ck t ha n a t
low ones a nd, a a previously st a ted, t he dra g of t he
m od el m a la r ger t ha n is t he ca s e f or t he m od els u sua lly
t es ted . An ot her fa ct in dica t in g t ha t t his cor rect ion is
sm all is t ha t , up t o t he point of ma ximum lift , t he lift
cu rves obt a in ed in t h e t un nel for s om e a i rfoi ls a r e ver y
nea rly st ra ight . Any a pprecia ble correct ion of t his
t ype w ould resuh in such lift curves being conca ve
upward.
CONCLUSIONS
1. The r esult s of t he in vest iga t ion sh ow no in ter -
fer en ce of t he m od el su ppor ts on t he m od el for Wh ich
cor rect ion s h a d n ot pr eviou sly been m a de.
2. Th e in ves tig a tion of t h e effect s of com pr es sed a i r
on t h e ef fect iv e w ei gh t of t h e m a n om et er l iq u id s how ed a
2.0 per cen t er r or i n t h e m ea s ur ed d yn a m ic pr es su r e; t h e
d yn a m ic p res su re a s pr ev iou sl y m ea s ur ed w a s t oo l a rg e.
3. The invest iga t ion of t he ca libr at ion of t he st a tic
pr es su re or hices s how ed a n er ror of 1.5 per cen t in t h is
ca l ib ra t ion ; t he d yn a mic pr es su re a s pr ev iou sly m ea s -
ured w a s t oo sma ll.
4. Th e t ot a l effect of t he in vest iga t ion is a ch an ge in
t he mea sured dyna mic pressure of 0.5 percent ; t he
d yn a m ic pr w s ur e a s pr ev iou sl y m ea s u red w a s t oo l a r ge.
D at a previously published (reference 2 md ea rlier
report s) t o w hich t hese cor rect ions ha ve not been
a pplied ma y be cor rect ed by c.h-~ t he coefficient s
t o correspond t o a reduct ion of mea sured dyna mic
pr m w re of 0.5 per cen t .
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264
REP ORTNO. 586-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
R E F E R E NC E S
1. J a c obs,E a a t r n a nN., a n d Abbot t , I m H . : Th e N. A. C . A.
Va r ia b le -D e ns it yWiid Tu n nel T. R , No. 416, ~ . A.
C. A. 1932.
2. J a c ob%E a s t m a n N., Wa r d , K en n et h E . , a n d P in k er t on ,
R ober t M .: Th e ch a r a c t er i st i csof 78 R ela t ed AWoi2
Sectionsfrom Teatsin the Variable-DensityWind Tun-
n eL T. I L N o. 460, N. A. C . A., 1933.
3. J a cob ~
E a s t m a nN., a n d P in k er L w n ,ober t M .: Te st s in
the Varf.a ble-DensityWiid Tunnel of RelatedAfrfoi ls
Ha vingthe MaximumCa mberUnusua llyFa r Forwa rcL
T. FLNo. 537,N. A. C. A. , 1935.
4. Wen zi ng er ,C a r l J ., a n d S h or t a l, J os eph A. : Th e Aer o-
d y n a m ic C h a r a ct e r is t icsf a S lot t e d C la r k Y Wing a s
Af Re t ed by t h e Au xi li a r yAir foi lP os it ion . T. R . No.
400,N. A. C. A. , 1931.
5. P la t t j R ober t C . , a n d Abbof i I r a H . : Ae rod y n a m icC h a r -
aoteristh of N. A. C. A.
23012 and 23o21
Airfoi2e with
20-PercenM2hord t irnal-Airfoi lFla psof N. A. C. A.
23012Section. T. FLNo.573,N. A. C. A. , 1936.
6. hI i llWan,C la r kB . : On t h e L t i D is t ri bu t ionor a Wfn g of
Arbit raryPlan Formin a CircularWindTunneL Pub-
licat ionNo.22,C . I . T. , 1932.
