Summary of Airfoil Data

TECl'i ';AL L1BR RY A JRES EA RCH r,j,'.NUF .CTU .i~G CO.

ACR No. L5C05 _00 1 S£?' LV~"A E iD r--------------------------·------~~~~~~~~---------------------, l NGL E\; 0 0 D, CM' ~ORI~IA

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NATIONAL ADVISORY CO MMITTEE FOR AERONAUTICS

ORIGINAL LY IS SUED March 1945 as Advance Confidential Report L5C05 ~ .

SUMMARY OF AIRFOIL DATA By Ira H. Abbott" Albert E. von Doenhof f , and Louis S. Stivers, Jr.

Langley l~orial Aeronautical Laboratory Langley Field, Va.

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

L - 560 I I NACA ACR No , L~C07 { o' ~UBLE OF CONTENT S Page SUlvlMARY , , , INTRODUCTION 2 ' .

SYMBOLS , , , 3 HI S TORICAL DEVEW}' MENT 7 DE SCRIPTION OF JI...IRFOILS 9 t · ~ethod of Conbining Mea..'1 Lir.:es a nd 'fhic::ness ::!iistributlons 9 NACA Four -D tgi t Ser·ies Airfoils 11 Numbe~ing system 11 'I'h l.ckness di8t~~butlor..s , . , 11 Me an line8 , , , , , , , , . 11 1I 1A CA Five-Digit Se ri eG hirfoi.13 12 Num.berin Y sy::;tem 12 Th :LclmesG distr2.butions 12 Mean Enes , . , , 12 NACA I - Series ,l\iX':0118 . , 12 Ni..u:nber:'DB sysT,em 12 'I~ick~ess distriblt io n Mean Ilnetl· , . ., .

, , NACA 6 - Series Air_o:ls , , NUillber tng system Thickn ess d istribut:Lon3 Mean lines , . , .

r~ACA 7 --Serie s Airfoils , " Numbering system 16 · Thicknes s di st r ibutions THEORETI CAL CONSIDEF~TIONS Pr essure Distribut io ns , , .

Me th ods of derivat10n of thickness distribut:l.ons 18

Rapid estimation of pressvre d istributions 21 Numerical examples Effect of cambe r on pr ess1.:.re distr ibution., Cr iti c al Mach Number , M om e nt Coefficient s , Metho d s of c alculation :~O Numerical examples P~gle of Ze r o L ift Methods of ca1.vu1ation Numerical examples Des c r iptio n of Flmr around Ai rf oils

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NACA ACR r o . L5C05

Page EXl ' ERIMENTAI.. CHAR,.'\.CTER I STICS Sources of Data . . . . . . . . . . . .

Dr ag Characte r 18tics of Smooth Air f oi ls

Dr ag cha -c acter.istics ::.n low-drag l ~ ange

Drag cha r acte r istics outside 10v;- drag range Ef fe c ts of type of section on dr ag characteris t ics 38 Effective aspect ratio . . . .

Effect of Surface Irregularitles on ~~ag Permis s ible r oug hness . . .

Permissible Jav i ness . . . . . . . .

Dr ag i{i th fixed transU:'on ....

Dr e.g \'7i th :f'racti c aJ. con <J truction met..'I1ods 43 41~ Effects of propeller slip s tream and air p lane vibration Lift Characte r istics . of Smooth Airfo i ls 45 1~5 Two-dimensi~~al da ta . , .. .. .

Three - dimensional data . . . . . . 49 Lift Characteristics of Rough ~\i r foils 'l'vlo - dimensional data

Three - dlmensional data 51

' Un co nse r vative Airf o ils 52

Pitching Moment . . . . .

l'osition of Ae r odynomlc Center High -L ift D evi.ces Lateral - Control Devices Lea d ing -Edge Air Intakes Interfe r enc~ . . . . . .

A?PLICATION TO WING DESIGJ Application of Secti on Data 58

Selection of.Root Secti on 60

Selectlon of Tip Section 61

C ONCLUSIONS . . 62

APPENDIX - ?--1ETHODS OF OBTAINING DATA IN THE LAlmLEY 'TWO - DIMEnSIONAl, LOW - 'I'URBULENCE TUNNELS Des cr iption ~ f Twll1els 65 .. List of Symbols 6'5 Meas ur eme n t of . Lift Meas ur ement of Dr8£ 72 Tunnel - Wall . Co rr e ct ions Co r rection for Block i ng at HI gh Lifts Comparison -.r:i . th Exper iment I ; NACA ACR No. L5CO:) Page

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REFERENCES TfJ3IE3 FIGURES (NUMBERED) Supplement page SUPPLEMENTARY DATA I .- Ba sic Tnic~ess Forms II . - Mean. Lines . . . .

III . - Airfoil OrcUna tes Dr . - Pred~ctGd Critical I'fach Hum.bero V .- Ae ro dynamic Character:iztics . 8111

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NACA A CR NQ. L5C05 NATIONj~ ADVISORY C O~ WITTEE FOR .~ONAUTICS J; DV A NCE CO NF IDENTIAL REPORT SU1Y W)RY OF AIRFOIL DATA BS Ira·Ii . Abbott ; Albe r t E. von Doenhoff, and Louis S . StIvers, Jr.

Recent ai rfoil data foX' both fUght and wind-"i:;unnel tests have been collecteel and. cor re lated :lnsofar as possible . The flight data consict largely of drag measu.rements made by the wake-surve y method. Most of the date . on airfoil section charac- teristies we r e obtained. in . the Lang J. e,Y" tvlO-d1mensional low- t urbul en c e pressure t.UI1..neL Detail da ta necessary for the a].iplica -ej .on of NACA 6- sE; rie::. airfoils t.o wing design are presented in su p:ple mentary 'figu:r>es] together vr:i.th recent (lat.a for the NACA 00.:., 14-, 24-,. 44 - , end 2 30 -seri e8 airfoils. The general

methods used to d. e riv e the basj.c t h ickn(1sS forillS for NACA 6-

and 7-serie8 airfoils and their co rr esponding pressure distri- buMon s are prese n ted. Data and methods are give n for rapidly obtaining the ap:9 roxlraate press ur e distrllrl.1.tlons for NACA four- digit , five - diGit, 6-, and 7-De r ies B . irfoils.

The r ep or t includes an ane,lysis of the lift, drag, pitching- moment, and cr itical-spee d' cha",(,t.:l.cteristics of the airfoils, together ",ith a d iscussion of t he effects c·f surface conditions.

Dat a on hieh-lift dev~ces are presented. Problema associated with lateral-con tr ol deVices, leading-edge air intakes, and inter- ference ace briefly discussed , The data indicate that "the effects of su rf ace condition on the lift and dr ag characteristics are at l08.st as large as the effects of the airfoil shape and must be considered in airfoil selection ~d the prediction of wing c har a cter istics . . Ai rf oils pe rm ittiIl['; extensive J.. eminar flo'", such as the NAC A 6- s er1e8 airfoils , ha.ve much lower drag c oef ficie n ts at high speed and cruisine lift coefficients than earlie r types of a.i rfoils ii' , and only if) the w"ing surfaces are sufficiently smo oth and fai r. The NAC .. 6 - series 'airfoils also have fav or a b le critical - speed 'Jh£l.racteristics anJ. do not appear to pr ese nt unusual p roblem s associated ,.r:i th the ap1JJ.ication of high-lift an0. l ater2. l- control o.evlces.

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NAC A ACR No '. L5C05 INTRODUCTION A considerable amount of ai rfoil dat a has been accumulated from tests tn the langley two-dimensional lo,of-turbulence tunnels .

Dat a have also been obtai ned from tests both in other wind tunnels and in fli g ht and include the effects of' high - lif't devices J su rf ace trr~gulcu~ i ti.es, and interfere nce. Some data are also available on the effects of alrfoil section on aileron characteristics . Although a large amount of these data has been published, the scattered nature of the data and the limited obje ctive s of the re ports have prevented ade(J.uate analysis and inte rpret ation of the resulto. The pUl~ pose of th is report is to summarize these d ata and to correlate and interpret them ins0far as possible .

Recent l nf ormatjo n on the aerodynamic characteristics of NACA airfo ils is p re se nt e.d . The historical develo p ment of NACA ai rfoil s is briefl ,)' r evieY Ted . Ne1" data are :presented that permit the ra ~i d calculation of the ap p roximate pressure distributions for the older NA CA four-dj.git and five-digit ai rfoils by the same methods used for the NACA 6 -se rie8 airfoils. The ge neral methods used to de ri vo the basic thiclm e ss foYIlls for NACA 6- and 7- s8 r 1e8 ai rfoil s together with their corr esp onding pressure diot:ribu tio ns are presented. Detail data nece s sary for the application of the ai rfoil s to wing d esign are presented in supIilementary figures placed at the end of the pape r. Th e report includ.es an analjs.fs of the lift, dr ag, pitching -m oment, an d critical-speed char a cteristics of the airfoils , together with a discussion of t.he effects of s urface c· ondi ti o ns. Availa ble data on high-lift devic es are . presented . Problems associated with lateral-control d evices , leading-edg e air intakes , end interference are briefly dis cussed, together with ae r odynami c problems of ~pp lication. - Numbered f'ilSureA ar e . used to il lustr ate the t ex t and to presen t miscellaneous da ta: SuppJ.,enenta.:ry. figures and tables are

not numb e red but are conve niently arranged · at the end of, the

report accord.ing to'the numeri cal de sig n at ion of the airfoil se.ction wi thin the fol16,.ring headj .n gs : . I. - Basic thickness form s' , II. - Mean lines 111 . - Ai rf oil ord i nates IT . - Pr edicted cri tical / Mach numbers V. - A erod~~amic characteristics NACA ACR No . L5C05 These supplementary figures and tables present the basic data fo r t he airfoils .

SYHBOI.8 &.spect. ratio Fou:de:c' series coeffic:i ents a meall -lir:.e 6.esigne.tio n , fraction of chord from leading e(~ ge oYer i·~hich desi gn load ":'8 uniform; in deri yation of thickneos cli3'L r il:utions, bas':'c length usually co n . i dere.'l. unity b i· Tin g s .Je~ TJ.

b . flaIl s)en, in1)oard f l b flap spen , outboard f o CD (t eas c ae ff i c i e nt C dra coefficient at zero Jift DL=o CL li f t coefficient 6C .o incren~ent of nJa.'Cit um lift caused by flap deflectlon L .L c cho r d C aileron chord a Cd sect:'on dr ag coe:'f'icient c minilllv_n se c ti0I'l clra, r:1 coeff " cient dmin .:> Cf. flap ch0rd, i~b02rd l c.f f lap chord , out.board o.

f lep-chor d ratio se c tion ailE-r on hin~e - m.omen t

coefficie nt ( q:c~

NACP. A CR Fo . L5C05 OC R incre~ n en-':; of ai leron hil1. f, e-moment c oe fficient at const :Ilt lift

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h i n ge -mon:ent p arameter section lift co effic i ent de s i{:i;n s ec ' ion Idt coeff..L.cient moment coefficient about ae r od yn c::mic center mone nt coe:i:'f i cie:J.t abo 'J,t qua:.':'ter-chcrd poi nt section ncrn:3.J. - force coefficient D drag 108S of total pr essu re free - sJ.:,ream total p r 68S1.~ r e secti . cn aD eron hing e mome n t h ex i t height constant L Ijft M Ma.ch n' .1l.i·foer- H cri tical l ,lach n umb er cr typical :9 oj.nte on uTper and lo we r s ur:'acGs of ai r~ oil r l'e :3SU Te eoe?fLi ent c ri tical pr essu re co e ff ic :1.ent r esultant pressu r e coeff ~, c ie n t ; d ifference bet.r ee n local u pp er- and 10'"er-surface rrc8sure c oefficientf:!

10caJ, statjc rre~ 8 ur e; al<'o, allsular velocity i n roll 'I n pb/2V f r ee - ct, reaIT1 st atic pr ess ux'e }.j.

NA CA ACH No . L5CO: helix engle of vling t::.p p b/2 V free - stream dynamic ~jre3sure R Reynola.8 n U!Jloe r R cri tiGal PeynoJcls numbel" cr I' ).

H - n

coefficient ( ~ _ o __ J

press LITe . \( qo fir st airfoil thiclmess ratio t,.., c

v frGe-ntreem veloc~t~

j n let veloci t.y v 10c81 "'-e~~oc i ty 6v in , !'ement of local - ,reJ.oci ty inere ent of local ve:'oc: T,y ca:1sed b- aidi tio~lal type c£' ~oad d:"st : dbution 'rei-oci ty :!. " at::'o co r resl · on ~ ling to thickn.e 3s tl veloci ty ratio corresponding to ~~~Lclmess t2 x distance along ~hord me~1 - 1~ne abscissa abscissa of lo~rer surface aoscise~ of upper surface chord-trise })osl " Gioll of transition • diEt,ance l)er},Jendi Jular " to chord - NACA AGR No . ~5C05 y m.ean - li~e orrlinate c ordinate of 101-ler s ur ace ordinate of sJmmetrical thickness di stribution o dinate of uPDer surface complex ·ariab ~e -:"n circle plane z complex variable in near - circle plane z' (1, 8:1g1e of atta.ck sec tion aileron effee ti ve ne ss paramet er J rat io of" ch8.11ge in sectton E;:1,'sle of £..tte.ck to :inc re ment of aileron dt~flecti(;n at a cons·:;ent value of lift coefficient ang10 of zero lift section fu!gle of ~tt&ck inc r ... ment of sec-:'io:1 angle of attacl<:: section angle of ettack correcponding to design lift coefficient flap or aHeron deflection; dOW:l c..ef10ct . ~on is posj.tive fl ag defl ection, j.nboal'd fl ap defl ec t io n~ ou tbo a rd aj.ri'cil parameter (¢ - e) E: TE valne of € at trailing edge " comp lex vari able in ai rfo H })larle

e angular coor d inate cf z ' ; also , a11g1e '.'T hose tangent

1(3 s l o} )e of mean. line Tip Chord0 tape r r atio .. _ ""' -_ .. - .

Root chorcl .

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~----~~ -- ---- ---- -- NACA ACR No . L5C05 T turbulence factor (Effecti ve RemoldS humber\ \; Test Reynos number ~ angular coor~inate of z

airfoil parameter determinin g radial coordinate of z

aver~e value of ,y, (~rrl :~)

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HISTORIC.AL DEVELOPMENT

The development of types of NACA airfoils now in common use

.Tas sta rted in: 1929 ,.i th a systematic investigat io n of a family of airfoils in the Langley yariable~densit y tunnel. Airfoils of this family were designated by numbers having four di gits, such as the NACA hl.L12 airfoil . .All airfoils of this family had the same basic thickness distribut10n (reference 1), and the amount and type of camber was systema.tically varied to produoe the family of related airfoils. Thi s investigation of the NACA airfoils of the four-digit series produced. ai:d'oH sect:~ons having higher

maximum iift coefficlents and lower minimulll drag coefficients than

those of sectjons deve lop ed before that time. The investigation also provided information on . the changes in aerodyna~ic charac- teristics re sulting from Variations of geometry of the mean line and thiclmess · ratio · (reference .. l) .

T~e investigation was extended in references 2 and 3 to include airfoils with the same th i ckness distribution but with nositions of the maximUm camber far fO~Nard on the airfoil. These airfOils were deSignated by numbers having five digits, such ?-s the NACA 23012 airfoU . . S(lme airfoils of . this family showed favorable aerodyna.m;i.c characteristics . except for a lar ge su dden loss in lift at the stall.

Although these lnvestigations were extended to include a limi ted number of a rfoils wi. th varied thickness distributions .

(references ~ and 3 to 6), no exten si ve investigations of thickness

distribution were made. Comparison of ex perime ntal drag data at 10'"' lift coefficients with the skin-friction coefficients for flat plates indicated that nearl;y all of the p rofile drag under such condit ions was attributable to skin friction. It was therefore apparent that any pronounced reduction of the p rofile drag must be obtained by a reduction of the skin friction throv~h increasing the relative exte~t of the laminar boundary layer.

NACA ACR No . L5C05 Decreasing pr essur e s in t he di r ection ' of flow and low air- st r eam turb u len ce we r e known to be favorable for laminar flow .

An attempt i,ras acco r dingly ma de to increase the relative extent of laminar flow by the d evelopment of airfoils having favorable press ur e gra d ie n ts over a gr eate r pr oportion of the chor d than

th e airfoi l s develope d i n r efe r e nc es 1, 2, 3, and 6 . The actual

atta:i.nment of extensive laminar boun d ary layers at lar ge Reynol ds numbers was a pre~iously unsolved experimental problem r equ i r ing the d evelopment of nei-' test equipment -1 th very low air- st r eam t ur bulence. This "'ork was gr eatly encourae:;ed by the experiments of Jones ( reference 7) } who demonstrated the possibility of obtaining extensive lam:i.nar layers in fl ig ht at relatively large Reynolds num b er s . Uncertainty "T1 th re gard to factors affecting separation of the turbulent bov.ndary layer requ) , red experiments to determ i ne the possibil'l ty of making the rather sharp pressure recover ie s required , over the rear portion of the new tJ~e of airfoil.

New 'Hind tunnels were designed specifically for testing air- foils under con d itions closely approaching flight conditions of air - stream ' turbuJ ,e nce and ReynolO,s ,number. The re sUlt ing wind tmmels ~ the La.ngley t' ,l o- clime n si onal low-turbulence tunnel (I..TT) and the Langley two- d imen3io~lal low- turbulence pressure tunnel (TDT) , and the methods used for obtaining and correcting d ~ta are briefly described in the appen dix . In these tunnels th e models completely span the com p aratively narrm'T test sections; two-dim ensio nal flow is thus provided} wh1ch obviates difficulties previollsly encountered in obtaining section data from tests of finite-span wlllgS and in cor r ecting ad equately fo r suppor t interference (r e ference 8).

Diff iculty '.-la s. encoun' cr ed in &.ttcmptinG to d0si-sn ai r - foils havin g desired pressure distributions because of the lack of adequate theory . The Theodorsen method (reference 9), as ordinarily use d for calc:u1ating the pressure distributions about airfoHs} was, not sui ' fi<::iently accurate near the lea ding edge for , pre d iction of the local pressure gradients. In the absence of a suitable theoretical method; the 9-percent-thick s~mnetrical airfoil of the NACA- 16-8e1'ie 8 (reference 10) was obtatned by empirical modification of the pr eviously ' used thiclmess distr ib utions

( reference 4) . These NACA 16-serie s sections re :r: res ented the first

family of the low- d.ra. g h igh - crItical-speed elections .

Successive attempts to d esisn airfoils by approxjmate theoretical methods led to familie s of al rf oils d esignate d NACA 2 - to 5-series sections (referenc e 11). Experience "ii th these sections showed that none of the aPl'r oximate methods tried was s m'f icient ly accurate to sho"," correctly the e ff ect of changes in p rof ile near the leading edge . \oJind-tmmel and flight t0StS of these a.' rfoils showed th a t e xt en sive laminar bo~dary layers could be maintai ned at NACP. ACR No. 1.5005 a t c om p arati ve l y 18.1~ go valueE? of th e Reynold.s 'number if the a ir - fo i l s ur faces were s uff i c "i ently fair and smooth. These tests also pr ovi d ed. qu alitative info X'l J1ation on the eff ect !'! of t.he rnae.;-ii tuc."..e of t h e fa v ore.ble p res s ure gradtent, lead :;'~··edg e r adius, en d ot h e r shap 'e variables . The ( l ata also showed that separation of t he t ur b ul ent boundary l ayer ove r the rear of the flection, especi.a::'ly wi th rough su r fac ' es, limite d 't!le ' extent of lamina r I D-y e ::.~ for \-lhiGh th e airfoils s hould be d esig n e d. The airfoils of theBe ear:!.; )' · fam il ies generally showed r elat~Lvely 101-1 ma..'C·mum lif t coefffcienJ· s an d , ' in many cases , we r e designed for a g reater extent of lruninar fl O1 , than I s pra.ctical . It ,· ras leal"Iled that, al t}lO ngh sections desig ned for an excessive extent of laminar flO1., ga ve extrem .eljr, lo w dr ag coefficients near the cteslgn lift coeffi~ient '\>Then smooth , th e dr ag of such sect io ns became undul y larg e when rOUgh; partic,\-l- larl y at lift coefficient s hi F~ her than the design lift. These families of ai r foils are a ccoI\i i.p..,'~ly considered ob~olete .

The NAC/\ 6 - ser5.es basic th i ck n ess fO!'rilB i·rere d erive d by new an d improved methods a.escribed. herein in th e r ection "Me tho ds of De r ivation of Thickness Dist r ibut:i.ons , " in accorde.nce w1th d69i5l'l c r i te r i'ons established "lith the objective of obtainin g desirable dr ag, c r itical J-. 'la ch number, and m~im.um-l 'ift characteristics. The pr ese n t report deals la r ge l y '..,i th the cnaracterist:.cs of t.hese sections . The de velo p ment of the NilCA 7 - s erie s faroiJ.y has also bee n started . 'This £'amily of airfoils is characterized 'by a .:; r eate r ext e nt of' lamLT!ar fl ow on the l o ver than on the u:;:Jpe:r surface .

Th e s e sections permit ImT pi tChing - momen -t coefficient,s with mo der ately hi8h d.e sig n 11ft coeff :l c ie n ts at the expense of some r ed uction in nlaximum lift aIld critIcal Mach number.

Acknmded ge ment 1.13 g rat ef ull y expressed for the expert guidFillce and many ori g ina..l c on t ribut:'ons of l'fJ.r . EactIllE'.Jl. N . J acooEJ , who su perv ised this work .

DESCRIPTI Ol OF ATIFOILS Method of Comb i n 5.ng Mean Lines and 'fhi cl m e ss Di strib ut ions The camber ed airfoil s ection G of ali NACA fam.Ll1es cons ide red.

herein are obtained by comb2.ning a mea.T! line and a thiclme::s .

d is'trlbution . The neces s ary geometric data and some theoretical aerodynamic data for the mean lines an d thic kne ss aistributions may be obtained f r om the su:yp lementar y fig1.U~es by t lle methoo.s d esc r ibe d for ' each faimly of airfo ils.

Q -' NACA ACR No . L5C05 'The process for ·. com.blni!1g a mean line ' and a thickness d ist ri ·· butio n to obtain the desired cambere d airfoil sectiqn j s illustrat ed in f igure 1 . The leading and ·t r ailj.l1;J ed {5 es a re defined as the forward end re arward extremi ti es, res pective ' ly, of the mean line .

The chord. line . is def ine d as the 8t Y' ai ~ht line con..n.ecting th e lea d ing arid t r ailing ed ge s . O rd .::'ne.tes of tile cem bererl a.irfoll are obtain ed by laying off the t:L1ickriess d istribut:i'o n perpendicula:c to the mean line. The abs c. issas , ordinate s, and slop~8 of the me[:L11.

line are d esignate d as xc, ' ',;'c ', end. tan ~ ) res .};j ecti vel y . If

Xu and yU re pr esent, re spectively J the · ab3c : i..3Sa. Pond. or d inate ' of

a typ ical poi nt of the uP?e r s ur fa.ce of the airfoil and Yt io t he ordinate of ' tbe s' ymme tr lcul t h ickness d istributlon at chorcbd!:le poai tio n ' x, the u:p per-surf' sc e . eoo rdina .tes are gi ven by the '.

following rel at ions: ::: X ' .

. . - (1)

sin ' 9 Yt

xu

r-: ) (2) - Gas J' + )Ie

Yi

U The corres po nding ex~ressio n s for . the lo1·;er ·· su rf ace Qoord.inates ar e

XL X +Ytsi n e

( ~ . ) v ' = y - y~ cos 9 ~ L . c '. v .

The center ' for the leadl ng - edge r a diu s i8 fOiilld b;y clra ·lin g a line through the end. of t~ec . h o rd .at · the 10 6, ding edge vTi th the slope eq ual to the slope of ttl-e mean. line a t .. that : point' ' and . ltij'in g of'f a d is tan ce from ' the J Gti ding edge along t hi s line eqyal' to ' the leading - edge r adi u s . This method c;>f construct:i.on cau s es t.he cambered a:i . rf oils to . p!' oject sl.ightly fOri-lard 'of t.he leadine -ed ge point. Because the slope at the leadin g ed ge i s the o reticall y infini te for the mean ' lines he .v ing a the o retically finite load. at the leading edge, the slo :p e of the rad ius t hroueh the end. of the chord for such mean LLn.es is usually take!1 as the sl op e of the mean

li ne at ~ = 0 .005 . This p rocedur e is .j u s tified ~ y the ma.:1ner in

vThieh t he slope increases to the theore ti callY ' infi . ni.te value · as x/c app:roaches O. The slope increa s es ' slm-rl: ....- . mtil very SIll8.11

values of x/c are re ache d. Large value 's of the slope are thus , '

limite d to values of x/c ver~ i cj:ose to 0 ahd may be , ne g lected in p ractical airfoil·design .

Tables of ordinates are incl in the supplementary data for J.ded ' a ll ai rf oj . ls for which stan dard characteristics are presented .

nACA Acn riO' ; L5C05 NACA Fo~C' - Di gi t·· Se r ies Airfoils Numbering system, - The n1.lmberil1(:, system for the N;\CA airfoils of the four-digit ser~e8 (r efere n ce l) is based on the airfoil geomet ry . The f,irst integer indicates the maximum value of the mean-line ordinate .Yc in p ercen t of the chord. The second integer indicateE; the distance from the J.,eading 'edge to t.he l.ocation of the ma:xim~l]lJ. camber in tenths of the chord . The last tivo integers indicate the ai rf oil th .. ckness in percent of the i chord. ThL:'S, Ue NAC!j 2 } 15 a1rfoH has 2-}"ercent camber at 0.4 of the c hord from. the leading ed ge and .is J..5 J?ercent thick.

The first tva .1.nte36r g taken tOGethe::.~ define the mean line, for exam Ie, the NAC.!" 24 mean line. The syuJ1letr:i.cal airfo:l sections r ep r e[lentjng the t,nicknecs distri'.J1..lt'..on for e family of airfoils are desiS-Tlated by zercs for the firs-:' t-,w integers, as i n the case of the I;AC1\ 0015 a.irfoil .

Thickness dJstriDutio!1s .. - Date . for the N.ACA 0006, 0008, 0009, 0010, 00l2, 0015 , OO:;."B, 0021, 3...Tld 0024 t.hiclmess dis-'-ributiom: i are p re sented. :'n the s UPl- 'leme n :a:L7 f:'gU1'6S. Ordinate3 for inter- mediate thic}:neS8eG may be obti"jned COY!.'6ctly by 8caLtnr, '~he tabulated orc.ine.teG :tn pr':>port· on to the thlcmes8 l'Ei.tio (r eference 1) . 'l'he lee.dL13 - e(1~}9 r adiu3 -rarieG 3.S the square of the thickness ra.t~ . o . Values of (v IV) '2, which h; ec~uj valent to the low-speed ~ re3 C1Ul~e distrilJ~'.t:Lon, C!.J.'ld of v/V are also presented.

These data we· e obta:L:'..ed by Theociorsen t s method ():'eference 9).

Values of the Yeloci ty increments f'::,va/V- induced b~T changinr; angle ll of attack ( see sectio n "Ra! .:,i d Estimati'on of I'ressure Distribution ) are also presented for an acldi tional Uft coefficient of approxi- mate13' U-.'1.ity . Values 0:' the velocity ratio v /V for intermediate thic1mess rati os may be obtained apj,lroximately by l).nea!' scalin3 of the velocity increments ebt.ained from. the tabulated values of v/V for the nearest thickness ratio; thus, V alues of the velocity-increment rat:'.o 6v /V may be obtained for a intermediate thicknesses by interpolatl n.

Hean lines. - Data fo r the NACA 62, E? 3, 61~, 6/} 66, and 67 mean

lines a r e presented tn the supplementary fisures . The dath presente d include tbe me a n-line OI'd.inatos Yc , the slope dYe/dx, -'- , he' d esign lift coefficient cl i illld the corres po nding desi gn engle of attack ~ , the moment coefficient cTIlc/4 the resultant J NAC/!,. ACR No . L5C05

preSS'l.lX'e coefficient PRJ and the velocity r atj,o t:,v IV . The

theoretical aerodynamic characcer:.i.stics Here cbt3.~ned from thi n- airfoil theory . .lU l tab ulated va:wes for eech mean l::i.ne, accordingly, vary linea rly with the maximum ordinate Yc , and data fo r simj .l a r mea..'Yl l ines ' vi th d.:i .ff erent emo1illts of comber 1·ri thi n the ust:al ran ge may 'oe obtained sinrpl by scali ng the tabulated v al ues . Data fo r t he NAC P- 22 mean line may tbus be o'btained by mul tiplying the data fo r the N .' . CA 62 mew- li ne by the ratio 2 : 6, am', for t he NACA q. mean Lne by mul t:Lplyi ng the data for the NACA 64 mean line by the r atio 4 : 6 .

NACA Five -D igit. , Series Airfoi l s Numbering system . - The numbering s:,' stem. :'or airfoils of the NACA fi ve - d .igi t series is b ased on a combinc ~ tion of theoretical aerodynamic characteristics ~Dd 3eometric characteristics (r eferences 2 an d .3 ) . The fl r st intege r indicates the em.ount of camber in terms of the r e le.ti ve :nagni tude of the desit)'11 lift coeff1cient; the de s i.gn lift coefficien'G in tenths is thuB t:h.ree - halves of the first intege r. The second and third 'lntegers to get her :indicate t he d s tance from the leading edge to the location of the w:..ximum. c embo:'C; thl .3 d ':stance in lx l Tcent of the chord is on e -h alf the numb er rep:reG':3ntel'i. by these intege:rs. The last. t y ro inte~e r s ind.ic a to the airfoil thiclme(~s in percent of the cho r d . The NACi , 2;01~~ airfoil t!1US has a design lift coefficient of 0 . 3, has :i. ta maximum cam.ber at 15 1. ercent of the chord, a.Dd has a thickness r atio of 12 percent .

Thickne ss dlstrib x ci ons . - The thicYw.'10S8 distributions fo r ai rf olls of the Ni'C_A fi ve-digi t se ri es are the same as those fo r airfoils of the NACA four - digit series .

Mean l~,nes . - Data for the !<T . • CA 210, 220, 230 , 2q-O J and 250 mean lines e r e pr osen-sed in the supplE-mentary figUl~es in the same form as fo r the mean lines gi'.,ren herein for the fou.:r - digit series.

All t ab u lated v alues for each mean line vary linearly with the maximum or d'nat or with the design l ift coefficient . Thus , data.

f or the NACA 430 mean line may be obtained by multiplying the data fo r the NACA 230 ~'1.ean li n e by 1:.11e r atio 4 : 2 and for t.ho NACA 640 mean line bJ roul tip l ying the da.ta for the NACA 240 mean l.ine by tho rati o 6 : 2 .

NACA I - Se r ies tirfoils ~Jumbering system . - The NAC,I.\ 1-series a:!. rf oile are designatod b y a five -d igit numbe r - aG, fo r e xrunp le , the NACA 16-212 sectio n .

Th e first integc~~ r ep r esents the series d.esignation. The seco nd j. ntog r indicates tho dietanc 6 1n tenths of' the chord from t h e lIIACA ACR No . 1,5C05 leading edge to the posit ion of m. llllmV1l1 pr es8ure fo r th e symmetrtcal section at zero lift . The first number follovi.nS the dash indicat e s t he am o un t of c81l1.ber expc.>essed 1n tec.'IllS of the d esign lift coef- f'ic i ent in tenth s , and. th e le8-:' tyro, numbers together indicate t~e th i ckness in percent of the chord. The commonly used sections of this farnily have minimum I; ressure at 0 . 6 of the chord from the leading edge and are u8'J.8.J . ly referr ed to as tho NACI1, 16 -ser ies sections .

rJ:'hi ckness distrib~~tj .o n s . - Da ta for the N _~ C J. 16 - 006, 16 -0 09 , 16-012, ].6- 015, 16-018 , and 16 - 021 thic~me 3s d1striOutions (r eferen~e 10) are r!'ese nted :1.n the 8up]J1ement8, ry figures. These (lata are si mil a r in f o rm t o those e.i. rf oils of the NACA four-digit series , and d.ata f or ~l.Ilt erm. e d.ia te th.ld::rJ.esG r at:i.os may be ob t aine d in the Sa5e manner .

l1ean lines . - Th e NACA 16 - ser:ies airfoils as commonly 'used are cambered with a mean line of the vniform-load tYIJe (a = 1 . 0), which is de sc r ibed u..'1.der '"he 8ec~~:i.on for the NACA 6 - se r :L8s airfoils that follows. If arw other tY "fi 6 of mean lirrs is uued} this fact sho uld be st E~ ted in the [~i r foil d,8IO'i{jnation .

'}.!P , CA 6 - Sec.>ies Ai rf oile ~umbering syst em . - The HAC;:, 6 - series airfoil,-: are usually designa.ted by a_ s1- -digit !Lmbe r' '.:;ogether 1.'.. th a. stat ement sho' , ring the type of mean l i ne used . F or exam~le, in the des l gnation

NAC A 65, 3 -2 18, [) = 0 .5, the " 6" i s the series designation. The 11 5

denotes the . chord o}'i8e pos1tio n of minimlJI lJ. pressure in tenths of the ch o rd behind the leading ed ge fo r the b asic symmetrical section at zero Eft . ThG " 3" folloving the connna gives "Chs range of lift coefficien t i n ' ~e n th8 above and belo~'T the design Ij,f-t coefficient in vrhich favorable pressure gr a dien ts eX::'st on both surfe.ces . The "2" follmling the dash gives the design lift coefficient in tenths .

Th e l as t tyro di gi t s i nd icate the airfoil t!1ickness in percent of

the chord . The d.esignation "a = 0 . 5 shows the ty-pe of mean line

used . Wnen the mean - line d esignatio n is not given, it is understood th at the vnHorm. - load meaIl Jine ( a := 1.0) he.s been used .

",Then the mean line used i s obtained by combining mQ:!:'e than o ne mean lin e, the d esign lift coefficient. u sed i n thE':: designation is the algebraic sum of the decoj.gn 1 ift coefficients of the moan lines used, a nd th e me[;.l1 lines are d esc ribGCl i n t he stateme nt follovTiIlB the number as in the following c ase : -, a a.5,

-= 0 . 3 l

c7,' /'- ~ ""' 81 l ....

NACA O)} j -C:J.. ,) /' a = 1.0, -0 1 I C7 • = • 1 - l ,-' JlJACA ACE No . L5C05 Airfoils hav i ng a th i ckne ss d ist r i b ution obtai n ed. by linea rly i ncre asi n g or dec r eas:Lng the or d.ina te s of cne of the origi n ally derived thiclrness d l st r iDut io n s are d. esignated a.3 i n t h e follo~.;i n g example : NACA 65(318 , - 217, . a ~ 0 . 5 The s ig ni fj.conce of all of the nUl'1J.oe r s except those in the :r. aren theses is t h e SaT:le as before . The first nUL'lber and the last two nunibe::.:s enclosed _ in the pe.: ~ enthe .3 es denote J r espe cti vely ) t he low-d:rag range and the ti1id ; ne8 s i n pel ' cen't of t...'1.e cho rd of the o ri g inally derived thiclm.ess d is tribu4 ~ior.. .

The mo r e r ecent NAC 6 ·- serj . es airfoils a r e c.erived as members of t hiclrn ess famil ies ha7 i n e; a simple relation s hip D eb'leen the conformal tr ans~ormat:;'on8 for airfoils of d.iffe r ent thic kn ess ratio s but having mi n im'J...7Jl p :c essure at the sarne ch o rd vise posItio n .

Th ese airfoil'" a re dlstincuished II ' om the ear ' lier indi v idually derived al r foils b y \rri ting the numb er indicating the lmv-d r ag ran ge e.s a Gubscr i:pt; for example, NACA 653 - 218, a·- 0 .5 For N JI.C II 6- ·s er:i .e s ai,rfoi l s havin g a thi.ckness r a t io less than 0 . 12 of th e chord the subscript n um b er in d icati n g the low-drag ran ge shou ld be less than unit y . Rather thfu~ ~se a fractio nal number ) a subscript of uni t3 ' w as o ri g inally em ployed f or th ese a i r fo ils . Si nc e this us age 1.s n ot c ons.Lste n t ~"i th the previous definition of a nll111De:::-- indicatin g th e lOvT -dr ag ran ge , the d .eslg n at i on s of ai r fo::'l sect i on s ha vin g a th ic kn ess r a tio less than 0 . 12 of the ch or d a r e now gi v en \V~l t hou t Guch a numb er . As an exa m ple , an NA CP . 6 - series ai rf oil havin g a thiclm.es8 r atio of 0 . 10 of t h e cho r d vr o uld be c.es igna ted.

