Document
NATIONAL ADVISORY COMMITTEE
FOR AERONAUTICS
REPORT No. 502
SCALE EFFECT ON CLARK Y AIRFOIL
CHARACTERISTICS FROM N.A.C.A. FULL-SCALE
WIND-TUNNEL TESTS
By ABE SILVERSTEIN For sale b7 the S aperlntend ent or Docaments, WashInllton, D .C. • • • • • • • • • • • • • • • • • • • • • • Price 10 ce nts
AERONAU T IC SYMB OLS
1. FUNDAMENT AL AN D DERIVED UNITS Metric English Symbol Abbrevi a- Abbrevia- Un it Unit tion tion meter __________ _ __ __ ___ Length __ __ ___ fo ot (or mile) ____ _____ l m ft . (or mi .)
second __ _______ __ __ _ ___ Time _____ ____ (or ho ur ) ___ _ ___ t s seco nd sec. ( or hr .)
F orce ______ __ _ weight of 1 kilogram _____ weight of 1 po und ___ __ F kg lb .
-
P ower ________ horsepower _ ___ ___ __ __ horsepower (metric) _ _____ hp.
P
---- --- ---
m il es per hOU L ____ ___ {kilometers per hour _ __ _ __ k . p.h . m .p .h.
S peed _____ __ __ V me ters per se cond __ _____ feet per second __ ______ m .p.s. f.p.B .
2. GENERAL SYMBOLS
w, Wei ght=mg v, Kin emat ic viscosity
p, D ensi ty (mass per unit volume)
g, S tan dard acceleration of gravity = 9.80665
2 2 Standard density of dry air, 0.12497 kg-m-'-s2 at m/s or 32.1740 ft./sec.
15° C. and 760 mm ; or 0.002378 Ib .-ft. -4 sec.
Mass = W
m, Specific weig ht of II st andard" air, 1.2255 k g/ m or g 0.07651 lb ./cu.ft.
I, M o ment of inertia = mk • (Indicate axis of
radius of gyration k by proper subscript.)
Coefficient of viscosity JJ., 3. AE RODYNAMIC SYMBOLS Area ~ID' Angle of setting of WlllgS (relative to thrust S, line) Area of wing SID' Angle of sta bilizer setting (relative to thrust Gap G, line) Span b, R e sultant moment Chord Q, C,
n, Resultant angular velocity
b Asp ec t ratio Vl
S'
p- , Re ynolds N umber, where l is a linear dimension Tr ue air speed V, JJ.
(e. g., for a model airfoil 3 in. chord, 10 0 m.p.h. normal pressure at 15° C., the cor-
q, D yn amic pressure = ~p \l
r es ponding number is 234,000; or for a model
L, Lift, absolute coefficient C. {s of 10 cm chord, 40 m.p . s. the corresponding
number is 274,000) D, Dr ag, absolute coefficient OD -::s Ce nt er-of-pressure co efficient (ratio of distance of c. p. from leading edge to chord length)
D., Profile drag, absol ute coefficient OD, = ~S Angle of atta ck
Angle of downwash
Induced drag, absolute coefficient OD, - ~
Angle of attack, infinite aspect ratio Angle of atta ck, induced P ara site drag, absolute coefficient OD - DSp Angle of attack, absolute (measured from zero- • q lift position) 0,
Cr oss-wind force, absolute coefficient 0 = q ~
Flight-path angle
R, Re s ultant force
REPORT No. 502
SCALE EFFECT ON CLARK Y AIRFOIL
CHARACTERISTICS FROM N.A.C.A. FULL- SCALE
WIND-TUNNEL TESTS
By ABE SILVER STE I N Langley Memorial Aeronautical Laboratory 72254-34 NATIONAL ADVI ORY C OMMITTEE FOR AERONAUTIC S HEADQ ARTER S, NAV Y BUILDl G, WASHINGTON, D.C.
LABORATORIE S, LA GLEY FIELD, VA .
Created by act of Congress approv d M arch 3, 1915, for thc supcrvision and direction of thc scielliific study of the problems of flight Its membcr hip wa increa 'ed to 15 by act approved March 2, 1929. The m emb 1'5 are appointed by the Pr esid ent, and scrvc as slich without compensation.
JO SEPH S. AMES, Ph . D., Chairman, WILLIAM P. MACCRACKEN, Jr., Ph.B., President, J ohns H opki ns nivcrsity, Baltimorc, Md. Washington, D.C.
DA\'l0 W . T AYLOR, D.En g., Vice Chairman, CHARLES F. MARVIN, Sc.D., Wa s hington, D.C. United States Weather Burcau.
CHARLES G. ABB OT, c.D., HENRY C. PRATT, Brigadicr General, Un it ed Statcs Army, ecretary, mith so nian In st itution. Chicf, Mat erie l Divi sion, Air Corps, Wright Ficld, Dayton, LYMAN J. BRIGG S, P h.D., Ohio.
Dir ccto r, Nationa l BlIl' cau of Standards. EUGE E L. VIDAL, C.E., BENJAMIN D . Fo LOIS, Major General, nited States ArUlY, Dircctor of Aeronautics, Dcpartment of Commcrce.
Chief of Ail' Corp s, War D epa rtm ent EDWARD P. WAR ER, M .. , HARRY F . G GGE HElM, M.A., Ed it or of Aviation, J York City.
cw P ort W ashington, L ong I s land, . Y. R. D. WEYERBACllER, Commander, niled I::>tatos uvy, ER E T J . KI NG, R ea r Admiral, nited States Na\ ' y, Bureau of Aeronautics, Navy Department Chie f, Bur ea u of Ael'Onautics, Navy D epa rtm ent . ORVILLE WRlGllT, Sc. D., CHARLES A. LINDBERGH, LL .D ., Dayton, Ohio.
ew York Cit y.
GEORGE W. LEWI S, Director oj Aeronautical Research JOHN F. VICTORY, Secreta7'y H";NRY J. E. REID, Engineer in Charge, Langley Memorial Aeronautical Laboratory, Langl ey Field, Va .
J OHN J . IDE, 'Technical Assistant in Burope, Pari~, France TE C HNI C AL COMMITTEES AERODY AMICS PROBLEMS O~ ' AIR NAV IG AT IO N POWER PLA TS ~ ' OR AIR C RAFT AIRCRA~'T A CC IDENTS MATERIALS FOR AIRCRAFT INVENTIONS AND DESIGN S Coordination oj Research}, eeds oj lIlilitary and Civil Aviation Pr eparation oj R esearch Programs Allocation oj Problems Prevention oj Duplication Consideration oj I nventions LANGLEY MEMORIAL AERONAUTICAL LABORATORY OFFICE OF AERONAUTICAL INTELUGEN CE LANGLEY FIELD , VA . WASHl NGT O ,D . C.
U nificd conduct for all agencies of CoJlcction, classification, compilation, sc i entific research on the fundamental and dissemination of sc ientific and prob l ems of flight. technical information on aeronautics.
REPORT No. 502
S CALE EFFECT ON CLARK Y AIRFOIL CHARACTERISTICS FROM N.A.C.A. FULL-
SCALE WIND-TUNNEL TESTS
By ABE SILVERSTEIN SUMMA R Y indica Led, however, thaL it is unusual to obta in th e same results from several tunnels, even when these Te ts were conducted in the N.A.G.A. full -scale wind fundamental similitude requirements arc sat isfied.
tunnel to determine the aerodynamic chamcteristics of Some of the more important sources of experime nt al the OZark Y airfoil over a large range of R eynolds Num - discrepancies are wind-tunnel boundary interference, bers. Three O1'rfo1ls of aspect ratio 6 and with 4-, 6-, airfoil- support interference, and air- tl'eam irregulari- and 8:foot chotds were tested at velocitie between .~5 and ti C's and asymmptl'irs.
118 miles pel' hour, and the ckaracterist1' cS wete obtained As a result of the failure of wind-tunnel te ting to Jor Reynold::; Numbers (based on the airfoil chonZ) in fulfU l the exacting requirements of similarity in b ot h the range between 1,000,000 and 9,000,000 at the low the flow and the test procedure, disagreements occur angles of attack, and between 1,000,000 and 6,000,000 in published results purporting to give the experi- at maximum lift . With increasing Reynol ds Number' the menta lly obtained characteristi cs of airfoils of the s ame airfoil characteristics are affected in the following section. T hese conflicting resul ts from tests in n um er- manner: The drag at zero l~ft decreases, the maximum ous wind tunnels confront the designer with an arduous lift increa es, the slope of the lift curve increases, the angle task. The variety of data must not only be ana lyzed of zero lift occurs at smaller negative angles, and the and interpreted for application to the particular design pitching moment at zero lift does not change appreciably.
problem, but it must al 0 be extrapolated to fli g ht The Gla?'!r Y airfm'l characteristic o bt ained from the R eynolds umboI'. This extension of the data has tests in the f11ll-scale tunnel are compated with those from usually been nece sary because experimental informa- the variable-density and the propeller- 7'esearch tunnels, tion ha not been available ,tbove a Reynolds Num ber and with the theoretical value. An analysis of the com- of about 3,000,000, whereas the night range lies between parat1've experimental data indicates that the air stream 2,000,000 and 25,000,000. There is no exact an d ra- of the full-scale tnnnel has a relatively low turbulence.
ti ona l method for making a trans formation from th e This injerence is substantiated by the close agreement best wind- tunnel information to the desired fli g ht obtained between the characteristics oj airplanes measured characteristics, although e:xperience serves a a useful in the jull-scale tunnel and those jrom flight tests, and by guide.
sphere drug measurements that show the t1lnnel has a Wi th the idea of belping the designer to span this ga p turbulence s1'milar to jree air. I t is the'refore believed between small-tunnel information and :£light conditions that the effects of turbulence on t he characteristics of an the study of airfoil characteristics has been continued airfoil tested 1"n the full- cale tunnel are small, and may be in the .A.C.A. full-scale wind tunnel. lIere u ni que neglected in applying the data to design.
equipment .is available for testing large size airfoils at R eynolds umbers comparable with those of fli ght .
I NTRODUC TION T he full-scale tunnel has a furt her advantage over The aerodynamic characteristics of airfoils ascer- smaller tunnels in that the full-seale-tunnel data on air- tained from different wind-tunnel investi gat ions are planes may be directly compared with tho e obta in ed frequently not in agreement. T he reasons for these in night tests, thus di closing any disturbing t unn el discrepancies are generally understood, having been effects and checking the wind-tunnel testing conditions revealed partly by theory and par t;ly through experi- and technic.
ment. The compJete force equation, w hi ch includes Tests were therefore mnde in the tunnel to determine the terms expressing dynamic imilitude, show theo- the aerodynamic characteri tic of the Clark Y airfoil retically that comparable wind- tunne l results hould umber. By tests of over a large range of Reynolds ar surfaces are be obtained when airfoils having simil airfoils with the same a pect rntio and chords of 4, 6, at the same Reynolds u mber in wind tunnels tested a nd 8 feet at velociti es from 25 to 118 miles p er hour, with like turbu lences. Exper i menta l research has the characteristics were invest i gated over a R eynolds 4 REPORT NA'l'lONAL ADVISOHY COMM I'l v l'EE FOR AERONAUTICS EQUI P ME TA D A IR FOILS LImbe r range from about 1,000,000 to 9,000,000, although datt1, were not ecured above a Reynolds The .A.C. A. full-scal e wind tunnel and equi pment umbe r of about 6,000,000 at maAimum l ift . A por- are described in reference 2. ince the general equip- tion of the e 1'e ult was u ed in an experimental veri- ment and apparatus used in these te t were essen tially the sa me a reported in the aforementioned reference, a further description will not be given.
