L-

.-

.

FOR AERONAUTICS

WARTIME lBIIIBOIU” ORIGINALLYISSUED August1945 = AdvanceConfidentid.ReyortL5G31

A SIMIZE METHODFOR ESTIMATINGTJmmNAL vmOOm

INCLUDINGEFFECTOF COMPRESSIB- ON

By ReLph P. Bielat

Laugley-. Memorial.Aeronautical.Laboratory LangleyField,Va.

NAC-A ., . ... &$!.4.(:.4 ~~~p/~~f LMVGL.E~-~.. WASHINGTON . -.~.tfIg.?~.4~.,! ~~[ja&A~ ~~t-~:, ‘-~@?ATo~y NACA WARTIME REPORT’Sarereprintsofpapersoriginallyissuedtoprovick%dpfdFdi.i@~$utionof advanceresearchresultstoanauthorizedgrouprequiringthemforthewar effort.Theywerepre- viouslyheldundera securitystatusbutarenow unclassified.Some ofthesereportswerenottech- nicallyedited.AU havebeenreproducedwithoutchangeinordertoexpeditegener~distribution.

L-78 ...______--______------__-- 3 1176013542007 X...... -.r

ADVANCE CONI’IIE?NI’IALREPCIR!!

A SIMPLE NETHOD FOR RSTIMA’TIJNG‘TdRMINAL VELOCITY

INCIX?DING EFFiWT OF COMPRESSIBILITY ON DRAG

By Ralph P. Bi,elat

EmmlMY

A generalized drag curve that provides an estimate for Eke drag rise 5.zeto compressibility has been obtained from an analysis of wind-tunnel data of several airfoils, i’uselagesj nacelles, and windshields at speeds up to and above the wing critical speed. The airfoils analyzed had little or no sweepback and effective aspect ratios above 6.5. A chart based on the generalized Cwag CUrVe is ~rese~~ea~ from which the ter:~inal v~lo~i’b~ of a conventional airplane that employs a w~-ngof’moderate aspect ratio and very little sweepback in tivertical c!ivemay be rapidly esti- mated, In order to use the chart, the only data that need be known about the airplane are a low-speed ~ the wing critical speed, and the v~in~ loading. The terminal velocities for three airplanes were computed in order to il~ustrate the use of the w,ethod and chart. Good agreement between the esthnated terminal vel.oci’tyand the measured flight terminal velocity was iridicated~or all tkwae airpl.an.ese

INTI?ODTJCTIO?!J

Sever&l high-speed military airplanes in dives have encountered difficulties that could not be easily con- trolled by normal means. These ~,ifficultiesj which may consist of’ diving momentsj large c:hang’esin trimj large stick forces, tail buffetin~, and the like} occur in high- speed dives when the speed of the airplane exceeds the critical speed by a large amount, l’or those airplanes for which m.axhm diving speeds are at or near the critical speed$ little or notrouble occurs. l%e More recent fighter airplanes, however, have terminal Mach- numbers well in excess of the critical Mach number and, as a result, often encounter difficulties in di.~-esbI)eterrni.-‘ nation of the terminal velocit:r of the airplane is there- fore import~.ntin or&4er.that t“? probabili~y of encoun- tertng trouble irldive’smay e ~~ti~L&itedb ● 2 MICA ACR NO. L5Cr31 ✎

The pro”~lem 0:: determ~rling t~w te:”x.:”ln:ilvelgclt~ for ., airplanes for which t:he terminal velaci~y is near the critical speed Is comparatively simple :.naswch as a cGn.stant value of d.ra~ coefficient can tie:assumed. The . diving speeds of most present-day airplanes, however, occur beyond. the critical spee-dand the ~~~bl~:~i is”not so simple. The fallowing two factors ape involved~ (1) the determination of the critical speed and (2) the rate...of‘ drag increase at speeds above the critical speed.

