1、L-.-.FOR AERONAUTICSWARTIMElBIIIBOIU”AORIGINALLYISSUEDAugust1945=AdvanceConfidentid.ReyortL5G31SIMIZE METHODFORESTIMATINGTJmmNAL vmOOmINCLUDINGEFFECTOF COMPRESSIB- ON DRAGBy ReLphP. BielatLaugleyMemorial.Aeronautical.Laboratory-.LangleyField,Va.NAC-A.,WASHINGTON. . outlined in references 1 and 2 can
2、 be usedfor the determination of the citical speed. Selection. .of the critical speed at the wing-roGt section for use interminal-velocity estimation is justified on the-Srouds.that the root section usually has a lower critical speedthan any other component part ofthe airplane. “TheJig.a current tra
3、nsport-model airfoil that has an NACA ?215section at the rcotiand tauers to sm NACA 2212 section atthe tip; an,the Davis air?oil with a ttd.cknessratio of20.15 percent. The low-drag airfoils inclde the followingNACA airfoil sections:1-23.5lc$-yl16-515.-21565(21S)-220The effectivetested varied fromas
4、pect ratio d the airfoil models665 tO irfillity.sle models.- Tk.efuselage models are tyical of :fuselrgsnapes in use on current airplanes. The variousfuselages represent bomber, fighter, and transport air-planes. 3igureI slhovsthe side-view drawing and the .fineness ratio in side elevation of the di
5、fferent fuselageshapes. These fuselage models were tested in conjunctionwith wings (shown as -shedlines in fig. 1) and representa wide variation in l-ni which consisted of theoutboard panel of a wing section designed for use on abomber airplane. Tke wing was a thiclclow-drag airfoilthat had an NACA
6、65(21-8)-222.section at the root .m.dtapered to an NACA 66(2x15)-.6 section.at the tip. Tilewindskdelds were testedwith a wing-fuselage combination.Drawings of the nacelle and windshiehl models are shownin figures 2 and , respectively.RESULTS AND DISCUSSIONErag CharacteiisticsDrag “anal;ysis.-In ord
7、er to obtain a correlation ofthe ro drag increase at speeds a“oovetb-ecriticalspeed, the drag results for the various component partsof the airplane have been reduced to nondimensional param-eters; that is? CDlin is plotted against IlMci*for each part tested. The use of these parametersrepresents a
8、convenient method ofmaking the data non-dimensional in such a manner that the unknown quantitiesare 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 presentedin figures -and 5, lj.gupe6 to ShOW the,variat
9、ion ofcD/Cnin with M/Mcr for the low-drag high-critica.l-speed airiOi,l.S.It w;ll be noted that all tk.eairfoilspresented in figures ,6, 7, and.8 exhibited approxi-rnate.1y thesame rate of drag increase at speeds ahovethecritical speed: for this reason a curve of the averagerate of drag increase at
10、speeds akove the critical speed maybeused. An average increase in drag of approximately 30 per-,. -.cr “:at speeds of o:al.y10 to 15 percent above the criticalspeed b-owever,the drag increased:aproxirnately 0to 200 percent. This rapid increase in dag at speedsabove the critical speed is associated w
11、iththe formation.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-6 KACA ACR No. L5G31Of compression shock waves and their affect on the hound.arylayer over the surface cf the airfoils. The faintly ofai.rfoi.lsused in fi,ure showed less percentage ofi
12、icreasein drag at the critical speed than tke iWC 0009,0012, or the low-drag high-critical-speed airfoil sections.Both published (reference 5) and unblished high-speeddata show tb.atthe NACA 230-series airfoils differ frommost of the other airfoils in that the critical speed canbe excseded by as mu
13、ch as 0.15 in Mach number before anyserious changes in the aerodynamic characteiisticsof theairfoil occur. The cr:tical speed of the NACA 230-seri.esairfoils is therefore exceeded by appo:imately7* percentbefore the same ,pm?centageof increase in drag oc this separation of flow will not appreciably
14、atfectthe determination of the terminal velocity for high-performanceairplanes for which t?.e-terminal veloityoccurs at seeds well above tb.ecritical speed.Figure 10 sb.owsthe variation of cD/C:in withM/Mcr for several fuselage shapes and fineness ratios,The drag increments for the nacelles and wind
15、shields tirepresentad,in figures 11 and 12, respectively. The criti-cal spezt,sfcr these bodies were based cn the wings iithwhich-.el-elsertested and were determined for thewing-root juncture. The effect of compressibility on therate of drag increase at speeds above the wing criticalspeed.for these
16、bodies is similar to that for the air-foils mXn the correlation.of t-e(averagedrag increases ofthe varioscompo-entscfthe a-:lanetbq?:hattheMach number range, a generaiize,ddrag curve was derivedProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-N#.CAACR