7. J a cob s, E a a tm a nN ., a n d P i nk er t on ,R ob er t M .: T- of
N. A. C. A. Airfoi lsin the Variable-Det i tyWindTun-
n eL Se r ie s230. T. N. No. 567, N. A. C . A. , 1936.
S. Andemon,R. F. : Determinat ionof the Char acter is t icsf
Ta p er edi t%- T. I L N o. 572, N. L C . A., 1936.
9. J acobs,Ea at rnanN., and C2ay,WilliamC.: Cha ra cterist ics
of the N. A. C. A. 23012Afrfoi2rom Textsin the FuR-
S ca 2ea n d Va r ia b leD en sit yTu rin * T. R . N o. 63o,
N. A. C. A. , 1935.
10. P 2a t t, R ob er t C .:
Turbulence
F a o t or aof N. A. U . A. Wind
Tunne2aa Detar mfnedby SpberaTests. T. R. No. 668
N. A. C . I L , 1936.
11. Sta ck,J ohn: Teetsfn the Var iable-DensityWindTunnelto
Investigateh e Effeotaof Sc.a2end Turbuknceon Air
foi2chara oter ist ica .T. N. No. 364 N. A. C. A. , 1931.
12. Toussain
, A., a n d J a cob s, E .: E sper fm en t a lMet h od s
WindTunne2a.Vol . I I I , d iv. I of AerodynarnfoTheory
W. F. Dura nd,editor,JuWa Springer(B erlin),1936,p.
332.
13. von Kdrm4n,Th. , and Mil.Wan,C. B. : On the Theory of
LaminaryB oundaryLa yersInvolving Separa t ion . T.
IL No. 504,N. A. C. A. , 1934.
14. D r yd en , H . L .: Ai r F low i n t h e B ou nd a r yL a y er N ea r a
P l a t e. T. R . N o. 662, N. A. C . A., 1936.
15. D r y d en , H . L ., a n d K u et h e, A. M .: E f fe ct of Tu r bu 2. en
in Wf nd Tu n ne lMa w m e r oe nt s . T. R . No. 342, N. A.
C. A. , 1930.
16. J acobs,Ea stma nN.: The Aerodyna micCha moterist ioaf
Eight Very Thiak Airfoihifrom Tests in the Variable
D en sit y Win d Tun nel. T. R . No. 391, N. A. C . A., 1931.
17. J on m, B . MelvfM Wa lling. I L A. S . J our ., vol. XXXvI II .
N o. 285, %p t . 1934, p p. 753-769.
18. H iggins, G orge J ., a nd J a cobs, E ast ma n N.: Th o E ffeot
of a Fla p a nd Ailerons on t h e N. A. C . A. -M6 Airfoil
&ct ion. T. R No. 260, N. A. C . A., 1927.
19. J a cobs, E ast ma n N., a nd P inker t on, Rober t M.: P remum
D ist ribut ion over a S ymmet rica l Airfoil S eot ion w it h
Tra fling E dge Fla p. T. R. No. 360, N. A. C . A., 1930.
20. Thompson, F. L., a nd K eia ter , P . H .: Lift a nd D ra g Cha r.
a ct er kt im of a C abin Mon opla ne D et er min ed in F ligh t.
T. N. No. 362, N. A. C . A., 1931.
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AI R F O I L SE C TI O NC H AR AC TE R I STI C AS AF F E C TE D B Y VAR I ATI O NSO F TH E
TAB LE I
I MP OR TAN T AI RF OI L S E CTI ON C HAR AC TE RI STI CS
N.
A. C.
A. aicfo41
m. .- . . . . . .- - -- -. . . . . . . . . . . . . . .
