i\JAc(^L-l^ ACR I?o. L^31 NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS WARTIME REPORT ORIGINALLY ISSUED Augiist 1945 as Advance Confidential Eeport L5G3I A SI24PLE METHOr FOE ESTIMATHKx TERMHIAL VILOCITY INCLUDING EFFECT OF COMPRESSIBILITr ON DRAG By Ralph P. Bielat Langley Memorial Aeronautical Laljoratory Lan^ey 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- '- viously held under a security status but are now unclassified. Seme of these reports were not tech- nically edited. All have been reproduced without change in order to expedite general distribution. 78 DOCUMENTS DEPARTMENT Digitized by tlie Internet Arcliive in 2011 witli funding from University of Florida, George A. Smathers Libraries with support from LYRASIS and the Sloan Foundation http://www.archive.org/details/simplemethodforeOOIang NACA ACR NOo LSG3I NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS ADVANCE COrlPIDENTIAL REPORT A SIMPLE METHOD FOR ESTIMATING TERMINAL VELOCITY INCLUDING EFFECT OF COMPRESSIBILITY ON DRAG By Ralph P. Bielat SUMMARY A generalized drag curve that provides an estimate for the drag rise due to conipressihlllty has heen obtained fron an analysis of wind-tunnel data of several airfoils, fuselages ;, nacelles, and v/indsiiields at speeds up to and above the v»ing critical speed. The airfoils analyzed had little or no sv/eepback and effective aspect ratios above 6.5. A chart based on the generalized drag curve is presented froiTi •.vhich the teminal velocity of a conventional airplane that eraploys a v/ing of mo-lerate aspect ratio and very little sv/eepback in a vertical dive nay be rapidly esti- mated. In order to use the chart, che only data that need be known about the airplane are a low- speed drag coefficient, the wing critical speed, and the vifing loading. The terminal velocities for three airplanes were computed in order to Illustrate the use of the method and chart. Good agreement betvv-een the estim.ated tenainal velocity and the measured flight terminal velocity was indicated for all trj?3e airolanes. INTRODUCTION Several high-speed military airplanes in dives have encountered difficulties that could not be easily con- trolled by noriaal means. These difficulties, which may consist of diving moments, large changes in trim, large stick forces, tail buffeting, and the like, occur in high- speed dives 'When the speed of the airplane exceeds the critical speed by a large amount. For those airplanes for which maximujn diving speeds are at or near the critical speed, little or no trouble occurs. The more recent fighter airplanes, hovvever, have tenninal Mach numbers well in excess of the critical Mach niijnber ana, as a result, often encounter difficulties in dives. Determ.i- nation of the terminal velocity of the airplane is there- fore important in order that the probability of encoun- tering trouble in dives may be estimated.. CONFIDENTIAL NACA ACR No. L5G3I The terminal velocity is also Importaat "because it iorms the outer lirriits of the V-G diagram. Usually the outer limit of the V-G diagram is estahllshod by multi- plying the iiiaximum level-flight speed of an airplane 'bj an arbitrary factor somewhat greater than 1.0. The termi- nal velocity of most recent airplanes, ho;T?sver, generally falls much below this arbitrary i.iaximum speed, and these airplanes are therefore unnecessarily penalized by extra v;eight because thejj- are designed for conditions that are not reached in actual flight. The present report outlines a simple 