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p( 7. ......... p U .: ;;;A 21,ii: pi ; ;: % 4. ....:. *" .. ..' .. .' .. :. .' : .; 4', Y. 'q$ W.Y... .. ... ... . .i :.: ': ;::.. .""" : : :'.:: ;:: .': "... . :..: : .... ......w ... ... ... . ~. :. ",; ~ i ':""".:' :;; .,' ; :7 :..:v.' :!.: fcQ. aNXT :kpj Fl 'Y.: Alk .'C' 4..i :.. : .r N`': .: ; i ". .'" :: ,"i I ., .:.1. : ,: :. t.: i: ... .... r. : .. ,:.. ::.., .... ;; .. .... .. ....... .. i .. : '.. .. :.' i, : :".:.: :':' ':. 3U~ " U". X::'i"'\ .0.. ,, ON JQ::.:: :'., . ::' :" :;':I;S `' ;i. ;.: :,r).. E7 ,,; .....,!.i. ,.:, .... ,: , ,: ,ijij ;l'.: .if.;::::,;. I :..'. .. >: ':;::/: i.B+:7:;( ., i': ;;: "'' :: .'':'" ... ,. ,.. .... : ,.:. :.: ..: si ' " 'm NACA RM No. ATA31a CONFIDENTIAL NATIONAL JVISORY CO.MMIITT'E FCR A iURO'AUTIC3 PE3ZEACE i.EM3,.j 'UM EXPEIiIENTAL INVESTIGATION OF THI EFFECTS OF VISCOSIT'Y Or: THE DRAG OF BODIES OF REV.LUTI'.:f AT :A I.CH NUMBER OF 1.5 By Dean E. Chapman cnd Edword V. P:rkins Tests were conducted to determine the *:ffects of viscosity on the drag and base pressure cheractorc'ietics of various b.dic of revolution at a Mach number of 1.5. The modola wore tested 'bDth with smooth surfaces and with roughness ai:t.od to ovT.luete the effects of Roynnclds number fcr both lamin:'n: and turbulent b:'und jry laye,rs. The principal geometric variables investlgatte were after body shape and lengthdimincc:r ratio. 'Fr most mind1ls, f','rcL tests and base pressure racasur iments w.re. miad? over a range of poyrrl si numbers, based on model length, frJm 0.C million to 5.0 millions. Schlicron photographs wort used to analyze the effects of viscosity cn flow separation and shockwave cnf'iguraticn near the base and to verify the condition of thi boundary layer as deduc:d from force tcst3. ThIc results are:. discussed and compared with theor.tical calculations. Tb.he esults show th"t viscosity effects are large and deacnd to a great d.groD on the body Lsh.c. Thie effects differ. gro.tl for laminaar and turbulr.nt flow in the boundary layer, and within e:ac regime depend upon the Roynolds number of the flow. Lominar flow was found uu to a Reynclds number of 6.5 millions and may possibly exist to higher values. The flow over th5 ofterbody and the shockwE.vo configuration near the base are shown to be very much diff:ront for la i:ncr than for turbulent flow in the boundary layer. Th' base piesure is much higher with the turbulent layor than with the laminar layer, result ing in a negative base dr:.g in some cases. Tho total drag c'ibracter istics at a given Peynolds number are affected c,nsiderably by the transition to turbulent flow. The fore drag of bodies without boat tailing or of boattailed bodies for which the effects of flow separation are negligible can be calculoatd by adding the ckin friction drag based upon the ascumptiion of th,! lowspeed friction characteristics to the theoretical wave drag. CONFIDENTIAL 2 COFOTITTDEFL 'AC,. R3: I;c. .7.'31 For laminar flow in th.: boundc.; 1.c"r t.:o :.'fr:ctz o' vr'ink the Reynolds number were fu,'nd to be la: _e, p:'._.x:'"matpl dc:bllng the base daCE in man: cases and increasing the t. tal drg debut 20 percent over the Reynolds number renge investl~sed _r'' turbulent flow in the b'undary layer, the effects cf va..;.pn tlhe Reynolds number usually changed the base drag and total drra coe.?C clients ccnslderblyr. ITODUCTION The effects of viscosity on the aerdyrnamic characteristcs of bodies moving at low subsonic speeds have been kn'wwni fto man years and have been evaluated by numerous investing tcrs. T. effects of viscosity at transonic speeds have be.r. Invest .,ated only recently, and relatively large effects on t:,e fl:w ove" r foils are reported o; Acho:ret (referer.2e 1) and Lpspann (eftrence 2). Alth:c.ugh the relative ti,'oni'rhnesa of thesz two inV,!E'tigatlons has furnished a *'ood start toward a satisfactory evaluation and under strndilng of thE. effects of visc :osity in transonic flow fdld. till very little is known about the effects at purely supersonic spe'ds. The experiments reported in references 3, 4, and 5 have succs3eed in evaluatilrn the mancntude of the skin friction for supersonic flows in pipes and on curved surfaces. Reference 6 contains a small amount of data on the effects of Reynolds number on the drag of a sphere and a circular cylinder; however, these data are not appli cable to eerjd;.'nrmic shapes which are practical for supciscni? fr ght. It has been gen.rrally assumed that the effects of viscosity are small rnd need be ccnidc'r.d only when dtnrmninn. the magnitude; of skin friction. In repviewing past data for the effects of visccsity it was found that in many reports, such as references 7 and b, the model size was not stated, th.orcby rand'.ing the calculation of Renilds number. qu'te difficult. Proelminar:r tests in the Ames 1 by 3coot supTssojni0 wind tunnel No. 1, which is a variablprorss.Lre tunnel, showed a r.latlvcly large effect of Roynolds number on the drag of bodiics of revolution. Th3 results of this cursory nvostigation wore not ro,.o ;td' b~c.aus the magnitude of support int.rforence was not known cnd because certain inaccuracies in the balance measurements wore kncw, to x.i:st in the data tak.n at low tunnel pr'ss3ur':s. An invosti:,otic n of w.nj body interaction at supe rsonic sp,:ed. has been ccndj.ct.d subsquontly and the results presented in rforonco 9. Bc'euse .if th, supnrrt interference and the boln:e inaccuracies nrtcd at low pros33ur'S. the dr.ts pr,:esntcd ther.ein of t,.r .lffoct of RP.ynolds numibr on th;' drag of smooth bodies are not sufficinr.tl:, accurate thr'uiout the r nGo of E;,T:nolds numbers for direct applicaton to tho conditions cf froo flight. . 3IFIDEnITT AL NACA RM No. ATA31a Since the effects of viscosity already were known to be relatively large at the :utset of t*his investigation, the purpose of the present research was made twofold. The primary puriji:se was to develop an understanding of the mechanism by which viscosity alters the theoretical inviscid flow over bodies of revolution at supersonic speeds, and the secondary purpose to determine the magni tude of these effects for the particular bodies investicatc.d. APPARATUS AID TEST METHODS Vind Tunnel and Instrumentation A general description of the wind tunnel and the principal instrumentation used can be found in reference 9. Included therein is a description of the schlieren apparatus, which forms an integral part of the windtunnel cqulpment, and the straingage balance system employed for measuring aerodynamic forces. In order to obtain accurate data at low as well as high tunnel pressures, a more sensi tive dra gage was used in the present investigation thbn in the investigation of reference 9; however, all other details of th; balance system cre the same. For the purposua of ti.e present investigation, it is p.Jrtinont to add that the tunnel is equipped with three turbulencereducing scrosns located in the settling chamber. The tunnel total pressure, the static reference pressure in the test sctien, and the pressure in the air cher.bc.r of the balan.:ce housing wore obsercvd on a mercury manometer. Because the differ once b. twoon the base pressure and the static rcforonce pressure in th.: tit suction is ordinarily too small (only 0.5 cm of mercury at low tunnel pressures) to be accurately road from a. orcury.manomoter, a supplementary manometer using a fluid of lower specific gravity : was employed. Dibutyl phthalate, havn a specific gravit;, of approximately 1.05 at rom temperatures, was used as an :ndicating fluid in this manometer instead of the conventional light mcannmeter fluids, such as water and alcohol, because of its lower vapcL: pres sure and its property of releasing little or no dissolved air when exposed to very low pressures. Models and Suppcrts Photographs of the models, which were made of aluminum alloy, are shown in fires 1 and 2, and their dimensions are given in figure 3. Models 1, 2, and 3 were each formed of a 10caliber ogive nose followed by a short cylindrical section; they differ from one another only in the amount of bcar tailing. The shape of the olve was not varied in this investigation because the flow over it is not affected appreciably by viscosity. Models 4, 5, and 6, which differ CONFIDENTIAL CONFIDENTIAL 4 CL'iJrF 'EI'TL'JL IL.C PM4 l.o, ..31* from one another only in thickness ratio, were formed by: pr.abotl arcs with the vortex at the position of maximum tihk.s. F: convenience, some of thi. more important geometric prp..rt:i t .f models 1 t;r'.iurt. 6 are listed in the following table: Nose Area L :. Base Model Frontal half volume diameter area area, anglo ratio Li ratio A(sq in) e(dog) A/(V)2/s L,/D A/A 1 1.227 18.2 0.302 7.0 1.00 2 1.227 18.2 .309 7.0 .5.8 3 1.227 18.2 .318 7.0 .348 4 .866 11 3 8.8 .191 5 1.758 15.9 .32 6.2 .186 6 3.426 21.8 .479 4.4 .187 In addition to the abovemontionod models, several other bodies were tested for certain specific purposes. Thus, models 7 and 8 woro made unusually 1ng so that the skin friction would be a. :.. portion of the messied drag, thereby enabling the condition of the boundary layer to be deduced from force tests. Various substitute c.gives, shown in figure 2(a), were made interchangeable with the smooth ocZve that is shown attached to the ylindrical a'fte'brod;. c model 8. Th3,e ogives were provided with different t;..Les and amounts of roughness and could be tested either alone or with the lcrnp cylindrical aftr.b:1dy attached. When the gives were tested alone, a shroud of the same diameter as the ogive was used to replace the cylindrical afterbody. MJ'del 9, a bfd.y. with a conical nose, and l.'del 10, a splere, were tested in order to compare the results of the present investigation with existing theoretical calculations and withthe results of other exper~e'im:nt:l investl;s tions. Il.:,dils 11, 12, 13, and 14 were constr.,ctr,.e to determine the effects of the lengthdiameter ratio for a fixed shape of aftei'bhdy. In all cases when a smooth surface was desired, the models were polished before testing to obtain a surface as free from scratches and machining marks as possible. The models were supported in two different .