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SAcACP N LL73
ACE No. L5G31 NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS WAR'RTIMi RI REPORT ORIGINALLY ISSUED August 1945 as Advance Confidential Report L5G31 A SIMPLE METHOD FOR ESTIMATING TERMINAL VELOCITY INCLUDING EFFECT OF COMPRESSIBILITY ON WRAG By Ralph P. Bielat Langley Memorial Aeronautical Laboratory Langley Field, Va. NACA WASHINGTON !, NACA WARTIME REPORTS are reprints of papers originally issued to provide rapid distribution of advance research results to an authorized group requiring them for the war effort. They were pre i viously held under a security status but are now unclassified. Some of these reports were not tech nically edited. All have been reproduced without change in order to expedite general distribution. L 78 DOCUMENTS DEPARTMENT Digitized by the Internet Archive in 2011 with funding from University of Florida, George A. Smathers Libraries with support from LYRASIS and the Sloan Foundation http://www.archive.org/details/simplemethodfore001ang TIACA ACR lio, L5G41 NATIONAL ADVISORY CCVMITTEE FOR AEt.O"AUTICS ,DVUIICE COi.PTIDEL!TIAL rFP'rT A SISLE ITSOD FOR .SI..*TI' TG T'RITlL VELOCITY I!' LTDIT'iG EF EC'T :F COYi PRL SIBLr TY ' DR .G By Ralph P. Bielat .. gner.lid .iJr'g curve that provides an estimate for the rag rise jne to c:p'es sibiity nas been obtained front an inal,:L s 'o .,inJ:ur.nnel data ..f several airfoils, fusela es3, nacellE:s. And ,Ird.idsia"e.l r" at :;cds up to and above tihe win,. critics.] need, hd air'fo'ils analyzed had little or no s.eei:oc: an,:' effective aspectt ratios above 6.5. A chart based on the ,.erneralizd d: C. curve is presented. fro., whichh the ter...nal vrlczity :f conventional airplane that employs a w'.n. 3f e: t &..suct ratio and very little s'.eepback' in vertical (dive ..y 0. rapidly esti mated. In rder t' uce thie chrt, che )nly data that ne.d bE .:novr abcut th.e airlate are a lo.i'oe.'d drag coefficient, t.ie v.ing critical seed, an, tlhe wing loading. The terriinal velocities for three airp'lcinc were computed in rider r to illustrate th.1 use of the method and chart. Good agreermnrt between the et.lrriated ttriAinal velocity and the .easured flight terminal vlocity was indicated for all three airplanes. Ii TRO UCT IO Several hl,.hsneec militar:. air'l,.anes in lives s have encountered difricultie that could not oe easily con trolled by normal means. These Cdifficult es, whi ch may consist of giving znor..ents. .arge charges in trim, large stick forces, tail buffetinc, in, the lile, occur in high soeed dives '.'when the sr.eed of the airplane exceeds the critical .speed by a large a:o'..Int. .,or th.se airpl.nes for which i,.aximun diving speeds are at or near the critical speed, little or no trouble occurs. The more recent fighter airplanes, i:,'ever, have Lerr,inal r'ach numbers well in excess of the critical ;.lrch number and, as a result, often encounter difficulties in dives. Determi nation of the terminal velocity of the airplane is there fore import.nt in order that thet probability of encoun tering trouble in divts ;iay be esti:;.ae. CONFTDEII'TAL NACA ACR No. L5G51 The terminal velocity is also impo rtant because it forms the outer limits of the VG diagram. Usually the outer limit of the VG diagram is established by multi plying the maximum levelflight speed of an airplane by an arbitrary factor somewhat greater than 1.0. The termi nal velocity of most recent airplanes, however, generallyy falls much below this arbitrary Miaximum speed, and these airplanes are therefore unnecessarily penalized by extra weight because they are designed for conditions that are not reached in actual flight. The present report outlines a si'inle method for obtaining the terminal velocity of an airplane in a verti cal dive and includes an estimate for the drag increase due to compressibility effects. The windtunnel test data were obtained from model tests conducted in the Langley 2Linch and 8foot