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 wind-tunnel test data were obtained from model tests conducted in the Langley 2li-inch and 8-foot high-speed tunnels. All the data presented herein v/ere obtained for zero lift. The problem of determining the terminal velocity for airplanes for which the terminal velocity is near the ci'itical speed is comparatively aimple inasmuch as a constant va.lue of drag coefficient can be assumed. The diving speeds of most present-day airplanes, however, occur beyond the critical speed o.nd the problem is noi: so simple. The following two factors are involved: (1) the determination of the critical speed and (2) the rate -of di'ag Increase at speeds above the critical speed. The critical speed used herein was arbitrarily taken as the critical speed of the wing-root section. Preaaure— distribution data obtained from wind- tunnel tests -^'sre used to determine the critical speed, which is defined, as the flight speed at which sonic velocity is readied locally. If experimental data are not available ,. ho-vTever,- 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 wing-root seci-ion for use in terminal- velocity estimation is justified on the_ grounds, that tlie root section usually has a lower crltica]. speed than any other component part of the airplane. 'The :.uog. root has the lo.vest critical speed because of its.. high thickness ratio and contributes a large part of the to±al . airplane drag because of the largo fraction of the .viiig. area concentrated at the inboard sections of tapered, ■citings. The rate of drag Increase at speeds above the. criti- cal speed is more difficult to determine in the calculation CONPIDSNTIAL NACA ACR No. L5G51 CONFIDEKTIAL of the terrainal velocity than the critical speed. A study of the drag of airfoils, fuselages, nacelles, and \vixid3hields has been made froin v/ind-tunnel test data in order to determine the effects of compressibility on the drag. Because the rate of drag increase at speeds above the critical speed is so great, it -./as foTTxid that, v\fithln the accuracy required for terminal- velocity calculations, an average rate of drag increase Kay be used, a curve indicating the average rate of drag increase is presented herein. This curve was derived from an analysis of wind- tunnel data. The method described herein for obtaining the terzni- nal velocity of an airplane in a vertical dive has been in use at the NACA since 191+1 • Publication of the method, however, 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 vv'ith several airplanes in order to compare terminal velocities obtained in flight with terminal velocities estimated by the simple method 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 gv/eepback due to wing taper ratio. S'xI'.^BOLS V velocity a speed of sound in air M Mach nu^nber (V/a) C-n drag coefficient Cl lift coefficient p mass density of air S wing area W weight of airplane p atmospheric pressure at any altitude CO?IPIDSNTIAL k CONFIDENTIAL NACA ACR No. L^GJl Y ratio of specific heats (I.I4.O for air) t/c ratio of thickness to chord, of wing ■Sub script 3 : cr critical (^vneu local sonic velocity has been reached on some point of Dody) i;iin mininiijua T terminal rE.SCRIPTION OP MODELS ii.irfoil models .