NACA 6 5-210 Ordi n ates f or the basi c t hick ne ss di st ribut~on6 d esig nated by a s ubscr ipt are slightly d iffe r ent from those for the co rre sponcUng indi vidually der ive d t hickne ss d, l. s t r nution s . As b e fore, if t he ordina t es of the 'b astc thiclme 8s d i s t ribut ion have te en changed by a f a c to r, the :tb\r- dr a8 r ange and. t hickn eRs r atio of the o' riginal t h ic knes s d is tr ibutio n are enc los ed in :pe r e ntheses as follows : a =: 0 . 5 If J hm . reve! ·, t he ordinates of a ba s ic t hickne ss c.istr 1 Dutio n havin g a thickne ss r atio le GS - than 0 . 12 of the chord. h ave been NACA A CR No. L5C05 changed by a factor, the nu m ber indiccttng the lou-drag range is eliminated and. only t~e orisi n .::.l thickness ' ratio is enclosed . in I, arentheses as follmvs : If the design lift coeff icient in tenths or the airfoil thickness in per cent of cho rd are not ,,,!lole intesers, the numbers giving t,hese quantj. ties are us-.. . lal: .y enclosed in parentheses as in the following desi g nation :

NACA 6')('")'8\-(1. )(16.5), a = 0 •. 5

, J .L) .

Some early experimental airfoils 'are designated by the insertion of the letter x immediately preceding the h;;'];!hen as in the designation 66,2x-115 . .

Thickness d.istributions. - Data for available NACA 6-seri68 thicb1ess forms ~e presented i n the supplementary . figures; These data are comparable with the similar dat £t for airfoils of the NAGA four-digit series, except that ordinates for intermediate thick-Dess8s may not be corr ectly obtained by scaling the tabulated ordinates proportion a l t o the thickness ratio. This method of changj.n g the ordinates by a f actor· will, hm.rever, produce shapes satisfactor ily approximating members of the familY 'i f the ch~~e in thickness ratio is small. Val es of v/V and 6va/V for intermedie:.te th,i. clmess r atios may be approximat ' sd as desc:ribed .

for the NAC1\. f?ur;-digH series ..

Mean lin es . - . The mean lineS commonly used ",i th the NACA 6-ser1e8 a irfoils - produce a uniform chord,tlJse loading from the leadin e; edge

to the point 2 = a and a linearly d8c:C6asin~.10ad from this point

to the tra.iling edge . . D a.ta for I'LACA raean lines vi th values of a

6Clual to 0 0 . 1,0.2). oj, o . 4~ 0.), 0.6, 0 . 7, 0.8, 0.9, end 1.0

8. re presented in ' the s u"(:rplementary figur~s. The ordine.tee "rere computed by the follmv;:ing formula, '\-Thich r ep resents ~. simp l ification of the origtnal expression for mean - line ordine.tes given in ref e renc e 11: .

, , . ~

NACI'. ACR no . 1,5805

,...

I 1 '-'

cI~ '2 Yc "-

x\

-< 1 I' ( - -~ - a

:"oge

=

c 2rr(a + c

cJ

1 ~ l l~ a I_~ ~

- [ ,2 \2] x, x \ ( x \ 1 (:

- ~ , \

- .:... ) leg 1 - -)+ - 1

- -- )

~1 - t(a

c ,e c 4

c j

c J

x -1

x

(6)

log , :?S h-, ) - -

+ e

c e c

cJ

where

- -~ )' +t

_.I

- a)2J + g

The ideal angle of attack ~i co rres po nding to the design lift coefficient is gi ven by C2; eXi =0 :' h 21((a -'- +T) The data are pre :=: ented for a de sign lift co efficien t cI i equal to un i ty . All tabul a ted. va lues -;i FJrY d ir e c tl;y with the design lift coeff tcient . Correspond : Lng (lata fo r similar mean lines with other design lift coefficients may accordingly be obtained si mp ly by multiplying the tabulated values by the de s ired desig n lift coefficient , In order to camber NA CA 6-series ai rfoil, mean lineR are usually used havin g values of a equal to or g rea te r than the d istance fr om t he lead ing ed3e t o the location of mi nimum IJ r es8 ure fo r the s elected thicki'1ess di stribution at zero 1ift , F0T special purposes , load di st r i bu tions othe r than thos e c o rre spo nding to the r simple mean 1 tnes rna: be obta :i .ned by c ombin i ng t,vo or more types of mean li ne ha ving ~ ) osi tive or negative valu es of the de s ign lift c efficient , The ge ometric and aeroc..ynamic characteristics of such combinati on s may be obtained by algebr ai c a dO .i t io n of the values for the com po n ent mean li ne s , NACA 7 - Series Ai rfoils Numberin g SY 8 ~~~ , - The NACA 7-ser 1es ai rfoils e re a ,eaigna t e d by a number of th e follm.;'in g type ( nference 12): N.li.CA 747A3 15 NACA ACR No . L5C05 The f i r st n umbe r "7 " i n dj _ c ates the se r ies number. The . ,second n um b e r "4" i nd icates the . extent over the upper surface, in te:c .. t.hs of t h e cho rd fro m the l eE' .d i n g ed ge) of the region of favorable pr essure gr adient at t h e des i gn . lift c oefficient . The third num be r "7 " i nd icates t h e ex te n t ove r the Im'Jer surface, in tenths of t h e cho r d from the l ea d ing ed ge ) of the region of favorable p re ssur e gr adien t at th e d esign li f t c oefficient . 'll1e significance of t he l ast gr oup of thr e e numb e rs is the same as for the previous NACA 6-se r ies airfoils . 'l'he lette r " A" which follows the first three numb ers is e. serial lette r to distinc;,uish different airfoils ha v i n g pa r ameters that Hou.ld co rr espond to the SaIne ... "lumerical d esig n atio n . Fo r exampJe , a second airfoil having the same extent of fav or ab l e pr essure grad:! en t eve r the ui1per and lovler surfaces) th e s ame de sign lif t c oeffiCient , and the same max:i.mUill thiclmess as the or iginal ai r foil but ha v ine a different mean-·line combination or t hiclme ss distribution ',vould. have the serial letter "B". Mean l i n es u se d for the N.CA 7 - series airfoils are obtained by combining t wo or mor e of the previously described me~~ lines. A list of the th i clm ess distribu.tions and mean l ines used to form these airfoils i s pr e s en te d ~n table I . The b asic thickness distri'bution is give n a designation similar to those of tbe ~inal c~bered airfoils .

F or eX8n:ple ) the basic th~clmess (Ustrib1..ltion for the NACA 7L.7A315 an d 747A415 airfoils is given the d.esignation NACA 747A015 even t hough minimUll1 l)l"essure occm"'" at O . 4c on both upper and lower s ur faces at zero lift . Combinat: .on of thl.s thickness distribution 1 vU h the mean lines listed in table I for the NACA 747A315 airfoil ch anges t h e pressure distribution to the desired type e.s shmm in f igure 2 .

Th i c lmess distri b utions . - Data for available NACA 7-serles thi c kn 8ss distributions a r e ' prese n ted in the supplementary figures.

Th ese thickn ess distributions a. r e individually derived and do not fo rm th ': ckn ess families . The t hickness ratio may, however, be c hange d a moder ate mnount - say 1 or 2 percent - by mul tiI · lying t he t ab ulate d ordina.tes 'by a suitable factor without seriously

a. lt er ing thei r charCJ.cter:tstic8 features . Values of (vjv)2 and

of v/V f or thinne r or thicke r thickness distributions m.e.y be a pproX imated by the method of equation (5) . If the change in t h ic kn ess r aUo is small, tabulated ValU06 of u.va/V TI!.h.y be aplilied di r e ct l~T w it h r easo n able accur a cy .

THEO:mTICAL CONSIDERJITIOlm Pressure Distributions A kn m oTl edge of the pr essure d ist:rHution ove r an airfoil is des i r able fo r stl ~ uctural d esign and fo r estimation of the critical NACA ACR No . L5C05 Mach number and moment coefficient if tests 8 ~e not available. The p re ss ure distribution also exe r ts a stron e or predominaJlt influence on the bound ar y· layer flm! and, hence, on the a::'rfoi1 characteristics .

It is therefore uS1..18 , 11y advisable to relate the airfoil charac- teristics to the pressure distribution rather t han directly to the airfoil geomet r y .

Methods of de:'ivatj.on of thiclmess di st riov . ti on s . - As m entioned :L n t he s ection It Hist.or1cal De velopment, It th e basic sym me t rical thj.ckness distribu t:J.o ~ 1S of the NAC/', 6·· a. 11d 7-, eries a irfoil s , together 'vi th their corresp ono.i ng ' l; re ssure dj .st ributi o ns, Ol'e derived . by means of conf o rmal t rfuiSf orm.&.tions . The tnmsforma ,tl .on s u se d to relate the ·kn01m flm { abou-(; a circ le to that about an a.il~foil sectlon were

developed b y Theodors en in ref erence 9. Fievre3 s hows s ch e matically

the si g nificance of the var:!.ous J.thase s of t he pr ocess .

Th e circl e about lvhich th e flow is origiIlal l · calcul a t ed has w ' its c ente r at the origin EU1d a radj .u8 of ae ;' o The equa tion of this c ircl e in complex c oo rdin a tes is tlJ +itY.

.0 'f z - ae wh e r e z complex variable in CI rc le ~ lane

¢ 2 ngular coordinate of z

a ba s ic len gt ~ UGu8 , 11y c onsiderod unity \j! 0 constant determining rad1us of ciY'cle Th1s true c ircle is transforme d "into an arbitrary) v. lmost circular curve by the r e l at ion (\jJ .. L~ ) ~.i ( n .. ¢) ( 8) z ! := e z the eCluati.on of t.he almost circ1)~ar curve J.8 NACA ACR No. L 5C05 where Zl comp lex variable in near- c ircl e plane aeW radi al coordinate of Zf

e aP~Qlar coord inate of Zl

In ord e r for t.he t ran sfo rlJ1..ati on (8) to be conformal~ it is necessary

that the quanti ty ( e - ¢) (gi ven the symbol - €) be the C onj uga te

func tio n of (W - Wo); that is] if e: is represented by a Fourier series of the f o rm i n n¢ then ( \jJ -- V o) is given by the rel ation co co

(1 - W ) :=L An cos n¢ + L_ Bn S j.n n¢

o 1 1 This relat ionship, indicat e s that, if the function £(¢) is given]

( \jJ .. W 0 ) can be c alculated as a fu..n.c tion of ¢. Means of performing

this calculation are pr esente d in refere nce 13. The transformation relatin g t he almost circular curv e to the a:rfoil shape j.s f- := Z t + a

!, zr

(10 )

where b i s the cOD~lex varia bl e in the airfoil p lane. The

coordinates of the airfoil x and ~T are the real and imaginary

l'arts of b} r espectively . These coord i nates are given by the

rel ations

x := 2a cosh \jJ co s e (11)

y := 2 a sinh V sin G (12)

The vel ocity distribution i n terms of the airfoil parameters W ' and £ is 81 ven exactly for perfect flu:! .d fl0"1 by the expression

/

NACA ACR No . L5C05 where v local velocity over surface of airfoil V free-stream velocity section angle of attack Clo average value of IjJ J \(to

(t.t\0

E: at t r aili n g edge value of fTE The basic s ymmetr ica l shapes were de r ive d. by assuming s uitable

values of dE: /d¢ as a function of ¢. These v al u es "ere chosen on

the bas i s of 1) revio118 experience fu"1. d are subject to t he condit'o n s that rr cl . E: := 0

r

. a(J.

J

o

and d(/d¢ at ¢ is equal to d. f/d¢ a-:' -¢. These conditions are

necessary f or obte . ining closed sY1ll metrjca1 3h apes . Va lue s of E:(¢) 'M ,

were obtained sir.lpl;y b:,r intel3rati · !l.. 3 d¢ a.¢: Values of <V(¢) "Tere

fovnd by obtaining t he conjugate of the curve of €(d) and adding

a valu e \(t o suffide n t to mE l. lce · the value of \(t equ~l to zero at ¢:= rr • . Thi s condi tj.on ass ures a sharp . trailing -edge sha p e.

In as much as sm a ll. changes in t he velo c it y di 87r ib ution at any dE:

point of t he surface are app roxImatel y proportional t o 1 + dif

( eee refel'ence 14) , the i n Hie . lly assume d values of d€/d¢ were altere d by a process oi' su ccessiv e ap p roximations until the desired ty pe of velocity d:l.str i bu ti on '!las ob tained. JI..fte r the f i n al values of \(t a nd E: were obta i ned, t he o rd inates of t. h e basic tilickness dis t ribut io n Here compu te d by equations (11) and (J.2).

When these compu tatio ns 'vlere made, j .t aI rpea r ed t hat there was an optimum v al ue of the leadj.ng - e dg e r a d ius d epen d ent upon t he ai r- foil thickness and the position of minimum pr ess ur e. If the lead1ng - e dg e r adius was too small, a pr cmat ur o ~eak in the p~essure distri- but io n oc curr ed in t h e j .mm e d j.at e v i c inity of the l eadi ng edge a s the ang1e of a ttack vlaS inc r eased . If the le adi ng -ed ge radius ~yas too lar ge, a pr emat ur e peak o ccurr ed a f ew pe rc e nt of the ch o rd behind the loading e dg e . With t h e cor r ect l ea d ing - edge r f::. dit<B, the pressu re dis t ribut ion becl?..m e n ea r ly fla t over the forward po r tion of t he air- foil b e fore the normal lea d ing - ed ge ~cak formed'at the h i&her lift

coefficient s . Curv es of tho paramoters \If J E: J d'iJ/d¢ J dt./d¢ plotte d

agai nst ¢ for the NP. CA 64 -01 8 ai rf oil sectio n are gi ven in figur e 4.

NA CA ACR No . L5C05 Expe r ie n ce has shmm the.t, Vlhc n the th~ c kness ratio of an or ig i nally d01'i vcd bas~,c form Wi .S l,ncreased merely by mul tlplying all t h e or d j,nates b;y a constan '~ factOl~, f:ill unnecessarily large dec re ase in the cr:;.tica l spee d of the resulting Election occurred .

R ed u c ing the thickness r a t io in a similar manJ."1er ca'J.sed an unn ec essarily large decrease in tbe low - d.rag ren;;e . For this r eason, eac h of the ea rl ie r FAC]" 6-se r ies sectj,on3 was 1nd1 vi dually d erived. . It ,.,as later f o'l;llC\. that it i,ra.s pO::3sible to derive basic ai r foil pa r arnete r s \j.r and. <:: that could be mul. ti:plied 'by a consta11.t -ractor to obtain a::.rf oi13 of various thickness ratios, F::.thou't having the afo re me n tio::led limitations in the res1..,l ting sections . Each of the m ore r e ce n t families of NACA 6-series air- foils , ~n vThieh nu merical su b scripts are use d in the designation, hav~. n g mi n i:nUID ~pres8ure at a g1 ve::l chord,dee :posl tion was obtaj,ned by scaling u :9 and dmm the basic values of the airfoil pcrtuneters \j.r an d <::.

.

T heo r etical prescure distributions ( indic:1ted by ( ~)) for

a f arnEy of 17ACA 65-series airfoils covering a range of thick.ness ra t ios are 151 ven L11. fi t' 1J2'''' 5( a). 'l'h.is figure shows the typical increase in the magnitude of the favorable :pressure 6radi8Clt,increase in max:LrlUID veJ.ocity over the sUl~face) and. increase in the relative J1ress u re recoveT" over the :. ear portion of the airfo:il ,.,:2. t~l increase in t h ickno GS r a. t.io . Figure 5 ( b) shows the l)reasure d5.s tri'bution for a seri08 of bes':'c thickneE,ls forJYIJ:: h&V:)11-13 e. thicl.:...'1cSS rat.:..o of 0.15 encl h avi nG m.i.nL1um ~ress ure at varioU8 chorc1.wise posi t':'ons. The value of the Ni . j,m um p re3Eur c coefficj,en":, 18 seen to decrease and the masni tude of the p re8G1.U ' O rf.,cover;r over the ru2:C portion of the ai r foil to inC:C 08. Se iVith rearward. movement of :;h0 point of miniu.u..':l .:. reSS1J~ ' e .

The pr csEmre distri-bt~tio n for one of the hasic symmetricaJ, thickness d istributions at va r ious lift coeffi",ients is shown in

figure 6 . . At ze r o lift the pr eSSITe distribution8 over the uppe'

and 1 0vE, r surfa es a r e tho same . As -;; h o lift coe f ficient is incremJed ) tho 810pe of the prossure distribut1.on over the for.~ard portion of t~e upper surfacQ decreases until .i. t 'Decolles flat at a 15ft coefficient of 0 . 22 (th o end of the lm,T-drag ra..11.ge). p,s the lift coe:ff~cl6n~ is incroLsed beyond thic valut) j the usual peak in tho pressure di 2.t ribution form. s at th E:; loading edBC' .

~api.9-~9t .i1:'la t io n of pr essure distributions . - In the discussion that foE.m.,8 , . the te r '!ll " .pressure dj.stribution" is used to signify t he d ist r ibutio n of the s't;atic pr ess ur es en the upper and lO'llfer surfaces ll of the air-foiJ alone the chor d . The term II load dj,strib'J.t i on is u sec1. to sJgnify the distribu -L.: ior. a long the chord. of tho normal force r es u lting from the o.iff crenco in ::; 1' o08uro on th0 u2p~r and lm{er s ur faces , NACA ACE No. L5C05 The pr essure distr:'bution about any airfoil : i.n potent2.al flow may be calculated accurately by 8 generaHzatlon of the methcds of the pr evious section . Although this method is not unduly laborious, the comp ut ations reCluired ar e too lo ng to perIni t Cluick and. easy calculations for large n~bers of airfoils . The need for a simple method of Quickly obtai.nil'1..g preesure distributiolll 3 vi th engineering acc1.1racy has led to the cleveloprr:ent of a me4 ~ hod (refere::1ce 15) cOL'ibining features of thin - and thiclc - airfoD. theory . This simple method mruces use of previously calculated characteri s tics of a lim::i.ted n1.":ID.be r of mean l ines and thickness distributions the.t may be combined to form large num b ers of a i rfoils .

Thin - airfoil theory ( references 16 t e 18) shows that the load

distribution of a thin airfoil may be considered to consist of : ( 1) a basic c.istribl'-tion at the ideaJ_ angle of attack and (2) an ad d itional dtstributio n pr opor tional to the angle of attack as measured f r om t he ideal angle of at t ack .

T'n8 first load distrjbution is a function only of the shape of the thin airfoil , o:c ( if the thin airfoil is considered to be a mean line) of the mean- line geometry . Integration of th::_ s load distribu t ion along the chor d r esult's in a nOY"_n a J_-force coefficient ,Thich, at small angles of attack , is 8ubsta..'l.tla lly equal to a lift coefficient cr l' .Thich is clesig n. :lted the ia.ea l or d.esign lift coe · 'ficient . I f , mo r eov er , t he camber of the mean 11ne is cl1anged by multiplying the mean - li ne ordinates by a const a nt factor, the r esulting load distributio n , the ideal or design ungle of attack G ~ l anct the design lift coeffio::ient cr . may be obtainecl simply l by multiplying the or iginal values by the same factor. The charac - te r istics of E, large number of mean lines are presenljed in both e;rar-hical and tabula r form in the supplementary figures . The load - d.istribution date- are pr esented both 1n the form of the resultant pressure coefficient PR and in t he form of the cor:'es?o n ding

veloci ty<ncl'em e nt ra.tios . 6v Iv. For posi -:::'1 ve design ' lift coefficients}

thes e velocity - in c rement r atios are positive on the upper surface and negative on thc lower smface j the opposite is true for negatiye desi&D lift coefficients .

The second 108.0_ (listribution) which re s ults f r om changing the angl.e of attack, 18 desic;nate d he~ein the "additional load distribution !!

and the corre8~onding liit coe~ficie~t is designa t ed the " additional lift coefficient . " This B.deli tional load distribution contrib u tes no moment· about the Cluarter - chor d point and, according to thin - airfoil theory, is ind.epend.ent of the airfoil geometry except fo r angle of atta.ck . The additional load distr i bution obtained from thin - airfoil theory i s of limited pr actical application, how'ever, because this simrle theor ' leads to infinite v3.1ues of the velocity at the r~ACA ACR No. L5C 05 leading edge. TIlis difficulty is obvi ated by the exact thick- airfoil theory (reference 9) ;'Thich also shows that the additional load distribution is neither completely indepe n dent of the airfoil shape nor eY..B , ctly a l i neer function of the 'l ift coeffic ie nt. For this reason, the aQditional . load distr ibution has been calcluated by the methods of reference 9 for each of the thi ckne ss distribu tio ns presented in the supplementary flgures. These dat a are Ilre s ente d in

the form of veloc i ty-increment ratios 6v /v correspon~ing to an

a addi tional lift coefficient of approximate ly unity. Fer posi ti ve additional lift coefficien~s, these velocity-increment r a t ios axe Ilosi ti ve on the upper surf a ces ana. nega tive on the Imver surfaces j the opposite is true for neg ative aC. di tlonal lift coefficients.

In addition to the Ilressure di s trib utions asso ci ated with these two load distributions, another p ressure distribution e xis ts which is associated ,'Ti th the basic symmetrical thickness foro. or thickness distribution of the airfoil. Thi s pressure distr i bution has been calculated by the methods described in the previous section for the condition of zero lift and is pr ese nted in the supplementary figures ( · 2

as \ ~) , which is equiv a lent a t lo w Mach numbers to ~118 pressure

coefficient S: a nd us the local veloc ity ratio viV o Thi s local v el ocity r a tio is alw ays posi ti ve anQ is the same for corresponding points on the upper and lm"er s 1.1Tf ac es of the thickness form.

The ve loc i ty di s tribution a bo ut the airfoil is thu s considered to be 'compo sed of thre e sepa.ra te e.nd. ind. epondcnt components as follows: (1) The distribution corr espond ing to the v elocity distribution over the b asic thickne ss form a t ze ro angle of attack (2) Th e d is tribution co rr es po ndin g to the design load di st ribution of the mea..'"l line (3) The di s tri'bution corr espon ding to the additional load distributi on ass ociat ed 101i th an gl e of attack

Th o vel oei ty,-iner e ment r atios 6 v IV fmd 6valV corr esponiing

to components (2) and ( 3) are add ed to the velocity ratio corre- spo ndin g to compone nt (1) to o bt ai n th e total velocity at one poi nt, from which the pr ess ur e coeffici e nt S i8 obtained.; thus, NACA ACR No . L5C05 When this formula is used, values of t~e ratios corresponding to one value of x are ad.ded together and the resl)~ ting value of the p ressure coefficient S is assigned to the airfoil Glu~face at the same value of x .

The valu es of v/V and of ~v/V in equation (14) should, of course, correspond to the ai rf oil geometry . ' Methods of obta.in::'ng the proper values of these rattos from the values tabulated i n the supp lementary fj,gures are presented in the previous section "Desoripthm of AlrfoilA . II . When the r atio 6va/V ha s tl1e valUe of zero, the resulting distribution of the pressure coefficient S will correspond approximately to the preseure distribution of the airfoil section a.t the design lift coefficient cl of the mean lin e , and the lift l ' coefficient may be assigned this value as a. first aJlproximation .

If the pressure-distribution cl:Lagr81n is integratecl, hO·vTever , the va;lue of c7, .,ill be fmmd. to b e greater than cl . by an amount l dependent on the thiclmess 1'e:t.io of the basic thickne ss form.

ThE? pressure distribution '\01111 usually be desired. at some s pecified lift coefficient not corresponding to cl .. For this 1.

purpose the ' r atio 6v /V, DlUSt be ass ign e d some value otto .ined. by a multiplying the tabulated value of th is ratio by a factor f(~) .

For a fir st approximat10n this factor Dlay be assignec't the value

(15)

;where c7, is thl9 lift coefficient for , '\oThich the pressure distribution is desired. If g re ater accuracy is desireG., the value of f(~) may be adjusted by trial and error to produce the actual desired lift coefficient as determined by i nte gr ation of the pressur ' e-distribution diagram .

Although this method of superposition of velocHie8 has inadequate theol"etical justification, experience ha s shown that the results obtained ' are ad.equate for engineering use . In fact, the results of ev (;m the first approx i mation s agree ' .Tell y.rith exper i mental

data and are adequate for a t least preli m~& ry consideration and

selection of airfoils . A , comparj .so n of a first-approximation t heore:tical . pressure distrib u t, ' ion vith an exp~rimenta.l distr:i.bution is shown in ' figv.re 7 . Some ' discrepancy naturally occurs oetiveen the results of experiment and. of any theoretical method based. on potential flo.l because of' the presence of the l)oundLU'Y layer. These effects are smsll, however , over the range of lift coefficiente for vThich th e boundar y layer is thin a nd th e dr ag coe fficient i s 10'\oT.

NACA AC-;'{ No. L5C05 ~ume r ical example~.- The folloh~ng numberical examples are included to illustrate th~ method of obt aining the first- appr oximation pressure distributions: Example 1: Find the pres~l.U'e coefficient S at the station

x = 0 . 50 on the upper and lOvTer surfaces of the NACA 653-41~ ~i~

foil at a lift coefficient of 0.2 .

From the description of the NACA 6-series airfoils, it is determined that this airfoil is obtained by combining the

NACA . 653-018 basic thickness form with the a = 1.0 type mean

line cambered to a a'esign lift coe'ffiCient of 0.4. The following data are obtained frdm the ' supplementary , figures for this thickness

form and mean line at ' y.. = 0.50: '

,y = 1.235

V ~va

= 0.157

V

6.v = 0.25 0

V The desired value of tWa/V i s computed as fol1ovTs by use of equation (15): 6.v a

-- = (0.157)(0.2 - O.h)

V

= -0.031

The desired value of 6.v/V is obtained by multiplying the tabulated value by the design l~ft coe fficient as stated in the descriDtion of the NACA 6 -ser ies a irfo ils~ Thus, 6v = (0. 256 ) (0 . 4) .

V -

= 0.100

Substi tuting tb.ese values in equation (14) gi.ves the following values of S: For the upper surface S = (1.2 35 + 0.100 ' - ' 0.031)2

= 1.700 , .'

L5005

NACA ACR No.

.

surface t he lower For + 0.031)2 S :: (1. ·235 ·- 0 ·.100

= 1. 360

the station 9t S at coef ficie pressure ' Find the Example 2: 65(215)-214, of the NACA s urface s and l01{e+' the upper = 0.25 on , x of 0.6.

' coefficient ' at a lift airfo~l a ·= 0.5 " ···.t.· ..

was o btained a irfoil th at this tion shows des igna The airfoil ordinates the by multip lying obtained s form g a thicknes combinin by

a = 0.5

",1 th the 14/15 by the factor NACA 652 -015 f orm of the of 0.2.

i cient ign l ift coeff to a de s cambered mean line type v /V of 1.182 for a v alue g ive figures supplementary The The form.

sic thickness .652 -015 ba t he NACA 0 .25 for at x::;: (5) as formula applying d by v/V is obtaine value of desired folloW's: v )1!±. . + ]

(1.182

.

V -- -- 15 ::;: 1.170 ~va/V values of following the figures s upplement8-~ From the thickness basic the fo llOiving 0.25 for

at x =

obtained are : forms I ~Va vat form ' / Th.iclrnsEis x ::;: 0 .25 0.290 652- 0 15 NACA .2 82 651-012 NACA assigned may be of 0 .2&( of ~va/V ' the value a t-ion : By ihte~pot then a /V is lue of ~v de s ired va . The form 14 - percent-thick to the io n (15): u se of equat f0110.m by as computed ~va 8 - 0 . 2) (0 . 2 7){0,6

--v- =

= 0.115

NACA A CR No . L5C05 Data presented. in the suppl ementary f igures for tl:e a = 0 .5 type .

mean lines give the v alu e of 0 . 333 for 6v/V at x ::;: 0 . 25. As stated in the description of t he NACA 6-series airfoils, the Qesired value of 6v/V is obtained b y multi plying the tabulated value by t he design lift coefficient . Thus, 6v ::;: (0 . 333 )( 0.2) V ::;: 0 . 0 67 Substituting the foregoing value s in eCluation ( 14) gives the values of S as follows : For the upper s~ T face S (1 . 170 + 0 . 067 + 0.115)2 ::;: 1.828 For the lo wer s urf ace 8 (1. 170 - 0 . 067 - 0.115)2 Exemp1e 3: Fincc the . pressure coefficien t - S at the station x = 0.30 on t. le uppe r and lo-:{ er su~ .. faces of the NACA 2412 8.lrfo : i.l at a lift coefi ' icien-c of 0 . 5 .

'l'he de s criytion of c:.i rf o5 _ ls of the ~JACA four-d : gi t series shows th a t th e ne ce s sary da.ta may be found from the NACA 0012 thlckne ss form and 64 m.ean line in the supplomentar;y figures . From th ese figures the fol1m·ring data are obtained:

At :x: = 0 . 30

At x = 0 . 30 6Ya

v' : 0 . 239

Fo r the NACA 64 lliean line a.t x: 0 . 30 6v 0 . 260 V ::;: NACA ACR No . L5C05

For the NA CA 64 mean line

c "L" = 0 .76

l

The va l ues of 6v IV and cI corresponding to t he ail ~ foj"l geo metry

i

are obtained by multiplying the fore going va1ues by the f a ct or 2/ 6

as eX l) la i ned i n the de s cription of these ai rf oils ; t hu s ,

6v , /2 )

(0 . 260)\t V

= 0 .0

c " (0 . 76~ ~)

I l - 0 .2,53

T he de si red v a lue of 6.va/v is obtai ned from equation (15)

as follov78 : 6v

---~ = (0 .2 39 )( 0 .5 - 0 .253)

V

;: 0 . 059

Substit ut ing the proper ~alues in e~uation (14) gives the

v al u es of S as f o ll mvs : For the uppe r surface S (1.162 + 0 . 087 - + 0 .059)2

= 1. 712

For the lowe r s ur face S (1 . 162 - 0 . 087 ~ 0 .059)2 1. 032 Effe ct of c8..'1lber on pressu :c e di s tribution . - At zero lift the pressure dis tr ib uti " ons o,r er t.le lJ.pper a..-n.d lowe r 81JIf8.cef.:l of a ba sic symmetr ical th~ ;_ c1G.le s dj.e tr ibution are, of CO' J ISe , id e::'lt:i.ca l. The e:fect of ~a1i1ber on the preS81JIe d.istritution at t~le desi.:p1 lift coeff ic::'e __ t ls to separg , te the pr eS81JJ'eG on the uppe r and. lm,rer 8Ul ~fac e8 b y fu"1 am o unt corr es ponding aPlJroximat ely to the design l oacl dist ril mUon of the: mean line '. itf.."1en th e local value of the d esign load d ist r:ibut.ion is positi v e, the p r e3sUl ~ e coefficient S on t!le upper surface i8 increased (d e creased a bsolute pr essure ) NAC!-. ACE Ho . L5C05 v .r hereas -tha-t on the lower 3 1.U~ fece is C\ecreFtsed . T!11s effect 1s shown in f igure 8(a) for variOl":'s amount a of camoer.

The maximum value of the })ressure coe~ficient on the 1..YIrper surface at the design lift coefficient increases with the desj .gn l if t coefficient and fo:;.' a given d.esi8n. lift coefflcient increases wi th decreaslng values of a . The :r.e s; .llt is to cause the critical Ma ch numb er at the deeign lift coe ffi ci ent to decrease with increas i ng c8.1i1.ber or with the use of t ypes of mean line concentrating the load ne ar the le a d ing edge . . F igure 8 ( b) 8hm;s that the location of minimum :;: r essm: 'e on botl1 snrfaces is not affected if a type of me8..L"'1 line is u se d havtn g a value of a at le ast as large 8S the value of x/c at the :posi tj.o n of mini:nv.Dl pressure on the basic thiclme s s distri"bution . If a meEil1 Hna "I-r:l th a smaller value of a i s used ) the possible extent of l ammar flo',J elong the up:!.)er surface will be reduc ed .

Cri tical .1ach Number The critic al speed. j.B defined as the free - stream speed. at whicl1 the veloci t ;y &.t emy :poin t along tr.e surface of the ai rfo il reaches the local veloc1ty of smmd . If the ma.'Cinrum value of the low - speed p re ssure coeffic 5. ent 2 is lmo;m ei t her experimentally or from theoretical methods. the criti cal Mach nvmber may be p:cedicted approximetely b y the von K.8n,l(3n method (reference 19) .

A curve re la t ing the critical Mach nu..ruber end. the Im·l- s:geed pr ecsUl 'e coeffic i ent S has be en calculated from the equations of r eference 19 and_ included in the sU:P:91er ' lenta:c~,r figures . These predicted. c1'1 tical • Mach nu ni be r s are useful f or prel":'minar: ' cons:"derations in the ebsence of test c,ata an d ap:pea .r to corre s :9ond fairly i-Tel2.. to the Mach 11.1.mibe rs at which t~e l ocal velocity of Go un d is reaciled. in the hi g h-cri tical- s:peed ran ge of lift coeff 2 .c i ent . This criterion does not, however, appecu' to p red i c t accurately the Nach numbers at - vr!1i c!.1 la:i:'ge chunges in ai r foil char ac ter istj. cs oc c ur) es:pecially when shar:p pressuro pealcs exist at the l ead.lng ed ge . A discussion of the characteristics of airfoil sect i ons at s up e r - cr itical I' lach numbers is beyond the scope of this report .

For conven iense , curves of pr edi ct ed. critical Mad number plott ed against the l ow-s:p eed section · 1ift coeffic:ient have been included in . th e supplementary · fi g ur es for a number of airfoils .

These f ig ures are somev rhat similar to th02e of Reaslet (reference 20) but are plott e d against tho lov y- speed lHt cOElffic:le nt rath er than against th e hi gh sPGed lift coefflclent, as :i .n r eference 20 . Righ- speed lift coefficients corresponding t o those of HGasl e t may b o ob~ ai ned by multipl ying tho lOYT - s :p oe d lift coefficient b;r the NACP . ACR No. L5C05 The critical Mavh num~ers have been predicted factor / - .

V 1 _ M2 fr om theoretical p re ssure dist ri butions . For airfoils of the NACA four - and five-digit series illld f or the NAC!. 7 -· serie8 air - foils J the theoretical pressure distributions ,·rere obtained by Theodorsen~s method . For the other airfoils the theoretical pressure distrlbutions ,{e re obtained b:r the app rox imate method described in the pr eceding section .

The data i n the supflementary figures show that for anyone type of ai rfoil, the ma:x.imum crl tical Mach number decreases rapidly as the thickness is increased . The effect of camber is to lower the maximum crltical Mach number and to s!1ift the range of high cri tical !vla.ch numbers in the SmIle me.nner as for the low o.rag range . Foc.' common types of camber the rr .: l.ni mum reduction in cri tical speed for a given design lift coeff .i..cient is obtained ... ,i th a lU1iform load type of mecm line . A comparison of the data presented in the suppl e mentary iigUl~es shm ... s that NACA 6-series sectio ns have conside rably hieher maximum critical Mach numbers than NACA 21~ _ , 44 ..." and 230-series ai r foils of corresponding thickne ss r atios.

Moment Coeffici . ents Methods of calculation . - Theoretical moment coefficients may be approximated · directly f r om the valu es presented in the supplementary fig ur es for the V8rious mean. lines . These v alues were obtained f r om thin-airfoil theory end may be scaled up or dOv-TJ1 linearly '-lith the design l ift coefficient or '.tli th t.h.e meen- line ordi n ates . These theoreticc:.l values are sufficiently accurate for preliminary considerations , but experimental values should be u se d for stability and control calc1JJ.ations.

~umerical.eJS.8m:e.~§1 _ .- The follm·ring mlll1erical examples illustrate the m ethods of calculating t.h.e moment coefficients : Example 1 : Find. the theo r etical moment coefficient about the quarter-chord point for the NACA 652-215, a = 0 . 5 airfoil .

The designa.tion of the ai rfoil sIlm·rs that the design lift co e ffici ent of this air£oil is 0 . 2 . From the data on the NACA a ' :;: 0 . 5 typ e mean Ij}l e includ ed in the supplementary figures,

the value of cm II is - 0 . 139 for a design lift coefficient

c !j- of 1. 0 . The dcsireo. v al ue of the moment coefficient is accordlngly

= ( -0 . 139) (0 .2)

Cm /4

c -- -0 . 028 ---- ---- -~ NAGA. ACR 1:;0 . L5G05 EXaI:lple 2 : F in d th e theore-sic [;1. 1 1:10ment coefficlent about the qu a. :-cte r- chord point fo r the NA CA L~415 ai rfoil .

