UNCLASSIFIED AD NUMBER LIMITATION CHANGES · were made vith the tunnel epeod held constant while...
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AIR DOCUMENTS DIVISION
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• -,;|'Ki •* iw in'
L I C
HEADQUARTERS AIR MATERIEL COMMAND
WRIGHT RELD. DAYTON, OHO
4,* •• * "JCJi»«.
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IS ABSOLVED
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f
NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
TECHNICAL NOTE
No. 1390
ffl MO,%T?JB
EFFECT OF COMPRESSIBILITY ON THE DISTRIBUTION
OF PRESSURES OVER A TAPERED WING OF
NACA 230 -SERIES AIRFOIL SECTIONS
By E. O. Pearson, Jr.
Langley Memorial Aeronautical Laboratory Langlpy Field, Va.
Washington July 1947
C?J
FILE COPY BfTURHTO
Air Documents Ci» wi • '.r «r> -nc« i hi i Wf(*hl t*u, UifM, Oka
„ B
NATIONAL ADVISORY CO-WITTE! FOR AERONAUTICS
TECHNICAL NOTS NO. 1390
EFFECT OF COMPSESSlBILmr OH THE DISTRIBUTION
OF PRESSURES OVER A TAPERED V3C OF
KACA 230-EERIHB AIHFOIL 3jäCTC0!E
By E. 0. Pearson, Jr.
SUMMARY.
•
The results of preonun»-distribution Boaouremonts msdo during high-speed wind-tuniMl toatc of a tapered wine of NACA t:30-series airfoil sections are preoented for angina uf attack ranging from 0.3° to 21.2° and for free-stream Mach nunbors ran/;lnß fron 0.2 to about O.Y.
Tho peak valuos of minimum pressure coefficient attained «ore found to correspond to local Mnch nunboru of 1.2 to 1.1» except at angloo of attack near tho low-apeod stall. The hlfhoct local Mach number measured vao 1.55.
In rest coses noticeable flow separation was lro'loAted only at stream .'loch numbern e-co' din,- those at which peak minimum pressure coefficients were reached.
At large angles of attack corresponding to those very near the low-speed stall there was sou Indication that tho flow about tho wing broke down when the critical proeoure coefficient war. reached.
A comparison uf asamrod and calculated ehordwiae pressure dis- tributions for several stations along the spra showed satisfactory agreement for purposes of structural design up to tho critical Mach number.
INTRODUCTION
A knowledge of tho magnitude of surface preasure• and their distribution along thu chord and span of wln#s at high speeds is required tor proper structural design. Because of the lack of an adequate theory for determining the prossuroa on ajrVnlls at super- critical speeds, the required lnfomstlon must be ibtalned ontlrely by uxperlaent. Tho purpose of the present paper, which fcivus the
HACA TM lie. 1390
detailed results of extensive pressure measurements over a tapered vine <"f HACA 230-series airf-'l sections. Is to add to the existing amount of high-speed pressure-distribution data, which are very limited In extent, particularly for finite Vn. a.
The pressure-distribution measurements reported herein were made during tests In the Longley 16-foot high-speed tunnel conducted priaaril. to determine the effects of Mach number on maximum lift and spanvlse load distribution of a tapered ving of HACA 230-series airfoil sections. The force measurements and the spanvlse load distributions obtained from the pressure measurements presented herein vere reported in reference 1.