*". : by a rear support and by a side support, as shown in f".:; v.: 4, 5, and 3. The rear .;_..pc't used in the :i.jori'. of the cases consists ci' a, s.n. which .1i1,.':.t t? . model and attaches to the balance beam. A thin steel shroud encloses the sti.n :rnd t,':b.' li:.r't.tes the aero dynamic tare forces. Use ':2 the rear S'.; :,.' allows force it., base ei.;: ,;:i',:. data, and schlieren pr : t ~:ro,.1: to be taken simultaneously. Th. side ?i;.ppojt which attaches to the lower side .. the ..:ik.'1 consists ..f a 6percentLh'c': airfoil of tra: ~e'i: s..r.:nts and 70 .Tiw tt... onl.: a.t the;l 1.:3adir and trailing .a:i Thc C :F T E'I IAL HACA RMI No. ATA31a CDjFIDE2JTIAL 5 side support was used to dotormine the effects of the axial variation in testsection static pressure on base pressure, and, in conjunc tion with a dummy r. ar support, to evaluate the effectss of support intrfcrerncs. Base pressure data and schlieren ph.,'t' ,'aphs can be obtained when the side support is used. Test Methods The tests wre conducted at zero anglo of attack in a flixd nozzle designed to provide a uniform Mach number of approximately 1.5 in the tost section. For the positions occupied by the different models, the frc.stream Mach number actually varied from 1.49 to 1.51. This is somewhat lower than the Mach number of the tests reported in reference 9, which were conducted farth,::r da:.matronc in the test section. Before ar d after each run precautions wore taken to test the pressure lines for leaks and the balance system for friction or zero shift. Each run we.s mad. by starting the tunnel at a low pressure, usually 3 pounds per square inch absolute, and taking data at different levels of tunnel stagnation pressure up to a maximum of 25 pounds per square inch absolute. Bccaus.. of the lag in the manometer system, approximately 15 minutes at low pr:ssurcs and 5 minutes at high pressures wore allowed for conditions to come to quilibrium. The overall variation in Reynolds number based on body length ranged from about 60,000 to 9.4 millions. The specific humidity of the air usually was maintained below 0.0001 pound of water per pound of dry air, and in all cases was below 0.0oo3. In general, coach body was tested with a polished surfa'c and then later with roughness added to fix transition. As illustrated in figure 2(a), several different methods of fixing transition on a body in a supersonic stream wore tried. The usual carborundum method employed in subsonic research was not used bcciiuse of the danger of blowing carborundum p.rticl:s into the tunneldrive compressors. The method finally adopted was to cement a 1/8inch wide band of particles of table salt around the body. This method proved successful at all but the very low Roynolds numbrs. On models 1, 2, 3, and 12 roughness was located oneighth inch down stream of the beginning of the cylindric'l section. On models 4, 5, and 6 the roughness was placed 4.5 inches from the nose and on model 8 oneighth inch upstream of the beginning of th,:: 7ylindiical aftorbody. Models 7, 9, 10, 11, 13, and 14 were tested in the smooth condition only. CONFIDENTIAL 6 COFENTIl .CA ::0 .7.31 T TI.LTS iedivtion of L.'ta The force data. 5nludd. in this rccr:t '.. b.c re.cd t the usual coefficient form through division by the p;:d.:. f the fjstream d,ncr.ic pressure and the f'cntal area o:f th! b U';. If it is desired to refer lTh.se coefficients to (IlvJ...) t; nocessary conversion factors can b: found. in the tbl. ofI t.; geometric p.:prtieo of tLc ilodjls includedd in th s.rtin .n models and supports In each case, conditions just ?h..' .f t':., nose of a model are taken as the fruostroam conditins. The measurements of the ur.essur; on tho base of o,.. !.,;:. i are ref .i . to freo stream static pressure and mai ." :n n"l. aJ t~rn':.h division by t..! freestroam dynamic pi s.;. T. t.. base pressure coefficient is calculated from the :quawt n wlhoro Pg base pressure coL.ff Lcient PB pressure ac't'n., on the base P1 f.. team static pressure q1 fr..'2.st..t :.vcl d r.u c pressure The dynamic pressure is cjcul:tAd from the isent)i', ... . ships. A small cxp .r:m.intally det.:i.L:nAd correcti:.n is .ppli.:i for the loss in total pressur, duo to condensation f wat.r va:;r in the nozzle. T!:, R..ynolds number is Lbszd upo t. b.d;.: ln'U.. and is calculated from the isontropic r:lat jns'.i,.: ,i'., Sutililand's formula for tbo vri:t .n. vi'scosiL' witi t: tomperaturo :f the air. It is convenient to consider th... frc. due to tLeo bas:. pr3ss as a s.. .r..rst, .:ompn.nt of th ttl i'g Acc:.rd:lnjl:', t bLsa. drac is r.f rr.A to th. frontal are, snd in c.;'i'.:..nt f.oi is "i von by %C = PB ( i" B P 'A " TD IF .i'ENTIAL i' MACA P11 F.. A;A31n CFFIDENTJAL 7 whcr" CDIB base. drO cc:fficiient A3 area of base A fr:ntal c2ea *:f the body The fore dral is defined as the sum of all .drag forces that act on the b:,d,' surface forward of the base. Hence, t3.e fore _l:i coefficient is given by F = CD CrB (3) wh.i' Cp is the trtal drag ccefficient and 1 .F the fore drag coeff'.cient. The c':ncept of fore drag coefficient is u'efl.il for several reasons. It is the fore drag that is of direct importance t the practical designeir when the pressure acting on the base of a bcdy is altered by jet of Eises from a power plant. Considerll.n the fcre 'ira a.s an independent c.monent of the total drag :'?atl1 srmplifies the drha anl.ysis of a given bo;r,. Finally, the fore draC, as will be exy^lineli later, is not affected appreciably by interference cf ti:e :ear supports used in the investigation. Since the nozzle calibration with no model present showed that the ctatic pressure el'ng the axis of the test section is not cnrjstant (fig. 7), tl.e measured coefficients have been corrected fC thie in:renent of dr. or pressure resulting from the axial 'essulre cadient. , detailed discussion of this cc:.rect'on is presented in appendi: A and the experimental justification shown in figures and .7 Precision The table which follows list.3 the total uncertainty that would be intoduced into each coefficient in the majority cf the results if all of the possible errors that are known to exist in the measurement o' tle forces and p:ssries and the determination of freestresam lich number and gradient corrections were to accumulate, Actually the errors may be expected to be partially c mpensating, so the probable in.ccui acy is about half tl.at given in the table, T::L sources and estimated magnitudes of the prbable .?irr:rs3 invol'.d are considered at zre te" length in appendix B. T'.e values in the following tabl are for the lowest and highest t.r:nrl pri?ru'es and vary lineariy in between The table does not applyy to data that are presented in figures 12(b), 16, 17 and for mcdeis 4, 5, and 6 in CC1TIIDTNTi4IAL NACA R, f?:_. !.".31 figures 2'(a) 2nd(a) aT) .Lr the possible variation in tlh. ral,nc: callbret i:n constant _,? increase the limits 2 cr: dils:.sd in appnd'.: B. Maximum value of im value value of ( efficientt error at lowest pressure c:roT' t h!1'..,at *.r.;Zi Total d: (2.I plus 0.004) + (I.r! plus 0.004) Fore dr?. (1..' plus O.COh) (0.' p1u 0. .) 3Baf .r ssur.: (0.1 plus 0.005) (0.." plus 0.':5) Base drag [0,.8 plus 0.005(;.,/A)] [0.. pls (A/A) EL'ects of Suppocrct Intorference .'_'.lous to the r.s'nt investigation an extensive sjrios of tests was c:'nd":t:J to determine Thc bL;' shapo and .?'.:p't combina tions necessary to eliminate or evaluate the support interferoncc, BEs:d upon the results obtainrid, a summary of vwh:;:i .p..'rsE in pp.ndix C, it is believed that all the droe dta., presented herein for the models tested in the smooth condition is free from support interference effects with the exception of the data shown in fil.ie 30. Fcr the models tested with r'ui.ness, the fore ira:. data are free from interference effects, but an uncertainty in the base pressure ccefficient exists which nsy vary from a mn'.nr.m of 0O.005 to a maximum of 00.015 for the different bodies. As a result, i2e base drag coefficients and total dra. .:e:ficients for the same test conditions are subject to a c:rrespond.ing small uncert.qint.:. Schlieren Ph to raphs Since much of the basic information contained in this report is obtained from schlieren pbct_.r'ap:'s, a somewhat detailed explana tion of their intrpretation is in order. A typ~:icl schlieren photograph taken with the knife edge vertical is shown in figure 1C. The various features of the flow are deagneted in this photograph which shows the entire field of view cf the sihlieren appciratus. Other items, such as the natural ralients inherent in the glass and the horizontal and vertical reference wires amounted outside of the tunnel are also apparent in this 9nd other phiotot.rrphs presented in the report. The horizontal streal:s that appear on some ct' ;he schlieren photcraphs are a, result of oil in the tunnel cicuit due to temporarily faulty gaskltirn in one of the main drive compressors. T;e mottled appearance of the background is believe' to result frcr the varying density grRdients in the boundcry layer flow on the glass windows. The schlieren photographs were taken with the knife edge both horizontal and vertical. Density grraiF:nts nDmrsl to the stream CON F IDENT IAL NACA P.I No. A7A31a direction are detected with the knife edge horizontal) whereas those parallel t the stream direction are detected with the ni.'fe J vertical. F:.i the horizontal orientation the i:.ife edge was pl c so thet increasing density rcdients in a d:_.rr1;.i.L direction .: ;p;.r as white .:]?eas on the photoraphs. For the vertical orientation the knife ed was plcrred (except for the pitraph in fig. 10 and the sph:re p:i oL.c;raphs in fig. 20) so that incre,lrn' density gradients in the downstream direction appear as white areas. Tho critical C lciulations Alth;ouih .t present no theoretical method is available for calculatin t! jase pressure and hence the total drag of a hb , sove:al neth cds are available which provide an excellent theoretical standard. t. w;ichi the experimental measurements of fore drag can be compared. In this re:port the theoretical fore ?rx5 is considered to bc; t.,: sum of the theoretical wave drag for an inviscid flow and tho .3skinfricti.n drag corresponding to the tp;t of boundary layer ti:t exists r.n thl. body. '. tj.icsl MIchi net and the corresponding pressure distribution for t'hl th;:ret.c .1 inviscid flT.r over one of the boattailed bodies testo:d in this investigation is shown in figure 11. For 'ur;p:'.,. of c ,mprisnr! the pre soie distribution as calculated by the liner their: f :n Kaman and ..r. is included as is the pressure coeffici nt a t t nc nose of a cone, the included ronl of which is equl t th: cr.'lc between the surface tangents at the nose of the c.gv... This 1 tt,:.r is obtained by the meth;i of references 10 and 11. Th wayv.: io'og for m?.rny of the bc.diULs tested was calculated by th. mcthld of characteristics for rotationally symmetric supersonic flow %s ,viv:;n in