,

CONFIDENTIAL

Copy No . 2~3

RM No. L7E08

RESEARC MEMORANDUM

MEASUREMENTS OF THE EFFECTS OF THICKNESS RATIO AND ASPECT

RATIO ON THE DRAG OF RECTANGULAR-PLAN-FORM

AIRFOILS AT TRANSONIC SPEEDS

By

Jim Rogers Thompson and Charles W. Mathews

Langley Memorial Aeronautical Laboratory Langley Field, Va.

CLASSl1'lEDDOCl1MElrr ~LASSIFICATIQ] C::A:'GED TO Thls document cont&1na clu.Uled lnformaUon

affect1ng the NaUonal Defense of lhof> United

~~ooo'",'i\"",:·;:~o:~=~ASSIFIED DATE 8-1 -54 revelaUon of Ita contents 1n any mlUUler to an unaulbortz.ed per80D 1a prohibited by law. lnfonnatloD !IO claaaified may be tmp&rt.ed

onll to peroono '" the military f't"I'i0 0LoIT'l' Ht, J. W. CltOWLEY services of the United Stales, app ~ n .1 J.':U."l. • civUian QUlcers ani employees of Ulo Federal Governm@Tlt wbo M ..... l~u.mat. lnterelt therein, W to United Stales clUzena of lmowc

=!~~~~lIOnwho or """.Sldt, ;FfA'NG E NO. 2348 E • LB.

NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS

WASHINGTON June 20, 1947

fI<' ~.: ( CONFIDENTIAL

https://ntrs.nasa.gov/search.jsp?R=19930085663 2020-04-21T12:37:36+00:00Z

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NACA RM No. L7E08 CQ!llFIDENTIAL

NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS

RESEARCH MEMORANDUM

MEASUREMENTS OF THE EFFECTS OF THICKNESS RATIO AND ASPECT

RATIO ON THE DRAG OF RECTANGULAR "PLAN -FORM

AIRFOILS AT TRANSONIC SPEEDS

:By J'im Rogers Thompson and Charles H. Mathe1vS

SUMMARY

As part of an 1nvestigation to determine the effect of variation of the basic airfoil parameters on airfoil drag characteristics at transonic and supersonic speeds, a series of rectangular-plan-form airfoils having aspect ratios of 7 ·6 and 5.1 and having NACA 65-006, 65-009, and 65-012 sections have been tested by the free-fall method. In the present paper results are presented for two airfoils of the series (those having NACA 65-012 sections and aspect ratios of 7.6 and 5.1) and are compared ivith results for other airfoils of the series ivhich ivere reported previously.

The results shovred that for the airfoils of thickness ratio 0.12 the effect of reduction of aspect r atio was the same as that previously determined for the airfoils of thickness ratio 0 .09j reduction of aspect ratio delayed the occurrence of the drag rise by about 0.02 Mach number and reduced the drag .. at speeds above the drag rise.

Comparison of results so far obtained indicated that reduction of airfoil-thickness r atio from 0 .12 to 0 .09 or from 0.09 to 0.06 delayed the occurrence of the drag rise by ebout 0 .02 Mach number; this delay was about one-half the concomitant increase in the theoretical critical Mach nunilier of the airfoil section.

At sonic and low super sonic speeds the pressure-drag coefficient wa.8 found to vary in proportion to the square of the thiclmess ratio between values of thiclmess rati o of 0 .09 and 0 .12 but betiveen values of thickness ratio of 0.06 and 0 .09 the exponent was somewhat less than 2.

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2 CONFIDENTIAL NACA RM No. L7E08

INTRODUCTION

One of the problems encountered in the design of a transonic or supersonic air plane of any fixed configuration is that of selecting the thickness of the vTing section so that ad.equate structural strength and a safe landing speed. may be obtained vTi thout penalizing the airplane in high-speed fli[Sht by excessive vring drag. It is ,.;ell knmm that the bes t comb ina tion of strength and landing speed is obtained by use of r ela ti vely thick "iings; however, thin -airfoil theory for supersonic speeds (reference 1 and many other papers) predicts that for unswept vrings of infinite aspect ratio the 'vine; drag is pr opor tional to the square of the airfoil-thickness ratio. Thus a small r eduction in wing thickness would result in a cons iderable saving in supersonic wing drag if the theory vTas directly applicable.