SYMBOLS
a
A
a
b
c
C*o
y
L
•
free-stream speed of sound, feet per second
locel speed of sound, feet per second
aspect ratio
corrected angle of attack of root section (section at plane of symmetry), decrees
ving span, feet
airfoil chord, feet
section profile-draa coefficient
section normal-force coefficient
ving lift coefficient ft)
(if A"«-)
ratio of specific nest at constant pressure to specific heat at constant volume
ving lift, pounds
three-dimensional lift-curve slopo, per redlan
tvo-dlmenslonal lift-curve alope, per radian
HACA SB Mo. 139°
I
Mo
M
Mcr
V
P
rmln
free-strean Mach number (V0/eo)
local Mech number (v/a)
critical Mach number (value of MQ idien M first reaches
a vaJua of unity)
free-atreain static pressure, pounds per aquaro foot
local atatlc pressure, pounds par square foot
/P " Po\ pressure coefficient l~~—|
critical pressure cooffieient (value of 1> correapondln3 to M - 1*0)
pressure coefficient corresponding to laximun local velocity
p free-stream aaea donnity, alupa per cubic foot o
q free-ßtream dynarJc proesure, pounds per Bquare foot ^2"P0T
0 )
S wing area, aquare foet
V free-atream velocity, feet per aecund o
V local volocitj, feet per second
x chordvise dlata.ice meaauree. from It din«, «-dgo, Toet
y aranvlBf dlotance meaaured from piano of oymactr}-, feot
Subscriptss
c compressible
1 lneornreaeible
V uppei surface
I lovor surface
:
HACA HI Bo. 1390
APPARATUS AMD MBTHODG
Tests ware conducted in ths Laneley l6-foot h: h-speod tunnel. The vin, tested had an aspect ratio of 6, a taper ratio of 2. no dihedral, 3.l8° aweepback of the quarter-chord lino, and U.2° of uniform geometric voshout • The vlng had an IIACA 23016 airfoil section at tho root and an KACA 23009 airfoil aoction at the con- struction tip. A diagrammatic sketch shovir.;, the principal dimen- sions of the viivj is given In figure 1.
Thlrt; -three pressure orifices were distributed over each of six vine aectlono, the spenvise locations of which are given in flGure 1. Also shown in figure 1 are the chordvlse locations of orifices aver a typical section-
Pressure tubes connectinc; *Jie orifices on the vlng with several multiple-tube manometers in the teat chamber wore brought out of the rear of tlie win • through a boom mounted rlgjdly to the vlng and a movable strut. This arrangement may be seen in figure 2, which is a photograph of tlie vim. mounted in the tunnel for the pressum-dlstrlbutlon tests. Pressures Indicated by the manometers were recorded phato-yaphieally. For a more detailed description of the modol and the apparatus, see reference 1.
TESTS
Most cf the test runs wore made with the angle of attack held constant vliilo the tunnel speed was varied from about 150 mi lea per hour to the maximum speed obtainable (not choking speed), which for win -, angles of attack betveen 0° and U° was cpproxlnstely 320 miles per hour. The corresponding ran;,« of the free-stream Mach number waa from 0.20 to about O.70. The Reynolds number varied from 3.0 v 10° to 6.1 x 10 , which corresponds roughl;- to that of a full-scale fighter airplane fl/in-, at the test Mach numbers st altitudes of about 33,000 to 1)0,000 feet. At the highest angles of attack the mr.xlcum obtainable tunnel speed was about ' S) miles per hour, which correspunds to a Mnch number of 0.ÖP5- A few additional test runs were made vith the tunnel epeod held constant while the angle of attack waa verier in the region near maximum lift. The angle-of- attack ran.,e covered in the pressure-Alatrlbutlon tests was approxi- mately from 0° to 21°.
Some of the tests were mode at angles of attack of 2.30 and 6.7° to determine the distribution of profile dra{. across the span. Vor these tests the pressure tubes and the trail."n;, boon were removed
MCA in no. 1390
from the wins, and a rake of total-pressure tubes MIS installed on the vertical strut rlovnstreait from the v?:..,. V'lti: t; -a apparatus, surveys of the vine take vero made at various points along the span. The position of the rake wi kept In a plane ptrper-icular to tho tunnel air stream and consequently the distance of tiie ralco from the vino trailing edge variec" from about 1/2 chord at the root to about 1- chords at the tip.
CORRECT!}? 0'
Angles of attack given in the present paper (fi... 3) have been corrected for tunnel-wall and other effoctn, so explained In detail in reference 1.
Supporting struts.- Tho effect of the supporting etruts vas to Increase the effective velocity at the wine posit'.on. A calibration of the tunnel with the struts Installed but -nth the wine removed showed that the increase in velocity variec" from r<bout U percent near the struts' to about 2 percent at the center of the tunnel. A mean value <:t effective velocity, weighted according to the wins area, V9s chosen, which represented an orer-all cnrroctlon of about 3 percent. Corresponding val-tus of static pressure and dynamic pressure vere used in computing pressure coefficients from the measured static pressures on the win,-.. This correction affects all data In fi-jure h and tho values of on in flgorM 5 and 6.