17、 No, L5G31 7.and is presented in figure 13. The data presented inflgures.,6, 7, s, 10, 11, and 12 were used to obtaintb.egeneralized drag curve. The Generalized drag curveis an average of the drag data for the airfoils, fuselages,nacelles, and windshields at speeds up to 10 percentabove the critical
18、 speed. Only the average drag of theairfoils 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 15to 25 percent above the critical seed. The straight-line extrapolation is believed.to be suffic
19、iently accuratefor estimation of the terminal velocity in this regionwhere the drag rises rapidly due to compressibilityeffects.Constriction aortiect.ions,-Clorrectionsfor constrictioneffecs have been applied to the data. The constriction.corrections have been determined from pressure measure-ments
20、obtained in the Langley 2)-inc-nand 8-foothigh- .speed tunnels on NACA 0012 airfoil models of varioussizes, The magnitude of the corrections.applied to thedrag coefficients amounted to less than one-half of 1 per-cent of the dynamic pressure q at low speeds andincreased to approximately 2 percent of
21、 q at the criti-cal speeds and.to approximately 5 percent of q at avalue of the Mach number below the choking speed of thetunnel. The carretctionsto theMach numbers amounted toapproximately Cne-.”halfof these values. Theconstrictioncorrections were such that the coefficients were reducedand theMach
22、numbers were increased by the values stated.The greatest percentage of increase in correction, aswould be expected, occurred for the models that had thelargest ratio of iOdel area to tunnel area.Comparison with flight data.- Fiure11+.shows thevariation of over-all drag coicient with Mach nu_w.ber-fo
23、r the XP-1 airplane as-measured in flight and thevariation with Mach number of the wing-profile drag atthemi.d-semisp_anstation measured by the wake-surveymethod. These flight data are peliminary as correctionsto the data have not been applied. The results obtainedby use of tho generalized drag curv
24、e in estimating thedrag increases with Mach number are also shown in fig-ure lkfor 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 bei to rise rther steeplyProvid
25、ed by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-8 TAcAJ!.CRNo, LGjl-.at about the saw.e llachnumber, This l%ct tends ta justifythe asslmptionthat the wi,ng-root critical speed iS asuitable criterion to use ia terminal-velocity calcula- tion.s. Theest!mated
26、 drag derived from the generalizeddrag relation indicates hi:ker drag coelficientsat Machnt.berof approxi.rlatelyC. to O.J than arc shown forboth the measured wing-profile drag and the over-all dragcoelficients. Of more importance, however, Is the gaodagreement tihatis shown torthe values obtafi.ned
27、by use ofthe generalized drag curve and the measured flight dataat Mach numbers greater than O.$ which is the regionwhere the terminal Mach number usually occufis.Figure 15 snows a comparison of Measured flight di-azand estimated drag for the XF2A-2 airplane of?mferance .An important difference in t
28、he drag curves occurs at Machlhe estiiatednumbers around the critical Mach rwaber,drag fndicates lower drag cofficients than do the flightmeasurements. Ts ffifferenceis believed to be due to acombination d earQ shock formation on the cowling and.airplane-wing rongbnessj which ia believed to have cau
29、sedsome separation ofthe flow. Good agreement is indicatedbetween the flight measurements and the estimated drag inthe region where the drag coefficients rise stee:ply,whichis the regionthat determines the terminal Mach number.The generalized drag curve (fig. i3) nay be used asan approxmation in det
30、ermining the terrlinalvelocity ofan airplane in a vertical dive. The terminal velocity isreached wlx+nthe drag of the air-planeis equal to theweiat of the airnlane. The dra,gcf the airplane in adive combines botbairplane and propeller characteristics.n the present analysis, howeverj zero prope?.lert
31、b?ustis assumed and the propeller then,wOf lfr and the terminal Machpscpminobtained by use offigure 16.In order to illustrate the method ofw Cal -beS%minfop given values.number can beobtaj.nintheterminal velocity graphically, the terminal veloci;ishave been calculated for the XF2A-2, P-39E-1, and P-
32、47 air-planes . The mrtin.ent data for these aplailas. are ivein the following table:TMJJH-lAIRPLANE DATA 1 wAirplanei J I CDcr min s!-J- !(lb/sq ft)-r- +_i XF2A-2 0.6+ (flight) ;0.022 (flight) I 26.1-1-.-l+. (c“rrected.- P-39N-1 .65 estimated) ,0.01 (estimated) 34.1.- -”P-L7 jOa61+(wind tunnel)O.02