Fr o;:J the descrilrt:!.on of the r::ACP. f01.11'-o..i;::i t series airfoils, the requi r ed data is found. to be 1'1 ~ esented for the rJ.AGA 61~ meen line in tho supplementary figlITes . The moment coefficient for this mean i.i.ne is - 0 . 157 . The r equj.red value is then I~ == (- 0 . 157)',,- Q - 0 . 105 &"'1£ 1e of Zero Lii't Methods of cg,lculatior.. . - Values of the ided or design angle of attack ~ correGPondh~g to the design l.i.ft coefficient c~ 1 are included. Bmong the date. for the v arious mean lines presented in the sup p lemcnt CJ ry fiG ur es . '1']::e app r oximate values of the angle of zero lift tilE,,:! be o"btalned fron:. the data bJ using the theoretical v a lue of the lift - clll've 8:.ope f x' thin airfoils , 2rc per radian.

'1'he "lJalue of ex,., in deg::' ee8 i~J then - ~o 57 . 3 = C:' - - -- c, '1. 2rc (, i

(16)

Th e- tp.buJ_B.ted values of ~ may be scaled. linearly vi th the desi gn lift coefl'i~ient or ',11th the mean-Une o rdin ates .

Al though ther:::e tbeoretical c " nsies of zero lift may be useful in p rel im::'nar;v- clesi:3rc, they 8hould no t be u"1cd. Hi thOl.1t experimental v eri fi catio n for such _ ur:pOGOS as est~bli8h::'nt; ~he washout of a ",ing .

.ITl,lIllG:d c e.l e~: _ ?J!r...@~f . - T h. e met.h.od of' computing 1s illustrated ~o j.n the folla, in;:; e::·"!l;2.eFJ : Exemple 1 : Find. -the theoretic&l an ~; le ot· zero lift of the NP CA 652 - 515) a 0 .5 ai r foil .

T his airfoil nu mber lndic-3.tes a des:i.fJl li:f:'t coefficient of 0 .5 .

Dat a fQr the NAGJ! a = 0 .5 mf.3an line tndicutb that \i'-: = 3.04 .Then

.L

cl = 1 .0 . The desi r ed value of 01 is then

i c-... .- (3 .- oJ.j.)(O . 5) ..l.

NACA A CR No . L5C05 Substitut:Lng in e Cl u atio n (16) gives ( 57 . 3 ) (0 .5) ~ ';: 1. 5 2 - .. _ - - 211 - --- o o ::: -· 3 . 0 Example 2 : Find the theoretical ang l e of ze r o l if t for the NACA 21~15 ai !' i'oil .

r.:ACA four· - digi t - series ai rfo ils 8h Q1.'TS The d es cription of t he

the _ t th e r equi r ed valu es of C'-:l. ,mo . c7. . "Xlay be obtained -b y

m"l)~ t iplying t ~1e co rr es:pono.::'ng v alues .c· the lITAC] : 64 mean lin e or

( see supplementary figs . ) by a facto r 2/6 then

j /2\ ::: (0 . 7~')U~) <4.

o ,..., ,,,0

. c....J

(2)

- (0 . 7 )\ 6 cl · ::: 0 . 253

G1ld f r om eq ua ti on ( 16 )

0 . 25 .- 211' ;: _2 . 0 Description of F10i { around Ai rf oi l s rerfect-fluid theory postulates that the f:::"ow follo,! the ai rf oil contour smoothly at a l l angles of attack "nth no loss of ener gy .

Consequently, pe ~fe G"L - fJ .u :lcl theory i tsalf gi- es n o information

conce rn ing th e pJ. " of : lle 0. 1" :::"< 3 or the rna~;:imuJ l1 11ft of ai:cfo:i.l sections .

Tile expla.nat~Lon of these .l)henomena is fO·L 1..nd fr om a conej.deration of the e ffec ts of viseoei ty , vhlch 8.re of pr i mar-;Yimportance in a thin r egion nea r the surface of t he a:l.rfo .n called. t he b oundary layer . .

Bovndary ' laye r s :in gone::."al are of tlW types , namely J ],amin ar an d t U . l"b1,ll ent . The f.lol-T in the laminar layer is smooth and f r ee f r om any e dd y:!.ng motio n . 'rhe fl o "T i.n · the tu r bulent laye r is char a c- te r ized by the p r esence of a large num ber of r elatively smal l e ddies .

NACA ACR No. L5C05 Because the eddies in the turbulent layer produce a tran.sfer of .

momentum from th& relatively fast-movin g puter parts of the boundary

layer tp the portio:Q.s , c' lofJer to ' the surf'ace " , the distribution of

av ' erage velocity is chaxacterized by relatively higher velocities near ' the surface and a greater total bbuhdary~layer , thickness in a turbulent boundary layer than in a laminar boundary " layer developed under 'o therwise identical condit io ns. Skin friction is therefore higher for turbulent boundary- lay er flow thal1. for laminar flow. ' vllien the pressures ' along the airfoil , surface axe , increasing in the direction of flow, a ' general , deceler a tion takes place. At the outer li~its of the boundary layer this decelerat ion takes place in accordance with , Bernoulli's law. Closer to the surface, no such simple ' law can be given because of the action of the viscous forces within the boundary layer . . ' in gen eral, however, the relative loss of speed is some.,hat g!"ea.ter ' for particles of fluid wi thin the boundary layer than for those at the ou ter limits of the layer because the reduced kinetic energy of the poundary-layer air limits its ability to flow ag~inst the 'a dver se p re ssure gradient. If the rise in ' pressure i s , sufnciently' great, portions of the fluid within the boundar y la yer may a ctu ally have their direction of motion reversed and may start mo ving upstream, When this reverse occurs, the flow in ' the 1.Joundary layer is , said to be "separated." Because of the incre ased inte:::-change of mo ment um from different parts of the l aye r, tUrbulent boundary layers are much more resistant to sep arat ion than are laminex layers. Lamina:':" boundary layers can only exist for a r elatively ' s hort distance in a region jn which the pressure inpri:-Cl.ses in the ' direction 'of f1m". , Formulas for calcula ting ma~ny of the bo~dary-layer characteristics are given in references 21 'Co 23. " After Im n in ar :so paration ' oocurs, the flo., may ei thor leave the surface permanently or rea.ttach itself in the ' form of a turbulent boundary layer. Not , much is known concerning the factors controlling this phenome non. Laminar separation on wings is usually not permanent at flight valu es of the Reynolds numbe.r excE:pt .Then lt occurs near the l ea d ing ed ge und er cond itions corresponding to maximum lift. T~G size of the locally separatGd region that is formed when th e laminar boundar y layer s epara t os and the flow returns to the s urfac e decreases , with increasin3 Reynolds number at a given angle of a t tack .

The i'lo~" ' over ', a,erodYnamically smooth airfoils at low and moderate lift ' coeff :L c Je nts is characterized by laminar boundary layers from th~ leading edge back to approximately the location of the first miIl lm um-pr:essure po int on both upper and lower surfaces.

If the region of ' laminar flm., is extensive, separation occurs NACA ACR No. L5C05 imm ediatel y down st ream from the lo cati on of minimum p re ssure (ref ere nce 21) and the flo., return s to the surface almost immedi- a tel y at fli ght R eynolds numbers as a turbulent boundary la ye r.

Thi s turbulent boundary layer . extends to the traJ:L;i.ng edge. " If the ' surfaces ' are riot s uffiCiently smooth and fair, if the air st ream is turbulent or perhaps i f the Reynolds nUmber is suffi cientl y . . , " .

large, tran sition from laminar to turbulent flow may occur anywhere upstream of the calcul at ' ed laminar s~paration point .

. ." . ' .

. , , ' .

For 1m -./' and mod.e r ate lift coef f ic ients 'There :lnappr eciable separation occurs, the ai rf oi l . profiie drag is largely caused by

sk in friction and the - value of the dr ag coefficient depends main1,.y

on the r el a t ive amoun t s of lami nar ano. turbulent fl ow ~ If the locatio n of transition i s ~own or assume. d, the dr ag coefficie n t may be calculated with ' r e4so nable ' ac curacy fl'om.boundary-layer theo ry by u se ' of ' the methocls .- of' refe ' ~en ces ' 21-1- to 26 •.

. As the lift co efficient of the airfoil is inc r ease d b~

' changing the an g le of atta.ck~ ' the re s1llting ' applicatio n of the addi tional tyPe" oJ l ift d. ist ribu ti'o n mov es th~ min imum· · pressure point upstre81T! on the 'upper surface~ and the possible extent . of lamin ' ar , flow is thus · l' ed uced . The r esulting .grea'ter proportion of tu r bule nt flow, togeth er wit4 .t he larger a vera 3e velocity of flow ov er the sUrfaces , causes ' the drag tb . increase 'Ti th lift coefficient.

In the: case of many 'of ' the ol der types of airfoils, this forwar d. m6 vement of transitio n is gr ad ual and th e resulting var ia tion of " drag ,\-lith lift coefficient occurs smoothly. The p re~sure dist r ibutio ns fo r NACA ' 6-series ai rfoil s are s u ch as to cause transition to niove fOT'l-Tard sudden ly at tr..e end of the low- drag range of l " ift coer'ficients. A sh arp increas .e in dr ag coefficient to ' the v al ue corresponding to a forward location of transition on t he upper surface re sults . ' S uch s udden shifts i n transition give the -t ypic al dra g c urv e for these a irfoil s wit h a 11 sag " or " bucket " in the low-dr ag range. The same characteristic is ShO.ffi to a s~ler degree by some qf the earlier airfoils s uch as the NACA 23015 vlhe n tested 1n a 10w-tUl'bulence st r eam .

.At· hi gh iift co'efficients', a large part of . the drag is co ntr i bu ted ' by pr essure or form dr ag r e.s ul ting from separation of the ' :flOi'T from the surface. ' The flOi" over the upper surface is characte r ized ' by a negative pressure p eak nenr the leading edge } which ca u ses lamina r separat10n . The onset of turbulence causes the floll t o return to th e ' s urf ace as a turbuJen t b01.Jnda r y layer.

High Reynolds rtl1mbers are favorable to the development of turbulence and a1 d in this process . If the lift coeffic i ent is suffiCiently high or if thE'; r cesta b,lis!lID. ent of' flow following I nminar separation is unduly delayed by low Reynolds nUmbers) the turbulent lay er will rTACA ACR 1'To. L5C05 sep a:r ,t e f r om the s ur face ne8 .:':' the trailing edge and will cause l ~ ~ g e d rag inc:;,~eaces . The eventual less in lift I·d th increas i ng ang l e of attac ~c rna ,/ :;"esu.l t ei"cher f r om relati vel~ sudden :permanent sepa:rati.o n of the lrun :I. nar bounda:r~r le , yer near the leadj.Y''';) edGe or from prog r essive forwexd w~vement of turbulent s8yarati on. Under t~1e latte r condi -cioll. the flow over a relativel y large portion of the sur .ta ce ma~T be s~parated, prior to maximum lift . A ~10re extended discussion of the flmT condi tj,ons aS80c::"ated ,'ri th m,'j,:i:im1.lIIl lift is given i n reference 5 .

EX:FER TI 01TAL CEARI.CTERISTICS So ur c es of Data The primary sour c e of the \-lind- tunnel data :preGented is from tests in the Langley t'Ho-d5mensiontll low - turbulence pressure tunnel ('I'DI') . '1 ' he methods use d to obtain and correct the data are sU1llm8.:::-ized in the append,ix . D esign data obtained from tests of 2 - foot. - chord mode~8 tn this tunnel are presented in the supplementary f igures .

Some "Tind- ttLl111el data presented were obtained in other RACA wi n d tunnels . In each case , the source of the dat a is indicated and the testing tecbr-iq'..les eno. correct:;'on3 used vTere conventionaJ.

unless o'lherwj.ue indicated .

Most of the fl ight data consist of drag measurcI:':mts made by ove the vrake - survey method on either the a:!.rplane wlng 0r a "gl " fitt8d over the viin i:;) as th e test specimen. 1:lhenever the measure- mer: , ts Wel'e obtained for a glove , this fect is indicated in th6 prc:;.:;r-mtaUOl: of the elata . All data obtain e d at high speeds have boen red , ue od to coefflcient form by comprossiCle-flow methods. In the ca.sE:; of Fl.;.1 s u ch F!\CA flight data, precauti ons hav o 'been taken to ensure 1 , .!:mt t?le :cesult s pres0nted are not invalidated by cross flovls of lm'T - enorgy ai r into or out of the survey ::;>lane.

Dr ag Char[.cteristics of Smooth Airfoils P!.C£ ch e.rac~e ri8t],cs in lov; - d:~ag ra..'1g c:; . - Tho yaluo of the drag coefficient in the low - drag ranb c fo r smooth airfo:.ls is ma':'nly, a flU ctlon of the Rcyno11s numb r 8.J."1i the relb.t ::. ve exten'::' 0:::' the laminar laycr and is mode r&tely c::.ffactuQ by the airfoil 'chic lmv8s r atio emd camber . Tho 0ffect on minir1UIn dr ag of the position of minim 1..U ll pressur e which dot(;)rmirlGs the p03siblo extent of laminar f l o'fT is 8. ho",'11. in figure 9 for some NACA 6-sorios airfoils. Tho data s h ow a rOgLl.lar d8croase in dr£!g coefficitmt I,Ti th rl:JDr"h'BTd movement of mini m um pressuro .

1'5 NAC. . P.CR No . L5C05 The variat~on of m:i.n mum drag coefficient with Reynolds number for seve r al. airfo: 1s is shmm in figure 10. The drag coefficiEmt ge n erally ciecreases with increasing Reynolds number 0 .

1.1.p to Reynolds num1)ers of the order of 20 )( 10 Above this Reynolds number the dr ag coefficient of the NACA 65 ( l.l 21)-420 ai rfoil remaj.ned substa.. l1. -J:,ially constant up to a Reynolds number 6 .

cf nearly 40 x 10 The earlier :in cr eacle in drag coeff1cient Shovffi by the NACA 66(2x15)-116 airfoil may be caused by surface i rr egulari ties because the specimen tested .TaS a pra ctical- construction mode l. It may be noted that the dr ag coefficient for the IJJlCA 653 - lJ.18 airfoil at 1m, . eynolds numbers is suo - stantiallJT hi g her than that of the NAC A 0012, i-lhe r eas at h igh Reynolds number s the opposite is the case . The iligher drag of the NACA 653 - 418 airfoil sect i on at low ReJ~olds ntunber s is caused b y a re latively extensive r egion of laminar separation downstream of the point of minimum p re ssure . This region decrea ses in size ,·,i th increasing Re;ynolcls number . ~'hese d.ata. illustrE:.te the inadequacy of low Reynolds number test data either to es t imate the full- scale characteristi c s 01· to determine the ' rela t i ve me r its of airfoil sectie .s at fl igh t Reynold.s numbers ( refere n ces 27 and 28) .

The varj.ation of minimum dr ag c oefficient ,1i th camber is sho,ffi in figure 11 for a nun ~be r of smooth 18-percent -t hick NACA 6-serie2 ai rfoil s . These data shmv very little chan ge in minimum drag coeff i cient vrith i ncrea se in camber . A lar ge amount of systemat::.c . da.ta j.B inc luded in figure 12 to shoy! the variation of mir:.imum drag . coefflciE.nt v1: Lth thickness ratio for a number of

NACA airfoil se tions . ran e;:i,ng in thickness from 6 r " ent to

2lJ. percent of · the chord . rL'he minimum drag coei'ficiont is seen to ii.1C r 8a Se l>1i th incrcl:so in thiclmess l"8 ,t ::. O for each ai rfoil series.

Thj Fl increase , hm"~vor) is g .ce o te r for the NACA four- and fivb - digit, · pE- ::::- ios al . !"foil s (fi g . 12( a )) than for the NP,CA 6 - 8 ri os .

ai rfo"1 8 (fi gs . 12(b) to 12(e)) .

Tho d ata pr esented in th e supplementary figures for the NACA 6 - 6er10s thickness form.s sho'·' tha.t the range of lift coefficients for low drag var ies :markedly with a ' rfoil thickness .

It has boen possible to deoj.gn airfoils of 12 - percent thickness with a total theoretical low - d ra tS rcmge of lift coefficients of 0 . 2 . Th::'s theo r eti c al range i " reases by approximately 0 . 2 fo r each 3- percent ine r eape of airfoil thickness. Figure 13 shovs that the theoretical extent of the low-dra , ..: range i8 approximately 6 .

r ea l ized at a Reynolds nmnber . of 9 X 10 Figure 13 also shoTS a c~aracterist:c tendoncy for the . dr ag to inc reas e to some extent t oward. tho up::?or end of tho low - drag rang e for moderately cambered airfolls :f particu~8.rly for the thick e r a irfolls . All data for the N.l\CA 6-sories ai rfoils show a o. ec r ease i n +he extent of the low -dr ag NACA ACR No. L5C05 ran ge 1-rith i ncreasing Reynolds number. Ext rapol atl on ... of the rate of decrease ob se rved at Reynolds numbers below 9 >- lOb ivould indicate a vanishingl y a~all low-dr ag r ange at flight values of the Reynolds number. Tests of a carefu~ y construc te d model of the NACA 65 (l~21) -420 airfoil showed, ho'V r ever, th at th e rate of reduction of the l o w-drag ran ge .... ri th incre asi ng ~eYl}old8 m;mller decreased markedly at Reynolds numbe~s above 9 x 10 (f ig. 14).

These dat a. indicate that the extent of the low-drag ran ge of this a i rfoil is reduced to about one-half the theoretical value at a ....

Reynolds number of 35 x 10 ° .

The value s of the lift coefficient . for which l ow draB is obtained are de termine d lar g ely b;r the amount of camber. , T'ne lift coefficient at the center of th e lOiv-drag re.nge c orresponds approximately to the design lift coefficient of the mean line.

The effect on the dr ag character :;:st:::.cs of -various aIn01.mts of camber is shov.'Il in figuxe 15. Section data indicc.te that the location of the lOi .... - drag range may be shifted -oy even such crude camber chan ~ e s as those cau s ed by small deflections of a plain fla p . ( See s upp lementar y f ig ', ) The loc a tion of the low-drag rar...g e ShOi{S some Y8.riatJ.on from that predicted by simple thip.- ai r foil theory. This departure appears to be a function of the t ;y-pe of lJlean line used (refe~ence 29) a..'1d the a irfo il thickness , T'ne effect of a.irfoil thickness i8 sh01m in figure 13, from which th e ce nter of the 10w -d,1 o.g ran ge is seen to sh if t to higher lift co efficients with increas · ing air- foil thickness . This shift. is partly expla.ined by the increase in lift co efficient a. bove t he design lift coefficient for the mean lin e obtained vThen the velocity in crements caused by the mea.."1 line ar e combine d \V"ith th e ve i. oc it- di stribution for the basic th i ckness form a cc o rdin g to the app ro ximat e methods previously descr i bed.

Dr ag characte ri stics outside lovl- drag range, - P.t the end of the low- dr ag r ange the dr ag inc re ases r apidly with increase in lift coeff i cient . For symm etr i c al and low-cambered airfoils, for wh ich the lift coefficient at the upper end of the low-drag ranclo is moderate, this high r at e . of increase does not continue . (See fig, 15.) For hi gh ly cam be red sections, for which the lift at the upper end of the lovr-dr ag r ange is already hi gh, the drag coeffic ient ShOViS a continued ra:pid increa.se . .

Com p aris on of data for airfoils camb er ed with a tmifolw-load mean line with data for a.ir foils c amb ered to carry the load farther forward shows that the uniform-load mea..'1 line is favorable for

obtaining lmv dr ag coeffic ie nts at high lift coe fficients (fig. 16

and reference 29 ).

NACA ACR No . L5C05 Dat a for many of the airfoils g iven ~n the suppleme ntar y figures s ho,,; large reduction s in dr ag vri th inc r easing Heyno ld s number at high lift coefficients. Th is scale eff ect is too la r ge to be accounted f or by the normal variatio n in skin friction and appe?rS to be asso ciated i-Ti th the ef fect of ' Reynold number on the o nset of turbulen t flow following lrunlnar sepa -r atior: near the leading edge (ref e rence 30 ).

Effects of type of sec tion on dr ag cha r acteristics .- A com pru:. ison of the dr ag characteri stic s of the NACA 23012 a.Tld, of three ' NACJ\. 6- series ai rfoil s is p re s ente d in figure 17 . Tile , drag for the N ACA 6 - se rie s secti ons i s s ubstan tial ly 10,wer than ' for the NACA 2 30 12 se ct id n in the range of lift c' oefficients corresponding to hig h- sp eod flight, an d this margin may usually be maintained t hr ou@l the r ange of lift COefficients useful for cruising by suitable choice of camber . , The NACA 6- series sections shOi' the higher maximum valu es of the lift-drag r a tio. At high , values of t he lift coeffic i ent , however, , the earlier NACA sectio n s have gener a lly 10vTer drag coefficients than t.he NACA 6- series a ir foils .

Effective aspe ct r a t i.9 .- The combin atio n of high dr ags at high l i ft coefficients, l ow drags at moderate lift coeff:Lcj_ents ) and the nonregul ar va r iatio n of drag with lift coe fficient shown

by , th e NAC A 6 - se ri es ai rf oils may lead t o paradoxic al r esults

when the span - efficie ncy co nc ept (r e fe rence 31). is u se d fo r the cal cul ation of ai rplan e pe rf ormance . In the usual application of this concept) ' the airplane drag charac teristi cs are appr oximated ' by a curv e of the type This curve is usu ally match ed to the actual d rag char ac te ris tics at a r athe r 10"T and at 5. moderately hi gh value of the lift coefficient (r efe r ence 32 ) .

Th e applicatio n of this concept to tvTO hypothetical airpla.. "1e s wit h NACA 230 - and 65- series sect io ns) r espec t :j.vely) is il:Lustrated in fig ur e 18(a) . The \V inG dra gs of the airplanes have been calc ul ated by ad din g the lnduced. drag s correspondiI13 1;0 an aspect rat io of , 10 with e ll iptical loac.ing to the profile - drag coeff icio nts of the NACA 23018 and 65)- - 418 airfoiJ,.s . . The se sections are'

consid e red ropr ese n tative of av erage wing soctio n s for a larg e

a irplane of this aspect ,r atio . ' Ordinate scales are given' in figure 18(a) for the 'iring dr ag and f or' the total airple.ne (li ~ ag coefficients ob tai ned by ad. j ng a re pr esentative consta.Tlt value of 0 .0150 to t he win g oJ:'ag c oefficie n ts . The resulting dra g coef ficie nt s NACA ACR No . L5C05 h ave been a:pp r o:x;im.ated by tyro c~ves correspondin g to equation (17) and matched to the drag curves at lift coefficient s of 0 . 2 and 1 .0.

'rhese tT I TO curves correspo nd. t o effecti 7e appect r a';;:i as of 9 . 29 fo r the a ir ~l ane 1dth R!l.CA 23018 Gectionc- and of 8.. 30 for the airplane wi th NACA 653 - 418 sectio n s and illustrate the typic[ , ~ large r ed uction i n the ' efi'ect1ve aspect ratio obtained. "lith S"I) .ch sections .

It should be noted., hCMeve r, that although equation ( 17) provides a rea so nably satis f actory approximati on to the drag of the a i rp lane y;-i t h RACA 2 30 18 s ections, such is not the caso for the alr1l1an e with the NACA 65 ? -4 . 18 sec t ion . The most importan t reason for u s in g h ig h . aspect ra . t{08 on lar ge airplanes is to reduce the dr ag at cruis:i.ng lift coeffi c i en ts and to obtain high maximum value s of th e l:i.ft - dra.g ratio . Fo r the tw'o ~ ' Ti n g8 ::;onside r ed, the maximum value of this ratio is app r eci[-.bly higher foI' the airj:.lane w it h NACA 65.3-h18 sections (19 . 8 as compared "Tith 18 .5) despite the fac t th at thi8 ai r- plene shows the lm"er effective aspect ratio.

Figur e 18 ( b) s hows a simile, r comp&riscn vlith siT!l:i.lar results for bora aiI'pla.n.es of aspec t r atio 8- Dnd rACA 2415 and 652-415 airfoils .

It is accordj . ngly concluded that the effecti'ie asy;ect r Citio i8 not a satisfa c to r y crJ.t e rion for use i n ai r foil selection .

Effect of S ur fa ce Irre gularities on Drag ~~~.li8Sj "ole rO~~'1es~ . · P re vious Hork has shown l ar36 drag inc r e me nte resul tin!]; from s uri' ace r oughness (reference 33) .

. 41though a lerge part of these dr ag incremente ";[f:.' Show'l1 to result f~o m fo:., ·· ·" :ard m.ovement of tra.. '1 sition, subste.ntial dr <...g ::'ncrerrJ.ents . r es u lted f:com surfa c e roug)me8s i n t he region of tm'r'.l.J..ent flow.

I t is accordingly imllor'tant to maintaLn. s~ooth stU'£'aces even' hen extem:!ive lamina r flo,,! cannot b e expecte d, but. the gains that may b e e~~pected from n18.intaining sm ooth sUl'fa(.;cs are greater for N'!..CA 6· or 7 -Ge ri. es a:!.rfci1s vTh en extenei ve lrunlnar flOlvs are poss:!.ble .

No accUI ate method of specifying the surface condi tiOll necessar: for extt.;ns':'ve lar,inar flo 'd a t h1gh Reynolds numbers has o ee n de 7elo:Jed , 0.1 thoue: some genora::. conclusionr: have been reached .

It Dl.:::t ;r be :presumed tha'::' for a [i ven Pe nolcs number and chord'vise position, the siL.e of t,he :Dc:"1!liss:'blG rows.rmess 1vill yary directly 'ivith tho cho rd of the a:i.rfoil . It is kno-m, at one extreme , that th e s ur faces do not havo 'co bo 'pclishe0_ or o;;tical2.y smooth . Such polishing or Haxing 1 as ehOl-m no i mprOV0!nont 1...'1 te at s in the Langley tVTo -d imensional lmf-turbulence tunneJ.s when appliGd to satiGfacto::'ily E2 nded s ur faces . Po2.:"shing or waxing a GU1'face that i 8 not ae r odyn8.li12.ce.lly smootb vill) of course, rl.sult i f\. improvement . and such fini sh63 may be of cons : ~ d e rabl e :practical value because NACA ACR No . :L5C05 det er io ratio n of the f1ni s h may be ea 8ily s een and poss i b ly post - po ned. . Lar ge models ha v i ng ch o::d lengths of 5 to 8 feet t e ste d in t e Lan 3 1e~r t '\.lO -d i mc ns .i. on al 10vi-turbulence turmel s a re us ually f i ni s he cl by sanding i~ the ch or dVlise directi on vli t h No . 320 carborundum pape r when anael~odynami.call;y smooth snrfa ce is cle si red . . Expe r i ence h as sLown the resulting finish to be sa tisfacto ry at flight values of the Reynolds number . "~l Y ro ug he r surface t exture 3h ould be c o ns 5_ dered as a po s 9i ble SO UI' ve of t r ansition, although slightly r ou ghe r surf aces have appea r ed to pr oduce sat is facto ry results in some cases .

vlj.ndtun"l.el experience i n testi ng J:..TACA. 6-serie 8 sectio n e and d ata of reference 3~' show t hat smal l pr otub eranc es extending a bove the general surface level of un othe r wise satis 'f actory surface are more H:tel; { to ca u se trans 1 tto n t han small depressions . Dus't particl es , for example) are more effec t ive than small scratches in LJl'oducing tran si tio n if the Dle.teric.l at the edges of the scratches i s not forced above the genera}, surface level . Dus t particles ad~_ e r :, 11£ 3 to t h e oil left on airf o ll 8Ul'faces by f i n g er p rints may b e expec t ed t o CEl-elSe t rCtns i tio n at high R e ~!nold 8 numbers .

Tr ansi tion sp r ea ds from an inc li vidual d iE: turbance 'vi th an included angle of about 15 (r e ferenc es 33 an d 35 ) .' A few sc tterecl specl i: s , es?ec :;'e . lly 11.ea::- th e leading e d ge, will cause the flow to be lar g ely turbulent . Th is fact ma k es necess ar y an extre ' ~el y th or o ugh ins ~J ectlon if 10'"' drag s e.re to be r eal i zed.

Specks suff lC i ently lar e to cau s e prem.e.t1.rre trensi tion on full- size 1 ,' i11.gs ce.,,"1 be felt -b ;y hand . The in sp ecti on ''',r ocedure used in the Lan g ley t"i-lO -d :i mens i onal l O',T - tv .r bulence tunnels i e to feel the entir e s1rrf'ace by hand after uh i eh the 8 urfa~e is t h c r ou ghly 1 · ripe d wi th a dry cloth .

It ha'3 been noti c ed that transition r e s ulting fro T: individual sma11 shar p r rotu ber a nce s , in c ont r a s t to vaves, tends to occ ur at the pr otub 3 :>" .<L 1J. ce . Tranai tion caused by surface wayiness appea.rs to appr o ch -!:.he vrave gradual l y as the Reynolds number or wave size is i n c r ea se;i . The heig:..f1t of a S TI" ..all cylindr ":'cal pro t tl be r ance neces s a:"7 to cause tr2.."1si tion '\'Then loc a ted at 5 p erce nt of the chord ,,;i th its a-.cis n oxmal to the surface is shovm in fig ur e 19 . These d ata ,.,rere obta: L ned at r s.the r l ow value3 of th e Reyn o lds number and shm." a l ar g e decre a s e in allo fable b.etght 1fi th increase i n Reyno ld s n um b er . 1111s o ffect of Re~TIolds nQmDer on pel1mis8ible su r face r ouglmes 8 is also evident :;'n f igure 20, in vThich sh gr p increasa in d.r ag at a Reynoli s number of a pp r oxir.1a.tely 20 x 10 o ccurs for th e model pa i n"ed with c a moufl a. ge lac1u er .

The raa g nitude of t h e favor a ble gr a di e nt a pp oars to have a small effe c v ' on the pe r missi'ble surf a ce r o ughnes s fo r laminar flow .

NACA ACR No . L5C05 Figure 21 shows that the rou ghn es s beco mes more important at the extremit i es . of the low-dra s range w.here the favorable pressure gr a dient is reduced on one s urface. The effect of increasing the Reynclds number for a .s urface of margin a,l smootp.ness, "Thich has an effe ct si milar to ' incre aEing the surface roug!'..ness for a given Reynolds number, is tc reduce ra pi dly the extent of the low-drag ran ge and then to increa se the minimU1l1 dr ag coefficient (fig. 21).

The d ata of . figure 21 w ere spe cially chosen to show this effect.

In most case s, the effect of Reynolds number pr edo minates over the effect . of decreasih g the me .gni tude of the favorable p ressure gradient to s'.lch an e~~tent t hat the only effe ct is the elimination of the low-dr ag range (reference 36 ).

Permiss ib le "Taviness. - Mo re diff iculty is generally encountered in reducing the waviness to permissible values for the maintenance of lamin ar flow than in obtaining the required surface smoo~Qness .

In addit i on, the speCification of the r equir~d free d om from surface ",av1n ess is more dHfJcul t than that of the required surface smoothness. The problem is not ltmited merely to finding the minimum wave si ze that w·i ll cause · tran si t_on und er given con d itions because the number of "Tave s and the shape of the waves require considerati o n.

If the wave is sufficiently large to affect the pressure d ist ributi on· in s uch a man ner tha t lamin ar separation is encounte r ed, there is little doubt that such a. wave will cause premature transition at a~l useful Reyno ld s numbers. A relation between the dimensions of a wave an d the pressure distributio!l may be found r b the metho ds of r efe r e nce 37. The size of the "Tave required to J revers e the favorable p re ss ure g radi ent increases with the pressure gradient . Large ne gati ve ~p r ossure gradients would therefore appear to be fav or a. ble for wavy surfaces . Exrerimental results have sho,m this conclusion to bc quali tati vely correct.

Li ttle j. nformation i s available on ,.aves too small to cause laminar separation or ev en reversal of the ~ressure gradient. Data fo r an airfoil sect.lon havin a relatl. vely long wave on the upper surface are gi v en tn f'i.gur e 22 . Marked increases in the dreg corresp6ndi 'ps to a r apid fOrl-rard movement of the transttion point 0 .

wer e n ot n oticeable b elo"T a Reynolds number of 44 >. 10 On the other hand, transition ha s been caused at co mpe . . ~ati vely low Reynolds

numb e rs by a se r .i.es of small ,,,aves with a vll:we height 0: the order of

a fEM ten - thoUS8.-11dths of a ,'l i nch and a "lE~ve length of tho order of 2 i nch es on the same 60-inch - cho rd model.

For tho types of· wave us u ally 8 nc olliltered on practical- con s truc t ion wings, the test of rocking a straight6dge over the surface in a chordwi se di r ectio n i s a fairly sattsfactory criterion.

NACA ACR No. 15C05 The straightedg e should rock smoothly without jar ring or cltcking.

The straightedge test wiil not shm1 the existence of 1t1aVes that leave t he surface convex, such as the wave of figure 22 and the se r ies of small vTaves p reviously mentioned. Tests of a large number of practical-construction models, hmTever, have shown that those . models which passed the straightedge test were sufficiently free of small waves to p ermit l ow drags t o be obtaine d at flight values of the Reynolds number .

It is not feasible to specify construction tolerances on ai r ·· foil ordinates ,.,i th sufficie nt accuracy to ensure adequate freedom from waviness. If care is taken to obt ain fair surfaces, normal " tolerances may be u sed i'11 "!:.hout causing serious alteration of the drBB character ist ic 3 .

· :pr~i th fixed ' tr~BHic~ .. _ . If the airfoil sUJ?face is suffiCiently rough to cause t ran sitio~ near the leading edge, large drag . ipcreases are to be expected . Figure 23 s ho 'v 1s that , although the degree of r oughne ss has some effect, the increment in minimum drag coefficient caused by the smallest roughness ca pa ble of p roduci ng tl~ansi tion is nearly ac gr eat as that caused by much larger graln r oug hness when tpe roughnes s is co nfined to the leading edge. .The deg ree of rougrmess has a much larger effect on the drag at high lift coefficients . If the rov.ghness is sufficiently large to caUGe transition at all Reynolds n~mbers conSidered, t~e dr ag of the airfoil ,·ri th rougp ooO n ess only at the leading edge decreases with ircreasing Reyno ld s numbe r (fig . 10 and r ef erence 38) .

TI1e effect of fixing t r ansition by means of a rougm1ess strip of carborlL~dum of O.Oll-inch gr ain is shown in figure 24. The minimurr. drag increases progressiv e ly with fOr1-lard movement of the roughne ss st ri p . The effect on the dr ag at high lift coefficients is not progressive; the drag i n creases r ap idly when the roughness is at the leading e dge. F~lgure 25 8hm.,s that the dra g coeffic 1e nts for the NACA 65(223)-422 and 63(420)-422 airfo i ls were nea rly the same throughout most of the lift. range 'Then the extent of laminar flov7 vras limited to O. 30c .

All recent airfoil d ata obtai ri ed in the Lal1g1ey tHo-dimensiona l low-turbul enc e pressu r e tunnel inclu de r es ults with roughened leading edge~ and these data are tncluded. in the supp lementary figures.

Tests with roughened l ea d ing ed ge .7e r e formerly m ade only for a limited number of airfoil sections, espeCially those having large thiclme ss ratio s (r eference 39 ) . The standard rou.sm1 GS S se lected for 24-inch-chord models consist s of O.Oll-inch carborundum gr ains applie d to the a irfo i l su rf ac e at the l ea ding edge over a surface length of 0 .080 measured. from the l e adin g edge on both surfaces .

The gr ains arc thinly sp r ead to cover 5 to 10 pe rcent of this 8.l'ea .

\ T his stan d ard roughness i8 conside r abl;/ nore severe t.~1an that i c au se d by t : ne u.s'.l al manu .f act'..U' ing irreertJ.lari t: es or deter:!.oration in se rv ic e b ut is c onsic , erably less severe than that likeJ.y to be en c01.mte re d in se rv ice as 8. r e 5ul t of accumulr:..tion of icE. or mud or darus.gf. in mill tary co n ioE' .t .

Tne v ariation of mi n itlUlll dr ag c oe: ' ficient 1vlth thiclmes8 r a t io fo r a number of ITACA a11'f oi13 w ith standard l ~ cughness is s ho wn in f1g u ,::,'e 12 . 'E.1ese d ate. 611m T t h at the magnitudes of the mi n imum dr ag coe~~ficients for the I·JAC;~ 6 - 8erie3 1O'.irfoi18 are less th a n the values fo r t h e NACA fo'J ..r- and five-dl.git-8eries airfoils .

The r at.e of i n crease of . dr ag vii t. thickness is greater for the a i rf oi l s i n the r Ci.lgl':. condi.tio n than in t.he smooth condition .