Because of the nonunlformlty of the vel;>cit;- across the tuni.ol, the minimum pressure coefficients shovn la fi^uro 7 for tho wins station nearest tho struts (station '») ore In a.vor from this source by about 5 percent at o » 0.2° and b;- about 2 percent et « « 17.?°- At tills station the minimum pressuro coefficients as presented are nopatively too large. At station 1 (noar the center of the tunnel) the minimum prossure coefficients as prcsontiV. ?re .ie atively too email, and hero the orror Js about, iielf that quoted for station k. The errors at stations 2, 3, li, and 6 aro aaellor sne< the error In minimum pressure coefficient et these stations <s of the order of 1 percent for all angles of attack.
Tunnol-wall interference.- Neither the pressure coefficients nor the stream Mach nunbor." have been corrected Tw tunnol-wall interference because of some uncertnintiae in the application of corrections to the pressure data for the present case of a relatively large finite vin; in a circular tun-el; also, a check of the order
of mnsnttudu of the errora Involved by the methods of references 2 and 3 Indicates that these errors do not significantly affect the conclusions reached«
The principal errors arise from the lncreaae In effective velocity at the vine position due to constriction of the tunnol by the large ving take st high an;lee of attack end hl.h Mach numbers «here the flow Is largely separated- As Ion;, as the flow over the vlng was smooth, the errors In pressure coefficient and Mach number from this source were found to be no;lifciblo. Under the conditions of strong ahock and extensive flov separation occurring et the hi;jueot test angles of attack and Mach numbers it wo determined that the Indicated dynamic pressure and Mach number were too low by as much as k percent and 2 percent, respectively. The test point on the curve of minimum pressure coefficient against Mach number In figure k(i), elvlng a pressure coefficient of -2.00 at M(
Is representstive of data obtained under these extreme conditions. For this point It Is probable that the minimum pressure coefficient Is negatively too lar^e by about 6 percent.
Since negative pressure coefficients are too largo negatively and stream Mach numbers are too low, local Mach numbers are affected by constriction to a much smaller extent than the pressure coeffi- cients as Illustrated by the follovlnc numerical example:
The equation relating local Mach number, stream Mach number, and pressure coefficient fur lsontroplc flov Is
2
It - 1 -^oS 2 °
Substitution of the values of prnssure coefficient and Mach number previously given
value of local Mach number of 1.3? Increased by S percent (corrected
0.622) in this equation glvea a If the stream Mach number is
and the preaauro coefficient is reduced numerically b." 6 percent (corrected P» -1.66) and these corrected values are substituted in the equation, a value of local Mach number of 1.31 la obtiinor1. The difference between corrected and uncorrected local Mac;, number Is seen le be less than 1 percent.
HACA Tfl It«. 1390
RESULTS AIJP DISCUSSION
Wing lift characteristics (trm force testa).- The lift curves for tho wins et verloue Mich numbers es determined from the force teeta reported In reference 1 «ro (jiven In figure 3 far purposes of correlation.
Prescure coefficients ar,d section normal-force coefficients.- Chordviso prossure-Sietrltv.iion diagrams far stations 2 and 3 (see fig. 1 for locations) are presented in figure -V fur a rsngo of angle of attack and Mach number. Tho variations wit;: Mach number of minimum pressure coefficient and section norusl-l'orce coefficient as obtained from Integration of the pressure-distribution diagrams are also shorn in figure k. In order to prevent possible confusion over two dis- tinctly different minimum values of pressure coefficient the following definition of terms is offered: 'lllnlmua pressure coefficient" refers to the largest negative value of pressure coefficient measured at a particular apariwlse station on tho win; for any anc,le of attack and Mach number. This minimum quant it." may bo obtained from the pressure- distribution diagrams of figure U. The tern 'peak minimum pressure coefficient" refers to the largest negative value attained by the curves of minimum pressure coefficient plotted a-jalnst Mach number, which are HIBO ,<»lven In figure fc.