In order to provide information on this and other basic problems encountered in the design of transoniC and super sonic airplanes, the Natlonal Advisory Committee for Aeronautics has instituted a general research program on the draG characteristics of airfoil sections, wing plan forms, body shapes, and Wing-body configurations at transonic and supersonic speeds . As part of this program, measurements have been made of the drag of NACA 65-006, 65 -009, ~~d 65-012 airfoils havinG rectongular plan forms of tyro different aspect ratios. Resul ts obtained for the 6 - and 9 -percent-thick airfoils are reported in references 2 to 4 and results for the 12-percent-thick airfoils are presented in this paper.

DraG results for the anfoils having NACA 65 -012 sections are presented as ct~ves showing the variation of drag coefficient 'vith Mach number in the transonic speed range. These results are compared vTi th the results of references 2 to 4 to determine the effects of thickness and aspect ratio on the airfoil drag. Although supersonic thin -airfoil theory doe s not dir ectly apply to the test results presented because of the ro\mded airfoil nose (resulting in mixed subsonic "supersonic flmvs occurring on the airfoil) ; finite thickness and . aspect ratio, possibility of separation effects; and so forth, the test results are compared ",ith the theory to provide some information on the importance of these differences.

The tests were per formed by the FHght Research Division of the Langley laboratory by means of the freeJ.y-falling-body method described in references 2 to 4.

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NACA RM No . L7E08 CO~'FIDENTIAT.J

APPARATUS AND METHOD

Test body and. a i rfo11s . - The general arrangement of the test configuratlon is shovm by the photograph (f ig. 1) and the o.etai l s and dimensions are shown on the line dJ.~aving (fiG' 2 ). The two test airfoils had r ectangular plan for ms and NACA 65 -0J.2 sections

3

of 8-inch chord; the over -all span of the front airfoil 'vas 60~ inches

and tha·t of the rear airfoil ,-ras 40t inches. The aspect ratios for

the test airfoils (including that part of the airfoils within the body) were 7.6 and 5. 1. The test airfoils entered the body through

rectangular slots 9~ inches long ano. 1 inch ,·,ide as did the airfoils

of r eferences 2 to 4. The body on which the airfoils were mounted had a flat base and was identical with the body used for the test of r ef erence 4. The body differed from those used in the tests of r eferences 2 and 3 only in that the short tail fairing used on the previous test bodies was replaced by the flat base.

MeasuromeI1ts .- Measurement of the desired quantities was accomplished as in previous tests (references 2 to 4) thr ough use of the NACA radio-telemetering system and radar and phototheodolite equipment . The following quantities were recorded at two separate ground stations by the telemetering system:

(1) Force exerted on body by each test airfoil as measured by a spring balance

(2) Total retardation of body and airfoils as measured by a sensitive accelerometer alined with longitudinal axis of body

A time history of the position of the body ,·ri th respect to ground axes during free fall was recor ded by r adar and phototheodolite equipment, and a survey of atmospheric cond.i tions applying to the test was obtained from synchronized records of atmospheric pressure) temperature , and geometric altitude taken during the descent of the airplane from "Thich the test body was o.ro:pped . The direction and speed of the horizontal component of the "Tind in the range of al ti tude for which data are presented ,·Tere obtained from radar and photothedoli te records of the path of the ascension of a free balloon.

Reduction of data.- As in the previous tests) the velocity of the body vi th respect to ground axes) hereinafter referred to as ground velOCity) was obtained both by differentiation of the flight path

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4 C01'J7IDENTIAL NACA RM No. L'(Eo8

determined by radar and phototheodolite equipment and by integration of the vector sums of gravitational acceleration and the directed retardation measured by the longi tudinal acceler ometer. The true airs:peed was obtained b;)l vectorially addi113 the Srolmd velod ty and the horizontal wind velocity measured at the appropriate altitud.e .