- The dirfoll models used herein represent two classes of airfoils - naxiiely. the conven- tional NACA sections and the more recent low-drag high- critical-speed NaGA sections. The conventional NACA air- foil sections are characterized by pressure distributions that have high peak pressures occurring near the leading edge. The low-drag NaCA airfoil sections have compara- tively flat pressure distributions with the peak pressures occurring at approximately 60 percent of the chord behind the leading edge . the tip: and the Davis airfoil with a thickness ratio of 20.15 percent. The lov/-drag airfoils include the following NaCa airfoil sections r IC-2I7 65-tyos modified, -- = O.I96 i^-53y 66.1-115 65 (218) -220 ^'^^ ^^^ The effective aspect ratio of the airfoil models tested varied from 6.S to infinity. D uselage models .- T':e fuselage models are tytlcal of fuselage snapes hi use on current airplanes. The various fuselages represent bomber, fighter, and transport air- planes. Figure 1 shows the 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 dashed lines In fig. 1) and represent a v/ide variation in wing-fuselage interference. gon?idl;ntial NACA nCR No. L5'^51 CONFIDENTIAL 5 Nacelle and windshield models .- The data for the various nacelles and windsriields were obtained from refer- ences 3 ^^^ hi respectively. The nacelle and windshield designations used herein correspond to the designations used in references 5 ^-nc? I|. All the nacelle models v>fere tested with the same wing model, which consisted of the outboard panel of a wing section designed for use on a bomber airplane. The wing was a thick low-drag airfoil that had an NACA 65(2l8)-221 section at the root and tapered to an NACA 66( 2x15 ) -i4-l6 section at the tip. The windshields were tested Y/ith a v.'ing-fuselage combination. Drawings of the nacelle and windshield models are shown in figures 2 and 5, respectively. RESULTS AND DISCItSSIOF Drag Characteristics Drag analysis .- In order to obtain a correlatioxi of the rate of drag increase at speeds above the critical speed, the drag results for the various component parts of the airjjlane have been reduced to nondimensional param- eters- that is, Cj^/C--^. is plotted against to/Mcr for each part tested. The use of th^se parameters represents a convenient method of making uhe 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 IIACA airfoils are presented in figures L and ^. Figures 6 to 9 s]'iOw the variation of Cq/Gtv . with K/M^r ^^^ ^^~^ lov/-drag high-critical- speed airfoils. It will be noted that all the airfoils presented in figures l^, 6, ^, and 8 exhibited approxi- mately 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 30 per- -•T cent above the minimiom. drcig was indicated at -^-— = 1.0: at speeds of only 10 to 15 percent above the critical speed, however, the ds-ag increased approximately 90 to 200 percent. This rapid increase in drag at speeds above the critical speed is associated with the formation 6 CONFIDENTIAL NACA aCR No. L5G31 of comDression shock vi/aves 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 OOO9, 0012, or the low-drag high- critica]. -speed airfoil sections. Both published (rei'erence 5) and unpublished high-speed data show that the NaC^. 25O- series airfoils differ from most of the other airfoils in that the critical speed can be exceeded by as much as O.IS in Mach number before any serious changes in the aerodynainic characteristics of the airfoil occur. The critical speed of the NaCA ZJO-series airfoils is therefore exceeded by approximately 7— 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 di'ag curve above the criti- cal speed on the estimation of terminal velocity is dis- cussed in the section entitled "Terminal-Velocity Calcula- tion." The rapid increase in drag before the critical