The critical speed used herein was ar?xttrarlly’taken as the critical speed of the wing-root section. Pres3ure- distri’rution data obtained from wind-tunnel te~ts..were used to determine the critical speed, which is defined. as the flight speed at which sonic vel~ctty is reached locally. Tf’experimental data are not available,.ho_wemn?,- the method; outlined in references 1 and 2 can be used for the determination of the c~itical speed. Selection. . of the critical speed at the wing-roGt section for use in terminal-velocity estimation is justified on the-Srouds. that the root section usually has a lower critical speed than any other component part of’the airplane. “The ~Jig.& . root has the lowest: critical speed because of..its..hghgh * thickness ratio and contributes a large part of the total airplane drag because of the large fraction of the “~~ing. area concentrated at the inboard sectio.nsd tapered,wings, ●

The rate of drag inc~eme at speeds above the..c~iti- cal speed is more difficult to determine in the calculation of the termj-nal velocity than the critical speed. A study of t-hedrag of airi’oiis, fuselages, nacellesj and windshields has been made froi~wind-tunnel test data in order to determine the effects of compressibility on the tirag. Eecause the rate of’drag increase at speeds above the critical speed is so great, it was found that, within the accuracy required for terminal-velocity calculations, an average rate of’drag increase may be used. ● A curve indicating the average rate of drag increase is presented herein. !I%is curve was derived from an analysis of wind- tun,neldata.

!?hemethod described herein,for obtaining tb.etermi- nal velocity of an airplane in a vertical dive has been in use at the NACA since 19)41. Publication of the method, howevm, had been delayed pending the investigation of constriction corrections to be applied to ~he wind-tunnel data and the completion of high-speed dive.tests made with several airplanes in order to compare terminal velocities obtatned in flight with terminal velocities estimated by the simple ineth-oddescribed herein. ThiS method is not applicable to airplanes that utilize wing shapes of low-aspect ratio and. large sweepback but should be applied only to airplanes of’ conventional design that employ wing shapes of m-oderate aspect ratio and small amounts of sweepbac7k due to wing ta-gerratio.

SYMBOIJS

v velocity a speed of sound in air M Mach number (V/a) CD drag coefficient

CL coefficient

P mass density of air s wing area W weight of airplane

P atmospheric pressure at any altitude

. . Y ratio of specific heats (1.1}0for air) . t\c ratio of thickness to chord of wing Subscripts : Cr critical (when local. sanic vtilocityhas beei~ reached on some point of body) mir& minimum T terminal

lL5.rfoilmJdels.- Tk.e dirfoil mod~ls used herein repre.s~nt tw~c=es c:?airfoils - nwfiel-y:the conven- tional j!YACAsections and ‘he,,. rr}mrerecent lmw-drag high- critical-speed WCA sections, The conventiorial N1.CA air- foil sections are characterized by pressure c!istributions that have high peak pressures occurring near the leadtng edge. The lo-w-dragNACA airfoil’ sections have co?nnar&- tively flat pressure distributions with the peak pressures occurring at approximately 60 percent of’the chor~ behind . the leading edge, Airfoils typical of the conv~ntio~-~l airf~ils sine t~.eNACA 0009-65, 0012-63, 2~012, and 2zOl~.T sections; a current transport-model airfoil that has an NACA ?215 section at the rcotiand tauers to sm NACA 2212 section at the tip; an~,the Davis air?oil with a ttd.ckness ratio of 20.15 percent. The low-drag airfoils inclde the following NACA airfoil sections: 1{..-23.5 lc$-yl~ 16-515 ~.~-215 65(21S)-220 The effective aspect ratio d the airfoil models tested varied from 665 tO ir~f’illity. ~~s~l~~e models.- Tk.efuselage models are ty~ical of : fuselrg~snapes in use on current airplanes. The various fuselages represent bomber, fighter, and transport air- planes. 3’igure I slhov~sthe side-view drawing and the . fineness ratio in side elevation of the different fuselage shapes. These fuselage models were tested in conjunction with wings (shown as ~-~shed lines in fig. 1) and represent a wide variation in @l-ni&%W?81!!l&!interference. NACA .ACRNO . L~G~l 5

Nacelle and windshield models .- The data f’orthe various nacelles and ]v~ndshields were obtained from refer- ences 3 and ~.,respectively. The nacelle and windshield designations used herein col’respond to the designations used in references 3 an~.4, All the nacelle models were tested wit-n the same wing model; which consisted of the outboard panel of a wing section designed for use on a bomber airplane. Tke wing was a thiclclow-drag airfoil that had an NACA 65(21-8)-222.section at the root .m.d tapered to an NACA 66(2x15)[email protected] section. at the tip. Tile windskdelds were tested’with a wing-fuselage combination. Drawings of the nacelle and windshiehl models are shown in figures 2 and ~, respectively.

