Document
U . S . DEPARTMENT O F COMMERCE
National Technical Information Service NACA WRL 345 PRELIMINARY REPORT ON LAMINAR-FLOW AIRFOILS AND NEW METHODS ADOPTED FOR AIRFOIL AND BOUNDARY-LAYERrINVEST- GATIONS NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS WASHINGTON, DC J U N 1939 i " ...................... J u_ 9 3 9
' NATION A L ADVISORY COMMITTEE FOR AERON A UTICS
TI tRTIMi RI Pi)RT
p O RIGINALLY ISSUED June 193 9 as Advance C o nfident i al R ep o rt PRE L IMINA R Y R EPO R T O N LAMINA_W-FLOWA I R FO IL S A ND KEW METHODS ADOPT E D F O R A I R FO IL A ND BOUNDA R Y-l A YE R INVESTIGATI O NS By E a st m an,1 1 .Jac o bs Langley M e morial Aeromautical Laborst o ry ' " L a ngley Field, V a . "....
'_ REPRODUCED B Y ' NATIO NAL TECHNICAL : I NF O RMAT IO N SE R V IC E U.S . D EPARTMENT O FCOMMERCE SP R I N GFIELD . V / _ 2 2 .16 I % .: ................. _ ........... . ........ _ ...........................
. . ... . . , . , . . . . . - . : : . .: . . .. ... . _. . _ :.' . ' " _!:::. .: :_:_:%:!.:_ . . - . ...'.
WASHINGTON _' NACA WA2TI / VI_ REPORTS are reprints of pap e rs originally issued to provide rapid distribution of , , advance research results to an authorized group requir i ng them for th e war effor t. They were pre- ; viousl_ held under a security status but are now unclassified . Some of these reports were not tech- , ) - nically edited. All ha_,_ been reproduced without change Lu order to expedite general distribution .
L- 345 PRELIMINARY REPORT 0N.LA_INAR-FLOW AIRFOILS AND NEW METHODS ADOPTED FOR AIRFOIL AND BOUNDARY-LAYER INVESTIGATIONS By Eastman N. Jacobs S UMM A RY Recent developments in airfoil-testing methods and fundamental air-flow investigations, as applied to air- foils at the N.A.C.A. laboratory, are discussed. Prelim- inary test results, obtained under conditions relatively free from stream turbulence and other disturbances, are presented. Suitable airfoils and airfoil-design princi- ples were developed to take advantage of the unusually extensive laminar-boundary layers that may be maintained under the improved testing conditions.
For practical consideration, these preliminary re- sults presented are of interest mainly in the lower Reynolds Number range below 6,000,000. Within this Reynolds Number range the new laminar-flow airfoils and the n ew airfoil- design principles may be expected to yield drag coefficients on actual wings of a markedly smaller order than those here- tofore obtained. For example, drag coefficients as low as 0.0022 and profile L / D values as high as 290 were meas- ured.
IN T RODUCTION During the past several years there has been a grow- ing conviction that large drag reductions should be pos- sible through the use on actual airfoils of the low-drag properties of laminar boundary layers. In the past, how- ever, the turbulence present in most wind tunnels tended to so hasten transition., in the usual full-scale range of the Reynolds Number, that the extent of the laminar layer appeared so small that only slight drag reductions could be expected from the low-drag properties of the laminar layers.
2 ( .
/ More rec ently, ho we v er , testssu ch as thos e mad e i n flig ht t o st udy th e o cc u rre n ce of t ra ns i t io n und e r co nd i- t io ns of s ma ll alr --st rea m t urbule n ce (refere n ce s I a n d 2) sugge st ed th at t ra ns itio n m ig ht occ u r much la t er. _ur t her- more , t es ts m ade i n t un n els h avi n g moderately l o w t urbu.
lence ten ded t o . sh ow s om e drag redi_ctio n owi n g t o t h e presence o f. laminar layers o f appreciable exte n t o n pr o pel- ler sections in t he l ow e r Rey no l d s Number range (reference S) and i n the l o wer full-scale ra n ge f o r airfoils (refer- once 4). The result s o f te st s (reference 5) i n the air stream o f the N.A ,C .A. sm o ke tunnel, which i8 k no w n t o have va n lshingly small turbule n ce, a s well as s o me o f @. I.
Taylor's theoretical c o nsiderati ons , led the "auth o r to the conclusion (refere n ce 8) that more exte ns ive lami n ar bo un dary layers an d co ns eq uentl y la rger drag r e d uc t i ons even at much larger Reynolds Numbers might be possible with suitable turb u le n ce-free c on ditio n s simu l ati n g close- ly the turbule n ce-f_ee atmosphere freq u e n t l y e n co un tered i n flight.
D u ri n g this period, p l a n s were started for suitable l o w-turb u le n ce large P _y n olds Number a i rfoi l te s ting eq u ip- ment. The first step was to e l imi n ate the complicatio n s of three-dlme ns lo n a l f l ows, th u s red u ci n g the probl . em to the two-dime n sional flow abo u t a n a i rfoil sectio n . T he n ew type of airfoil testi n g equipme n t wa s therefore referred to as a "two-dlme n slo n al flow tu nn el. _ The proposed meth- o ds o f inve s tigating airfoils extendi n g acro ss a compara- tively narrow test sectioD were thus tz u ly tests of the airf oi l s ectio n . In o rder t o re d uce the tu r bule n ce to suc h a level that its effect on tra ns iti on sh o uld tend to va n - i sh, variat i ons o f the methods employed in the N.A.C,A.
s moke tun n el were c o ntemplated, The next step was to verify the proposed methods of airfoil te s ting. A small model of the new equipment was co n sidered, but i n o r d er to obtain c oncl u s.lve results a tunnel _ufficiently large to reach the lower range of flight Reynolds Numbers was agreed upon.
The first and most difficult problem with the new equipment was to reduce the turbulence to the desired level.
The usual methods of measurement were not sufficiently sen- sitive. Recourse was therefore had to the direct compari- son bf actual tra n sition effects o n a i rfoils as o bserved in flight, in the new tunnel, and in other tunnels. Such comparisons indicated that the turbulence as affecting transition could be reduced below the level of other tun- t nels and, in most ca_e s , be lgw t2e leve l inferred from many of the flight tests. (Compare, for example, fig. 13 of reference 2. Values of Jones t N exceeding 60500,000 have been obtained from some of t he recent tests of air- foils in the new tunnel.) Such comparisons suggest that transition _as hastene& i n flight by other disturbing ef- fects. IB the t u nnel, disturbances Such as those due to surface roughness were. carefully avoided a n d vibratio;_ ef- fects were probably unimportant, at least at the lower air speeds. It remains impzobable, nevertheless, that the d e- sired effective zero turbulence (vanishing effect on tram- sition) has yet been attained. _he turbulence level was considered sufficiently low, however, pending more relia- ble comparisons with flight, to justify the airfoil devel- opment and the transition work herein reported in prelimi- nary form.
In many ways, the preliminary results of these inves- tigations have proved illumi n ating. It appears that, un- der these conditions of vanishing turbulencs, transitio n may be of a di f ferent character than in the usual tunnel.
The laminar-boundary layers ahead of transition .fte n ac- curately follow the lami n ar-boundary layer theory a n d ap_ pear to be free or nearly free from unsteadiness or fluc- tuations of the Dryden type_ Thus the skin-friction drags prod u ced by these laminar la_ers at ths comparatively large Reynolds Numbers attainable with the new equipment are no greater than the values predicted by the laminar- boundary layer theory.
The experimental airfoil investigations covered in a preliminary form in this report, moreover, are believed to be the first showing large drag reductions practically realizable through the design of airfoil sections to ben- efit from very extensive laminar-boundary layers, When airfoils are so designed that laminar separation is avoided, and particularly when falling pressures in the downstream direction are provided over a considerable portion of both upper and lower surfaces, laminar-boundary layers may be maintained up to Reynolds Num_bers of 6,000,000 or more if sufficient ca rm is exercised to eliminate disturbances from air-stream turbulence, surface roughness, and vibra- tion. Such methods are show n to yield, within this rela- tively low Reynolds N umber range, unusual drag reductions.
D ERI V A T ION O F A I RFO ILS " ' _ T he part of t h e investig a tion t h at r e sulted in t h e d evelop m e n t of the n ew s ectio ns is be e t described by giv- i n g a brief chro n ological accou n t of the work. Ma n y asso- cletes co n tributed to the projec t , i n part i cular, Pi n ker- to n, yo n D oe nh off , Ab b o tt , Stac k, R o bi n so n , A l l e n , Bic kn ell, a n d Miss A lice R u dee n, w ho made man y of t h e pres s ure - dis- tr i b u t i o n calcu l a tio n s . Thei r ge n e ral as s i s t anc e an d con- tributlo n e a re ack n ow l e d ge d h ere_ for bre v it y i n l ie u of defi n ite refere n ces to t h e detaile d parts contributed b y each.
T h e project was first undertaken as the result o f reaso n i n g llke that prese n ted i n refere n ce 6, which sug- gested possible l a te tra n sitio n s i n the prese n ce of favor- able pressure variatio n s. Airfoil s h apes were t h erefore sought havi n g the m i n i m u m press u re o n both surfaces well bac k . T rial shapes were used a n d results were checked by mea n s of calculatio n s accordi n g to Th eodorse n Vs method of refere n ce ?. Pi n kerto n , i n particula r , was successf u l i n fi n d ln- g a sha pe ( fig. 2) t ha t wa s co n sidered r e aso na b l y s a tisf a ctory for pr el imi na ry tests , al t h o u g h no t a s t h e b a si s o f a fa mily . Ho d e ls ha v in g t h i s s ectio n were c on- structed for tests i n t he v a r ia b l e-de n sity t unn e l a n d i n the n ew t u n n el.
S o m e doubt was expres s ed as to possible drag reduc - ti on s, o wi n g to the severity of the trailing-edge shape.