The drag D of each 8.irfoll W'as obtai.ned from the relation

R measured reactlon betw'cen airfoil and body, pounds

\-IT il8iGht of airfoil assembly supported on spring balance ) pounds

ae readin3 of accelerometer (retardati on), g

The atmo pheric pressure P: the temperature T, and the airfoil frontal ar ea F were combined ,v-t t h siml..'.l taneous values of true a i rspeed and airfoil drag D to obtain Mach number M and t he ratio D!Fp . . Values of conventional drag coefficient CD"" were

li

obtai ned from the r elation

"There the ratio of coefficients base' the va.lues of CD:F

D/Fp =

speci fic heats I "Tas taken as l.h. Drag on plan area CD ,.;ere obtained by multi plying by the r atio of frontal area to plan area. Areas

used did not include that area enclosed ,'Ii thin the body.

RESULTS AND DISCUSSION

A time history of important quanti ties obtained in the present test is presented as figure 3·

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NACA R.'v1 No. L'lE08 CO};""FIDENTIAIJ 5

The grOlli"'lC, -veloci ty data obtained from each of the t,·!O independent methods of measurement are presented in fiGure 3j the data obtained from the acceleroraeter are shmm as a dashed line and the data obtained from the r adar ~nd phototheodolite equipment , by the test points. The radar and phototheodolite o.ata are evenly distributed about the accelerometer data but contain a scatter somewhat lar3er than usual for this equipment. This scatter results from partial fai lure of equipment during the test, ",hich necessitated. use of a less precise a'uxlliary recordi ng device. Velocit;y data from the r adar and nhototheoCl.oli 'ce eaUi']Jm.ent E!.re not 'pre sented for the last 6 seconds ~f the free fal l ;'8 t .hs photoeraJ?h~ , which normally allm., corrections to be made for cmall tracking errors J \·T81'e not obtai ned during this period. 'rne true airspeed ilas obtained from the ground veloci ty by use of the ,nnCl. data ana. is shovm on the time l1istory by a sol id line. The Mach nwnber was calculated from the true airspeed and temper ature data and i s be l ieved accurate vIi thin to .01.

The results of the airfoi2. drag measurement.3 are summarized in fiGure 4 where ClU'ves are presented lihi eh ShovT the measured variations of D/Fp, CDn: and CD for the airfoils having rffiCA 65 -012 sections

1:'

and a spect ratios of 7.6 ffild 5·1.

Inasmuch as the spri ng balances with \-Thich t he airfoil dra3 force s are measured must 'I-lithstand the high drag forces occurring at supers oni c Mach n !D1bers and high pressures (1m·, alt:L tudes), they are neces sarily relat i vely insensitive to the small drag forces occQrring at subcri tical Mach number s and 1m., :9r8ssures (high altitudes ). The drag parameters are therefore les8 accurate at the lov.res t Mach numbers for \,Thicll data are presented than at 8upersonic speeds ",here the draG is hi::;h. The values of t he r atio D/FP are believed to be accvrate 'Ioi'ithin about 10.012 at M = 0.8 and to vrithin 10.007 at M = l .ll ~. Correspondin,7, values of C are wi thin +0.003 - ~ D -at M = 0 . 8 and vi thin to.0025 at 1 = 1.14 . Thes e values correspond t o an el'ror in dre.g mea urement of about 1 11ercent of the full -scale ­balance ranee for values of D/'F?; hOI-rever ; the values of CD include

an adcU tional increment ('IoThich is appreciable only '. when CD 1s large)

due to the possible uncer~~int- ir- Mach number of ±0 .01 .

The drfl£ of the f r ont air foil exceec.ed the renge of the drag balance about 6 seconds before iLllJ?act (8ee fi g . 3 ). No Significant da ta were lost,hmrever, as the Mach number did not j.ncrease appreciably after thi, time .