RESULTS AND DISCUSSION Erag Charactei~istics

Drag “anal;ysis.-In order to obtain a correlation of the r~~o~ drag increase at speeds a“oovetb-e critical speed, the drag results for the various component parts of the airplane have been reduced to nondimensional param- eters; that is? CD l~~in is plotted against I~l~Mci* for each part tested. The use of these parameters represents a convenient method of’making the data non- dimensional in such a manner that the unknown quantities are expressed in terms of the known quantities.

The drag results at speeds up to and above the criti- cal speed for the conventional HAGA airfoils are presented in figures ~-and 5, ~lj.gupe~6 to ~ ShOW the,variation of cD/C~nin with M/Mcr for the low-drag high-critica.l- speed airi’Oi,l.S.It w;ll be noted that all tk.eairfoils presented in figures ~~, 6, 7, and.8 exhibited approxi- rnate.1y t’hesame rate of drag increase at speeds a’hove the critical speed: for this reason a curve of the average rate of drag increase at speeds akove the critical speed maybe used. An average increase in drag of approximately 30 per- ,. -. Tit “ — = i.O; &eht above the mini~ww. drag was indicated at ~cr “: at speeds of o:al.y10 to 15 percent above the critical speed> b-owever, the drag increased:ap~roxirnately ~0 to 200 percent. This rapid increase in ~dag at speeds above the critical speed is associated ‘with the formation

. 6 KACA ACR No. L5G31

Of compression shock waves and their affect on the hound.ary layer over the surface cf the airfoils. The faintly of ai.rfoi.ls used in fi,~ure ~ showed less percentage of i.i~crease in drag at the critical speed than tke iWC~ 0009, 0012, or the low-drag high-critical-speed airfoil sections. Both published (reference 5) and un~~blished high-speed data show tb.atthe NACA 230-series airfoils differ from most of the other airfoils in that the critical speed can be excseded by as much as 0.15 in Mach number before any serious changes in the aerodynamic charactei’istics of the airfoil occur. The cr:tical speed of the NACA 230-seri.es airfoils is therefore exceeded by app~o:~imately 7* percent before the same ,pm?centage of increase in drag oc&s as is shown for t“he other airfoils. The i,mport~nce of this difference in the shape of the drag curve above the criti- cal sneed on the estimation of terminal velocity is dis- cussed i.nthe section entitled ‘lq!emfiinal-Velocit:$Calcula- tion.l!

The rapid increase in drag tiefore the critical speed is reachedj which is shown for the NACA 67-LI~.Ij airfail in figure 9, is due to early separation of the f?low ~ver the af’tergortion of the airfoil. This candition also affects the method f~r estiraating the terminal velocity, An error in.estimating the t~r~i.~al velccit~ when tine flow separates will occur only for those airplailesfor whi,ch terminal velocities are at or ne~r trie critical speed; this separation of flow will not appreciably atfect the determination of the terminal velocity for high- perf’ormance airplanes for which t?.e-terminal velo~ity occurs at s~eeds well above tb.e critical s~peed.

Figure 10 sb.ows the variation of cD/C~:in with M/Mcr for several fuselage shapes and fineness ratios, The drag increments for the nacelles and windshields tire presentad, in figures 11 and 12, respectively. The criti- cal spezt,sfcr these bodies were based cn the wings ~i~ith which- ~.~~e~l~~-els~~er~ tested and were determined for the wing-root juncture. The effect of compressibility on the rate of drag increase at speeds above the wing critical speed.for these bodies is similar to that for the air- foils m

Xn the correlation. of t~-e(average drag increases of the vario~~s compo~-entscf’the a~-:~:~lanetbq~~?:~ha~tthe Mach number range, a generaiize,d drag curve was derived .. N#.CAACR No, L5G31 ~ 7.