W12-----------------------------
c4J15.._ . . . .__. __.. _....__.
mu-----------------------------
2412 _._.. _... __.__ -------
mu.. -... -... --.-. -.- . . . ------
m a- s - - -- - -- - -- - -- - -- - -- - -- - --
2R1r2 . . . . .__. .._. _.__._-..
am----------------------------
4412------------------------------
1416------------------------------
Ha------------------------------
& 470
8.233
0.10I
3.410
L 760
.ES2
.440
. ZM
.142
%370
am
O.m
3.E40
L 740
.871
.49
8.610
Hll
1.730
.874
:E
.113
7.340
IL240
X&x
1. m
.EQ9
.4S3
.214
. ma
8.240
0.Mm
3.420
LZ36
:2
.218
.110
W
0.070
3.4m
L7WI
.s34
.449
.221
.112
am
&3W
3.%30
L 760
%
8.370
a 310
1540
L 770
.W4
.454
awl
S.670
3.340
L7KI
.Sm
:E
.110
: %
am
L6WI
.674
.433
.219
.111
7. m
O.m
2340
L730
.SS1
.431
.219
.110
8.210
O.Crm
3.3m
L7@I
.ssl
.441
.219
.110
-------
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
:
0
0
0
0
0
0
8
2 o
21
z o
21
21
2 o
22
L 3
-------
L 2
-L 2
L 2
-L 2
L 2
L 3
L 6
-L 4
L2
1. 2
L 2
L 2
L 2
L4
. 6
. 7
.
i
28
. 9
3. 9
3. 9
-4.0
-4.0
-4.1
4. 1
3. 7
26
4. o
-4.1
3;
-4,3
z:
-2 a
-4.0
-4.0
-4.1
-4.2
4. 3
-4.4
+4
3. 1
-h 9
h 9
-e% 1
6. 2
-0.3
&2
h 9
5. 4
%,,,
.-------
0
:
0
;
o
0
0
0
0
0
0
o
0
0
0
0
0
.-----
o
0
0
0
0
:
0
.14
.14
.U
:Z
.42
.ZJ
--..---
.a s
.a s
.Cs
.16
.2a
.12
.27
.m
.m
.10
.23
.2%
.10
.40
.10
.02
.11
. 22
:a
.23
.23
:2
::
.67
.n
.3 2
%
.37
.35
.51
.b7
.22
.m
.22
.31
:%
.40
.69
:Z
%
::
.70
%.f.
10,W1
.m
.W
.Wi2
:%%
.W
.0131
.0123
.Wi9
.WJ3
.mn
.W77
.0376
:E
.Im77
.OK1
.@35
.m
.W84
.mn
.0149
.Olhs
.B38
.W92
.m
.0103
.ola4
.0427
.0179
.U207
.W1
.W@I
:E
.W J
.0337
.Olm
.0m7
*.m
.@mo
.Im79
.WJ3
.Wm
.ms4
.WB3
.0179
.0162
. mm
.m75
.0)76
.mn
:%
.m
.m
.0377
.m
.m
.OHS
.Wi3
:%
.W34
.m
:l%x
.Olw
.m
:%%
.W
.ml
.Olw
.0184
.G276
.Cwo
.Cm3
.W4
.Wxl
.0103
.0423
.01%3
.OmB
. ml
%%
.0104
.W
.0129
.0205
.Olm
c
-..,.
----------
0
0
0
0
:
0
0
0
0
0
0
0
.------
0
0
I
0
.---- - - . - -
.-----
0
0
8
0
0
------ - - - -
.. . . . . . . .
. 043
. Cu3
-.045
. 045
. 034
----------
.
m
. m
. 037
. 01 2
. 010
,---- ..---,
,.--.-.-.-,
,--------
. 010
. 010
. 011
-.014
-.011
-.014
.W
.033
.m
: E
---------
. ass
-. m
. m
. Q32
. w
--------
--------- .
.
w
-. cm
.
091
. 0a5
.
m
- -- -. -- -- .
---------.
.
C&5
. am
. mu
. 093
. 092
.--------
. . . . . . . . . -
--------- -
. 133
. m
. 431
. 135
N U M B E R
,
a. L
I
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-------.._.-.--_--
LO
LO :
H
:
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----------- ----------
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---------- --------- -
.6 3
.6 3
3
i;
4
LI 3
-------- - - ._____
------ ---- .-- --. -. .-
L2
4
L1 3
1
k:
L6 :
---------- ---------
- -. -- -. .-. - -- -- ._. -- --
----------- -----------
L7
4
8
:: 3
0
: o
0
---------- -----------
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.5 3
3
ii
:
ii 0
---.--.----------------
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---.--..---------------
-----------------------
7
H 7
5
i:
20
;
---------- . - ----------
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. ------- . - ----------
.6 6
5
i;
.9
:
.9
.4 ?