highspeed tunnels. All the data presented herein .;ere obtained for zero lift. The problem of determ'rnirn the terminal velocity for airplanes for which the terminal velocity is near the critical sDeed is c:aratively simple inasmuch as a constant value of drag coefficient can be assumed. The diving speeds of most presentday airplanes, however, occur beyond the critical speed ond the problem is'not so simple. The following two factors are involved: (1) the determination of the critical speed and (2) the rateof ' drag increase at soeez above the critical speed. The critical speed used herein was arbitrarily'taken as the critical speed of the wingroot section. Pressure distribution data obtained from windtunnel testswere used to determine the critical seed, which is defined as the flight speed at which sonic velocity is reached locally. If experimental data are not available,. however, the methods outlined in references 1 and 2 can be used for the determination of the critical speed. Selection. of the critical speed at the wingroot section for use in terminalvelocity estimation is justified on the. grounds. that the root section usually has a lower critical s'eed than any other component cart of the airplane. The j.iiag. root has the lowest critical speed because of .itshigh thickness ratio an contributes a large part of the total airplane drag because of the large fraction of the wing_ area concentrated at the inboard sections .of tapered wings. The rate of drag increase at speeds above the. cliti cal speed is more difficult to determine in the calculations C CO ID 'TIAL NACA ACR No. L5G351 of the terminal velocity than the critical speed. A study of the drag of airfoils, fuselages, nacelles, and windshields has been mae fro.n .,indtunnel test data in order to determine che effects of cmxiressibility on the drag. Because the rate of draw inc'ese at spees above the critical seed is so great, it ..a fond that, within the accuracy required for terminalvelocity calculations, an average rate of' drag increase O'.ay be used. .4 curve indicating the average rate of drag incre se is presented herein. This ci'.rve wvas derived from an analysis of wind tunnel data. The method described herein for obtaining the termi nal velocity of an airplane in a vertical dive has been in use at the NACA since 1901. Publication of the method, however, had been delayed pending. the investigation of constriction corrections to be applied to ..he windtunnel data and the com'plcti'n of highsprecd five tests made with several airplanes in order to compare term'Linal velocities obtained in flight oith terminal velocities estimated by the simn.le :rethod described 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 moderate aspect ratio and small amounts of seaspback due to wing taper rat.io. S L BC L3 V velocity a speed of sound in air MI Mach numbEr (V/a) CD drag coefficient CL lift coefficient p mass density of air S wing area "'V weight of airplane p atImosoheric pressure at any altitude COTrFIDENTIAL C NFIDEI'TIAL C :'C. ACR No. L5G51 ratio of specific heats (1.40 for air) t/c ratio of thickness to chord of wing , scriptst: or critical (when local sonic valocit has been reached on some point of body) m in minimum T terminal DECD.IPTIOT! OF YODELS Airfoil models. The airfoil models used herein represent two classes of airfoils namely, the conven tional NACA sections and the more recent lowdrag higih criticalspeed NACA sections. The conventional .'