and is presented in figure 13. The data presented in f’lgures ~., 6, 7, s, 10, 11, and 12 were used to obtain tb.egeneralized drag curve. The Generalized drag curve is an average of the drag data for the airfoils, fuselages, nacelles, and windshields at speeds up to 10 percent above the critical speed. Only the average drag of the airfoils at speeds from 10 to 15 percent above the criti- cal speed was used. The generalized drag curve was extra- polated by use of a straight-line extrapolation from 15 to 25 percent above the critical s~eed. The straight- line extrapolation is believed. to be sufficiently accurate for estimation of the terminal velocity in this region where the drag rises rapidly due to compressibility effects.

Constriction aortiect.ions,-Clorrections for constriction effec~s have been applied. to the data. The constriction corrections have been determined from pressure measure- ments obtained in the Langley 2)~-inc-nand 8-f’oot high- . speed tunnels on NACA 0012 airfoil models of various sizes, The magnitude of the corrections. applied to the drag coefficients amounted to less than one-half of 1 per- cent of the dynamic pressure q at low speeds and increased to approximately 2 percent of q at the criti- cal speeds and.to approximately 5 percent of q at a value of the Mach number below the choking speed of the tunnel. The carretctions to the Mach numbers amounted to approximately Cne-.”halfof these values. ‘The constriction corrections were such that the coefficients were reduced and t’heMach numbers were increased by the values stated. The greatest percentage of increase in correction, as would be expected, occurred for the models that had the largest ratio of ~iOdel area to tunnel area.

Comparison with flight data.- F’i~ure 11+.shows the variation of over-all drag co~icient with Mach nu_w.ber- for the XP-~1 airplane as-measured in flight and the variation with Mach number of the wing-profile drag at themi.d-semisp_anstation measured by the wake-survey method. These flight data are p~eliminary as corrections to the data have not been applied. The results obtained by use of tho generalized drag curve in estimating the drag increases with Mach number are also shown in fig- ure l~kfor comparison with the flight measurements of , over-all dra~ and wing-profile-drag data of the XP-51 air- plane. The curves for the wing-profile drag and the over- all airplane drag in flight be~i~ to rise r~ther steeply 8 -.~TAcAJ!.CRNo , L~Gjl ‘ at about the saw.e llach number, This l%ct tends ta justify the ass~lmption that the wi,ng-root critical speed iS a suitable criterion to use ia terminal-velocity calcula- ‘ tion.s. ‘Theest!mated drag derived from the generalized drag relation indicates hi:ker drag coel’f’icientsat Mach nt~.ber~ of approxi.rlatelyC.~~ to O.~J than arc shown for both the measured wing-profile drag and the over-all drag coel’ficients. Of more importance, however, Is the gaod agreement tihatis shown t’or the values obtafi.nedby use of the generalized drag curve and the measured flight data at Mach numbers greater than O.~~$ which is the region where the terminal Mach number usually occufis.

Figure 15 snows a comparison of Measured flight di-a and estimated drag for the XF2A-2 airplane of’?mferance z . An important difference in the drag curves occurs at Mach numbers around the critical Mach rwaber, lhe esti~iated drag fndicates lower drag co~fficients than do the flight measurements. T~~s ffifference is believed to be due to a combination d earQ shock formation on the cowling and. airplane-wing rongbnessj which ia believed to have caused some separation of’the flow. Good agreement is indicated between the flight measurements and the estimated drag in the region where the drag coefficients rise stee:ply,which is the re~gion that determines the terminal Mach number.

The generalized drag curve (fig. i3) nay be used as an approx~mation in determining the terrlinal velocity of an airplane in a vertical dive. The terminal velocity is reached wlx+n the drag of the air-plane is equal to the wei@at of the airnlane. The dra,gcf the airplane in a dive combines bot’b airplane and characteristics. ~n the present analysis, howeverj zero prope?.ler tb?ust is assumed and the propeller &aL20r thrust is therefore neglected. lit supercritical speeds tile drag or thrust cmsed by the propeller is considered to be negligible as compared with the drag of the alrnlane, particularly if the pilot throttles the engine an~ adjusts the propeller to a high blade-angle position. . .