The Q- "curves of figure 4 8hmV' that for the front airfoil Fp

(aspect ratio 7.6) the drag r ose from 0.02 of atmospheriC pressure

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6 CO:r.J""FI DENTIAL NACA RM No . L7E08

per unit of f r ontal ar ea at M = O.ee to 0·50 at M = 0.97 and then incr eased at a slover r ate to 0 .68 at M = 1.14. The dra5 of the r ear airfoil. (aspect ratio 5.1) rose from 0.02 of atmospheric pressure per unit of frontal area at .M = 0 . 84 to 0.45 at M = 1.00 and then increased to 0.67 at M =; 1.15·

D The - -da ta of figure 4 ar e compared in figure 5 vri th results

Fp obtained in previous free-fall tests of airfoils having NACA 65 -006 and 65 -009 sections . The as:l?ect r atiO, airfoil section; and r efer ence from whi ch these data vere t aken are g iven in tabular f orm in the fiGure . Examinati on of this fiGure r eveals that the curves are sim:l.lar in s hape ana. are nearly parallel during the abr upt rise which char acterized the curves at Mach numbers just belml 1 .00 . I n thi s paper the difference in Ma ch number bet"reen these par allel portions of the drag C1..:lrves is defined as the drag ­r ise delay. It is apparent that reduction in aspect ratio or thickness ratio is effective i n delayine; the clrag r ise to slightly higher Mach number s j r eduction in aspect r a ti o from 7·6 to 5·1 delays the draG rise by about 0.02 Mach ntunber J and reduction of the airfoil ··thickness r atio from 0 .12 to 0.09 or from 0.09 to 0 .06 de l ays the drag r ise a simHar amount. Th e drag-rise delay r esulting f r om reduction in airfoil thicknes s is about one -half the concomitant increase in the theoretical critical Mach number for the air foil section.

The drasrrise delays resulting from reduction of aspect r atio and thickness rati o are r e2.atively small l"i th respect to the over-all accuracy of Mach nuniber measurement ("'i thin to .01) . The results presented herein show, hovlever" that the magnitude of the drag -rise delay due to reduction of aspect ratio reported in reference 3 for airfoils ha ving NACA 65 -009 section s is about the same ('vi thin the limi t of accuracy of the te s ts) for "Tings having NACA 65 -012 sections .

For application to practical air plane co~SiGurations J the magnitude of the drag -r ise effects presented herein may requi re some modification to account for the effect of the o:gen slots through 1-Thich the air foils entered the body . '1'he effect of these slots is not knovm but is bel'ievec1. to be small . In additi on f or the airfoils having NACA 65-012 sections, a small effect on the drag of the airfoil of aspect r atio 5·1 results from its location to the rear and at a r ight anGle to the air foi.l of [.spe t r atio 1.6 tested on t he same b ody . Previous ;~est8 (references 2 and 3) 1"here identical air foiln wer e tested in the t1VO positions showed TJ11iximum discrepancies in the region of the drag rise of the order of 0.01 Mach number , the or c.er of accur acy of the Mach number meas ureyaent .

CONFIDENTI AL

NACA RM No . L7E08 CONFIDEl'J'I'IAL 7

The varJation of airfoil total -drag coefficient CD vri th

thickneE'·s r atio tic is sh01m in fiBure 6 . For the airfoi l s of aspect r atio 7.6, an increase in t hi cImess ratio from 0 .06 to 0.09 resulted in an increase in d~~J coefficient froID 0.032 to about 0.055 for Mach numbers in the ranGe from 1·00 to 1 .15 . In t he same Mach number range ; an i ncrease in tili cImes s ra ti 0 from 0.0.9 to 0 .12 resulted in an increase in drae coeffi cient from about 0.055 to 0 .090 · Similarly) for the air foil of aspect r atio 5.1, an increase i n thickness r atio f rom 0.09 to 0.12 resulted in an increase i n drag coefficient from about 0.050 to 0 .085 ·

The variation of airfoil pres sure-drag coefficient Ctp with

thickness r atio tic is sho,m plotted in 10Barithmic form in figure 7 for Nll.CA 65 -serJes airfoils at sonic and lov supersonic speeds. Separate plots (figs . 7(a) and 7(b)) ar e presented for the two aspect ratios for vTbich measurements have been made . Airfoils tested in the front position on the body ar e used in figure 7(a ) but airfoils tested in the rear position are used in fie;ure 7(b) because of the limited an ount of test data available. An estimated fr iction -draG coefficient of 0 .006 has been subtracted from the data. to obtain pressure -dra..rl coefficients.