r:. foroncos 12 and 13. In accordance with the the.ci ticm1 rosuiits of reference 14, the fluid rotation produc:i by the. very small curvature of the head shock wave was neglected. This proc.dur: is justified expcr.imntally in reforonco 8, w tre the thior.?tic.l calculation using th.; method of characteristics as pr..sont;'d in r'.:'renco 12 ore shown to be in excellent agreement with thr. c m:csurc pressure distributions forogivos with ',ln ndrical eftcrbodics. Th_ calculation of the skinfriction drag in any given case requires a kno.wlcdg of the condition of the boundary layer. In the cases for which the sc:liciren photographs and the force tests indi cated t!:t thi entire boundary layer was lonhinr, the curve of th. core.tical fcor. drag used for comparison with the experimental results was obtained by adding to the wave i:.g a t"'.:or.'tical skinfriction drag calculated by using the lowspeed sir,fictiorn co.fficcnts fcr laminar boundary l;,yr flow at the Roynolds number C OIF IIT..L _T.L COTNFIDENTITAL 10 COMrfDEITIJ. NAC.A :_M i. A.. 3L based on the full length of the m.del. Ti':n r .':d'::'e, wic 1 in accordance with reference 3, g ves the oqaation S= ACfi,(rA) (/)) where CDf sk:'nfr''*tion dr'a co?2f:":'ient for the model at the Reynolds niur'.Cr, r.e, based on the full length of the model Cfram low z.ped skinfriction coefficient for laminar bo.nc.i.' layer flow at Re AF wetted area of the macie1 forward. of the base A frontal area of the model F'.r the dels with r'ug..nes. added it was assumed that t!e disturbance of the boundary layer resulting from the salt lIndl was sufficient to cause transition to a. turbulent bc'.nd.cy 1:.r to occur at the band. The theoretical skinfriction ::: was th'.r. obtained by means of the equation "Lf = C4lam ) + f Aturb ~ C turb (Alm where Cflam lowspeed skinfriction coefficient for laminar bi.undr, l:ye flow at the effective Reynolds numbr,, Re', bDuse'. on the length of the mnr?l from the nose to the :.ont where the salt band was isliod Alam wetted area of thft portion of the 7r~irli frvwi^A .:I the salt band Cfturb lowspeed skirfriction coefficient for turbulent b.dry layer flow at the P.ei.lida rn' L:r 7., based on the full lenr,gth. the :r.adel Chturb lzwspied skinfriction coefficient for turbulent 'c undari la'ye_ flow at th3 effective R.enmlds number:. F." C 01ID ETTLAL NACA PJ.l I'To. A7A31a This meth'd of calculation rreurmez that the fT.:.i ro""':;;rs: was of such a nature as to cause the turbulent b:jund'ir, layer :;'lw dcwnstream of the print where the roughness was addslle to be the same as would have existed had the boundar..layer flow hecr turbulent all the way from the nose of the bod.d. D:3CUS3 I;i Flow Characteristics Before analyzing the effects of viscosity on the drag of the bodies of revolution, it is convenient to consider qualitatively the effects on the general characteristics of the observed low. In s doing it is adv.nta.eouz to consider first the condition cf te t:unda sr layer characterized by whether it is laminar or tr blent and then the effect of variation in Reynolds number on flow sep?rat:n for each typo 'f. boundary lyer. Once the effects, on flew ser aration, of the Reynolds number and the condition of t'e bcundas.: layer are known, the observed effects on the shockwave configuation at the base of the model are easily explained. Likewise, once the effects on flow separation and sijockw;ve confiiurticn are Inclri, the resulting effects of viscosity on the fcr": drag, base darg, and total drag are easily understood. Cr.dition of the boundary layer. Since results !:.bsvod at transoni c speed s F:'fo rnces 1 and 2) have shown that tL.: n'al flow pattern about a, body depends to a marked degree on the t;,. of boundary layer present, it is possible that the boundary 1c.:,. flow at supersonic speeds also may be of primary importance in dt.tJrmininj, the overall aerodynamic characteristics of a. b:. Cocnsequently, the determination of the extent of the laminar boundary; layer under normal test conditions is of fudanental importance. In an attcmot to determine the highest Ecnn:lds nmaLnb: at which lamina' flow exists on models tested in this investi ltiLn, a relatively long polished body (model 7) was tested from a low pressure up to the highest tunnel pressure obtainable. In this case, the diameter of the sh:ud which encloses the rear E.n.'t sting was made the same as the diameter of the body. T'. fore drag nasurcmcnnt on this model are shown in figure 12(a). Snc th: skin friction is a relatively large portion of the measured for.: drag, the condition of the boundary layer can be da:'.:!i fr. these force tests. Th1 data iniicntj that tC: boundary layor on this body is still laminar up to the hih:st obtainable _c:..:ld number cf 6.5 millions. Thc computed fore drs data used for ccmparison are obtain ;,d by adding a laminar or t.u:ri.l:nt skin frictin co'fficic.t bas:d on lowspeed characteristics to t': !*'r',?F 1,E!'T !.L :'NT TEEIJT.AL experimental wave dr. of the cgi'l nose. This letter is dotormincd by subtract.ing frm the fore is a data :D SIn"lo 16 Cr. Ic. ss ..d laminar s: inf;r'ctin cc ffici:nts for the smooth civ. at t:., h.:.rj Reynolds numbers where the error, result'n :'fo tie .ss'zp tion of the lowspeed cc;fficcint3, is a. smli percent of the d:duic.d wave d;''. Schlioren photgra;.hs frL'i.r which the condition of the boundary layor maa," be obs.rv.:d arc i.o'.mn in figur. 13. They confirm the previous f'ndini by showing that transition does not occur on the body, but begins a short distance doKnstrcn 'r': the base of the model, as indicated by arrow 1 in tl.: p:.t ral:.. A close examination of the iph, .toGr'aph in fir:roe 13 reveals that the 1oJinn ng of transition (arrow 1) is located at tc., same point on the supiiF'rt c':rcud. as the waves (arrows 2 and 3) which originate from a disturbance of the boundary layer. It was found by measuremonts on the schl:lron phVtog:c'p:1s that the point of or'.in of those waves on the shroud and the intersection with the shroud of the bow wave, which has been reflected by the test  t. on side walls, coincide. This su.z; ts tbht transition on the s1 :.'1. is being brought about p:~aotu.rcly by the a, ficct... b':r waves. ,.l tional evidence that.thi.: is not natural t3an'ition is obtained in notin from figure 13 Lthat the point where transition bZI'.ns d. not move with a. change in .I:. .l, nbr. l t modol were i:nr than a critical length, whic:i is about 11 inches for the conditions of the pi'.s:nt tests, tU sa. reflected waves would strike the m:71,d somewhere on the aft.;bod;' and premature transition would i ::xrctod to affect the results. F"i urc. 12(b) shows the results of tho measurements of fore drag on a, 16.7inch b:.7,d (model 8), is!ich is considerably longer t:hn the critical length. I.. force dc t confirm the above conjocturo by clearly indlcotIn a partially turbulent boundary I;' on the body oven at Roynolds numbers as low as 2 millions. The schlieron photz:.?hi of the flow over this body are presented in figure 14. It is soon thEt, in this case also, the transition to turbulent flow (arrow 1) is ic2t.,d 't th] some point as th waves (arrows 2 .nd 3) originating t':m the di'turb':*c: of the bound~irjy 1 ;.. by the r:'floctod bow wave. Similarly, an additional small wave (arrow 4) can be traced binc': to a d:stu'bnc. of the boundary Ic, causedby a sh.ck wave originating from a vory slightly imp.:rfoct fit of the slass windows in the sid..' w.ll . Alth'ugh the main:e'it possible extent of laminar flow that m2; be :ajct.i on bodis of revolution cannot be d, t r.in.d on the basis of the present tests because of this Jintrf.rk.n: from the reflected shock waves, the f'rie~rng results show thl.. t, nd.r the conditions cf those tests, a mi'n3or boundor; l';r ;rists over th. entire surface of a smooth model about 11 inches l1n3 up to at l .st 6.5 millions REynolds ntur,.b.r. In cnrmprison to th.: values n:.inr.llrj enrr''ut..l.i 4it subsoDnic speeds, a R::.nlds number of 6.5 m31iiimne at fljt '.),crs tc b,: NACA: 71.[ T.11 .ATA31A c('o T'...1.T=I'L NACA RM No. A7A31a somcwhst hiCih for maintenance of lamino:r flow over a b;od.r, unless favorable pressure gradients exist over tho entire length of that body. The pressure distribution over madel 7, shown in flj'r: 15, has been dotormined by superimposing the pressure distribution which exists along the :xis of the nozzle with no model pros':nt upon the thc: cLical prossuro distribution calculated for model 7 by the mia:tod of characteristics. The resulting pressure distribution shows that the pressure gradient is favorable over the ogivo, but is actually adverse over the cylindrical aftorbody. This suggests that the stability of the laminar boundary layer at a Mach number of 1.5 may b: considerably greater than at low Mach numbers. An increase in the stability of the laminar boundary layer with an increase in Mach number has been indicated previously by the theoretical work of references 15 and 16, and is confirmed experi mentally for subsonic flows by the results of references 6 and 17 as well as by the experimental data given for airfoils in reference 15. Some of the experimental research carried out in Germany are in disagreement with these results. In fact, part IV of reference 1l reports that the schlieren observations made in the supersonic wind tunnels at Kochel indicated that the Reynolds number of transi tion to turbulent flow on cones was even less than the value for an incompressible flow with no pressure gradient. On the basis of the description of the Kochel wind tunnels given in part I of reference 18, it appears that because of several factors the condi tions of flow therein are somewhat adverse to the formation of laminar boundary layers as extensive as those that would exist in free flight. One of the more important of these factors is believed to be the large number of shock waves which originate from imperfections in the nozzle walls and disturb the boundary layer over the body. These shock waves ordinarily number about 15 and are readily visible in various schlieren photographs. (See reference 21, for example.) In order to cause the laminar boundary layer to become tur bulent in this investigation, an artifice such as adding rou2hness was necessary. In a supersonic stream, however, the addition of roughness to a body also will increase the wave drag of that body. The magnitude of the wave drag due to roughness was determined by testing with full diameter shrouding and no afterbody attached, first the smooth ogive, and then the ogives with various amounts and kinds