~r ag Ki.th pi .' actica l coust r ,lct::'~ !l metho~~ . - The section d.rag c o ef f ic i en ts of se ver al al r :pJ.ene .,l .ngs have been mee.sured tn fl ig ht by t h e . !fu\:e - S1..U've ,Y metho d ( :;.eference ~.O)) and L1. number of pr acti c al - co n struction wins sect5.orlE: he.ve been -\~ested in the Lan gl eJ t wo - d1mensionaJ. lov!-turbulence pressure tUll.L!el at flight valu es of the Reyno}.rls number . Fli&-'1t da-sa obtained by t.he :NACA (r e f e r e n ce 40) are sUL-rn.arized in fig ur e 26 and some data obtained b y th e ComJOL.o.ated 'Vul tee Ai r craft Corporation are pre",ented in f igu re 27 . D ata obte.ined. in the Langley t'·TQ-dine:m'lional low,..

t urbul en ce pr essu r e tl.lll.!1.el for typj.cal practical-const r uction se c t i on s ar e presented in fig1..U ' ez 28 to 32. Figure 33 presents a c om pa r isoa of the drag coeffj.cients obtained in thi.s ",tnG. tunIlel f or a modeJ. of the Fj'Cj\~ 0012 section and in fliGht for the same mo del m ounte d on an ail ' })lane , For this case) ·che vind.-turmel al1d fli ght (l at£~ agree to .T1 th.i.n the x.perimental error .

All wings for 1Vhich fli3ht data. are presented i:::1 figure 26

.T er e c a r efully finished to pro d uce smooth surfaces . Greut care was take n to reel . lee surface ,·ravj.ness to a m~nimum for all the se ct io n s e::ccel-'t t h e NACJl. 2415 . 5; N· · 22 ) Republic 8-3)13) and the N/. CA 27 -2 12 . Cl.l !'v aturf;- . i:J.c;e measurements 01' surface w·aviness for so me of t~lese airfoils are presented in re:'e:oence 1~0 . Surface con ditions cox-r esponding t.o the duta of figure 27 c::.re d.escribed in t h e f ig ur e . 'I'hez6 d.ata shmv that the sections perLlitting exten"'ive l ami nar f low had substeni~ially 10lvor drug c06ff::.c ieuts 'IThen smooth t h an t he other sections .

The -vri n d-t1illllel tests of pr acti c al-conr-;truction i·Ting sections as de l i v e::,,'e d by the manufactu r e r 8hm-Jed miniI'm!'! drag coefficients of t h e orde r of 0 . 0070 to 0 , 0080 .in nea r ly all cases reGa r dless of t h e ai rf o Il se c tion l.~sed ( figs . 28 to 32) . Such values may be r egar ded. as- typical for oo d cu rr ent construction practice .

F i n is h ing t he sec tionEJ t o pro d uce smoot h · sQrfaces a.hrays produced s ub s tan tia l dr ag rt;:!du.ct1.ons alt h ough cOUi:i2.dcrable waviness usually NACA ACR No. L5C05 r e main ed . rone of t he i:le c t ions '!:;ested had fair s ur faces at the front sp a r. Unle s s 8pecial car e is tat:en to prod uc e fai r s urf aces at the f r ont spar, the re 3u ltin g wave may be expecte d to cau"'e transition either at the .s par l ocat i on or 2, sho r t distcnco be h in d it. On o practic a l-construction spec im en tested vii th smooth surfaces maintai n ed l' el ati ,-ely lou drags up to Reynolds numbers of approzim ate ly 30 ). 10 (N ACA 66 (2x1 5 ) -116 airfoil of fig . 10) .

This specim en h ad no spar fO r' ,Tard of auou"!:' 35-pe rcen t chord from the leading edge and n o 8.?&."!\·7is ,.:: st iffe ne r s fO l''i oJard of the spars .

This t.ype of co n .... tructio n resulted i n unusua ll y fair surfaces and is be i.ng used on some modern hit3h-performance ai rplanes .

A com-parison of the effect of air:':'oil section on the mlnlllJ.1..1ID drag wi th p racti caJ. -con st :!:" ' uct::'on s u ::cfaces is ver~T d l ff:'cul t because the q ualit y of t he su r fa ce has more ef fect on the drag th an the type of section . ?roba b ly the best c om pari8cn can be obtai ned from p airs of models const r ucted at the same t:i.me by "(,he same manuf act urer s .

Data for such pai r s of mo dels a r e p re sent.ed in fig'.ITes 30 to 32 .

The result s indicate that as 2_ong as current const r uctlon p ract i ces a re used the type of SSlctton has rela t:;'vely litt l e effect at flight va lues of t he Reynolds nur rfbe r for military ai r planee .

Importan t savings in dr ag rna;;, be obtained. at h~.g h Re;ynolds number s by keeping the surfaces smoo th even ~.f extensi ve laminar flow is not re a l ized. Dr ag increments r esulti ng fr om surface r ou ghne gs~ n tu rb 1)~ent fl o T have bee n shovm to 013 impo rt ant (refere nce 33) . '1' 11 e eff ects of su rf ace roughness on t.he. vartation of dr ag ",i t h Reyno ld s 11.'\.1lll0er a r e s h ow 'n in figure 29 , in which t he favora.ble s c ale effect usu n..l ly expected at h:: .gh Reynolds numbers ',.;as n o~ r ealized . '1"ni 8 type of scale effect may b e compared. vri t h that shown fo r the Nl;CA 6 ( 420 ) - ~ · 22 airfoil 1"i th r ough l ea d i n g edge but othor-~r i.s e smooth surfaces (f ig . 1 0) . Drag i ncr emen ts obtained in flight r esulting from J:"oug hr.. ess j.n the tU!'bule n t boun d e. r y l aye r wi th fixed tr a m:i tion a re I)r esente d in referenc e 41 .

Tne effect of the ap.,)lic.&tion ~f de - i.cer s to the le ding edge of tw o smoot h a ir foils . is s hmm in figure 34 . The de-icer "b oots " were i n stalled in b oth cases ;.)Y the m2nufo.ci.':LJ.rer to r e; r esent goo d t yg ic a l lnstallations . The m':'niml'c!2 drag coefficients fo r both sec ti ons with de--icers i n sta lled ,i8re of the ('rdo r of 0 . 0070 at h ig h Reynold .s mlT.lbe r s .

~ffectG of \) 1'2'26110r s lipst_ e.8.lli and a ll~:Jla."1e vib2. ~ ation . - Very f ew data al ~ e avai labl e on t h e effect of pr opeller slipstream en tran si tio n or ai rfo il dr a J'j tho dO .ta that are aveilable do not G hm.; cons iste n t r esults . 'TI1is :i .n consistenc· rna ; )' r es ult f' rom v a ri 3.tio ns in li f t cod'fi.ci nt, s ur face cono.i ti.on, air - st r eam tu rbul en ce , NACA ACE Eo. L5C0'5 prop eller advance- d i2IDe-:,er ra-~io, and' n:mlber of blades. Tests in the LaTlgle:r 8-foot high-s:peeri tUlmel indicated transition occurring from 5 to 10 pe r cent of the chord f ro m the lead ing edge (reference 42) .

D:..'ag measU1~ement s made in the Lc ngley 19-foot pressure tw.p.el

(fig. 35) indicated only mod.erate drag increments resulting from a

win d.lJlil ling propell er. Although the de ,ta of figure 35 may not be

very ac cur ate because of the difficll.l t;y of making .rake s·<.lrveys in the s li pstrea~ , these data seem to ~reclude very large drag in cr ements such as ,,!ould re su.Lt :["rolll movement of the transi tjon to a position c lose to the leading edge . These data also seem to be confirmed by rece nt NACA flight (l ata ( fig . 36) , "Th ieh sho.r transiti on as far be , ck as 20 percent of the cho r d in the slipstream. Other lm published NACA fEght d .ata on -'vransiJ::,j.on on all S- 3 ,14.6 airfoil in the sl i pstreem indicate o. that laUlino.r rIm', occur:red a3 far back as 0.2c .

Even leAS d ata a r e available on the effects of v:Lbration on t ran si tion . 'l'ests ill the La.Tl::'] e:,r 8--foot hiq..'1-s:;::eed tunnel (ref e r ence 1: . 2) sho,.red negligible effects but the range of fre<].uencies te5ted may no t he . ve been suffl.ciently vide. Some unpubl~shed flight d ata shoved ST1lB_ll but consistent I'Gt.!'\lG.rd mO'lements of trallsi tion outside tho slip.3tream i-Th3n the pro p ellers -ilere feathered. This effect was notic ed even i{hen the IJl'opeller on the opposite side of the airplane from the surVE-Y plcu:e Tas fe.::cthered. unO. ·w as b.ccordin ly attri b uted to vibration . Recont tests in the A:nes full - scale tunnel shoved ],JX'ernature adve r 3e scale effect on drag coefficients m easu r ed by the i, rake -sarv e;y method vhen a model-support strut vibrated .

Lift Characte r lstlcs of Smooth Airfoils Tw o - 9-2.men sio n al da~§: . - _to,s oxplained in the section "Pngle of ZE, ro Lift, II the &"Ylgle of zero lift of an a i rfoil ie largely detormined. by the camber . Th2.n-e.i~foil theoTj :provides a means for computing -t he fu"1gle cf ze r o lift from the meon- line dnta presented i n the supplementary figures. Tho c,grcement betMeEln the calculated and the eXIlcl'imental ans l o of z ero Ij.ft dep end.s en the type of moan lin e used . COl1lpa:;.~ison of tho c x~ er im.entcl values of th& cngle of ze r o l ift obtained from the supplementary f~gurv8 and the theoret::'cal valu es tE'tken from the mea.Tl - line data shows that the ag r ee men t is good except for the uniform-lo ad type (a = 1.0) moun l ine . The angles of zero lift for this type mean line gonerally have valu es more positive than those pr edlCtcd . The experimental v aluos of the Eill.::;les 0"': ze r o lift for a number of NACA four- and fi vo - digi t and NP ,CA 6 - series a~ r foils .arc presentod. in figure 37 .

The ai rfo U thicknHls appen r s' to have littl e effect on the value of the angle of zoro lift rG C~ r dlGs8 of tho airfoil series. For the NACA ACR ~o . L5C05 NA CA fo ur- digit - se r ie o,i 1:' fo1.1s, t.he angles of zero lift are app r oximately 0 .93 of the va lu e give n by tbin - airfo:"l theo r Yi for th e NAC_~> 230 - ser:"es p ~ irfo~ls , tj.~~ fa~"(,or i3 8. pproximatel;'" 1.08 · ane. for t h e NACA 6-ser';'es ai:cfolls with uniform · load ·t.j'I !8 mean l:i..ne , this fact.or is apr;ro.7.imat ely 0 : 7 ~· .

The lift - cuyve olo:pes ( fig . 38) for o. irfoi.1s teste d in the Longlej' two-d:"mensionaJ. lm.'-turbulence Iressure tunnel a r e h igher than those previously obtai n ed . ~n th e te.:,-cs re})orted in reference 8 .

It is not c l ear whether' this o. iffe r ence in slope 18 cause d b;y th e d i f fe r en ce in air - atredID turbulence or by the d:!.ffer ences in test metho d s, since the section data of' refe r ence 8 "ler e infer r ed from te s ts of mo d els of aspect ratio 6 . The p:eesent values of the lift ·-

c ur ve slope were mec.sured i'o.. a Reynold.s number of 9 >. 10 and at

va lu es of the lift coe.:'ficient app::' oximatel;/ equal to the desig n l ift c oeffi c ient of the al r fo~l section . For the NAC A 6 - series ai r foils this lift coefficj . ent' f ' aI , proximately in the cente r of the lov - drag range . For airfoil s D "'ving thicknesses in the r ange f r om 6 to 10 percent the N.CA fOl~r - and. f.I.\re · d. igit series and the NACA 64 .. series a:'cr foil sectio n s have values of lift - curve slope ve r y cl ose t o the value f or thin airfoils ( 211: per X'E.dian or 0 . 1 10 ller degree) . Variat.ion in Re; ynolds number beh-leen 3 X 10 an d 9 '< 10 6 and va r iations in airfoil camber U,9 to 4 ller cent chor d a pea r to have ~10 systematic ef fect on values of l:'.ft .. curve s l ope .

The a i rfoil thickness and the type of th:i.ck.noss dist r "Lb u tion appea r to be the pr 7.mary v8. riables . For the NACA four - an d f ve-· d igi t·-se r ies ai r foil sections , the lift - curve slope dec r eases w ith inc r ease in airfo~l thickn e ss . For the NACA 6 - se r ies airfoil se c tions , however , +he lift-curvo slope increases 1 .,i th inc r ease in t h ic kn ess and foryTard movement of the pos. tion of minimum pressure of t h e basi c t h ickness foY'Lll at. zero lift .

Some NAC_I4 . 6 - ser1e~ airfoils ehm., JOBS in the Hft cu r ve at t he e nd of the l o,~ - d.re.g rp..nge, especially at low RGynold , ~ nuraber s . This jog becomes more pronounced v;i th increase of cambe:::' or thickness an d w j tll rear'tl8..Y'c. movement of the l)Os:l tion of minimum press ur e on the b asic thiclmess form . This joe; decre[tse n r a pic.tly i 1 seve r ity with i n cref'.s.Lng Be molds m.unber .• bCCOr.1 C8 merely a ch , mBe in li .... t - c ur ve slo1;.0 , and is prac tically nonGx ~.s t e_ t a. t a R<3;ynolds nlllnbor of 9 x 10 for most ail ~ fons that ,m u ld be Jonsidered fo r pr acti c al application . Th:i.s jog may be a considera-r,lon in the selection of ai r fo1.1s fo r sill:lil low - E)": ') eed ai r ..;,lanes . In analysj.s of the flay!

conditio n s l eadIng to thie jog i8 presented in refe r ence 30 .

Tne variation of' maximU':!l l::'ft coefficient vii t h a.ir fo i l t hickn ess r atio at a Roynolds munb -r of 6 X 10 is shown in fig ur e 39 fo r a nu.mbe r of IJACA airfoil EJections . The a.irfoils fo r vr h ic h d at.a a r e pr ese n te d in this figure have a r ange of thickness r atio NF.CP. P. CR No. L5C05 fro m 6 to 24 percent and. camber s up to 4 - pe r cent chord. . From the dat a for t h e [{P ·_ Cp . f o ur - and. fi v e - digi t - series airfoil sections (f ig . 39(a)), the ma.xim um lift coeffici ents for the plain alrfoils app ea r to b e t he greatest - for a thi c kn ess of 12 percent. In general, the ret e of cliange of maximum lift coefficient "ri th thickness ratio appea. r s t f.'l b e grea t est f or ai r f oi ls hav ing a thickness le ss th8Jl 12 pe rc e nt . The da. ta fer the NACA 6 - seriE's airfoils ( fit~s . 39(b) t o (e)) also show a r ar'i d. incr e ase in maximum lift cOE..ff:i.cient Ivi th j.ncreasi n g thicknesG rati o for thicl:;:ness ratios of l ess than 12 p (; r- c ent . For rpCA 6 - s o ri Es r:: irf oil sec t ions camb 3red to give a design 11ft co effi c ient of not mor e than 0 . 2, the op timum thickne ss ratio for maximum lift co effi ci e nt app ear s to b e between 12 and 15 p3rcent , ex c ept for the ai rfoil s havin g the posit ion of minimum pressure at 60 percent ch o rd . The o pti m um th i ckn e es l'atio for th e NACA 66-serieo sections ce.mb e recl fo r a d e si ~lll l if t c oeffici nt of not mor e than 0 . 2 ap p ea r s to b e 15 p e rc e nt or gr e, at o r. Th e available data indica t e th a t a thickn ess r atio of J.2 percent or less i s o::;>timum for airfoils h a vin g a de sign lift coefficient of 0 . 4 .

Til . maximum lift coeffici e nt is least sensitive to variat::'ons in position of m:i-nimum pr ess Ul ne on th e bn8ic thickne8s form for ai r- foil s hl:.ving thickness ra tios of 6, 18 , or 21 p e rcent. The D1..a.ximv.m lift 00effici c nts corr 6s p on d ing to i.n termediate thickness ratios i ncr ease ", i th forward rnov em '3 nt of th e position of minimum pressur e , particula:rly for those airfoils h aving design lift coeffici e nt s of 0 . 2 or less .

The mc.x:Lmurn lift coefficients of moderately cam-berGd rU·CA 6-se r ies s E. ctions incrE;ase Iv-ith inc r easing camber (fig. 39 (b) t.o 39(f")). The addit i on of cambe r to the symmet ric al airfoils causes the greatest increment . of maximum li ft coefficient for airfoil thickness ratios varying from 6 to 12 percent . Tne ef f' ect:t .v eness of camb er as a m0ans of inc :c easing the ma.xil"llli'1l lift coefficient senerally decrease s as the airfo il thickn ess inc r eases beyond 12 or 15 p ercent . The availablE: da .ta indic a t A t h at t h e corrbination of a 12 - percent - thick section and a mean line cambered for a de 19T1 lift coefficient of 0 .4 ;;'ields tho h ighest maximum lift coefficient .

The varia ,tio n of ma.·xj.mum lift "ri th type of moan line 1.s shmm in fi g ur e 40 for on e 6 - series t hickne ss a.istribut::'on . No systematic d a"a ar e av ailable for mean lines vith valu's of a less than 0.5 .

It s h ou ld be not e d; hov ev E:.: r , that ai !" foils s uch as the NACA 230-s e ri e s sections '.Ji th t:1( "1a.ximum cambe r far fo:nv-ard 3hmi larg6 val~es of maximum l if t . .cJ.rfo i l s0ct:i.ona v l.l. th me.xjmum. camber far forward an d vl i th thiclrness ratios of 6 to 12 pE..rcerit usual ly staJl from the leading e d 3e ',ri th la:;.ng e sudden 10f:'ses in lift . A more d esi rable gradual stall is obtaiaed 1-Th en th 6 location of maximum carr.b '3 r is fartbe r bad{, as for t h e IJA CA 24 - , 4h -, and. 6 - series sl:ctiom: with normal types of camb e r.

NACP. ACR No . L5C05 ~ c o mp~.ri 8 0n of the iTh' ''t ,Jd.T ' lum lift coefficients of NACA 64 - se r ie8 a i rf oi l s e; tiruls c mber ed for a desig n lift c o efficient of 0 . 4 with th os e of tl.1e N! ;. CA 44 - a.'i.d . 230 - se1' i e 8 sections ( ng . 39) shows that the maximum lift coefficients of t he N ACA 61} - s er 5 .es ai r foils are as h ::'8 h or hi ' he:i.~ t han those of the NACA 44-serie8 s ec t ior. s t n al l c as es . The NACA 230 -s er1es a i r f oi l s~c-Lions have ma.xtmum l:tft co eff:iclen ts so meuhat h:' ghe r -i,:;han those of the NJ>..CA 64 - series sections .

The sca le effect on the max im wn lift coefficient of a large number of NACA ai. r foil sections fo r Reynolds nu.mbers fr om 3 x 10 to 9 A 10 6 l s shOlm in n. g ur e ~ . l. ' rhe scal e e ffect for the NA CA 24 -, 44 - , a nd. 2 30 - 8e r1e s airfol1s (fi gs . ~ . l( a ) and (b)) ha vi n g t h i ckness r ati os from 12 to 24 pe r cent is fa v orable and nearl y independent of the ai r foil th t cl mess . Inc r ea sin g the Re~'1l01ds number from 3 x 10 to 9 >'~ .10 result s i n an inc r ease in the maximum li:::'t coefficient of a~n) r 0x jm ately 0 . 15 to 0 .2 0 . The scale effect on the ITACA 00- .

and ' ll ~ - se r ies ail ~ foils h t! vih,g thiclmess rati os le ss th[Jl 0 . 12c is ver y smal l .

The' scale -· effect d ata for t..he NACA 6-8er ies a.irfoi1s ( figs . 41 ( c) to (.l. ~ )) do no-;; show an ent j rely systemati c vc-..riation .

In ge "eral, the sca le effe ct is fa,vorable fo r these airfo~l se c tio n s .

For the NACA 6~ - and 64 - 8e ri es air f oils wit h sma ll camber, the increase in ma .- ~:i J)m lift c oefficient '\vi th increRse in Reynolc.s number i s generally small fo r t hi c kn ess ratios of l ess than 12 percent but i s s ome'lt!hat large::. ' fo r the th:'cker se ct. io ns . The character of the scale ef:;.~oct for the Nf , CA 6~ - an 1. 60-series airfoll se c tions is similar to 2.:.h3,t fo r the N ACA 03- an d 6~ . - 8eries ai r foils bn"':. t h e tr e nds a::"e not so vell (lef i ned . I n most cases the scale effect :0 1' N. CA 6 - 3e r 1es a o ::cfoil sectio . ['. camber ed for a de s:'S Il lift coefficient 01.' O. L. or 0 .6 does not var~r much vTi t h R';' r ' fo i]" thickness ratio . . The d ata of figure 42 s h o ,,; t h at the maxJmum lift co ef fic ie nt for t h e N.~CA 63 ( 420) - ~ · 22 ai rfoil conti.nues to increC'.,.se with Rey nolds number, a t l e&st U) to a Reyno l ds nu.llber of 26 >' 10 b .

The values of the m&:c J mum l ift co effi ci en t p r ese n te d were obta'ned for stead y conditJ.on s . Tho maximum lift coefficient may b e hie;her 1,7hen th e angl e of attack s inc:::oeasing . Suc h a c o..11. di tion m'ibh t occur dur 'ing austs a nd landi n g maneuvers . ( See r eference 43 . ) The s~-9te m ati c invoetig3.tion of NACA 6 - 86 ri 8s c.. irfoils i nclud e d tests of th o ai r foils io r: i th a siUlllated split flal! d efle ct ed 60 • I t 'ioTaS believed that th ese te s ts w ou ld se rve as an in ication of th e ef f e cti ve n ess of mor o :901 ve rful types of' trailing-edge 'h ig h - lift .

de vic es a l t hough s u fficie nt d ata to verify this asslunption have n ot b ee n obtained . The ma.xi mum lift coefficients for a l arge numbe r of NACA air1'o il se c ions obtai n ed from. te""ts "ith the s imul ated split fl ap a r e presented i n f 1g ur e 39 .

NA CA A CE No . L5C05 The da t a fo r t he N_ A CA 00 - a..ll.d 1 4 - se r ies a ir foil s equippe d with spl i t fl ap f or t hickn ess ra ti o s fr om 6 to 12 pe r cent s h mr a con s i d er abl e i n c r e a se in maxi m um l i f t c oeffici e nt with inc r ease in thi c kn e s s r a t io . Co rr e sponding da ta f or the NACA 44 - se r ies a.irfoils wi t h th ickn ess r at i os f r om 12 t o 24 p e rc ent shm., ve r y li tt2.e variation in maximum lif t c oe ffici e nt vii t h thic lmE ,s s. Fo r NACP. 6-series air - fo i ls e quipp e d \ ,r i t h s plit f J. ap s th e max i m um lif t coefficients increase r api d l y wi t h in c r ea s in g t h iclm e s s ov e r a r anse of thickness ra.tio, the r ange be g inni ng a t th i ckn e s s r a ti os b e h ree n 6 and 9 percent, dep~nding upo n the camb er . '1'h e u pp er l imi t of t hi s range for the symme trical NA CA 6 4 - an d 65 - sGr ies a i rf o il s a-p pe a r s to be g r eate r than 21 percent and f or the NACA 63 - an d 66- se ri ~; ai rf oils app r oximately 18 percent .

Be tvr ee n thickn ess r a ti os of 6 and 9 p e rc ent the values of maxjJnum lift c oe ffici e nt f or th e s ymm e tr i c al N ACA 6- se r ies ai r foils are essentially th e sam e r ega. rdl ess of t h i ckn ess r atio and posi t ion of minimum press ur e on th e b as ic t hi c kn ess f o rm . Th e maxi m um lift coefficient decreases wi th r e arwa r d mov emen t of minimum pr ess ur e for the a.ir foils having th i ckn ess r atios b eh · Tee n 9 and 1 8 pe r cent.

S ub stant i al inc r emen ts i n maxim um l:i,ft coeff1c:' e nt \lith increase i n camb er are s h mm fo r th e NACA 6 - se r i es airfoils of modera.te thickn ess l~ atios (1 0 to 15 p e rc e nt C hOl ~ d) with sp::'i t f'le.ps . For the ai rf o il s h a vi ne thi ckn ess r atios of 6 pe:::'c8nt and for the airfoils h a v ing t hi ckness r atios of 18 o r 21 percent, the maximum lift coeffi c ie n t is affecte d ve r y little by a change in camber. For thi c kn ess r atios gr eate r than 15 percent, the meximum li~t coefficients of the NACA 6 3 - and 64 - se1'ie l3 ai r foil s cambered for a design lift c o effic ie n t of 0 . 4 equ:i.p:pecL "li th SIlE t flc.ps ar e greater than thE: corr es p o nd i n8 JJlaJC i mU Dl lift coe f ficients of the N1~Cf. , 44-series airfoils .

Thr ee -dim en sional d ate. .- No r ece n t systematic three - dimensional w ing da t a ob tai n e d at hlgh ReynoldG num - D ~ rs are available, GO that i t i s diff i cu lt to mak e any compa r ison ,ri t.h the section elata . "!hen t h e maximum- li ft d ata fo r t hr ee - d imensional wings ar _ compared ¥ith se cti on d ata , ac c o un t s h oul d b e tElken of the span load distribution ov e r U ~ e ~ ·T in g . Th e pr edicte d m aximUl.'1 lift c0 0 ffici e nt for the ~Ning will b e som 8\., h at lo,,'e r t h an t h e maximum lift cO E: fficients of the se c t i on s u se d b eca u se of th6 non un if'ormi T,y of the sp2.ml'is(; c_istributio n of l i ft c oe f ficiunt . Th e d iffe r en ce 8nlOuntC to about 4 to 7 p e rcent f or a r e ct ang u lar wing w it h fu, aspect r atio of 6.

Ivla.xi mum - l ift data ob tai n e d f r om tests of a. numbe r of >.nngs and a irplan e m odels in the Langl e y 19 - foot pressure tunnel are pres0nt ed in t ab l e II . Al tho u gh se c tion data at the Reynolds mlIllO e rS n e c ess ary to p e rm it a d etailed comparison ar(; not ave.ilabl (; J the max imum l if t coefficie n t fo r pl ai n wings given in tabl e II appt;ars NACA A CE No . L5C05 to be j. n ' ge neral ag reement wit h values ex pect ed from se c tion d ata .

The d ~ ta f or the aiipl,ane mo dels a re pr esented to ind icate the maximum lift co efficient s obtai n ed w ith various " ai rf oils and conf ig ur atio n s .

Lift Ch a r a cteri stics of ROU~l Ai r foils Two-dimens io nal d ata .- Most recent airfoil tests, especi ally of airfoils ".,i th the thicker s ec tj.ons, have i ncluded tests "T !_ th r oug h e ned leadin g ed ge (r eference 39 ), and the available d ata are i ncluded i .n the SUI J pl ement .a r ,y fi gures .

The effect on maxiill1.:"''1l lift coefficient · of various degrees of rou~ess applied to the l ea d ing edge of the NACA 63 ( 420) ·-422 ai r f o il is s hown in figure 23 . ' rhe maximum lift coeffident decreases pro::> essively vrith increasi ng rou ghness (reference 38) .

For a given s urface condi t :i.o n at the leading edge, the maximum lift coefficient inc re ases sl ovrly \-l ith l ncreas ing Reynolds number (fig. 43). Fi6ure 24 s hows t hat roug hn ess strips located mo r e than

o .2 0 c from the le a ding edge have li tt le effec t on the maximum lift

coefficient or lift ·-curv e slope . The result s presented in figure 38 shm" that th e effec t of standard lee . ding edge l~ o ughness i s to de c re ase the l i ft-curve slope, particularly for the thicker ai rf oi l s havin g t he pos iti on of min.:i.mum :gressure fa r · back . These data are f or a Reynolds nm ~be r of 6r ~ 10 • Maximum- 1ift - coefficient d ata at a Reynolds numb er of 6 x 10 f or a large nUL1be r of NACA ai rf oil sections id th stanc t ard r oughness are ; J re sented in figures 39 and l~l . The variation of maximmu lift coefficie nt with thi ckn ess for the NACA four - and five-di git -serie s a1rfoil sections with standard roughness s h ows the same t r ends as those for the smoo th ai rf oils except that the va lue ", are consid er ably r educed for all of t h ese a ir foils ot her than t he N.ACA 00 - se r ies al1'foils of 6 pe rc ent thickness . For a given thick n ess r atio greate r than 15 percent, the v alues of maximum lift coefficient f or the fotIT - and fi ve - digi t se r ies a j. r foils are s ub stantiall;:r the same.

M u ch less variation in maximum lift, coefficient T ITl th thiclmess r a t io is sho".nl by th e NACA 6 - 8e r ies airfoil sections in the r ough condi tio n than wi th smooth leadin g e dge. '1'h6 maximum Hft coefficients of the 6 - pe rc ent-thick ai rfoil s are ~ssentially the same for both smooth an d r ough condit:;' ons . The variation of maximuIll lift coeffi cie nt w lth camber, hmiever, is about the same for the e.i rf oi1s vTi th s ta.'1da r d r oug hn ess as fo r the gmooth t:l cctions . The maximum lift coeffi c ie n t of ai rfoil s "i t h standard roughne s s ge_le 1' al1;:;" decreases so m evr h at \'1i th reaX'\va1'd m ovement of the position of minimum press ur e ex c ept for airfoils having thickness r a t i os gr eat.o r than 18 pe rc ent , in 1ihich c ase some sl ig h t ga:Ln i n m2...ximum lift coefficient re8ul t 8 f r om a re arwa rd mo v eme n t of' t h e posi t ion of minimum I) resSllr e .

NACA ACR No. L5C05 EXce pt fo r the NA CA 4 4- series airfoils of 12 to 15 percent thic kn ess, the pr esent d ata i nd icate that the rough NACA 64-series ai rf oi l se c tions camber ed fo r .a design lift coefficient of 0.4 h ave maximum lift coef f icients c onslstent · ly higher t..h.an the rough ai r foils of the NACA 24 -, 44 -, and 230-serie8 airfoils of compar able thicIDless.· Stan dar d rouglllless causes decrements in maximt un lift coefficient of the a i rfoils with ~plit flap s that are substantially the s~e as those observed for the plain airfoils.

The maximum lift coeffic ient may be Im.;ered by failure to main tain the true airfoi.l c ontour near the leading edge, but no systematic data on this effect have been obta:Lned. Examples of this eff ec t t h at were acci d entally encoIDltered are presented in fig ur e 44, in which 11ft · ch aract,er:l.stlcs are given for accurate and s l ig h tly ina c curate models . The model inaccuracies were so small tha t t h ey wel~e not found ~~ViOU8 to the tests.

Three-dimensional d ata . - Tests of several airplanes in the

Langley full-scale uUlllel ( reference 44) show that many factors

besides the airfoil sections affect the maximum lift coefficient of ai r planes. Such factors ~s roughness, leakage, leading-edge air intakes, armament installations, nacelles, and fuselages make it diffic u lt to correlate the airplane maximum lift with the airfoils u se d, even when the flaps are retracted. The various flap c onf:i.g ur atiom.: used me.ke such a correlation even more difficult " Then the flaps are · deflec ted . When the flaps were retrac ted, both the highest and the lowest maxlmuID. lift coefficients obtained in r ecent tests of airplanes and complete mock-ups of conventional configurations in the Langley full-scale tIDlllel ,.,ere those obtained wi th NACA 6 ·· series . airfoils .

Results obtained from tests of a model of an airplane in the Langl ey 19-foot pressure tIDlllel an~ of the airplane in the Langl ey full - scale tIDllleJ, are presented in figure 45. Both tests were ma de at approximately the same Reynolds number. The results show that the airplane in the serYice cond itio n had a maximum lift coefficient more . than 0 . 2· lo,,,,,er than that of the model, as "Tell as a love r. lift-curve slope. Some improvement in the airplane 11ft characteri sti cs was o bt ai ned by sealing leaks. These restLl ts show that airflan~ lift characteristics are stro~31y affected by details not r eproduced on large-ec ale smooth models .

. .Lj. ft characte r istics obtained in the Lani:51ey 19-foot pressure tIDlllel, for t1VO airpla.lle models in the smooth condition and wi th trans i tion fixed at·the front spar are presented in figures 46 anet 47. In both cases, the lift-·curve slope "Tas decreased through- out most of the · Hft range with fix ed "transition. The maximum lift coefficient ",as decreased in one case but vlas increased in the other case .

NACA ACR No . L5C 05 Unconservative Airfoils The attempt to o bta , in low drags: especially for long · ·range a:L r plenes, leads to hi~h ving loadings togetber vTi til relatively 10 vl sp an load i ngs . This tendency r esul t.s in wings of high aspect r atio that r equire lal"3e spar de pt hs for stlClctural efficiency.

The :Large spar d epths require the use of thick r oot sections .

This t r end to thicl\ rootsectio1'ls has been encouraged by the r elatively smal l inGr ease in drag coefficient with thickness ratio of smo~th airfo , Hs (f:j.g ,. 12) . Unf ortunately , airplane ,vings a r e not usually con st ru c ted with s mooth , surfaces and, in any case, the surfaces ca.D:9 ot be r elied upon ' to ' 8, tay smooth under all service condi t:Lons. 'Th e effect of roughening the leadllltS edges of thick ai r foil l to cause large increases in the drag coefficient at ' h ig h Uft coeff . ic ients . Ti...1e resulting drag coeffic ients may be ex c essive at cruising lift coefficients , for heavily loaded, hi8h- oo altitude at r p18nes ,. A;:' rf' oi.+ sectio ns that have s ui ta ble charac te r istics vThen smooth bnt have excessive drag coefficients when r ough at li'ft coefficients corre spo nd ing to crulsing or climbing Gondi ti ' ons are cle ,ssifi ed as l LT1C On Se rvat j,ve.

The deci slo n as to ,;'r hether a given airfoil section is conserva'ti ve 1,,111 de pe nd u po n the pm.er and the ~ring ~oB:dino of'

the ai r plane . ' The de cis j on may be affected by expected , service

and operating conCl.i tions . For eXCilllJ' ?le, the abili ty of a multi - ' engine airplane to fly vit.h one or more engines inoperative in icing conditions or after suffering dm aege in combat may be a consideration .

, , ' As an aid in judging whether' the secti,ons are conservative, the lift ' coefficient corresponding to R drag ,coef ficient of 0 . 02 ',"8.8 det ermi ned from thE3 su~plementary figures for' a l arge number of NACA airfoil s~cti on s wit.h rough e ned leading ed ges . The variation of this cr i t'ical lift coefficient ,.;i th aj,rfoiJ. thickness rati'o and cember Is ' s hown i n , fig lIe 4.8 . These dat a shoH tha t , i~ general, the ' lift ' coef fi cien t at v-.rh .ich' the dra.g coefficient ' is 0 . 02 decreaSes wi th ' rearward movement, of pos 'i tion of n:inim1.l1ll pressure . The thickness ratio fo r "i ' 711ich this l5 . ft coefficient J,S a maximum u8u21ly lies bet ,ree n 12 and 15 lle rcentj var.iations i n , thickness ratio from this optirm .. un ran ge gone ra ll cause rath er s ns.rp d ec reas es j:n the cr i tical lift co efficie nt . 'rhe ad dition of camber to the symmetrical airfoils usuall:',' caases &I1 .1. ~1C r ease in the critical lift coefficient except for the very thick sections ) in , vlhlch case increas Ing the cambe r becomes r elati vely iheff'ectual and may b e actually harmful .

All the data of figur e 49 correspond to a Reypolds numbor of 6 x 10 .

NA CA AC R No . 15C 05 As sho wn i n f i g ur e 49 , t he dr ag coeff ici e nt at flig ht valu es of t he Reynolds number m ay be con s i der a bl y lm.p r t han the drag coef f ic i ent a t a Reynold s n um ber of 6 x 10 if ' ", he roughne8s ia con fi n ed to the l e adill6 e clg e .

Pi tch i nc H om ent Th e variatio n of t he qua rter-c hor d :::>itching-moment coei'ficient at ze r o angle of a tt ack ' v! i th airf oil thickness ratio and c81nber is p re se n te d in fig ur e 50 for se v eral NAC A ai r foil sections . The quar ter-c h ord pit ch ing -molllent co ef f i c i en ts of the NACA four- and fi ve -d i gi t- ser i es airfoils become le s s n egat;i ve vTi t h in cr e asing a i r foil thickness. Alm o st no v ar i a tion in qu arte r- cho rd pitchin~ moment coeffi c ient wi th a i r foi l t hi ckne ss ratio or position of minimum pressure is sho wn by t he NACA 6-se r ies airfoil sections.

As might be ex pected, i ncrea s in g th e amount of camber causes an a lm ost uniform ne gati ve in c rea s e in t he pitching-moment coefficient .

As d is cus se d pr evi o usl y, th e pit ch ing moment of an airfoil sect 5 .on is pr i marily a funct io n of it s caLlber , and th.l.n- airfoil theo r y p rovid es a me an s f or est i ma t in g the pitching moment from the mean- line dat a p resent ed in t he su ppl ementary figures . A comperieon of the exp erimental mom en t c oef fi c i en t and theoretical velu0s for the mean l i ne s is pr e sente d i n f lg ure 51 . The exper imen tal values of t he mo men t coe ff i cient s for NACA 6- 8eries ai r foi l s cambered with the uniform- loa d typ e mean l i ne a re u8u ally about three-quarters of the the or e t ic a l va lues (f ig s . 50 an d 51) . AHfoils emlloying mean lin es with r al ues of a less th an unity , howeve r, have moment coeffic ients s om e"T h at mor e n egative t han those indicated by theory .