.CA air foil sections are characterized by pressure distributions that have high peak pressures occurring near the leading edge. The lowa:g NACA airfoil sections have comoiara tively flat pressure distributions iith the peak pressures occurring at approximately 60 percent of the chord behind the leading edge. Airfoils typical of the conventional airfoils are the NACA 000963, 001263, 25012, and 23014.7 sections; a current transportmodel airfoil that has an i.iA 2215 section at the root and tapers to an TACA 2212 section at the tip; and the Davis airfoil with a thickness ratio of 20.15 percent. The lowdr.g airfoils include the following NACA airfoil sections! t 16215 65type modified, = 0.156 1650Q 66, 1115 16515 67111 5 1.7215 67 0215 65(21,8)220 The effective as,)."ct ratio of the airfoil models tested varied from 6.5 to infinity. Fuselage models. T'.e fusele models are t.ical of fusel7s7X:i ", i se on current airplanes. T.,e various fusel,'es rec' :sent bomber, fijhter, and trans.,;rt air planes. Figure 1 shovws the sideview draw"inf n," the fineness ratio in sir; elevation of the different fuselage sha,'rs. These fusel';g! models were tested in conjunction with win.Ls (shown as dashed lines in fl.1. 1) and represent a wide variation in winmfuselj,. interference. ': I 'T"IL CCNFLE'TIAL HACA ACR No. L5.331 CONFIDENTIAL 5 iacelle and windshield models. The data for the various nacelles and windshields were obtained from refer ences 5 and 4, respectively. The nacelle and windshield designations used herein correzoond t) the designations used in references 5 and 4. All the nacelle models were tested with the same wing model, which consisted of the outboard panel of a wing section designed for use on a bomber airplane. The ,,1ing was a thick lowdrag airfoil that had an .ACA. 65(21E)221 section at the root and tapered to an NACa 66(,215)146 section at the t.p. The windshields were tested with a w*.ingfuselage combination. Drawings of the nacelle and windshield models are shown in figures 2 and 5, respectivel.7. RES'TLTS AD DISCl'ZsTljr Dra; Characteristi cs Drag analysis. In order to ottain a correlation of the rate of drag increase at speec.s abooe the critical speed, the drag results for the various component parts of the airplane have been reduced to nondimensional carwrn: eter that is, CD/ Cmin is plotted against M/I r for each part tested. The use of thse parameters represents a convenient method of ina;ring 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 seed for the conventional ULKCA airfoils are presented in figures 1 and c.. Figures 6 to 9 show the variation of CD/Cin :ith M/Mcr for the lowdrag highcritical spseel airfoils. It will be noted that all the airfoils presented in figures 4, 6, 7, and 8 cxhioited approxi nately the sa.ne rate of drag increase at speeds above the critical speed* for this reason a curve of the average rate of drag increase at speeds above the critical speed maybe used. An average increase in drag of approximately 50 per cent above the minimum drag was indicated at 1.0; Mcr at speeds of only 10 to 15 percent above the critical speed, however, the drag increased approximately 90 to 200 percent. This rapid increase in drag at speeds above the critical speed is associated with the formation CCo:FIDENT IAL TUACA ACR No. L5G31 of compression shock waves and their effect on the boundary layer over the surface of the airfoils. The family of airfoils used in figure 5 showed less percentage of increase in drag at the critical speed than the NACA 0009, 0012, or the lowdrag highcriticalspeed airfoil sections. Both published (reference 5) and unpublished highspeed data show that the NACA 230series airfoils differ from most of the other airfoils in that the critical speed can be exceeded by as much as 0.15 in I.ach number before any serious changes in the aerodynamiic characteristics of the airfoil occur. The critical speed of the NACA 250series airfoils is therefore exceeded by approximately 71 percent before the same percentage of increase in drag occurs as is shown for the other airfoils. The importance of this difference in the shape of the ir:b curve above the criti cal speed on the estimation of terminal velocity is dis cussed in the section entitled "TerminalVelocity Calcula tion." Tie rapid increase in drag before the critical speed is reached, which is shown for the NACA 67114.5 airfoil in figure 9, is due to early separation of the flow over the after portion of the airfoil. This condition