Thin-airfoil theory for supersonic speeds, as presen ted in reference 1 and in numerous other :papers, leads to the conclusion that for a gi ven Mach nunilier and airfoil section the presstrre-drag coeffic ient is proportional to ~~e squ~re of the airfoil -thickness r atio. This relation> \Thich may be represented in figtrre 7 as a straight line of slope 2, is arbitrarily j?laced on the figure so that it passes through the test points for a thickness r atio of 0 .09 . Examination of fiGure 7(a ) sholls that the test points for a thickness r atio of 0 .12 lie on the line of slope 2 thr oU0h the points of thickness ratio 0.09) but the test poLTlts of thickness ratio 0 .06 l ie some,.ha t above the line. Thus, in the r B.l16e of 0 .09 to 0 .12) the drag coefficient varies Ivi tll t..l1iclmess r atio about as the square of the thickness ratioj wherea~ in the r anDe from 0.06 to 0.09 the exponent i s someiihat smaller.

Similar results are obtained for the Imler aspect ratio (fig. r(b) ) alt~ough the peints at thickness ratio 0 .06 are not directly compar able vii th the other d.a ta . These points, vThich are taken from r eference 5, appl:,' to airfoils h9.vin::; an' aspect ratio of 4. 9) NACA 16-006 sections)and used a s stabilizing tail surfaces for a body of revolution. As this air fo'l section is not a?preciably different f r om the NACA 65 -006 section and as in the -cest of reference 5 the effect of the location of the air foi l s partly in the 'vake of the body may be presumed to be l imited to a slight reduction

CO:NFlDENTIAL

8 CO:NFIDENTIAL NACA RM No. L7E08

in the drag of the airfoils, the location of the test points from reference 5 above the line of slvpe 2 in fi~tre 7(b) provides additional confir mation of the result observed in figure 7(a).

Thus, if the a ssumption of a constant friction-drag coefficient is valid, the experimental results show the same variation of pressure­draB coefficient vTi t h thickness ratio for the thicker airfoils as that indicated by thjn-airfoil tp.eory. The theory is not strictly appH cable in this case J ho\iever) because of the rounded airfoil nose (resultin:] in mixed subsonic -super sonic flows occv.rring on the airfoil), finite thickness and aspect ~atios , ~~d so forth. As prelinU.nary consideration of the pl'oblem indJ. cates t hat an ac.di tional variation of pressure -dre·G coeffi cient ui th thickness ratio miGht result from other sources of pressure draG not considered in the theory (separation, for example), no conclusion can be reached concerning the applicabi lity of the theory .

It is considered desirable that further research be performed to determine , .. hether the variation of draB coefficient vTi th thickness r atio here obtained is valid a t Mach numbers beyond the l ow super­sonic r ange J for thickness ratios smaller than those already tested., and for other airfoH secti0 1s and plan forms (particularl;')' the so -called "suyersonic" air oil sections) . If the trend here indicated at lov thiclmess r atl03 is found to be generally applicable, the large savings in vring -rag "Thj.ch are estimated by means of supersonic thin-airfoil theory to result from reducing the airfoil-thickness ratiO ,muld be consio.erably reduced end the design considerations in regard to use of extremely thin "'Tings on supersonic aircraft could be modified .

CONCLUDING REMARKS

Measurements have been :.:nade by the freely fa.lling body method of the drag of' airfoils havh1.S NACJl. 65 -012 sections and rectangular plan forms of aspect ratio 7·6 and 5 .1. Compari son of the results presented herein i-1i th r esults of similar meaSl .. 1.rements of the draG of airfoils which had NACA 65-009 sections and identical aspect ratios and of an airfoil "\<Thich had NACA 65 -006 sections and an aspect ratio of 7.6 8hm-TS that :

1. Rec.uction of aspect rati o from 7.6 to 5.1 delayed the occvxrence of the drag rise for the airfoils havinc NACA 65 -012 sections by about 0.02 iach num.ber and reduced the drag throue;hout the explored Mach num.ber range. These results are in a.greement with previously reported results for airfoils havi ng NACA 65 -009 sections.