During the tests the airfoils were mounted in the jet, a shown in figure 1, on supports that attach to the air- foils at the one-quarter-chord point, and tra.nsmit the force s to the balance below . The mall diagonal t reclm line ar ms connected to the rear of the airfoil erve to change the angle of attack by pivoting it nbout the main support pin. The lower ends of these dia go nal arms arc attached to screw mechani ms by mean of which the angle is adjuste 1 to within ± 0.05 °, Th e fairings over the airfoil supports arc not connected to the ba lance but are independently upported at the balance-house roof. The short exposed uppe r por- tions of the ma in supports have Navy no. 1 str u t sec- tions, and taper to a cross section of about 1 by 3 inches where they connect to the airfoil.
Three melal lark Y airfoils with 4-, 0-, and 8-foot t:bords and of aspecL rcltlo 6 were used. The airfoil covering of }{6 -inch aitUllillUJ11 s heeL wa s aLlacbed to a rigid internal sLrucLure by means of flush cOlUltersllnk screw . The spars were teel barns and the pro fil e was formed by aluminum ribs paced at 12 - inch interva l.
Acces to the airfoil support pins was provided by FIGURE I.- The 6 by 36 airC oil mounled in the Cull-scale tunnel.
removable plates which were screwed flush with the fication of the theoret ical jet - boundary cOlTeetion for s UJ-face during the tests. Tapped opening fo r fitted the elliptical-jet wind tunne l which has been reported eyebolts were spaced over the airfoil for a Wiac h me n ts in reference 1.
when taking tare meas urements. F lu sh screw pl ugs FIG UIt E 2. -. \ lare·Coree seL·up wiLb invcrled -6 by 36 airfoil.
SCALE EFFECT 0 CLARK Y AIRFOIL FROM N.A.C.A. FULL-SCALE WIND-TUN EL TESTS 5
were inserted in these opening during the regular force when applying the result to the airfoil. Interference tests. The smooth aluminum surfaces of the airfoil drag for the 6 by 36 airfoil wa interpolated f['Om dn.ta were covered with a. protective coa.t of varnish. The on the other two airfoils.
airfoils were manufactured under careful in pection so Static and dynamic pressure surveys were made a to maintain the specified ordinates, H,nd were accu- everal chord lengths ahead of the 4 by 24 and by rately measured just before testing. The specified and 4 airfoils to determine the blocking effect of the air- measured ordinates are given in table 1. 0 appreci- foils upon the tunnel stream. These surveys were a.ble twists, deformations, or local irregularities changed made at a number of angle of attack between zero the a.irfoil accura.cy during the period of the tests. and maximum lift. For the 6 by 36 airfoil the block- ing efrect was int.erpolat.ed f!'Om data on the other two TESTS aidoils.
CORRECTION OF DATA The lift, dmg, a.nd pitching moments were measured at ix speeds between 25 n.nd 118 miles per hour over a The uncorrected lift a.nd drag forces on the airfoi ls range of angles of attack from - 8° to 24 0. These tests were measlll'ed on recording scales, and the pitching were made with the airfoils in an upright posi tion in moment was computed by multiplying the lift and the tunnel, and then repeated through an angle range drag forces by the proper lever arms. The observed wind-tunnel data were then corrected in the following of -8° to 5° with the airfoils inverted.
Tare force on the supports were measured with the manner: airfoils in the test position but supported independently (a) The first process in correcting the data was to of the regular support and rigidly held in place by adjust the mea ured dynamic pre sures. The dy- namic pressure of the wind-tunnel jet is measured with aLL\"iliary cables (fig. 2). The tare-force mea urements therefore include the in te rf erence of the airfoils 1I pon a manometer, which indicates the pres ure difference the upports. Tare forces were mea ured for all Lhe bet.ween the return ptlSsage and the tesL chamber airfoils a,t five angles of attack and at all I.e t speed . (reference 2) . The dynamic pressure in the jet is The interference or the supports upon the 8 by 48 obt.ained by a calibration . PrevioLls study has shown airfoil was ascertained by adding duplicate support- that this indicated velocit.y head, obtained from It ing struts to the normal instaUa.tion (fig. 3). A these calibration with no body ill the jet, is in error owing dummy strut were not connected to the airfoil or to t.he blocking action of the body in the air stream.
balance, any change in the mea.sured characteri ~ tic The blocking increases with the angle of attack; th with the truts in place could be attrihuted to tbeir Reynold umber of the test are therefore slightly interference. A imilar method was employed for the difl' rent at the low and high angle of attack. A tesLs of Lhe 4 by 24 airfoil II ing, however, only a ingle full di cu ion of the correction it applied to the air- dummy support and dOli bling the interference enect foil data is giYen in reference l. The magnitude of FIGURE 3. -Dummy s upports added to the by 4 airfoil s et·up Cor int e rCerence t es ts.
REPORT NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS drag values at zero lift, with and without the dummy the blocking effect of the th r ee airfoils is shown in support struts, showed that the supports exerted i:l.
figure 4.
large unfavorable interference in the upright tests, (b) T are force and moment coefficients were then and a slightly favorable one when the airfoil was computed and deducted from the gross force co e ffi - inv erted. In all cases for the upright tests th e effects cien ts to obtain net va lues. The tare drag is about became very small on both drag and lift abo ve a lift 2 percent of the minimum drag for the 8 by 48 airfoil coefficient of 0.3.
( d) Upright and inverted tests on the airfoils indi-
1 _ 1 1, 1. )1
--0- 4 by;:4 Clark ) (m~asLre~ +-
cat ed that the air stream had an initial downflow ..
(interpo l ated ) - - 6by36 ..
(measured) r- - x- 8by48 angle; it was necessary to correct the charact eristics -I for this effect. In order to determine the magnitude A
r-
- of the air-stream angle, plots were made of the DjL
-x _
against OL for the upright and inverted airfoil tests (fig . 6). The D jL ordinat e between the two curves is equal to 2 sin /3, where /3 is the air-stre.1m angle.
A check on the air- stream angle is possible by noting
o 4 8 12 16
-4 20 th e separation of the upright and inverted lift curves.
Anq le of attock. deqrees FIG U RE 4. -Blocking corrections for the tbree airfoils tested in the full-scale tun nel.
. /0 and 10 percent of the minimum drag for the 4 by 24
I~L e ctlo n
p -, airfoil. T he tare lifts and moments are negligible. ~ . 09 -Tun n el a xi s (c) Inte rference effects of the struts on the airfoils were then included. Figure 5 illustrates the in ter-
1/
~ 1 '-l ·08 ference cau ed by two stru ts on the lower mfac e of Air foil t es ted up ri ght. - _.
V
V the 8 by 48 airfoil. The effect on the drag i quite ./'
li§.07
~/
.5 05 V
I I I I /1 I
V
2 si n /3 = 0.0 1 5 0 .06 ). /3 =0.43 ° /
I 1 I
« A irfoil fe sie d .4 i"- / " 'No correc - .
inv e rted - ~V I 1 I . 05
hon to ~t=
li f t curv e
/
0 3(5 (S.3 required .
o .I .2 .3 .4 .5 .6 .7 .8
/
/ for int er -r--
LiTt coeffiCient. C f e ren ce L
V
/
F IGU RE 6.- Metb od of o bt aining air-stream angl es fr om uprig bt and inve rt ed t ts .
V
Reynolds umber, 6. 12 X 10 '; 8 by 48 airfoil.
J I
~ ---0-- N orm al _I
~ ~ b
s et- up -I--.
-- --
- - Since the separation of the upright and inverted lift
- x- Two dum n;r- supp or t s curves, when plotted as values of OL against (x, is due
/ adde d
to th e air-stream angl e, the value of the air-s tream
--- Co r r ec t ed J
/ for in te r-- de fl ection is equal to one-half the angle between the (e rence two C Llr ves. If the interference effects are not prop- -.1
V
I I erly a cc ounted for, the value of the air-stream angle,
/
1 1 from th e two methods, will not agree. Th e angles -. 2 -8 -6 - 4 -2 0 2 4 6 det ermined by these two methods generally agreed Ang le o f a tto ck. deg rees within about 0.1 D. The average value was taken as FIG U RE 5.- The effect of strut int erferen ce on th e characteristi cs of the 8 b y 48 the true air-stream angle, although no rational excuse Cla rk Y airfoil wben t es ted uprigbt. Re ynolds Num ber. 6. 1 2X lO '.
can be offered for this practice, except that the prob- large in the region of zero lift, but decreases and be- able percentage of error is reduced.
comes negligible at higher l ift coefficients. The inter- (e) The limited boundaries of the wind-tunnel jet ference effect on the li ft is negligible and within the are a source of error in ascertaining the characteristics e>rperimen tal errol'.
of any body tested therein. A correction for this The support inte rference on the 4 by 24 airfoil h~td boundary interference was therefore applied to the an effect similar to changing the camber of the au·foil. airfoil angle of attack and the drag coefficient. For T he angle of zero lift was changed by the interference these tests the correction factor was determined when the airfoil was tested both in the upright and experimentally by an extrapolation of the airfoil data i nverted positions. A comparison of the measured to free air values. A complete description of this
SCALE EFFECT ON CLARK Y AIRFOIL FROM N.A.C.A. FULL-SCALE WIND-TUN EL TESTS 7
method with the values of the experimental and aspect-ratio characteristics by the following formulas: theoretical corrections 1 is given in reference 1.
ao = a - ~.R(1 + 7) 57 .3
..
,./ - 08 :::.:,.22 OL
u ODO = OD - 7rR(l + 0-)
V /
\;)
.E
......
o V
where
1 /
07 g.
/ ao IS the angle of a ttack in degrees at which an o {;
V
/ Q) airfoil with infinite span would give the same 'tJ V Q, Qj
V
/
lift coefficient as the airfoil tested in the § .18 06~ "\5
V tunneL
'tJ / I - i-- ·S - Q) I..
ODO' the profile-drag coefficient.
g
~ / os.;2 0.16 R, the aspect ratio.
/ ·S
II
V l
/ r-- - l.
7, a factor correcting the induced angle of attack, ~ .;2 lJ
V
/
to allow for the change from elliptical span '-- 04(2 "- l." /4 o loading to one resulting from the use of an ..... / r::.
V
lJ ~ airfoil with re ctangular plan form.
~ lJ
1/ V
03 Qj r::. .12 IJ, a factor correcting the induced drag, to allow .0 t: .;::
/ V
for the change from elliptical span loading to lJ
<3
Q) one resulting from the use of an airfoil with
V
l . lo 02
rectangular plan form .
and where a, OL, and OD, are the corrected character- 3 4 5 B 7 8 9 A spect rotio , b ~ S istics for finite as pect ratio . The angle of attack, a, FIOIIRF. 7 . Corr ec tion factors for transforming r ec taogulnr airfo il s fr om fini te to is in degrees. Values of 7 and (J are taken from figLU'e 7, infinite aspect ratio.
and are based on th e assumptions of a theoretical rectangular lo ading, and a value of 0. 101 for the slope (j ) The corrected characteristics for the airfoils with of the infinite-aspect-ratio lift C LU've. E xperimentally aspect ratio 6 were then transformed into infinite- the rectangular airfoil did not have a loading identical 1 Th e co rr ec tions reported in tbis reference were fr om th e r es ult s of t es ts at a to the theoretical, owing to jet-boundar y effects and R ey no ld s N um ber of 2 ,000 , 000 . When tbe complete results of the airfo il s at a ll R ey nolds Num be rs we re a nalyzed it was found tbat valu es were obtained for the velocity asymmetrie . This variation would require Jet-boundary co rrection which were s li ghtly d ifI ere nt fr om those reported, aD d the use of values for (J and 7 slightly lar ger than tho e a pproached even mo re cl os el y the theoreti ca l valu es given iu referen ce I. 'l'b ese co rr ec ted factors have heen applied to the prese nt data. in figure 7. Sin ce resul ts were not available to indicate -loa 40 . /0 I I C. p. I - 80 36~ .4 4 .0 9 <!'
g
1) I 1.. - 60 2.0 .40 .0 8 -: 3 2t o I c: .c I I \ I .~ ::'-40 . 07 28 "\5 1.8 . 36 \ l ~o II i i o .- 1- -- - ~ ci Q) I 1\ ~ .i- -- -- ~-20 1.6 .32 .06 0 2 4~ U Q I
III !