The developme n t of a suitable fam il y was therefore n o t stressed, pe n di n g the completi on of the n ew tu n nel and the te s t s of thi s first s ecti o n. I n con n ection w i th S tackts project on propeller section s for high speeds, h o wever, a special mea n -li n e shape was derive_ by yon Doe n hoff a n d the author from thi n a irf o il theory to give a uniform ch o rd- l oad distributio n . When presa u re-distrlbuti on calculations became available f o r some propeller sections having this mea n l i n e, it was appare n t that its use, through add i ng a small consta n t vel o city i n creme n t to the upper s urface a n d d educting an equal i n crement fr o m the lower surface, tended t o leave both surface pre s sure di s tribution s substant i ally u naltered. Hence it became necessary on ly t o develop s u i ta- ble t h ickness distribution s f o r symmetrical airfo i ls gi v ing the desired surface pressure variati o ns.
In the meantime, the new airfoil testi n g equipment had been c o mpleted, a n d the first new airfoil (fig. 2) _as test L , ed i n Jur . e 1938. I n comparison w .i t h an N.A.C.A . 0012 air- foil, tested under the same conditions, the new ai r foil showed very. extensive laminar-bottndary layers, as expected, and the unusually low minimum drag coefficient of 0.0030.
Comparative tests of the same airfoil in the variable- density tunnel, however, fai . led to show unusually low drag coefficients. Two very important conclusions therefore resulted from these preliminary tests. First, it - is feasi- ble to realize large drag reductions by designing airfoils to promote extensive laminar-boundary layers, even if such designs lead to an abnormally abrupt fairing in the trail- ing-edge region of the airfoil. Second, such airfoils mus.t be investigated under conditions approaching freedom from turbulence.
A development program for th ' is new airfoil type was therefore begun at once. The outstanding objectives of the investigation were to determine a limiting extent of the backward movement of the minimum pressure point on the airfoil surface and to investigate, in particular, various degrees of favorable pressure gradient in the forward or laminar region. Suitable thickness distributions (symmet- rical airfoils) were therefore sought; and, to save time, these shapes were to be combined with only one mean camber selected to give the desired pressure distribution at c_ = 0.2, a reasonable high-speed or cruising llft coeffi- cient.
The desired s ymmetrica l air , foil s were based on ones for which calculatio n s had been made in connection with the high-speed airfoil investigations. One worked out by Robinson, through , the process of pressure calculations f ollowing small empirical change s made to produce a nearly uniform pressure along the surface from a point near the leading edge to the 0. 7 c station was considered satis f ac- tory as a member of the family havi n g zero pressure gradi- ent and was there f ore designated N.A.C.A. 0 7 .
Another airfoil, herein designated N.A.C.A. 16, was taken as a ba s e for the n ext family, having favorable pre s - s ure gradient s over the f orward part of the pro f ile. This base section may be considered th¢ extension of the f amily of reference 3 that would therein have bee n given the n um- ber N.A.C,A. 0009- 4 5, and may be accordingly derived.
Other air f oils of the same series were then derived to investigate the effects of a progressive backward movement of the minimum pres s ure p o int. A c o mpres s ing function was applied to the tall portion of the airfoil the function being so chosen as to leave the airfoil unaltered at maxi- mum thickness where the two parts join. The function is g ive n by 2k L J W he r e x re p r es e n t s t h e or i gi na l st a tio n for t h e a irf o i l of 'uni t cho r d , an d x I represe n ts t h e n ew st a t i o n. Th e re su lt i ng ai r f o il w a s s u bseq u e n tly stret ch ed uni f o r m ly bac k t o i ts no rm a l ch o rd le n gt h , t h e fi na l res u lt b e in g a bac k wa r d mo v e m e n t o f t h e maximum t h i c k n e ss st a tio n. P r e s- sur e ca l cu l a t ion s f or t his g rou p o f ai rfo i ls havin g va r i- o us p o siti ons o f t h e • maximum t hic k n ess i n d i c a ted t ha t s uch a ser i e s s h o u ld be s a t isfac to r y . Th e me m bers of t h is f a m i- ly of a &rfo i l s t h erefor e r e c ei v ed des i g na t i o n num be rs a s ' follows : N . A . C . A .
d e s i g na tio n 16 1 8 19 Po s it i o n of ma xi m u m t h ic kn e s s 0 .5 c 0.6 c 0 .7 c Appr o x i m a te pos i t ion of mi n im um p r essure 0 .6c 0.8c 0.9c L e a ding-e d ge r ad i u s i nde x ( r efere n c e 3) 4 3 3 T h us t h e num ber 16 s ugg e sts t h e fo r m of t he t h ick n e s s distr i but i o n a n d the c o mplete de s ignat i on n umbe r N.A.C.A.
1 6 -20 9 for example, is f ormed by add i ng three more dig i t s after the da s h. The fir s t dig i t i ncrea s e s w i th camber a n d refer s to the l l ft coeff i cien t , 0.2 in thi s ca s e , f o r which the a i rf oi l i s de s igned. T he la s t two d i git s refer to the thickne ss , 0.0 9 o, i n thi s example.
'F i nally, the te s t re s ult s for these airf o il s and par- t i cularly f o r the mod i f i cat io n s inve s tigated w i th c us p- type exten s ion s at the trail i ng e dge to rel i eve the s ever- ity o f the flow c o nditi o n s in thi s v i c in ity, led to the devel o pment o f a s econd s erie s de s ig n ated 2 7 . Thi s modl- lied s erie s , de si gnated by the f i r s t d i git 2 , is much l i ke the first, but the th i ckne ss distr i but i on i s mod i fied t o L produce a tendency toward a cusp-type tail. The mean line is also modified slightly near the trailing edge so that the lift-load distribution instead of being constant along the entire chord is constant only over the forward 80 per- cent and then tapers off progressively toward zero at the tail. This mean-line modification was considered desira- ble further to relieve the severity of the adverse pres- sure.gradients in the turbulent-boundary-layer region near the trailing edge. This modified mean line was also used with some of the airfoils of the first series. The air- foil profiles included in this. investigation are shown in figure 3.
AIRFOIL 0RDINATES The airfoil ordinates may be derived by combining the camber and the thickness #orms in the usual way, as ex" plained in reference 8. The mean-line form may be found from ti_e following general expression, worked out by Pinker- ton and Allen:
" yc = _Uag_ b-a
- ,n l -xl+ - -
x I n x hx i J
g- b-a a- k] - In b-
! (a _ I1 In b _ F 1 II _ 4j .2 h = b- - -a "_ (l-a) 2 _n(l-a:) - 21 (l_b) 2 _n(l-b). + i 2 _ _ s_
+ _ (l-b) 1 (l-a) j . + g
where the chord is unity an:d the load is uniform from the leading edge (x = 0) to the chordwise position x =_ a, then tapers off' uniformly to zero at x = b, and remains zero from this point to the trailing edge at x _ 1. For the N.A.C.A. 2V-215 airfoil with 0.5c trailing-edge exten- I. 6 2 sion, a = --3--- and b - 3" For the usual 27 group of air£oils, a = 0.8, b = l, and two other airfoils desig- A !
nated N.A.C.A . 07 , 8-209 a n d 16 , 8-215 have this same mean llne. For the rest of the airfoils having the uniform- load mean llne, a=b=l, and the expression for the mean ll n e reduces to t h e simple form originally derived by yon Doenh o ff and the author:
Y c = - _'W (l -x ) _.n(1 -. x)+_ x t n x
d x 4 _ dY-- - _ c = c_ [_ n (l- x )- _ n.x ] Th e v a lue in d ica te d by c _ I s t h e " ide al " li ft c o effic i e n t for w hi c h t h e airfoil i s designed, 0 .2 far m o st o f t h e pres- ent s ection s . All the mean-l ln e ordi n ates a n d slopes at standard s tatio ns are g i ve n in table . I .
Ordinate s for the thickn ess f o rm s (symmetrical airf o ils of the one maximum thick n ess 0 . 1 2c ) are given in table If.
Variou s airfoils of the prese n t families may thus be de - rived by combination s of s ui table camber and thicknes s f o rms. The meth o d, n o w empl o yed by so me manufact u rer s , of laying o ut full scale the thickness ordi n ates perpe n d i cu- lar t o the m e an l in e at the s tandard s tatio n s , is def i n i tely rec o mme n ded for practical us er s of airf o ils o f these new fam i lies.
TE S T METHOD S The airfoil models tested were of S-foot span and usu- ally o f 5-foot ch o rd. (See fig. 1.) They were of wood caref u lly machi n ed to accurately laid-out and faired tem- plets. Duri n g the investigati on the matter of surface fin- is h received mu c h attention. S lig h t wavi n ess or r ou ghness was fo un d t o h asten transition so th a t d u ri n g t h e earlier test s , the lacquer surfa c e finish wa s pr o gres si vely im - pr o ved by sanding and f il ling t o reduce any unfairness and small- s cale r ou ghness.
The first model was built by a ttaching a cover to a wo o de n _ frame but the slight tendency toward dimpling at the points of attachment gave marked adverse effects , on tran- sit i on. I n fact t it appears that no percept i ble three- dimensional d i mples o f thi s type ca n be t o lerated. S uch compos i te meth o d s of c o nstructi o n were theref o re abandoned.
No additional gain in surface _ smoothness on transition was _ realized, h o wever, beyond t h at o btained by t h e use of 400 water cloth, working in the directi o n o f the air flow to remove all appearances of slight depress io ns or elevations , alth o ugh some sl i ght gain may appear from p o lish i ng the extreme nose port io n of the airf oi l where the b o u n dary layer is very th i n. A s urface R .M. S . roughness read in g o f l0 m i llionths o f an i nch was obtained from a "pr o fil o meter" measurement on a typical model. A better qualitative i m_ pressi o n o f the surface co n d i tio n may perhaps be had from the estimate that the fi n i sh did n ot n eed to be a s s mooth as a high-grade aut o mobile fin is h.
N o attempt will be ma d e t o describe the tunnel a n d the deta i led testing meth o ds in th is preliminary report.
The air-flow u n iformity in re s pect t o b o th turbulence a nd distribution throughout the test Section is such that de- partures from the desired conditions are extremely diffi- cult to determine.
The investigations were _generally of an exploratory nature and followed no routine lorocedure. It was at _ first plmnned to use a balance to obtain some force measurements, but it later appeared that air-flow and wake-survey meth- ods were giving all the information required for the pre- liminary tests. Consequently, a tunnel balance has not been installed.