The us e of a mean l i ne hav ing a v al ue of a less than unity , the r efore, brin gs about o nl y a slig ht r ed uction in pitching-moment c oef ficien t f or a gi ven d esig n li f t coefficient whe n com:ferecl with the va lue o bt ai ned ~ -ri t h a un ifo rm - load type mean line . Th8 experiment al mom ent c oef f i c ie nt s f or t he NACA 24-; 11.4 - , ar.d 230 - 8er ie8 ai r f o ils ar e also less negative than thODe ind . icateo . by the o ry but t he ag r eemen t is clo s er t h eJl for airfoils _ having the uniform - l oa d type me an li ne .

Th e pi tch inG-m ome n t data f or t he airfoils equip.:ed vTi tIl simulat ed spL.t fl a ps d ef 2. ecte d 60 ( fig . 50) indicate that the valu e of t he qu m'te r-cho r d pi t ch ing -- moment coefficient becomes more negat i 'Te vri t h 1ncr easi ng thi c kness fo r all t}:e airfoils tested.

For th e th i ck er NA CA 6- se r :'e8 se c tions t..'l-J.E. Ill2..gn:" tude of the moment coeffic i ent incr ea ses Ivi th r earw' ard movement qf the :p08i 1;;ion of mini mum pr es s ur e .

NACA ACR No . L5C05 Posi'~j . on of Aerod;vnamic Center Tne va.riation of chordwise :pos:" tion of 6he aerodynanllc cel1ter corresponding to a Re ynolds number of 6 ' 10 fo~ ~ large number of rACA a.i.rfoils is presented in fi.gure 52. From 1:.1:.e data g iven in the supplementar ; }' fi gu..L es t here appears to he ],1 0 sys tematic var-:'ation of chordwi se 1)081 tio n of aerodynam i c center with I\eyno ld s number .

The dat a fo r t he NACA 00- and l4-seriei3 airfoils ) presel1ted fo r thickness rati os le8s tl:.an 12 percent, sho'\? that the cho:;.'d:wise posl tion of the aerodynemic center :i.S a.t the quar ter-chOTa. poillt fu'1d doe s no t . vary ,vi th Etirfoil thicknes8 . For the NACJ.\ 24 -) .4 :.-, and 230-series ai r foils wit h thickness ru.tios rand ing from 12 to· 21~ percent, the chorel.wi se r08i tio n of the aerodynamic center is ahead of the qu arter-chord poin1:. and moves for-ward with increase in thickness ratio.

Tne chordivise i!osi tion of the a erodynamic center is behind the quarter-ch o rd po~nt for the NP , .C :' . 6- series a::"rf ::>i J.s 8..."'1d moves reaYWBTd with inc r ease in airfoil thickness , ,·,J.!.j.ch is in acc ordE-l'lce wi th the trend" indicated by r-erfect - fluid theo~o:'y. There appears to be no systematic variation of ch o rd. rise po si " ~jo n of the !?e ro ·- dynamic center ,.j.th camber or posi tj.on of minimum pre·ss u:::'e on the basic thiclmess form fo r the8e a irf oils.

The data of ref ere ce 45 Sl10W impor:;ant f,)rwaY'cl movements of

the aerodynmnlc cente r v' th incre.?s:!..ng traiL.ng -ed Ge (.:'I ng . le :'01' a iven airfoil thj . ckness . For the I ACA 24 -, 1~4-, ana. 230-s · erie8 airfoils (fi e; . 52) the effect of incl'easing traHing - edgo anele is

apparently greate r thaD. the effect 0-:: increasing thjclmess: For

. the NACA 6 - seriee airfoils, 1:,he o.:;>pos:" te aplJea:::'s to be the case.

Eig h - L:i.ft Dev ices Lift · charact e ri stics for t 1O NAC!.\. "-8erles airfoilr equip1-ed wi th plain fla ps are presented. in fig-nre 53. These dail:: show that the max i mum 11ft coeffiC ie nt inc rea ses less rapidly .... THh flap defl.ection f or the more highly cambered sect.io n . Lift charac- teristics of three NACA 6-serie s airfoils I vith split flaps are

presented in refer e nc e 45 hl1d fJgure ~4. The maximum-lift

increments f or the 12-percent - thick sections iwre only about three- fourths of that for the 16 - percont - thick section . The maximum. lEt coefficient for the thick er section with flap deflected is a -0 01;.t the sa.':le as that obtained for the NJ\C" : 23012 ai rf0 11 in the nO'll obsolete La ngley var ia ble· ·den si ty tLmnel (referonce 47) and in tho Langley 7- by 10-fo ot tunnel (r efe r ence 48) .

NACA ACR No . L5C05 T ests of a number of slotted flaps on NACA 6-series ai rfoils ( s u pplementary figures and r efe r ence 49) in dicate that the design parameters ne cessary to obtain high YtJ.a.-..::imum lifts are es s ent~ €Illy s~_ m ilar to those f o!' the N! ~ CA 230- n eries sect2.ons (re ferences 50 8...Tld 51) . Lift d.ata obtainecc for tYl)ical h:l.ne:,ed Single· slotted J O. 25c flaps (fiC; . 55 (a ) ) on the NACA 63,4-420 airfo .il 8!'e I resented in figure 55(0) . A maximum 11 ft coefficient of approximately 2.95 1vas obtained for one of the flaps . Lift characteri8tics for the NACA 65"1 - 118 airfoil fitted with a double-slotted flap (reference 1~9 an d fig ·. 56 ( a) ) are 'p r esented in figure 56(b) . A l:laxlmU11. Lft coeffic:l.ent of 3 .2 8 was obtained . It TilEy be concluded that no sp ec ial difficultie s exi st in obtaining ~1igh may..imum lift coefJ:'ic i en·~ wi th slotte d flaps on moderately thick NACP . 6-series sec t.ions .

Tests of airplanes in the Langley full-scale tunnel (reference 4h) have shown that expected increments of maximum lift coeff'lcient are obtained for split fla::'8 (iiG . 5"() 1ut no ·" for dotted fl8 .p s ( fig . 58) . This fa::'lure to obtain the expected maximum-lift increments ,,, ith slotte d flaps may be attributed to l.naccurfi.c~es of flap contour an d location, roughness near he flap leadinr.:; edge, le&kage J ~nter fe r en c e from flap supports, and deflection of f18:9 and lip under load .

Lateral-Control De-..rices p~ ade~uate discussior- of lateral-control dev i ces is outs:de the scope of this re~ort. The following brief discussion is therefo r e lim:i.ted to con :1.derations of effects of airfoil sha:pe on aileron cha r acteri tics .

The effect of ai rfo il shape on aileron effectiveness may be infer r ed from the data of figure 59 a.'1d reference 52 . The .sed_o n ec fla:;.J - eff .Liven8ss parameter 600/65 is :;:lot ted against the- aile r on - chord ratio ca lc for a numb er of airfoils of different type in fi b ure 59 . Table III) vh ieh presents supplGUlen..l.:,ary .nformation reg!li'ding the data ) is rlaced olr;osi to fit;UT8 59 to :'ac:ilitate its use . Also Sh0'11 in this f .igure E'.!'e the , theo:.'et:::'ca1 values of t h e :farametcr .. or thin airfoil. The data shovr no lu.r~e consJstent t:cen cls of a.'; leron-effectivenes< vaT .L'ti on vi th alrfoil section for a ,vide ranGe of thicfu""1.CSS distribu t, ons and -chick..'1cs"3 r atios . In order to evaluate a.ile_ on characte:rlst-ics from sect,ion data, a method of ana.l · sis is necesc8..i.'Y that 1-Till 1eklCl to :i.~E:sul ts comJ?ar ab l e to the usual curves of stick ferc€; e.gains-c heliX an • ..:.;le pb/2v for threG -d :;'mensional data . The arlalysis that fo1lo;·78 is con s ider ed suitable for comparing the relat -Lve merit s of aile:rons from t..TO - dimens :L on al data .

NACA ~ CR No . I-,5C05 Two-dimimeion.3.1 data are presentee. in the form of th e equivalent c lange in se ct io n angle of c..ttaclc [:,ao · required to maintain a cons:'r.:mt coection lift coefficient fo:;.~ var i.ous deflections of th e aileron J. r om neutral . r r his equi vale!lt, chanese i n all...gle of att ack i.s ·:p lotted. against th e h-!.nge - moment }Js .t'ameter 6.cRc, "Thieh ':'s th e pr oduct of the a .... le1'o n de flection from n eutrcd and the . resulting i nvre me nt of hinge-moment c oeft-.cient based on the 't.'"ing choro. . Til:: s metho d of ana . lysis ta1(es into e.ccount the alleron effecti~'eness , tDe hinGe mome nt c , a nd. the poss:U) le mech8. n.i.,~al advantage between the controls and. the a.i.leronc . The larger the value of 6.00 for a gJven value Ol~ the htnge -m oment paramet.er, the I10 r e adva!lta 'Yeous the comb3. nat ion sho ul d be for pro v liine; a 1,:;.r8e val ~ le of pb !2V f or a given co nt r oJ. for ,(3 . The a8sumpt.Lon th8.°~ the aileron o:;:-el'a tes at. a con s tant li:!,'t coeffJcient as the i. rplane r o ll s :"12 not enti re ly corr(3 c ~,:" hmvever, GIld in701Yes an over

estimation 0 the effect of chmgl1 e em ~le of at tack on the h ing e-

moment co efficient . In addit~on, the S~LU1 of ~he eilGrons and othe r ::,")0831b1e throe-dirr.enGionaJ. er'fects E.2:'e not considered . In spi \.,e of t he .3e l. n a~cure. c~ .es , the method [ll·vvid.es a u .'3E:;ful means of com:,;Ja r ing "'he t~.yo - diL1ens :r. o " aJ. c _arn.cte X' ::'f 5 tics n:" different aIlerons .

F or the 'P ur pose of evo . luating the effect of aJ r foi: ~hal>e on he aile r on chart. c teristlcs ) i t is de ui r ab le to malce the cOlapm :- i.son i;ith unba la n ce d ailerons to avqj.d confusion . Plots of the l·a ramete r s :01' plain un balan c ed flaps of ' trua airfoil cuntour on three atrfo~l sec-i.;ion s are sh own in fidu.re 60 . T"lle chFlre.cte~ist~.cs of the NA CA 66 ( 215)-216, a = G.6 sec t :' on are e..;se:1ti.:J.11~- the same as those for the NACA 0009 airfoil wi thtn t· ... e .canr;e of d.eflect~ . on for i-rhi ch data are 8. vailabJ.e . . The NAC.£'" 6 ~>,2 -( 1.4)(1 3 . 5) e. irfoil 8ho\012 app r eciably 81:nal1e.r values of 6cRo for e. given value of l.\0'O t han t.hE ot he r sect1.ow' prese n :cE,c. . No explunation f or this difference can be offe r ed , althO'L:gh some of the d1.ff erence Dlay r es ult from the fl J. ight.ly sOO:.1er chori of t~e fle:;:) for th is combinaticn .

The effe ct ... of u sing st r aight - sldod ailero n s 'nstead of ai l e r ons of l:.:r'1.l e ai r foil contour ?J. ~ e nhmm in figure 61 fo:: bm !I;JI.CA 6 - 13e r ies airfoils· . One of th0 t,;.;Q combinatio n s for wh ::. ch d ata are available was provi ded nth an interne .l oalfulce whereas tl10 other coml'ination .;ras without balance . 'I'hie difference :r-revents a ny c ompa ris on bet;..~ee·'1. the two combination,:> but does not ar'i"ect comparison of the t i ·ro contours for each case . For the

NACA 66 ( 215) -2 16, a = 0 .6 airfOil, th e straight-sided a~leron ha3

more d esir8b:~e characte ri sti cs for th r c..nge 01' deflectiorm for wh i ch da ta a.re a va ilab l e . I t appears, !1ov1eve r, that t..'1e st . rai g ht- side d aileron -;vou1d bo l ess a(lv&nta.!<:eouf' thc.n the ailero n of true n 0 contom for yOGi tive deflec t .LoZls (' r ~ater then 12 . In -eho ca SG of' the NACA 63,4-1+ (17 . 8) ai foil , t.ho straight - sided e.il.oron a I.pe ars NA CA .A CR Eo . L5C05 t o ha ve no advantc.ge ove r t he a.i..':'eron d' true aj:::,foil contour.

The ad v antage of using .st::-c.i3 ht -8::'d.ed aileronE' a:: " pear:3 to depend marke dl ;r or. the c:irfoil u 3e d bu t suff i cient data are not ava:l.la"ble to d e t ermin e ~he · sj.g n ifi c ant a i rfoil :parame tera . Fi3~u'e 62 shovTs t h e.t i n o ne case t h e ef fe ct of l ea.dt n g-edge rou3hness on the ai ler on c ha r acteristics is l. mfavo r able .

LeadlD.g··Ed.Je Air Intake s The probJ.em of c.esj suing satis:'act , ory leadi . ng - edge air intakes is to mai n tai n t h e 11ft ) d.r8.r~ ) an .d crit:i.cBl-speed characte r istics of t h e sections ,, 7hl1e proviclinf"j lov! ;i.n~ ~ ake losses over a wide ranGe of l ift coefficIents ill1.d into , ke veloc Hy ra t .:. os. 'Ehe da~a of r ef ~ r en ce 67 r::hoy; that de~~ . :::, . ble intake !04"'ld drag cha:ro.cteristics can ea si l y b e ma i n t ained ove:r a rathe:." small range of lift c o eff icients fo -r IV-\CP 6 - series airfoL.s . The de , ta of reference 67 Sh OH t ha t t he intake losses l.ncre9.se r apidly at moderf'tely high l if t c oefficients for the sila , res tested. Unl , ublished data taken at t h e La.."1.t';le~r Le-boraca r y imlicate t h at shapes such as those of re fe r e nc e 67 have 1m., maximum-lift coe:ff LciE:nts. Hecent data shm.

th a t a ir - in t ake sha1 ~ es caD be prov,:,c. ed for Euch airfoil sections w it h d esirEtble al r ··intake characteristics and. \·rithout 10s8 in maxi.m um lift coefficie n t (fi (~ . 63) . Some lll'eSsv.re-distr.lbution dat a fo r the air tnte.kes s~101m in figv.re 63 indicate tha:r. the c r it ic al s p ee d. of the S8ct 2 .on has been low e red only slightly and t h at f al l irLg pressu r es i:::1 tho direction of flow were maintal.ned f or so me d istance from the lead~.ng edge on both surfaces at LLft c oe ffi cients near the de"ign 1 i..ft coefficJent for the section .

Su ffi c ient info:-me.tion is not 8.va::'lable to ::,;ermj t such desir9.ble confi g ur at i ons to be desiQ:ed ' ithout e:~J)er;ment3.1 development.

Interference Th e main problem of i. nterferonco at 1m·, Mach number8 .~8 con- s id er ed t o be thu.t of avoid:'n .:;- b Ol'LTlda r y - layer Se2Brs.tioll reEmlting fr om r api d f1m·, G:~qJent,icns cauGed by the addition of ino.uced velo c i ties about bod. ies and the bOl'..."'lde.ry-la;yer accumulations near j, n te r sec tions . No r ecent sy~tematic inv8stigations of interference s u ch as the invest.igation of r e:i:'erbnC(; 68 have be en made .

Some tests have been made of ai r foil sections ,{ .' . th intersect i ng fl at plates (r e:':croncc 69) . TheBe cor.si£UTat::.ons may 'be considere d to r ep r esent 8, p}.1roximately the condition of a. ying int.ersection .... ri th a l arge f l at - sided f'tl8elag8 . In this caso; the interference ooy be con s id e r od to rE.' , sul t f r om the e ff ect on t.he "ri.ng of -i,:,he fully d ev e lo pe d tu rbu lont bo un dary l ayer on t~L fusolage or flat plate en d <:)7 -- .

l ____ _

the accumuJation of b011.ndal'Y l aye r j;n the in·cer se c tion. . The se t est s s howed little int er:'er en c e e:-:c . ept in cases for 'Thich the boundarJ laye::~ on t 1e ai r foil alone , ,'as a pI-roa h i ng con cU t·io n s of separe . tion s uch s were n Qte d with t he less c' om:ervati ve ai r- foils at mod er ately high lUt cgef f:lcienm.

Som e scat tered data on th e ch aracteristi c s of n acelles mo un t ed on air'foils p erm i·~ting exte ns ive lamina r flm v are presented i n references 70 to 72 . '1'he d ata aJ.peaT to j.ndi c ate t h at the 1 ntel'fe l' ence .: r oblems fo r cOllse rv aU ve N:\ CA o-se r ies sections a re si m ilar to those en co1Llterei i· ... i t h ot.her t~'1'es of airfo il . The d et a il sh apesfm opti..m J:'u :nterfering bodies and f:'.llets may, h owever., be d iffe rent for va::,iOl~S G6ctj.ons 1.:;:' local excessive expar..sions in the flmv are tc bo a·,'oideu., Some lift B.n d dr ag d ata for an a":'rfoil ~/lith p usiler - l,r olJell er- s h aft housin, ~p a r e J.l r esen·~ed in re.l. e re nce 73. These re suJts i nd :i ca t e t ha t }:,rotubc " 8.11.ces n ear the tra':'line; ed. ge of win gs should be ca r efully d esig...l1.e d t o avoi d Ulmece8sary drag increments .

Anoth e r type of interference of l-articul81~ . importance fo r high-speed airpla.nes results in the r ec luction of t h e cr iti ca l ]\1aC_ 1 number of the combin ation oeca1..'. se of the addition of the :... nduced v elocities asso c l.:,ted "J1th ach b ody (reference 74) . This ef fect may b e kept to mJnimu:.ll by the URe of bodies ' ui th lm1 in duc ed v el oc : tie s , by se: ?are ti on of l nt erferi~g bod ie s to the g re a te st possible extent , and. b~.r such selection 8...11.d a rrangem.ent of c ombinati o ns tho t the :pointG of maximtull induced v elocity f or ea ch bo dy do n ot coincide , De ta il con si de r ation of the ve. rious factors affecting idug desi gn lies outside the scope of t his reI-ort . The foJ lm>i ng dis(;U8Sion is therefore l:nU.ted to f:l Oine iID})O rt ant o.er odynamlc features t h at must b e co n si de red in the 8. pplication of i~he data pr esente d.

.A}?)l:tcation of Sc·:;tion Do .to.

1 -ling characte r i.stics a r c u oue.l ly pr e dicted f r om ai rf otl - se ct ion data by use of methods bDse d on cimple lift l. ng-line t h eo ry (referenco s 75 to 78) . ApI) licat ic-n of such methods 'to 'I r ings of c on ventional phU1 fo r m , ~L th i) ut sra.nv:;"sG l:"eco nt j. nui ties y i e ld s resu.l t8 oi ' reasor.able en;51nee1'1ng ac cur acy (refe r ence 79) , esp e ci aJ l y with r egerd to such · .IDpo r t.:mt che.rac::.te~lstics as the angle of zero lift, the l:}.ft-cUI've slDpe, the pitching moment, a nd the dr ag . Bb.s:tcal ly si m ilar methoele not reot>.lring the

assu m ption of l :i.ne.3T se c tion lift c hare~-;:,er-,-stics (references eo

e.nd.81 ) appear capable 'o f yiel d ing r esults of greater e.ccvracy, espe c ia l l;y at h':'gh lift co e ff ic jents . Fnrther ref~ne!Jlent may be made by co n sideration of the c ho r d ·rise dtstribui..ion of lift ( r e fere n ce 82) . lVir..gs , ,, ith J.arl.;e amo'llts of s~ ... ee:i? require special conside r ation ( reference 83) .

Th e usual 11ing t:.180ry ass'JmeG that the result-cnt air force a nd m or,J. en -c, on any vinS section are f·,mct::.ons of only the section lift c oe f fi c ient ( or angle of attack) and the seetlon sh~pe.

Ac :; or di ng to t h is assumption, the D.il~ forcee and moments on an;y section are not affected by ad .j&.cent rections or ot.her :'eaturcs of t.h e w':'Y'..g except as such se;:;tions 0:;' features af:'ect the li;t d ist r ib u tio n an et thus the local lift of the 88C1.:10n uJlder con- si d er ation . Those a..3sum:r-tions ob'riously are not va.lid near vT:ine; tips , neal' dissont: . nuHies in deflected fla:;Js or alleroIl(:, n.ea:c disi,-;nrbing bodies, or fo r ~·'ings vrl th ~roI)ou..."1cod. S Hoe } or s·J.dden ch anges in pla.:."l form, sectj.or.., or twict.. U~1der such circv.mstcnces , c r oss flo lS res ut :in Ii brefJ.kdo;..'ll cf " ehe concept of two-dilnenslonal flmi oYer the a5.r·foil sections . In a ddition to these cross flows, indu c ed effects eA:ist that are e<iuivalent to a ch8l1,3e In caI'lber.

Suc h effects ere pa.rticu:.i.arly marked near -;;'he vTinZ tips for ' wings of norm al plan form and for Hin.s of low as}ect ra.tio or unus-aal p l an :o r. n . Lifting-surface theory (see, for eJ:a.'U:ple, reference 83) pr ovides a lUeallS i'or calculating ving c!1/:.racteristic& mo re a ccur atel;;; than the simple liftinJ - line theory .

Al though syan load iistrt -but.-.on3 caJ.cuh;.tpd for ,·rings with d iscont i nui ties such as are found 'I .. ;ith 'p6rtial - spe-n flaps (r efe :,:en ces 84 and. 85) ;"'1[l.' be su.ff·~c:Lcnc:;ly ac cta'a 'J e f'or structural d et:l5 gn, such diRtr i butions are not SUl table fOl' predlctl.ng D1a."'.{imum - lift and s t al l ing chao acte r is t:l..cs . Unt "'.::'" sufficient d.nta are ob te.i n ed to permit the predlct10n of the maximum-lift and stalling c ha r acteristi c s of 1vings ~; t -;:' .. 1 d is conti:lUi ties, theSE:; characteristics m ay bos t be estimate d from pr eviouB results 'fith similar wiIlBs or, i n t h e c ase of unusual config'ITatiol1.s, should be obtained by test .

'I'he characteristics of intermediate 'Vrl.ng sections must be kn o 'V ;n fo r the appl i cation of 1rT.i.ng theory, but data for such sections a r e sel d om avai~G . ble . Tests of a number of such intermediate sectio n s obtained by se veral manufacturers for 'HngS formed. by s t r8.iGht~line fairing have indicated that the character·~st:i.cs of s uc h sectioI1~' may b8 obtained vrtth reasonable &ceuracy by inte r polat:i.o:n of the root &:nd tllo characteristics according to the thickness variation .

...

NACA ACR No . L5C0 5 Se le ction of Root Section T:'1e chaC'acte r il:lti.cs of a -wtr :.3 a.re c..ffecte d to a larGe extent by the r oot z0ctio:1. . I n t he caRe of t~.pered wings foxmed by straight-ljne fairIng, the :c psult1.ng nonlDl.ear variation cf section along t he spar.. ca uses the sho .pe:J of the sectlons to be r: ~ed.oUlinantl y affected. bJ the 1'00t , 8ct';'on ove r a ' lc:.rge Pill~t of the i'rin€:, area .

The des i r r:. b ili ty of ha- jng a th:i.c k win g 'chat p:co vide s spo.ce for ho u sing fuel and e q ui )m ent and red u cen s·,. ructural ,,1eig ht or pe rmits large spazlR .1suaJ. ly 10E'd.z to ttle sele ct ion of the thickest root section t:o.8.t ts e :::' od ' TIamj calli feasible. The compar atively smal l v ariatto:::1 of minjmum drag coeff::'cient with t..'l:ticlaless ratio for smooth e.i rf o:Lls j.n the n mmal rfu"1 'sO 0; t1 iclWleos :cat.ios and the mai ntenan ce of h 1g h lift coefficient i'CJ.~ th.!..ck se tions v: th flaps deflec t ed us nally res .... ll t i n li:ni tation of thickness r atio by char - ac t6ris ti.cs othe r than m:::.xi l"lU.Dl l:' " ft >: d. m":':1. imum dr2.g .

The cri t5.ceJ 1I1e ,cll nurr.'ber of t1:8 eectio:::1 is e1e nost s~rious limHation of thiclmes8 ratio I'or high - sreec. a':"rplanes . I t is de s i r able to se 1 eet a ro ot sec tion "d. th a c1'i t:cal M a ch nuniber E' uffic ~.e ntly h1.3h to avo~.d se r .ous dy ag in , reaSeS r esul tine from comr-res sibiEt y ef::ec'!:'s at t h e h io he st levol - fliB;ht sr.-eed. of the ai r J;lar18, allowancE) being mo..d .6 fo r the ':::'ncreb.sea. veloci t;y of flo VT ove r the wi:::1g r s: ~l ting from .i.nte:"ferenc& of bodies an d sL.pstre am .

Avu.ilab l e d uta inrlic a.t e that a small marg;n exi st s beb-feen the cr i t.ical Bach munber a nd the Mach numb er &t ,,,hich the drag in ,r eases s!'J.arply . As airplane speeds increase, it ecomes incro a sin gly d ifficu lt and. f::'nally imposr3ible to o.voj.d t he drz:.g increases r esul ting from cOillJ, r essioili ty effectE' 'by reduction of the airfo:i.l t h i ckn ess r ~~ tio .

In t:r..e cases of ai rrlan 6s of s · t.l.ch ~m{ SlJoeds that compressi - b il1ty cor~siderctio n s do not limit the thicknvGS r atio to values l ess than a'bolAt 0.20, the mc..:ximum th::'ckr .. oss r a,t.io is liml t; d b;y excessive d2,~ug coefi : Lc },entl-3 t~t. mod.erat.o 2:'."lCl. h113"" 1ift coeffic~.e n ts w th the 8Ul "fQ. ce~1 r O' . 'jh. In ~.:.he"e caLas, the ac [;·;.~al surface co n di t,j,ons expocted :': '0 1' th& alrr-lane s· _ould bo cons i.clered in selecting the Gectjon . Cons.i.J.erat::'on shouJd also be gjven to 1.Ulusual conai tinns su ch as i ce) mnd, and d.e;.maGe cau3o d. in mili texy comb at , especiall ;y in the case of muJ.tivngj,ne ab : planes for ,·,hich ab11i t. to fly undar ouch con:1i t:'ons 1. ~ d.esL cd 'loTi th one or more engin e s ino::.-er a'(,j ve . In cases f or \· , h:i.c1: root sections hav~.ng large th ickness r atios ar e unl e r conside r ation to pormit the usc of h igh aspect r a.tios, a 2,"oa1 8'(;lc ar;;prt'160.1 rf the c.rag coe ~fic ients of eu ch sections .vi th thG expecte d ;:m rfc:.c e conditions c. t moderately h 1gh lift coefficients will indicE.te an op-c.imurn aspoct r atio beyo nd w hich c orrespondtng inc r eas· s in as;,;cct r at~o and root thicknoss r atio will result in rednc e d l ,e r :.. ornan~G .

NACA ACR No . L5C05 Inboard sectio n s of wln ge on conven tio na l ai r planes are subject to inte r fe rence effe cts and ma:'t be in the pro:;?eller sl.ip - stream . The w::'ng surf a ce s are likely to be rOU3he::1ed by access doors: landi n g - gea r retrac tion well s , and armament i nstallation s .

At t ai nment of exten si ve l.:uninar flows is, the re fore, less likely on the i nb oard vine; panels than on the outboard panels . Unless su ch ef fects are minimized ., I tttle dr ag reduc tion 18 to be expected from the use of se c tlo n :"' p erm :' tting exten sive laminar flo,,-. Under these cona i tions , the us e of s ect ions SUCll a s the RACA 6 3 - series w'ill pr ovide advantages i f the sections are thick , because such sect~ _ on8 are mo re c on s erva t i ve than tho se permi ttin5 more extensive laminar flow .

Se lect io n of '.i:ip Section In orde r to promote desirable sta lling ch aracte r istics , the ti p section shoul" have a .h igh ma..'Cimum lift coefficient a.nd a lar ge r ange of angle of attack 'o eti'leen zero and maximum lift as compared v1i th the r oo t section , It is a1::;0 deE irable "that the tip sectio n Etall i·~it~iout a large su Lden loss in lift. The attainment of a hiGh m.wc";.uw:J. l~ft coeffioien t is often more cl ifficul t at the tip sectj . on than at the r oot s ect io n for "C&pered 'lings because of t he imler He;ynolds mmiber of the t:Lp section . For "rings with small camber, t.ho most efI ' ecti ve vray of increasing t..he section IDa.x.i.mum lift c oefficient is to :'ncreare the camber . The amount. of camber u sed will bo limci.ted in most cases by either the crit ical-speed r equi r ements or by the re quiremen t. t h3.t the sec-t-ion have 10"" drag at the high-s~eed lift coefficient , The selection of the optimum type of cambe r for the ti:p section p r esent~ pr obl e ms for i-[hich no catergori . cal a;"lswers ca...J. b e give n on the basis of existing data . The usc of a type of cambor that im I, oses heavy l o ads on the aile r ons complicates the des-,.gn of th e lateral - control system and incl ~ ea8es it s ,· ;eight. The use of a type of cam.ber thr..t ca rr ies tile lift farther forTlard. on the sectio n and. thus r elieves the ' ailerons vTill , hOTrev e r, ha"J"e little effect on th e maximum lift coefficient of th8 section unless the max:!.m1X)l-camb e r pos ition is well fonTard, as for the NACA 230-series sectj _on'"' . In this case a sudden l OE::s of i.ift at the stall may be expected . Tne effects ' on the cambe r of modifications to the air- f oil contour near the t r ailing edge , ·hich may be made in designing the aile r ons, should not be overlooked in estimating the charac- teristics of the wing . .

If th e r oot sections a r e at least moderately thick, it is u sual l y d esire.ble to select a tip se ction with a somovlhat r ed:lccd thickness r atio , This r educt io n in thi ckness ratiO, togct..11er "lith N.I '!; CP. ACR No . L5C05 the absence of induced velocities f r om interferi n g bodies, gi ves a margin i n c 1'i ttcaJ. s1 eed that permi ts the C8l:1ber of the tip sec ti on to be i ncr ease d . This re d uct ::'o n in thickness ratio vHl probably be l im ited by the loss in maximuDl l'ft coefficient re s ul t1ng from t oo thin a section.

A Slnall an o un t of aerodynamic 1.,ashout may also be u s e f\u as e.n aid i n "{; he 'a v oi dance of tip sta lJ _ ing. The pe!'lilissib l e amount of Tas h out may n ot be lim it ed b y the increase in induced dr ag , 0 0 1{hich is small for 1 or 2 of 'ITO.shout (r eference 75). The limiting I{' .s hout may be that wh i ch cau ses th e tip sectio n to ope r ate o',xtside the lmr-- dr €'.g raIl6e a t the hioh- sp eed lift c oe fficien t . This limi tEl,tien may be so severe as to requ ire some adjustme n t of th e camber to penni t the u se of any I{ashout .

A chal1ge i n airfoil se c tion betw een the r oot and tip may be d esi ra ble to obtain f av o r a~ le sta ll i n3 characte risti cs or to uuce ad.var..ta 8 of ~he greater ex t ent of l aminar flol-T that may be possible b on the outboar d se ct io ns. 'l ' hus, such cOlJlbinations as an Nh.CA 230- se r ies r oot sec t io n w ith an IiJI :. Ci\ 44 - se ri .eG tip ' se ct io n or an ::~ACA 63-se ri es r oot s ec t i on with an NACA 65-s ' eries t i p section Iru y be des J. r able .

It sho uld. be n oted that t h e tip sections may easil y be so heavily l oadect by the u se of an unfavorable plan form as to c aus e tip stalling with any re aso n able choice of sectio n and w as h o ut .

Both h igh t.a· er r atj.os Eti1.d l p ...rge amounts of sweer b ack a r e unfavora"ble in th i s r espect and a r e p a rt i cu lar l ' bad when used toge th e r, beca us e the result i ng t"ip sta l l plnomotes longi t1ldinal ins t abili t y at the stall in addition t o the usual lateral instability .

CONCLUSIONS The follmvj.ng conclusions ma y be drawn f r om the data pr esente d .

Most of the data, par ticu:J..arly for t h e l ift, dreg , and pitching- moment chn .r9-cteristics, wer e obtai ned at PeynnlG.s number s from 3 to 9 X lOt) .

1. Ail " foil .sections jJerlJlit~ :., i n0 extensive laminar flow, such as the EACft., 6- and. 7 - e6r:Les se ct ions, r CGul·t; in substptl1 tia l r eductions i n dra at hig.."h - sp0e d. and cruis ' ng lift coeffic:'ents Li S compare d Hi th ether sect:LOns if ) and only if' ) the ,;ring c 1.7.rfaceG EQ'e fa ir 8.J."1. d sm oot.h .

2. Ex:;erience w ' ith fLG.l-sL:c Fingo has shmm. that extensive lam inar flovTS a r o octa:'nab l e if the surface ,fin~sh is as smooth as NACA ACh No . L5C05 that p rov ided by sa.."'1dlng jn the ch or dwise direction lith No . 320 cf'.J:'b orundum. paper and if the surface is free from small scattered defeG -cs and sp ecks. 8at::'sfactory :r-e :, ul ts ere usuctily obteJ.ne d if t he &urface 1.8 9ufficiently fa:'r to perm._ t a straight - e d ge to be recked smoothly ::" n the ch o rd;'T 1..;;e direction "Tl thout Jarring or c ::"i c--iI16.

3 . Fo r ,·dngs of moderate thickneE18 ratios with surface condi t j. ons correspond i. r.. S to t~1o s e obta.i ned vri tIl c1.irrent ,,0:1 - strv.ction me thod .s , mini~ l '1 dra g c oe!f:l c ient& of the ol'der Gf o . 0080 ma~ ~ be e; : pected . The va .lu es of the minimum dra g coeff:.cient for such ;.;rings depend pr l marU _y on the s urface condi t10n rathel' than on the ai r foil se ct ion .

4. Sub3t&'"ltial re(2"t~ct.l()n8 in dr &g ccefficient at h igh Re,7JloJ.ds number e may be obta' ne d. by smoothing the wi .ng Gurfe.ces, e',ren if extensi ve l~iner flm·! 10 not obt2.ined .

5 . rrhe max'mULl l i ft coefficient 8 for nVJderately cF.L'11bered smoot h NACA 6 - se r ies ai rfoile ',Ii til the u:r; ifO!"lll-load type of m09.l1 l ine nre as r;i3h as t hose for NJ:.CA 24·· and. 44 - ser:'_e6 alrfo':'ls.

The NACA 23 0 - se ri es aj . rf0ils have some,\<ih2.t higher ma~dmum ::"ift c oefficients f or t..h i cJme fs rat j.os le ss than 0 . 20.

6 . The m.a.ximl1In lift coefficients of a':'rf0:l1s with fi .... })s ore about th e srun.e fo r madeY'ate] y t h ick N[~CA 6-ret' :'.ed sect.i.onB as fo:c the N.":.CA 2 3012 sectio n but f~p}e3.r to to com .:~ .. (.;Y'ubly 10w'er for thinner NPCA 6-serje s sections.

? T :te lift-curve slopes for smooth ~~ACA 6-:::er _68 a':':doile are slightly hi gher than for NJl.CA 24 -} 4~. -, end 230 801';:,e8 airJ.'o.i.ls end u ::m ally exceed the theoretical v2.1ue for th:in airfoils .

8 . Le.3.c1ini ; - e<.'l-ee ro uchneS8 c auses lerg0 reduct:..ons in mcY..:..nllllil J _ift coef'fic j ent :or both plain a ir- fa l l::: a~ld :::.i rfoils equi}Jlx.:d.

wi th SI ,l i t. fl aps deflec te d. 60 • The d .ec remen t i..'1 m:J.Xiuv.m 1 if t co eff5 c ie n t r esv~ tine from 8tfu~dal'd roughn68s is 8s8crrt.ial:.y the same for the plain ai.rfoi l fJ 8.3 for the airfo~ 18 bCl.u.~p:ped. v1 th the 60 ~):t: l i t flap f; .

9 . The efi'ee (, of leading·-edgc roughn ess ::'8 to decl'oase the l i ft - curv e s l ope , :r;a-rticulal'ly for the thicker s(,etions huYing the posl tio n of mi r.L :Unvm r-ressure f ex be.ck, 10 . Chu-ac te r ls';'-'ic5 of ai r foil sections wi -eh t.he expected surfac e condi t iol1G mw: ~ t be }:novm or est i mated to pro'; J,de a satiR- f a ctory b anis fo r th e predlctioll of t . he ch ~ ractel'13ticG of l,Jre.cT,-,-cal - c on st ruction "\-Tin. <3S 3_'1d ·(,h0 selection of' airfoi ls for such \-1ings .