L -- - + - ~ - 1 / __ I,~ I --- I - I- 1.4 . 28 "'f: g' .0 5 28 ~ 0 20 -0
:9u: [
Cl 111 --
W-L t-- -
. ~ -l3 ~
, - Q.
a .t
f' :--....
~ 1~ 1 -
24 ~ 20 r--
=t- t- 1 .2 ~ . 2 4 :i. ~ .0 4
I. /6 ~ q.p ')l I ~ I-- -.. ~ ~ '--- j"'-.. - ; V I-'- r-
T ID
ic- V
I E~ I-- P r-.
~ 20 t: 4 0 I. O ~ .208 ~ . 03 ~, . C:
t
~ a 1+' /I I -.:: : ~ 0> Cl . ¢: I, .l I I I I I I Vi S 8 ' .8~ ./6 ~ .02
if 16'1; 6 0
I..
If 1 / .I I I I £ 11 I.. L ~ Cl I ~ I I ~ "l5 12.E. 8 0 .6 u ./2 .0 1
I -
4-'<:.
IJ ~ ~ u I / I - U s: - ;I "- Cl ~ I "\ I /"" - ~ B 0100 .4 -.J .08 0 O ~ j II"" I \ 1 I:l
-("
f--+-t--t "- t .......
CD
a 4 ~ - .2 . 04 ~ - . / 4'0
,/' ]I I--"'C ~ •
...-
. .g L I t
~
L -+- - -8 g-
o 0 't - .2
~ 0 ~ I
rr i
A i rfo il: Clark Y Size: 8 'x 48 ' a oo:: c: u ~' RN of zero li ft : 6. lex 10 - 1 ! I - .2 .... - .3 /2 -4 ~ R.N at maximum Ht : 5 38 x 1 0-' c: I I I I _.
'- - r- <..i ~- T ested in F. 5.r. Results cor - I I _.
'"
. -t-+- - /6
- 8 - .4 g-A f-+-
rec te d for tunnel -w all effect , ~ -8 -4 o 4 8 /2 16 20 24 28 32
-;4 ~2 o .2 .4 .6 .8 lO /,2 1.4 /. 6 1 .8
Angle o( o/I ock , deqrpe s . d Li ft coefficie n t, C L FIGURE 8 .- Characteristies of the 8 by 48 Clark Y airfoil at a Reynolds Number of about 6 ,000,000 .
8 REPORT NATIONAL ADVISORY C OMMITTEE FOR AERONAUTICS
the pr essure distribution over the airfoils in th e tunn el, covers the change in the angle of attack for zero lift this e ff ect, which is small in ma gnitud e, is noL in clud ed . with R eynolds Number. R es ult s from the val' iabl<'-
den ity and propeller-research tunnel , a well as a
RES LT 'd. I 10 'd
I I I I
-- I- Th e corrected resu lt s are tabu lated giving values of 1
"-
~ 4 b; 24 dlar~ ~
r.:J. IOO
+
OL, Ci, OD, L ID, and c.p. for the Olark Y airfoil w ith 'd o 6 by 36
:: I
/), 8 by 48 aspect ratio 6, a nd va lu es of Cio, ODO, a nd Om for the Q) J I (.090
airfoil with infinite a pect ratio . Th e e data for the ( Theoretical J I
~ ~ ~
a
three airfoils at all R eynolds umbers te ted are ~.080 I-
..::: variabIJJen~if~ )u;LI
prese nt ed in tables II to XX , inclusive. Value of ....
.....
1 t I: 1 ' ~ 1 I. t" •
o C.p. are given in percent chord . A typical pIoL of th E'
~~--f ~. !
Q).070 t- -
- I' Propeller - research fu nnel data from table XVIII is give n in fi gure I
&
- 2 3 45 6 ti) 0 7 The curv es ummarizing variations of the principl1 l ReynOlds Number airfoil c hara cteris tics with R eynolds um ber are of FIGUIlE ll. - Variation with R eynolds Number 01 the slope of the lift cur ve for the Cl ark Y ai rfoil (s lope for an airloil of aspect r atio 6; at in degrees). P rope ll er-researcb I .B tunnel va lue Irom reference 3. Variable- density-tunne l value from reference 6.
'l'heoretical \ 'a lue from reference 5.
~
~ 4 b; 2~ ClarA Y
"'1.7 o 6 by 36 " theoretical value from reference 5, are also included on /), 8 by 48 " ,
~'I.6 tills figure. In a similar ml1nner, figure 11 pr e ents
Variable - tjensity tunnel <;:: the ch ange in slope of the lift curve with scal e. Th e '- I Q) , f.--
X
8/.
,
V
I
- -
c- !~
i 1 i ~ i -H-
--Full scale tunnel
r---
Iv
V
V
o ·1 by 24 ClarA Y \.) 0110 g/ v:
/ o 6 by 36 .. I I
~ c. . .. : OJ) _
" 8 by 48 .. I
'V 0
I I-L-J
'C~_.OIOO -Propeller-research tunnel ~
r Vanoble - denSity tunnel
/V ........
8'~
1"1 I I I I I
::::-- - G ~.0090 q 2 3 4 5 6 , -
Reynolds Number , r It...I-L1 J~
\c.1 . _ Propeller-research tunnel
a (J0080
FIGURE 9.-Va ri atio n with Reynolds N umber of maximum-lift coe ffi ci ents for the -
1- -
l Cla rk Yai rfoil. Propeller-research-tllnnel va lue fr olll referen ce 3. Variable-den-
1/1/11/1 n-
ll.
sity-t unn el data from reference 4. o ? J ./ 5 6
He'ynolds Number FIGURE 12.-Variation witb Reynolds 1 umber 01 tbe Clark Y profile-drag coeffi- particular intere t . Fi gure 9 shows the va riation of cient at zero lift. Propeller-research-tunnel value from reference 3. Variabl e- the maximum lift coefficient for the lark Y airfoil density-tunnel value from reference 6.
over a Reynolds N um bel' r ange from 1,000, 000 to rtirfoil profile-drag coe ffi cie nt at zero lift is shown on 6, 000,000 . In thi s figure the results of Olark Y tests fi gure 12 over a R eyn olds umber range from 1,000,000 -6.B
""'- -...: to 9,000,000, and valu es from the va riable-dens ity a nd
:.::: 0 4 b; 2 1 dlar~ ~ -
+--
o 6 bY3~ f:'
-6 .4 'O~~~~~~r - .--.~I~.II-;~~ _ ll-d~LI.I~J~l~I_J~I~.l~l~ " 8 by 48 ..
~ , , " , -j • Proflle-droq at zero 11ft
'" l.. Full-scale tunnel
,- n :1 [ Clark Y olrr:o~s
~ ~-6.0
"" r==:::::.. 0
I'< .004 LLLL
g~ ~o
. .. -Theoreticol f---::l:--i~ -,--_0- rt-+-I-- .
--f- :::: ~ -5.6 I-Sktn fnctlon for flat -.· --:;::::: Z o . .
I plate wtfh turbulent .....
0 I-boun dory layer ~~-r+t~~HHH- I - -+-r~+4 - ~+ Propellfr-research tunnel o -5.2 '002r--r----r-f-+-rl-+-++-H--H-i-+++-I+-l--I-~l-l-W . , ,.:' - Variable-density tunnel f---+-t--I-+-+-+-H-+-+-++l-H-l/), 8 by 48 Clar k Y
t
c:
t- -+~I-t-+- H-++t+++++1 0 6 by 36 .. Ll
~
o 4b y24 .. I I
3 456 7 8x10' Reynolds Number O~~~ ~~~LL~LU~ uiDIII~I~LI~I~I~.
I 2 3 4 5 6 7 8 9 xl0 FI GURE IO. - Variation with Reyn olds Number of the Clark Y angle of attack at Reyn oldS Number zero lift. Prope ll er-research-t unn el value fr om reference 3. Variable-density- FIGURE 1 3.-Compa ri son of the Clark Y profile-drag coefficient at zero lift with the tunnel va lue from reference 4. 'l'heoreti cn l value fr om referenro 5.
skin- fri ction drag coefficient for a O at pl ate h av ing a completely turhul e nt hO ll n<1Rry layer. C, for ui l'foils based Oil actual surfat'tl area.
in the I .A.O. . va ri<tble-de ll s ity wind tUllnel OYe r rt runge from 1,000,000 to 3,000,000 arc also given. A the propeller-research tunnels are again included. In single point give the maximum lift obtained on the figure 13 the profile-drag coefficient rtt zero lift for the Olark Y airfoil in the propeller-research tunnel at a airfoil i co mpar ed with the skin-friction drag coeffi- Reynolds umber of about 2,000,000. Figur e 10 cient for a flat plat e with turbulent boundary la yer.
SCALE EFFECT ON CLARK Y AIRFOIL FROM N.A.C.A. FULL-SCALE WIND-TUNNEL TESTS 9
reference base may be changed to the hypothetical Curves in figure 14 represent the profile-drag coeffi- cient at OL values of 0.1 and 0.2 plotted against characteristics which the ai1joil would have in fl'ee ail' Reynolds umber. The variation of pitching-moment at the same Reynolds Number and turbulence. This attitude has been adopted in considering the accuracy coefficient at zero lift and the maximum value of L ID of the results found in this investigation.
are plotted against the Reynolds N lilllber in figures The exactness with which the finlll precision may be 15 and 16, respectively.
predicted depends upon the thorougbness with which " c.1 the following factors are known:
6 4 b; 2~ ~/ar~ j
-.0120 ..
o 6 by 36 (a) Regularity and accuracy in measuring air- c: . - ..
(l) £\ 8 by 48 stream velocity and angularity.
v . DIDO " C ; 02 ' f-.. ( b) Rigidity of airfoil supports and accurllcy of L t-- 0
'- \lJ
.
.
() .
setting the angle of n,ttack .
.
\J 0080 (c) Accuracy of balance readings.
8'
(d) AccuracjT of the airfoils.
b.OIDD I g 't-- 0 t-- L (e) Accuracy of measured support interferences.
C =~L , . . .