also affects the method for estimating the terminal velocity. An error in estimating the terminal velocity when the flow separates will occur only for those airplanes for which t.rninal velocities are at or near the critical speed; this separation of flow will not appreciably affect the determination of the terminal velocity for high performance airplanes for which the terminal velocity occurs at speeds well above the critical speed. Figure 10 shows the variation of CD/CD.in with M/Mcr for several fuselage shapes and fineness ratios. The drag increments for the nacelles and windshields are presented in figures 11 and 12, respectively. The criti cal s:e .s for these bodies were based on the wings with which the '.dels were tested and were determined for the wingroot juncture. TheL effect of compressibility on the rate of drag increase at sp.ds above the wing critical speed for these bodies is similar to that for the air foils, In the correlation of the avera,; drag increases of the various co onrenLs of the airplane throughut the Mach number range, a generalizedd drag curve was derived CC "T'DENTIAL COF IDL'TIAL HACA ACR o0. L5G51 and is presented in figure 13. The data presented in figures ., 6, 7, C, 10, 11, and 12 were used to obtain the generalized 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 straightline extrapolation from 15 to 25 percent above the critical speed. 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 correctjons. Corrections for constriction effects have been applied to the data. The constriction corrections have been determined from pressure measure ments obtained in the Langley 24inch and 8foot high speed tunnels on NhCA 0012 airfoil models of various sizes. The magnitude of the corrections applied to the drag coefficients amounted to less uhan onehalf of 1 per cent of the dyna:,ic pressure q at low speec.s 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 corrections to the Mach numbers amounted to approximately onehalf of these values. The constriction corrections were such that the coefficients were reduced and the Mach 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 model area to tunnel area. Comparison with flight data. Figure 1i shows the variation of overall drag coefficient with Miach number for the XP51 airplane as measured in flight and the variation with Mach number of the wingprofile drag at the rridsemispan station measured by the wakesurvey method. These flight data are preliminary as corrections to the data have not been applied. The results obtained by use of the generalized drag curve in estimating the drag increases with Mach number are also shown in fig ure 14 for comparison with the flight measurements of overall drag and wingprofiledrag data of the XP51 air plane. The curves for the wingprofile drag and the over all airplane drag in flight begin to rise rather steeply CONFIDENTIAL CONFIDENTTIAL NACA ACR No. L5G31 at about the same Mach number. This fact tends to justify the assumption that the wingroot critical speed is a suitable criterion to use in terminalvelocity calcula tions. The estimated drag derived from the generalized drag relation indicates higher drug coefficients at Mach numbers of a0pro;imately 0.55 to 0.75 than are shown for both the measured wingprofile drag and the overall drag coefficients. Of more importance, however, is the good agreement that is shown for the values obtained by use of the genralized drag curve and the measured flight data at Mach numbers greater than 0.75, which is the region where the terminal Mach number usually occurs. Figure 15 shows a comparison of measured flight drag and estimated drag for the FkFi2 airplane of reference 6. An important difference in the drag curves occurs at Miach numbers around the critical Mach number. The estimated. drag indicates lower drag coefficients than do the flight measurements. This difference is believed to be due to a combination of early shock formation on the cowling and airplanewing roi;ness, which is believed to have caused some separation of the flow. Good arrerment is indicated between the flight measurements and the estimated fra., in the region where the drag coefficients rise steeply, which is the region that determines the terminal iTch number. TerminalVelocity Calculation The generalized drag curve (fig. 15) may be used as an approximation in determining the terminal velocity of an airplane in a vertical dive. 