Stations P. and 3 were chosen for discussion because minimum pressure coefficients end otxUiura normal-force coefficients occurred in this region on the wine* The pcsltlon of these minimum and maximum coeffielünts shifted fr.nn station 2 to station 3 as the angle of attach WOP lncrasec' from about 2° t" that value coi-reapendinß to the stall; at a » 8.Q° tlwi coefficients were about the same in msgnltudn at both of these stations. Compere figures U{() and 4(e).
The curves of minimum pressure coefficient 3.1 'ust ctream Mach number for most of the angle-of-attack range (fi..s. l»(e) to '»(c)) ahnw that local Mach numbers Increased end local pressures decreased with Increasing free-ntreaa Mach r-umber in thi usual manner until peak minimum pressure coefficients vhlch corresponded to local Mach numbers from 1.2 to l.U were reached. In general, maximum local Mach numbers and peak vnluos of minimum pressure coefficient did not occur at tho some fruo-atream Mach number; maximum local Mach numbers were reached at s.mvhat h.'. jier stieim Mach numbers than peek values of minimum pressure coefficient. The maxfcwm value of local Mach n-jciber measured v-s ubout 1.55 (fig. 4(f)).
The evidence shown in fl^nre k indicates that aver most of the an^le-of-attack range noticeable flow separation, as Indicated by a deficiency in pressure recovery near the treillr..- edge, dl<\ not occur
SACA TB He. 1390
until the stream Mach number corresponding to the attainment of peak minimum preaaure coefficient.: had been veil exceeded. The normal- farce coefficient, however, generally ahowed aone departure from the smooth oubcrlticul trend at Mach nunbere only slightly In excess of the critical, even thou.J: little If any flow aeparatlon ««a Indi- cated' For an example of beginning aeparatlon nee the preaaure dis- tribution far a Mach mmbor of 0.651 In figure k(t). However, the poaaiblllty of the occurrence of a local aeparatlon confined to the region of ccapreaalon shock at lower auporcritlcal Mach numbers cannot be excluded (reference k).
At angles of attack very near tho lov-opeer stall (fig. U(j)) the rather meager data appear to ahov that «hen the critical preaaure coefficient la reached tho flow can tolerate little If any shock disturbance vlthout breaking dovn. The result.- on this wing pre- sented In reference 5 more strongly corroborate this indication.
The subcrit'cal rlao in normal-forco coefficient with Mach number haa been compared with that given by the snail-disturbance theory as applied tc the ftnlte wing by A. D. Younn In n Britlnh paper of limited distribution. Tho equation far the ratio of noraril- force coefficient *t any XaWltl—1 Mach number to normal-force coefficient at M » 0 lr 'js follows:
cnx " »1 ' «oi V»oc • *)
_2£ fr-tf
•01 it.
Gft»)* xA The value of the lov-speed tTo-dlaenaional lift-curve alope m^,
waa taken aa t»:at for thin airfoils (Sit). value for a,,, tha equation became
Cnc.
Upon substitution of this
<T..
HACA m No. 1390
Aa nay bo seen In figure h the curve« calculated from the fore- going equation are In excellent agreement with tho experimental normal-force-coefflclent curvea up to the force-break Mach number, beyond which large differences between the experimental and theo- retical results are shown.
Contours of pressure coefficient over the upper surface of the wing are shown la fleures 5 and 6 for several Mach numbers and for angles of attach of 2.3° and 6.7s. Included in these fi,-urea are curves showing the spanvina distribution of normal-force coefficient and profile-drag coefficient for correlation wJth the data given in figures U(a) and U(e).
These figures serve to show hew the re Jon of supersonic flow ahead of the conproaslon snick or shocks formed an? expanded wltn Increasing Mnch number. Of Interest is the fact that st the highest Mach numbers (r: s. 5(f) snd 6(f)) the drag coefficient Increased to about two or thro times Its loi-spoed veluc, "tiile the normal-force coefficient remained eEsent'.all; unaffected.
Ccmparlson of thoorrtlcal and experimental chcravlse pressure dlntrtbutionn.- Thu measured and celculatsd cinrd.wiae pressure dis- tributions over the wins sections at six spciwlso scations aro given in flguro 7 for a range of an^le of attack and Mi.:h number.