~ ~
(j) Accuracy of the applied jet-boundn,ry correction .
e · OD8DD 2 3 4 5 6 a.: Repeat runs indicated that the accidental errors, Rey nold s Number sllch as are to a large extent included in (a), (b), and FIGURE 14. - Variation with the Reynolds Number of Lhe Clark Y profile-drag (c) of the foregoing, were small, and within the follow- coefficient at lift coefficienLs of 0.1 and 0.2.
ing limits: Re ynol ds Numb er a= ± 0.05° 2 345 6 7 8 x lD 6 18f ~- Va riable - density. tun n el 1 OL",ax = ± 0.01 I
I I I I I
I
dOL d 0 0 -1- = ± 0.001 per egree Full- sc a le tun n el (a
LI
l- f-- t ~ i-- . --
0 = ± 0.0002 (OL = O)
- I I ·t l -c bt.-
IliTI T he o retlcol 0 = ± 0.0010 (0 ,= J) Prope ll e r -res e ar c h t unnel I
I I I 1
4 by 24 Cla r ki Y
I
o 6 b y 36 1 :.
0"'0 /4 = ± 0.001
£\ 8 by 48 .. I
A deflection of the airfoil supports introduces an FIGURE 15. - VariaLion with Reynolds umber of Lhe Clark Y pitching-momen L error into the pitching-moment coefficients. In these coefficient at zero lift. Propeller-research-tunuel value from reference 3. Va ri able- density-tnnnel value from reference 6. Theoretical value from reference 5.
test, however, the strong tripod type of construction u ed in the airfoil upports and the relatively short cantilever section reduced deflections to negligible 0 4 b ) 2~ tlor ~ ~ - ..
o 6 by 36 amount. Errors from tIllS source may therefore be .. t- I- " 8 b y 48 - di regarded.
- l- I- l- t-
It wa found impossible to evaluate the 10 in
i- e- I-- I-- 0 0 precision due to differences between the specified and 1- - I-- measured airfoil ordinates. Variable-den ity-tunnel 2 345 6 7 8 x lD6 te t have bown that mall errors in the nose profile Reynalds Number of model airfoil are quite critical, while difference FIGURE J6 . -VariaLion wiLb Reynolds Number of the maximum "alue of L I D for Lhe Cla rk Y airfoil. farther back along the chord are not of great impor- tllnce. From an examination of tllble I, it may be P RECIS IO N een that the airfoils were not constructed exactly in The number of va riables involved make s the preci- accordance with the specified ordinate , and that there were small differences between measured and pecified sion of all wind-tunnel results exceedingly difficult to estimate. The reference for gaging the preci ion of ordinate at the airfoil no e; the surfaces, however, were fair in all Cll e. The lack of any erious system- wind-tunnel airfoil results should be the chal'acteri tics which the specified airfoil would have in flight at the atic disagreement in the results from the several particular Reynolds Number. Wind-tunnel result airfoile indicates that error from tIll source were not would then include accidental error of mea urement, large enough to be siO'nificant.
The experimentll11y derived values of wind-tunnel errors in the application of wind-tunnel interferences, and support interference were ubject to the same and variations of the characteristics due to differences in airfoil accuracy and turbulence. [f the turbulence accidental and inherent errors as the tests proper, is considered as a parameter with which character.istic but the e errors would have only a econdary effect on vary rather than as a source of error in precision, the the finlll results. From II consideration of all the
10 REPORT NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
contributing errors the estimated final precision is Clark Y airfoil gave similar results. It may therefore fi S follows: be stated that the comparatively low values of maAri-
mum lift coefficients in the full-scale tunnel signify a
a = ± O.l O small turbulence. Results of other tests indicate the OL = ± 0. 03 e}..ristence of a turbulent condition in this tunnel similar max to that in free air. The critical Reynolds umber for
dOL 1
~= ± 0.0015 per cegrce a sphere investigated in the full-scale tunnel (fig. 17) ODO = ± 0.0004 (OL = O) .6 I
I
ODO = ± 0.0015 (OL = l.0) CI. T fligh f
I
.5 1 1 I t- O mel4 = ± 0.003 ~ Full - scale tunnel
'- r-::- 1 ",\ ' /5 feef from .tunnel
\'
'. ~~ center line DISCUSSION .- f- Lift.- The maximum lift coefficient, the angle of I"-- I"-- -
-
f \- Va ri Oble ~r \
zero lift, and the slope of the lift curve for the Clark \ density I"-- Fu ll-sc a le tunnel .
Y airfoil vary with the Reynolds Number (figs. 9, 10, - tunne l on If '
t unnel ce n - 1_
and 11) . Perhaps of greatest interest because of fer line "--i ~ . I their significance in regard to the question of turbu - I--- I'- lence are the maximum lift coefficients, particularly in comparison with those from the variable-density 2 3 4 5 6xlQ5
o
R eynolds Num be r tunnel (reference 4) and the value from the propeller- research tunnel (reference 3) shown in figure 9. There FIG U RE 17. - Spb e re dra g coefficie nt s obt a ined from ni g ht a nd wind · tunn el test s, C ri t i ca l R ey no ld s Nnmb er oc cur s a t C o eq uals 0.3. Fli g ht r es ul ts fr om re feren ce 8.
is an excellent agreement between the value of the Varia ble- de nsi t y ·tunn el res ult s (rom re ference 4.
maximum lift coefficient from the propeller-research Lunn el and the full-scale tunnel at a Reynolds Number agree closely with the critical value obtained in of about 2,000,000; however, the val'iable-density- flight (r'eference 8). Based on the method of Dryden tunn el results are from 10 to 13 percent higher than (reference 9), the turbulence in the full-scale tunnel is those from the full-scale tunnel at the same Reynolds about 0.35 percent, which value is almost identical umbers. This difference between variable-density with the value obtained by measurements in free air.
and full-seale-tunnel maximum lift coefficients is The critical Reynolds Number in the variable-density be li eved to be largely due to the unlike turbulences
tunnel (reference 4) indicates a turbulence of abou t
in th e two tunnels; the agreement with the propeller- 2.fi percent ,,2 research tunnel suggests that it has the same turbu- The good agreemellt bet.ween full-scale tunnel and lence as the full-scale tunnel.
flight characteristics on airplanes presents further Several experimenters have shown that one of the evidence of the small effects of turblllencA on the wiud- effects of turbulence on medium-cambered medium- tunnel measurements. The following tabulated data thick airfoils, such as the Clark Y, is to increase the illustmte the comparison between wind tnnnel and maximum lift coefficien t. Tbis beneficial effect of night, results.
turbulence is attributed to the mixing and eddying COMPARISO OF PULL - SCALE WIND TU NEL A D flow in the turbulent boundary layer around tbe air- FLTGHT RESULT. ON 'EVERAL AIRPLANES foil, which provides for a larger transfer of momentum A p pr ox i· from tb e general £low to the boundary layer than :is l na te Airplane So ur ce of res ult s R ey nold s possible in a laminar stream. When changing from N umb er laminar to turbulent flow, the augmented momentum Full- sc ale tunn eL ___ __ ___ __ _ ____ 0,065 M a rtin XDM - L _ __ 3, 000, 000 in the boundary layer serves to move the separation _ ____ do ______ ___ __ ___ ___ _ ____ __ ___ .064 D o __ _ _______ _ __ 5, ODD , 000 D o ________ ___ __ 13 , 000, 000 Fh g bL _ _____ ____ _ ____ __ _ __ _ ___ .062 point of the flow rearward along the upper urface of F a i rc hild F - 22 ____ _ __ 3, 500, 000 Full -scale tunn eL __ ___ 1. 40 .058 Fli g hL _ __ __ _ __ __ ___ __ 1. 36 ______ ___ _ Do __________ _ __ 3,5 00, 000 the airfoil. This rearward motion allows the airfoil Do _ ____ _ ______ 6, 000.000 __ ___ do _ __ __ ________ ___ _ __ ___ ___ __ . 0 58 Boe in g PIV - 9 __ ___ 3,5 00, 000 Full· sca le tunneL _____ 1. 19 .0 54 to att a in a higher angle of attack n,nd lift coefficient Fli g bL ___ _ ________ _ 1. 21 ____ _ __ _ D o___ ______ _ _ 3, 500, 000 D o ___ _______ _ 7, 000, 000 ___ __ do ___ ___ ___ ___ ___ __ __ ____ __ __ .0 53 before the separation point moves forward again, with increasing angle, to the point at which the general I 'rhe miss in g va lu es were not meas ur ed .
flow breaks down. A complete discussion of this phenomenon is given in reference 7, and the results In all cases the checks are within the experimental of tests included in this reference show that it is limits of accuracy, An appreciable change of mini- possible to increase the lift coefficient of an .A.C.A.
mum drag coefficient with Reynolds Number is to be 2412 airfoil as much as 30 percent by the introduction observed in the case of the XBM-1, where the of turbulence. Earlier tests in the variable-density 'S li g bt modifica tion s ha ve be en made to the va riable·den s ity t unn el since these tunnel (reference 4) on the effects of turbulence on a turbulence m eas urement ~ were made.
SCALE EFFECT 0 CLARK Y AIRFOIL FROM N.A.C.A. FULL-SCALE WIND-TUNNEL TESTS 11
Reynolds Number reached in flight. is considerably upon the lift-curve slope as increased Reynolds N um- higher than those of the tunnel. ber, which might eJ..J)lain the slightly higher variable The experimental evidence suggests that the tur- density tunnel result.
D rag.-Figure 12 indicates that the profile-drag co- bulence of the full-scale tunnel is small and exerts efficient at zero lift for the Clark Y airfoil decreases 1.0 rapidly between the Reynolds umbers of 1,000,000 ",_--Upper surface and 3,000,000, and then decreases at a constant but much lower rate over the range between 3,000,000 and 9,000,000. The considerable scattering of the experi- mental points at the lower Reynolds Numbers may possibly be accounted for either by the decreased pre- cision in measuring the extremely small forces or by the uncertain nature of the flow over the lower sur- face of the airfoil at this angle of attack. The latter factor was discussed when considering the angle of at- tack for zero lift. Since the greater proportion of the profile drag at zero lift is friction drag, the decrease FIGURE IS . -Theoretical pr ess ure distribution on a Clark Y airfoil at the angle of zero lift. Reproduced from reference 5.
with Reynolds Number is to be expected. The man- ner in which the friction drag of flat plates changes only a negligible effect on the characteristics of bodies with the Reynolds Number has been subjected to the tested.
most complete theoretical and experimental study, and The change in the angle of zero lift with Reynolds a comprehensive review of the subject is given in refer- umber (fig. 10) is, to a large e~tent, a phenomenon ence 10. Figure 13 presents the drag curve of the flat similar to the variation of maximum lift. The angle plate with completely turbulent boundary layer from of zero lift occurs at smaller negative angles with in- this reference. The profile-drag coefficients at zero creasing Reynolds Number. This phenomenon can lift from the present airfoil tests are also shown on be explained by reference to the pressure distribution tlus curve. These coefficients have been reduced to over the airfoil for the zero-lift condition (fig. 18). the same form as those for the .flat plate by using the Owing to the large adverse gradient of pres ure at the true surface area of the airfoil in the drag equation.
forward portion of the lower surface of the airfoil (a The values for the airfoils lie above those for the flat condition similar to that on the upper surface at maxi- plate with completely turbulent boundary layer, and mum lift) the stability of the .flow is critical; at low the shape of the curve suggests that it might lie on Reynolds Numbers there is an early breakdown of this one of the intermediaLe transition curves beLween Lhose flow. This large adverse pressure gradient not only for the laminar and turbulent flow if the pressure causes an early breakdown of the £low, but also results drag were deducted.
in an earlier separation of the £low, which reduces the The profile-drag coefficients calculated from Lhe slope of the lift curve in the range of zero lift, and re- results of airfoil tests in the propeller-research and quires that the airfoil be turned to a larger negative yariable-density tunnels are presented in figure 12, angle to reach zero lift. With large Reynolds um- and their values are in fair agreement. The propeller- bers and considerable initial turbulence the break- research-tunnel value i within the experimenLal down of flow is delayed so that zero lift i reached at scattering of the point from the full-scale tunnel; the smaller negative angles. The smaller negative angle variable-density-tunnel value is only slightly higher.
of zero lift from the more turbulent variable density The variable-density-tunllel value for an airfoil wiLh tunnel tests shown in figure 10 agree well with this the corresponding thickness and camber taken from conception. The experimental value for the angle of the results of tests on related airfoil (reference 6) has zero lift from the full-scale wind tunnel agrees with been given rather than the results from an earlier the theoretical value (reference 3) at a Reynolds um- test on a Clark Y airfoil, because the more recent tests are believed to be more accurate.
ber of 3,500,000.