of roughness added (fig, 2(a)). The corresponding fore drag measurements are shown in figure 16. These data illustrate that little additional drag is attributable to roughness at the low Reynolds numbers where the boundary layer is relatively thick, but that an appreciable amount of wave drag is attributable to it at the higher Peynolds numbers. For all subsequent results presented, the amount of drag caused by the artificial roughness is subtracted from the measured iata taken for the bodies CCNFIDENT'IAL COM7IDEI.TIAL 14 C OnF IT'MITT L NACA ?7 :l. A .: tested with transition fixed. In .":r to calculate the amount of drag caused by the roi hr.n s for "mod.ls of diasaeters different ...: the ogives tested, it was assumed that for any model tLe :r.._"?e.t in d.r7 coefficient attributable to th, di.L of thy .t.ificial ro'u.ness was inv;rsl,.. prcpc:_tional to tho diameter cf the .: at the station at which the r.t,iness was aeplied. The fore drag measurements of model 8, which: consists of a cylindrical afterbcdiy with an.: one of the interchanreable c lec directly attacLed, are presented in figure 17. TreZe deta~, D..I which the dros, increment due to the adied rc'igriess has ;enr sub tracted as noted previously, show that the '.rees of r:v;l.r?. prod'iced by sand jlating the surface of the C. ive is ins.,Iff :"ent to cause transition at low ?eynolds numbers; whereas, the ri .: ss produced by the 3/16inch or the 3/iir.nhwide' salt band caused transition at all .e:.'nlds numbers. A vivid illust!.rtion of the turbulent character of the boundary layer on those bodies with :ru.hness addedd is given by the schlieren phct;'i,'ra;'5s in fl'::ve 1. The b' .ndary layer is best seen in the phc.to..'. taken with the knife edge horizontal. A :.jp'son of these pio. L: '' z witi. those of laminar boundary :l.;es (fi'. .*, for example) illustrtes how the condition of the b 'Lundr'r layer is ppuarent f':re schlieren ph.t~gr'ahs. The results at tsnzonic speeds r'eported in references 1 and 2 have s:'.; wrn that the same :chnges in prezs'ire distribution arnd 'hoc' wave configuration 'r:u b:t about by transition i to inherent bcundarylayer instability at biTh Reynolds numbers can also be br'.u.lt about at those speeds by any cf several means. T !. artifices ..sed in references 1 and 2 included finegrain ruli.nes., f  stream turbulence, and a" single large dist.ubance; the result:n: aerodynamic effects were the same, provided in each case the the ..'.r:7 layer was ch~i.ned from laminar to turb'l..nt. ,cne.,ently, no matter what causes the boundry layer to become turbulent in "':. flight, it seems l'k:ly thot, excl'..dinc poz;:.ble snall d ?fff rera. in s:irn f.ict crn, the resulting efects on the c.:..r.c.l.c 0'..'sc~tr istics of th bo.dy will be very r.narly the same as if the b.'..cr" layerwore mrde turbulent by rcughness alone, as is the case in t!e experiments ~nducted in this investigation. Flow eSnration. Changes in flow separation brought ab:,ut by chan:inr, tle b:,ndqr layer flow fr:,r laminar to turbulent alter the effective shape of the bc.dy, the shockwave configurati'n, and also the dra.'. It is therefore essential to consider the effects on flow separation of bth the 'nd.ttion of the bo'undary: la'.. and the Reynolds number. Tie location and degree of separation cf the la.a'nr: boundary layer for the b'at tailed bodies tested in the sm:.;th rcndition COF 7DI7ENTIAL T:AC;. F.I.1 P . .AL31a varied nti.esbly w'.th the Beynolds numbe of f'1 w. ITh schlieren photo'gaphs f Model 6 in figure 19 are typical o this e.'ect. Additional p!:Ltojr';ph, presented in figure 20, illustrate the same open.omena in the flow over models 2, 3, and 10, each at two different .e.ynclds numbers. In each case, as the Eeynl'ds number of the flow is increased, the separation de:reses, the convergence rf the wake increases, and the trailing shock wave moves forw rd. 3epraration of an apparently laminar boundary layer has been pointed out previously by Ferri in reference 19 for the two dimensional suner3onic flow over the surface cf curved aifoiizl Tha schlieren photcgrap'hs therein indicate that a shock wave forms at the point of laminar separation. On the other h:nd, the schlieren pictures of the flow fields for the bodies f revolution tested in the present investigation, show no definite shock wave a':o,, n:inr separation except for the sphere (fig. 20) in which case the shock wave is very weak indeed. It may be concluded, te before, that a separation of the laminar boundary layer is not necessarily accompanied by a shock wave at supersonic speels. The same con clusion for transonic flows has been drawn in reference 2. It might be surmised that the trailing shock wave situated some distance downstream of the separation point is interacting with or, perhaps, even causing the flow separation by virtue of pressure disturbances propagated upstream thrzo.',h the subsonic portion of the wake and boundary layer. Some indication that this is not the case is given by the schlieren photographs in figures 19 and 20. It can be seen from these photograp.'hs that the trailing shock wave moves upstream and the point of separation moves downstream as the Re:ynlds number is inceased. It would logically be expected th'r this decrease in the distance between the shock wave and the se'paira tion point would intensify any pcss'ble interaction between these two elements. The photographs show, however, that the degree :.f separa tion actually decreases as the trailing shock wave moves u,,t'aesm. This suggests that the trailing shock wave does not have much influence *:n the laminar separation. Additional evidence which corroborates this conjecture was noted in the course of th investiga tion of support interference, wherein it was found that if the diameter of the support behind models 2 and 3 was increased, the trailing s.ck wave moved forward, but the base pressure and laminar separation did not change. On this basis it appears likely that the cause of the laminar separaticn is not associated with a shock wave, but with othar. phenomena. In order to analyze more closely the details of the flow sCpar'ation, the pressure distribution along the streamline just outside of the sp:nra2ted b'urndary levye was calculated for several flow conditions over models 3 and 6. The calculations were made using the method of characteristics, and obtaining the cornt;.'r of the streamline just outside the separated boundary layer 1rcom enlargements of the schlieren ph:t=graphs. Typical results frci COIFIDENTIAL COF I0 D E'TIALT, 16 COTFINTIAL IJA A F.J N. A, .P31l these calculations for model 3 are presented ir. : ;ure 21 It i7 seen that the pressure on the outside of thl b,;.ndar;: layer i approximately constant, dcwnst:am of the ;::int o 'e 'JraLir:'n, s3 is ~ .araAteristic Elcn.g the bo:.undcy of a ead w:te re in. The pressure along the line of seoparat'on can be :. ted to be z.. x mately equal to that in th! dead irter egiro, end ien:c, eq'. l to the base pressure. A cmr.:.rison of the calculated values of the average ra .u.'e in the de?ewater re.i:n with the ma.9':rd values of the base pressure for several cr.nditions :f flow over models 3 and 6 is given in the fcll.wing table: Calculated e s're \. e:: :i. coeffi L.. cient of dead. r. :''e Model Fe.:,n :.is number water ". :,ion coeffi ie'.t 3 0.6 x 106 0.06 0.: 3 2.0 x 1I .11 .12 6 .6 x 10 .10 .11 6 1.5 x 10a 13 .13 The pr'eceding results indicate that for lamlnar flow the base pressure, at least for boattt"'ld bodies, is det:rm'n:d 3bj t:.. degree of separat: n which occurs forward of the base. This rlug:,:s that, if a means can be found, to control the separation, the base prj';su:. also can be controlled. The theoretical pressure distributions on models 4 and 5 are similar to the r..: .sre distribution on model 6, whTi'h is s:. :fn in figure ?'. In each case, the leminar s.p'.rtion bL.eiv.:d in tih: schlloren ph, to r,oA,t is located at a point ;uptr.::'i .:.f which the pressure decreases *::ntlnu'_lly .alcng the di:'r:ction of fl':w. For subsonic flow this condition ordclnrily wui.lld be ten;ued favorble. and s.:.' ction would not be expected. It thus cap.i'irs that thli separation ohenr.inml observed are of a diffcr.nit nature f'rc tih.;sc. which commonly result from a retardation of the flu.'.d partl't.s in the b.:undiar;' layer. Fiurthr? research on this subjct is n.oase.3ry in rord,er to gain a satisfactory understanding of the observed results. The :find'.n; of p:'. ious investigations in l.w ope>d flows indicate that if a b,undajry layer wh'.ch is normally lkni2n'na over the aftcrb.ody is made turbulent by either natural or artificial means, the resistance to separation is '.n.rcased ,r~atl:. Thr. t.sts on models 2, 3, 4, 5, and 6 with roughness addjd show clc1l. tiat this is also the case in supo..s.nic flows The two schlior n photographs presented in figure 23 were takcn of mid.l t with and without r~,ughnl.ss added and aro typic)ol of this ff'. A oap:r son of the two phhotogrphs shows that, without rou'3nus: ad', s'parqt ti.n occurs near the pint of maxim:.sL thLckn.ss, but if transition is fix'ed ahead of this point su.' spcrat.i n n: l rngcr occurs. C ONFIP EiT AL :;A,?. 1 FfM ro. ATl.:.7?: _,I __TLqL 1T S.T.:.i. 'n 'ra tio It is to be ::::.:ted that the changes in fl w soperation duo to chngcs in the condition of the o;.nd'y 1;.: an;nd in the Roynolds number of the flow will brinr. *' ..t c'::..nj:s in t:.; slhcuwave c:rnf.u'ation at the base .' a bd. IT'. schlieron e":t.:^ rj:.s of fi:.ur.s 19 ornd 20, which show how the laminar >.;..:_a t"'.n i:'oases and the cinv.~r':nc'. of the wake increases as the R;.r:lds number is inrr. si, also show that those phi.n.rrn ere Sc:L.::.nlod by a forward motion of the trailing shock wave. In :. n.j, as long as the boundary layer is laminar, the trrell!n,: .::.k ,:vo moves forward as the Reynolds number increases, ;. Lo no inoj:; ch:r.:, in the shockwave confij':r1ti.nr takes place. i.: shockwave c:nfig:i.ution with a. turbulent boundary leyor, !h ::w..:.r, is very much different from the ccrnfiguration with a 1:m.'.r,"r layer, as is illustrated by the schlioron phot ..phs of .1 shown in figure 23. Such cc'f rationin ':.; du2 to tP.: t2nsition to turbulent boundarylayer flow correlate quite ':11 with t'E. angleo that the t:rncjnt to the a. 'K'ace just ;:h.:. :f tl.e base makes with the axis of synmetry. Figure 24 3bi.'