The terminal velocity for zero-lift conditions is given by the relation . . . NAGA ACR ?To.L5G31 ~ 9

w2~ “VT= \~~cDI (1) Y or ~ in terms of the terminal Mach number %! with the speed of sound equal to \ ~, r

(2)

Equation (2) can be rewritten in the form

(3)

~,’vi where is constant for each airplane at the psc~min altitude for which MT is calculated and

‘lIT\ CTJ P =L— }~cr 1 C%in ( )

which is obtainable from the generalized drag curve. Equation (3) can then be solved for the parsmeter W Figure 16 shows solutions of equation (3) for psc~, - “ -LILL.L1 v{ various values of Mcr and P~c~in “

computations of the terminal velocity, the onlY data that m.~~stbe known about t’neairplane a~~ the min~mum 10 ,.

drag coefficient at zero (or approximately zero) lift caef’ficient or a low-speed drag coefficient whereby the

~Lini~&? drag Coefficient can be CO~13Utedby use Of the generalized drag curve, the wing cr~tical speed, and the wing loading: Values of’these quantities, all of which are used in calculations other than those for the terniinal velocity~ are easily obtained. With these values known 9,? w for a particular air~lane$ the parameter Cal -be ‘S%min calculated for different d.titudes; then, fop given. values w Of lf~r and — the terminal Mach number can be pscpmin’ obtained by use of’figure 16.

In order to illustrate the method of’obtaj.nin~ the terminal velocity graphically, the terminal veloci;i~s have been calculated for the XF2A-2, P-39E-1, and P-47 air- planes . The mrtin.ent data for these a~~plailas. are ~ive~~ in the following table: .

TMJJH-l

AIRPLANE DATA

—.. ——— ~ w 1 ]J I CD Airplanei cr min s ! !(lb/sq ft) —--J------r’——--——— +______i ~ XF2A-2 ~0.6+ (flight) ;0.022 (flight) I 26.1 -.-----l+. (c“rrected~.–—-—- -1 ——— P-39N-1 [@.6~5 {estimated) ,~0.01~ (estimated) ~ 34.1 .——- –-—~——” P-L7 jOa61+ ()~O.020 (flight) i 45.0 ~ ~ .69 (corrected) ~ I --— t J ,,.. bi BJ use of these data the parameter — As-! psfc~jllin com~u.tedfor each airplane. The use of figure 16 to * estimate the terminal Mach number is illustrated for tk~e P-i!L7airplane at 15,000 feet altitude. The variation of NACA ACR NO. L5G31 ~ 11

terminal Mach number with altltude thus obtained for the these airplanes is presented in.figure 17.

Also included ~n figure 17, for comparison with the estimated variation of terminal Mach number ‘with altitude, are records of flight data for the XF2A-2, the P-~7, the P-47C-1-RE, and the P-39N-I airplanes. The flight record for the P-~~C-l-RE ai~plane was obtained by the late Ma,jor Perry Ritchie in a terminal-velocity dive made at Wright Field in July 1943, The points represented by circles were obtained from a dive of a P-)+7 airplane made by a test pilot for the Republic Aviation Coi-poration. Unfortunately, a complete dive history is not available for this dive but it is believed that, had one been available, it would lnavefollowed a path similar to that obtained by the lake Major Ritchie for the P-~.7C-l-RE air- plane. It is further believed that the test points obtained at altitudes of 22~000 feet and 10,000 feet represent e~.t~y into and pullpout from the dives respec- .. tively. Data for the XF2A-2 airplane were obtained from reference 6 and the data for the P-59N-1 were obtained from dive tests made at }!es Aeronautical Laboratory. The s present method for estimatingthe terminal Mach number yields results that compare favorably with the flight measurements; the difference between the two is no greater

than 0.02 in Mach number. This method f’or estimating the terminal Mach number is therefore believed to be suffi- ciently accurate f’orusual engineering purposes.