The slope of the lift curve (fig. 11) shows a constant A characteristic of great interest to the designer is increase with Reynolds umber. The experimental the profile-drag coefficien t at the lift coefficient for slope varies from about 85 to 90 percent of the slope maximum speed. These high-speed lift coefficients theoretically predicted in reference 5. The slope of the 1I ually lie in a range from about OL=O.1 to 0.2, and lift curve, obtained from the variable density tunnel Lbe value of the profile-drag coefficient for these two tests on an airfoil of this thickness (reference 6), at a lift coefficients are plotted against Reynolds umber Reynolds umber of 3,000,000 is slightly greater than in figure 14. These curves have the same general the value found in the present tests, whereas the pro- characteristics as the drag at zero lift.
peller research tunnel value is slightly less. Increased The pitching-moment coefficient at zero lift (fig. 15) turbulence for the Clark Y may have the same effect does not change with increase in scale, which indicates
J
12 REPORT NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
that the pressure distribution along the chord does not tunnel before correlation and tanda rdization of w incl - vary great ly with the Reynolds umbel'. Th e maxi- tunnel data to a ni gh t basis ca n be effected.
mum L ID value (fig. 16) show a considerable scatter - ing of results. For the three Olark Yairfoil no definite change in maximum LID ratio wi th Reynold s Number L ANGLEY MEMORIAL AERONAUTICAL LABORATORY, was observed.
ATIO AL ADVISORY OOMMITTEE FOR AERO AUTICS, CO CLu m G REMARKS LANGLEY FIELD, VA., J une 14, 1934.
The appreciable variations of Ol ark Y character istics R EFE RE CES with Reynolds J umber have their greatest ignificance 1. Theodors c n, Theodor e. and ilvcrstein, Abe: Experimental in reeml ha izing the importance of a more compl ete Verific at ion of th e Th cory of Wind-Tunnel Boundary and thorough knowledge of the. ca le effect on all air- Int erfercnce. T .R . 0. 478, .A.C.A., 1934.
foil seetions. Re nits of te t that h ave al!'eady been 2. DeFrance, Smith J. : Th e .A.C .A. Full-Heale Wind Tunnel.
T .R. o. 459, .A.C.A., 1933.
conducted in the variab l e-clen ity tunnel indicate that 3. Wood, Donald H. : Tc sts of Largc Airfoils in the Propeller thin, meclium, and thick airfoils with different cam- Re earch Tunnel, Including Two with Corrugated Ul'- bers respond differently to chana-es in scale.
faces. T .R . No. 336, N.A.C.A., 1929.
The appreciable .effect of turbulence are shown, by 4. tack, John: T e t in the Variable Den s ity Wind Tunnel t o comparison of data from the full- cale and variable- Inv es tigat e the Effects of Scalc and Turbulence on Air- foil Characteristic s. T.~ . No. 364, .A.C .A., 1931.
density tunnels, to be equa lly as important as R eynolds 5. Garrick, 1. E.: Detcrmination of the Theoretical Pr esslI re umber effect and, for this reason, make the forma- Di tdblltion for Tw e nty Airfoil s. T.R. 0.465, N.A.C.A., tion of any exact rule or formula for transfo]'mina- 1933.
variable-density or other sma ll-tunn el data to the 6. Jacobs, Eastmall N ., Ward, K cnneth E., and Pinkerton, equiva l ent full-scale resu lts quite impossib le until fur- Rob c rt M.: Th c Characteristics of 7 Related Airfoil f:lectioll s from Te sts in the Variable- Density 'Vi nd Tun- the!' lara-e- ancl small- cale in fOl'mation is ava ilable on ne l. T.R. No. 460, N.A.C.A., 1933.
the eH'ects of turbulence on a number of airfoil section.
7. von K :l. rm :i n, Th. : Qu e lque s Probleme s Actuels de L'Aero- A program for continuing th study of the effects of d yna miquc . Pap er read before J ournces T chniques sca le and tu rbulence upon tbe h aracte ri tic of air- Int e rnationale s de L' Ae ronautique, Chambre Syndica le foil ha s been planned for both the variable-den ityand des Indu st ri e Aeronautiques, Dec. 1, 1932.
8. Millikan, C. B., an I Klein, A. L .: The Effect of lUl'l ulence.
full- cale tunnels and has a lr eady been started in the Aircraft Enginccring, August 1933, pp. 169- 174.
variable-den ity tunnel.
9. Drydcn, Hugh L. : Reduction of Turbulcnce in Wind Tun- In general, it may be stated that a com plete q uanti- nels. T.R. 0.392, N.A .C.A., 1931.
tative evalu at ion of the [a ,ctors that are the sources of 10. von K:irmllll, Th. : Turbulcnce and Skin Friction . Jour. of experimenta l discrepancy lllU St be made fo]' each wind the Acro . Scicnc s vol. I, no . ], January 19 34, pp. 1- 20.
TABLE SPECIFIED AND AVERAGE MEASURED ORD I ATES OF THE CLARK Y AIRFOILS 4- by 2Hoot 6- b y 36- f oot 8· by 4 ·f oot Slandard o rdin ates Di sta nce in percen t of cho rd fr om Uppe r s urf ace Upper s urf ace T ,ower s urf ace UP I) er s urf ace Lower s urfo ce Lower s urfa ce lea din g edge in .-- --- perce nt A "e rage Avera ge Avera ge A\ ' era ge Average A "erage of c hord
I Specified I Speoified pper Lower Specified Specified Specified Specified
mea s ur ed measured meas ur ed me as ur ed me as ured 1l1en su red surface s urf ace inche s inches inches inches inche s inche - in ches inches inches inches inch inches --- --- --- --- --- --- --- --- --- --- --- -- ---
--
3.50 3 .. ,0 1.(' I. 68 ~ - - _ .. - 2 .5 2 2.52 3.31i 3.36 0 ---- --- - - - --- - 5.45 2.62 2. 63 .9:3 0. 92 3. 92 :1. Y2 I. 39 U9 5.23 5.25 1.85 I.
1.25 I. 93 5 I. 47 3.12 3. II . it .68 4.68 4. 67 1.0(; I. 05 6.2-l 6.26 I. 41 I. 40 2. 5 6.50 3.77 .45 . 43 5.69 5.69 . li7 . GG 7 .58 7.58 .90 .89 5 7 .9 0 .93 3. 79 4.25 4.24 . 30 .2'J 6.37 6.37 .4 5 .45 .52 .52 . 60 .6 1 7.5 8.85 .63 .42 4. 61 4.60 .20 . 20 Ii. 91 6.92 .30 .:3 0 9.21 9.22 . 40 .40 10 9. 60 . 15 5.13 5. 13 .07 . 08 7.69 i.71 . 11 . 12 10 .26 10 .26 . 14 . 14 15 10 . 68 20 II. 36 5.45 5.43 .01 . 02 8. 18 8.20 .02 . 05 10 .9 1 10.91 .03 .02 . 03 II. 70 5.62 5.61 .00 . 00 8.42 8. 4~ . 00 .01 II. 23 II. 25 .00 . 00 30 . 00 40 II. 40 5.47 5. 46 .00 . 00 .2 1 .25 . 00 .00 10.94 10.95 .00 .00 . 00 10 .5 2 5.05 5. 04 .00 . 00 7 .5 7 7 .6 1 . 00 .01 10 . 09 10 . II .00 . 00 50 .00 9. 15 .00 4.39 4.3 .00 .00 6.59 6. 6·1 . 00 . 01 8.78 8.78 .00 . 00 7. 35 .00 3.53 3.52 . 00 .00 5.29 5.36 . 00 .02 7.05 7. 06 .00 . 00 5.22 2 .5 1 2. 50 .00 .00 3.76 3.8 4 . 00 . 02 5.01 5.02 . 00 .00 80 . 00 2.80 I. 34 I. 34 . 00 .00 2.02 2.08 . 00 . 01 2. 69 2. 68 . 00 . 00 90 . 00 95 I. 49 .00 .72 .7 1 .00 -.01 1.0 1.11 .00 . 01 l. 'l:l I. 42 .00 .00 100 . 12 .0 6 . 00 ._. .09 . 11 . flO .02 . 12 . ()<J .00 - . 02 . 00 --- - -- --- ---
SCALE EFFECT ON C LARK Y AIRFOIL FROM N .A.C.A. FULL-SCALE WI ND-TUN EL 'rESTS 13
TABLE II TABLE V 4 BY 24 CLARK Y AIRFOIL CHARACTERISTICS 4 BY 24 CLARK Y AIRFOIL CHARACTERISTICS R.N. : ZERO LIFT = l.12 X I0 6, MAX. LIFT = 1.07 X I0 6 R.N .: ZE RO LIFT = 2.81X 10 , MAX. LIFT = 2.62 XI 06
I
Cr. a CL Cr) LI D c.p. Cno ern e /. ao
Cn I L I D Cno I a
"
------ --- -- -- --- -- ---
~I~
-° 0.0120 -JR.7 -1 1.1 -0.072 0.0098 ' -8~ 3 -0.2 0.0110 -8.5 -1 -0.077 -7~ -0.2 9. 0 .3 -13.6 O.OQ~ -44.7 -.070 -.1 -.1 -7.7 .0100 -10.0 .0094 -7.3 -7.2 .0098 -1 0.2 -51. 7 -.077 .0000 -6.8 .0090 0 -6.2 .0097 0 -.068 -6.2 0 -5.8 .0089 0 - . 077 .0090 -5.8 ----- ---93T .0096 - 1.4 .0094 . 1 -4.8 .0102 9.8 - .0 68 -5.2 .1 .0100 0.0 100.8 -.075 -4.8 .2 -3.3 .01 20 16 .7 58.7 - . 067 - 4.0 .2 -3.0 .0120 6.7 62.2 -.074 -3.7 :~n~ .3 -1.9 .0155 19.6 4 .0 - .0 66 -3.0 .3 -1.6 .0157 :~~~ 9. I 49.0 -.072 -2.7 -.065 .0 111 .0112 • <I -.5 . 0200 20.0 41. 2 -1.9 .4 -.2 .0201 0.9 42.5 -.070 -1.6 -.065 .0115 .5 .9 .0254 19 .7 38.0 -.9 .• S 1.2 .02C., .9 as. 4 -.067 .0126 -.6
I 2.:\ -.06.S . 0120
.6 .0320 I . A 35.8 .2 .6 2. .S .0:1:lO .0 36.1 -.067 .0130 .4 - . 064 .0119 I .7 3.7 .0392 17 .9 31. I 1.2 .7 3.9 .0111 7.0 34.7 -. OfJ8 .0I:l1\ 1.4 .01:17 .8 S.2 .0493 16.2 32.7 -.062 2. 3 .8 .s.3 0507 5.8 33. fi -.OM .015 1 2. I .0 6.7 . 0600 I~ . 0 31. ~ -.059 .0150 3. .s . U 6.8 0620 1..1 32. fi -.068 .0170 3.6 - .O :;(i .0 1 81 1.0 .3 .073R 13.7 30.6 4.7 1.0 8.2 .07W 3. I 31. .1 -.06.1 .01\12 1.6 - .0 53 .0227 1.1 10. I .090 1 1 2.2 29.8 Ii. 2 1.1 0.8 .0001 2.2 30. R -.064 .0227 5.0 - .050 1.2 12.0 . 10 92 11.0 29.2 .0290 7.7 1.2 11..s · 10~2 1.1 30.3 -. on3 .02R0 7.2 8. (j I. 227 1 3.0 .1240 9.9 30. I -.062 .O·u.s 1.3 13 . I . 1200 0.4 29.0 -.06.1 .0318 8. .1 1.2 14. <I . 15(iO 7.7 31. 7 -.081 10. I I. 370 14 . 4 9.7 29.9 -.0f>7 .0360 9. .s · 07~~ · 1\01\ 1.1 17 .2 .2 160 S.l 33 . 3 -.092 . 1 486 1 3.3 1.3 16.4 .2015 6 .• 1 31. 5 - . 05 . 1073 II.