.,s the F:'.Enr:.; in shockwave configuration for models 1 through 6 r:j e.. ir: _'de of inr,ras:lng angle P. It is seen that, on the boat tllecd bodies with a small ?nJle 0, the transition to a turbulent b :..uar;n: .e: is accompanied by the appearance of a weak shock w:. or:'i tng at the base of the body (r. d,_ei 4 and 2). For bodies with larger boat tail angles (model 5) the strength of this wsve, hereafter termed the "base shock wave," increases until it is approxL:iatly as strong as the c.r..inal trailing shock wave. For evin la:er boattail anglles, the base shock wave becomes more d.ist'n.t, and eventually is the only appreciable shock wave exist in' news" the base of the body (models 3 and 6). In such a. case, t:.e .nrpressi :n through the base shock wave occurs forward of the base. This, as will be shown later, greatly increases the base pressir'e and decreases the base drag. Sin're the change in shock w:ve configuration caused by the addition of roughness is due to t .e reater resistance to flow separation of the turbullent boundary ly'er, ;i may be eee::ted that the above shockwave configurations f.'r L.'ie tur'bulent boundary layer will be obtained regardless of the cause "' transition. comparedd to the phenomena observe.d with'a laminar boundary layer (fi:. 1?), changes in the Reynolds number for a bod; with a turbulent b,.undry;. layer do not alter the shock wave configuration to any 3si_niflcant extent, because tiL turbulent la;.:, even at low Reayn: ls numbers, ordinarily does not soparote. This fact is evident in figure 25, '.hl".ch shows the schlieren phot...Jmrahs of model 3 at different Reynolds numbers with rc'u:Tlner, added. No sapo:rznt change in the flow characteristics takes place as the Reynolds number is inr'rasid. With a turbulent toundry layer, thhrefore, the effect on base drag of varying the Reynolds number may be expected to be much less than with a laminar layer. CC :TIT TTIAL b10 C ;.' .i l :.L !..... RIM No. A7A1'.a Analysis of the Dr,s ,ts The qualitative effects of viscosity on flow separation and on shockwave confi'.ro tin, which have been :.:.u3ssd in the prsedLng, sect:ins, provide the pL;.:3lsl basis for understanding the off e*ts .. v:;.:.' n. the Reynolds nu:ib. and :1h!ancing the condition of the boundary layer on the cdAr' f coefficients of the vrrious bodies tesLtd. Fore drag. The fore d*as; coefficients of mod3is 1 thri' :u 6 with laminar flow in the boundary layer are shown in figure 2C(a) as a, f.un"tion of the Reynolds number. These data. show that, over the Reyrn.ld, number range covered in t er tests, thr fore drag of model 1 decreases about 2C' ': .ent, while tl.j t of model 6 increases about 15 percent. The fore drag of the othe bodies does not change ap' iably. The reason the effects of Reynolds number vary considerably with different body olapes is clearly illustrated by a comparison of the measured fore drags with the theoretical fore drags. In figure 27(a) the theoretical and measured values of fore drag are compared for model 1, which has no beat tailing, snd for model 3, which is typical of the boattailed models. From this c:,.r~.rison, it is seen that, as previously noted for other m .22ls without boat toilln:, the ti,:o;etical and experimental fore drago: for model 1 are in good creecment. The decrease in fore drt with increasing Reynolds number for the bodies without boat tailing is duo entirely to the decrease in skinfriction cc.,~7ficient. For model 3, which has conrl.d.:rable boat tailing, the curves of figure 27(a) show that the theoretical and experimental fore drags agree only at 1igh r:ynolds numbers. At the low Reynolds numbers the measured fore drags are lower than the. theoretical values because of the separation of the laminar bounder y layer as previouslr illustrated by tio schlieren pLhtcgrsphs in figures 19 and 20. With Esp irtion, the flow over the boat tail does not follow the contour of the boi;d, and the pressure in the acc .mpqrnyiT.ri deadwater roji:n is lihcr than it would be if the sLo ratl:n did not occur (fig. 21). This makrcs the actual fore drag lower than the theoretical value for a flow without separa tion. At tli. hir RE:;Tnlds numbers, th separation is rn"lillble and t.j flow closely follows the contour of the tLcdd; hence, t: theoretical and exp:q:i:.cntal fore dras.i agree. The rJason f:,r the 1::'"'ri m.t.l: constant for. iragz of models 2, 3, 4, and 5, th:.r., ore, is that the chan7..s duo to skin friction and flow scparaton are compensating. For m;dul 6 with a smooth suirfco, the fore dra& shown in f..uri' 26(a) rises rather rap:dl;r at low Reynolds numbers because the separation effects for this relat:.vjly thick body (:.'i. 19) more th'.n compmnatc for tbh changf, in skin friction due to th. variation of the .;,ynolds ni.nbe:.. Figuro 2(b), which shows thj f..rc dragf coeff cients :.f model 1 t;.u.'.ch 6 with r'uhns..s :'dd.d, indic2tus th.t tlhe for drsa for all the bod.Ls docroases as the Pc.yn Ide numnb.r incroass ab;ve a C OTTFI ENTIAL NACA F.I T:o. AT7.31l Roynolds number of 1.75 millions. This is to be exp:ctod, since with the change to turbulent boundary layer and c:nsquicnt climnnation f sparation, the only factor roncininC to influence the fore drc i c'.cff'.'icnts is th decrease of skinfrlction coefficients with incro:ss in Roynolds number. Below a Reynolds number of 1.75 millions, however, thu fore; drag of all the mod.ls cxc'pt model 1 increases with increasing Roynolds number. The cause of this sl:w'i:.t puzzling bchl!vi :r is apparent upon closer examination of the data. Fi.ue 27(b) shows a comparison of the theoretical fcore draogs with the experimental values for models 1 and 3 with roughness added. The theoretical value for skinfriction drag was calculated assuming. laminar flow up to the location of the roughness, and turbulent flow behind it. This value of drag was added to the theoretial wave drag to obtain the theoretical fore .;.ag. It is seen from f'.gure 27(b) that for Lodel 1 the curves of theoretical and experimental fore dra_ have the previously indicated trend of decreasing drag with increasing Reynolds nuimbor over the entire range. .nwever, for model 3, which is typical of the boattailed bodies, the measured fore drag at low Reynolds numbers falls considerably belcw the theoretical value in the manner previously noted. The reason for this is evident from an examination of the schlieren phcto7gaphs shown in figure 28, which were taken of the flow over models 3 and 6 with roughness added. They show that at the low R:e.,nold numbers a flow separation similar to that observed for an undisturbed laminar boundary layer (fig. 19) is evident, and the resulting shockwave configuration is characteristic cf the config uration for a laminar boundary layer rather than that for a turbu lent boundary layer. It appears that, at the low Reynolds numbers, the amount of roughness added does not cause transition far enough upstream of the point for laminar separation so that the free stream can pzvv.ide the bcundary layer with the necessary additional momentum to prevent separc tion. Ih portions of the Ira;, curves in which the desired transition was not realized are shown dotted over the region in which sepa~rtion was apparent from the schlieren pictures. For model 1, the schlieren phcto rai.phs shi:wed that at the low Reynolds numbers the amount of roughness added was suffi cient to effect transition some distance ahead of the base, although not immediately aft of the roughness. The agreement between the experimental and the thortical results obtained by the use of equations (4) and (5) indicates that, aL a Mach number of 1.5 and in the range of Rernolds numbers covered by this investigation, the familiar lowspeed skinfriction coefficients can be used to estimate drag due to skin friction at supersonic speeds. This confirms the results of references 3, 4, and ) and extends their application to the evaluaticn of skinfriction drag for supersonic flow on bodies of revolution. CONFIDEITIALL C N0IDEFrTIAL 20 C,.:T_ L:;TIAL NACA 7 i No. A7.J31a A comnnrison of the curves of figures ."(a) and '6(b) shows that for a given body at a givenn value of the Ielno!lds number the. fore drag with r. uihne.:s added is consistently higher than tL. corres' 4.d1in,; fore drag of the :: tl, s..'.faced body. In the general case, this overall increase in fore drag is ett'ib .table both to the increase in the skinfriction drag of the body and to the elimination of E,,:ration with consequent increase in the pressure drag of the boat tail. F:r model 1, which has no boat t:illn., the increase in skin friction is the sole factor contribut ing to the increase in fore drag. I, r.rs ue and bose drac. Figure 29(a) shows the bc.Se pressure coefficients plotted as a function of the e'rnclds n'.:.ibe for models 1 through 6, each with a. smooth surface. It is evident from the data in this figure that the effects of ?e;,nrlds number on base pressure for a body with a laminar boundary layer are quite large. In the :.rn:e of Reyrn:li' nr.uabern cov.c.i, the base pressure coeffi cient of model 1 increases about 60 percent, and the ,:'.,efficPjents of models 2, 3, and 4 more than dc.;.bl_. The t"!.':..r bodies, models 5 and 6, do not exhibit such l~,.:. chlan.c in base 'ejsurs clocfficient, for the coefficients apparently reach a maximum at a relatively low F.:ynolds numblir, and then decrease with further increase in the  ;..rnA.: number. The base pressure coefficients for models 1 thro.i.h 6 with roughness added are shown in figure 29(b). Here a.in, the portions of the curves which e1 respo.n. to the low ernli number rein wherein t:ra'nsiion did not occur far enough upstream to prevent separation are shown as dotted lines. Model 1 exhibits the lowest bse pressure and model 6 the ;ehest; in this latter case the base pressure is even higher than the freestream static pressure. The physical reason for t":.s is evident from the schlieren pihot.raph at the bottom of f:i:..e 23, which shows that a compression throughh the sh .ck wave occurs just ahead of the boase of model 6. Except for the large c''en.es in pressure coefficient at low e;e'ncllis nri:i,eri's where the desired transition was not effc.'tei, the variation of base pressure coefficient with Reynolds number is relnt'iv3.r small for the bodies with ro..ghnes3s added. From a comparison of the curves for the brdiles with ro.ugh.nss 3.i.ed .to the corrs;'r.n'n i curves for the smoothsurfaced bodies, it is evident that a, l:rle chan3e in the base pressure zcefficient is attributable to the cihnge in the condition of the boundary layer. In rnerml, the base pressures :for 1:dles with rouglness aided are ccnsiirabl/y :1 ler than the correspndn base presses for the smoothsurfec,:d bodies. In the case tf ,heboattailed bodies the rhsll reason for this increase in the base presure is the ap..srnc, of t:.o base shock wave, as shown in figure 24. Fc,: modrl 1, which has no boat tailing, the .lx.inj a'ti:n and .'retor thickness of the turbulent boundary layer are probably '~~'_T~~lrZ :TL'JI .'