The chordwlse pressure distributions were calculated by the method of reference 6 for each section so that tie lift coefficients were In nyreument vith tliose obtained experimental!,: at a Mach number of about 0.2. The calculated pressure coefficients were then extrapolate* to hi,-nor Mach numbers by the von K-irman-TcJ'.-n relation, which is recommended In reference 6.
The von Karman-Tslen theory, of crurao, is not valid at Mach numbers higher than Mie critical, but the comparison is continued to supercritical speods to show the departure of the meesured flov rrom that predicted by the first approximation of the theory. It should be noted that suca calculations lesd to the impossible condition of pressure coefficients which correspond to pressures leas than absolute toro.
At an angle of attack of 21.2° (fig. 7(f)) the win& was completely stalled at all Mach numbers, and consequent.ly tlic calculated pressure dlatributlcns are not given for this condition.
An examination of figure 7 shows that for purposes of structural design the method of referer.ee 6 elves results In satisfactory agree- ment '..-lth experiment at Mach numbers U;J to the critical.
iß HAGA TB No. I39O
Pressure distributions at nestions very near Uie viiig ein are undoubtedly distorted by the llov around the tip. For the teat ving, however, the area so affected ic snail,
distortion at station 6 1~JL ' 0.9U)
:io evidenced by the very small
CCKCLUEIOBS
1. Peak valuer of minima» pressure coefficients vere found to correspond to local Mach nwjbers of 1.2 to l.U. Local Mcch numbers generally continued to lncrurse with increasing stream Mach auKoer beyond that ut which pc.l. ninimKa procsure coefficients occurred. The K 'Xinuc local Mach r.'-r.bcr measured ves cbout 1.55.
2. In general no noticeable indication of flow separation vac observed until 'he stream Much nuriber corresponding to the attain- ment of peak pressure coefficients hud been veil exceeded.
3« At angles of attack very near those corresponding to the lov-speed stall there voo seme indication that the flov about the ving broke do-.:n vhen the critical pressure coefficient (local Mach number • 1.0) vc-s reached.
h. The measured rate of increcoe with Mach number of cection normal-force coefficient at subc.*itical values of Mach number vau in excellent a^Tetntnt vltli that predicted from the small-disturbance theory. large differences lotvoen the theoretical :ni experimental results occurred at high supercritical cpeeda.
5. The method used for calculating; the chordvise prescure dis- tribution gave results in satisfactory agreement vith experiment for the purpose of structural design at Mach numcere up to the critical.
Lonfcley Meuorial Aeronautical Laboratory Rational Advisory Comnitteo for Aoronautic3
Lungley Field, Va., May 7, IJhJ
HACA TH Mo. 1390 11
Mom
1. Pearson, T.. 0., Jr., Evans, A. J., and «Teat, F. E., Jr.: Effects of Compressibility on the Maximum Lift Characteristics and Spanvlse Load Distribution of a 12-Foot-Cpan Fighter-Type Wing of HACA 230-Serles Airfoil Sections. HACA ACH Ho. I$010, 1945.
2. Thcc, A.: Blockage Corrections in a Closed High-Speed Tunnel. B. " M. Ko. 2033, British A .B.C., 10l»3»
3. Allen, n. Julian, and Vincentl, Welter C: The Wall Interference In a 'IVo-Dinonoicnal-Flcv Wind Tunnel with Consideration of the Effect of Compressibility. HAW Hep. No. 7ÖE, 19M.
4. Wood, Clotalre, and Zalovclk, John '. •: Flight Investigation at High Speods of Flow conditions over MI Airplane Wing as Indicated by Surface Tufts. HACA CB Ho. L5E22, I9U5.
5. Furlone, 0* Chester, and Fitzpatrlck, Janen £.: Fffectn of Mach Hucuior end Reynolds Humbor on the Maximum Lift Coefficient of a Wing of HACA 230-Series Airfoil Sections. HACA TH Ho. IE99,
6. Anon: Chordwiae Air-Load Distribution. AHC-1 (2), Army-Havy- Clvll Ccesnittee on Aircraft Design Criteria, Oct. 28, lpt2.