1.0 20. 2 . 2759 3. (i 34 .7 -. 100 16.6 1.2 17 .4 .2260 5.3 32.2 -.087 .1458 13. I
: ~~~~ .9 20.7 2 .7 36 .7 -. 1l 3 17.5 1.1 20.0 .2788 3.9 33.9 -.100 .2114 16. I
:~~~~ 22.5 2.1 40.0 -. 1 33 .3 5 04 19.6 1.0 22 . I .3260 3. I 36 . 2 -.116 .2703 18. 5
I
TABL E III TABLE VI 4 BY 24 CLARK Y AIRFOIL CR ARACTERI TIC 4 BY 24 CLARK Y AIRFOIL CR ARA CTERISTI CF; 6 6 R .. : ZERO LTFT = 1. 55X 10 , MAX . LIFT = 1. 4 X I0 6 R. .. ZERO LI FT 3.19X 10 , MAX. LI FT 2.96 X I06 - - -- (,,,
CL a I ,ID C.p. em .. l. C ('I. ('/I /,1]) C.p. (Ino Ct
I ('Wlt/.
o .-- -- --- -- - 0.2 -9.0 0.0120 -1ft 7 - 13 .1 -0.076 0.0 -8~4 -0 .080
-0.2 -\.1 0.0100 -~n.o -15.1 -7.8
-.1 -7.7 .0099 -10.1 -.10.7 -.076 .0 -7.3 -.1 -7. 1 009.1 - 10. 5 -.12.7 -.078 -6 .7 -6.2 .0092 0 -.076 .0 -6.2 -.1 . 7 0 0 -fl. 7 . 0089 0 -.077 . 1 - 1. 9 . 0093 10.R 99.9 - .074 .0 -0.3 -\.7 . 1 - ~ :I .009., 10.0 100 .R -.07" .2 -3. 4 .0 112 17.9 61.7 -.073 .0 - 4.1 .2 -2.9 · Oll~ 17.0 62.2 -.074 -3.6 .3 -2. 0 .0 1 45 20.7 48.7 -.07 1 .0 -3. 1 -2.6 .3 -l.fi .01Sfi 10.4 40.0 -.072 .4 -.6 .0192 20.8 42.0 -.068 .0 -2.0 - 1. .1 .4 -.1 .0202 19.8 42.0 -.070 .5 .0242 20.6 38.0 -.065 .0 -1.0 . 5 1.3 .0270 18.5 38.6 -.068 -.5 2J . 6 .0312 19.2 35 . 6 -.064 .0 .1 .6 2.7 .0340 17.4 36 . 3 -.068 .6 .7 3. 6 .0395 li.9 33.8 -.062 .0 1.1 .7 4.0 .0425 16.5 34.7 -.068 1.5 .8 5. 0 .0485 16.5 32.7 -.062 .0 2.1 2.5 . 8 5.4 .0525 15.2 33.4 -.067 .9 6 .4 .0582 15.5 31. 9 -.062 .0 3.2 -.067 .9 6.9 .0638 14.1 32 . 4 3.7 7 .9 .0700 14.3 31. 2 -.062 .0 4.3 1.0 1.0 8.2 .07.15 13.2 31. 6 -.066 4.6 1.1 9.6 .OS6 0 12 .8 30.7 -.063 .0 5.7 1.1 9. .0000 12.2 30.9 - .OC'" 5.9 1.2 11.7 . 1003 11.0 30.3 -.Of),! .0 7. <I 1.2 11. 3 . lOS!} II. 3 30.0 -.OftO 7.0 1. 2.15 13 .7 . 1.140 8.1 31. 0 -.075 9.2 1.3 13. I .1261 10.3 29.5 -.05~ 8.5 1.2 16.4 .2118 n.7 32.8 -.00·1 . 1 12 . I -.070 1. 381 14 .9 .11'2 n.3 30. I 10 .0 1.1 19 .4 .2660 4. I 34.5 .1 1 0.5 1.3 1.1.0 WOO KI 31.0 -.078 10 . I 1.0 20.4 .2900 a.5 as. I .2 16.8 -.(1';1(1 13.8
=: :~ 1.2 18. I 2100 5.0 :12.4
.9 20. 9 .3039 3. 0 38.3 -.128 .2 17.7 1.1 20.7 2900 3. ~ -.106 16.
:14.41 1.0 22.7 33% 35.5 -.111 19.1 2. 9 I VII TABLE TABL E IV AIRFO[L CHARACTER l TI CS 4 BY 24 CLARK Y 4 BY 24 CLARK Y AIRFOIL CHARACTERISTIC.
6, MAX. 6 1AX. L IFT 3.50 X 10 RN .: ZERO LIFT 3.59 X 10 , R .. : ZERO LIFT = 2.06 X 10 LIFT = 1.96 X 10 c.p.
Cn LID C .... ~/4 Cn.
a CO LID C.p.
Cm,. I Coo I Ct.
I_CL I~_a I
I~
-------- -- I 0 0.()()Rf> -7.7 -0.075 -0.2 - .4 O.OIOS -1.5 -13.0 -0.2 -8.8 0.0116 -17.2 -13.1 -0.076 0.0094 - ~ I -.075 .00h8 -6.6 -.1 -7.0 . 0094 -10.0 -49.7 -.1 -7.4 .0005 -10.5 -49.7 -.075 · ()()!'9 -7.0 .00,9 -5.6 -5.6 007 0 -.07.1 .0090 0 -.074 .0090 -6.0 0 0 -6.0 ()()!I4 -.071 .00"li -4.6 -;).0 .1 -4.2 10.6 00.7 .1 -1.6 .0099 10. I 00.8 -.074 .0093
I
-.073 .()()!IO -3 . .1 .2 -2.1> 0117 17. I f1l.fl .2 .0 1/8 16.9 61. 7 -.073 .0096 -3.9 -.0,2 0100 -2.5 .3 -1.4 OIM) 20.0 19 .0 .0151 19.9 49.0 -.072 .0101 -2.9 .3
=n -.071 OliO -1.4
.1 0 .01!1fI 20.1 42 . S . 1 -.4 .0197 20.:1 12 . .s -.070 · 010~ -1.
-.070 .0121 -.1 .5 1.1 02f,o 19.2 39.0 .0255 IV. 6 39.0 -.070 .0116 .. 1 1.0
-.'
-.()(l>, Vi 03aR 36.3 .Ol~ .7 -.069 .0125 .:1 .6 .6 2. I . 0:125 I~. 5 36.5 :~: 7 I 1.1 0420 34.6 -.067 .01.13 1.6 1 7.3 31. 7 -.068 .0131 1.3 .7 .7 3.8 .0·\0·1 2.7 .8 0.6 .0030 15. I 33.2 -.066 .0174 33.4 -.067 . 0134 2. I .8 5.0 .0·190 16.3 .0611 14. I 32.2 -.06,1 . 0191 3.
-.066 .0162 3.5 .9 7.0 .9 6.7 . 0612 14.7 32.3 .0770 31. I -.064 .02 13 4.8 -.065 .0192 4. (; 1.0 R4
1.0 .0749 13.4 31. 5 13. °
fl. 1 1.1 10.0 .0920 lUI 30.7 -.063 .02·If> g:~ 12.2 .0227 5 .0 1.1 .0001 --- --- --. ----- 7.2 1.2 II. 5 II.I 30.2 -.062 . 02i .10"0 1.3 13. I .12CtO 10.3 29. f> -.060 .o.11R .0 .0371 0.7 1.4 14.7 .1161 9.6 29.3 -. Of to .0l06 10. I I. 420 15.2 .1.128 9.3 29.5 -.Of"!
10.5 l.4 15.5 .1.175 K9 29. -.067 .0485 -.100 .1492 13.9 1.3 1 .5 .2134 5.3 32.6 -.100 .1 9f> 15. I 1.2 19.4 . 269S 4.4 34.0 -.116 16.9 1.1 20. .29 2 3.7 36.2 .23°S 1 -.11 19.6 1.0 23.2 3.0 36.2 . Zi9," .3355 I REPORT NATIONAL ADVISORY C OM MITTEE F OR AERONAUTICS TABLE VI n TABLE XI 6 BY 36 CLARK Y AIRFOIL CHARACTER I ST I CS 6 BY 36 CLARK Y AIRFOIL CHARACTER I STICS R.N.: ZERO LIF T = 2. 07 XI 0 6, MAX. LIFT= 1. 90 X I Oo R.N.: ZERO LI FT=4. 1 5XIO·, MAX. L I FT=3.64XI 06 I c.p . C,_ c.p.
GL a Go LID I Cmr,14 Goo a Go LID Orne/'. Goo ao ao --- -- - -- - - - - -- - -- --- --- ------ --- ------ - - -- - -- -0.1 -7 . 0 0.0110 -9.0 0. 0105 -6.6 -0.2 .4 -7.7 - -------- ------ - -- ------ -- - -- --- -- - -- -- - -- -- -- ----- -------- -5.7 . 0100 .0100 -5.7 -.1 -6.9 0. 0098 -10.2 -58.6 -0.084 0.0092 -6.5 0 0 .. _- -- - -- -- ---- -- .0096 -4.7 -5.6 .0088 0 -.080 .0088 -5.6 .1 -4.3 .0102 9.8 - _. -.-.- 0 ---- - ---- -- -- -- - 17.1 .0091 -3 . 5 -4.2 .009-1 10.6 102.8 -.077 -4.6 .2 -2 . 8 .0117 .1 -------- ------. - :gg~ .0145 . 0095 -2.6 -2.7 .0111 18.0 62.6 -.075 -3.4 .3 -1.3 20.7 ------- --- -- - .2 -.1 .0189 21. 2 .0092 -1.5 .:3 -1.3 .0 1 45 20.7 49.4 -.073 .0095 -2.4 . 4 -- . ----- --- .