33、0 (flight) i 45.0 .69 (corrected) It- J,biBJ use of these data the parameter -!Aspsfcjllincomu.tedfor each airplane. The use of figure 16 toestimate the terminal Mach number is illustrated for tkeP-i!L7airplane at 15,000 feet altitude. The variation of.*Provided by IHSNot for ResaleNo reproduction o
34、r networking permitted without license from IHS-,-,-NACA ACR NO. L5G31 11sterminal Mach number with altltude thus obtained for thethese airplanes is presented in.figure 17.Also included n figure 17, for comparison with theestimated variation of terminal Mach number withaltitude,are records of flight
35、 data for the XF2A-2, the P-7,the P-47C-1-RE, and the P-39N-I airplanes. The flightrecord for the P-C-l-RE aiplane was obtained by thelate Ma,jorPerry Ritchie in a terminal-velocity dive madeat Wright Field in July 1943, The points represented bycircles were obtained from a dive of a P-)+7airplane m
36、adeby a test pilot for the Republic Aviation Coi-poration.Unfortunately, a complete dive history is not availablefor this dive but it is believed that, had one beenavailable, it would lnavefollowed a path similar to thatobtained by the lake Major Ritchie for the P-.7C-l-REair-plane. It is further be
37、lieved that the test pointsobtained at altitudes of 22000 feet and 10,000 feetrepresente.ty into and pullpout from the dives respec-tively. Data for the XF2A-2 airplane were obtained fromreference 6 and the data for the P-59N-1 were obtainedfrom dive tests made at !es Aeronautical Laboratory. Thepre
38、sent method for estimatingthe terminal Mach numberyields results that compare favorably with the flightmeasurements; the difference between the two is no greaterthan 0.02 in Mach number. This method forestimating theterminal Mach number is therefore believed to be suffi-ciently accurate forusual eng
39、ineering purposes.The section entitled “Drag Characteristics indicatesthat the NACA 230-series airfoils and airfoils similar tothe NACA 230-series could exceed the critical speed byapproximately 0.05 to 0.15 in Mach number before anyimportant changes in the aerodynamic characteristics. .,foccurred.
40、At -= 1.0, tnereforeMcr the NACA 230-seriesairfoils and similar airfoils did not show the samepercentage increase in drag as was shown for aimost allthe other airfoils and for the generalized drag curve.Since in the calculation of the telinal velocity thecritical speed of the airplane is based on th
41、e criticalspeed of the wing, it can be expected that for airplanesutilizing NACA 230-series airfoil sections or similarsections the estimation of the terminal velocity will bein error. IJ?the generalized drag curve is used in theestimation of the terminal vel.ocitythe indicated wing*W.;,L*1critical
42、speed must be increased approximately 7- percent. 2Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-for the hTACA 230-series sectians. This correction was .applied to the critical speeds of the P-).+7and X.F2A-2air-planes (see table 1), since these ai
43、rplanes.nave NACA 230-series sections. The das.edcmve on figure 17 forMr = 0,64 is the result obtained ifthe indicated criti-cal Mach number is used rathe; than the effective criticalachnber, which is about 7L percent hiGher.2Langley Memorial Aeronautical Laboratory.- National Advisoryolittt?e forLa
44、ngley Field, Va.:fiRJ1. Robinson, Russell G., and Wright,of Critical Speeds of Airfoils3od.ies. IJACAJ-LCR,March 194.0,Ray H.: Estimationand Streamline2. Heaslet, Max. A.: Critical Mach Numbers of VariousAirfoil Sections . NACA Mm NO. )pm, 19L43. Becker, John V.: High-Speed Tests of Radial-EngineYac
45、elles on a Thick Low-Drag Wing. NACA ACR, lfitiy1942eI+. Delano, James E., and Wright, Ray E.: Investigationof Drag and Pressure Distribution of Windshields atHigh Speeds. NACA ARR, Jan. lom Pb-k view profi Iee- d -3!L-3A/acei/e / Nacek 2Elliptical cross sc +ion Circular cross Sec+ion-. +NACA 16-509
46、 /4 . 16-5)S /12/ -_1.0 / Figure 6. Vcvnu+ion of ra+to Co/CDm;n wi+h MMcrfor A/AC14 16509 Qnd 16-515 cwdoils.fkd U+ 0./0 CA ord.77run 6/ +/ohProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Fig. 7a,b NACA ACR No. L5G31Mi6/.4/!2Airfoil Sec +ionsIVACr4
47、66 /-/5. 47-215. 670 -25 /6-215.1b1!0= =“ -* tNATIONAL ADVISORY* COHMInEE FORAEIWJAUTc.3.4 .5 .6.78 .8 Lo L/ 12J,Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-. .NACA ACR NO. L5G31.Fig. 82.6 Im I1Z4 - Airfoil sections. NACA 47-215. 60-21!5. . 16-2i
48、52.Z “ ,20 IIIII8 I4/.6 / PII4 /!l,4/12 A/4/A / .Y “p“0. - a u+ioh of m+tofor Sevrffi NACA uirfoih CDCDin w/fh MMcrNo +ransi+iofl.*Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Fig. 9 NACA AC!ROc L5G31Z82.6M/McrF;gun 9.- Variation of ratio CJCD ofor Davis U;rf
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