LO 7
L1
LO
:
0
i 0
. . . . . . . . ..- - ..-. -.. ..
.6 2
i;
i
L1
L4
z.
. . . . . . . . . .- - .. -----
----------- _ __ _____
.- .-.-.- - . . . . . . . ..- .
.8 2
i -;
L2
5
L1
8
----------- ---------
.--- .. --- _ -------- .
----------- - --. ..-. ..
LO 1
L4
L4
:
L7 -4
1.4
8
----------- . .--- . --
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---------- ------------
1
i?
;
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---------- -- ---- . .
,.------. -. ----------
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/A/B/c/.
-
8/11/2019 NACA-All-Re
40/41
...
A. . .
RE P ORT NO. 586-NATIONAL AD VI SORY COMMI TTE E FOR AE RONAU TI CS
TAB L E I C on t in u ed
Import a nt AIRFOI L S E CTION CH ARAC1E RIS TI C3 -Cont inuei
N. A. C. A. alrfdl
me------------------------
so-----------------------
me--------------------------
fwkb Splftip at m .)
me-----------------------
fwithplft
ip a t @)O.)
m12--------..---.. -.--...
mkh SPlftflap at 75.)
ala-------------------------
m15----------------------
(wfth splft t i p a t 7s 0. )
m l ---------------------
ml..----._---. --_--.-.-,
miti a lift filmat 75.)
mu..---..---------..
m12..-..-..--__ ._--. __.-.
miti .mlft tip at 75.)
w12-----------------------
(with 2w2 llflp w Up.)
E.TW -.._-__.__ .__. -----
(with 236r2 flap set m.)
X3 r k Y 1 0--------------------
V i I t h HfmdleYage slot. )
&ml
:%
L 7S9
.S22
.449
.222
.112
&
4m
;g
:911
.449
.224
. m
8.110
5.910
am
3.433
L 740
.919
.449
ILlm
%
(Ax
.8s2
.444
8. Ifn
H%
L 740
.S37
.446
Km
km
8.210
w
L8@
.924
.4m
&
210
:%J
:H
8.124
w
L~
.m
.423
am
Lmo
.449
&240
%
L 740
.857
.449
& 210
~ lm
33m
LtS6
%
8.140
&m
% 41 0
L~
L7@l
.m
.441
9. m
&m
4m
3.frm
2 C40
L2M
:%
.261
.135
(d=$.)
7. 3
7. 4
7. 4
7. 6
7.8
h 7
-46
-3.9
7. 2
7. 3
7. 4
7. 6
K 7
9. o
9. 2
&o
l& 1
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am
.Qa5
:E
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--- .. .
.035
i%
.Ca3
.U3
:%
.077
J.am
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14. 3
$.
m
1& 6
L 1
16.
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.0$3
s.ma
. . . . . . . . .
--. . .. . .
L 2
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. 0 3 2
. . . . . . . . .
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17.3
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.
.
:
.
8
i :
13.8
----
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12 .5
.---
11.9
--------
-4.2
43
-4.2
-4.2
-4.1
-41
2;
-4.1
+.a
~.
0a4
.------- .
.----- .
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--------
---------
.KrJ
.-.-.-.--
..-.---
J.ma
.------
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.-.---
.----
.101
. lMI
. Im
.0a7
%%
J.102
-------
.------
J.la3
,-.-----
S.la
,--
$.m
J.m
~.m
~.m
J.IB3
J.m
.--.-..--
--------
,--------
.---
%*PC
0.3
.%
.?i
.C
.%
i :
- . m
. 24
. 1(
.31
.3f
.a
::
-------
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.......
.10
------
.07
------
,.---
,------
-------
------
. .. ..
----
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------,
.-.---,
...-.