The section entitled “Drag Characteristics\’ indicates that the NACA 230-series airfoils and airfoils similar to the NACA 230-series could exceed the critical speed by approximately 0.05 to 0.15 in Mach number before any important changes in the aerodynamic characteristics . . ~,f occurred. At -= 1.0, t’nerefore} the NACA 230-series Mcr airfoils and similar airfoils did not show the same percentage increase in drag as was shown for aimost all the other airfoils and for the generalized drag curve.

Since in the calculation of the te~linal velocity the critical speed of the airplane is based on the critical speed of the wing, it can be expected that for airplanes utilizing NACA 230-series airfoil sections or similar sections the estimation of the terminal velocity will be in error. IJ?the generalized drag curve is used in the estimation of the terminal vel.ocity~ the indicated wing **W...... ~;,L* 1 critical speed must be increased approximately 7- percent .. 2 . for the hTACA 230-series sectians. This correction was applied to the critical speeds of the P-).+7and X.F2A-2 air- planes (see table 1), since these airplanes.nave NACA 230- series sections. The das~.ed cmve on figure 17 for M~r = 0,64 is the result obtained if’the indicated criti- cal Mach number is used rathe; than the effective critical ]~ach n~ber, which is about 7L percent hiGher. 2

Langley.- Memorial Aeronautical Laboratory National Advisory ~o~littt?e for Langley Field, Va.

~:fi’~R~J~~~

1. Robinson, Russell G., and Wright, Ray H.: Estimation of Critical Speeds of Airfoils and Streamline 3od.ies. IJACAJ-LCR,March 194.0,

2. Heaslet, Max. A.: Critical Mach Numbers of Various Airfoil Sections . NACA Mm NO. )pm, 19L4..

3. Becker, John V.: High-Speed Tests of Radial-Engine Yacelles on a Thick Low-Drag Wing. NACA ACR, lfitiy 1942 e

I+. Delano, James E., and Wright, Ray E.: Investigation of Drag and Pressure Distribution of Windshields at High Speeds. NACA ARR, Jan. l~&.2.

5. Becker, John V.: Hi&h-Speed Nind-Tunnel ‘Testsof the NACA 25012 and. 23012-6~ Airfoils. iVACAACR, Feb. 1941,

6. Rhode, Ri chard V., and Pearson, H. A. : Observations CM Compressibility Phenomena in Flight, NACA AC!R No. 3D15$ 19430 .. No. L5G31 Fig. la-g

,.

. ,. (a)

~inen@s ratio, 10~3Z

(b)

~n en ess ratio , 6,65

(0

““fineness rafiO , 7.30

.. d .,

Fineness ratio , 6.14

(e)

5,60

(f)

fineness ratio , 4.75

.

* NATIONAL ADVISORY (9) i-’’22%--- COMUITTEE FORAERONAUTICS

Ei’nene5s ra+io , 3.30 * Figure / . – 5 id~ - view a!hawhg o-F various fuselage shapes.

. Fig. 2 NACA ACR NO. L5G31

——

Pb-k view profi Ie CircUfUr cross sect;om

e- d -3!L-3

A/acei/e / Nacek 2

Elliptical cross s~c +i’on Circular cross Sec+ion

-~~>. +~<-.

Nacek 3 Nate k 4 1 J

Circuk7r cross Section

Nacelle 5 NATIONAL ADVISORY 1~ COMMITTEE FORAERONAUTICS Figure Z.- ~Nac~Hes tesfed.

. .

Windshie/c# I-_A 3-H Q I I )

I I I

2-0”3 ~

, ‘4.0.3 A I NATIONAL ADVISORY COMMITTEE FOR ASRONAUTK6 x-I “LA Plcme A-A -oF -ulb wincish ie Ids is Iocu+ed u+ Same poSition on fuselage . .

Figure 3.- Windshields tes fed. (l)esignati’ons from reference 4.) Fig. 4 NACA ACR No. L5G31

,.