1 NACA TN No. 1390 Fig. 1
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NACA TN No. 1390 Fig. 2
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016 cd o 008;
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(c)M0'0603 (d)M0-0658
Figure 5.—Contours of pressure coefficient over upper surface of
fighter-type wing and spanwise distribution of normal-force and
profile-drog coefficients as affected by compressibility a«23' ^L
Flg. 5e,f NACA TN No. 1390
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•
Fig. 6
NACA TN NO. 1390
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Calculated M (a) (T-0.2C
FiaureT-Measured and calculated pressure distributions
and angles of attack.
Fig. 7b
NACA TN NO. 1390
\
Figure 7-Continued
Fig. 7c NACA TN No. 1390
M0=0204 M0=0.507
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Calculated
(c) <r - 8.9°.
Figure 7 - Continued.
V :
NACA TN No. 1390
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Calculated
(d)tf- 13.2°.
Figure 7 - Continued. 32.
Fig. 7e NACA TN No. 1390
Measured Calculated
(e)<r-l7.5°. Figure 7-Continued.
! NACA TN No. 1390
Fig. 7f
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•
Figure 7-Concluded.
—— Measured
(0<r-2i.2°.
"3 V
TITLE: Effect of Compressibility on the Distribution of Pressures over a Tapered Wing of NACA 230-Series Airfoil Sections
AUTHOR(S): Pearson, E. O. ORIGINATING AGENCY: National Advisory Committee for Aeronautics, Washington, D. C. PUBLISHED BY: (Same)
ATO- 9573
(None) OHIO. AOENCT NO.
TH-1390 MtSilSKINO AOEMCT KO.
July '47 Unclass. U.S. Eng. MOES 34
llUlfTUTIONS photos, graphs, drwg
ABSTRACT:
An investigation is presented of the effect of compressibility on the distribution of pressures of a tapered wing. Peak values of minimum pressure coefficient attained were found to correspond to local Mach numbers of from 1.2 to 1.4, except at angles of attack near low speed stall. In most cases noticeable flow separation was Indicated only at stream Mach numbers exceeding those at which peak minimum pressure co- efficients were reached. At large angles of attack, near low stall speed, there was some indication that flow about wing broke down when critical pressure coefficients
' were reached.
DISTRIBUTION: Request copies of this report only from Originating Agency DIVISION: Aerodynamics (2) SECTION: Wings and Airfoils (8)
ATI SHEET NO.:R-2-8-*0
SUBJECT HEADINGS: Pressure distribution - Wings (74500); Airfoils - Compressibility effects (08032)
Air Documents Division, Intolllnonco Doportmonl Air ttotoriol r
AIQ YBCHNICAL IMOGÄ Wrloht-Portoraon Air Porto Dnso Dayton, Ohio
-I
TITLE: Effect of Compressibility on the Distribution of Pressures over a Tapered Wing of NACA 230-Series Airfoil Sections
AUTHOR(S): Pearson, E. O. t !--PAGINATING AGENCY: National Advisory Committee for Aeronautics, Washington, D. C. |^V5) SHED BY: '(Same)
M ^47. DOC CUUS. Unclass.
couNrar U.S. Eng. 34
OTO-9573
JSsasL OtHO. AOENCT HO.
TN-1390 PUOUSKtNO AOGNCT MO.
•lUniDATUKO photos, graphs, drwg
An Investigation is presented of the effect of compressibility on the distribution of pressures of a tapered wing. Peak values of minimum pressure coefficient attained -' were found to correspond to local Mach numbers of from 1.2 to 1.4, except at angles of attack near low speed stall. In most cases noticeable flow separation was Indicated only at stream Mach numbers exceeding those at which peak minimum pressure co- efficients were reached. At large angles of attack, near low stall speed, there was some indication that flow about wing broke down when critical pressure coefficients were reached. /\ ^ *, / ^ ^^^
Request copies of this report only from Originating Agecay=" Aerodynamics (2) Wings and Airfoils (6)
iTI SHEET NO.: R-2-6-SO
SUBJECT HEÄDINSSfPressure üstrlbuUon>-\Wings>(74500); Airfoils - CompresBSSSti7=enBete=<08S32)
Air Documonti Division, InrolllQonco Dopartmont Air Matoriol Command
Ala TECHNICAL iMDtUl Wrf0rrt.Pul1mt.il Air Ferco Doso Dayton, Ohio