speed is reached, which is shown for the NACA 67-llIj-.'3 airfoil in figure 9> is due to early separation of the flow over the after portion of the airfoil. This condition also affects the m.ethod for estimating the terminal velocity. An error in estimating the terminal velocity when the flow separates will occur only for those airplanes for which terminal velocities are at or near tne 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 Cq/Cj)^. with M/Mqp for several fuselage shapes and fineness ratios. The drag increments for the nacelles and v;indshields are presented in figures 11 and 12, respectively. The criti- cal speeds for these bodies v/ere based on the wings v;ith which the models were 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. In the correlation of the average drag increases of the various components of the airplane throughout the Mach number range, a generalized drag curve was derived CONFIDENTIAL NACA ACR No. L5G5I CONFIDENTIAL and Is presented in figure I5 . The data presented in figures I]., 6, 7> Sj 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 I5 percent above the criti- cal speed v;as used. The generali2;ed drag curve v/as extra- polated by use of a straight-line extrapolation from I5 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 drsg rises rapidly due to compressibility^ effects . C onstriction corrections .- Corrections for constriction effects have been applied to the data. The constriction corrections have been determined from pressure measure- ments obtained in the Langley 2l|.-inch and 8-foot 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 nijmiber below the choking speed of the tunnel. The corrections to the Mach numbers amounted to approximately one-half of these values. The constriction corrections were such that the coefficients were reduced and the Mach numbers v/ere 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. Com.parison with flight data .- Figure li| shows the variation of over-all drag coefficient with Mach nuinber for the XP-51 airplane as measured in flight and the variation v/ith Mach nuTPiber of the wing-profile drag at the irid-semi span station measured by the wake-survey 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 llj. for comparison with the flight measurements of over-all drag and wing-profile-drag data of the XP-5I air- plane. The curves for the wing-profile drag and the over- all airplane drag in flight begin to rise rather steeply CONFIDENTIAL 8 CONFIDENTIAL VaCA ACR No. L5G3I at about the same Ivlach number. This fact tends to justify the assumption that the v/ing-root critical speed is a suitable criterion to use in teri.nlnal-veloclty calcula- tions. The estimated drag deidved from the generalized drag relation indicates higher drag coefficients at Mach numbers of ar)pro:cimately 0.55 to 0.75 than are shovvn for both the measured wing-profile drag and the over-all drag coefficients. Of mere importance, ho'.vever, is the good agreement that is shown for the values obtained by use of the generalized drag curve and the m.easured flight data at Mach numbers greater than O.'J'-}, v«hich is the region where the terminal Mach number usually occurs. Figure 15 shows a comDarison of measured flight drag and estimated drag for the XP2A-2 airplane of reference o. An important difference in the drag curves occurs at Mach numbers around the critical Mach number. The estimated drag indicates lower drag coefficients than do the flight measurements o This difference is believed to be