The usual testing procedure was first to estimate the drag from the integral of total-pressure-defect measure- ments in the wake for s_veral angles of attack near that of minimum drag to find the angle corresponding to the most favorable flow conditions on the airfoil. Later an "inte- grating" manometer c onneoted with a aurvey "zake" was em- ployed. This arrangement gave a direct indication of the drag by the depression in th_ _2neral liquid level in the unaffected tubes, which are associated _ith the rake tubes that lie o_tside the wake. The metho_ should be apparent from figure 4, which shows the wak@ from 0.1-inch-diameter tubes spaced on 0.2-inch centera and 16_cated in the wake 0.4c behind the trailing edge of the _-foot-chord models.
The wake in figure 4(a) is from an N.A.C.A. 0012 airfoil at zero lift and the wake in figu_re 4(b) is from one of the low-drag airfoils at approximately its design lift. The separate tubes at the left indicate the tunnel dynamic pressure and the wake static pressure.
The airfoil drags were thus estimated over a range of I 0 , , an gles an -d Rey no lds Num be rs t o de f ine t h e r e gio n to b e cov er e d by b o u n d a ry -la y er s u rveys an d p r ess u re - d i strib u tio n deter m i n at ion s . Th ese determi na tio n s by m e an s of a " mou se" s om ew ha t lik e t h ose d es c rib e d in re f ere nc e 2 (see a lso f i g .
i ) were usua l l y r estr ic ted to t h e an gle of m os_ . f avora ble f l ow c o n d i t ions Th e prl nc i p a l obje c t iv es were t o st u dy t h e b oundar y l a yers an d t h e tr ans itio n p o in ts a s a f u n c- t ion o f t h e l_ey n o l ds N u m b er, to c o mpare t h e e x pe r i m e n t al an d t h eor e ti cal press u re d i strib u t i o ns , to in vest i g a te pos - s i b le reg ion s of se pa r a tio n ( bot h l a mi na r an d t ur b ul e n t) an d t h eir effe c ts, an d fi na lly £@ determi n e t he opti mum li ft co effi ci e n t . S o me of t h ese d et e rm ina t i o n s a r e f u r - t h e r di s cuss e d w hen t h e res u lts a r e prese n ted .
F i na l l y, so me oI t h e a irfoils were t e sted i n t h e v arl - a b le- de n sit y t unn el i n order to I n di ca t a t h e usual over -a ll a i r fo i l cha r ac ter i st ic s an d als o t h e dr a g cha r ac terist ics f or e x treme l y lar ge R e y n o ld s Nu m bers o r ot h er case s w h ere tran s iti on effects te n d to be s u ppresse d . Th ese re s u l ts may also be empl o yed to estimate the maximum llft to be ex- pected i n flight. T he test s therefore include some i n which split flaps are app l ied to the secti on s.
R E SULTS No attempt has been made to pre s e n t t h ese preli mina ry re s ults i n a c o mpl e te or f i n al f o rm. O n ly the more sig n if- icant results are i nclu d ed a n d n o corrections have been ap- pl i ed, except to the results from the variable-den s lty tu n - n el. The cd val u e s give n are simply the integral s from • t h e t o t al -press u re-defect meas u re m e n ts. A sm al l correc- tion will eventually be applied for the s urvey-tube size (effect i ve centers n o t the geometr i c ce n ter s ). Perhap s a n improv e d appr o ximation to the true drag results wo u ld have bee n obtained by the use of the Jo n e s f o rmula, but n o cor- rectio ns of th i s type are being made pe ndin g the comple- ti on of an inve s t i ga t ion n o w in pr o gress t o determine the correct meth o d s of drag mea s urement by the wake- s urvey method i n a closed tunnel. In general, it appears that the more exact method s w i ll always re s ult in c o rrect io ns that will reduce the drag values prese n ted. The_ . e c o rrectio n s may, i n so me case s , be of the order of 15 percent.
Tun n el-wall correct i ons sh o uld also be applied to the result s of pre ss ure measuremen'ts o n the airf o il surfaces.
In the future, this diff i culty will probably be av o ided by ll testS n g an airfoil somew h at t h i n ner t h an the section it is_ to represe n t. For e_ample, _he surfac . e pressure drop near the minimum-pressure point on a n airfoil of 5-foot chard with a 18-percent-thick section in the tunnel is abo u t 8 per c ent more tha n it would be _n free air. Such " restric- tio n effects, of cou r se, influence the lift results from the pressure determi n ati o ns, alth ou gh this error has bee n approximately removed by correcti o n fr o m s o me of the re- sults for comparison width th o se fr o m the variable- d ensity tunnel a n d prese n ted in f i gures 2 8 to 33. A small velocity- measurement error, of the type'that has sometimes been er- r o neously referred to ms "bl_cki n g, '' ma_ als o be present tending further to reduce th e coeffic - ient values.
Tr ans ition was ju d ged from observati o ns of' impact pressu r es from the inner mouse tube, which rested with its flattened lewer w a ll against the wing surface. The effec- tive he_g_ of the t_be was "u . sually about 0.00 8 inch. The vel o city i n di c ated by the di f ference between this impact pre s sure and the static pressure fr o m the mouse static tube thus indicated the surface velocity gradie n t and . c o nse- qu:ently the local skin Triction. Transition was judged as ths beginning of a s udden and marked increase i n this vel o c- ity as the tunnel s peed was grad u ally i ncreased to move the tran s ition p o int acr o ss the w in g-surface station _nd_r o b- s ervati o n.
L ater ' , an improved method t h at gave more precise re-
( qs)13
°!
sults was adopted, The function _" where qs is tlie dynamic pre s sure i n dicated by the s urface tube and q is the s tream dynamic pressu . re, was plotted a gainst J-_ .
This pr o cedure i a sub s % an_tlally the equ i valent of plott i ng again s t the Rey n old s Number R a funct io n of the surface veloci_y_ gradie n t: d Us / U °
d ys T
which tends t o remain independent of the Reynolds Number as long as the surface tube remains relatively closeto the surface in a truly laminar layer. Figure 5 sh o ws the method applied to the deteI'mination of three transition poi n t s o n t h e }, ' . A. C . A. 27 - 212. I t will b e n oted t h at t h e function remain s con s t a nt in d ic a ting a tr u ly laminar layer in t h e low-speed r an g e a nd t h en ri s e s a br u ptly in t h e tran- slti o n region. T he transitio n p o ints we r e take n as the po si ti on s ind i cated by the arrow8 in fig u re 5 at the kn ee of each c u rve.
T he c o nditio n of the bou n dary layer Dust pr i or to transitio n was i nvestigated by the hot-wire method to study i n greater detail the nature o f tran s ition, a n d to fi n d an explan a t i on f6r the te n dency of the trans i ti on functi o ._ to rise slightly before the appearance of marked tra n siti o n effects. A fi n e hot wire was used with a high- gain d . c. amplif i er and a cath o de-ray oscill o sc o pe. The results obtained, s o me of wh i ch are indic a ted in figure 5, are rather s ignificant. Well ahead of the tran si tion pQi n t the lami na r-boundary layer was remarkably ste a dy and appeared to be free, or nearly free, from unstead i ness or fluctuations o f the Dryde n type. Perhaps such steady lam- inar layer s should have bee n expecte d under the test con- diti on s of very low turbulence in the new tun n el, particu- larly after it had been dem o nstrated that the experime n tal and.theoretical b o undary layers agreed excellently, b o th wit h respect to total l a yer t h ick n es s a n d the velocity prof i le withi n the layer, but Dryden (reference 9) had f o und from exper i me n ts that so me layer s may become markedl y u n steady while, at the s ame t i me, reta i ni n g lam in ar pr o p- ertias, at lea s t much more nearly l a m i nar tha n turbule n t.
The osc i ll os cope showed, h o wever, a quite d i ffere n t behav- i o r as the Reyn o ld s Number was i ncrea s ed to bring about tra n sit i on. Ins tead o f fluctuatio ns in the laminar layer, the observat io ns ind i cated momentary transiti o ns to s k i n- fr i ction intensitie s c o mparable with th os e of a f u lly de- veloped turbulent layer but of extremely sh o rt durati o n, perhap s le ss t h an 0.01 s econd and at first occurring only once every several sec o nd s . These very s h o rt bur s ts o f turbulence were much to o fast t o a ppear in the over-damped mouse measurement s , wh i ch i nd i cated o nly a mean re s ult.
The rea s on f o r the early gradual rise o f the transit i on fu_ctlon is thus apparent. The t o tal time durati o n o f the turbulent type o f flow was o f the o rder o f 1 percent when the "transiti o n point" ind i cated by the arrow at R = 6,000,000 i n figure 5 was reached. As th_ Reyn o lds Num- ber was further increased, the frequency, a_d also the duration, o f each of the t u rb ul e n t bur s ts increased s o that the relative total t i me in this c o ndition i ncreased as i ndicated by the percentage values given " o pposito the points in figure 5.
!
.] Pressure-distribution results, both theoretical and experimental, when extensive mouse static-pressure obser- vations were made, are presented together in figures 6 to 21. In some cases, the theoretical pressures were obtained directly from calculations bit The0dorsen's method (refer- ence 7) and, in o_ther s , by Allen's method (reference 10) of velocity-increment addition to the velocities abot_t the basic symmetrical section: to allow for the lift-_oad dis- tribution This methcl i s very sim_01 e and may be readily applied to the prediction of _ressure distributions and critical speeds for other deri#_d airfoils Of the mew fam- ilies. For such purposes, th e theoretical basic pressur e distributions for the symmetrical sections are given in figure 22 and in tables llI to VII.
Certain additional i_portant data are also included In figures 6 to 21, in addition to the arrows indicating the measured transition-point positions, and the corresponding wing Reynolds Numbers indicated in millions near each ar- row. S eparation of the flow is al_o indicated as judged from the mouse measurements, Included al s o are the angle of attack, the corresponding mea s ured minimum drag c0effi- c isnt, and the Reynolds Number at which it occurred. The theoretical compre:ssibility-burble speeds, expressed as the ratio M c of the critical speed to the sp.eed of sound obtained both f:rom the measured and the theoretical peak negative pressure coefficients by the method of reference ll, are also included in each figure.