.CA .=. ::c A7..1l C 'Z mTAL 21 responsibiD for the ..b.erved increase. The foregoin, data show that th;e effec t .f : *n'l~3 number srnd crnilt.liln of the l. unda'r layer on the base pressure of a 1: ?' movirn' it 5.ies, Dni speels daee.r consid.ei',rbly.u pc.n the Z n,. of the afte  b'.d,. ITn crdr to ascertain whether the effects of viscosity also dLpend uwpn the len.thdi..neter ratio for a fixed sl.. ie of after: b:id s:me m,io 13 of different length diameter ratios were tested and the dcts ipr3: t.ed in figures 30(a) and 3.'(b) which show the variation nf b':3 pressure coefficient with aeynolds number. iie data present.id in this figure are not free of support interference. From these data it is apparent that the effects of viscosity on the base pressure incrase with the longthdiameter ratio of the cdy;'. It is to be noted thnt thj b ? pressure in crcsc as the lonjt'. diameter ratio ircaesz7. This is somewhat at variance with the results of :''ference 2C (also rcpcrted in reference 18), which showed an effect, bot not a systematic one, of lenitthdiameter ratio on the base prszuru of br.dies without boat tailln,g. The base drag oc.efficient can be obtained frr. the base pressure coifficicnt of the models by using. equation (2). T:,: base drag coefi'cients for the smooth surfaced bods are presented in figurec. 31(a) and fc the bodies with roughness added in figure 31(b). l. ,curves are, of course, similar to the c:i':esp.nd'nn curves of base pressure coefficient given in fi u:'cs 29(a) and 29(b). In this form the ordinates can be added directly to the fore drag coeffi cients of figure 26 to obtain the total drag c.;fficient of a given bod;. It is seen that the contribution of the base pressure to the tctal drag is very small for models with large amounts of boat tailing, such as model 3, 4, 5, and 6. Total dras. The total d.7 c'oefficients for models 1 through 6 with smo:th surfaces are shown in f.'.Ve 32(a) as a function of Pe.lis nutbecr. These data show that the drag .:.coffcients of both models 1 and 2 with a laminar boundary layer increase a little over 2C pe_cct from the lowest to the high,st value of Reynolds numib.r obtained in the tests. The other models exhibit sc:~ii,; sualler changc.s. The data presented in figures 26 and 31 indicate tht the prin.lipal effect controlling the variation of total drag with Reyl.nlds nur.ber for laminar flow in the b urndary layer is the effect of Reynolds number on the base drag of the bodies. For the speccil cas of highly boattailed bodies, however, this effect is of little, relative inportanc.:, because the base drag is a small part of the ttal draq. In such cases, the overall variation of drag cocfficiLnt is due almost entirely to the variation of fore dr.rg with _Rc\nolds number. Fig.uru 32(b) shows the total dra, coefficients plotted as a. furction of the ?e;ynml.s number for models 1 trouh 6 with rough noss add:d. Again, the portions of thu curves that are shown dotted COT IDEi TRIAL NACA PM No. AT.31l represent the Reynolds number region in which the amount of :ouglness added is insufficient to cause transition far enough lupstreim so that s_a'ation is prevented. All the curves have appr'x::latelJr the same trand, t', overall effect on the drag :fficiaetsbeln, about 15 .:,. nt or less for the various bodies. A :mprilson of the curves of total drag for bodies with rough ness added to the corresponding curves for bodies with smooth surfaces shows an interesting phhn'uenn.. At the higher Reynolds numbers the drag of models 1 and 6 is actually dece.azd slightly by the addition of roughness, in spite of the cc,:res,. morning increase in skinfri t.:n drag. 7The reason is, of course, that the base drags are very much lower for the turbulent boundary layer than for the laminar. The drag c: ffLcients of the other bodies (models 2, 3, 4, and 5) are somewhat :lT:;:*r with r'j:ghr:ss added, because the increase in friction drag of the ti.ubilnt boundary layer is greater than the decrease in base dreg. I'. importance of always considering both the .In:.1J:,1 number of the flow and c nd'.tion of the boundary layer is illustrated by the total drag characteristics of model 2. For example, if model 2 were tested with a turbulent boundary layer at a ::ynolds number of 2 millions, the d':.. would be about 35 percent higher than if tested. with a laminar b'.'unry layer at a, E .:T:l4 number of onehalf million. Alt::.:.h discrepancies as large as these have not been reported as yet in the drag data from different supersonic wind tunnels, certain consistent differences, v.Lr;:n f':m about 5 to 25 percent, have been reported (reference 21) in the drag data of similar projectiles tested in the Gottingen and the Kochol tunnels. AlthcuL'. in r forence 21 the disci_:p.n.:Les between t:.. two tunnels wore attributed Tr.lr to the variation in :l::n friction with Reynolds number, it appears from the results of the present investigation that such disci ~:.ncies are attributable ixpi:.:.rily to differences in flow separation and base pressure. A comparison of the effects of viscosity for pointed b.ices with the effects for a blunt body shows clearly t. t body s:c must be considered, and that conclusions about viscosity :ffects based upon tests of blunt bodies i'. be ccm.ll:.tely Irnpplic.itl3 to the aerodynamic shapes which are suitable for supersonic flight. For example, in the case of a z:.h'r: at 1.5 Mach number wit, an over all Reynolds number variation of from 7.5 x 104 to 9.0 X 10", the agreement between the drx. data from Gtt:n.rr (rerence 7), Poonomundo (r feronc 21), andthe p.r s;nt wind tunnel is within 1 percent of tr. values measured for fr :i.1ght referencess 7 and 22). It is ovidont that the ::ffacts of viscosity on Lthe. drag of a sphcie are quite different from the :ffocts on the pointed bodies tested in this inv:sti :tion. C L IDENTICAL C C INFT? ILIL C 17 rP .TLT C 01 'I U.jU, i; 7, The cor.clusions which follow apply for a Mach n'ib.br D 1.5 and at R:.oli. numbers ba.:d unon model length ui! to about 5 millions for bodi:: revolution similar to the ones tested. 1. Th effects of viscosity differ grealy for laminar and turwl.: :'low in the boLunT r:" layer, and within each r:li.: e >:.n v:; h. inolds number of the flow and the shape of the body. 2. Linar flow was found on the smooth bci e up' to a Ieyr..,ids nrn.ber _' 6.5 millions and may possibly exist to :gr.:drlr..r higher al;1> .. SA cc.marison between the test results for laminar and. for tulu.l.. .'low in the boundary layer at a fixed value .' the Reynolds ri .:w: that: I ) The. resistance to separation with turbulent flow in the bundary layer is much greater. (b) Th= shockwave confiMui'atlon near the base depends upon) he ..;,.o of the boundarylayer flow and the relative d.r .: of boat tp.l~;,r. (') The fore drag c.fiicients with turbulent boundary i:.yer ordinarily are hl_her. id) The b'aSe pressure is much higher vith the .u'bul boundary layer. (e) The total drar is usually higher with the turbulent boundary layer. 4. For laminar flow in the boundary 1...;'rr the following Eff  e wrl found: (s.) Th; laminar boundary layer separates for.:ari of the bc..ae on all boattailed bodies tes ed, and the pcc.tion of separation varies noticeably with rTynLlds number. Laminar separation is not necessarily accor,:.ni*ed by a shock wave originat:ln from Ihe ,: int of separation. On many of the models the zar ion is located in a region upstream of vi:hich ;.h! treasure continually decreases in zhe direction of the flow. (b) The trailing shock wave moves forward slightly as the RFynolds r.ur.Fer is increased, but no :~r.i 'icant .hCg: ta'2es place in the shockwave configuration near the base. C CI7 IDETITIAL . C .' TT I A 7,'1 1, n,.'.C.. ri A'. .. ;',  SKAA iM No. ATA312 (c) With increasing R.ynolds numbers, the fare ._. ..: i cionts increase for highly boatt I.l .i bodies and decrease for bodies without boat trll!n. :: modor atoly boatteilod bodies the variation of the fore drag c.ffclont with 7.;:n:lci. number is rolativ'lyr small. (d) i: base pressure of the bcbctt 11ii bodies is controlled byj the laminar soparaticn end o:. n : Z.: .d; with Reynolds number. :. ':d.s with tho same _ft lrb;. shape, the ba'. prossuro else SJnrd.: upon the 1ntL diaotor retio to tb: i. (o) t!l dr.g varies conside oIblj with BRynolds n.:i.', .nrg more tin 20 percent for savoral fi thu models. 5. F7 tui.l. nt flow in the bciundr. laer theo following .lfocts wour found: (.) 5: :'. tLon doo3 not ordinarily. occur. (b) Tho shockwavo v :.fri iguration noar tho baseo ".3 not c',n' noticeably as tl., Rynolds nurbor c'.'.s. (c) Tho foro drag j.f.icionts decrease sli hitly as the F n: 1is number is increased. (d) lih base pressure changes vory little with c.':n lri E.ynolds number. (c) The total drag docroa.sos as t: Rcynolds number is incr. i'. Aros .:. :r ..t ical L'.: ,tory, 1a.tf.tonal Advisory Committco fo: Aronautics, .ifett Field, Crli. CC'TTI.iTLAL c, 'i "T! L NACA i:; .. /'".?1 *C;L _'.TT.L 29 PFEITWIX A V.:.TATICI OF TESSTSECTIOC' STATIC P..STUr Since tie static pressure with no m:liel present varied along tle a x:. of ths test section as shcwn in figure 7, it was necessary to r.ppl. a correztijn to the meassured 7efficients to account for the :i;'rc.ment in drag or pressure resulting from this axial pressure C'd.."ent. A.lthc.uh the axial variation of testsection static ore2surs is not m:'nctonic, the pressures at tIh downstream end of tl] tLest section are uniformly lower than the pressures of the up stream end where the nose of the .rm:dels are ordinarily placed. This r'.tr.3 that ti:e c tul1 preserre exerted at a. "'Iven point on a body is wer th n it .r.uld be if the embient pressure gradient were zero es it is In free fli,.t. The gr.dier.t corrections are calculated on ti:e assumption that the magnitude of the pressure exerted at an airbltr'; point sn t'e body in the tunnel is lower than it would be if no gradient were present by an increment ecual to tle amount whi:h t'e static pressure d.crcases (with no model present) from t.ze : .siti;n cf tihe model nose to the position of the arbitrary p:'.nt. It :.3 not necessary to include the c:,lres~onding axial vaiat.icn of dynamic pressure in the corrections since it varies cnl .: : '.? per'.ent from the mean testsection value used in all .;lculot:'.cns. The corrections to the measured .:.Cefficients of model 1 li ztei 2... inr:ies downstream from the reference pressure orifice, fr e.xajmle, :unt to +0.012 in fore dsSe efficient and 0.02' in bao.e dra'3 ,:ceffi.lent; the corresponding pir:er.ntaes of the U.nc,: ire.ectc cce 21cients of fore drag and base rc;;u.'e are 12 and 1^, r: .:? tlv;c '. _.e.'