due to a combination of early shock formation on the cowling and airplane-wing roughness, which is believed to have caused some separation of the flow. Good agreement is indicated betvi/een the flight measurements and the estimated drag in the region where the drag coefficients rise steeply, which is the region that determines the terminal Mach number. Terminal-Velocity Calculation The generalized drag curve (fig. ij ) nay be used as an approximation in determining the terminal velocity of an airplane in a vertical dive. The 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 pi'opeller characteristics. Tn the present analysis, however, zero propeller thrust is assumed and the propeller drag or tlirust is therefore neglected. At supercritical speeds the drag or tlirust caused by the propeller is considered to be negligible as compared with the drag of the airplane, particularly if the pilot throttles the engine and adjusts the pi'opeller to a high blade-angle position. Tlie terminal velocity for zero-lift conditions is given by the relation CONFIDEiYTIAL NACA ACR No. L5G31 CONFIDENTIAL S=\Wfh (1) Js P Cq or, In terms of the terminal Mach number Mrp with the /yp speed oi sound equal to \/-^, ^ a y S Y P C3 Equation (2) can ue rewritten in the form %^ifh.^ ir.in / Mrain (3) _ . /2 W 1 W where is constant for each airplane at the PSC^ . mm altitude for which T.Im is calculated and which is obtainable from the. generalized drag curve. Equation (J) can then be solved for the parameter W ' ^ Figure lo shovvs solutions of equation (J) for psc^„. tiin various values of Mq-t. and - pi»C-> ■^lin In computations of the terminal velocity, the only data that m.ust be known about the airplane are the minim.'ora CONFIDENTIAL 10 COIIPIDEHTIAL ■^J ACA ACR No. L5G51 drag coefricieiit at zero (or approxiBiately zero) lift coefficient or a low-speed, drag coefficient whereby the minirn'om drag coefficient can be computed by use of the generalized drag curve, the wing critical speed, and the wing loading. Values of these quantities, all of which are used in calculations other than those for the terminal velocity, are easily obtained. A'ith these values known for ^articular air-olane . the parameter can be ■"^in calculated for different altitudes; then, for given values the terminal Mach number can be of M^^p and ^^ , pSCn. . obtained bv use of fl£:ure l6 In order to illustrate the method of obtaining the terminal velocity graphically, the terminal velocities have been calculated for the XP2a~?., P-i'41^~1, and P-I|.7 air- planes. The pe^ti.l^:■nt data for these airplanes are given in the following tables TABLE" I AIRPLANE DATA Airplane cr Cd mm W 3 XF2A-2 i0.6l (flight) j 0.022 (flight) I ,66 (corrected) I (Ib/sq ft) 26.1 P-39F-1 ;0.675 (estimated) ;0,OlS (estimated)! 3k^^ P-^7 10.61; (wind tunnel) . .020 (flight) ' .69 (corrected) i 1-5.0 By use of these data the parameter IS 'min computed for each airplane. The use of figure 16 to estimate the terminal Mach number is Illustrated for the P-ii.7 airplane at 15,C00 feet altitude. The variation of CONFIDENTIAL NACA ACR No. L5G51 CONFIDENTIAL 11 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 Mach number with altitude, are records of flight data for the XF2A-2, the P-kl , the P-U7C-I-RE, and the P-39N-I airplanes. The flight record for the P-[|-7C-1-RE airplane was obtained by the late Major Perry Ritchie in a terminal- veloci ty dive made at Vi^rlght Field in July 19^5* The points represented by circles were obtained from a dive of a P-Ii-7 