Some other experimental data are presented with the discussion. Data dealing with further details of scale- effect calculations, skin-frictlon distribution, and bound- ary-layer studies in compariso'n with th e ory, the analysis of the transition _ata, the e xtension of these airfoil de- velopments ta higher Heynold_ Numbers and speeds, studies of the relative tunnel turbulence, an& check tests in oth- er tunnels and i_ flight will be separately presented and discussed by various authors in st_bsequent papers.
DISCUSS ION Best Airfoil, the Optimum Reynolds Number Range This discussion will first consider the experimental data on the various airfoil forms almost without regard to the Reynolds Number, considering mainly the minimum_drag i 16 I beginning of the p r es s ure r ecovery and hence ma'ke s the . given adver s e gradient relatively m o re s evere. Under ex- treme c o ndition s , turbulent separation may be expected.
Such c o nsiderati o n s led to the development of the N.A.C. A . 27 series (fig. Ii) whic h was designed to relieve the severity o f the flow c o nditi o ns i n the pressure-recov" ery region behind the m ini mum pressure point. The ex- pected reducti on in drag at Reyn o lds Numbers ab o ve that for the minimum is shown in figure 25 a n d more particular- ly f o r the 12-pe r cent-thlck section i n figure 26. The marked fav o rable result is n o t i nd i cated f o r the N.A.C.A.
27-21 5 secti o n (f i g. 27), but the ordinate s for the 27 series were rev i sed between the time the 15 a i rfoil and the other airfoIIs were c o nstructed, The o rdinates of the airfoil that was tested are not now considered satis- fact o ry as a member o f the 27 family. The test results, t alth o ugh included, sh o uld therefore be disc o unted.
I A n o ther u n anticipated result of changing from the 18 to the 27 serie s was the s h i ft o f the min i mum drag to l o wer Reynolds Eumbers. The same result is aga i n ind i cat- ed i n figure 25 in changing the minimum pressure farther forward fr o m 0.7c t o 0.6c i n g oi ng fr o m the 27 t o the 16 I series. The opposite shift of the minimum drag to higher Reyn o lds Numbers was expected o w i ng t o the l o wer local Reynolds Number at the minimum pressure station at a given wing Reynolds Number. The explanation is that minimum n drag with t h ese airf oi ls does n ot o c' c ur when transition is n ear the m i nimum pressure point, o r even f o rward of the lamlnar-separation po in t. (Se e f i gs. 12 and 18.) These q experimental data do no t conflict with the laminar-separa- tion theory (reference 13), which places the laminar sep- i aratlon point very near the minimum pressure point after the layer has become thickened by its long run over the forward portion of the airfoil. When the minimum pressure E I point is not well back, minimum drag occurs at a Reynolds Number so low that moderately extensive laminar separation I is actually present. The transition occurs soon enough to close in and permit the pressure recovery but not soon : enough at minimum drag to produce excessive turbulent skin E frictions. In the separated or adverse pressure range, : h owever, t h i s transition te n ds to occur at a reduced Reynolds Number.
t Figure 25 also throws some light on the Question of how steep the favorable pressure gradient should be over the forward part of the airfoil. A comparison of the [ _ 17 t_ N:A.C.A. 07-209 and the _.A.C.A_ 2?.-209 a_rf0ils shows a higher minimum drag a nd_ an earlier rise with increasing Reynolds NUmbe_ for the airfoil with the f!a_t pressure di st ri but ion.
A tentative explanation can be given _ as the result of further fundamental boundary layer .and transition studies not included in this report, .The_difficulty with the flat pressure distribution is not primaril_ that tran$ition nec- essarily occurs at a "much smaller value.,of R 8 in ,the ab- sence of a favorable pres sure'_i21d, although th:ere may be some slight tendency in th_is _irection. bu_ that very small dis,turbances such as.sligh_ _mperfections in the model, slight_ depart._res from the d.esign angle of attack, or slight flow f luc._uations may produce regions of local ad- verse pressure gradient: "This conditio_ tends to produce regions of excessive boundary-layer thickness (or even lo- cal separation), which tend to grow three dimensionally in the absence of .a_ favorable pressure gradient impelling the low-energy air.along in. the normal flow direction. Hence, excessive values of _R8 ma3" appear local l y leading, in turn, to & premature _transition. The.optimum magnitude of ' the favorable pressur_gradieut for these airfoils there- fore becomes largely a_matter of practical compromise.
Small gradients requize _extreme care:in the elimination of disturbances, whereas large gradients cause excessive skin friction, excessive form drag due to th@ more severe l_res - sure recoveries, and low critical speeds due to the exces- sive peak negative pressures.
Appl ic.at ions It thus appears that, within the Reynolds Number range considered, the N.A.C.A. 27 senies represents a reasonable approximation to the best compTomise. _e lift at which the minimum drag occurs may be varied .at liberty to meet particular design requirements. The extent to which the optimum lift may be increased is suggesSed by the results for the N.A.C.A, 27-2012 in figure 16. This airfoil w a s desi@ned for an optimum llft coefficient of 2.0. Such an extreme procedure probably pushes the pTesent design principles too far, but high-li_'t airfoils of this type may find some application. The ultimate _erformance of an airfoil section for application such a_ long_-range alr- planes, gliders designe_ for small gliding angles, blower and propeller blades, guide vanes, etc., is measured by the maximum profile L / D for the section. With these new 1 8 airfoil-design principles, low-drag coefficients may be at- talned at rather high lift coefficients. With the older type of flapped airfoil, for example, the pressure recov- ery real_zable over the uppe_- surface of the flap was re- 4 stricted by the excessive thicknes 9 of the turbulent layer i n this vicinity. Owing to the possibility of maintaining laminar flows over the forward portion of the new airfoils, the turbulent layer at the after part of the airfoil may be relatively thin with the result that relatively abrupt pressure recoveries are attainable. Although the boundary- layer studies o n the N.A.C.A_ 2 7 -2012 indicated that the lift i n this case had probably been pushed too high, a maximum profile L / D of over 2 9 0 was attained. For air- foils similarly designed but with slightly lower optimum lifts, the turbulent separation that occurs near the trail- ing edge may be sufficiently reduced to produce even higher L / D rat Io s.
By a suitable choice of the camber to give the desired optim u m lift, t h e llft ra n ge o . f"low drag (figs. 2 8 to 32) will be suf . ficient for many practical applicati o ns. O ut- s i de the l o w-drag range, the variable- d ensity tunnel re- s u lt_s s uggest that the a i rfoil drag will n o t be excessive.
The results pre s e n ted herei n are applicable on ly within the l o wer Reynolds Number ra n ge and theref o re appear most n atura l ly s uited f o r applicatio n to small aircraft and glider s . I t shoul d not be overlooked that they may have m u c h wider app l icatio n to specia l des i g ns i n w hi c h it i s fea s ible by reduction of wi n g ch o rd or den s ity at high al- titude s to achieve the pr o per R e yn o ld s Number. In ap p lica- tio n to airpla n e wi n g de s ign the camber will pr o bably be selected so that the optimum llft will occur near the cru is - i n g s peed. An airf o il s omewhere between the N.A.C.A. 2 7 -I12 and N.A.C.A. 2 7 - 5 12 w i ll thu s probably be empl o yed. The ad- va n tage of the new s ection s will the n appear thr o ugh in- crea s ed curising s peed s and i n more ec o nomical o peratio n w i th in thi s s peed range.
I t s hould be empha s ized, however, that the gains w i ll n ot b e mar k ed unle ss s uitab l e a p plication s are s elected.
I t may be desirable to employ u nu su ally large a s pect rat ios " in order to reduce the induced drag and to reduce the ch o rd sufficie n tly to obtai n a suitably low Reynold s Number.
The wi n g surface mu s t, of cour s e, be . fa i r and s mooth o ver the forward 8 0 percent . V i brati o n sh o uld be avoided and, in all probability, the propeller slipstream o n the wing mu s t be eliminated. Pu s her propeller s are therefore to be recomme n ded pending a n e xper i mental dem o nstration that the di s turbing effects of the tract o r pr o peller can be t o ler- ated. Di s turbance s arising forward o f the wi n g al o ng the fu s elage will affect o n ly small portion s of the wing ad- j_ 19 -- + ja c e n t t o t h e fusel a ge. 0 nly t ha t part o f t h e wi n g in side a line extendi n g from a point at the leading edge just out- side the fuselage_-boundary layer backward toward the trail- i n g edge and o utward wit h t h e Tlow direction at an angle probably less than 8 ° need necessarily be subjected to the usual high turbulent skin friction.
Most important of all in an_ application, however, is the reduction of fuselage_ tail-surface, and parasite drags to a reasonable minimum. High parasite drag s may easily mask any marked gain from a large reduction in wing-section drag. One private-owner type of airplane tested in the N.A.C.A. full-scale tunnel showed for exam- ple, a drag coefficient of approximately 0.0600. A reduc- tion o T wing drag from 0.0080 to 0.0030 would consequently have reduced the over all drag of the airplane only in the ratio 80 / 60 The resulting sp_ed increase would thus rep- resent an almost inappreciable gain. On the other hand, if the airplane to wnlch the new wing is applied is so clean that the wing-profile drag represents a large part of the entire drag, the performance gains will be very large. The higher speeds attainable, in turn, reduce the induced power, and often improve the propeller efficiency.
Particularly in bucking a head wind, the time s a ving and tae economy expressed in miles per gallon, a matter of vi- tal importance to the private flyer, should thus be im- prQved to a very marked extent by the application of the n ew wi n g sections..