'Te terminal velocity is reached when the drag of the airplane is equal to the weight of the airplane. The drag of the airplane in a dive combines both airplane and propeller characteristics. Tn the present analysis, however, zero prrpller thrust is asrunied and the ,ropeller drag or thrust is therefore neglected. At supercritical speeds the drag or thrust caused by the propeller is considered to be negliAible as compared with the c.raZ of the airlane, particularly if the pilot throttles the engine and adjusts the pri.peller to a high bladeangle position. The tmrn.inral velocity for zerolift conditions is given by the relation CON IDEiTIAL CONPIDE!UTIAL NACA ACR D LC5G51 CONFIDENTIAL 9 V=V (1) 1 3SP CD or, in terms of the terminal Mach number Mirp with the speed of sound equal to , VT 2 1 1(2) a QS p C3 Equation (2) can be rewritten in the frm 2. = h 2 1 1 1 S y P CD/Ci 12 "Y 'min CD/CD.uin where is constant for each airplane at the PSCDmin altitude for which MT is calculated and CD K (MT ' C^nin \ cr which is obtainable from the generalized drag curve. Equation (3) can then be solved for the paramr.eter V9 . Figure 16 sho31s soluti,'ns of equation (3) for pSCDmin various values of M'cr and ,. In computations of the terminal velocity, the only data that must be known about the airplane are uhe minimum CONFIDENTIAL NACA ACR No. L5G51 drag coefficient at zero (or a,prox.riately zero) lift coefficient or a lowsreed drag coefficient whereby the minimum drag coefficient can be computed by use of the generalized drag curve, the ,v.ig critical speed, and the wi.i.; loading. Values of these quantities, all of which are used in calculations other than those for the terminal velocity, are easily obtained. With these values known for a ..drticular airplane, the parameter can be ZDmin calculated for different altitudes; then, for given values W of Mcr and the terminal Mach number can be obtained by use of figure 16. In order to illustrate the method of obtaiirdni the terminal velocity ..i Lcally, the terminal velocities have been calculate'. i'or the ':2..2, P3Tl, and P47 air planes. The pertL ent data for these airpha *.s are given in the following Lable: TABLE I AiF:FLA:TB DATA CD Airplane Mcr min XF2A2 o0.61 (flight) 0.022 (fli:.ht) .66 (corrected) P39N17 0.675 (estimated) I0.019 (estimated) P7 GO.'!,. (wind tunnel) 0.020 (fliht) .69 (corrected) (Ib/sq ft) 26.1 5k.1 h5.o L._____ By use of these ita th, parameter is Dmin co,.' uted for each airplane. The use of figure 16 to esr.4mate the terminal Mach number is illustrated for the P47 airplane at 15,000 feet altitude. The variation of C O fIT' :TIAL CO;PIDEi;TIAL NACA ACR No. L5G51 terminal Mach number with altitude thus obtained for the three airplanes is presented in figure 17. Also included in figure 17, for comparison with the estimated variation of terminal M'ach number with altitude, are records of flight data for the XF2A2, the P47, the P47C1RE, and the P59N1 airplanes. The flight record for the P47C1RE airplane .;as obtained by the late Major Perry Ritchie in a terminalvelocity dive made at Wright Field in July 1943. The points represented by circles were obtained from a dive of a P47 airplane made by a test pilot for the Republic Aviation Corporation. Unfortunately, a complete dive history is not available for this dive but it is believed that, had one been available, it would have followed a path similar to that obtained by the late Wajor Ritchie for the P47C1RE air plane. It is further believed that the test points obtained at