NACA ACR ro o, L'5C05 11. The Nt. CA 6- s er:.e s ai: d o·o ls pr ov ide highe r critical Mac h n IDl b e r s f or hig h- :3peed wd cr uis::.ng l ift Goefficients t h arl ea.r li er types 0:: sectio n s 8!ld ha ve 8 r e "i..:lcnable range of l ift coefi icaen t s wi t h :'n -,ihich high crt tical i'i ach n'lAIllbe r s ,",-a~' be otta:Lne d 0 12 0 The Nl' C, ~. 6 - s er i e s s e ctio n s pr ovic_e ower :,) r edict e d c r :~ tical n Ma ch n um be r s at mo d e2. ' ate l y h ig h lift coef: 1c::'en-;-;8 than t lle ee.rlJer t ypes of sectio ns 0 The I l L i te d da t a availeble s'L .ggest , howe rer , that th e NACA 6- "!e r ies s ec '"ions re'tain satisfe..ctor - lift charac- t e r iGtics up :'0 ~ igh er . "I&c h n umbe r s t han. 'Lhe ea r l . ie l' sectiono 0 1 3 0 T he NA CA 6 - 2e r :. e s a ir f oils d o no+ a:?pear ·to pr eoent u-''1.usual pr ob l em s '\Vi t h rega r d to t he 8.}'pLc 8 .tion 0_ a.ile~onG , 1 4 , ? l' ob lems associat ed vri th t he avoi.dance cf 0un da r y - J.ayer se p ara tio n c aus e d b y i n t eri'er ence ar e expec ed to 'I)e sim'lla r fo r c on se rv at.iv e :JACA 6-se ~ te,3 s ecti0ns and. other sood airfoils 0 Detail s ha pes fo r optimum lnte r fe rin g bociies and I'i llets nay be ciifferent f or var ious sec tio n s if l oc al exce s s i ve e~:pa:l8ions. ";' n the flm-oj d ' e to be a y oide o. o 15 . Sn t i.::; fa cto r y l ea din g - e d ce atr intake E: ' may be lJ r ovidGd 'o r N CA 6 - se r .ies sectio n s , b ut i n suffic i ent info:rrJlat~on ex-i.sts to allovr s uch in takes 'Co i)e desig n ed wj .t ho u t eX'~er::.mentE',J. 0.evelo}..ment .

Langley M emor ia l Ae r o n:= \.Ut-i..co.l L':!.bo:::"2tory N ationa l Ad visory Cornmi ttee £'0 1' :.e ro11lmti;:;:'3 Ianc1ey F:e l c:. , Va .

l

NACA ACR No . 1 5C05 APPEND :LZ ME'l110D3 OF OBTAIND'JG D ATA I N THE Ll\lTGLEY Tltro ··DI MENE3IOIJAL LOH -TURBULENC E TUNNEI..8 By Mil ton M. Klein Description of Tunnels ':The Langley tvo -d imensionE'.l 10lv··tu.rbulence tunnels are closed - thro a t .. r ind tunnel s hav:lng rec tangular test sectio ns 3 feet .. Tide a...'1d 7~ feet hi gh and are d esJgnec 't to test model .) completely spannin g the width of the t unnel in t-;m-dimensional flo.r. The 10'.-T- tur bulence level of t he s e t u.rmel s , amounting to only a few hlmdred ths of 1 pe rc en t , is achieved by the lar(~e contraction ratio in the en trance cone ( approx . 20 : 1) arld by the introduction of a n1J.lIlber of fin e -wire sma ll-me s h tu:-cocl.lence-reducing screens in the wi de st pa r t of the ent rru1 ce cone . ':The chord of models tested in these tunnel s is usually about 2 feet, al thOl1gh the characteristics at low l if t coefficients of mo de ls hav ing chords as large as 8 feet may be detenn i n e d.

T'n e Langley two - dimensional 10 H- turbulence tunnel operates at at mo sp he ri c pressu r e and he.s a maximum speed of approximately 155 miles pe r hour . The La n gley t.to -d i mensional lOyl- turbulence pressUl~e tunnel operetes a t pressures V.p to 10 atmospheres absolut e m1d ha G a maxim~m speed of approximately 300 ntles per hour at atmospheric pl~e ss ur e . StEL T1c. ar d airfoil tests in this tunnEl are made of 2-foo t- c ho rd VTooden mod els up to Reynolds numbers of app r o xi mately 9 x 10 a t a pressure of 4 atmo€~heres absolute.

The lif t and dr ag characterist :i. c f3 of airfoas tested. in these tunnel s are usuaJ.ly mem:ured by met h ods ot her the.n the use of b alances . The l ift i8 eV'- v luated from measurements of the pressure reactions on t h e floor an d c eili.ng of the tunn el . The dra g is obta:..ned from measurements of sta.ti c and toto.l ~.'reGs ures in the ,,,,ake . .r.-loment s are ucually measured b y a balance.

Symbols A , A ..• A coefficients of pote ntia 1 function for a 2 J l n s;ymmetrical b ody a frac tio n of chord from leading edge over which d esign lond is unifor m NACA ACR No . L?C05 B dimensi o nle ss con s tan t determLn.ing Yitd th of wake c chord dr ag coefficient co rre cte d for tmmel -,: · rall effects C I dra g coeffi c ie n t un corrected for tmme]_-, y al l effects d dr~~ coef f ~cie n t measUloed ~n tmmel section lift coeffic~ent correct ed for tUtlIlel - wal l eff ec ts sect :~on lift coe~ficient ll."lc o rrected for tu nnel-v iall effects design lift coef.Licient l ift coeff i cient mea su::'°e d in tmmel m oment coeffic j .ent about quarter-chord point corrected for tu."lllel -i ·rall effects t moment coe::ficient about quarter-cho rd point measured

c /4

Ille in tunnel F a ver age of velocity re acUn gs of orifices on floor e nd ceiling used to mea su r e b locking at hi gh lifts Fa ave r age value of F in lov - lift range f potentia l. fllnction used to obtain 1~ -fa .c ta r Ho total. p re ssure in fr on t of a irfoil Hl to t al p res e ur e in w ake of airfo i l Hc coefficient of loss of total pre ~ su re in the (Ro - H l\ wake .( - --- ) qo maxim um va lue of Hc hT t~~l heigh t l cd K ==-

Cttr

KACA ACR No . L5C05 L true lift resulting f r om a point vortex L t lift assoc' ate('~ ,ri th a poi nt vortex as measured by integrating manometers ill up st ream limit of lntegration of floor and cej.ling pressures n downstream limit of integ ra tion of floor and ceiling pressures re sultant p res8ure coefficientj difference between local upper - an d lower - su rf ace pressure coefficients static pressure in the wake f~ee-stream dynamic pressure

s

static-p~essure coef~icient \~ ;I

( , .. \~ "_ 1

(Ho - Pl\

static-pre s su re coeffj cient in the wake \'-~-J s di stance along ai rfo il sl.U'face u veloc ity, due to row of vortices, at any point along tunnel va.lls v free-stream velocity 6V increment in free - stream. velo ci t,Y due to blocking

v' correc ted indicated tun."'1.e l veloc i ty

VII tunnel velocity measured by static-pressure orifices v local veloc:ty at any point on a i rfoil surface w potentjal function for flow pa st a symmetrical body x distance along cho rd or center line of tunnel / .

BYw') y ( v adable of integ ration , c / y d istance perpe nd icluar to stream direction ~ ----- _._--_ . -- _. --~ -~-- .

NACA ACR No. L5C05

ordinate 0: S3'!llmetrical tnickness distri~)Utlon

Yt distance perpendicular to stream direction from position of HCmax slope of surface of symmetrical thickness distribution z complex variable (x -:- iY') angle of zero lift section angle of ettack corrected for tunnel-wall effects ct ' section angle of atteck measured in tUIL'tlel o stren ~t h of a sin81e vortex

r

r atio of measured lift to actual lift for any type of lift distribution 11a TJ-factor for a dditi ona .l. -typ e loading 11'0 Tl-factor for ba sic mean-line loading Tlx l -f acto r 3pplying to a point vortex

A component of blocking factor dependent on shape of body

S quantity used for correcting effect of body upon velocity

measured by static-pressure orifices cr component of blocking factor dependent on size of body .

¢ potential functiorl

~ stream function Measu re ment of Lift The lift carried by the airfoil induces an equal and opposite react ion upon t he floor and ce ili ng of the tuxme l. The lift may therefore be obtained by integ r ating the pressure dj_st ribut ion along the floor and ceiling of the tunnel, the i nt eg ration being

accomplished vn th an integrating rnanom ete r. Because the press ure

field theoretically extends to infinity in both the upstream and the NACA ACR No. 15C0 5 downstl ' eam directlons, not all the lift 1s in(;lv.ded in the leIlBth over which th e inte g ration is performed. I-c is therefo re necessary to apply a correction factor 1) that gi v es the ra tio of the me as ured E f t to the ac tu (.'. l lif t f or any lift distribution. The calculation ,yas p erformed by fir st findin g the cor re ction factor 1)x ap plying to a poi nt vortex and t hen de termining t. h e weighted ave ra ge of this factor over the ch ord of the model.

The factor TJx "TEl .S ob ta.i ned as follo ws : The image system '\oTh i ch gJ ve s only a tange n t ial component of veloei ty along the j tunnel walls is ma d e Ul of EUl infinite vertical rOi-T of vortices of alternating sign as shown in f lg ur e 64. If the s:gn of the vortex at the o r: i.g:i n is assumed t o be I , osit:Lve, the complex potentia l function f for thi s image system is ,,,here

r 8 t reng t h of a 8 i ngle vo r tex

z co m:n 1ex variable (x +.i.y) hT tunnel height The veloci t ;y u, du e to the ?:'my of vortices} at any point along the t unnel '\oralls where y = is t hen obta ., ned as sech rex U hT where x j.s :' he hor i zon tal distance from the point, on the wall to the or ig in. The r es ul ~ant pressure c oefficient P is then gl ven by R 4').

P R -- V (20 ) wh e re V is the f r ee - st r eam veloc it y.

NACA ACR No . L5C05 The l ift manomete rs i n t e grate the ?ress ure distribution a lo ng the floor and cei l ing fr om t he do wnstream p os itio n n to t he u pst ream. position ill ( fig . 6L~). For a point vortex loca t ed a dis tance x from t he or igin alo ng the cente r l i ne of the tunnel) t he lilllits of i n teg ra tion be come n - x an d m - x . The lif t I,' associate d "lith a point vo rt ex) as measured by the inte gr ating manometers ) is given by (21) whE;lre go is the free - stre am dynru:D.j .c pressure .

Th e true lift L r e sulting from the poin t vortex is gi ven by Th e corr e ction fa cto r ~x is th en re x se ch -- dx hT which yield s (22 ) In the Langley two -d i me ns io nal low-tur bul e nce tunnels) the or ifices in the floor and ceilin g of the tunnel us ed to m ea sure th e lift e xt e nd over a length of appro ximat ely 13 feet . A plot 0f ~x against x fo r th e Langley tw o - dj~ens i o na l low -turb ule nc e pressur e tunnel is s hown in figu r e 65. The oj - factor for a g iven lif t di s tr i bution is obtained from th e erpressi on

· I x "

PRTJx d,. c)

L \.. ,cho rd .

./x ·' (23)

P Cl\ - i

[ R , c, t~cho rd .

NACA A~R No . L5C05 The valu es of Tlb and T) a for the Langley two-dllnensional low-turbulence ~ressur e tunnel are gi v en in the following table for a m odel havin g a cho rd length of 2 feet , where TJb is the TJ-factor co rr e s~ond i ng to th e ba n ic mean- line loading (indicated by the value of a) and 1')a j.s the ll -fac tor for the additional type of loadin g as Bi ven by thin-airfoil theory:

- . --~- .. - -. -- . 1)b -_ O J

-1-.0----+-- 0- · .93}+71 .8 . 9342', .6 .9336

.4 .93 jO

.2 .9 32 5 0 .9 322 ..-l . - ---- -_ . -- --.

In o rd er to ch e ck th e variation of TJ with var ~_a tion8 in a th e addition al type of 1if t d _i str:l. bu t ion , th e valu e of fJ . wa s a rec alculated for th e class C ad.·ii tional lift distribution given in f igure 6 of r ef er e nce 76. The value of' T la for this case wes 0 .9 304 , a s com"?are d. with 0 .9 '2. 96 for a thin airfoil. Because of the small variat i on of l a wi t h t he type of ad.ditional lift, the value for thin-ai . rfoil ad ditional l ift was used for all cal culati ons. The lift c oef ficient of th e mod . el in the tunnel uncorr e ct e d for blocking c2 ' is g iven :i.n terms of the lift c oe ff icient m eas ured in th e tunn el c and t h e design lift LT co eff ic 5 .e nt of the ai rfo il c2' by th e following 6X}lression : l C t

( 24 )

Bec a u se TJb does not dif f er m"J.ch f rom fin' It. lS not necessary that the bas ic loading or th e design lift coef f i ci e nt be known with great a ccur acy .

B eca u se of tunn el -wall a .... rid. othe r effects, the 11ft d .i strlbutim over th e ai r foil in t h e t tmn e l does n ot a gr ee e xactly with th e a ssum e d lift distribution . Bec ause of the small variations of 1') 1" i th lift di s tr i but ion , e rr or s caused by this e ffect a r e considered ne g ligibl e . It can als o b e sho~n tha t e rrors cau se d by neglecting th e ef f ect of airfoil thickness on th e d:i.stribution of th e lift l r eac t i on alon g the tunne: • walls ar e smal l .

PeCR No . L5C05 NACA of Dr ag urement Meas s ob 8 ervation i n ed from may be obta ai rf oil dra g ' of en The ima ti on A.11. app rox ce 86).

e (r efe ren in t he ,,,at pres s ure s of the air in of . the p ressure 108 s jn total by the 'is g iven to the dl'ag measured is of to t al pressure The los e a i rf oil .

of the t!1e ,. rake t o t al v ·t hen the the ,.,ake .

tube s i n l-pressure ke of tota b y a ra d re presentG ,· rake a re i n the ai rf oil and of t he s in front pressure ta . illed nt oo d.r ag coefficie vely, th e re sp ect i an d HI , by Ho c~ i s p res8ure of total from lo ss t,

. '

d;Tw (25)

--

li ed T ""

cc

!

"'Take \4 where th e i· rake s ure i!l t o tal ' pres of loss of f .i,cient Hc ,. coef l-'Osition from st re am direction to ' perpendicular distance H of Cma...x Pl' nted by 1s re pr ese in ti . le we.ke p re ss ur e he static If t I may be k i ng . cd ed for bloc l.mcorr e ct ff i clent dr ag coe the true P.6) ( reference t o ' be shewn " f I . (26) / v. i wake wake ie n t in the e c oef:'i c c - p re 8s ur t he s t e. ti whe re is '10 s ure acros tota l 2! r ess of the va r i8ti.on made t h ai., ption is The assum e . The curv al pro b a bility by a n orm e nt ed e c an b e repres the 'I ' Tak e ments fr om measur obta. in ab le easil ;r I is th en Cd drag co e fficient t edT' c t o ratio of K, the of a factor by me e ns d

of Cttr

If th e of Hc .

va lue the Taax~mUL1 8 . and nds only on d e~e which n of t ~e eq l. 1.ati9 H .

6sent,ed by i s r ep r ue of H,., val Cmax J maximum is . b::'ll ty ct).Yve proba the n ormal I \ 'B"fT ' 2 ' T' J . ~ . c· ) ,.,. ' .. ' . ...

·, H = .t1c e c max NACA A CR No. L5C 05 ,.,here B is a dimensi o nl ess con stant that dete rmines the width of the ... rake. If a conY en i ent variable of i nte gr ation Byw

y = -- i s used, the ratio K is

c

=

and is in depend ent of the ".rid t h of the ,-rake . The quantity K has been evalu at ed f or variou G va lues of HC v and 8 by m .. JiJ.

assumin g 3 to . be cons tant across the 'tr ake. The drag coefficIent l cd may thus be obtain ed fr om tllih~el measurementg of cd , H cIllS-X ' T and 8 , A plo t of K a s a function of Hcmax with 8 as parameter is given i n figu re 66 . A parallel treatment of this pro blem is given i n refer ence 87 .

T1mn~l -\'-iall Correct io ns In two-dimen sio nal fl m-r , the tunnel ,.,ails may be conveniently conside red as hav i ng two di st nc t effects upon the flm., over a model in a tunnel: (1) an inc re ase in the free-stream velocity in the neighborhood of the mo del because of a c onst riction of the flow and (2 ) a distortion of t he lift d istribution from the induced curvatur e of the flm-r.

The i ncre ase in free - s tr e am ve locity caused b~ the tunnel walls ( blocking effect ) i s obtaine d fro m consideration of an infinite ver tical ro w of images of a symm et r .!.cal body as given in r e ference 88; the images represent the effect of the t UIlllel walls .

The :potential fu nct ion for a symmetrical body is given 'f by Al A2 An

''I' = Vz +- + --

+ (28) zn z2· z vlhe re V 12 the fr ee -s tream v elocity and the c oefficients AI, P"2, ••. ar e comple x. I f the t unn el heigh t is lar ge compared NACA ACR NOI L5C05 to the si ze of the body, powers of l./z great er than 1 may be ne gl ected and

w = y z

T hi s ope ra tion is e q uivalent tc: rep18,cing the bo(~ y by E-. circ l e of which the double t str en gt h is 2 n:} \ 1; the term A l/z r ep r esents the disturb anc e to the fre ",::,- stTeam flow . The total in d uce v elocj,ty at the cen te r of the body due to all tne images i s ex~resse d i n refer-

ence 88 as

]{2 (30 )

where the term Al :8 the same as the ljerm of r eference 88

, For c on v enien ce in t1.. Uh 'lsl calculation s , the ex:t;reus i on of 6V m ay b e y,iri tten 6V =A (J V whe r e The f acto r a depends only on the size of the body and is easily ca lculated . The fact or A depends on t he shape of th6 body and i s mo r e diffi c; ul t to ca lculate . For bod:i.es such as Rankine o va l s and e llip ses , simpJe formulas may ' be ootai ned for calculating

A. In the ge ner a l case , the va lu e of A may be obtai ned from t he

ve locity di stri buti on over the body by the exp r essio n NACA ACR No . L5C05 wher e v is the velocity at any lJ oi n t on the airfoil surface and dY t /dx is the slope of the airfoil surface at any point of ~'Thic h th e ordinate is Yt .

In o rder to obtai n this expres sion, con s ider the flow past a symmetr i cal body as shovm in figure 67. The potential func t io n for this flmT is give n by equation (28) . Dlfferentic.t ing and mul ti:i;1 1ying

e~uation (2 8) by z giv es

Al dw - Vz "

Zaz

z zn

The line i nte gra l about a closed curve 1 z ~ dz will depend

only all the term - Al/z and., fr om the theor; / of res i( lues, is giv en b y - 2rriA, .L but <i i- ;

Z dz- dz = z dw

= (x + .i.y) (d¢ + i d *)

I" here ¢ is the potential f 1)nc tion fu"lG. l!J is the st ream functi.on.

On th e su rf ace of the body d,\~f :'= 0, v O that dw

:"1 J'"

Qz dz

= /

; + d¢ + i CY d¢ \.. I C Since the body is symmetrical) the term x d¢ ,,;ill have e~ual numer ical values but opposite signs at c o rresponc1ing points of

the upper and lowe r surfa.ces , and. f' x d¢ will vanish. The

lie

term y d¢ 1"ill have equal values at corresponding points of the

uppe~ , a....'1Q. lower su rfa.ce s , and jy d¢ may be repluced by an

C i ntegration over the up pe r surfac~; ' therefore, NACA ACR No L5C05

dw /'

= 2 i I y d¢ (c ounte rc lockwise direction )

a:z dz

w or Reversing the r.ath of integ r ation , re placing d¢ by

-a. ...,-· 2 "

"'t

replacing ds by 1 + dx d X, and sol vine for A

I

gives

d. (!: )

A \c '\oThe r e the integratio n is t aken f r om the leading ed ge to the trailing ed ge ov er the uplJer su rf ace .

In addition to the error c aus ed by blocking , i.'in e rr o l!' exists in the meas ur ed tunne l veJ. oci ty becua se of' the i nterference effec ·t.s of t he mo de l upon the v el o ci t y _nd icated by t he static - p re ssur e ori fi ces located a few fe et up s tream of t he model an d h a lf iVay between floor and eelling . In order t.Q correc t fo r this e rror an analysis "TaS m ade of the velocity 0. 1 st r J.bution along the streamline halfway betwee n the upper and the lover t unn el ,.,al18 for ' Rankine ovals of vari ous sizes and thickness ra tios . The analysis s howed that the c or r ectj.on could be eX Ilr essed, Hi thin the r ange of conventional- airfo il thickness r at ios, as a pr o duc t of a thickness f actor gi ven

by t he blocking factor A and a factor S which de pe nded upo n the

s ize of tbe model and the di stan ce from the stati c-pressure . o rific es to the midcho rd point of the mod el . The cor rected i ndicated tunnel t v elo c ity V could then be vr itte n V t =: V", ( 1 + ~ ) (36) .There V" is t he velocity mes. su :ced by t he stati.c - p re ss ur e orifices; In the Langley - ti 'T o dimen siona .l lO'\ol. - turbulenc e tmmels, the distance from the static - p re ssure orifices to the nidchord point of the model

is a::;:p r oximat e ly 5.5 f eetj the co r res p onding value of S for a

2-fo ot - chord model J.S approximately 0.002.

In o rd er to calcu. late the e ff ect of t he t unn e.l ,.-all s upon the lif t d is tribut io n, a compari so n is made of t he Eft distribution of a given airfoil in a trumel ar.d i n f r ee ai r on the ba sis of NACA p, CR No. L5C05 th i n- air f oil the ory . It is I'lss1Jlll.e1 the. t the floH condi tions in the tmmel corres po nd most cl 08 e ly to thooe in free air \-Then the addi tional lift in the tunn e l a."'l d in free &i1' are the same

(reference B9) . On t h is ba . sis th e i ~ ollO\v l ng correct.ions aJ. e derived

(refere nce 89 ), jo n .Thieh t he primed quant:!. ties refer to the

coefficients measured i n the turulel: In t.he fo r egoing equations, t he t erm s a re u sually negligible for 2-foot-chord, models in the Lel1€l).ey t;.yo·- dimens io nal low - tu r bulence tunnels .

When the effect of t he humel .Tall ", on the pressur~ d. .Lst rlbution o ver th e model is small , t he wall effect on the dxC'-.b is merely t: a.t correspond i ng to an inc r ease in tile tun nel s?eed. Tne correction to the dr ag coeffjc::'en t ts t herefore given 'by the follow:i.ng relation :

(4 0)

Similar con sid era tions ha ve been appl:'ed to the deve lo pment of correc tio ns f or t he pr essu r e o .lst rltu '_ i on ..L-Tl r ef er e nc e 8.9.

Equation (i-!O) ne g lect s tile block:in{:.:; due to t he 'irc::..ke , su ch blocking be i ng smal1 a. t 1m! to moder ate d.rags. ' rh o ef f ect of a pressure gr a dient , in the tunn . el upon loss of total :p r ess1.~o in the wake is n ot e asi ly c .<J.lalyz ed "but is es timated to be s me . l:'.. . The effec t of the pr essure gr e. dient upon the drag haS the r efo re been disreg~u · d e d. Wh en the drag is ::nea s ured by b. bala..lce} the effect of

t he pr ess ur e gr adient up on the drag Is C: ; rec tly ac..<U ti ve aIle a

co rr e c tio!l should be app lied . For laree models, eS.f;lScial ly at hig .. ~ lift coefflc ie nt s , t he effect of the tunnel 1!TallG 'is t.o d':'stort t he pr essure distrnuti on . app_"eciably . Su.c:" dis t ort.:.o ns of the p re ss ure d istribution ma~T ca use larg e chaTlges in the boundB2."Y flmT ~md no adequat e c or rect i ons to any of t~.1e coefficients) particularly the dra g, can be found.

I NACA A CR No . I,5C05 Co rrect :i.o n l or Blockin g at High Lif t s So l ong as t he fl O\ ,T 1' 01 10,, -2 the airfoil s ur fac e , the fo re goi!l-.:S re lations a c c oun t :f or t he eff e cts of the tun n el w al l s w:i.th sufficient ac cur acy . When t he fl o ,, ! l e aves t he surface, · t h e b loc :ing increases becau se of the pre domin an t effec~~ of the -,rake upo n t he free-st r eam vel oc ity . Si nc 'e t h e wake effect s h miS 'Up primari l y i n the (lr8.b; the i ncre ase in blo c ki ng wo uld. logically be exp r ess ed in term s of the dr ag . TDe ac cur at e m eas u:~e mG n t of dr 8f~ unde r t h es e c on d itions by mean s of a r ake ie impr ac t i cD.J. because of span 'Tise movements of lOi- i- ener gy ai r. A me t h od of co rr ecti ng for inc r ease d blockj.ng at hi13.1 ang le s of attac k I ,Ti thout dr ag meas ur emtns has the r efo r e 'been devised f or u se i n the Langley t wo -d imenEional 10 ·r- tu r bulence tu:me 18 .

Rea d ings of t h e flool~ end ceilin6 veloc:i. ties are take n a. i'm·!

inc h es ahead of the ~uarte r -chord }}oint ar:tc. avera.ged to remove the effect of l : Lft . . This ave r ~"3e iF , Hhieh:;'s a. mCClS;xce of the ef f ective tunnel velocity, is essentially constant :'n t} - ,e low - lift r ange . 'The Quant :L t;y :Ii' /F , ,,'her e Fo is the a ver8.,s8 value of F o i n the lo - w-lift ronge , ho~{ev e r, 8h o'\o7s a vn.riatir ,n f::.~om un~ .'\j;y in the . h ig h-l ift r ange for any a:i.rfoH teste<l in t:h.e t1.U1Ile . l; th in variatio n i nd i c ates u cheDbe in b lo c ki n g at h] gh J _if t s . A :plot of .F/B'o agai n st angle of at t ack 00 ' for a 2-foo't - chord m0cl.el of' tho

NAC .A. 64 3-418 ai r foil. if: g :i .ve n in.'f':'gure 68. T:le Qua.."ltHy · :F/F

o i s n early constant for vaJueG of 0. up t 'o 12° ; but fo).' · valuos 0 ' S' f 00 greate r t h an 120., J!'/F 0 lnCY 6r:..S88 2 ~'1d. t h e increase is ' particula r ly n oticea b le at 8. l1d over the c tal::' .

A theo r etical compar j.Bon '/la2 made of thE:; bl ockj.ng facto r A cr, and t h e v eloc:l ty me asu r 0 cl. by the floor and ceiling or Hices fo r e se r ies of Rankine ovals of Y~rj,oU2 s iz es end. thickness r ati08 . 'rhe qua r ter - cho rd point of each ov al "ras located at t h e 'Pivot poi n t , t h e usua l },Josition of an ai r foil in the t mnel . The anal"i3is show'ed the r elatj.o n b etwee n the b l o c k:~rv[ fac tor Acr mid ':he ch e. n ;. zG in F ~ , '-' to "00 uniQue f or c ho rd l en gth .::; up to 50 inches i n that djffer e nt b od ies havtng t he same bl ock: l ng factor Acr gave a.PP1 " oxime.teJy tho BElnle v alue of JP. Fo r c hord n u:? to 50 inche[! , the rej.a tion3hip is / 6,V == 0 . 45 ( X.

(L~l ) V \ Fo , w he r e tN Iv is t h e trL~e i n crement i n tm1nol. voJ.oci t;;r due 'Co blockil18 .

The foregoing r elation io Tas aclopted. to obtain the con"ect :i.o n to t h e b l oc kin g ' in t he ra.llge of lift wl1ere .. . L > 1 .

Fa ConsiderabJ.e un.cer ta i nl: ! exist. s reGarding the correct numerical va lu e of the coefficient occurrins _ 11 equation ( 1+1) . y' 0. rm f of NAC}\. A CR No . 1,5C05 sources, rahter than the Ranlc ine ovals used ln the p resent analysis, is considered t o represent the ef ' fect of the wal'\:e, the value of the coefficient in equation (41) would be approxirr..ately t"rice the value used . Fo rtun ately, the c o rr ectio n am01mts to only about 2 percent at max imum li f t for an ex t reme condition w1 th a 2-foot-chord mod.el.

Further re finem en t of this c o rr e cti on has therefore not been attem pte d.

Comnarison with Experlment A check of the val i d ity of the tunnel - "r all corrections has been

made in reference · 89, which gi v es lift and moment cur-,res for models

havin g various rati os of chord to tunnel he1ght, uncorrected. and . corrected for turmel-vTall effects . The u;ener31 agreement of the co rr e cted curves shOivs' that the method of correcting the l i fts and moments is valid .

A compar.L so n i s nL8.de :t n r eference 89 beti·reen t:i16 theoretical correction factor (equation (40)) and the ex:perimentally derived c orrec tions of r eference 90 . The theoretical correGt.1.on factors ;.,ere found to be in good ag reement ',lith those obta i ned eX:i?crimentE'~ly .

. Xn ord. er to check the validity of the T) - fa.ctor, a cOI1i:.sribon has b een mad.e of lift values obtG.ined from pressure d.istributions ",i th those obta.ined. from the integration of the floor and ' ce j. ling p re SSUl"eS in the tunnel . A com:;!8.T1.son :01' two air ' 0':"18 3i ven in figure 69 shovrs that the tvro methods of measuring lift give l'esu.l ts that m~e in goo d agl " eement . The T)-factor ht.:.s a lso been checked by compari so n of the .lift otta.tne d from bale.nce measurements with tho integra ting -ma;nometer vaJ.ues in figurE> 70.

Finally, a check h as been mads of the methoct of correcting pressure ' distr1butions (reference 89) for NAC!>. 6-se~ LOS airfOils of two chord lengths at zero angle of attack in figm"e 71, in .rhj.:::h the pressure coefficients are plotted against chordvrise positioll x/c. The ur3 r OeD16nt betw ee n the corrected pressure distribut-Lonc for both models verifi es the method of making the tun..TlC'l-ub.ll corrections.

NACA ACR No . L5C05 REi".l!1· t ENCE S 1. J a cob s , Ea s tman N ., W ar d, Kerme th E., and f- ink e rton, Robert LvI.: The Ch aracte ri stics of 7 8 Re l ated Ai rfoil Sections from Tests i n t h e Var iabl e-Den sity 'Wind Tunnel. NACA Rep . No . 460 , 19 33 .

2. J a cob s, Eastman N ., an d Pinke r ton , Robe r t M .: Tests in the V ariab le-D en ci ty W i nd Tun ne l of Related Airfoils Hav ing 'che Maxim um Cam be r Un u sua l ly l~ar Fon-Tard. NACA R ep . No . 53 7 , 1935 .

3 . Jacob s , Eastman N ., Pi nke rto n, Robert M . , and Gr ee n berg, HaT r y : Tests of Re l ate d Forw-ard- Cam b er Air foils in the Variable - Den sity Wind Tunnel . NACA Rep. No. 610 , 1937 .

4 . Stack, J o~ , and von D oe~~o f f , Albert E .: Tests of 16 Related Ai r foils at High Speeds. NACA Rep. No. 492, 1934 '.

5 . J a c obs , Eastman N. , and ShermB... Tl , Albert: Airfoil Section Char a cteristics as P.f'fected by Variations of the Reynolds numbe r. NACA Rep . No . 586, 1937.

6. Pinke r ton , Robert 1'-1 . , an d Greenberg, Har r y : Aerod;ynmr.ic Chara c te r istics of a Large Number of Alrfoils Tested in the Variable -D ensity Hind TUl m el. NACA Rep . No . 628, 1938 . .

7 . J ones; B . Melvil l : Flight Exper jmen ts on the Boundary Layer .

8, Jour . Aero . Sei., vol. 5, no . 3, Jan . 193 pp . Bl-9h.

8 . J acobs, Eastman N ., an d Abbott, Ir a R . : A::r.foil Sect:tol1 Data Obtained. in the N.A.C. A. Va ri able -Den sIty fu'1l1el e.s Affected by Support Inte r ference a..'1.d Other Corrections . NACA Rep . No . 669, 1939 .

9 . Theodorsen, Theodore : Theory of "({in e; ~~e ctions of 1.r bi t~a ry Shupe . NACARep . No . l~l l , 19 31.

10 . Staok, John : Test s of kLrfoils Designed to Dela.;y t Il t' C0mpressibili ty Bu:cble . NACA TrY No . 976 J D ec . 19l1~~ .

(Repr 1 nt of NACA ACR, June 1939.)

11 . Jaco b s , Eastman ~ ~ .: Preliminary Report on Lam~n2.r - F1mT Airfoils end New Methods !idopted for I'I.il"foj .l ond Boundary .. Layor Inveshgations . NACA i'.CB ] J lIDe 1939 .

NACA ACR No. L5C 05 12. von Doenhoff~ Albert E., and S t i v ers ~ Louis S. , Jr .: Aerodynami c Characteristics of the NACA 747A 315 an d 74 7A 4 l5 Airfoils from Te sts i n the NACA 'I\,ro-Dimensio na l LOif- ·Turbul ence Pressure 'funnel. NACA CB No. L4125~ 1944 .

13. Naiman, Irven: Numerical Evaluat ion by Harmoni c An al ys is of th e E -Function of the The odo rs en Arbitrary-Airfoil Potential Theor y. NACA ARB No. L5Hl 8, 1945 .

14. The odor s en, Theodore : Airf oil--Contour Modificatio n Ba s ed on E -Curve Method of Calculatin g Pr essure D istri b ution NACA ARB No. L4G 0 5~ 1944.

15. Allen, H. Julian: A Simplifi ed Met ho d for the Calcul ation of Airfoil Pressure Distributi o n. NACA TN No . 7 08 ~ 1939 .

16. Munk, Max M.: Element s of the "'i ng Sectio n Theo ry and the Wing Theory. NACA Rep . No. 191, 192 4.

17. Glauert, H.: The E lements of Ae rof oi l and Airscrew Theory.

Cambridge Univ. Press, 1926, pp . 87-93 .

18. Theodo rsen, The o dore: On the Theory of Wi ng Se ct io ns with Part i cular Refer ence t o the Lift Distri b utio n. NACA R ep. No. 38 3, 19 31.

19. von KBr~~ Th.: Com p ressib i li t y Ef fects i n Ae r odynamics .

Jour. Aero. Sc i ., vol. 8, no . 9, July 1941, pp. 337-356 .

20. Heaslet, Max. A.: Crit i cal Mach Num bers of Various Airfoil Sections. NACA ACR No . 4G1 8, 1944 .

21. von Doenho ff, Albert E.: A M e th od of Rapidl y Estimating the Po sition of th e Laminar 'Separ at ion Point . NA C A TN No. 671, 1938.

22. Jacobs, E. N., and von Doenhoff, A. E. : Formulas for Use in Boundary-Layer Calculations on Low-Drag W i ngs. NA C A ACR, Au g . 19 41.

23. von Doenhoff, Albert E., and Teterv in , Nea l: Dete rmination of General Relat i ons for the Beha vi or of Turbule nt Boun d ary Layers. NACA ACR No. 3G13, 19 43.

24. Squire, H. B., and Youn g, A. D.: Th e Calcul atio n of the Profil e Drag of Aerofoi1s. R. & M. N o . 1 838 , Brit i sh A. R.C., 1938.

NACJ". ACB No . L5C05 25 . Nitz b er g , Ger a l d E . : A Co n cise Theoretical Met h od for Frofile- Drag Ca l culation . NAC.A ACR No . 4B05 , 191~4 .

26 . Teterv i n, Neal : A Met h od fo r t he Rap· i. d Estimation of Turbule n t BQ1.IDdary - Laye r r hicknesses fo r Calculating Frof He Drag .

HAC.l\ ACB No . L4G14, 1944 .

27 . 0uinn, John H. , Jr ., and. Tucker, Warren A. : "Scale and Turbulence Effects 0;': the Lif t and DraS Char c1.c"Cerlstic8 of the NACA 65r }18, a = l.0 Ai::.~foil Section . NPC .A ACR No . L4Hll , 1944 . ~ 28. Tucker, ,(larren P " and Wallace, Arthur R .: Sca l e - Effect Tests J

~n 8 . Tn r b111ent Tun nel of the Nt-CP. 65..,··418, a = 1 .0 Ai r foil

C'ection with 0 . 20 - Airf'oi1-CL1ord Split Flap . NACA ACE No . L4I22, 1944 .

29 . D avidson , Mil to n, and 'l'l l rr..er) Ha.rol.d B . , J r . : Effects of Mean- Line LoadlDg on tl'1e Aerodjl.'lamic Chc.racteristics of Some I.ow- Drp.g Airfo··ls. NACA .ACB No. 3127; 194 3 .