Applicatio n s at Rey no lds Nu m bers Above t h e Opt i mum Little . will be said regarding the application of these data at the higher Reynolds Num bers becau s e further investigations outside the scope o f this report are n o w i n pr o gre s s t o develop methods of maintaining these same l o w- drag properties at very high Rey no ld s Numbers. I t a ppear s , h o wever, that comparatively small gains 0f this same type may be readily realized at the higher Reyn o l d s Number s by maintaining the laminar layers over o n ly a comparatively small portion.of the f o rward _ a rt of the airfoil. I n fact, full-scale tunnel testa o f t h e N. A .C.A. 23 0 12 airfoil (ref- erence 4), and of the N.A.C.A. symmetrical airfoils (ref- erence 14), as well as tests of the N.A.C.A. 28012 airfoil to study roughness effects iD the 8-foot high-speed tunnel, indicated that som_ gains of this type would be possible on existing airplanes if sufficient attention were given to the surface condition onthe forward part of the wing.
2O Actually the ga in s mig h t be no ti c eably larger in flight o wing t o tunnel-turbulence effect s present in the test re- sults. On the o ther hand, these types o f airfoil are in- h erently u ns u ited to t h e desired flow conditions, except ° p os sibly at extremely large Reynold s Numbers. The " a ddi- ti o nal" type o f llft distribut i on ass o ciated with the s ym- metrical airf o il, f o r example, cause s a minlmum-pressure peak to occur very near the lead i ng edge o n the upper sur- face. ( S ee reference s 15 and i 0.) This c o ndit io n always tends t o lead t o premature lam i nar separation or transi - t i on .
An obvi o u s impr o vement in the medium Reynolds Number range is p o ssible with an airfo i l l i ke the N.A.C.A. 2412-3 4 fr o m the family of reference 5 . Thi s type o f airf o il has a b e tter lift-load distributi o n and a thickne s s di s tribu- ti o n that d o e s n o t pr o duce a mlnim u m-pre ss ure pe a k exces- sively far f o rward. The N.A.C,A° 2 4 12-34 and N.A.C.A.
1 4 12-3 4 airf o il s are theref o re t o be te s ted i n the new tun- n el and will be separat e ly reported whe n the re s ult s are avallable.
I t sh o uld be urged, h o wever, that snap judgment s based o n bo u ndary- l ayer calculations along the lines suggested by reason i ng similar t o that presented in the preceding para- graphs be withheld pending f u rther experimental investiga- t io ns. Some of the test result s (figs. 1 5 and 26, for ex- ample) s h o w large drag increa s es as so ciated w i th compara- tively small f o rward movements o f the transit io n point.
The cause o f th i s rather peculiar behavior of the drag was f o und, as the result o f a s upplementary investigati o n to be s eparately rep o rted, to be a s s o ciated with the very h i gh skTn-friction inten s itie s usually present at the o nset of turbulence i n the boundary layer, The adver s e effects o f the high frlctl o n inten s it i e s are m o derated, h o wever, when the transit i on o ccur s in a region o f pres _ _ure recovery as it does on the best section s in the optimum o perating con- dition. I n fact, the type o f flow leading to a relat i vely high intensity skin fricti o n is then actually desirable i n o rder t o avoid separat io n. I t thu s a ppears that it may alway s be desirable t o effect s o me pre s sure, recovery in the neighborh o od of the transiti o n point, not only becau s e of the immediate saving in ski n fricti o n and lower losse s as- sociated with recovery but also because the turbulent layer is left t o run over the rema i nder o f the airf o il in a thick- er, and hence lo_er, drag condition.
The same conclusion was reached in a different _ay, which actually l ed t o the design of the 0.Sc-chord exten- sion on the N.A.C.A. 27-21 5 airfo i l. If chords longer than the o ptimum, that is higher Reynolds Numbers must be employed, the least adverse drag effects should be expect- ed when the best possible sect i on is chosen for the for- ward part of the airfoil and the remainder, which must be exposed to turbulent skin friction anyway, is added as a relatively thin extension lying i n the wake of the forward part where the velocities and turbulent-friction intensi- ties are a minimum. Alth o ugh the test result s in figure 24 cannot be said t o substantiate these views, neither can they be said to disprove them. Owing to the larger chord and the resulting different relative position of the sur- vey rake, the results for this airfo i l should not be con- sidered strictly comparable, and conclusions should be withheld pending f u rther tests. It is apparent, neverthe- less, that drag gai n s will be much less marked if any large forward movement of the transit i qn po i nt is all o wed to re s ult from Increasing values of the Reynolds Number.
CONCLUSION For airplane wing design and for other airfoil and streamline body applications in the lower Reynolds Number range the new laminar-flo_ airfoils and the general de- sign principles deduced from the present investigations may be expected to yield actual wing-drag coefficients markedly smaller than those heretofore possible.
Airfoil and flow investigations of the type consid- ered must be made under tunn.el-flo_ conditions approach- ing freedom from turbulence. Under these suitable condi- tions, truly laminar-bou n dary layers may be maintained to unusual!y high values of the Reynolds _lumber. Transition appears to be sensitive to very small disturbances of var- ious kinds including surface roughness and air-stream tur- bulence and, in the absence of such disturbances, appears to be of a differen t character from that usually observed in wind-tunnel testing.
Langley Memorial Aeronautical Laboratory, National Advisory Co_nittee for Aeronautics, Langley Field, Va., April 25, 19_9.
REFERENCES it i . St u per, J.: I n vestigation o f Boundary Layers on an Airplane Wing in Free Flight. T.M. No. 751, N.A,C.A., 1934.
2. Jones, Melvill: Flight Experiments on the Boundary LaYer. Jour. Aero. Sci., vol. 5, no. 3, Jan. 1938, pp. 81-94.
3. Stack, John, and yon Doenhoff, Albert E.: Tests of 16 Related Airfmils at High Speeds. T.R. No. 492, N.A.C.A,, 1934.
4. Jacobs, Eastman N., and Clay, William C.: Characteris- tics of the N.A.C.A. 23012 Airfoil from Tests in the Full-Scale and Variable-Density Tunnels. T.R. No.
530, N.A.C,A., 1935.
5. yon Doenhoff, Albert E.: A Preliminary Investigation of Boundary-Layer Transition along a Flat Plate with Adverse Pressure Gradient. T.N. No. 639, N.A.C.A., 1938.
6. Jacobs, Eastman N.: Laminar and Turbulent Boundary Layers as Affecting Practical Aerodynamics. S.A.E.
Jo ur., v o l. 41, no . 4, O ct. 1937, pp. 468-472.
7. Theodorsen, Theodore: Theory of Wing Sections of Ar- bitrary Shapes. T.R. No. 411, }_.A.C.A., 1931.
8. Jacobs, Eastman N., Ward, Kenneth E., and Pinkerton, Robert M.: The Characteristics of 78 Related Air- foil Sections from Tests in the Variable-Density Wind Tunnel. T.R. No. 460, N.A.C.A,, 1933.
9. Dryden, Hugh L.: Turbulence and the Boundary Layer.
Jour. Aero. Sci., vol. 6, no. 3, Jan. 1939, pp.
85- i00.
i0. Allen, H. Julian: A Simplified Method for Calculation of Airfoil Pressure Distribution. T.M. No. 708, N.A.C.A,, 1939.
ll. Jacobs, Eastman N.: Methods Employed in America for the Experimental Investigation of Aerodynamic Phe- nomena at High Speeds. Misc. Paper No. 42, N.A.C.A., 1936.
\
½
9.
-L 12. von Doenhoff, Albert E., and Jacobs, Eastman N.: Tran- sition as It Occurs Associated with and Following Laminar Separation. (Paper Presente_ before Fifth International Congress for Applied Mechanics, Cam- bridge, Mass., Sept. 12-16, 1938.)
13. von Doenhoff, Albert Eo: A Method of Rapidly Estimat- ing the Position of the Laminar Separation Point.
T.N. No. 671, N.A.C.A., 1938.
14, Silverstein, Abe, and Becker, John V.: Determination of Boundary-Layer Transition on Three Symmetrical Airfoils in the N.A.C.A. Full-Scale Wind Tunnel.
T.R. No. 637, N.A.C.A,, 1939, 15. Jacobs, Eastma;_ N., and Rhode, R, V.: Airfoil Section Characteristics as Applied to the Prediction of Air Forces and Their Distribution on Wings. T.R, No.
631, N.A.C.A,, 1938.
N
=_
Ji
°
o o o o o o ,, oo . - o o o
S1 1" LI £' _ Ol _ , ' _ fzl l r' / £££ ' 1 £6 g g gO0 "- 8 £ 0 " 1 8 6b0 " - OT, _ " 9 99tz0 "-: 91 £ " $6 I _ L " _ . £ b, _'_ dV . V b , " l e . gg " l b 6 9 £6o0 " - i 9 bo ' l bo r 2 0 '- £ Z _ ' _L£ b O '- : 1 6 ) £ , t ;, 6 ' ¢ ) 9 _'_ 6 F. I '_ _L 6 " l 960" _ " _ 6 _ t _ OlO ' - L g JO " 61 1 _ ;0 '- O i _ E " L _ £ O ' - 6 b b ' _ G j _ £ b _'_ _ L _ '¢ ._ g/x '_ " g/ . _ ' _ Zl _ .¢ '_ 06 @.¢ l/0 "- 68 '0 " 81/$ 0 '- _ Jgl _ ' L 6 1 _ o '- L I - ¢" 0 6 6 0£ " I .F . _ ' _ 31 9' _ , 7 _ 9 ' £ I t _ ' E" -_ g I 0 _ 10 " - 2 - ¢/ " b gL _ ,O '- g . ¢L ' I ? L Z :O '- _ L g" . _ 9 k Og ' e. . _ g '_ 9 I _ ' - q 6 0 . _' tz g 6 I ' i P _ . _ 1 _ '1 _ 0 9 I - _ 6 1 ¢ _' - " _ lr _ " I _ t EO ' - t _ . ¢ 6 " ? 0" _' - ? 6L " O g £ _ 1"/ 5 " Z 6 L c " _ F = = ) ' _ ' £80 = 9 t _ ' _ S L . F g. _ O ' - k# £ " 0 91 _ 0 '- 00/ 7 6 _ Ll O ' - 5 ( _ g ' S L 0 9 _' / 000 " _ " _ g ' S e6 l i E OL _ ' -F" tR£ '£ OL .F I ? £ O ' - Z O£ " %¢ L/O' - gO _' l 6 I _ E I O'- _ Z6 " OL L/ _ '? _ / _ 6 _ /L 6". _ 9 _ L ' £ 6o _'_ _ ' _ LL O ? O ' - Z I _ L" I0 _ 10 ' - ! _ , '1 $9 _ 00 '- 0 £ 0"1 . F 9 _ 1 1 " £ S _ 6' - _ 000 "_ 9 £ _ ' _ t _ 9 " _ Z g '# _ O _ _ OL g O '- _ 90"1 I _ ZO( _ '- 6' _ '£ ' / _ / _ 00 '- I L O'I 0 _ ) I _ I 'F £ _ 9 ' _ " _ _ ' L 6" . _ 000 " 9 1 _ ) 6 " _ " _ . _ b£ 9 S 0 "- $ F 1 £' 1 9( _ 00' - £ . ¢ _' 1 61 _ 000 " - $ 6 0 " 1 -¢ ' -¢ g LO' _ ' £ Ol _ _ 6 _ ' _ OG 6 "_ , c 000 " 9 £ G6"5 " O. F t " dL'dO '- g g . _ ' l I _ lO0 " L . ¢ ' £ ' 1 " - _ OI " / OS ' o S') _ = )£ . - _ " .. ¢ £ LL _ ' g 0 6 _ l _ 6 L¢ " .. c ' _ 0 £ _ /0 '- g g _' / Z9 £ 00" £/ _ £ ' 1 6 / £ 00 " . . _ 6 0 ' 1 .. ¢'6 , .