.a3
-------
------,
------.
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-. .-.-,
-. ----,
------.
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.07
.15
.19
.13
:~
.45
------.
-------
.70
-------
.IK1
------.
.76
.76
.69
:8
.a
::
.64
.@
a. c.
I
u
o . {.
%&
(Pa-c%(wA C)
I I I I
: y;: -o. lWJ
L 2 -2
. 197 -4
.0120 -. K@ ii -8
.0124
. 210
. Ola . . . . . . . . . . . . . --1:. . . .. -. . . .
.Ui 3 -- --- --- --- - . . . . . . . . . . . . . . . . . . . . . . . .
. Oim --- --- --- -- - . . . . . . . . . . . . . . . . . . . . . . . .
.0411 . . . . . . . . . ..- . . . . . . . . ...- . . . . . . . .. . . .
.0127
-.132 L 5 2
.01Z3 . Ha
.Olm
. 133
;: :
.0140
. 137
. Ol?a . .. . .. .. . . .. . . ...J .. ..-. -..:-
.0215 . . . . . . . . . ..- . . . . . . . . .. . . . . . . . . . . . . . .
.02.m ------------ . . . . . . . .. . . . . . . . . . . . . . . .
.Im2 ------------ ------------ . . . . . . . . . . . .
~.167
1-4~
.6 a
------------ . . . . . . . . . . . . . . . . . . . . . . . . --------- . . .
.-- . .. ---- ---------- .- . . . . . . . . . . . .
. . . . . . . . . . . .
------------ ---------- -. . . . . . . . . . . . .
. . . . . . . . . . . .
------------ ------------ ----------- . . . . . . . . . . . . .
----------- . . . . . . . . ..- - . . . . . . . . . .. . . . . . . . . . . . . .
------------ ------------ . . . . . . . . . . . . . . . . . . . . . . . .
7.169
$_. ~
1.2
7
------------ ------------ ------------ . . . . . . . . . . . .
------------ . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . .
...........- ----------- ....----.... -------.....
............ ............ ------------ .......... ..
---------- ............ ............ ............
7.201
s=
L 2
7
.. . . . . . . . ..- . . . . . . . ..- . . . . . . . . . . . . . . . . . . . . . . . . . .
.. . . . . . . . . . . ------------ . . . . . . . . . ..- . . . . . . . . . . . .
------------ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.- -------- ------------ . . . . . . . . . . . . . . . . . . . . . . . .
..-. .----- ---.-.----.- . . . . . . . . . . .- . . . . . . . . . . . .
. 03S1 . m 1.1 6
------------ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.m
1 245
1.1 6
.. . . . . . . . . . . . . . . . . . . . . . . ------------ . . . . . . . . . . . .
.---------.- ------------ . . . . . . . . . . . . . . . . . . . . . .- .
----------- . . . . . . . . . . . .- ------------ . . . . . . . . . . . .
.. . . . . . . . . . . . . . . . . .._ . . . . . . . . . . . . . . . . . . . . . . . .
----------- ------------ . . . . . . . . . . . . . . . . . . . . . . . .
.0101 . m 23 7
.. . . . . . . . . . . . . . . . . . . . ..- ----------- . . . . . . . . . . . . .
. . . . . . . . ..- ------------ . . . . . . . . . . . . . . . . . . . . . . . .
----------- ------------ . . . . . . . . . . . . . . . . . . . . . . . .
-------- . . . .. ------ . --------- -. . . . . . . . . . . . .
. . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.191 1 .~ 23 7
-.-..-.---- ------------ . . ------- --- . . . . . . . . ----
----------- . . . . . . . . . ..- . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . ..- . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . .- . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . ..- ------------ . . . . . . . . . . . . . . . . . . . . . . . .
.m
. 019 1.0
7
----------- . . . . . . . . . ..- . . . . . . . . . .. . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . ..- . . . . . . . . . .. . . . . . . . . . . . . .
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----------- - . . . . . . . . ..- . . . . . . . . . . . . - . . . . . . . . . . .