30 . von Doen.hoff, Plbert E. , and Tetervin, . Neal : Investigation cf the V ., :01 a ti I)n of "Llft Coeffic lent with Reyno l ds 'N umber at a 1od'3rate ,~ J1g1e of P.ttack on a Low- Dr ag Ai r foil.

NPCA CB, Nov. 1942 .

31. Oswald, ·Tt l. Bailey : Gene~al Formulas and Charts fo r the Calculation of . irl'lfule pe r forma.lJ.ce. K<'.CA Rep . No . 408, 1932 .

32 . Millikan , Cl ar k B . : Aerod.ynamics of the Ai.rplane .

John vlile y ,~ Sons, 1941, pp . 108 - 109 .

33 . Hood, Manley J . : The Effec ts of Some Commo n Surface Irregularities on 'vI ing Dra g .

NACA TN No . 695, 1939 .

34 . Loftin, Lau:rence K . , Jr . : Effects' of Specific Types of Sm.' face Roughness on Boundary - Layer Trens ).t:lo n . NACA ACR No . L5J29a , 1946 .

35 . Char te rs , Ale x C. : T1'a..'18i tion between Laminar aDd rfurbu.lent Flo""l by Tl~ansv0rse Contaminatlor.. .. NACA IITl Yo . 891 ) 1943 .

36 . Braslol{, J\lbert L .: J.nvesti ::.;.ation of Effects of VariQl.lS CWllc · hl.'lage Paints and f'ai nt ". ng Froc~du r es. on the D rag

Char8cte r i~t::~ S of T en. NACA 65(4?l)-420 ) a = 1. 0 Airfoil

Section . f. ,A Ct, CB Tilo. I J4G 17, 19I.f.4.

rJACA ACR No . L'5C05 37 . A llen, H . Ju.l ian : Hotes on t h e Effec t of S urfaoo D istortions on t h e Dr ag and Critical Me.ch Number of jl.-1..rfoils .

NP C l. ACR No . 3129 , 19)+3 .

38 . A bb ott, Frank T . , Jr . } /illcl TtU'ner, Harold R . , Jr.: The Effects of Roug lu1 ees at High Reynolds Numbers on the Lift and Drag Ch aracteristics of T hr ee Th ic k Airfoils . NACA ACR No . L4H21 , 19 ~· 4 .

39 . J a c ob s} Ea stman :N . , Abbott, Ira H ., fu'1d D avid.son, Mil ton : Inve s ti gatio n of Extreme Leading-Edge Roushness on Thick Low-Dr aG jI ,:L r foils to InCij.cate Tho se Critical to Separatlon .

NACA CB, Jun e 1942 .

40. Zalovc i k, J'o ill ;, .: l'lnofi . le - Dl" ag Coefficients of Conventional and Lm'T - Drag Ai rf o:~1t: as ObtainE.d in Flight . N_.3CA ACt<. No. L4E31 , 1944 .

41. ZalovciJc, J ohn }'\ . , an6. ood, Clotaire: :- Flight Investigation of the :Effect of Surface TIoup;hness on ;-liru.; Lrofi.l63 Drag ,·ri th Trans i tion Fixed . N;,CA .Allli riO . O~I25} 1944 .

42. Hood, Manl ey J . } and O0yO.08, 11. Ed';<Tard: EffGctf' of P:r'oT)ellers aIld of Vibretion on the Extent of LQl!l':'nar I ' low in the N . P . C.l . 27 - 212 Airfoil. NJ,Ci:. _ '\CR, Oct . 1939.

4 3 . Sil v erstein , P.be} K6 . tsoff, S . , and Hootmar.., Ja1'1es 1\ . : Comparative Fl.:Lght and Full. - Sce..le l.Jind - Tunnel Meas"t;.Tements of the Maximum 'r l'.cot of 0'" "i r -l.ane 1\'j I' CJ' Re-' "-)0 o"lQ 1('.38 .J..J ..i c..;....L~ .!"":. __ _ 1.... _ • II, ... '"'\. '. ~ 1". J.. . L, ;1 • 44. Sw "e b e r g , Harold, H ., an d Dingelcte::'n, Richard C .! Summary of Measurements in the Iangle-' -F'ull-Sc a l o Tunnel of Maxinn.:m Lif'l ~ C oeff:i..cients :m cl Stalling Chareci..8r.i..stics of "' irplanes .

NACA A-:;n L5C2!~, 19h5 .

4,). P ur se r, Paul :IT: . , and. Joh..'l so n, Harol.d S. : Effects of Trailing - Edge Mocliflcations on 1"i tchjng - ~ ' .1oment Characteristics of Ai r foils . r/',C ' CB No . L4130, 1944 .

46 . F v.llmer, Fdiden F .} Jr .: Hind - Tunnel Inves t· ga tion of Nf:.Cr 66(215 ) - 21°, 66 }1- 212 , and 65,-212 Airfoils with 0 . 20 - hi rfo j,1 - Cl::.ord Split Flaps . Nfc.!, CB ii.o. L4GlO, 1944 .

47 . 4bb ott ) I ra H . , un o.. Greenbe r t:;, Harry: Tests tn the VE .. riable-

D ensity Wind. 'lunnel of the N.J' . C ./ •. 23012 . irfoil "",i th Plain an d Split Flaps . NAC.~ Rep . Ho . !~61 ) 1939 .

NACA ACR No . L5C05 48 . We n zinger, Carl cT . , a ne. He. r r is , 'l'homac A .: Wind- Tunn el Investi- g ation of NACr ".. 230],2, 23 021, and. 23030 Ai rfoils \Vi th VaJ.'ious Sizes of Split Fla . RACA Rep . No. 662., 1939 .

1~9 . Bogdonoff, Se ;ymour M .: 1tlin d - Tunnel Investigat.i.on of El Low- Drag Ai r foil Se ction " it h a Double Slctted Flef . NACP. ACR No . 3 120, 194 :) .

50 . Henzi~c.(,r, C82. ~ l J . , and He . rr is , Thomas A . : I·lind - Tunnel Investi - gation of &1 N .A. C .h . 2 3012 Airfoil with Various Ar r ange m en t s of Slo"vted Fla p.:; . NA CA Rep . No. 6 64, 1939 .

51 . ,\>l e nzin gc r, Carl J . , fu"1d Ba rr} s , 'TI'lOma s A .: \-l i n d- Tunnel I nvesti - gation of an N .A. C . J. .. 2 30 21 i:~foil with Var io us Ar r ange men ts of Slotted Flaps . NAC.t\ Rep. No . 6"(7 J 1939 .

52 . S" lanson, Ro bert S . , and Crandall , Ste,.;ra rt M. : A nalysis of AvailabJe Data on the Effectiveness of A ileron s without Ex:posed Overhe.IlB Bdan e . NP.Cf' ACP. No . j) j.E0 1 , 1944 .

53 . St r eet, WHlialn B . , and. haes , M::'l ton B ., Jr .: .Pressure - Distribut J on lnvest i sut:i. on of an N.J .C . P. , 0009 ,!l.irfoil wit h a 50 - pe rcen t - Cho rd PJ ain l'lap a.l1.d Three Ta bs . NACA TN No . 734, 1939 .

54 . Ame s , Mjl t on B . , J r . , and Sears , R ~ .c h a rd 1. : Pr ess ur e -D ist r i b utio n Invest.L gatio n of an N ,CA 0009 Air f oil ,·ri th ttrl Bo - Pe r cent - C hord PIQln Flap and Three Ta b s . NACA TI~ No. 761 , 1940 .

55 . Ame s , Milto n B . , Jr. , en c '1 Sea r s , Richo,rd 1. : [' re s sure - Distri b ution Invest j .g at-:'on of a.11. JA CA 0009 A:r f 0 11 "t Tl th a 30 - Percent- Chord P la j n :na p an e'.. Three T ~.bs . 'NA CA TN No . 759, 19 40 .

56 . Sears , Richard 1. : \ .rin d - 'l"t mnel Inv estiGat ion of Control - Su r face Characteristics . I - Ef?ect of Ga p on the Ae rodyn a mic CharacterU lt .i.es of ' an NAC!·. 000 9 A irfoil '\ori th a 30 - Pe r cent - Chord Plain Fl ap . J:J ACA A..RR , J l~e 194 1 .

57 . J anos, Robert T . , and f ~ 8 , ' -1il'ton B . , Jr .: Wind - Tunnel Inve stig8tio n of Control - SUrface C IlG r a cter tsti cs . V - Th e Us e of b. B evele d Tre l.ll in g Edge to Re duce the Hi n g e Moment of a Co ntrol Surface . N }J C . ", i\R~ , March 1 942 .

58 . Sea r s , Richard 1. , and Liddell, Ro bert B. : W i nd - Tunnel Inv esti g atio n of Control -3 urf ace Characte r istics . VI - A 30 -~ e rcent - C:1ord Plain Flap on the Nfl. CP. 0015 Airfoil. .

N.CA ARR , Jun e 1942 .

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

NA CA ACR No . L5C05 59 . Wenzinger, Carl J. , and D elano, Je.rlles B.: Fressure Distribution over an N . A. C .A. 2~012 Airfoil with a SJ_otted anet a Plain Flap . NPCA Rep . N~ . 63~ , 193 8 .

60 . G illi8 , Clarence L ., and Lockvood, Yernard E. : Wind-Tunnel I nvestigQtion cf Control - Surface Characteristics.

XIII - Various Flay , Ove:.h811 ,s Used. witil a 30··}ercent-Chord FlaF on an Nf,CA 66 - 009 Airfo i1. NACA ACR 1':0. 3G20, 1943.

61. Rogallo, F .M .: ColJ.ect';.on of Balanced - Aileron Test Data.

NACA !.CR No . 4All, 1944.

62. D enacl, H.G., and Bird, J. D.: Wind - Tunnel Tests of Ailerons at Various Sreed3 . iI - Ailerons of 0 . 20 Airfoil Chord and Tr ue Coatour .,ith 0 . 60 Aileron-Chcrd Sealed Intel~al Ba lance on the NPCA 66,2 ~ 216 Aix-foil . NA CA 1..CR No. 31'18, 1943.

63 . Purser , Faul E . , and :8iebe, . John M. : l-Jind.-Tmll1e1 Investif;ation of Cont~"'ol - Surf'ace Characteristlcs. Tv - Var ie u 3 Contour Modif:i.c a7. on8 of a 0 . 30 -i.irfoil-CJ:>ord Plain F]ap on an NACA 66(215)-01L:. Ai foil. HACP. ~R l\"o . 3I~20,. 1943.

61L BrasImr, JUbe rt L.: ~ hl1 d - 'I''LiIT.lel Investigati on of Ailercn Effectivene s s of 0 . 20 - A':' rf oi l-Ch o rd 1'1<lin Ailerons of True Airfoi.l Con~our on IV.CA 652 - 415" 65') - 418, end 654-421 Airfoil Sections. TJAC A CB :io . I"4:a:12, 1944 . · 65 . Sears , R:'.chard 1. J and Purser, Paul E . : 1,v:'.nd - Tunnel Inve stig ation of Control - Surface Charv . cteri8ti.;s . XIV - NACA 0009 Airfoil y;rith ~ 20 - F ercent - Chord Double Plain Flap. NACA ARR No . 3F29, 1943 .

66 . C rane, Robert . , and Hol tzcL 9. w, Ralph 'vI.: 1,hnd-Tl.rrill"=ll Inv8s tigc.. tl on of A ile r ons on a Low-Drag .Ai. rf oil . I - The Effect of Aileron Profile . NACA ACR No . 4.JI.ll.j., 1944.

67 . von ~oenhoff, A lbert E., ~~d Horton, Elmer A.: Preliminary Invest igetio n in the NAC ]" I~ow-Turbulence Tunnel of Low-Drag- Airfoil Sections Sui t[;.ble for Ad."!li tt:,ng Jlir at the Le n d.ing Edge . NACA ACR, July 1942 .

68 . J acobs , E as tm an N. , and'waJ."d, Kenneth E.: Interference ofW1ng 8.'1d Fus e lag e from T es ts of 209 Comb i nations iT. the N.A.C.A.

Va ri u. ble-Density Tunnel. NAC} Re:r:. No. 540, 1935 .

69. Abbott, Ira R . : Interfe r ence Effects of Longitudinal Flat

Plates on Lew-Drag A~rfol1G. NACP CB, Nov. 1942.

NACA ACR No. L5C 05 70 . Ell is , Macon C. , Jr .: SOlUe Li.f t and Dr ag Measurements of a Repre se nt p.ti Y6 Bom ber Nac el le on a Low- Drag "ltling - II.

NACj\ CB, SeI,t . 19 42 .

71. E11:;'s, Macon C . , Jr ,: Effe cts of ::.. Typical Nacelle 011 the Character :LF' tic . of a Th ick L ow - Drad Ai rf oil Cr iti cally Affected by Leadin3 - Ede;e TIoug hn es8 . nACA C :3 No . 3D27, 1943 .

72 . All en , H . J ulia..YJ. , an d. :F' r ':'ck, Charles W ., Jr . : Ex pe r ime ntal Investiga~cion of a Ne -, r TJl:le of Lm-l -Dra g vling -N acelle Comb i n ation . N.t..CA !I C:R, J u ly 19 +2 .

7 3 . Abbott, Frank T ., J r .: L ::.. ft and D rag D ata for ~ O Pushe::..'- Pror el le r Shaft HO~1 Ll~~S en N.A .CA 65,3 - 018- Ai rfoil Section . NAC A , CR , fO. 3Kl3, 19 .;-3.

7 4 . Robins o n, Ru ss el] G., an Q Wr ig lt , Ray E.: Est i mat ion of Critical Spee ds of Airfoils e nd Strea."1line Bodies . NP, CA ACR, March 1940.

75 . Ander so n, Ra~Tmond F. : D et e rm in a t io"" of the Ch racter isti cs of Ta :p ered Winss . NACA Rep . No . 5"(2, 1936.

76. J a c o bs) Eastillrul N. , and Rhode, R . V. : _ irfoil Section Chare.c-eer .Lstics as P pplie ci t o -ehe Predic tion of Air Fo r ces an d The i r Distr ib ution on Wlngs. I~ACf. Rep . No . 6 31 , 1938 .

/ 77. ~ouIe , H. A., and Anderson, R . F .: D sign Charts Relatlng to t he Stall i ng of Tap ered 1.1ings . NAC] Rep . No . 7 03 , 1940 .

7 8 . Harmon, Sidney M. : Additional Design Cha rt s Relating t o the St a11i T1 .[; of T a~ ered Wings . r. ACt. ARR, J rul . 19 +3 .

79 . Ander 8o n, Re.ymond F .: The E..x-pe ri mental and Calcu la t ed Characte r :st~cs of 22 T a) ered Wings . NAC A Rep. No . 627, 1938.

eo . Tani, IUro : A Simrie 1'-'Iethod of CE' ~ lculating the I nduced

Veloci ty of a Monepl3J1e H:"ng . Rep. No . :11 (V ol. IX, 3 )} P,ero . Res . Ins "..; .} Tokyc. Imperia: Uni v .} Aug . 1934 .

81 . S hel~ an } Albert : A Si.mple i·lethod of Ob ta ining Span L oa d Disi..r ib u t:.ons . N.A C JI. TN lJo. 732; 1939 .

82 . J ones , Robert T .: C or rec tion of the I"ifting - Line The ory f or t h e Effect. of t h e Chor d . NACA 'IN No. 817 , 1941 .

83 . Cohe n) Dor is : Th eo r et ic 8.1 Di st r ibution of L oa d o ver a SW'ept- B ack 'voT :Lng . NA CA .£\F J<) Oct. 1942 .

NACA ACR No . L5C05 8 4. Pe arso n, H. A.: Span Lo ad D istri b ution for Tapered Fings wj th Partia l- Sp an Flaps . NACA Rep. No . 585, 1937.

8~ . Pearson, Henry A. , and Pn d erson , Raym o nd F.: Calculation of the Aerodynamic C haracteristics of Ta pe red Wings with Partial--Span Flaps . NACA Rep . Ho. 66:5, 1939.

86. The Ca mbr5dge University Aeronautics Laboratory : The M e asurement of FrofUe Drag by the Pi t ot --'lraverse Method.

R . & M. No . 1688 , Bd t ::'sh A . R . C., 1936 .

e7 . SH verstei n , A. , and Kat z off , S .: A S::mplined Method for

Determining Wing Frofi l e Drag in FLght. Jour. Aero. SCi., vo l. 7, no . 7 J May 1940, pp . ~9 ')--301.

88 . Glauert , H. : Wind TurE1.e l Interfer .:mc8 en 'v . Tings, Bodieo and Airscrews. R. & M. No . 1566, BrJ.ti"'h A.R.C., 1933.

89 . Allen, H. Jt:.l:i. an, and Vincenti, Falter G.: Hall Inte :,:, ference in a Two-D :l mensional - Fl ow vlind Tunnel "Tith Consideration of the Effect of Compressi b ility . NLCA APB No. 4K03, 1944.

90 . Fage, A .: On the TwC'r-Djmer.sic:nal Flow pas t 12 Body of Symmetrical Cross-Secti on Mounted in a Channel ::-f .:ii'i nite Breadth.

R. & M. No . 1223 , British A. R. C. , 1929.

- -- - --~ z > (:) (") > > (") :::0 z r CJl (") o CJl CXJ CXJ 1.0 = 0.100 a 0.9 lift = a design 0.8 Y :: the a SOR I of AERONAUTICS ADV 0.7 FOR = a -0.463 -0.463 NATIONAL magnitude 0.6 COMMITTEE = the & l ate c 0.5 :: indi a " DERIVATION • combination I 0.4 :: 0.763 0.763 a AIRFOIL TABLE combination OF Mean-line 0.3 = a an-line .ANALYSIS -"'e 0.2 • e d & head 0.1 :: a columns = a various d.

...

the •• u Baaio tora in t 747A015 747A015 thiclm 1.5 numbers 7A3 coefficien Airfoil 747A4 1 The de~ignation \.

z :> ~ Z o (") o (Xl <0 :> (J :> (J r- (]1 (]1 - out s stall y ng or o flaps flap tip full- ct.

entire str extremely for a span for tips p - sat1sfactory; severe ti satisfa ll; Oata in sta nected, envelopes artial to'ft'ard characteristIcs p no with progresses de ry toward lted s neutral, ll t and cto stall ted; oo resu flap. stall sta r flap sfa tallIng flaps S th th rupt pro&resslon flow 3pan .. abrupt wIng - from neutral deflec At Unsat1 Abrupt N.1 "" 1 3 8 4 ~ E 8 07 0~ 06 50 4~ 52 l 49 13 29 34 .

Lm ·51 . 'f4 ·5 .

1.26 1.72 1.J 1.9~ C 1.,6 1. 1. 1.9 2 . 1.97 2 2 . 2.04 2 . 11 2.15 2.40 2 · 2 2 2.49 2 · l. 1.29 1.27 2 2 . 2 . 2',6 2. 2 ~ ~.31 3 . 1.1 1.,7 1. 1.17 1.31 1.

TUNNEL 6 6 6 10 10 10 10 TICS SURE H • x • • U . 6 .

.6 . 6 .6 .6 . 6 .6 .1 ·1 ISORY PRES 2.6 ,.6 2.6 ,.6 2.6 , . 6 2.6 , . 6 2 . 6 ,.6 2 . 6 , . 6 2 . 6 ,.6 2.1 2.8 ~.3 2 2.~ ~ 2.1 2.~ 3. 2.1 2.~ 3. 3.0 5 7.4 ~.~ 5 · 7.2 AERONA ADV fo rOA 1'OOT b ~7 37 --- --- None an b) ' Flap s p 19 - ITTEE percent fi 5~ 5~ --- --- NATIONAL b MM None I ... CO NACA rd cfo 10 20 ~O ~O --- --- None c)

I

THE ?lap cho

I

fi 10 20 ~O lC 20 ~O ~O IN (percent C --- --- None · 0 -- Ofo --- 60 ~o --- - le 1'ES'l'EO ng Flap a (d.~) fi II ' -.- 6. 30 35 30 --- --- - !!ODELS ard

TAtiLE I

pl1t OF bo wler t None > Fo None ou None Flap I STIGS t r d wl.er pl1 S Po None ~on8 None Inboa 6 0 0 0 0 . 6 CHARACTER 15 0 . 0 -116 0 ~ - 0 1.5 4.0 ) )-019 chord )-216 8 8) t, ut, 25 tlcs (' . hou 0.

hout, h hout, 0 66(215)-21 66(215 65(31 65(31 STALLINr. 66(215 66(215)-216 65(318)- 65(318)-015 93 A A was ••• .... '" .... ot A mstrl0 o ACA o 21.

l AJ!D aoterl NAC N NAC 5 NAC Ge s I 00 rlc s, rio .

NAC a. NACA N~CA N~C'" 3 25 .5 trio 7 . 1.00 7 . 0 0 7.3 0.2 7. 0 .

t: t: : t: t : cbar LIFT = o..,~t t1on = t10na line = = = = weepbaok )..= A Roo Tip: A Ge ~oo Tip A ).. Geometri Rou Tip: A Roo Tip: A Geomet S ). = ')eome 3ectlon Section Sec Sec v'AHMtJ1,1 view i on Front at .J nfigur view Co ..

Plan L.. ~ ~ ~ l I 1" II TIT ~:ode <D o Z !l> (') !l> !l> (') z o r-' (') ::0 CJl o CJl - tls satts- •• wlth tory 'N1th progresslon progression character1.t1cs tips tlpa data stall stall thrac No Sa factory toward factory toward Stalilng Abrupt Abrupt Cr."ax 1.40 1.52 1.55 2.10 2.19 2.21 2.23 1.3<+ 1.39 1.39 1.87 1.91 1.92 1.33 2.85 1.32 2.2 2.7 1.91 2.22 6 6 6 6 10 10 10 10 R • • x " .0

3.2 5.~ 7 . 3.3 7·0 3.3 P 3.3 5·1 5.8 5.1 5.1 2.4 2.4 2.4 2.5 2.5

U

I t ro --- --- --- 38 38 b --- 48 bJ Flap ~pan ft 1

1 I I I I

(percent b 60 60 50 60 60 t I

!

--- 25 35 20 Cro --- --- --- cJ Flop chord I f I I AERONAUTICS.

! I

(percent 20 AOVISORY Crt 25 25 25 35 Contlnued FOR - 0 0 t --- --- 30 4B 6<l °t --- --- Flap (deg) 1 NATION"l angle 0 0 0 0 I MODELS °f 50 50 55 4Il COHHITIEE OF

1 l I ~

one Zap ,t None None Spl1t Double Outboard .lotted Continued Flap -

l 1 ~ ~ t

.- II Plain Plain Zap Split Double -_ Inboard .lotted CHARACTERISTICS TABLE STALLING 0 0 0 ",~D 1.!l)(15.5), tics 0.0 2.0 2.5 2.5 H 5 )-(1.8)12, 1s 65.3-318, LIFT tric r 65(318)-316.

te hout, hout, o. 66F15 o. ahout, o. AeA 67(11!)-116 66~215)-(l.8)(15.5~ "~i 67,1-1 o.ome 66~2l5)-(1.8)12. o. 66~215 O. 0.8 - ••• 3 •• s ••• .alhout.

•• % 2 = MAXIM1J1,! oharac .. e. ..

I .. .. a IIACA BiCA IIAOA Mad.

IIAC4 MD4 lIACA .ACA .~~ : 0.4 O. 5.8~ 0.4 8.09 0.5 6.7 10nll t = = ~ ~ ~ ~ A: A Tip: ).= Root Tlp: A GeaD8~~lc Root: Tlp: A Jeometrl0 Root: Tlp: A X Oeometrl0 Root. A Oeo~etrl0 Sec $ectl0Tl.11 Sectlo(u Sectional - view =0 Front Ih....===- -=0=-- 1gurat1on Cont view Plan

l1~' +

~

~

V VI VII VIII Model I o r z > (') > > (') ::D z (J1 (') o (J1 <D t-' y r y tory tor n racterlstlce isfactory cha tierac atisfactory Satlat"acto Sat Satlsfa S Sa Stalling 9 6 1 7 5 19 21 06 ,7 . 20 .00 r",ax 1.A2 1.98 1.9~ 2.0 2.13 2.01 2. 2.2 L95 2 . 1.21 1. 1. 1.~6 1. 1.96 1.

C 1.38 1.97 1.~ 1. 2 .11 1.47 "1.37 "'1.1K 0.1.45 0. 0.2 0.2. 0.2 0.2.06 0.2 lOb lcP lrP la' 10 R x x )( " x ~ .4 ./ .0 ·9 .1 .

2·5 3.7 2.~ 3. 5. 2 5'

3.5 ,.6 3. '.5 ,.1 2.~ 5.' 2.~ ,. 5.4 5 · 2

"t 4.0 4·1 4·1 4.8 r l·l 4.8 ,.

I

ro ---

b --- --- --- --- --- --- , --- ... --. -_. --- 30

b) AERONAUTICS Flap span ADVISORY rl I (percent --- --. 65 b 60 60 --- 60 70 FOR

ro 1

---

c --- --- --- --- 20 --- --- --- --. --- --- --- 20

c) NATIONAL Flap chord COMMITIn Cont1nuod percent I (

c r 1 --- --- --- 20 25 --- 20

20 20 -

I

--- 60

Oro --- --- --- --- 55 --- --- --- --- ---

l:C,GELS !i;~r. (deg) 1 -

f 0 1

Or -- 55 --- --- 55 35 60 --- 60 45 60 OF

I

\ I ontinued one c N Split nne Nco. Spl1t None None Outboard - II Flap odg.

t CHARAC"r.lRISTICS

I

t lit tted

I

o plit TABLE None Spli Split Sp S None Spl1t Split None None Inboard sl Extensible EXtenslble ~raillng 0 8 0 0 STALLING 0.0 -418 1. 1.00 -4111.

5 1.0 2.8 15 15 s AND ic ut, .2x- ho hout, hout, 66(215)-016 64(21,) 64(21U-418 64(21~)-41 63(420) 1.0 1.0 LIFT 66.2x- 66 65Z-41 5. 66(215 )-016 66.2x- .a.hout, wa.hout, ..... .... • • ....

.. ..

.oteri.t IiACA } NACA NACA lIACA IIACA o.ometrlc •• al IIACA lUCA 'l NACA 92 33 HACA rio lirA .6 tric n.1 n't 0.]3 : D. , 0. 7.77 0.50 5.3 0 8.92 8.~ etrio 8.

: t: :,IAXDlUIo! char 10n t: = = = om = ometrl0 = oo Ip A= A= A= Tip: A = Root: T1p : A Geome Root T A Root Tip. A Roo T1p: A ,,= Geomet R A Geoll"letrlc Ge Ge Section Section Sectio sect Sectio - view ){Q}1 ==0- Fron t ~ ~ -~)V- --.0- iguration Conf vie.

Plan wlndml111ng.

+ + + T

+

rs X IX XI XII 110001 XIU &Propelle z » (") » » (") o r-' to (\J ::0 Z CJ1 (") o (]l , I - pro le ng stalling tions for wi rull- stall ory II'lng cond i lett tIp extensIb except ps all lott the ti satIsfaetory ry stall, ory f or severe or satisfaet characterhtlcs th l , wi y, stall, aract toward idl flap, tl abrupt cond1tions first llap Sa Satislacto talUng stall rap n.p S all abrupt otted llt atislactory very gression stalls sl 'p s ror s pan Abrupt Very Extremely Un 6 0 27 37 CI; 46 1>5 76 .~ .1 1-

1.~ 1.46 2 . 2 2 · 2 . 2.1~ 2 2.02 2.12 2 .17 I.H 1. 1.RI> 1.50

1. 2 . 2·50 2·52 1. 2.01 2.15 2 •21 1.}8 2 . 2.69 1.}7 2.41> 2 . 1.1>5 2.57 2.86 C~u b ~:~ 6 6 6 6

10 10 10

R • • • • • 106 .1 .6 .~ ·9 .1 .6 .1 .8 ~.6 ~ 5.6 } ~ .1 2.8 }.6 } 2.8 }.6 3 . 1 2

l·t l·2 ~.5 5·9 U 5·9 U'10 U 5. ~.o 5·0 2·9 4 . 0 4.9 4.9 4 . 9

to -- ~

! l

b --- --- --- --- --- --- - --- --- }1 }1 }1 b) Flap .pan .

( (

I

btl 60 60 50 65 65 65 (percent - to

I I I J

--- --- --- --- --- 25 C --- -- --- --- 25 25 AIRONAUTICS c) ADVISORY Flep chord. 1

Continued I

I I I

fot (percent Ct 20 20 24 25 25 25 - ' 0 0 0 ~ 0 I I O. --- --- --- --- --- --- --- --- --- 25 25 ~5 NATIONAL lap COHHITTEE YODELS F (deg) angle 1 0 0 0 0 0 I 0 I I °t ~5 50 50 50 38 45 55 55 OF

I l

I !

None None tboa:-d None RISTICS Double slotted Double dotted Double slotted Continued Ou - lap II ARACTE P t CH

lit le l I I

I I I ble

lotted Sp tenlible SpU TABLE Inboard dotted dotted S Slotted slotted Dou .1ottAd Double Extensible Ex Doub dotted STALLrNG 0 0 6 0 0 0 AND ~~18.5) -11 1.0 ight 1.0 1.00 3.0 0 . 0 2.0 ) , , ice ~~2 atZ'.lght LIPl' c 216) -215. stra s,traight 015 .6 , 2-118 216)-215 .

out, OO9 hout, bout hout. hout ~~~216)-215. 65~216)-215. O.

ah 2} 66 ~~~ 0 . 5 0.5 lIne 2} 66(2Jc15 65(216)-215. 65(216)-215.

•• .... .... • ••• lin' • w.thout, • .. 0.5 .... lin' ~A6Zrm .65( Qeom.tri o .. a • • ItAXD(1)!

aracterist NAC. MAC! i C 8 KACA M~C! II!C!

a. NACA NAC, a. 08 a. lAC. 08 chord _. N N~~ 52 HAC.

trl0 tno oh , : 0.45 ohord. : 0.1>5 ohord.

5.a2 o. etric 5.5 0·. etrio 6 .9 9. 9 . 0 ·45 9 .08 ;: : tional ome = = = tion" = = = = = = ~ }..

~r~ A }. = Gecom Root Tip A Geom Root Tlp: A Geometri Rootz Tlp: A ,,= Geometrl0 0 . 2 Root Tlp: A }.. Oeome -0,10 Root: Tlp: A Oe 1.1 Sect1on Seetion Sec Section Sec Section view '€I ~ @

--

--- --

Front

-

nfiguration Co vie.

lan P ~ reMOved.

~ +

T ~

+

XV xrv XVI XII XVII ptlleta Model xvrII b o z > (") > > ~ z r-' n o (Jl to (J.l n (Jl tlps at occurs atall eharactert"tlcs Satt.factory S.tl.f.ctory Satisfactory Satisfactory Satlafactory lnitial talling s Poor, 51 8 0 1.~7 2.23 2.30 Cr",ax 1.45 2.65 1.2~ 1.4~ 1.90 2.0~ 2.~ 2.4~ ~:~g 2.02 1.38 1.57 1.61 1.83 1.99 2.02 1.}~ ~:~} 1.85 1.92 2.01 1.17 1.27 2.21

2·~7 1. 1. Ut

6 6 6 6 6 6 10 10 10 10 10 R x x x x • 10 x · 5 5.5 5· 5 5 2. 9 4 . 0 4.9 }.O 4.0 4.9 } . O 4.} 5 ·1 5·2 4.1 4·9 4.1 2.9 4.1 4. 2.9 4.1 5·0 2.9 4.2 5·0 }.O 4.2 5·1 1.5 2.2 2.8 1.4 1.9 2·7 ro b I ,--- b) Flap SpM rl (oereent b 50 50

' ' 150 150 :5~1

nn

AUOHAUTICS.

ero 2[ --- 20 --- --- ---

c) I 1 1 ncludod rcent fOR l Flap chord Co

( pe CC 2(

20 18 - '20 120 '20 NATIONAL ADVISORY Oro 55 60 --- --- COMMITTEE I 1--- ODELS (dog) l Flap angle

t I

o Or 55 45 60 45 45 45 40 OF M ISTICS None

-...,. None

.slotted Double Split None 11000 Outboard Concluded lap I F - e t ARACTER II CR Split Non. Hono Spli None Split liODO Split Inboard Doubl slotted Fo.ler 8LE A 'l' ALLINO 0 0 0 0 0 0 ST .0 1,0 2.5 0 2.5 2.5 opt 8 2.5 )-U6 straight straight •• atralght ArID tIes stralght ut, 2-118 (216) -215, rl3 hout, 0 nout, 65 0.8 0.5 66 line 11.n. 66,2-118 ahout, lIne 66,2-11 66,2-118 ahout, 11"" 65(223)-221, 1.0 LIFT line 65(216)-215, 66(2;15 66(2:.15 )-116 66(2:.15 )-116 66(2:.15 )-116 66(215 )-316, -= % w.aho .aahout, ••• •• }.5 ••• •• :r • 0.6 rd o.ometric • a a o • • araote l , I lIACA !lCA HACl HACA rd HACA llAC.l HACA ohord a, ohord ohord oh •• lIACA HACA HACA nCA lAC!

ch ohord 9.08 0.45 , 6.25 0.~5 6.25 0.~5 6.25 0.35 ..... 6.1 12.8 O.}} IIAXDI1JI( = ~75 fo = = = = = ~75 = .. .

00t 10.= A ;\= Root: Tip: A Geo_trio 0.20 Root, Tip: A Geollletri O Root, Tip: A .\ = 0.~75 Root, Tip: A GeOlllatrie 0.375 Tip: A A= 0.47 0 Root, Tip: A ;\= Geometrio 1I (;oometrie GeoaMtrl0 5eetlcma. Seetiona Sectlon section. Section. Section --1 - view o --- ,", -*- * ...,I,.

~ - Front - onflguration C view Plan

T

+

T ~

T

T

------,--- 1-1 xx XXI uv XXII XXIV Model XXIII I.

0 ':I:J 1-" ~ z » (") » » (") ;:u z 0 L' CJ1 (") CJ1 OQ X I 1.00 ~3

~

YL cos cos 0 -.01055 -.02,01 -.041 -.00865 a -.04 t Yt '1 AERONAUTICS + - ADVISORY xL c .0570b .25565 ·50000 .74689 FOR .00923 Yc '1 0 1.00000

= =

forms.

L U Yu '1 NATIONAL y airfoil.

.05029 .1~OO5 COMMITTEE .01455 .11653 .0 a ::::::::=-- 9 thickness Xu 1.0.

THE.

.00077 .04294 .24435 ·50000 ·75311

65.3-018 =

0 1.00000 sin sin OF i 5 5 3 5 basic

t c~

Yt Yt

073 44 NACA

1.0) - + 0~7 and .012 • .0 .08 .04

=

x x 0 0 the ytcos9 for

= =

(a of line DERIVATION lines ~ xL line sin9 .0070b .00423 .00565 t a -.00311 FOR y a 0 ordinate mea., Chord AIRFOIL M~an ordinates the .9 ·99756 .99756 cos9 ~ 0.9~76A chord) 1.00000 of

rr=

from 65.3-818 22 chord.

combining CALCULATIONS 0.8 of of .1 .06979 sin9

percent NACA ------- ------- 0.3~32 0 -.06979

chard end obtained 0.5 SAMPLE 7 line.

of Method at .1 .0699 tan9 a -.06996 end

-------- CO.3t~ -------- ------- -------

mean through 1.- 8O slope the Yc (b) .00200 .01264 .0tE- .0 .03580 distribution of through 0 0 radius Figure 31 5b of Yt (a) o~ (mean-line .01~2Jt .0 .0~92 \ Radius • .0 ~I 0 a ordinates Slope c ~ThiCkness \ :x .05 .25 ·50 .005 ·75 0 1.00 ~,-

Y o

.10 -.10 . 2 Fig L5C05 No.

NACA ACR 2.0 1.8 ~ ~ f.--

~

~ V 747A;15

V NACA -

~

Upper surface 1.6 y Lower surface

V

I'v -

basic 747A015 NACA

"b(

- distribution thickness .::::::"

I

-

1.~ I----

I'----

h(

V

I I ~

/'" ~

V

i'--

~

V

.::::lI 1.2 L ~

...-

I

-

~ "",

I---

..---

1.0 ""'",

V

I-

"-

f7

.8

""

. I

~

.6

.4

ADVISORY NATIONAL .

FOIl AERONAUTICS COMMITTEE • 2

o

1.0 .6 .8 ·9 .2. .4. ·7 o .1 ·5 x/a 747A;15 airfoil the NACA tian for pressure dlstribu Theoretical 2.- Figure thick- 747A015 basic the NACA and lift coefficient at the desi~ section distribution.

ness - ---" o r -r--- Fig. 3 .