, Q@_ '.F 1 £ £ L ¢ o0 " ) _ 6 g L ' _ _"_ ' @ L k 6" g 0 / _ £11oo '- L I L "1 91 6 00 " 9 0 £ '/ . . o / _ Oa " /Z O ' l Ok o00" _ _ _ 9o ' .F 9 _ £ _ L9S ' S E Lg '. ¢ S £ _ geO0' ¢ ¢ff 'l _£ . /0' _ S ¢' 1 . £ 9600 " 0 £ 0 7 .¢£ LI 6".. _ _ SL' _ .¢8 0 ' _ 6 67 _ ' - ¢ LI &_ E6 _ O _ . ¢ _ L I 0" £_? ' 1 £ _ LIO " _ LI ' I 6 _ , £ 10 " " dL 6 " 0£ £ g?_ ? ___ / i_ . o _ L ' /;. £ _ J 6" / _ sgo ' £ L Z t _ '. _ 9 _ £. _ g o" £_ g . 'l O _ gZ O " b 'LO ' l 61 _ L IO " .¢ 6 9" .¢ _ " Zo £' . ¢ " 9/ _ 0 '_ $ 2f£' _ b _ z _ Y z b _ ' L , , £ $ 0 ' _ 0 3 £0 9£ 0" L 9 £ ' 1 _ hL Z O " g f;, 6 " ")0 7 ; _ :0 ' 9 6 L " 0; _ OLL 'P ¢) _ J - _ ' £ 6 ' 1 _ '. c _ £o 'v _ , £1 '_ , Liz ._' t _ . _' / I _ TJIz O ' I = P l ' l _ ) L ££ 0 ' I _ L " I g L ff O " £ L _ " _¢ / 1 _ ( TF t _ 96" _- " d_ 91" £ Ft£ 'F_ 9 . V _ , ' £ t 'JS" _ O 9 £ 0 = )0 ' " _ 6 g" _ 1 _ / _ 7 " " )09 ' L S b _ O ' t 1 5" OI 6 . ¢ J _' ¢ £ _ S ;' _ _ g/' _ S _ 6" _ _ £ 0" £ 0t _ i _' £ $7. "g'£6'_ 0 ' t , £ L' .C Z Lb O" _ ) 6 1 _ ' e _ '6 _ ' O ' I _ ff lz " 3 " Z L ' ) 6" _ OFI ' 6 _ o£' _ ' _ b '_ OlS ' _ 0 ; _ 6 " _ O _ F I ¢' lgO " . _ . q " _ P b . _ S O " L9£ " ,Pg gtxO ' @ 1 £ ' O L¢ " / _ Jl '_ _ J _* g ' / b . _ ' ) ' l 9L / ' I 9 0 g '/ Z Z g ",3' S " _ " gS' OOl " 0 3 ' £ ' " £ Z g=_ 0 ' c '/ _" I£ gcO " _ ) _ 1 " _ "_ @. . qS ' / '_ 6 0 " / _ gl ' l I/ _" 1 7 5 6 _ '/ O i lY ' . F ' _ ' / _ , g _ 'l l " £ g l " £ L O@O " _ _ 1 " I _ S '&_ O " L O / " . 5"_' I S _ Z ' _ ' _ " . c _ g " ? :06" _" . F_ '_'£ 1 ' £ 6 0 ' £ 9 _ / , 0 " _ 0 ' ££ / _ 'o ' 6 - , c 0 " _ )' _ ; " L _ . _" 0 _" _ , _" £ " _ t _ 5 " l ' _ $0 ' _ 1 _ ) 01 " Z £ O" 8£ ' _ ' 6 0" g'_ O" £ ' O 0 0 0 0 0 O _ O _ 0 0 p . ' _ [ o / u _a o _ - S _ / Z _ /P- < O "._ /_- La,'_ , " :_ 'VW l a&; _ "_ s u _ F _ 7 ._ d _ p T_, ( _ ._ ,u oo < _ 4 - z _ . /p x o s_¥ = lql _ ls z_ ' s_ 4Ol _ pu _ sa p z _ u , !p ._ O a u /- / u z _ a/ _ g 0 0 0 0 o 0 001 " " t , 6LL " _ . g_" _Q 6 ' _ , & ' &?6 ' " ¢g6 ' . St G 0 0 0 0 0 (? 12 0 1 _' _ Q Y I_ 0 .' 1 . g £ O 'l _ 0 ' 1 S_ . # ' I , _ 10 ' / 0 6 _ l " t _ -- OZ 6 _" L £ 6 " . F L 6 " 000 7 _ 10"1 o110 7 .c ' 6 6 6 _' 1 I .. ¢ _ '1 . F o _ 'I % _ 1 "1 _ o1' 1 67 0 ' 1 O _ SZ _ Z ; 7 O/ _g 'l " # £ Z, ' l $ ' 61 " 1 lt ; ,l ' l R 60"I O G l ob ' " _ . _ ' 1 J 3 L ' _ ' I _ C P2 ¢ '1 6 _ 1 " 1 1 7b o ' i OL o 6 - qS ' l ?_ I _' I _=_' I 2Sg'l L _ I ' I 0 _ I 'I o g / _' / _Z £ ' l S a_ 'l e/ _' l _ I _ I ' I _ 6o ' I O _ e o . ¢ ' l _ o _ , ' l t/ £ ' / I _ ,' 1 _' / ' / £ o / ' / OZ / .¢_' 1 . F O £' / £_' 1 Z ( 7 _' / Z _ l ' / / & O ' l O ._ t - • . ¢ fY l _ - _£' / - ¢ Z _ 'l oo _ '1 t _ £/ ' 1 6 9 o " 1 o ? @_ f _ ' l _ ¢ / _£" 1 g _ 'l Z& l ' / 0 _ / ' 1 % _ 0 '/ 0/ 7 . F ol ,' l 61£ ' 1 .F _,_' I LLI'I el/ ' / gL O ' l 0 .¢ 3' 6 £ 7 I ? _ £ ' 1 _"_' 1 9gl ' l t _ 1 '1 190 7 0 £ _£ ' / £6a '/ _ Z? _' / £_ 1 ' t 9 0/ 7 IL O ' I O b / _ ' £ '/ _ ' 6_ . ' / #£' C ' / _ )L l ' l L /I V _Y LO ' I O _ 6 ££ ; 1 E L _' I // _' 1 _ q - q ' Z OI 7 9 _ 0 " I 0 £ 0 £ E ' 1 &L_ :'I t _" l &_ l ' l II1 ' 1 . F ZO'l . ¢ / - 01 = ' 1 .F 3" _ , 'l " _ O _ ,'l O _ q/'/ 0o1 " 1 " ) ' )O'l o _ g & _ '/ _ c ' _ 'l I _ q ' ¢'/ & . Cl'l , cO/'/ OLO ' / a l 1 6 8 "/ "E _ , _ 'I • k 6 1 "/ F t _ '['I LEO ' / _,_ o'/ . _ I E L _ "/ gE' C"1 _ /W 'I 0 -¢ 1 '1 / 0 / 7 _ ') 0 ' / . g ' / & _ l S _ ' / 0 _ I' / S _ I ' I 1 6 0'1 O _ O ' l Ol L _ C'I Ol' _ ' l I g l 'l I/ _ I ' / L 6 0'/ S _ O ' / 0 _" _ e, Y _ 0 _' I _9 1 "/ 7 _ I 'I l eO ' / _ 0 7 _ 'L .¢ L 9 ' I L f/ ' / -_ I ' / /// 7 S _ O'/ 6 _ 0 "I _'_ I _ 0 " I _Z_ / . / _Z O 'I e . c o / ok O ' l _ ov _ ¢' _ o o o o o o o ._'h_g' O t _ 0 6 "0 _6" 0 o0o'1 6 " 00 "1 ZO O 7 _'_ '1 _/o -= 3/ s/o - ; / _ 1 0 -_ , 1 6 oo -_ p l @ oo -_ 1 _ , oO - _ l 3_ 0 0 0 0 o 0 o ! ' V '_' V 21 /I '_ ' °o' V 'v ' V'D ° V°, v "_ " 3'v° /V ' p '_ 'p " A/ " V'_ ' V'N 'V " O' b " /V ' V' O'V' /V "v'_ ' y " N _'V " 3' k " / y 'v '_ ' v'W "V "o' V' / v o _ .