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 Major Ritchie for the P-I4.7C-I-RE 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 pull-out from the dive, respec- tively. Data for the XP2A-2 airplane were obtained from reference 6 and the data for the P-JQN-l were obtained from dive tests made at Ames 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 230-serles airfoils and airfoils similar to the NACA 250-series could exceed the critical speed by appror.imately O.O5 to O.15 in Mach number before any important changes in the aerodynamic characteristics occurred. At -i^^i— = 1.0, therefore, the NACA 250-series M 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 250-series 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 teiininal velocity, the indicated wing critical speed must be increased approximately 'J— percent CONFIDENTIAL 12 CONFIDENTIAL KAGii ACR No. L5G31 for the NACA 2J0-series sections. This correction was applied to the critical speeds of the P-ij-7 and XP2A-2 air- planes (see table I), since these airplanes have NACA 250- series sections. The dashed curve on figure I7 for Kcr = 0.61}. is the result obtained if the indicated criti- cal rach number is used rather than the effective critical 1 Mach number, which is about 7-^ percent hi^^her. Langley MeR:orial Aeronautical Laboratory National Advisory Conirr.ittee for Aeronautics Langley Field, Va . REFERENCES 1. Robinson, Russell G., and Wright, Ray H.: Estii-nation of Critical Speeds of airfoils and Streanline Bodies. NAC^/aCR, March 19ij-0 . 2. Keaslet. Max. A.: Critical l.lach Nurnbers of Various Airfoil Sections. N^-iCA ACR No. kaiS; 1914^. 5. Becker^ John V.: High-Speed Tests of Radial-Engine Nacelles on a Thick Low-Drag V/lng . NACA ACR, May 19k2. ii.. Delano, Jaznes B., and V/right, Ray H.: Investigation of Drag and Pressure Distribution of '/windshields at High Speeds, NACA aRR , Jan. 19v2 . 5. Becker, Jolin V.: Kigh-Soeed .Vind-TunJiel Tests of the NACA 23012 and 23012-611 Airfoils. NACA aCR, Feb. I9I1-I. 6. Rhode, Richard V., and Pearson, H. A,: Observations of Cornoressibilitv Phenomena in Flight. NACA ACR No. 3015, 19ir3. CONFIDENTIAL NACA ACR No. L5G31 Fig. la-g CONFIDENTIAL (a) ( ^ -^ /"//-i eo e55 r<::7 f / o , 10.32. (b) ^ f/r\e>^ess raiio , 6.65 (c) C^_^II f/r^e/^ess rafio, 7.30 (d) ^ Finer^GSS raiio , 6/4 (e) _; Fir\er\e55 raiio t 5. 7 •" Voriafion of ratio ^0/^0^10 '^''^^ ^^l^^cr tbr several Nfi^CA airfoils . I.Z NACA ACR No. L5G31 Fig. 8 2.6 ZA zz 2.0 «•' 1.8 Q U 1.6 1.4 I.Z 1.0 .5 CONFIDENTIAL 1 1 Airfoil seciions f ^ACA 47-215 67,0-Zl5 /6-2/5 i J / 1 1 / '/ (' A / ^^ ^ ■:> .S'Z ~^^ ^^ — ==^ ^^ CON FIDE MTIA - NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS .6 .7 .a .9 /O /./ /2 cr Figure & ■- Variafioi^ of ratio Ci^/Cq^-^ \^i+h K^/f^cr ■For several NACA airfoils . No frans-iiior^. Fig. 9 NACA ACR No. L5G31 CO CONFIDENTIAL 1 1 , 2.6 / Z.A Airfoil secf/o/ns | MACAe5CEie)-2ZO ,, / 65-f(^e modified, ^/c =0.I96\ Dav^is airfoil^ ^/c '=0.20l5 / 67-/ 14. 5 1 ZZ \ 2.0 / / / / /i \ 1 /' 1 /.6 y / // / / / / / / /.4 / 1 / / / / 1 / / \.Z / / / 1 / / ^ . ^ ^ / 1.0 "^^c ^ ^ ^^^ _ " ^ r^ ^ CONF DENI riAL 1 1 1 NATIONAL ADVISORV COMMITTEE FM AEKOMiUTICi • ^ ? .'< ^ i 5 .t 3 .i r i J S ? /. o / 1 1. 2 J^^jt^cr Fic^ure 9.- Variation of ratio Cf^/Cc^j^ \^}th, /V^/a^^^/- for Davis airfoil arid .several NACA airfoils . NACA ACR No. L5G31 Fig. 10 Q Q U 2.2 CONF IDENTIAL Fuse/oge Fineness (See fig.l') ratio (a) 10. 