.0095 -.5 .1 .0lOl 20.9 42.2 -.069 .0102 -1.3 .5 1.3 .0234 21. 4 ---.- --. . I 20.0 .0100 .6 .5 1.5 .0243 20.6 38.2 -.066 . o to! -.3 . 6 2.7 .0300 --- --- --- .0109 I.fi .fi 2. \I 19.2 35.5 -.063 .01l3 .8 .7 4.0 .0382 IS.3 5.4 .0476 16.8 .0 1 20 2,.1 :g~~ .7 1.2 I .1 33.8 -.062 .0115 1.7 . 8 15.2 .01:l1 3.7 .X fi.7 .0.l78 16.7 32.7 -.062 .0122 2.R • U 6. n .0591 -- .0708 14.1 .0151 4. 7 .n 7. I .0585 15 . 4 31. 8 -.061 .013., 3. n I.IJ S.3 ----- -- -- 1.1 10 . I .0863 12.7 .0179 r. . 0 1.0 x. fI .0701 \4.3 31. 0 -.060 .0144 4.11 --- -- -- 11.7 .0218 7.4 10.1 .0841 13.1 30.3 -.058 .0150 6.2 1.2 .1020 11. S 1.1 ------- -----.- .1264 10.2 .0:34 '1 9. 0 II. 6 .099 12.1 29.8 -.057 .0187 7.3 I. 285 1 3.6 -------- -------.- 1.2 1 .1 .2265 . 1463 13.R 13.3 .1167 11.1 29.3 -.055 .0225 8.7 1.2 5.3 .---- - - 1.:1
-------
In.7 4.2 .19:12 15.R \5.0 .1382 9.9 30.4 - . 073 .0334 10. \ I.l .2606 . ------ -----_ .. I. 371 21. 5 .3081 3. 2 .2,534 1 7.0 15.6 . 1695 7.7 29.8 -.062 .0753 II. 0 1.0 .------- --------- 1.3 1.2 18.5 . 2338 5.1 32.4 -.090 .1536 14.2 21. 2 .2858 3.8 34.1 -.102 .2184 17.3 1.1 I Not measured.
T ABLE I X TABLE XII 6 BY 36 CLARK Y A IR FOIL CHA R ACTE RI S TI CS R.N.: Zr <;RO LI FT=3. 0 4X I0 6, MAX . LIFT = 2. 7 5X I O· fi BY 36 CLARK Y AIRFOIL CHARAC T ERIST I CS R. .: Z ERO LI FT = 4.77 XIOB, MAX . LI F T = 4.20X I0 6 C,_ a J,f f) C.p.
Cn C"'r / ~ en o ao -- -- --- -- --- -- -- J,ffl (', . a C/J C.p. mc ! 4 a.
G' ('''0 _° ,9 -10.4 -5'1.7 -0.080 0.0090 -n.!)
O. I 6 0.0096 -- -- --
I
-.077 .008R -li.r. 0 n -5.6 .0088 0 - --- ---.
-8.2 0.0122 -16.\ -18.6 -0.087 0.0100 -7 . :1 99 . 7 -.074 .0087 -4.6 - 0.2 .1 -4.2 .0093 10.8 -9.9 -54.6 -.080 .0095 -6.1 - . 068 . 0090 -3.5 -.1 -0.8 .0tOl .2 -2.8 .0112 17.8 59.2 - . 076 .00 9 -5.6 47.3 - . 067 .0095 -2.5 0 -5.6 .00 9 0 .3 -1.4 .0145 20.7 -- ----- -4.1 10.7 - . 073 -4.5 21. 2 41. 2 -.065 .0100 -1.4 . 1 .0093 98.7 .4 0 .0189 -2.7 .0110 1 8.2 60.1 -.070 -3.4 -.064 .0100 -.4 .2
.5 1.4 .0239 20.9 37.8 :~~
-1.4 .0140 21.4 47.4 -.067 .0090 -2.5 19.4 35.3 -.062 .0110 .7 .3 .6 2. S . 0310 -.1 21. 5 41. 3 - . 065 .0097 -1.5 33.7 -.061 .0114 1.6 .4 .016 .7 4.1 . 0387 .0234 21.4 37.8 -.064 .0095 -.4
:U 32.2 -.058 .0120 2.7 .5 1.4
. S 5.6 . 0476 -.063 .0100 . 5 -.057 .0130 3.S .6 2.6 .0300 20.0 35.5 .9 7.0 . 0585 15.4 31. 3 -.061 .0103 1.4 30.6 -.056 . 0145 4. 7 .7 3.9 .0376 18.6 33.7 1.0 8.3 . 0697 14.3 16.8 32 . 5 - . 060 .0119 2. 5 13 . 0 29.8 -.053 .0163 6.1 .8 5. 4 .0475 1.1 10 . 0 .OS43 - . 060 .0120 3. 5 12.1 29.2 -.050 . 0188 7.2 .9 6.7 .0570 15.8 31. 7 1.2 1 1. 5 .0990 -.060 .0119 4.4 11.0 28.8 -.049 .0238 8.7 1.0 8.0 .0676 14.8 31. 0 1.3 13.3 .!lSO .0124 1.1 9.4 .0798 13.8 30.3 - . 058 5. 5 1.330 14.2 . 1307 28.9 -.052 .0322 9.5 10:~ 1.2 10.8 .0935 12.9 29.7 -.056 .0133 6.5 1.3 14.7 . 1485 S. 30.0 -.065 .0543 to . I 1.3 12.4 . \096 11.9 29. I -.053 .0154 7.8 1.2 18.9 .2440 4. 9 32.2 -.087 .1638 14.6 1.4 14.3 .1299 10.8 28.7 -.052 .0209 9. :3 1.1 20.7 .2828 :3.9 :1I.2 -.104 .2154 16.8 I. 4~S 15.6 .1483 9.8 29.3 -.062 .0313 10.4 1.0 22.0 .3295 3.0 36.2 - . 1 17 .2638 I .4 1.4 . 1 530 9.2 29.8 -.067 . ().j40 10.8 1.'. 8 - 1.3 16 . 0 .1815 7.2 30. 3 -.069 .0873 11.4 I.,. :j 1.2 19.6 .2675 4.5 33.1 -.099 .2593 J.I 22.8 .3396 3.2 34.3 -. 1 06 .2722 I .9 TABL IG X fi BY 36 CLA RK Y AIR FO I L CH ARACTER I STICS R.N.: ZE R O LIF T =3.64X I0 6, M AX . LIF T = 3. 2 2XlO" TABLE Xl n 6 BY 36 CLARK Y A IR FO I L CHA RACT E RI S TI CS GL a CD LID Gno ao C·1'· CIt' e /4 R.N. : ZE R O LI F T =5 . 86X I0 6 -- - - - -- --- --- --- --- --- -- -6.9 0.0101 -9.9 -57.6 -0.083 0.0095 -6~5 -0.1 GL a GD LID c.p. Gvo a Orne!'
-5.5 .0090 0 -.080 .0090 -5.5 o ------ -- -4.2 .0095 10.5 103.8 -.078 .00 9 -4.6 .1 --- --- --- --- --- --- ---
---
-2.7 .0112 17.9 62.6 -.075 .0090 -3.4 .2 -6.9 0.0097 10.3 -56.5 -0 . 082 0_ 0091 -6~5 -1.3 .0145 20.7 48.7 -.07 1 .0095 -2.4 -0.1 .3 .0090 0 -.077 .0090 -5.5 .1 .0194 20.6 42.0 -.068 . 0098 -1.3 0 -5 . 5 .- .4 ----- -4. <I .0094 to. 6 98.7 -.073 -4.5 .0246 20.3 3 .0 -.065 .0107 -.3 . 1 .0088 .5 1.5 .0112 17.9 60.1 -.070 .0090 -3.3 .0312 19.2 35.5 -.063 .0112 .7 .2 -2.6 .6 2.8 -1.2 .0147 20.4 47.7 .0097 -2.2 4.2 17.7 33.7 -.061 . 01 23 1.7 .3 -.068 .7 .0396 .0200 20.0 41.8 -.067 .0111 -1.2 5.7 .0491 16.3 32.5 -.060 . 0134 2.8 .4 .2 .8 19.7 -.065 .Otl5 -.1 15.4 31.7 -.060 . 01 40 3.8 .5 1.7 .0254 38.0 .9 7.0 .0585 18.6 -.064 .0\22 14.1 31. 0 -.060 .0147 4.8 .6 3.1 .0322 35.6 1.0 1.0 8.4 . 0708 . ().j02 17.4 34.0 -.063 .0 1 29 2.0 13 . 3 30.5 -.060 .01M 6.0 .7 4.3 1.1 9.9 .0828 16.2 -.063 .0 1 40 11.4 12 . 3 30 . 0 -.060 . 0176 7. 1 .8 5.8 .0496 32.9 3.0 1.2 .09 78 13.0 .1155 11. 3 29.3 -.056 .0213 8. 4 1.3 9. 8 29.0 -.055 .0353 9.8 1. 36 14.7 .1383 8.4 29.7 -.061 .0613 10.4 1.3 15.0 .1555 19.2 . 2545 4.7 33.4 -.102 .1743 14.9 1.2 . 3033 3.6 35.2 -.115 .2359 17.7 1.1 21. 6 I I -- ~~--~-------~ SCALE EFFECT ON CLARK Y AIRFOIL FROM N.A.C.A. FULL-SCALE WIND-TUNNEL TESTS TABLE XVII TABLE XIV 8 BY 48 CLARK Y AIRFOIL CIIARACTERISTICf:) 8 BY 48 CLARK Y AIRFOIL CHARACTERISTICS 6 R. .: ZERO LIFT 5.58XIOB, MAX. LTFT=4.43XIO" R.N.: ZERO LIFT = 2.20 X 10 , MAX. LIFT = 1.84 X 10 C.p. a, c.p. CL a Cn LID Crtae!. Coo CL a Cn LID ePPlel Cn. a.
I
._-- --- --- -- -r- --- ---- --- -- --- --- --- ---- -- -15.1 0.0097 -7~4 ° -0.2 -R.1 0.0119 -16.8 -O.OBO -0.2 ° -7.7 -8.4 0.0131 -15.3 -15.6 0.0100 .0092 -6.4 -.1 -6. .0098 -10.2 -51. 7 -.077 -~:~~ -.1 -7.0 .0108 -9.3 -52.5 .0103 -6.6 -S.4 .0 -5.4 .0088 0 -.076 .0088 0 -5.6 .0099 0 -.075 .0099 -5.6 -- --- - -~---- -4.4 .1 -4.00 .0091 11.0 100.6 -.075 .0085 .1 -4.2 .0099 10 .1 98.7 -.073 .0093 -4.5 .0084 -3.3 .2 -2.6 .0106 18.9 62.6 -.075 .2 -2.8 .0110 18.2 60.6 -. 071 .0088 -3.6 .00 7 -2.3 .~ -1.2 . 0137 21. 9 49.7 -.074 .3 - 1.4 .0134 22.4 4S .4 -.070 .OOS 4 -2.5 .0091 -1.3 . 1 2 .018a 21. 0 1 3.5 -.074 .4 .0175 22.0 42 .. 5 -.070 .OOS6 -1.4 I ., 009f> -.3 .5 02:14 21.1 :39.6 -.073 .r, 1.4 .0230 21. 7 -.069 .0091 -.4 38.~ .7 .6 2. R .0303 Hl. R 36. R -.071 .0102 .r, 2.7 .0.305 19.7 :16.3 -.06R .0101 .!i 1 .7 .7 4.2 .0282 18. 3 3;;.0 -.070 .0109 .7 4 1 .0.387 18 .1 34.4 -.066 .011 1 1.0 .011.1 2. Ii R .~. :) .0 16 5 17.2 3~. Ii -.069 ~ 5.!i .0183 16 .6 33.1 -.Of.'; .0127 2.7 a.7 .n 6. !I .057R Jr,. 6 :12.1 067 .0127 7.0 .0590 15 . :\ 32.2 -.06:; .0139 3. R II .01:m 4.7 .0(;:; 1.0 R 3 . Ofi96 11.:\ :ll. 5 -.06,'; .0721 13.9 31.5 . 0164 5.0 1.0 8.6 .'1.11 11 H. R .0Sal 1:1.2 :11.0 -.000 .0162 1.1 10 .2 .0876 12.0 30.7 -. OC,1 .02 02 Ii.:!