• " " 3Vi _N 3(]I. _ T _ O0 7 7 [ _.7 7 _ V _.Z. ' =,.,. ,, , , o._ , ,o , , 0 0 0 0 0 0 qOl 0 0 0 0 0 0 00/ _ t _ eJ ' I, .F Z ' _ )O g " _ ,. ¢ _ " . ¢ 0 6 " = ) £ 6" .- ¢6 t ; ,O B' ' _ 6"" 06 6" _ 10"/ 0" _ 0 " / .. ¢ 1 0 " / . _ 6 0 _ 6 " _ g6 " . F IO ' I 6 _ 0 " 1 6 _ 0 " 1 _ ' g 'O ' l 06 ,¢66" . .F _ q'/ . F . F' O'I . F. _ O 7 ..W _ O ' I 1 £ 0 7 0 0 (; l _ k ' l 0 _¢,' 1 /9 _' 1 _ 0 _ , ' 1 9 _ 1 ' 1 ; E 60 ' I 0 _ . t _ S _' I .¢6 _' / ? E _ 'I 6 L l ' l _ t ll 'l ( _ LO ' I O _ " _ /.g ' / 6ot _ , ' / LI E '/ _'£ _ ' / . _ ' . F' / ' I _ 0 /'/ 0/. " _ /1 _ , ' 1 L £ £ ' 1 L _ J _ ' / 00 _ ' 1 / _ gl ' l _ 0'/ O , _ 1¢1 06 £' 1 " _ 0 £ ' 1 " _ , _ , ' 1 0 _ 1 ' 1 660 " 1 (7 7 0 1 1 _ ' I _ £ £' 1 E _ ' _ 7 901 7 0 £ /7 LgO'l 12 9 I. _ ' _" 1 _¢ 9 _' 1 -I _ ' _ , ' 1 01" _ ' 1 O ' l x [I _ Y60 ' I O _ . C Of _" / _ . _ ' 1 E " J' _ ' l 76[ ' ( O F .IV Z _ O' l 0- _ _ Jlt x 'l / E'£ 'I I _ ' _ '1 L61 "l 0£1 " i LgO ' I 0 _ , #1 1 _' 1 Ok.£ ' l • L 9_ 7 6 _ 1 " 1 £ £ 1 " 1 60 0"1 01 7 0 9£ " 1 • o I £ " 1 . F M _ ' I " _ gl'l I _ 1"1 le o " 1 f 2 _ '_ _ p ' l I .F £' I LL _ V _ C r & " 1 9 _ ("1 "_ 6 0"1 0 _ ' t _ ' 1 £ 9 _' 1 S 3g '/ 9 < )1 " 1 _ 11"1 . . . c Z O ' l O _ E' _ , _" / £ F £ " 1 £ 8_ '1 I 1 _ 7 O _ ,l ' l £ 80 7 0 " _ / ._' 1 IZ _ * / _' 1 _ ; '/ I T / ' ZOl ' l IZO 'l S = ) _' / L £ _ £ ' [ I _ L 3 " l ZO ? _ 7 L £ I ' I 1 6 0 7 _ ci 6 0 £ ' / L S 3 " / ._ 0 _ , '/ ! _ SI 7 " _ 0/'/ _ ) 0 " 1 O / 3t _" l i _2£ "1 . F 2 _' I 0 0 _ ' / 5 "£ 1 " 1 060 7 ( 2 I _ J _' l I _ ' 1 ff _ [ 'l L_ P / ' / g60"l _ c90 " / J _ ' L ..F I¢, 'I I _ g _ , ' l _' 1 " _ 61 7 / _ 1 " / 690 7 . _ " _ 0 £ ' _ ' 1 L 1 2_' 1 9 Z I '1 _ £ 1 " 1 _ 60 " 1 190 7 O L d " 0 0 _ '1 . _ L _ '/ _ 'E _ 7 0 6 f l / _ £ 1 1 _ gO 7 o '. _ 6 _ 0" / L/ I ' I ! ;, , _ /' / Z I / ' l t _ 0 " 1 _ . _ 0 " / ._"_" f £ " d ' / _ t _' 1 0 £ _ 7 _ ' _ 1"1 6 _ 1 7 g _ ' O ' / _ q' ; _ ( _i_1_ '0 1 " )6 " 0 _ o ' 1 "_ SO ' l £S0 ' 1 _ 70" 1 .E "_ " I LO £Y' O _ SO ' ( _ S I 7 _ 1 " 1 "_"_ 1 " 1 SBo ' I . _ _ y 0 0 o o 0 0 o 0 0 0 0 ( 7 o 0 "_' O' V'N " V 'O ' V W " V '2 ' t V WI'_' O'V ' N 'V "_'_W 'V'o 'V'/ V 'V'O'V '_ V ' 3"V W "_ " O '_ v'_ 'V'_' V'N V' o'V ' H '_'_ ' V '_ 7 - _? TABLE Vll I I Basic Pressure Distribution Values of Pressure coefficient ,wS, St_+ion c 19-004 i9-006 19-009 19-012 19-015 19-018 percent I_.A.C.A. N.A.C. A . N.A.C.A. N.A.C.A. fIN "A'C' A ' N.A.O.A.
0 0 0 0 0 0 0 i .25 1.009 1.010 1.000 0.989 0.972 0.955 2.5 1.027 1.039 1.056 1.075 1.092 I.I06 5.0 1.044 1.065 1.097 1.129 1.162 1.197 7.5 1.050 1.075 1.113 1.1 5 1 1.190 1.230 i0 1.053 1.080 1.121 i.161 1.202 1.246 15 1.056 1.085 1.126 1.170 1.214 1.260 20 1.057 1.087 i .130 1,175 I .222 1.272 30 1.060 1.091 1.138 1.18"8 1.242 1.300 40 1.064 1.097 1.146 1.201 1.261 1.328 50 1.070 1.105 1.159 i 218 1.285 1.360 60 1.079 1.118 1 .'177 1.240 1.311 i._95 70 1.095 1.141 1.210 1.285 1.355 1.455 80 1.129 1.195 1.297 1.404 1.518 i.651 90 1.172 1.259 1,392 1.515 1.625 1.709 95 1.091 1.135 1.195 1. 2 39 1.263 1.264 I00 0 0 0 0 0 0 |_ N.A.C. A . Fi gs . 1, 3 , 4.
- _ ::: :!::?!!ii:ii?!)_;ililiiiiiZlZi!_i![??- : Ji:i i_i i::_?:iiiii_!iiii!!i!ii!!!ii_i!_?:i_i_ i!i :: iiii!_ , _ Q 0 _ e -t ,,-I
• i :° "
:_: i iiiiii!iiiiiiii ®
• i:,:.::iiiiiiiii i i::;i;iiiii!i_2iN_._._ ii!_:_ii!_i_iii!iii_iiiiii!_ .,. , :.: :: :: : : : ::: : : . : ::. :::.:::::: :: : : :; : :::::::::: : :::::: _ :: :::::. • _ . _ :_i_i_i_ii_ illli i ii iiiiiiiiiiiii! i li_i_iiiiiii!iii!!ii!iii!!iii i !ii!ii!_ ) i q I NACA IS- _. 0 4 N £ CA _ 9- 20 9 ram-" . -, _ m,-- . N A SA # 8- _ 04 NACA _ 8- _0_ _ ACA 18 - a _ NAC A 1 8 - _ 1 5 NACA I _ - 20 9 WITH CU S p m,,-, '-'ql
I
NACA 27 "E08 NAC.A _ 7- 2 1a NA C A E' 7- 2 1 _ NACA 07,_ - _0 9 NACA Fig. 2 I16 .,- U pp e r "_ \'N 1 . 2 _
.8 t t
/ '\t
" il
• I !
: J
0 50 i00 Fib-Are 2.. Preliminary form of laminar-flow airfoil, (NACA 25 B 09-46).
_ NACA Fig. , 5 , , ,, i
L
!
S 4 5 6 7 8 Reynolds number, million_ Fixate 5.- Method of trazsition measurement. Variation of the "transition function" and correlation with hot-wire studies.
1.SAGA Fig. 6 1.6 .4 0 50 I00 Theory 0 ° 0.2 0.84 - Experimentl0 _ - .8310.0022 at R=4,2x106 Fi_ure 6.- NACA 18-204 airfoil.
3 /
N_CA F ig . 7 | , 1.6 4 .3 S , -- ----'- " 5 , 2 '_
, f - -.-
.8 0 50 I00 Theory 0° O. 2 O . 811 Experiment 1 / 2 ° - ,8210.0029 at R--4.6 x lO6 Figure 7 .- NACA 19-204 airfoil.
3_
_ NACA Fig. 8 r L Q4 "" 0 50 i00 T he o ry 0 ° 0.2 0.71 -
t leaf
Experiment i / 2 ° - , _ 0.00S9 a t R=4.6x106 Figure 8.- NA C A 19-209 a i r fo i l .
: Z3
• NACA Fig. 9 .4 ,,, " • ! L . ,,,, -_s e eFigu_ e ii .
0 5O i00 Theory 0° 0 . 2 0.77 - Experiment 1 / 4° - .76• 0.0026 at R=5.3x106 Figure 9:- NACA 18-20 9 airf o il.
\ 4 NACA Fig.lO --j- c, o .-.J .4 I _see Figur_ ii.
0 50 I00 Theory 0° 0.2 0.76 - ExperimentlO° l - .74 0.0026 at R=5.Sxl06 Fig_are I0.- NACA 18-209 airfoil with 3in cusp extension.
, _ NACA ' Fig . ii .... ' I
I
l
-------- -_
- !
I
!
I , i, 1.6 I 7 6 6 4 5.6 . _i
i _"
_._ If " __ ' _----.,_--__
i io
a . E\
t ' 1
' /
t I !
Laminar _eparatior,. (_losed in _ I
i i t '
able indiieate8 ReynOlds n_ tuber,i I
] , I !
0 50 !C0 Theory 0 o O. 2 O. 77 - Experiment t / 2 ° .22! .75 0.0027 at R=4.6×106 Arrows indicate location of transition correspondin_ to the Reynolds ntumber indicated in millions.
Figure ii.- NACA 27-209 airfoil.
NACA Fig. 12
I
!
I i
1.6 I 1.2 .8
i
!
.4
0 50 I00 Theory 0 _ 0.2 0 . 781 -" ExperimentI0 _ - .7610.0031 at R:3.8XI06 Arrows indicate _ocation of transition corresponding to the Reynolds number in millions.
Figure 12.- NACA 16 = 209 airfoil.
i , NACA Fig.