.sc the .gradient correction is relatively I:.e in the pr.'sent te3st3 .and apparently has not been ep':'l'.i in the past to su.:ecr,,ic win4tu.nel data, an experimental justification of such thcor:ticl co;:.lceticns is in order. The validity; of the corrections as epplied t.. fore d Lra.is confirmed by tests on model 9, which .cc'rssts cf .. .cnicil nose with a 200 included angle and a short cylind.rical olftcrbc~ ..i. The theoretical fore drag of this bridj, which is eqi.ual to th: s31 of the wave and friction drags, can be assill, clculot.,Id s function of Reynolds number. The wave d:n. of the cor.i:al ncse is :lven accurately by the experimentally confirmed calculat.'.cns of T';.l.r and Maccoll (references 10 and 11). The fictional drIe can be calculated using the l:wsncd laminar skin frict' n c:cifficients in accO:,idance with references 3 and 11, since the bounder.; layer was completely laminar over this model. A com ea:is:n of the corrected and uncorrected fore dc:s with the theo rctical fc.re' dar is shown in fi:, re 8. The corrected fore ir coefficients are seen to be in good :r. oemcnt with tho theoretical values, whrceas the. uncorrected data fcll below the wave L': at hi*:. tunnel pressures. .This latter condition, of course, represents an impossible situation for a body without boat tailing. COTIF IDTITIAL v:,: ""La T In order to check e;oi':lientallj the validity :,f the corrections as applied to the measured base p_ esI..re, .ic'.;l 1 was tested on the side support t a :'ve different p:.itions 2lL the axis of the test section. 35 .auc, the support s;.:te r.mrne d fixed relative to th: body, the interference of the support is the same in each case, hcr.co, any d'sc*,:,.}n? ies in the measured base pressures at the various pr'tions are a.ttif'Ltt.bls only to the pressure gradient alnr t.1 tunnel axis. iuire 9 shows that the uncorrected base pressure data talen at the five different psltions differ c' about 'L percent, but the corrtsj.:i : five sets of corrected data fall within about 1.5 percent of their mean, thus crnf'rming the validity cf the c.rrczt`ion. COFID2T TITAL T.c.. M UD. ...A..11 ,AC.A FM Nc A7A31a A.IZ7:.Z:. B R ,Ig. ;.; OF i,'TA .5 ac,..:". f the rez.zlts pre3ented can be estl:iac'.d b; ccicr.'cing thoe ?:.slle errors that are known to be involved in th; mea uoment .f the forces and press''ec, and in the dcote'in;c tion c.f tie f:..st'eam Mach number and grad." nt corrections. T1?. f:'rc. msurements are subject to errcrs frcm s:.fts in th: bcl_nco. zer !ue to temperature effects, and also from a shift In th. cLlibraTlcn constant. The zero shift, which is less th;an 1 o. 'c;nt of the fi.rce data at low pressures and less than 0.2 prcent at LTi,.h p.'esures, was checked periodically by running the t.;:nnl tthr',u the complete temp:iatiur range with no force acpliad t. t:e b>lanc:. In the majority of cases the variation of the balance calibratt:n constant, which was checked before and after ech: se'Cies of tests, permitted a possible deviation of 0.3 p r:'ent in the force dat2. All data presented in fif'.res 12(b), 16, 17, and 1 .e a ca f'r models 4,.5, and 6 in fic:re. 26(a) and 32(a) were :L..ne.d idurin a period between two consecutive balance calibrations for which' t:he cnszant differed by 6.4 pe_'cent. A comparison of the der~i obtained during this period with theoretical results and with the esults of subsecuont reruns of some of the same models indicates t!h't the .'i'ne In balance calibration occurred before e the data in qLuesti:; \/ere obcsined. The results in the aforementioned figures were tlhecrfce cc'nruted on the basis of the later calibration. It is estimated that the maximum error in the balance calibration ccnr!tear for th.esCe results is at worst no Cgreter than +0.3 to 7. pe. ...s.L. The pres3uce datt, including the dynamic pressure, are 3Ubject to szall errors resulting fron p:z'Ible inexact readings of the ..e';1ury mnc.neterz. 'Te base pressure data are also "':.>.ct to an additi.'nnal err: r resultin.n from the small variation in the specific grav't;:' of the dibutyl phthalate indicating fluid. At the most, the2e sa;uces can cause an error in the total and fore drag .:effi cients of about '.3 percent, and in the base dra coefficient of Eb:.uT =1.' percent. The error in dynamic pressure due to the unc:ertainty in the freestream Mach njuber is nell1ibile, since the isentr:pic relation for the dynamic p:essure as a function of Mach n'aber Is near a maximum at a Mach number of 1.5. For slender bodies cf re.vlutlon the variation of the force coefficients with Miach number is quite small; hence, errors resulting from the variation of freestream Mach number from 1.49 to 1.51 are neglijibl3. LCn the basis cf the data presented in figures 8 and 9, it is estimated that f:rr all tunnel pressures the uncertainty in the gradient corrections to total drog, fore drag, and base prc3essu'e coefficienx.s can cause at the most an error in these coefficients CGF IDEIiTIL CONFID2NTIAI_ 2?. Cx DE]'TiLL I.ACL i .R .7.?.1 of 0.004, 0.004,aOnd O.C,':, I:;c,tively. It .::;ild be nrted that in the table on p.'eci ln, n:3,resent in the setion on results, this source of error, which is independent cof tunnel pressure, is expressed as an increment and not as a pier'etage of the i, '..ie. ". :'icient. envious ir.v';stir,2t'Lons have shown that an uncertainty :.; be introduced in se'.'s':nic windtunnel dIita 'f the ilj'ty of the tunnel air is '.bhih. To determine the effects of this var.i3le in the :s,:nt investigation, tl}. specific i .nility was varied from the lowest values (app':rxiaitely O.OC''i) to values appr:xirmtli 20 times those normally encountered in the tests. TrIa. and base pressure measurements were taken on a body with a conical bead 'ind also on a :..ere. The results showed no appreciable effect of humidity over a range much greater than thit encountered in the prn..;:.t tests, provit ., the variation in testsection d. nC..': pressure with the in.'.: in .luni1i ty was tLa'n into account in tf reduction .' t:.. data. It is ba.li,ved, t.l:r.fore, that the precision F t.: resilIts presented in this report is un'ffuct,1 by tunidit,. .c'TTFID 'TIALT I;A':A .: !'. 7A31'7 :.T 29 EFFECT OF SU,.'?T ''? .L7", :.". nowl,:. of the c:fects of 3upp,:rt nt.:ie'erence .i:.n the d:to .in question is essential to an underst:.nd.in of its a'.pi':l, bil'ty to fr:: flight conditions. Previous to the present inveati rt'In an extensive series of tests were conducted to dctermino the b: .:y Ci:,:pe and supp':rt combinations necessary to evaluate the support int:rfe: ence. In gcneral, it was found that for the models tested in the smooth condition laminarr boundary layer) the effect :f the rear sup'l.'ts used in th; present investigation was negligible in all r s,'cts for t;h b. :Ltt'ilcd models 2 and 3 and was appreciable only in the bese pr;....... measurements for model 1. On the basis of these results it 1. believed that the rear supports used for the other highly boat tail:d bodies (mrd.1is 4, 5, and 6) have a nr _,l "'le. oiffct on the dr: :f the model. For model 1 combinations of rear supp.:rt and side s,.rpprt,t were used to evaluate the effect of the rear support on the bz.: ''essure. The evaluation was made on the assumption of no w.s!l interference between the rear support and side support, and \ra: cracked by the use of two different combinations of side support nd _:e'".r support. The data indicate that the assumption is justified wi;.:ln th; limits of the e.:e:r'i..ntal accuracy and that the corrected, int rf:eencefree base pressures deduced by this method differ only siigiLlr .y :.r those measured with the side s.ppcrt alone. For the b:dl.:s with roughness added (producing a turbulent bcOri'.Uty layer) a clplote investigation of the support interference ws net made; consequently, a dfinite quantitative evaluation of thr irnt:rfeornce effects for each body in this condition cannot be given. From the data that were obtained it has been found that the f:r.: L'ag is unaffected by the presence of the supports used in the pr:.snt investi7 tion, but that a small amount of interference is cvid.nt in the base pressure, coefficient which may vary from a mlr.nuLnjm f 0.005 to a maximum of 0,015 for the different bodies. This uncertainty in the base pressure coefficient results in a cor :repond n,'l.ri small uncertainty in the base drag coefficient srn in th,. t:t.l dri: c. T'ficiont. COIF L,'ZiT:7I'.L 30 L:.J ,r7TL'.L "'A .. IT..7A31. 1. Aclxret, J., "Fli..:nn, F., and Rott, N.: Invost.'ati..s f Compression Shocks and Boundary Ln .,.. in Gases Mnovn_ at 'F _ Spood. IACA TV No. 1113, 1947. 2. i.' i.nn, H.W.: _urti Investigations : the Interaction of Boundary Layor and S::ckr Wavos in Transonic Flow. Jour. Aero. ., vol. 13, no. 12, Dcc. 1946. 3. Thoodorson, ..'ro, eand F:. ..:r, Arthur: .:.::,:imonts on 1I'; of 5:.'lving Disks, Cylindors and Ptre'amin ERods at 1i,, Seeods. NACA IAC No. L4F16, 1944. 4. Koonan, Joseph H., and I"..km.nn, Lrn::t P.: rilction in Fl.: at .i.' sonic and Subsonic Velocities. NACA TN I': 963, 1945. 5. Frosoll, W.: Flow in Smooth Straight Pip:: aat Volocitios t'bove and l.:w ;.nd Velocity. .:.. M No, 1 6. F _ri, Antonio: Influenza daol i'.~x: : d I:'. :1iz ai G.'nc'. iNumcri di Mach. Atti di Guidonia No. 67 j, 1942. 7 Walchnor, 0.: Systematische Goschca~s: .: .:' ".n Inl':i:.l LilionthalG :. 11ch .ft fur Luft2ph' tfc.: o 3. : 1I, Toil 1, Oct. 1941 6. Bach, F.: Druckverteilungsmossungen an(; _. :d. ill r. Deutscho Luft: VL h''frschung, .ii 6'i 7, Mar. 1945 9. Van r: , Milton D.: A... i. ChL:..:t.ristics Including Scale if:oc t of Several Wlr. and Bodi. Alone and in Combina tion at a Mach .tmbor of 1.53. NACA Ri. No. A6K22, 1946. 10. Maccoll, J.W.: Tho Conical .c: Wvoe F:..t~' by a Cone Movinc at a High J; ....i Proc. cf theo .:;al Soc. of L.nd.:n, sur. A, vol. 159, Apr. 1, 1,' 11. Taylor, G.I and i.:.coll, J.W.: Th Air frr.3 a:'o on a Cono Movin at TT4h Spoods, Proc. of the Royal Soc. of LI.nd:n, ser. A, vol 139, F.b. 1, 1933 12. Sauer, R.: Method of Characteristics for ThreeDimensricnal Axially Symmretrical Supersonic Flows. NACA TM No. 1133, 1947. CC. TIDEN TIAL ir.'! m1 No. A,".'