----------- . . . . . . . . . ..- - . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . ..- . . . . . . . . . ..- . . . . . . . . . ..- . . . . . . . . . . . .
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.0161
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.0242 . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . .. . . . .
.0249 . . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . .. . .
.0230 ------------ . . . . . . . . . . .. . . . . . . . . .. . .
.O.wl ------------ . . . . . . . . . ..- . . . . . . . .. . . .
.0264 . . . . . . . .. . . . . . . . . . . .. . . . . . . . . .. . . . . .
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. ml . . .. . .. . .. . . . . .. .. . .. ..- . .. . .. . .. .. .
. oml . . .. . . . .. . . . . . . .. . . . .. . . . . . .. . . . .. . .
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1 e footnDtal
39 .
Weofzm t d ~ ~m t i m tm e apmmbmtfw~ti
7V81W ofthedrf gthat8ppfk9approximately over the entire umfuf rango of 11 1
Uft ma
CmJ6dents
J Slope of Ifft cnrm determfnd
from lfnmr Ifft un-ve appmxfmatlng -anti
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llft ~
~et at M@ liftdan~
Dfawntinnfty premnt fn the @e offti
. . . . . f s taken abcmt tbe aaredynamfo center of the wing w4th nap neutral and Is
fdrf mutantatbkh Ifft tidenb.
IO%ot N. A. O. A.
-
8/11/2019 NACA-All-Re
41/41
AI RF OI L S E C TI ON
CHARACTERISTICSAS
AIRFOJ L
AFFE C TE D B Y VARI ATI ONS OF TH E RE YNOLD S NU MB ER 267
TAB LE II
S E C TI O N C H AR AC I E R I S TI C S
OkuffkMon
N. A. afrfoff
OhordI
ao9 . . . . . .._.. .-_ . . . . . . . . ..___ .-_.__.
am ... . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . .
W15-----------------------------------------
mls-----------------------------------------
%12.. .. .. .. ..- . .. . .. .-----------------------
23012. . . . . . . . . .._ . . . .._. _-.-. __ . . ..__
ml%33.._ . . . . ._. __ . . . . . . . . _________
2R112.- . . . ..-_ -_ . . . . . . . . . .._.. _....._-
Mm-----------------------------------------
u12.._.._.__.-. .-.__ . .. .. .. ...___ . .
4416-----------------------------------------
6412_... _... -_._ . . . . . . . . . . . . . . . . . .. . . . .
m12----------------------------------------
m18-----------------------------------------
wm Mth split t ip at w--------------------
2X112 Wltb eput Imp at w..-. _________
mlz Wltb 2put Ilap at 76------------------
m16----------------------------------------
23015Wftb aput tip at 7P-.. __________
We-...-.- . . . . . . ..-.. --.. -.-. . . . . . . . . . . . . . .
23021wfth splft f lnp at
7 b 0 _. _ . . . . . . _-. -_
W IL --------------------------------------
4W2 Wthql l ftipat 760_. -... -----------
mlz WftbZ301z
f lap
3
rip___________
ZJI12 Wltb ZJ312de aet m..._._..._.-
&
fazk Y wfth Han ey Page slot 1o------.
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7.84
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7.92
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4.102
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meannm.
@310M 0[ Il ft cnrve dekmnfned from f fnmz l ff t orzrve appmxfmntfng axperfmanhl
~ Type of Me affact on mazinmm Mt.
Il ft me.
j Type of Uftimrve x m shown fn the sktim below:
7 Ve,fne of the drag that applfw approxfrzmtaly over the autfre nzafrd range of IUt
~.~/:-p ~:~.ft.dm.
.,,. Is taken about the rIer@mamfa mntw of the pkdn wfng and Is fafdy con.
~0- fe tien about the aanxfymemfa cent8r of the * wfth tip neutral (??)
and k fafrly mnstant at hfgh Ifft tidant&
t Tnrbulenm ferlor fs 264.
10NOt N. A. C. A.
J Angla of zero lfft detamfned from lfnaar Mft URVe appmzfznetfng ezperfmentaf