.. 3.0

2.8

2.6

Akfoi/ sec+oms 2.4“ / —— — ——— ——— —.— — 0009 -6S 2.2 —.. — -. mt 2-6a I

2.(I I [I i 1.8 ;

1.6 /

/.4

1*Z“ 4 HA./ < ~“ A+<. . Lo ‘- ‘+ 2 ~ — — - ‘1 NATIOWALADVISORY COMMITTEE~ ASROUAUTICS .3 ,4 .5 .6 .7 .8 .@ 10 Al L2 M/M=/- .. Figure 4.- Vurta?+’on of /-c? tio ca/c~m;n wh.% /Wk9&- f~ ~/4CA 0009 and 00/2 Qirfoi}s .

*.. “. ..* : .. ~-m 4

NACA ACR No. L5G31 Figs. 5,6 .. . . 18 ~ ‘--

L6 I Airfoil Sec%ons . /VACA 230/2 —— —. 2 30/4.7 / /!4 .—— — .— 2215(root) +02212 c+f@) / / t ,/ 4 /.2

A_ ~ / 10”‘-- ‘ ‘- ~ ‘ NATIONAL ADVISORY COMMITTEEFORAERONAUTICS .3 .4 .5 *6 ,7, .8 .9 10 L/ 12

Figure 5; - Vuriuflon d rq +io CD/CDmin with M/Mcr for +h-ee Conven%oncd iWCA airfoi/S.

*

\ i

16 Airfoil sectiom >NACA 16-509 .———.— / [4 16-5)S / /

12

/ ~ -_ — ~ / < 1.0 NATIONAL ADVISORY COMMITTEEFORAERONAUTICS w -. .6 .7 \ .3 .4 ,5 .8 “.9 10 Al AZ . . #:w%%#’’$3+r .

> , Figure 6. – Vcvn’u+ion of ra+t’o Co/CDm;n wi+h M~Mcr for A/AC14 16’509 Qnd 16-515 cwdoils. 77run 6/’ +/’oh fkd U+ 0./0 CA ord. Fig. 7a,b NACA ACR No. L5G31

.1

Airfoil Sec +ions IVACr4 66> /-[/5 .— — 47-215 .. ——.——— 670 -2}5 ——— — /6-215

M b

i6

/.4

/!2 1

~ !0 = = “ — — — —-~* ~ t NATIONAL ADVISORY J * COHMInEE FORAEIWJAUT~c~ .3.4 .5’ .6.7..8 .8 Lo L/ 12 , ..

NACA ACR NO. L5G31 Fig. 8 . . .

2.6

Im 1I Airfoil sections Z4 - . NACA 47-215 —. — 6~0-21!5 ———. —. 16-2i5 2.Z “ ,

II 20 \ II I I [8 * 4 /.6 // I / PI /!l .. [4 ‘ ,,4 / A‘/ 12 / 4 / / / \ A @ “ \ .Y — & p“ [0.‘ ‘ ‘- a’ ‘ ‘ NATIONAL ADVISoRy COMMITTEEFORAERoNAUTICS .3 .4. .5 .6 .7 . .8 .9 Lo 1./ 12 W-cr

w>. ....”. ?’~-”+m Figure 8 .- Vur;u+ioh of m+t’o CD]CD~in w/’fh M~Mcr for Sev~rffi NACA uirfoih . No +ransi+iofl. . Fig. 9 NACA AC!R~Oc L5G31 . .

..

Z8

2.6

M/Mcr

F;gun 9.- Variation of ratio CJCD o id% M/Mcp

for Davis U;rfoi/ czad &everal &?A Ulw’o;ls ● NACA ACR No. L5G31 Fig. 10 ‘

I I I I I I I I Fff.fe/uge fineoes 2.z (See fjg. d rarlo (a) /0.32 . .— — —————— ( b) 6.65 i 2.0 (c) 7.30I 111)!11 —-—– p; 6. J4 —--— -- 3.60 I —. --— --- (f) 4.75 —-— — !8

16 .

/.4 8

12

\

NATIONAL ADVISORY COMMITTEEFORAERONAUTI=

3 .4 .5 .6 .7 .8 .9 40 .lf L2 ‘/”cr

Figure 10 ● - Variation of rafio cD/cDmb WI% ?W/Mcr * fbr several Judage shape S.

b

, , Figs. 11,12 NACA ACR No. L5G31

., /.8 I /Vffce//e C.See /ig Z,) * 1 16 ——— ; .—— ——— 3 ——— — —--——- ./ /.4 : /

/2

1.0’ - NATIONAL ADVISORY COHIIITTEEFORAERON@TIGS ,3 ,4 ,5 ,6 .7 ,9 /.0 /./ Lz fwikgr

Figure // .- Vtmbfion of rwtio CDjCD~i~ wi+h &?~/WcP for several nacelle shapes.