.31a C0HFiI:"'LAL 31 J .. ., .. B .o. .....31a 13. S., R.: Thoorotlscho Erl 'i:r. in die Gesdyna.mk. B.: iJn, Spr inc. ', 1 ~3 (Reprinted '.. L: A'i ds L1.'3., '.nn .'"b , Mich., 14. T~llncin, W., and 'e..for, M.: Retati .zc: Inl.. t'.scho3 Uborschallstrmun'ac: n Lil intl21Gosellschaft fur 1.ftfhAhtforschung, r..'.ct 139, Toil 2, Oct., 1,71. 15. ll11. n, E. Julian, and ;i;tzborg, Gerald E.: The Effect cf Comprossibility on the Growth of the Leminar Boundary Lay: on LowDr?. Wings and Bcri:..z. l.CA ACR, Jan. 1943. 16. Loc, Lostor, and Lin, Chia Chiao: Invostigation of the Stability of the Laminar B.irndrey Layor in a Compressiblo Fluid. KACA TM 11. 1115, 1946. 17. H.t, H.: 3c:hl nd. vind_:.its.m:s'in:nr an Rundund Profilst'rns.:n versche li n.:r Durchnmossor. Lilienthal Gosollschaft fur Luftfa]:tfco.'?:hing,:n, Boricht 156, Oct. 1942. 18. Cw:., P.p.: Note on the Apparatus and Work of the W.V.A. :rs onc Institute at Kochol, S. Germany. Pert I, (?1. I7i EC0. 1711) Oct. 19U5, and Part IT, ('s :;:.. 1742) Jan. 1946. (British/U.S. Restricted). 19. 7 A:.. Antonio: Experimental Results with Airfoils Tested in tho HighSpeod. Tunn. e at Gr i'.nin. NACA TM No. 946, 1940. 20. Er ar.n, S.: Widorstandsbos.timnumg Von Kogoln und Kugoln aus de.r Druckvortoilung boi Urb.,s: 2,'lloschwi r. . ;]:it. LilionthalG: s.11sh i:t fur Luftfahi'tforschunegn, Boricht 139, Toil 2, Oct. 1941. 21. Lehnort, R.: Systomatischo :'. jur. .:n an noun .; n.achon Goschossfonon im Vorgloich zu T S:.'.ngr:n dor AVAGottingon. Lilionthal Gosollschaft fur Luf fsBhrtf ':.r.?h'T.:r:, Bericht 139, Toil 2, 1'1. 22. ,hsrt .r., A.C., and Thomas, R.N.: TIh: Aorodynamic P.. formanco of Small Sph.rc.s from Subso3rn:. to High Supersonic Velocities. Jour. Acro. Sci., vol. 12, no. 4, Oct. 1945. COFIiET'TL TL [ACA RM No. A7A31 a CONFIDENTIAL Ki ? b .'. .. ., .. *1 '::::.; :". . ";. .. '.;.;'.~ i ... " : .: : i.. HH . ^~~~~~r '****^^^^ ^^^ ^ B . i *";? .. *',, : :: .! .. : :': ..... 1i.t ':' ?:. .,+. + . .. .:. "i.: .:p "'... ...,*,.i. .. ..... ...."..'..  ~~~~~:. ~.F.,j ;.' ..,:... . CONFIDENTIAL Figui'e 1 NI oa c,' U. cS IP 01 > pg Mr ... ... .. :. :.;, :.. ,, .:: :NACA RM No. A7A31 a CONFIDENTIAL Figure 2a (a) Models used for boundarylayer tests and for comparison tests with other investigation. FIGULE 2.Specialpurpose models. CONFIDENTIAL NACA RM No. A7A31 ,NACA RM No. A7A31 a (hI Models used to evaluate effect of lengthdiameter ratio on chase pressuIe. FIGURE 2.Concluded. CONFIDENTIAL CONFIDENTIAL Figiire 2b 0ONFIDZITIAL 14 14 f4 01 0 w z z P( 0 ui z J J 0 z coooo ui L 1 w i 00000 0 0000 2 22 i Cn c6 OONFIDENTIAL IAOA RM No. Fig. a 4 z< z<_  Nr w ooo 000 2 E 7* N > > SIACA RM No. A7A31 a A,"/,WS ..*. NACA A10584 10146 FIGURE 4.Sichematic diagram of mo.l.l installation v'.it, rear suLppor))t and Idrag gage. CONFIDENTIAL CONFIDENTIAL Figure 4 GAGE" /,A NACA RM No. A7A31a FIGURE 5.Schematic diagram of model installed with side support. CONFIDENTIAL Figure 5 CONFIDENTIAL NACA RM No. A7A31 a (hi Side support. FIGURE 6.Typical model installations. CONFIDENTIAL Figure 6 CONFIDENTIAL B..: I NALA RM No. AA31l CONFIDENTIAL 5 Ii( 4d I I I I oe Sd 4 0 a o i 0 0 0F 0 .4 I a ., Sa o 0    ^ > o  ^ /(  __ __ _^ : __ _ l> < ^ o 35 to o aD 040 100 do f i.l4 t.4. 0a  E et C X ^ a rp w 3 4 * S* = 5 3  0041i % 4e W O .4, 0 0 0 0 0 0 0 1 CD 1 m 1 O1 b/"dd 'e.nsneeed eoueozoej o pezeoez eajnesezd oTlse v o uaTOTEPeo CONFIDENTIAL Figs. 7,8 H.e 11. II do a o OO >4 0 0 00 .4 0 o o atm" aM Ok 00 .4 O.4 0O o O 014 owl *t 04' +j o v 4.. 04' * 14 r4 0. 4El C a 0 .60 * . Q 0 i o, a!*Od .ro '' 'i: S NACA RU No. A7A31a CONFIDENTIAL el Model 1 2 Reynolds number, Re, millions Figure 9. Comparison of base pressure coefficients'on model 1 measured at various positions along the tunnel axis, with and without corrections applied for the variation of testsection static pressure. CONFIDENTIAL .24 .20 .16 .24 .20 .16 r Fig. 9 NACA RM No. A7A31 a CONCEAL SHOCK WAVE ON NOSE OF MODEL I HOC f. '.'ES FNGiNT.jCT, F'ROM1 TUNNEL .VALLS CONFIDENTIAL Figure 10 SHOCK WAVE ON NOjSE OF MODEL SUPPORT MODEL SUPPORT " TURBULENT .'.. BEHIPrr r.IOCF' SMOCK, WA/E NACA A9224 11446 FIGURE 10.Typical schlieren photograph. CONFIDENTIAL NAOA RM No. A7A31a Fig. 11 CONFIDENTIAL SL'nACE TANGENTS AT THE NOSE MACH NET MODEL 3 *'. aLUE GI.'ENJ BY TAYLOR .32 r,, FOP iN 12 CONE, 16 S\ LINEAR & MACCOLL REFERENCE 10. NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS THEORY, REFERENCE 13. )D OF CHARACTERISTICS. REFERENCE 12. PRESSURE DISTRIBUTION M = 1.5 FIGURE Ii.TYPICAL MACH NET AND PRESSURE DISTRIBUTION FOR THE FLOW OVER A BOAT TAILED BODY. CONFIDENTIAL NACA AO1683 102146 r (I IAOA RM No. AT731a ni. is CONFIDENTIAL 4 I~~~~~~iiiiii1IC 4 10 144 0 0 ,o a 0 4 0D_ _J, ^  53 Is43 o / 00 "a . 4 4 oo [4*$ o 0 o 1414 0 a S0 0 o 0 "o 0 d 0 _ L 14i o qc V n 0/ I 0,s 0 'v i to ce C o / Cu C% 80 :QO 'a U w0 eo w3JP 0 . 4 4 0 o o 0. 0.o 'T.4 To 04 0. D 14 0 4 A 4 D 4 Wt I: ___ ___  I~*Hl I IS*tah3 0 o Pd E* I I 1 N 4 i( *>_ II< I I I UP rr I  I 1   I   I   I  he ft, c LOD 'Y8u 3rOT;J oo s zx *zoj CONFIDENTIAL I *NACA RM No. A7A31 a Re=3.7 x 106. Re=6.5 x 106. FICURE 13.Schlieren photographs showing laminar flow over the cylindrical afterbody of model 7 at two values of the Reynolds number. Knife edge horizontal. CONFIDENTIAL CONFIDENTIAL Figure 13 NACA RM No. A7A31 a ,i (a) Knife edge vertical. (b) Knife edge horizontal. FICrRE 14.Schlieren photograph showing premature transition on the cylinder afterbody of model 8. Reynolds number 9.35 million. CONFIDENTIAL CONFIDENTIAL Figure 14 IAOA RM No. A7A31& CONFIDENTIAL ce 0 0 w g 0 *. _ a ^  g : A ,a so. I , SO O f 0 0 '. TT o I / l^e I kM a) \ O p D 0. 10 o 0o . ,,r*,rE CY I ;* "I OTA RESEARCH LIBRARY . I I 1 O l I l n1 0 0 0 0 0 0 !I Cl Tb/Td d d 0n9ttjO eG.rnsseZe d CONf'IDEUTIAL rigm. 15,16 1 NACA RM No. A7A31a CONFIDENTIAL /Roughness added 6.7 'Shroud NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS Experimental wave drag plue turbulent friction 'Experimental wave drag ~I plus laminar friction 'Experimental wave drag o Smooth surface_ 0 1/4 inch knurled band SOgive completely sandblasted a 3/8 inch salt.band v 3/16 inch salt band 2 4 6 8 10 11 Reynolds number, Re, millions Figure 17. Variation of fore drag coefficient with Reynolds number for model 8 with various amounts of roughness. CONFIDENTIAL .28 .24 N. 20 o 0 o .08 04 0 0 Fig. 17 (I NACA RM No. ATA31 a (a) Knife edge vertical. rr;;.: .:"".. iSH ^"c ".... ..^i (b) Knife edge horizontal. FIGURE 18.Schlieren photographs of model 8 with transition fixed. Reynolds number 7.2 million. CONFIDENTIAL CONFIDENTIAL Figure 18 /j i ii '? " it I r NACA RM No. A7A31 a CONFIDENTIAL Figuriv 19 Re=.i.hS x Hr. Re=0.87 x 106. Re 1.1 x 1 .. Re=1.4 x 10G. 'IGURE 19.Schlieren photographs showing the effect of Reynolds number on laminar separation for nmolel 6. Knife edge vertical. CONFIDENTIAL 4 I; NACA RM No. A7A31 a re=ti.7,i lii . Re=3.8 x 100. Model 2 Re= 1.2 x 11. Re=3.8 x 10g. Model 3 Re=0.1u x 1U". Re=0.45 x 106. Model 10 FIGURE 20.Schlieren photographs showing the effect of Reynolds number on laminar separation for models 2. 3, and 10. Knife edge vertical. CONFIDENTIAL CONFIDENTIAL Figure 20     NAOA RM No. A7A31a Figs. 21,22 0 4, I o 0 a o . o 4. 4 ID 0  02 $4 a) __ ( r ** 'o Tb/Td d 'ue0ToT jjoo eznaeedez Tb/Td d 'unaTOT;;jOoo aZnseez CONFIDEHTIAL I I: NACA RM No. A7A31a iI I CONFIDENTIAL (a) Laminar boundary layer, Re=0.87 x 106. r (b) Turbulent boundary layer, Re=0.87 x 106. IGURE 23.Schlieren photographs of model 6 illustrating the effect on flow separation of the condition of the boundary layer. CONFIDENTIAL Figure 2: NACA RM No. A7A31 a Model 1 Re=3.8 x 10". Model 4 Re 4.0 x 10'. 3=8.550. Model 2 Re=3.8 x 10'. p=19.08'. Model 5 Re2.7 x 10". 3=t l 12.13 . Model 3 Re=3.8 x 10'. 15.250. Model 6 Re1.1 x 10. 9=16.75 . Laminar. Turbulent. FIGURE 24.Schlieren photographs showing the effect of turbulent boundary layer on shockwave con figuration at base of models 1, 2, 3, 4, 5, and 6. Knife edge vertical. CONFIDENTIAL CONFIDENTIAL Figures 24 r; NACA RM No. A7A31 a Re1.2 x 10'. Re=2.6 x 100.  Re . l1p. Re=5.1x 106. FIGURE 25.Schlieren photographs showing the absence of any effect of Reynolds number on the flow over the afterbody of model 3 with roughness added. Knife edge vertical. CONFIDENTIAL CONFIDENTIAL Figure 27) NACA RM No. A7A31a 0 CT d 0 ma or e CONFIDENTIAL 1 I r I ** 1 I I UCl S) S = 5 Fi a6 i/ a, a ) _ _____ _L__4 0 1 Lm m0 \\ o   LO E4 E 0 U" E_ 0 o0 _C .4  4 0_ o 0 0 0 o o 0 0 0 Oao '4ueToFTJeoo sTip ezoJ CONFIDENTIAL Tl V) IRV tf3  I Ur 0 +4 a r o d r  r4 O *d a 0a 0de to 0 t C 04 r4 ro V 4S a a t i 4 F4 o 00 ef oa a +> a a .40 oo a 0 cg 0*0 .4 (M 0 o( 0 ) I1 ( 1 ; IACA RM No. A7A31a CONFIDENTIAL JaO 'Ue TOT$J;joo sXp OaoI a0c '!t=UOT;3SOQ B2zp *iog OOEFIDENTXL Fig. 27 14 0 a " O .4k ID 0 so 14 I. (0 TI t *~ n NACA RM No. A7A31 a Model P. Re='I.I2 x 1l". IGLURE 28.Schlieren photographs at low Rey nolds numbers of models : and 6 with roughness added. Knife edge vertical. CONFIDENTIAL CONFIDENTIAL Figure 28 Mod, el :'.. n1=1,..s 11. . d NAOA RM lo. A7A31a 0 1 2 3 4 5 0 1 2 3 4 5 Reynolds number, Re, millions Reynolds number, Re, millions Figure 29. Variation of base pressure coefficient with Reynolds number for models 1, 2, 3, 4, 5, and 6 in the smooth condition and with roughness added.  ~ ~ ~ ~ ~ ~ 0 ^  ^^^Z ~       .16 NATIONAL ADVISORY COM..ITTES_ FOR AERONAUTICS a"    1 1 1 1 1 1 11   .08\ .04 (a) 8mootn condition (b) Rouhness added I I II I I I I__ _ 0 1 2 3 Reynolds number, 4 Re, millions 1 2 3 4 Reynolds number, be, millions figure 30. Variation of base pressure coefficient with Reynolds number for bodies without boattailing but with different lengthdiameter ratioe. CONFIDENTIAL .0 Model 11 L/D 4.34. 0 12 5.00 0 13 6.00 S" 1 7.00 v 14 9.00 Figs. 29,30 O Mode A "  5.0 T.0 a CONFIDENTIAL .24 r  1 Note: Flagged eymoole denote reruns S: / i I  10^    0 __model 1  m 04 (a) Smootn condition (b) Roughness added 0 L 2 a 4 5 0 1 a 3 4 5 Reynolds number, Re, millions Reynolds number, Re, millions Figure 31. Variation of base drag coefficient with Reynolds number for models 1, 21, 3, 4, 5 and 6 In smooth condition and with oughnee added .3e 0  s' " o "" '  o , d. 61 FOR AERONAUTIC 0 (a)I I (b Rougne added nA 1 0 1 a2 4 5 0 1 3 4 5 Reynolds number, Re, millions Reynolds number, Re, millions Figure 32. Variation of totaldrag coefficient with Reynolds number for models 1, 8, 3, 4, 5 and 6 in the smooth condition and with roughness added. 00NDENTIAL Fige. 31,38 NACA RM No. A'Aola 6A 1: 6 IVERSIIF FLORIDA 3 262 81C 5 580 TP t T',' ,,l 'Y"t, 7 ''7 4A :'l Q, IT, 'TT *4,VjL VK ,t ITT t 'wl it' Co" "I "30 4 TI, o Jo 44 j fit l TTl Tol ITT t' Tilt tT l :# 'A fl ip "'T gj 11, , oil 