altitudes of 22,000 feet and 10,000 feet represent entry into and pullout from the dive, respec tively. Data for the XF2A2 airplane were obtained from reference 6 and the data for the P359N1 were obtained from dive tests made at Aries Aeronautical Laboratory. The present method for estimating the 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 for estimating the terminal Mach number is therefore believed to be suffi ciently accurate for usual engineering purposes. The section entitled "Drag Characteristics" indicates that the NACA 250series airfoils and airfoils similar to the NACA 250series could exceed the critical speed by approximately 0.05 to 0.15 in Mach number before any important changes in the aerodynamic characteristics occurred. At =L 1.0, therefore, the NACA 250series cr airfoils and similar airfoils did not show the same percentage increase in drag as was shown for almost all the other airfoils and for the generalized drag curve. Since in the calculation of the terminal 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 250series airfoil sections or similar sections the estimation of the terminal velocity will be in error. If the generalized drag curve is used in the estimation of the terminal velocity, the indicated wing 1 critical speed must be increased approximately 72 percent CONFIDENTIAL CONFIDENTIAL NACA ACR No. L5G51 for the NACA 250series sections. This correction was applied to the critical speeds of the P47 and E.F2.2 air planes (see table I), since these airplanes have NACA 250 series sections. The dashed curve on figure 17 for M*cr = 0.64 is the result obtained if the indicated criti cal Uach number is used rather than the effective critical 1 Mach number, which is about T, percent higher. Langley Memorial Aeronautical Laboratory national Advisory Committee for Aeronautics Langley Field, Va. ,R LFE."CES 1. Robinson, Russell G., and ..ight, Ray H.: Estimation of Critical Speeds of Airfoils and Streamline Bodies. LACA ACR, March 1940. 2. Heaslet, >.;.. A.: Critical M'ach iuTn.bers of Various Airfoil Sections. ,iA.CA ACR No. 4G18, 1944. 5. 3ecker, John V.: HighSpeed. Tsts of RadialEngine "acelles on a Thick LowDrr.. ing. 1,ACA ACR, May 19LJ2. 4. Delano, Janes B., and Vri.?ht, Ray H.: Investigation of Drag and Pressure Distribution of ..i'ishields at Hi9. Speeds. NACA ARR, Jan. 1942. 5. Becker, John V.: HighSpeed ..ii LTunnel Tests of the A.A 27.12 and :'01264 Airfoils. isC? ACR, Feb. 1941. 6. Rhode, Richard V., and Pearson, H. A.: Observations of C: orssibility YhZr',,ena in Fli ht. NtC, eCR 7.. 3D15, 194). CO1'I DENTAL CONFIDENTIAL NACA ACR No. L5G31 CONFIDENTIAL Firetness ra io, 10.32 F'ne ess raLio, 6.65 Pr'eress raiio 7.30 Fireress rahio 6.14 Firieness r*io 5.60 F~ineress ratio 4.75 NATIONAL ADVISORY C) COMMITTEE FOI AElRONUtniCS CONFIDENTIAL Fineres5 rafio 3.30 Figure / . 5ide view drawirqng of various fuselage shape. Fig. lag NACA ACR No. L5G31 CONFIDENTIAL Circular cross section Nacelle I Elliptical cross section 4^E ^> Nacelle i Circular cross Nacelle 5 Circular cross Secfion Nacelle 4 section NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS CONFIDENTIAL Figure Z. Nacelles ( Des 5 ignatiors From tested. reference e Planview profile Nacelle 3.) Fig. 2 NACA ACR No. L5G31 Windshield 311 203 CONFIDENTIAL A ^biWA K2IL"~hj> 403 NATIONAL ADliSOAV COMMITTEE FO AmIONWATICS XI A Plane AA of all windshields is located at Same posiiion on fJs5elaqe . Figure 3. Windshields tested. (Designoationrs fror reFerence 4.) CONFIDENTIAL Fig. 3 NACA ACR No. L5G31 Q C) Q C) CONFIDENTIAL 68* Airfroil sech ons 4/'ACA 000962 000963 S 000964  000965  006  .8         ? .8 i !.4 f. NATIONAL ADVISORY CONFIDENTIAL COnNITTIE For "AIITIrcs /./ /.Z. Fi'gure 4. Variab/on of ra/Ao Co/Com,Vn wi/h M/^lcr for A//4CA 0009 anod 0012 Q0rfil6. Fig. 4 .3 .4 .5 .6 .7 . A*Adcr NACA ACR No. L5G31 18 1.6 t 1.O 1.0 Figure 5. Variafion of rcf io CD/CoD,. w/ih AM/MAcr For threee Conventinal/ AI/ACA cirO/'r/s. /.6 Q0 U 1.0 .4 .5 .7 .8 .8 /.0 // / AM/A4cr Figure 6. Varia/iori of roaio COCo/C,, wifLh A4M/4cr for NACIA 16509 anrd 16515 Q rfoi/5. TrQisi'/i/on fixed a' 0.10 chord. CONFIDENTIAL Airfoil sec ion s /ACA 23012  230/4.7  2l(root) o 22/2 (4) NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS ........ I l l i Airfoil sec t'os NACA /6509  16515 / NATIONAL ADVISORY CONFIDENTIAL COMMITTEE FOR AERONAUTICS Figs. 5,6 .7 .8 M/IAr .9 10 Fig. 7a,b 18 16 14  Sis  NACA ACR No. L5G31 (a) Trancidiion fixed oj 0.10 chord. Airfoil section NACA 66, ///5 472/5 67,02/5 /62/5 16 1.0 to 3 .4 .5 .6 .7 .8 (b) Transi/tion f xed ai 0.40 chord. Figure 7 . Vcar/a f/on oAf roa//o Co/Corn for severe/ NACA oi/rfoi/ls . 1.0 l 12. With A t/41"cr NATIONAL ADVISORY CONFIDENTIAL CObMITTEE Imf AEAU TIKS *. NACA ACR No. L5G31 b I CONFIDENTIAL  Airfoil sec+iorins 4 NACA 47215  67,02/5 /62/5 2.0_ 18 1.6   / 14 10 NATIONAL ADVISORY S___ CONF IDEN TIAL ____ COMMITTEE FOR AEROMUTICS .3 .4 .5 .6 .7 .8 A/Amcr Figure 8 . Var/atioti of rafio CD/Co,, with A1/A4lcr for several NACA airroils No "frao ils>ioor). .9 10 /.1 l/ C 0 Fig. 8 NACA ACR No. L5G31 .c Q C) I I CONFIDENTIAL Airfoil sections NACA 65(218)220 65fype raodfied, c =0./ 96   D iS oil, t/c =0.20/5 S  67114.5 , 2.0 LL 77 1  t>  1. 1 / 1.2 1 / 4 1  __ / NATIONAL ADVISORY S CONFIDENTIAL COMMITTEE Iro AEIouAwTICS .5 .6 .7 .8 AM/MAcr .9 /.t 1.1 12 FicuLre 9 . Variafiorw of ratio C/Ci wl Ah M/A4cr for Davis airfoil and several NACA airfoils. Fig. 9 NACA ACR No. L5G31 CONFIDENTIAL 2. 2 Fuselage Fireness (See /ig. I.) ratio (0) 10.32_  ( b) 6.65 /  ) 730 (d) 6. 14  e) S.60  f) 4.75 12  3.30  10 NATIONAL. ADVISORY CONFIDENTIAL COMMITTEE FOl AERONAUTIcS .3 .4 .5 .6 7 c M2/A4cr .9 1O 1/1 12 FigLdure /0. Variafion of ratio C/CD wi/h A^4/Mcr for several Fuselage .sapes. C 0 0 U Fig. 10 NACA ACR No. L5G31 " CONFIDENTIAL Nacelle (See 2g. 2) 16 I2 ~2 ~3 4 / 4 1.40 NATIONAL ADVISORY COMMITTEE FOR AEMONaITICS .3 .4 .5 .6 .7 .8 A/IAcr .9 1.0 1./ 1.2 Figure // Variciori of rafio C/Comi, wHih ,///Vlcr for several nacell//e sAapes. .3 .4 .5 .6 .7 .05 MA4f/ Cr .9 10 i. /Z Fiqcgre /12 . Variaifon of rafio CD/Co, wvith /V/A1cr for several wincidshiel/c shapes. Q (~1 Q 0 W/i 'shie/dc (See fg7.3) 311  312I  203   403 XI 7 ^^ _  NATIONAL ADVISORY CONFIDENTIAL COMMITTEE fM AEtOIAUTICS Figs. 11,12 A NACA ACR No. L5G31 0 U 0 C) CONFIDENTIAL 4I2 5.4,  24 . 5.0 2.    i 4.6 .4 3.8  1. h NEATIONApo ADVISORY CONFIETIAL COMMITTEE F AERONAUICS .3 .4 .5 .6 .7 .6 .3 A1lA4cr Fibwre 13. Geeeralized dfrcxg clrvoe. 1.0 1/ /2 1.3 Fig. 13 Figs. 14,15 CON .05 O .04 C .03 *0 U u i .201 NACA ACR No. LGI71 Aach ndA mber, Av4 Figure /4. Varic oro o F measured y'lht' d Or acid esfiPmaed dcrag wi#/A /vlch rmimber for XP51 Cf/rpfarme . .0 0 +. o .0 .0 S.0 .1 .2 .j .4 . .0 AMach rtcrmber, AM .7 .0 Figure /5. Variafioor) of measured y/4Af drag cOnd estimated drcq with /tvich riLumber for XF2/t2 oirp/one . 5  Overall cdroa (qigt/ ) ,/ 4 Estimao+ed drag from / generoalhed drag c"rve /, ,i   NATIONAL ADVISORY CONFIDENTIAL CONMITTEE rOI MAEROMWCS 7.. f NACA ACR No. L5G31 Fig. 16 CONFIDENTIAL % A/ /. 25   ^  5. 8 5.4 4.6 120 4.2 3.4 3.0 /.15 A, X. VIA 1.4 101 .95 S.90 " , AY .77 II .65 / "', .....a.,5000 i g 7 07. .. X e 6 . i r .I ..... ol, I / :II I I /" ~ A 5L, ::: rfci A/c nuimbe:., M : .,wr /6.' Te mia Mc k num er... _ _ _ ^ I I I I I ll _ _ ^ Z ' ^ : : :_ _ ,, I I I I I I I I I 1 1 1 [ 1 1 I ll'.^ ^ 7 _ < O FIE TA /.o  i II 1i ",N^T  /i[i C$ 0 .155 70_ __ . ^0 85 .9 Z ^_ .95 lO_ __ ? ___ _________ __ loc/ ^ ._7^/_ e r __ _c r __ _ F<.re1 .__ _ Termi ^7^l _7kc/ rl__^ner cr_, NACA ACR No. L5G31 SI oI    S 0 ) 0\ Q 2 %  ,   ^^^T^TA   5 Cz  ^8^ ^i ^^^^  S *1 ~ ~ ,. ^ ^v _ o   ~5rk  t ___ Z mmm~dr^8E 0 N N 0 00 0 CD 00 CD G Io Ias .dquwnu, YpokV /O4lous.v/q N Pig. 17 < u % O }I 'N 0 .0 I' 1z N, ci. (ib 23s UNIVERSITY OF FLORIDA 3 1262 08105 001 4 U: ,.,E, T',' OF F..O IDA DOCUJMErNTS DR.rTENT 120 IIARSTON SCiENCE LIBRARY .U. OX 117011 GAINESVILLE, FL 326117011 USA .i :: i'! 