NACA ACR No. L5C05

z - p Ion e t-----f-----'-----1

Z I - P Ion e r----t"--------'---I

NATION,U ADVISORY COHMlnEE fill AEROUUTlCS.

y

.

r=X+Z?I

~igure 3.-Illustration of transformations used to

derive airfoils and calculate pressure distributions.

Fig. 4 NACA ACR No. L5C05 .16

~

/

1\

V

I(

/1\

~

.08

V

V\

~

\ /

L l\

lr d (

V

dj

\

'-"

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I

o

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II j

"'"

l\ II

\d¢y

\

IV

/

-.08

V

\ /

~ V

J

\

-.16

V

"

V

l'\

---

V

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.16

1)Iy

\

I\~

1\/ (

V

II

.08

\

V

\ /

1)1, ( ~ NATIONAL ADVISORY

V

/ COMMITTEE FOR AERONAUTICS

~ \ ./

o

V

1\

V--

\

V

r\

-.08

~

V

I'-----' -.16

o 6 21'1'

4 1 2 ¢, radians d I/t dE Figure 4 ·- Var ia tion of ai rfo il parameters 1)1, (, d¢' d¢ with ¢ for the NACA 643-018 ai r foil-sect io n ba sic t h ickness form.

'Xj f-" CJ1 0' z CJ1 o CJ1 III z :x:- C") :x:- :x:- C") ::0 o r' C") oq I I .

1.0

.~

AERONAUTICS pressure.

ADVISORY -0 -015

-=======-

2 2 FOR

64 ~~

652-01 66 67,1-015 ~

.8 minimum NATIONAL

lCA ACA ACA .\

N"ACA

~

N N COMMITTEE of ~

~""

c

.6 6-series /-

~ ~

position NACA 70/0

/

II ~

with

.4

/

/

~

/ symmetrical

-1

-- ~

Variation .2 basic

~

(b)

~

some lift.

(

o o .8 .~ for 2..D 1.6 1.2 zero at

~)

(

.1 .

airfoils distributions I 1.0 AERONAUTICS

t:0.. ~

- ADVISORY I

::>- pressure

FOR

~

----- I

..

- .8 NATIONAL 651-012 652 65}-018 I

"-

COMMITTEE 1.

: ~ C4 Theoretical ACA

--- -

N

C ~

.6 5.- thickness.

! ~

~~ l

I ';c

II

.L..

with -j~ f-i'\ Figure .4 V I-- f.--:"" Variation

r::- r-

!--- .2 (a)

~

~

V

{

o o

.8 ·4

2.0 1.6 1.2

(~)2

Fig . 6 NACA ACR No . L5C05 5.0 ~.o 2.0 o NATIONAL ADVISORY CO MM I TTEE FOIl AERONAUT I CS .

Figur e 6.- Th e or et ic al p reseur e d istri b uti o ns fo r the NACA 652-015 airfoil at s everal 11ft coeffici e nt e.

e-~~-- ----- - --- ----- ------ --~ ----- -- - NACA ACR No . L5C05 F i g. 7

c ____ ~

NACA 66(215)-216, a = 0 .6 2.

r-- Uppe r surf a ce /:: L --"l..

1.

f---o-

V

\ ./

()

~ c

I-- ~

\

~I ~ -r.-

1.

I

~Lower surface

\ 0

~ 2

\.

~

• .)

~

'Iheory Experiment I.

• NATIONA L A DV ISO RY COMMITT EE FOR A ERON AUTlC~ 1.0

o .2 .4 .6 .8

x/c

Figure I.- Com p arison of theoretica l agd e xperiment a l pressure

distr butions for the NACA 66 ( 21 5 ) -216, a = 0.6 airfoil; c~ = 0.23 .

Fi g. 8 a,b NACA ACR No . L5 C0 5 2.0 _____ NACA 652 - 0 ~ ~ I-- ~ NACA 652 - 2

/'"

£, _____ NA CA 65 -

l.----- ~ 415

1.6 -

/" 15 ~ NA CA 652 - 6 V-

-

~ ,

!/ /'

tJZ ~

c= __ ~

-

---....

~ -

':j

-

-,

it ...- ~ ~

1.2

-

'1/ "'-", - , /'

--

/ //

-

~ "" ~ ~ ~

"'- "'-

/; / ~ -- ~

"'- I

~

" ~ liACA 652-215

.8 ,

"

"'- Upper surface i------ "- ",-' ., --- Lower surface - .4 NATIONAL ADVISORY COMMITTEE FOR AERO NAUTI CS.

o o .2 6 .8 1.0 .4 1.

x c ( a) Amount of camb er .

a = o. 3 ~ - r--r----'

a = 0· 5 2\

a = 0.7 \\ \ '\ '\-\- \\ \ +-+- \----1r-----l ·4 J- -I------11-- -- Uppe r Bu r f a ce - - Low e r sur f ace

o t-----t----t- I I I I I

o .2 .4 .6 .8 1.0 x/c (b) Type of camb er .

Effec t of am oun t an d type of camber on pressure dis tr i bution Fi gure 8 .- at d e si gn 11f t.

J

.....

'%J cD QQ o o C}1 z o > > (') ::0 Z l' C}1 (') > .

I , i

x 10 presBure CS TI

·7

R, RONAU I AE ADVISORY minimum OA F of I

.6

TTEE MI NATIONAL I thickness.

COM x/c position and

·5

with ~

I

camber

2-215

pressure,

632-215 642-215 652-215 66 67,1-215 r--

o

I

.4

same NACA NACA NACA NACA NACA ~

I

coefficient the o A v; minimum

o o

of of

r---

drag ., airfoils minimum Position .2 of 6-series .1 Variation NACA

9.-

some ) for Figure

.012 .008 .004

.016

.s

.rf

s:: <D o :if s:: o () ~ § s:: () (l) () () H ~ ~ ~ ~ '0 -rl .p ~ ~ :;g .p z > > > (") Z o 'XJ ..... o (") ::0 l' CJ1 (:) o CJ1 f-' OQ l0 x

A

• .

tl]) edge) edga) for AERONAUrCS ADVISORY coef- ~ t-----. ~r.o ~.

~

fOi .

number leading leading

-- NATIONAL

23021 23021 63{420l-42 COMMITTEE

/a-o-

(rough

(rough ~ /

I .

I NACA Reynolds NACA skin-friction ~

-

I

~A :;..--- -

with r p...,.. t')... -.......J

V ·'r- I

l ~ ...............

I--

I

R turbulent Laminar

~

--= ;::::::::::

T 4

65(421)-420 653-418 66(2x15)-116 and - coefficient ~ -.:::::: ~ number, NACA NACA NACA Turbulent drag laminar

-

~

---

[\ ~

I-' \ \

"

with Reynolds minimum of plate.

----...,.,--

I--.. f---~ ~

1.0 ..-:- r-....

- flat

"

"- r--....

NACA .8 a - ........

I- Variation

-

rYi r--- ~

for .6 - airfoils,together '-.....

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

........

10.- ~ '- -, .4 0- ure several ficients ~

--=-

Fig .3 "'-

~

r------.

.2

.04 .02 .010 .008 .006 .005 .004 • 003 .00 .001

.05 .03 s:: ..

J

() s:: Q) () Q) 0 () til al H s:: 0 () Q) 0) ~ s:: .j..l orl orl ;:,;; .j..l orl orl 'H 'H 'Cl orl r Fig. 11 NACA ACR Na . L5C05 ..

~ NACA ai rfo il

c

~ .012

o 6 R-s e rles

C)

"ori o 6 -

«+-i

o 6 ~-

«+-i CD

l:::. 6 -

o

'iJ' 65,3-818

Q .008 ~

I

as H 'd ~ ~ :;F ~

g .004

ori ~ Q CD y NATIONAL ADVISOR OJ CpMMI~T E E fpR AE~ONAUr I CS .2

. 6

1.0 .8

Design sectio n 11ft coefficient, Figure 11.- Variation of section minimum dr ag coefficient with c amb er for several NACA - series airfoil sectio ng of 18- percent thick-

ness ratio. R, 6 x 1 0 •

Fi g. 12a, b NACA ACR No. L5C05 Series

OO}

[) di

~ (4 - git)

8.

\'l 230 (5-digit) .016 .~~

-- ~

.012

.--w-

. ..... --

--~ ~

. ~~

.,..-

;r-_ ....

. -0- Rough -"1 c .008 ~ ....;

~

-< ~ ~ ~ ()

r

-I J.-.O-i

;r Snooth .. .004 +J c Q) ....; () ....; ~ ~

o

Q) o () (a) NACA four- and five -di git series.

til al H .012 'd ~ C

&--

o ~ - .., ....; "" ~~ +J ~-- 1>-- -~ () 1r< .r--- Rough ~ .008 o 0 0 0.2 ~\l ~ i.

~ <) . 8. O.L.

- Smooth \'l 0.6 NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS

o

o 12

8 16 20 Airfoil thic k ness, percent of chord (b) NACA 63 - series.

Figure 12.- Variation of section minimum dra g coefficient with airfoil thickness r a tio for several NACA airfoil sections of different gambers in bot h smooth and rough

conditions. R, 6 x 10 •

Fig. 12c-e NACA ACR NO. L5C05 .012 ~ -G ~-- A :-"V "t--

~-1

r-o..(

"> Rough

< ' r--i

.0oB c~l

o 0

[:) 0.1 ~ ~

'>:/ o 0.2

..A--( 'r f- .004 Smooth 8. 0.1.

"l 0.6

o

(c) NACA 64- series •

• 012 ~

~--

~ --~ ~ - '1""-- ~-~ -%~ (~-- Rough c~ - .0oB i

o 0

o 0.2

Jii

-4

....

8. 0.4

r;" .004 V'

"l 0.6

Smooth

o

(d) NACA 65- series.

~ .012 "'.- -v ~'" 8.

--~ "~ -~

" ,.--

-O-.! " ~1--- Rough - .008 c~ i 00.2 ...(:') , 8. 0.4 .A. ..( " 'V v Smooth <" NATIONAL ADVISORY COMM ITTEE fOA AERONAUTICS

o

o

8 12 16

4 20

Airfoil thickn ess, percent of chord (e) NACA 66- series.

Figure 12.- Concl uded.

-- ~. -- - - - Fig. 13 NACA ACR No. L5C05 NACA 641-412 El NACA 642-415 .028

NACA 64;-4 1 8

e.

NACA 644-421 ~ .024 ..

., c Q) ....

....

• 020 ~ ~ C) (J f co

P

as .016 s..

rC

1)

Ir..

t!

t:: .... ~I/ ~ +> ~ (J

'A \

.012 C) . CI)

V

~ l'--

~

V

~

~

~

.008 .~ """i ......

""0: ~

~

kl

....

f){', Vlo...d" ~

~ . . '\;F

~ .004 NATIONAL ADVISORY

-

COMMITTEE FOR AERONAUTICS .

I I I I

() 1

-1.6 -1.2 o 1.2 1.6

-.8 .4 .8

-.4

Section 11ft coef~iclent,c~

Figure 1;.- Drag characteristics of same NACA 64-series airfoil

sections of various thicknesses. cambered to a design lift coefficient of ?4; R. 9 x 10 • TDT tests 682, 73;. 735, and 691.

J

j

I

NA CA AC R No . L5C05 Fig. 14a, b 1.2 I I I I I I I I I -0 Upper limit ot 10w-drag r~ 0-.

LoweI' I1m1t B r---., ~ low-drag range I r--

V

' r- .8 ...

- r-

/ t-- '" ..;

V

a CD .4 ....

.... /

...

...

L

..., V ' .... cr' .....

M a .4

0 -

.....

..., .8 .8

-

NATIONAL ADVISORY _ COMMITIEE rot AERONAuncs i -1. 2 o 8 ( a> variation ot uppe r and lower limiU ot low-dr ..

range with R e-,nolca nUlllber • • O~ .0}2 B O x 10 . 028

t' [:J .0

~ 9.0 '0 .to.

l5·~ 0 v 25.0 ?

~ 35.0 . 02 4 ...,' a CD ....

....

...

... • 020

CD bO as i> '0 .01 6 " <: ....

..., CD

~

. 012 CI.

~ ~N

:~ I!

. 0 0B ~ ~ rt.f !Jilt,. ...1l .

,)!ji Ja.

~ "" .004 NATIONAL ADVISORY COMMITTEE rot AERONAUTICS -

1 1

1 1 1

o - 1.2 -.8 - .4 0 .4 .8 1.2 1.6 Se ction 11ft coefficient, c~ (b) S ecti on drag oharacteristics at various Reynolds numb e rs, Figure 14.- Var1a.ion of low-dra g range with Reynolds number for the NACA 65(421)-420 aiI'foil; 'lDT tests }OO, 312, and 328.

Fig. 15 N ACA ACR NQ. L5C05 .0 28 NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS .024- 'd f;::, C)

~I

..

.p .020 s:: (j) orl

U

C) . 'I orl t+-t NACA 653-418 \

)

t+-t K /7

(j) .016 I I I I C)

1\ f\

f\ JA NAC A 65 -218

~ \

\

CIl ~

'\

I I I I H

~/

.r.,. 1\

~. l"i tf11

'd .012 NACA 653-018 , ~ s::

~

/j £

~ . \

orl ~

.p 0.

C) CD

J

~~ I ~ ~

(/) .008 ~"

~ w

"0

I f

r\

1M ~ ~

~ ~,.1

f'v-~ .A 4

!8

~

i1m

--.r v

~t\ TV";'

io-J

~ .004 NACA 653-618-

~\

\ NACA 65,3-818

o

o .8 1.2 1.6

-1.2 -.8 .4

-.4

Section lift coefficient, cL Figure 15.- Drag characteristics of s ome NA CA 65-series airfoil sections of 18 percent thickness wit h various amounts of camber.

R, 6 x 10 ; TDT tests 163, 314, 802, 813, and 830.

z z (}l o (}l "'.l 1-" f-' ()) » o » » o ::0 o L' o OQ o 2'.

1.6 jERONjUTICi' - ADVISORY Q fOIl Ip i I r 1.2 V y/o

I

-.060 -.047 ~y 11/ 1 position NATIONAL COMjlTTEE

~ lip

o.

t

frY

.S

x/c .267 c a . .265 ~~ , ],0

- 0.5

0.5 ,

=

= 0.5 ~ .4 - a a = I--- t---- I--

I

a .8

--- -

--- - b.~ coefficient, -418 3-418 ,

- -418

-

.5 653-418, 6 65

- ~

1-- 0 . 6 lift 65 653-418.

= CA CA ~ I I NACA a NA NA ~ -4J.8 x/c -.4- [J 3 o NACA MACA 8 , I ~ and ·4 Q G> Ssction "'\i - CA I II A ~ N 653 -.8 411.

CA 6?3-418 .2 NA and

-- --

-I -

NACA -1.2 406.

~ ---

'--- ,/ r- the I-- l.6 of 320, -.1 -.2 -.~ .032 .008 .0 ·024 .020 .016 .012 .004 0 co 314.

't:I S 0 <l ., 0 " 0 ~ co ... <l 0 0 "

...," .,., .,., ... ... 't:I .,., ..., (/) 0 s:: " 0 8 0 s:: " S 0

...," .,., .,., ... ... ..., :II

tests ICS, TDT

~ I

characteristics

_. 24

'"

~ f\\ I

100; AERONAUT deg ADVISORY x • ~ !if'

I

fOIl o a

r---...., ~ of

vr I

aerodynam19 r;f) NATIONAL tp'

I

COMMITTEE S the 0.5 - - nunbar

L ~ttack. of

= d a of on

f

I

~ ReynOlds -418) angle a

I

Caapar1~ 653-418 65 ...c

II

at -8

J

..

. - NACA NACA Section o [J _r airfoils Figure r -24 .8 ·4 .4 .8 2.8 2.4 2.0 1.6 1.2 - - -1.6 -1.2 .... " 0 <l " 0 Q) 0 0 <l 0

..., .,., ... ... ... ..., 0 "

~ ..-< ... ..., (/)

-.2 -.~ -·4 ~-.1 SO a " 0 ., 0 0 a ., ~

...," ... .,., ... ... ..., :01

'ZJ 1-"' f-' -...:l Z :t> (") :t> :t> (') ::0 ()1 z o L' (") o ()1 OQ .0 ,- 2 CS I' I 1.

r

AERONAU ADVISORY rt~

W V I

DA f 'V

I

;

'\

/;

}\ 2

~ !

i

I

1.

; Y

MITTE[

/ NATIONAL

7 \ .~

,, '4\ I, '/

Cr

/\"

"- ./

!

'" '" ~ "\. /

I . 8

/~ c

"-., c~

>i

lit

~ .gt0

, yl the

I I ,

-. - - . 0 -.105

i n ~ 2?::i!

I 10 position I .4 x .

R -;:: ~ f>. 65 9 :r-p- I 9 9 6 - 9 xlc I '~f . 2 .26 .2 a . c . tests coefficient .A , I ess I om , fr Ob ~ ~ ughn 10~ I

I 10 10 lift

)- ro x l x x x R 4.

-415 f\ m;::: I

I -4J.5

2 2 .0 .0 \ -.

9.0 § ' o 9

\

2R012 6 2-415 64 65 66(215 airfoils

~ ~ ~

I I

o o c. 'fil Section CA Standard ACA

~

I NACA N NA NACA NACA 8

NACA -.

"

o o o /!. "i' '"

~

I

somB of -1.2 .

el I 3 ) 2 tunn 24 16 04 -1.6

3 2 °

020 008 .0 .028 .0 .0 .01 . .0 - . 1 -.2 -.3 ~ II

;1 .. ., o " ... ~ g " " " ~ " " o " c ., 8

~ ] .... .... '" ~ " ... ... .... .... " :IE

<I) characteristic.

pressure !

l:!.

~ -v

"

f\

aerodynamic - ~~ ~ .p M ~ the ~ deg low-turbulence ~~ of

~ ~

/, no'

I lh W

10 8 x j

R -

#;

~

I 9 9 6 9 9 ~

Ii Comparison

. attack, I

}l

two-dimensional of

Ii

'l

I I )- 17.-

oughness J

r l

4J.5 II

I

I - angle 2 r d -8 Langley ~

:II

-'-

2Ro 6 2-415 64 652-415 66(215 I Fi~re ion tanda CA CA CA S I NACA NA NA NACA NA Sect -16 o 0 o /!. "i' I 1-- I-- 1-- I-- 8 B 2 6 4 0 6 2 4 4 -24 2. 8 2 . 2. 1. 1.

-1. -1.

-

" " " " " 0 " " 0 "

,; "" "" .... .... " .... .... rl "" " .. '"

-.4 -.2 -·3 ~-.l cf c ., " " 0 " c " §

,,' ... ... .... .... " :E

z ;l> () ;l> () :::0 z o (Jl o (Jl ">:J 1-"' I--' en ;l> L' () aq

-I

,

It? l

16.8 .-

/ 8.

1.2 / 17·7

=

I

I

, tJ

=

Airplane ratio

/ AERONAUTICS

II 1 l/

I ADVISORY max 1.0 ) Airplane j FOR ~ ~ V

V II

8 8 aspect

//

~ 2 '

6. 97 f-{ff)max

7.46 NATIONAL L .8 of ) C COMMITTEE L

~ I'--- I C

ratio, ratio, airfoils the ratio, ratio, wings

~ .0456

I ct .6 of to + pe

'\ g

I aspect as 2415

wing, 2 W

aspect aspect L C

~ types

V' .0042 I wing. and 415 .4 loadin

,i =

wing, - coefficient, wing, ~ .y', ~ i I two.

652 .0427 CD # 2-415 span -415 Lift + y (.

for ' 2 effective effective 65 2 .2

"

65 2415 NACA NACA ,

-

/

• NACA

"- -

=

V

NACA NACA o elliptical o G ---- - (b) CD an 06 05 o . . .0 .03 .02 .01 .08 .07 to characteristics , <1 0 8 0 00 00 ., !l ..... .. ~ ~ c.f t: !1 drag o .10 .09 .08 .07 .06 .05 .0 .02 .01 <1 " g 00 .. H " Iii eo J' .; ';1 ..... .... ';l 'd ...... :;l corresponding ect-ratio p 8.5 as drag , -

! =

I 10.

I 19.8 1.2

!

o ~ Airplane = I ti finite max induced r a

/)

) irplane of AERON.IITICS

v

~ D I ADVISORY I A 2 L J/': 1.0 FOIl C ect the p

r- ~ ~( I I

(;)msx

as arison

"'

.,0 p

10 ~ L

8 9.29 .0,83 NATIOINAL of coefficients.

C .8 adding ~ +

A COMMITTEE Com

7'

t , by ratio, ratio,lO drag .- wings ratio, ratio,

~ r

.0045 .6 ; ect ct = p ~

A ~

ure aspect as pe r 2,018 obtained wing C g section L as aspect coeffic1en C

wing, ~ ~ I'-- Fi

and .4 wing; -418 wing; .........-:

~ I" Lift

.0,43 65 23018 + ~

V

effecfive effective 65,-418 .2 - 65:;-418 2301.8 NACA NACA

i/'

I .0068 - NACA 'V - = -

NACA V

NACA o l o O '-...

- CD (a - - 06 0 .0 . .05 .04 .03 .02 .01 .

• p 0 g .., .. H .., u ., ..... .... .... ,., 'd ~ 6~ 08 0 .09 . . 07 .0 . .C4!1 .03 .02 .01 .10 A ' <1 " 0 " 0 0 ~ H " 5 eo <> ., ..... ..... .... .... 'd ..... ..... « ~ 1-" I-' <D z z OQ :x> (") :x> :x> (") ;:0 o ()l o ()l r (") )(l0' with chord.

pro- diameter symmetrical 70-percent 9 at cylindrical a O.035-inch of 90-inch-chord has pressure a

I

height of

-

R minimum

--

r, - minimum

-

Protuberance with - numbe the and ~ of 5-percent-chord

~

...... at --.......I Reynolds -

'"

number transition. thickness Wing

~

4.

located

~

is Reynolds ~ premature

"''"'

and l5-percent , wing of

~

I

cause with

I

z to surface

AERONAUTICS ADVISORY section

I

wing FOR to Variation necessary airfoil

NATIONAL I

COMMITTEE 19.- normal

o

o

·050

.040 .030 • .010 tuberance axis 6-series • ..

C ~ ~ ..-1 Figure • • H I. 1.0 III C t» tl H tl ~ CH Q

.-( ...-i 'd ~ LJ"'\;::1

:::: ...-ia> f'('\'" 00 OD. r....t i ...-i ~

~ -- ':z;l t\:l o III 0" 1-" z L' (Jl 0 0 CJl OQ z :x> 0 :x> :x> 0 ::0 0

, I

- , ICS I

, I

10' T x x I

, I

to 60 AERONAU fot I ' I ~ ~ I I NATIONAL ADVISORY COMMITTEE

0°1

"""I

I

the of 5?

model

I

1-0

L.6L

I

teat 0-inch-chord a 6 44 IDT for 328 • painting; number R test R after TOT .,.

.

lr.\ Reynolds nUJDber, ~6 ~ number, ion; t ~ (.

with conditions.

unimproved condi -'" ~ Reynolds rl Reynolds icient surface f VO' Smooth /, v coef two camouflage

Vo g

(a) 20 ~8 ra for a~ d

I

of Lacquer airfoil .

(b) "" )- Variation "'0

cchhJo 65(421

20.- ~

iii

NACA Figure I~

I

I 4

-1---+---1--

-D

I

--+- 1-1 o o °8

. 0 .0041 • .008

.012 'tl 'tl o <l o to o c ., '" o o o o '" ., ., () oS § () '" ..., ..... ;: .... .... ..... ..., CI) ..., ..... ;: .... .... ,a.OO4 ..... ..., O'l

!

Figs. 21,22 NACA ACR No . L5C05 R 6 Smooth c ondl"lon

~ i4:§ x 10 }

S ynthetic ename l camoufla ge o 2 4.8 with a ll specks e'lt off - .012 r-- 6 ~ 6 Vlith bl ade '0 : 6 '<i1 I ...,

-

I': Q) ; .....

&' • 008 .....

~ ...

~

... ~ ~

"""<A;: v Q) ~ f1' .A 0 / l!~ ~ ~ . "" as

'"

...

.004 '0 I': ..... NATION AL AD VI SOR Y ..., 0 C OMMITTEE FOIl AE RON AUTI CS .

Q) CI.l I I I I o o .B 1 .2 - .8 -.4 ·4 Secti on 11ft coeffic i ent. c l Figur e 21 . - Dr ag c harac t e ri s ti cs of 'NAC A 65 (421 )-420 ai rfo il for two sur f ace coridit i ons ; TD T tests ;0 0 and 4 86,

r- Center of wave

C_t_ ' -=----------=-~J

__________________________ ~ ~~ Departure from fair ~--------6 0 in.

airfoil surface

I

OOB -n.

o ..., I': ~ .Oob o .....

...

/

...

Q) "- ~V o r----

-

o .004 as

'"

...

'0 I': ~ . 002 ..., o Q) ~ATIONAL ADVISORY CI.l COjHITTjE FOR tEROrUTIiS - 22 26 30 10 18 46 50 Win g Reynolds number, Figure 22 .- Experimental curve shoViin g variation of drag coefficient wit h Reynolds number for the NACA 65(421) - 420 airfoil section with a s mall amount of surface waviness, t\:: tN z U1 U1 'XJ 1-"' z ~ '-> ~ ~ '-> ::0 o L' '-> o OQ • I • • 2.4 . _ L.E L.E L.E i • -grain on on on .E I I L 2.0 •• nch-grain •• i AERONAUTICS on ADVISORY I FOR Oll-inch .004-

I I

O. rou~hne 0.002-1nch-grain roughness roughpe 1.6 v 80 X v f.. Shellac

NATIONAL I

~ COMMITTEE

/'

---

~ V 1--+

f!

1.2

Smoot~

/ +jJ 0 0t

I A

~J ~

~

V l4-

.

.8 ~ .v /J ::::- «' -v ~ coeffioient, .!j., ~ airfoil lift ~ "" il- Section

~ r---

.

+-;!- 63(420)-422 -.4 edge.

"- ~ ~F"';'::- ~

NACA

~ ~

ll\ an

u.;: -.8

\\

l

t'-+. of leading l~ '\ the -1.2 at o -1.6 .040 .036 .032 .028 .024- characteristics .020 .or6 .012 .008 .004 roughness

'"

0 c C> 0 ~ 0 ~ co c 0 0 C> ,; .... ... .... .... ~ .... ., r1l of drag i - 24 - - and

-¥

~ I degrees Lift "lIO:- ~ 262 k2' I 16 deg 0., ' and ~ I o 23.- various 63(420)-422 a

b

255 I 6 in.

~V with

NACA Figure , 36 TDT I : )( attaok, J : 26 I of

I

/ Tpste I Airfoil R: Chord:

/

angle

!

- j

~f C

Seotion -16 .

-24 . 8 .4 -.4 -.8 2.4 2.0 1.6 1.2 ....

-1.2 -1.6 o o o C> ~ " g ., g r1l ... ... ... ... ... ... .-< ... ., ~ Z :t=- O :t=- :t=- O z o (Jl 'z:l ,...... [\J ::0 l' o o (Jl aq !

2.4 p

H

p stri . _

I

2.0 etri ess 0 20c Oc

I

at ess O.

ughn AERONAUTICS ADVISORY : Ro at 1.6 x fOIl -+' x

• Roughn I I I

+

K

VJ I I

1 Smooth NATIONAL

I x 1.2

j

o COMMITTEE c~ "/:

rr R

, ./ / x' / Va K.

.8 x /+ -+' _ .fi with + if p ,-...- - .

.4 coefficient stri + - ..".- ""

I

airfoil ss lift L.E.

b.;- o on ughne ....

'- <

........... "'- Ro ection S O

~ i'-- !----

"' 63(420)-422

-.4 ~ i'-. ~ r---<: ~ locations.

'" NACA

y ~

",- an 0..

~ -.8

~

of

""

.ff chordwiee -1.2 UB o ri va o 12 -1.6 aracteristics at . 040 .0,6 .0 .032 .02 . 024 .020 .008 .004 .016 ch s s "(j

g .., Q\ ~ c 0 "

" " " "(j ..... ..., ~ g ~ ..... ..... '-< '-< dra .

roughne and ~ f t ain - 422 """ c Li gr deg ~ 0- - 1,(-+ ~ «0' 63(420) Zij.

l-inch- .

l

T

6 in

IV NACA

O.O

I' 36

I Figure

: x 'roT 255 attack, Il

f

: 26 d : of o or

.I

irfoil est

I T

~ R: Ch

/

angle

~

I

-8 ~ < ection

}

S -16 6 0 4- 2' 6 . 8 . 4 .8 - 24 2 . 4 2 . 0 1. 1 . 2 -. ,.

-1. -1.

... ; " c " " 0 c 0 ... ..... ..... " " " " '-< '-< ..., '-< ..... ..... ..... .., ell Fig. 25 NACA ACR No . L5C05 () .o~6 .02.B

-

NATIONAL ADVISORY COMMITTEE fOR AERONAUTICS .

..

~ .

c G)

'6 .020

oM 'H 'H

+

Q) o o

/

Ii) .016 as ~+ NACA 65(223)-422 (modi fied) ~

/ I ~ f I I I

'd ,0 NACA 63(420 )-422 C o

0,.. V

/

~ .012 o t)

~

Cf) ~ ~

~

~ ~~

.008 -: f:::::o.

,-

-.K

W

.004 R: 26 x 10 o

-1.2 o .8 1.2 1.6

-.8

-·4

Section lift coefficient, c~ Figure 25.- Drag characteristics of two NACA 6-series airfoils with O.OII-inch-grain roughness at O.,Oc.

NACA ACR No. L5C05 Fig . 26 x 10 ~ It: ..

H Q)

e

~ q) 'd r-i ~ ~

.56 .64 .72

0 . 08 .1 6 .24 .,2

Sect ion l~ft coefficient, c~ 'd ()

.. . 008

.p ~ Q) .....

() .007

.....

<o-t <o-t Q) .006 () ~ gj .005

.a

s:: .0 04 .....

.p a Q) Ol .5 6 .64 .72 0 . 08 Section lift coefficient, c~ NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS Figure 26.- Comparison of section drag coefficients obtained in flight on various airfoils. Tests of NACA 27-212 and 35-215 sections made on gloves.

'%J ...... N --J CJ1 o CJ1 z :x:- (") :x:- :x:- (") ::d z o l' (") OQ

, ed, d ed

I waxe remov appli flap I sealed

.7

cusp of reduced, section.

gap cusp camouflage sanded, L__ cusped flap filled, compound effect wing flap flap .6 flap glazed, waves the finish, waviness of I camouflage, removed, surface, cusped surfacing camouflage, i<-l Surface Factory Surface Visible .5 66(21,)-1(14.5)

r--G

I- I-- l'- 1"--8 ' "'" ~ measurements .

CL NACA

kR' ~

r-- 1\

.4

.

\ an

I

I----

of flight

--

-<)--1- ~I-- ~~ r drag AERONAUTICS .

.3 ADVISORY coeffioient, - . on fOR J:l.-- v

~ I

t---

Lift ..,..

NATIONAL ~.

!---

- I .2

COMMITTEE .........

.

-..:r .A-' condition :

""

Consolidated-Vultee

==

"'(:]' <>--~.y--

~

'"

.1 27.-

surface wing Figure .LU o X 20 10 R .012 .008 .004 ..

<0 0 be til s:: 0 () Q) () s:: Q) () Q) ()

+> ..-l 'H 'H .a ..-l +> CIl

..-l z :x>- 'Xj 1--" t\:) en C) :x>- :x>- C) ::0 z 0 r-' U1 CJ1 0 0 aq X ~6 - .

..t:\,

I

NAUTICS the

I

RO AE ADVISORY of r.c FOR

I

model

.-'

~.

I

NATIONAL \ "\ COMMITTEE ~ ..".-..(:l.

-r.< ~ ~ L:.

- -

~pprox~.

0.2 spar

=

R c~ rear practical-construction sanded to

r r r

number,

-=

section.

lightly -tr finished Reynolds and IOO-inch-chord except airfoil on painte~ effect received as scale surfaces Dra~ Surfaces Both o s 28.- 6S(216)-3(16.5)(approx.)

CA NA Figure

o

.008 .012 .004 ..

'Cl c Q) 0 bO 0 Q) 0 C\l c 0 0 Q)

~ oH ~ <H <H .8 ~

oH CI) NACA ACR No . L5C 0 5 Fig. 29 S i mu la t ed d oo r jo i n t.

0. 910 - R )2.5 (log

[-

.010 .L I I 'tl . 009 C) ;- J f='~l<.

-

.008 -r :)(;.<

~ f--- =;;x:: Jr>. X .. .-i I&i 0<;

- I-

r-

.., ---- r--

- -+

. 007 t- '+=-++"-4' s:: CD r-

-

..... . 006 ~ C) ..... / .005 ~ Tu r bulent

~ -

-r- ~ CD

-

.004 C) NATIONAL ADVISORY tJ() COMMITTEE FOR AERONAUTICS .

as .003 I I I I I I il t c Condition of Wodel 2 . 65R- = § Cd

" ~

~ .....

l("

.., <:) As received 0.079 . 002 C) "- Painted with gra~ primer () 0.077 + (/) ~ surfacer x Camouflage palnted with

""- 0.074

simulated door jolnts ~ Laminar ' .......

I I '---.,

I I 1 I IllIIIIIlll

.001 10 20 2 30 40 50 60 100x 10 1 4 5 6 Re ynolds number, R Figure 29 .- V ar i a tion of th e drag c oefficient with Reynolds number for the MACA 23016 airfoil sect i on together with laminar and tur bule nt s k i n -frict io n coef fi c i e nts for a flat plate.

NACA ACR No. L5C05 Figs. 30,31 . 016 bunt I\ ONACA 65(216)-417(approx.) as ,""ONACA 2301') (approx.) as built

\\

·.012 +' C ~

V

Q) orl

\\ . ~ /

o orl ....

~ .... ~

V

K

8 .008 o t() as H 'd c ;: .004 +' o r5l . NATIONA L ADVISORY - COMHITT EE fOA AERONAUTICS .

I I I I o •• 2 o .2 .6 .8 .4 Secti nn 11f t coefficient; c~

Fi~e ,0.- Drag characberistics of the NACA 65,2-417 (approx.)

and NACA 23015 (approx.) airfoil aections built by praotical- 6

construction methods by the same manufacturer. R = 10.23 x 10 •

- 0 mCA 66(21S)-116. 100-inch chord,

e~ = 0.15

.016 r-- G NAeA 66(215)-116 (rebuilt model), 84i ino h chord,

o = 0.19

rl · RAOA 23016, 100-looh .h.,d, 'd '" NACA 23016 (rebuilt model), 100-inch chord, c 0.1

o = 9

•• 012 +' C Q)

\~

orl 1\\

o orl ....

....

~\ I~ 1\

~ .008 o Jo..-

.\

.../> t()

M

as "-'l" .

H 'd

V

C I~

V

;: .0 04 +' o Q) CIl - NATIONAL ADVISORY COHHITTEj fOA 4£RONAUTICS I I I o _ 16 28 o 8 12 20 Reynol d s number, R Figure 31.- Scale effect on dra g of the NACA 66(215)-116 and NACA 23016 airfoil sections built by pra ctical-construction methods by the same manuf a cturer and tested as received.

NA CA ACR No . L5C0 5 Fi gs . 32,33 . 0 16 o

""

.012 0 Davis win g, or i gi nal condi t ion

. '

..., 0 NACA 65 -s er les w ing, or ig i nal condition __ <=

~

Q) .....

o .... ....,..

...

t--...

~~

~ .008 o o ..

as s..

'" g .OO4 .....

..., o NATIONAL ADVISOR Y _ Q) CJl COMMITTEE FOR AERONAU TI CS

I I

I I

o o 12 16 20 28 R eyn olds number, R ri ~' 32.- Drag so~ • • ff eo~ for a model of the HAC A 65- .er i e. a1r! o11 . eo~ion 18.27 perc en ~ ~hiok and the DaTis a1r!oi1 ssction 18. 27 peroent thiok, bui lt by praotical-oonstruotion method. by the eame IP1Ultaowrer. 0 - 0.46 (approx. ) • • 012 '" .. ; 0 W i nd tunnel t: Q) [;J Flight .....

.008 .....

...

...

Q) 0 ' . .rL ~ '-' til as s..

.0C4

'"

t: .....

..., NATIONAL ADVISORY COMMITTEE FOR AERON AUTICS Q) CI) I I I o 8 12 16 20 Reyn ol d s n um be r, R F igur e " .- Compari s on of dra g c oef f icients mea sured in f light an d wind t unnel fo r th e NACA 0 01 2 airfo il se c t i on a t ze ro lift.

'x;J Z :t> (") :t> :t> (") ;:0 Z o (J1 o (J1

1--. (N *'" l' (")

OQ x

\ I

0.40 = .

!

~ les c I

I

0 . 29 AERONAUT ADVISORY

=

I 1

FOR ~ surfaCe} with c

} I I

NATIONAL upper COMMITTEE

I