3Z fb) 6.65 CO 7.30 Cd) 6.'a (e) S.60 1 i 2.0 1.8 rf ) 4.75 rg) 3.30 I i 1.6 1.4 / ' 1.2 A f ^/^ / 1.0 ^ ^ ^i^ -^ =-« ^^= ^ ^ J^Z- CONFIDENTI AL NATIONAL ADVISORY COMMITTCt FM A£ROM»UTICS •%. 3 .^ t 4 5" ■i 5 . 7 .6 c J /. o 1. / I.Z VW/v/cr Flexure lO . - Variafion of rofio Cp^Cp . wiiH f\yl/hylcr for several fu&eh<^e. s/^apes. '^'^ Figs. 11,12 NACA ACR No. L5G31 18 i.e .c Q lA u c? I.Z 1.0 CONFIDENTIAL 1 1 i Nacelle. CSee 1 ' f,g. 2 ) 2 3 4 5 / / / ^ - -. — ^^^ , -- --p^ ^ ^ NATIONAL ADVISORY COMMITTEE FM AEBOMAUTIC-S .4 .6 .7 e I.O I.I I.Z Figure II .~ Var/a-lion of rafio ^o/^Dmin ^^''''^ ^^/l^cr for several r^acellQ shapes. Q O^ 2.0 1.8 1.6 1.4 I.Z 1.0 ■ ■■ windshield C See fia.3) 3-1-1 3-l-Z 2-0-3 4-0-3 1 '/ 1 x-i y / A f 1 '/' / / <^ V ^ y ==s^ ^ t^' ^ cc )NFID ENTI AL NATIONAL ADVISORY COMMITTEE FM AEHONAUTICS .4 .7 a 1.0 I.I I.Z rie^L^re 12. .- Variaf/'on of ra+io Cq/Cq^j^ wi+h /\yi/l\y1^^ for several \A/ir\d shield shapes. NACA ACR No. L5G21 Fig. 13 o.o a DNF IDE STI AL 5.4 1 / ; 5.0 / ; / ; 1 4.6 / ; ; 4.2 ; / / 3.8 / / / Q 3.4 — Exirapolaied I ; / / "%.o 1 / / ; 2.6 ' 2.2 / / 1.8 / / 1.4 y / y 1.0 . - CO NFI DEN TIA L NATIONAL ADVISORY COMMITTEE F0« AERONAUTICS .3 .4 .5 .6 .7 .Q .9 1.0 I.I I.Z 1.5 Figs. 14,15 NACA ACR i\o. L5G31 k i u OS CONFIDENTIAL 1 1 — o- — Over-a// draq yO, J 0- — Ovepall drag (F/igh-t^ — Esfima+ed drag from generaliged drag Ci^rve J '> 6' ,._J f 'J X y / - ^ "-^ -—- "^ CON FIDE^ TIAL NATIONAL ADVISORY COMMITTEE F0« AE«ON«UTICS • / .1 7 ,^ J A V i J i 5 • t 7 .6 ? fsytach riumber, J\ri Figure /5 .- Vnriai-ior^ of measured fZ/gf^'^' o/rac/ and esf/nnafed drag vaz/V/i f^ach, number for XF2/\-2 QJrp/ane • NACA ACR No. L5G31 Fig. 16 ' ' ' r— V^/ ■ i35C» . I.Z5 "min s.% 5.4- 5.0 4.6 4.2 J.8 3.4 3.0 2.6 f / / f / I.ZO /■ /" / / /• /' / / / /' /' / ,. /'. / / / / / / / / 1.15 / y / / / y / / ^/ / 2.2 / f / / / / / / f y / / / / / p / f / / / / / ■^ UO ^ 'h / / / / / / / / /' / / / / /.4 / ^ / / / y / / / / / / / ^ / / / / / / / / 1.05 / ^ / / / / / / / / / / / / k / /' / / / / / / / / / / y y 1.0 ^ / / / / / / / y ^ I.OO A < y / / / f. / A ~^ / / / / / ^ y* y )ii / / / / / ^ y Q> / f / / / / / X -Q / / / / / y / ^ / / / / y .8 / / / / / / / / / / / / / y / f / / / / y y' ^ .90 / f- / / / / / t^ y / / / / / / A / / / / /' / y . / / / / / y .7 / /■ / / / / ^ / y - / ^ / / / !> /■ ^ y A y .85 ■^ / / / ^ y y / / / / / y / / , / f / y , H y .6 ? - -■ -- • - -- ' ~f ^. ■/^ ^ / / 1^ / y — -l / / z L^ y ^ y iS .80 / / f / X / / / ^ / / / / / 1 > / / y / / A / A ^ / / ^ ^ 1 / / / . / / }, / ^ .5 .75 / / /* / / / ,\ A / / / / / '\/ ■' ^ / / / / /t y / / / / y 1 y / / / /■ y .70 / ^ / / y 1 .4 / / y 1 - > / / 1^ y / y -- / , y* 1 .65 /■ y L^ — ^-47 airplame af I5.000 fi ^ y^ 1 1 1 .60 1 1 ID NA TION kL ADVISORY ~| 1 COMMITTEE FM A IM MA Ul L& 1 .60 .65 .70 .75 .80 .85 .90 .95 CrU-i'cal Syfact^ number , Aylcr Fi<^re /6 .~ Terminal Sylactn r\umber chari. I.OO Fig. 17 NACA ACR No. L5G3.1 0) f "5 u >- P " 2 o 2 !i>o < ^ z ^ ^1 ,h^f t ^ "i ill 1 ^ 1 r ■ tn •o 1 1 \ / / \ y \ \ \ } (1) ^J \ Y \ \ '\ \ \ \ \ \ \ V .c: \ \ \ \ O -1 \ \ \ \ ^J 1- \ v \ \ \ / _l < o \ \ \ \ \ 1 \ \ / Z b. 2 o \ \ \ \ \ / \ ii. O 1 1 \ \ \ / / z o u 10 > i / >^' \ \ \ ■5 1 \ \ \ \ \ \ \\ \ •< 1 \ \ \ \. ^ Oi \ { \ \ \ •^ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ «o \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ o o 0) D a a J D C 4 01 3 i! D f J C ) CI: -^T^V ' jsqujDL/ ^ooyy /ouiu/joi I UNIVERSITY OF FLORIDA 262 08105 00 UMiVERSl-n^ OF FLORIDA DOCUMENTS DEPARTMENT 1 20 MARSTON SCBnICE UBRARY P.O. BOX 117011 GAINESVILLE. FL 32611-7011 USA