NACA-All-Re

8/11/2019 NACA-All-Re

1/41

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 .


3/41

AIRFOIL SE CTION CHARACTERIS TICSAS AFFE CTED BY

7hickness

N.A.CM.

0012

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VAR I ATI ON S O F TH E R E YN OL D S N U M B E R 229

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430/2

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Clark Y

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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.


4/41

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.


5/41

AIRFOIL SEC TION CHARACTERISTIC-SAS AFFECTED BY VARIATIONSOF THE REYNOLDS NUMB ER 231

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6/41

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232

REP ORTNO. 686-NATIONJ iL ADVISORYC OMMITTEE FOR AERONAUTICS

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7/41

AI R F O I 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 NOL D S NU M B E R 233

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s)

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-.4 -.2 0 .2 .4 .6

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kgle

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L i f f c oe f ic ien~ C.

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.


8/41

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234

REP ORT NO. .580-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS

o

1.8

1.6

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t --- 6459000

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9/41

AIRFOIL SEC TION CHARACTERISTICSAS AFFEC TED BY VARIATIONSOF THE REYNOLDS ITUMB ER

235

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10/41

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A

REP ORTNO. 586-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS

.11

.10

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11/41

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

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..5 28 : 5 x3 0

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O of e :3 -3 5

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-.4

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1 1

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-8-404

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

e

4~ -

.G

z%

$

Ou

&

8

___ .. L ._.

. .. .. .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


35/41

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.


37/41

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 .


38/41

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.


39/41

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

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0

0

I

0

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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

--------

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.

w

-. cm

.

091

. 0a5

.

m

- -- -. -- -- .

---------.

.

C&5

. am

. mu

. 093

. 092

.--------

. . . . . . . . . -

--------- -

. 133

. m

. 431

. 135

N U M B E R

,

a. L

I

&t@ t c)

-------.._.-.--_--

LO

LO :

H

:

- .. .- -. - . --__. -- -- -

----------- ----------

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.6 3

.6 3

3

i;

4

LI 3

-------- - - ._____

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

L2

4

L1 3

1

k:

L6 :

---------- ---------

- -. -- -. .-. - -- -- ._. -- --

----------- -----------

L7

4

8

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0

: o

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.5 3

3

ii

:

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7

H 7

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i:

20

;

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.6 6

5

i;

.9

:

.9

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LO 7

L1

LO

:

0

i 0

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

.6 2

i;

i

L1

L4

z.

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

.8 2

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LO 1

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1

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/A/B/c/.


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

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.035

i%

.Ca3

.U3

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.077

J.am

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$.

m

1& 6

L 1

16.

2

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s.ma

. . . . . . . . .

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L 2

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-4.2

-4.2

-4.1

-41

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+.a

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0a4

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.-.-.-.--

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J.ma

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.101

. lMI

. Im

.0a7

%%

J.102

-------

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J.la3

,-.-----

S.la

,--

$.m

J.m

~.m

~.m

J.IB3

J.m

.--.-..--

--------

,--------

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%*PC

0.3

.%

.?i

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.%

i :

- . m

. 24

. 1(

.31

.3f

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.07

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,.---

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.a3

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.07

.15

.19

.13

:~

.45

------.

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.70

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.76

.76

.69

:8

.a

::

.64

.@

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I

u

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(Pa-c%(wA C)

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: 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

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

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

. . . . . . . . . . . .

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

. . . . . . . . . . . .

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

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7.169

$_. ~

1.2

7

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

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

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7.201

s=

L 2

7

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

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

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

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

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

. 03S1 . m 1.1 6

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

7.m

1 245

1.1 6

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

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

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

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

.0101 . m 23 7

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

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

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

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

. . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.191 1 .~ 23 7

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

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

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

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

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

.m

. 019 1.0

7

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

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

1.m

s. ~

1.0

7

. . . . . . . . . . . . A----- - . . . . . . . . . . . . . . . . . . . . . . . .

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

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

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

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

.We9

.m

.6 8

.m74

:%

9

.m

;::

.WS

.011 H

.OxQ ------------ . .._.. .:_ . . .. . . . .. . . .

.0119 . . . . . . . . . ..- . . . . . . . . . . . . . . . . . . . . . . . .

.0161

$.~

.5

8

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

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

.0184

1-. @-J

L 2 11

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

. W8 . .. . .. . .. .. . . .. . .. . .. . .. . . .. . .. .. . ..

. . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . . . . ..

.0242 . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . .. . . . .

.0249 . . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . .. . .

.0230 ------------ . . . . . . . . . . .. . . . . . . . . .. . .

.O.wl ------------ . . . . . . . . . ..- . . . . . . . .. . . .

.0264 . . . . . . . .. . . . . . . . . . . .. . . . . . . . . .. . . . . .

.W2 . .. .. . .. . ..- . .. . .. . .. . .. . .. . .. . .. .. .

. ml . . .. . .. . .. . . . . .. .. . .. ..- . .. . .. . .. .. .

. oml . . .. . . . .. . . . . . . .. . . . .. . . . . . .. . . . .. . .

.m . .. .. . . .. ..- . . . .. .. .. . . . . .. .. . .. . . ..

. M81 .-- . . ...- . .. . .. . .. . .. . . .. . .. . .. ..

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

-..,. fe taken about the wm@namfo cantea of the Plafn wfng and k fafrly con.

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.


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------.

SE 2

c

. . .

R, ~

(znfflfons)

8.29

a37

&61

7.84

&24

&16

arm

Hl

7.92

7.92

a 21

&10

a45

&11

am

a 10

&37

a 21

&21

&Is

azu

:2

8.14

am

Funds.nzantel.wMon chaiaotdstks

o

0

0

i

o

L2

L 2

-i :

2:

5. 9

7. 3

7. 2

12 1

14. 3

lh 6

L 1

le. 2

L 2

16. 5

23

17. 3

-Ti :

-4.3

am

.Ow

.W7

.

fm

.039

. lIN

.Qa7

.C@s

.02a

:%

.W3

.@J6

.W5

@.wl

4.W4

O.@s

.0%3

d.a36

.092

6.094

. l fm

O.m

.101

4.102

O.m

o

0

0

0

.14

.a3

.20

.10

.%

.32

.22

.37

.35

.24

-------

-------

I

-------

.10

-------

.07

-------

.26

.....-.

.07

.45

.76

Lm&

.mn

S&

.Cc170

:%%

.W-3

:$%

.ml

.0115

.0127

.167

. lGS

.231

.ml

1.1fr3

.0101

T.191

.W76

r.m

.W

.0161

.0248

I

e=

..&

o

0

0

0

.

6f3

. cm

. 010

: E

. w

-. 0s.5

. la

. 169

. 132

. ZO

.230

l_. ~

. m

. 245

. W5

. m

. 019

. 225

: E

.-- .. ..

a.

L @rcent

c

from@)

1.0

i

L7

i:

i;

.6

Jj

1.2

Lb

i;

H

k:

23

LO

LO

.5

.5

-------

AbovI

b

:

4

3

7

6

;

2

1

;

;

7

7

6

6

7

7

:

8

8

-------

1

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

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