7.1 7. r, 11 .100a 12.0 30 . Ii -.067 .0201 1.2 11. :; aO.2 -.062 .0238 1.2 I 11.9 .10 10 . 1182 11. 0 30.2 -.067 .0241 8.4 1.:\ .1232 10. :; 2O.R -.062 .0201 0.0 1.3 13.0 13. 7 .1388 10.1 30.0 -.069 .0296 O.S . 1309 9.5 30.0 -. Of16 .0420 10 .0 1.4 14.8 I. :\25 11.7 9.1 29.7 -.068 .0413 11.0 1,';.8 .1644 7.9 31. 0 -.078 .0703 11. 2 1.46 16.2 .1600 1.3 . 17C,s 7.9 30.0 -.069 .0676 11. 9 33.0 -.006 .1331 13 .4 1.4 16.0 1.2 17.7 .2133 5.6 31. 9 -.090 .1251 13. I 4.2 35.0 -.112 .19 17 15.6 1.3 17 .7 .2190 5.9 1.1 19.6 .2591 35.2 -.125 .2106 17.8 37.0 -.125 .2635 18.3 l.2 22. I .3210 3.7 1.0 21. 9 .3101 3. I
I
TABLE XVIII TABLE XV R BY 48 CLARK Y AIRFOIL CHARACTERISTICS 8 BY 48 CLARK Y AIRFOIL CHARACTERISTICS R. .: ZERO LIFT =6. 12 X IO B, MAX. LIFT 5.38X 10" R.N.: ZERO LIFT =3. IO X I0 6, MAX. LIFT = 2.59XIO· --- c.p. ('n. an Cr . a { "n e"",./4 (,,, c.p. ('111,/4 ('0(1 r,. a LIn
I
--- --
". --
~I
--
-7~ I - 16 .1 -15.0 -0.080 0.0102 ° -0.2 -8.1 0.0124 -0.084 O .OIOS -7.6 -0.2 -"8.3 0.0130 -15.4 -17.0 -54.0 -.078 .0001 -6.3 -.1 -6.7 .0007 -10.3 -.080 .0095 -6.6 -.1 -7.0 .0101 -0.9 -54.6 -.076 .0086 -5.3 .0 -.1.3 .0086 0 -------- -.075 .0091 -5.5 -5.5 .0091 0 0 .------ 96.1 -.075 .0083 -4.3 .1 -3.9 .00 9 10.2 -.073 .0087 -4.5 .1 -4.1 .0093 10.8 98.7 -.073 .0084 -3.3 .2 -2.6 .0106 18.9 61.9 -.070 .0084 -3.4 .2 -2.7 .0106 18.9 60.1 -.072 .0089 -2.3 .3 -1.2 .0139 21. 6 49.5 -.069 .00 1 -2.4 .3 -1.3 .0131 22.9 48.0 -.072 .0092 -l.3 .4 .2 .0181 22.1 43.0 -.067 .0091 -1.3 .4 .1 .010 22.2 41. 8 -.071 .0095 -.3 .5 1.5 .0234 21.4 39.5 -.067 .0095 -.4 .5 1.5 .0234 21. 4 3S.4 -.071 .0104 .7 .6 2.8 .0305 19.7 37.0 -.067 .0104 .7 .6 2.S .0305 19.7 36.2 -.071 .0109 1.7 .7 4.2 .03H2 18.3 35.0 -.067 .0 116 1.7 .7 4.2 .0389 18.0 34.5 -.071 .0120 2.7 5.6 .0476 16.8 34.0 .8 -.067 .0125 2.7 .S 5.6 .0481 16.6 33.4 -.070 .0130 3.7 6.9 .0581 15.5 33.0 .9 -.067 .0138 3.8 .9 7.0 .0590 15.3 32.4 -.070 .0139 4.8 8.4 .0696 14.4 32.1 1.0 -.067 .0164 5.0 1.0 8.6 .0721 13.8 31. 7 .0162 5.9 .0836 13.2 31. 3 -.070 1.1 9.8 .0196 6.2 .0870 12.7 31. 2 -.068 1.1 10.1 7.0 .0909 12.0 30.9 -.070 .0186 1.2 11. 3 .0244 7.5 1l.8 .1046 11. 5 30.6 -.067 1.2 .02:11 8.3 .1 170 1l. 0 30.3 -.070 1.3 12.9 .0.111 R.9 1.3 13.6 .1228 10.6 30.2 -.067 .om 9.7 . 13!1O 10.1 30.0 -.070 1.4 11.7 .0412 10.3 15.2 .1442 9.4 29.9 -.066 I. 36 .0390 11. 3 . 16f,o 9.1 20.9 -.070 I.S1 16.7 .0831 11.8 16.4 .1772 7.3 31. 9 -.090 I.a . OSlo 12 .3 . 1 III 0 7.3 2Il.R -.060 1.4 17. a -. 106 . 1531 14.1 18 .4 .2333 5.1 33.S 1.2 -. 110 . 1631 14.6 .2.'i70 S.1 :13.6 1.3 IV. 2 -.llfi .2137 16.6 20.6 .2811 3.9 35.3 1.1 17 .7 .3150 3.8 34.9 -.11S .2346 1.2 22.0 -. 120 .3597 19.3 22.R .3256 3.1 36.5 1.0 TABLE XIX TABLE XVI 8 BY 48 CLARK Y AIRFOIL CHARACTERISTICS 8 BY 48 CLARK Y AIRFOIL CHARACTERISTICS R N.: ZERO LIFT = 7.53 Xl0 R.N.: ZERO LIFT=4.13 X IO·, MAX. LIFT=3.78Xl06 a CD LID C.p. CPle/4 CL Cn. I a.
CL a Cn Cmdt CDC a.
LID I C.p.
--- --- --- ---
--- --
_os. 3 0.0104 -7. 6 -1,';.9 -15.1 -0.080 -0.2 0.0126 -0.084 0.0104
0.0126 -15 .9 . -17.1 -t5 .0091 -6.4
-0.2 -8.2 -10.3 -51. 7 -.077 -.1 -6.8 .0097 -.079 .0094 -6.5 .0100 -10 .0 -53.6 .0086 -5.3 -.1 -6.9 0 -.075 .0 -5.3 .00R6 -----_.- -.075 .0090 -5.5 .0090 0 .0086 -4.2 0 -5.5 -------- 10.9 09.6 -.074 .1 -3.8 .0092 -.073 .00 9 -4.5 -4.1 .0095 10.5 9S.7 .0090 -3.0 .1 17.9 61. 6 -.073 .2 -2.3 .0112 -.071 .00 7 -3.5 -2.8 .0100 1 .4 60.6 -.071 .0097 -2.1 .2 .0147 20.1 4 .7 .3 -1.0 4S.4 -.070 .00 7 -2.5 -1.4 .0137 21.9 .0094 -1.2 .3 42.5 -.070 .4 .3 :0183 42.5 -.070 .OOS6 -1.4 .0175 22.0 .4 0 ~J 39.0 -.070 .5 1.6 .0240
.0101 I -.2
39.0 -.070 .0089 -.5 1.3 .0228 21. 9 -.070 .0104 .5 19.7 36.7 .6 2.9 .0305 36.5 -.069 .0094 .5 2.6 .0295 20.3 -.070 .0112 1.
.6 18.2 35.0 .7 4.3 .0385 34.8 -.069 .0104 1.5 4.0 .0377 IS.6 .0108 2.7 .7 17.3 33.9 -.071 5.6 .0464 17.2 33.5 -.068 .0 100 2.5 5.3 0165 .8 32.6 -.068 .0 122 3.5 6.7 .0573 15.7 . 1 .9
•
31.8 -.068 . 01 33 4.6 S.2 .0690 14.5 1.0 31.1 -.067 .0150 5.7 1.1 9.6 .0824 13.3 TABLE XX 30.5 -.066 .0196 6.9 1.2 11. 2 .0098 12.0 30.0 -.065 .0241 8.2 12.8 11. 0 1.3 8 BY 48 CLARK Y AIRFOIL CHARACTERISTIC 9.7
: :j~~ 29.7 -.065 .0306
1.4 14.7 10·0 R .. : ZERO LIFT=8.77XI0~ -.075 .0387 10.7 .1550 30.2 1. 445 15.9 -.075 .0066 12.4 17.4 .2058 30.4 1.4
n
3 2.3 -.005 .1551 14.4 19.0 .2492 5.2 1.3 -.120 .2301 17.3 .2832 4.2 34.8 c.p. CPPl !.
1.2 21. 6 a CD LID e CL
I
~I~
- ---
----- --- -- --
_° . -55.7 -6.8
7 2 0.0095 -10.5 -0.081 I 0.0089
-0.1 -5.4 - .0 76 .0087 -5.4 .0087 0
.0 -- - ~
-4.1 II. 0 09.0 071 .0085 -3.7 .0091 .1 -3.0 1 .. 5 61.6 I -.on 0086 -2.3 .0108 -. 1 .2 49.0 -.072 -1.0 .0139 21.6 .3 .00891-2.1 .0091 -1.2 2'l.2 -.070 .2 .010 .4
42. I .0090 -.:1
39.2 -.071 .0229 21.
.5 37.0 .0084 .6 U .0285 21. 6 -.072, .6
I
U. S. GOVERNMENT PRINTING OFFICE I 1:134
l
.....
"
" ......
"
Z Positive directions of axes and angles (forces and moments) are shown by arrows Axis Moment a.bout a.xis Angle Velocities Force (parallel Linear to axis) Sym - Sym- Positive Designa- Sym- (compo- Angular Designation symbol Designation bol bol direction tion bol nent along axis) RolIing _____ RoIL ____ LongitudinaL __ X L Y--tZ 'U X cJ> P LateraL _______ Pitching ____ Pitch ____ q Y Y M Z---+X 8 v NormaL _______ yawing _____ yaw _____ r Z Z N X--tY w if!
, Angle of set of control surface (relative to neutral Absolute coefficients of moment
p os ition), o. (Indicate surface by proper subscript.)
N
c=-'£ (], = M
n G = qbS I qbS m qcS (rolling) (pitching) (yawing) 4. PROPELLER SYMBOLS D, Diameter p
P, Power, absolute coefficient G = pn~D6
p, Geometric pitch
Pitch ratio pID, G., Speed-power coefficient = ~ ~~: Inflow velocity V', Efficiency Slipstream velocity 7], V" 11. , Revolutions per second, r.p.s.
T, Thrust, absolute coefficient G = ~ D 4
T pn
Effective helix angle = tan- (2:11.)
Torque, absolute coefficient G = 9 6
Q, Q
D pn
5. NUMERICAL RELATIO NS 1 hp. = 76.04 kg-m/s = 550 ft-Ib ./sec. 1 lb. = 0.4536 kg.
1 kg=2 .2046 lb.
1 metric horsepower = 1.0132 hp.
1 mi . =1,609 . 35 m=5,280 ft .
1 m.p.h. = 0.4470 m.p.s.
1 m =3.2808 ft.
1 m.p.s.=2 .2369 m.p . h.