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NACA RM No. 1 'lEO 8 CONFIDENTL41 9

2. Reduction of the thicknesJ ratio of NACA 65-series airfoils from 0.12 to 0 .09 and from 0.09 to 0 .06 also delayed the occurrence of drag rise by about 0 .02 Mach number. The drag'Tise delay ,,,hich resnl ted from reduction in e.il'foil - thickness rat:Lo ,.ras about one ­half the concomitant increase in the theoretical critical Mach number for the airfoil section .

3. At Mach numbers from 1.00 to 1 .15 the pressure-dras coeffic ient increased in proportion to the sQuare of the thiclmess r atio between thickness r a-t:!..os of 0.09 and 0 .12 but increased in proportion to a sommrhat smaller power of the thickness r atio betvreen thickness ratios of 0 .06 and 0.09. F'lU'ther re3earch should be performed t o deter1l1ine vlhether the variation of drag coefficient vli th thickness ratio herein presented is valid for other airfoil sections and at hit:;her Mach m.:unbers and "rhe ther the trend is contim'.ed at thickness r atios 10l·;er tban thos e so far tested.

Lru1sley Memoria.l Aeronautical La'boratory National fldvisory Comni ttee for Aeronautics

Langley Fiel d } Va.

10 CO:NFIDENTIAL NACA RM No. L7E08

REFERENCES

1 . Lighthill, M. J.: Two-Dimensional Supersonic Aerofoil 'Theor y. R . &. M. No. 1929) Bri tisl! A.R . C " 1944.

2. Mathews, Charles Vl" and Thompson, Jim Rogere : Comparative Drag Mea sl) .. rements at Transonic Speeds of RectMgnlar and S,.,ept ­Bacl~ NACA 651 -009 Airfoils Mounted on a Freely Falling Body.

NACA ACR . No. L5G30 , 194·5 ·

3 . MatheYTs , Charles 1-7 . , and Thompson) Jim Rogers: Drag Measurements at Transonic Speeds of NACA 65-009 Airfoils Mounted on a J!reely Falling Body to Deterllline the Effects of Sweepback and Aspect Ratio. NAGA RM No . L6K08c, 1947 .

4 . Thorr.ps on, J im Rogers) Emd Marchner , Bernar d W. : Compar ative Drag Heasurements at Transonic Speeds of an NACA 65 -006 Airfoil and a Symmetri cal Circular-arc Airfoil . NACA RM No . L6J30, 1946 .

5 . Bailey, F . J. , Jr., Mathews, Charles vL, and ThoID:pson, Jim Rogers: Drag Measurements at Trans onlc Speeds on a Freely Falling Bodj". NACA ACB No . L5E03 , 1945.

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NACA RM No. L7E08 CONFIDENTIAL

Figure 1. - Three -quarter front view of airfoil test body.

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Fig. 1

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40 I CENTER- OF' Gl'?t9VIT~1 ~ LOCATION

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NATIONAL ADVISORY COMMITTEE fOR AERONAUTICS

/iIRFOIL - SECTION COORDINIf/E oS (NACA 65-012 SECTION)

X Y X Y X Y .CVO .000 1. 600 .3.S18 5200 .352

.0-10 .074- e.ooo .-132 5600 .Res

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1. ZOO .352 -1.800 .89tl L.E. RADII./S : 0.080

Figure 2 . _ General arrangement and dimensions of airfoil test b ody . All dimensions are in inches .

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Fig. 3 NACA RM No. L7E08

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CONFIDENTIAL J 1

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NACA RM No. L7E08

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Fig. 4

Figure 4.- The measured variation with Mach number of drag coefficients and D/Fp for airfoils having NACA 65-012 sections and aspect ratios of 7.6 and 5.1.

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Ftgure 5.- Comparison of free-faIl-test results for NACA 65-series airfoil sections.

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Figure 6 .- Variation of drag coefficient with thickness ratio for ACA 65-series airfuils at low supersonic Mach numbers .

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Figure 7.- Variation of pressure-drag coefficient with airfoil-thickness ratio at low supersonic Mach numbers. Data are taken from references 2 to 5 and from the present test.

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NATIONAL ADVISORY COMMITTEE FOA AERONAUTICS

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