I
1.,_ 6.05. o 4.6 3.8 3.4
. x x" < _" ,_ x L ., -- 1 . 2 \ "_ , ,. 5. _ I ,__"-_: i . 8 ........ I 1.
i
.4 , t 1 I
' 1
1 I , ,, . ,f , }
0 50 i00 Theory 0.2 0 , 79 - E_perimentalll / 2°1 - .76 0.0034 at R=3.3×I06 Fibre 13.- NACA 07,8- 2 09 airfoil.
NACA Fig. 15 7.3 -- 5.2 I 1.6 ! 6.0 ( _. . I / _._---- _---_ , . _ -.
Y
_-_ . _ '---_,. ,_
S f 6 8 5, ._ .4
! !
0 50 i00 Theory 0'° 0.2 0.74 1 Experiment JI / 2 ° .19 .72 I 0.0029 at R=4.6xl06 Figure 15.- NACA 27-212 airfoil.
3 7
NACA Fig. 14 7.3 3.8 1 . 2 i 16. 5
'! i?/
"_ .,)
i i
l !
0 50 I00 Theory 0 ° 0.2 0.73 - Experimentl 0 ° - .72 0.0033 at R=5.3XI06 Figure 14.- NA_A 18-212 airfoil.
NACA • Fig . 16
/ \
/ Z . - - , _ \'l _ .
/
/ . _
2.4 / ! , ,, , \ \\
/ _ / o o l ; / \ \\ I I , • I I " \ 2.0 / , ' \ , I \ / , i ! " / , '_ i_
1.61 1 i _ _
1 I . indicati,ns of I f i / 50 X tulbul.en t Separation _ S L 7" _ ': _ , . -----.-.-- I , ., ,A I0° o \ _ 1 . 2 I . 8 ,,, \\ .I .
'li a • c% M c Cd_ _ .
Expe_iment 7° 1.78 .52 0.0 at R:2.3xlC6 0 50 I00 Figure 16.- NACA 27-2012 airfoil, _ NASA F ig . 17 | ........
i ,, 4 ' 0 5 0 i 0 0 Theory b ° 0 0 74 - I_ I c _ ] M c I c dm i n Experiment O O 0 173 0.007 1 at R--4.6 x l O6 Figu r e 17.- N AC _ 0012 a i rfoil.
_A0& Fig. 18 !
W r 7.6 5.8 / I 4.R
1,s + '
, x _ " |3 . 0* 1.2 t ." _ ""'_" _'_" _"_ _" 7.0 ¢ " ; <,
s , \
.8 14 ,,, 0 50 I00 Theory 0° 0.2 0. 7 2 -
• i+i.i,1 ,n
Experiment .1 / 2° .18 .70 0.0041 at R--4.6x106 Figure 18.- I_ACAig,8-215 airfoil,
/3
NAO-A Fig. 19 P I I 0 5O I00 Theory 0° 0. 2 0 -
f I. o Experimentjl /2 ° - .72 0.0036 at R=5.4xl06
Figure 19.- NACA 18-215 airfoil.
y /
N&CA F i g . 20 I
I , !
, I [
I i _ ..... I i I _ i,, . _ Jr ! I "-----J ' _II _ "_ J
" ! . i ....... _ i
!
i i ' I 5.7" i I 6.0 4.8 1.6 I i I _ I
:.2 / i i , , "-'-"-"-'-_
/ i i , i --- \\
i , _------r--_ I ,
// F j , I \ \
s t; _ , j I " \ '
! / i ' , ,' " '
._ i i I - I
! ! I,., I
i J j I i , _
, , i i t I [
i i j _ I
i ! l t _ i
• I ' 1 /
; ! i
i I f .... L
| i i I , i ,J , i i , • t ,, I i 1 i
I i , I , i
0 50 i00 cc i c% Mc ! Cd m i n Theory 0° i0.2 0.7i I - Experiment 1 / 2°I - .70!0.0035 a_ R = 4.6x106 Figure 20.- NACA 27-215 air f oil.
NACA Fig. 21 t h _'_._ ...__ _ .. ___..._. L f_-
lo._
_ 6,.4* 1.6 x i !
× \ N S _'_ _ x × x .8 ,4
!!
t 0 5O !00 Theory 0°_.133 0.71
Experiment 1 / 21 - 69 0.00_ atR:8.0n0 "_
Figure 21.- NACA 27-215 airfoil with .5c extension.
NACA Fig. 22 -,T I _ a • , 1.6 b
12 I -_ r _7
NA;A 001 _ NACA 37-018 .8 7 .4 O ....
S NA_A I_- )12 NACA 87-012 .4 O .,, o8 " , NA_;A i8- _12 NACA L9-01_ ,4
i I
0 50 I00 0 50 i00 Figure 22.- Theoretical pressure distributions for the basic symmetrical sections.
NACA Fig. 23 I -I .0120 ' ' NAC_ airfc '_i a, deg _: 1_ -204 0 16 -204 0 •OlO0 ...... Tur oulent skin fri ztion ...... .......... Lami n ar slain fri :tion
.oo_o ,_
Cdmi n _ _ """ _ // .....
l oo o \
t
1 /
• 0040
I / i
•0020 I I J 0 2 4 6 8 i0 Reynolds number, millions Figure 23.- Minimum drag coeffic i ents of 4-percent- thick airfoils• -, NACA Fi_ = . 24 ,) J -< ,.L NA '&'air: oil__, k _, d_ g____
.Olin ...... o " 19:,209 .1 / 2
o 18:209 1 1 4
" _ 18;209 C in c'.@p / O o 27.215 .5c ext.
•0010 .... .
.... Tur ,ulent skin fri__tion kk ....Lain nar sl.in fri,,,tion 0080 ", .< Cdmin , . . W _.
• 0060 \ o ,_
\
•0020 "_ , ,, . , _ ,,, ., s !
0 2 4 6 8 i0 Reynolds number, millions Figure 24.- Minimum drag coefficients• _ACA Fig. 25 I_ACA _irfoi_ _, d=_g .0120 ....
27. _ . 09 1 / 2 + 07,8- 309 1 / 2 X 16- _09 0 I .... T _rbule it ski .0100 f "ictio i.
-- L Lminar skin fi'ictloll.
\
•00ao k_ Cdmi n •0060 ___ . _: .it-
.._ /
• 00 , %0 _ ,_ , , "
\
• 0020 _-.
L !
0 2 4 6 8 l0 Reynol is n umb e r, millions Figure 25o- Minimt_ d_ag coefficients of 9-percent-thicX airfoils.
NACA Fig. 26 | --4 • I .0120 NACA ai rfoil--m, deg-- 18- _12 0 • 27-212 1 / 2 + -27-2012 5 O O01Z 0 \ •0100 - ...... Tur )ulent skin
friltion \
--Lam .nar s tin k frictio n . 0080 ...... _:.
Cdmin -.. . - ¢ 0 • 0 ' _ 4 - _" L "'-.-
_o /
.0040 ",, _'_. f"' " /
\
.0020 -_ _ ._ O B 4 6 8 I0 Reyno l ds n_nber, millions Figure 26.- Minimum drag coefficients of 12-percent-thick airfoils.
NACA Fig. 27 NACA _irfo_[ _, deg •0120 Zk 18- 215 I • 27- 215 1 / 2
' x 16,_ -215 1 / 2
i i , .0100 .... ' -- Turl alent s_{.n friotion \ k i_ La m laar sl_',in \ . ! friction .ooao N_.
J_ Cdmi n _ __. _ •0060 o
• \ lA "N
_x_._ 7 x
• 0020 0 2 4 6 8 I0 Reynolds number, millions Figure 27,- Minim m n drag coefficients of 15-percent-thick airfoils.
N.A. C .A. Fig. 3 _
Reproduced by NTIS
National Technical Information Service
U. S . Department of Commerce
Springfield, VA 22161
Thi s reportwas p r i ntedspe c ifically for you
order f rom our collection of morethan 1.5
million t e chnicalr e po rt s.
_ J
_) Ir = .l • F o r e con om y and eff ici en cy, NTI S does no t mai n ta i ns t o ck of i t s v ast (_ 1 ( _ J _. coll e ction o f technicalreports. Ra t her,mo st documen t sare p r int e d for eachorder. Yourcop y isthe b e st possible reproduction available f rom __J _ . _ r _ ou r mas t e r ar c hive. I f you havea ny qu e st i ons c oncerning t his documen t _ or an y orderyou placedwi t h NTI S ,pleasecallour C us t omer S ervices
( J
= ; _ l Depa rt men t a t ( 7 03)487-4660.
_ _ Alwaysthink o f NTI S whenyou wan t : _ 4 _ _ . r _ j • Accessto the technical,scien t i f ic,andengineering r e sul t sgen e ra t ed • R &Dre s ult s from J a p a n , W e st Ge rm a ny,Gr ea t Bri ta in, a nd s om e 2 0 _ o t her countries,mos t of i t reportedin English.
_ [,_ _ b y the ongoingmulti b illi o n dollarR & Dpr og ramo f t he U . S .Gov e rn m e n t .
_ j _ NTI S alsoope r atestwo centersthat c an provideyou wi t h valuable i nform a tion : Q _ 4- J • The Fe d e r a lC o m pu ter Produ c ts C ente r- offe r s so f twar e a nd • The Center f or the Utilizationof F e deral ' T e chnolog y - gives y ou O accesst o th e bes t of Fed e r a l te c hno l ogiesan d la b ora t ory re sou r c e s.
! . _ _ _ - __ da t a fil es p r o du ce d b y Fede r a la gencies.
1 _ v-_ _ p _ For mo r e in f ormationabou t NT I S ,send for our FREE NT/$ Produc t s foreign Governmen t t e chnology. C a ll(703)487-4650 or se nd this ( _ ) she et t o NTIS ,U. S . D epa rt men t o f C omme r c e ,S p ri ng f ield, V A 221 61 .
c , _ _ __ As k fo r c ata l og , PR -8 Z 7.
8", e
l_ _ _:_ Add ress , _ ( _ _ ( _ _ Te l e phone
_ ; _ l_ ._ . _ - YourSo urceto U.S. and Forei gn Governme nt
Research and Technol og y.