2.()

[8 Wi%’shield (See $iu.3) 3-i-1 .— _ 3-/-2 —————— Z-O-3 —— —— 16 —-. —-- x- / /.4 L {4’,. / / 5Y/ /’ 12 //, ~ // / / / / ‘ + 2~“ ~ / ‘ /0 NAT 10NAl ADVISORY COMHITTEEFORAERONAUTICS ,3 ,4 .5 ,6 ,7 ,8 .@ 40 if /2 ~l~cf

Figure /2 .- Vuria+l”on OF ratio CD/ COmjj for several wi~c?shield shapes. NACA ACR No. L5G31 ., “Fig.’l3

58-

* t 5.4 r I .8 1’ 5.0 I I / 4.6 I I I 4.2 I I / 3.8 I / I –––-–– Exfmpfa+ed / 3.4 I / I 1 3.0 . 1 I I 2.6 /

2.2 / /

1.8 I

/ / 1.4 / /

1.0 NATIONAL ADVISORY COMMITTEE FORAERONAUTICS .3 .4 .5 .6 .7 ;8 .9 /.0 1,1 12 L3 MIMcr

Figure t3. - Getierwll’zed dkq curve. . ● &+aMmm . 1

Figs . 14,15 hACA ACR NO. L5G?1 ‘

OWFUIId~9, cL< az ,05 — —

Q .04 Q

f ● .% .03 .+u k g *O2“ u m A A g ,01‘ A A

MATIONALADVISORY COMMITTEEF~ AMONAUTICS

o .1 .2 .3 .4 .5 6 .7 .8 Mach number ~M

Figure 14.- Vi+riuf ion # rnea~umct P/i@h+ dbg U. estt’mated dmg w!fh ~A numhev- for X%51 @p/cme.

.05

,“9,04 enerolized drag curve

/ +- ~ j / .. .03- c) q .,i 0 /‘ G / $ ~ Y—p.>- g .02 * = .,,. ,* u

i?.01 a

NATIONAL ADVISORY COMMITTEE F~ AERONAUTICS o .1 .Z .3 .4 .5 .6 .7 .8 Mach number, M

Figure /5.- ‘dariu+ion d measured #lkJH dmg U!d es flrnafeci d~g wi+h Mach humber for XF24-2 U/Yp/ume. NACA ACR No. L5G31 ‘ Fig. 16 ?

1*

*-

.

Crib’ccd Much number j Mct- Fiqwe /6 .- Terminal MUCh number char+. * .90

,88 R.d/-out=- Termlnd - En+ru

.86

—P-47C -I - ~ E a{~daw .84 ‘ (Flioh+ dda) c) / ‘ / 0- / - P-39N-I uir lane .8Z / Es f!ma+ed f / / P-47 uikplune / ‘ / ‘ 0 f(Esfimafed; MCP=0.64) / ‘ / 0 / ‘ / / ‘ //“/ ,80— q / ‘ / / ‘ / ? / ‘ F47 ~ /“ ,, ~ +-- ~ “F39N-1~ / ~“ / ‘ / - +V .78 ; / XF24 -2 airplane / - / < fimQ+@dj Mw 3 ,:$- / / / ~ ,.. -6 / ‘ --- ‘ corrected +0 0.66) / -/ / “ .. i . ‘ “- /0 / -’. * .76 ~ “ “; / .- / ~ / / / ~ . / - 1- / A .74“- - / P > / N - XF2A -2 airpkvne ---- (Flfghf duiu) / ‘ / / ‘ 1 ,72 / ‘ R.&ou++ Termiwl + Enfry \ I .70 NATIONAL ADVISORY COMMITTEEFM AERONAUTICS o 5 10 /5 20 25 30 x /03