L ENGINEERING RESEARCH INSTITUTE Page UNIVERSITY OF MICHIGAN AT l..AC.NMB,1 93 Pripard by jr.d.A:,prc:?tvd by, dl, RUt'tk- ki September 15, 1948

EJ135R- ' ENGINEERING RESEARCH INSTIT TE Page UNIVERSITY OF MICHIGAN _ TABLE OF CONTENTS Ivz8 Introduction * * ~ * *.- * Sunmary.... * ~ * * * * * ~ Symbols *., *. * & 9 Diosussion. * *. * ll us rations Sketch of Miodel (Figure ) 1). Photographs (Figuars 2 and )., ~ * Pressuro Coefficients (Figuro 4 - 9) ~ Lift and Drag Coeffiients c; (Fiur73 i0) Center of Pressure Location. (Fig;zre 11) Ieferenoes *. a a * a * a * a* * 0 0 1 * a a C * a * 0 *. 0 10 * a 11 a * *13 ~. o 19 * ~,20 * a 6.,C 0 & 4 r- - e ~ S.-, I

ENGINEERING RESEARCH INSTITUTE Page _" 3^__; 1__UNIVERSITY OF MICHIGAN Page I i ir strodu tion Suvers onic wind tunmel tests on various configura tions are being con-f uc ted to provide basic aaerodynaosic dat&a Initially, a serioe of pressure rSurvXey tests are being run as a firt.t part of a bro4d progremx The first of the aeries of Dpressre c distribution tests were radle on a. 200 included aig!e cone t.odal at; a- Maeh number of 1,93. These tests provide data for cormi::atrison eva lua&tic. of the wind tunnel test results on a simple model with,that of ot-ier tunes as well as with t-her.etical results.

I I I ENGINEERING RESEARCH INSTITl TE Pa'e.i____;__,UNIVERSITY OF MICHIGAN 2 Wind tunneel rressure tests were run on a 20~ included angle cone at a Maach number of 1 93 and the resutlts are comrpsred' with existing theorey and tes.t result's of other organiz.tions, On the basis of the ibest resaults the following conc lusions are dra w1. The numerical integration method of Taylor and Macoll tabuleted in Referes'xce 1 gives value of drag coefficient slightly lower in magnitude than actually ocours. However, tih differenoe in magnitude' betTeen experiment and theory is not sigifi oa.t. 2* The linearizsed theory, give reasonably oorrect values of pressure coefficient at zero anglo of attack for the 20~ o0 on 3. Those -tets indio.ate that coni.os.e flow may not be preserved at ang.oles of attack as is asstud by the linearized theories of Tsien and Von Kaxman and Moore. However, at small angles of attack the deprarture of the flow field frori the conical con;.ditiont is slight* 4. Thteapproximatel met.hod advanced by Reference 3 will giv value1s of drag coeffici.ent fairly correct in magnitude but will predict a lift coefficient higher than that v-ioh actually ocoars due mostly to the assumption of conical flow at anles of attack, and the omission of viscositi;y effects,. The data detra.ni ned by these tests quan-titatively, cheoks with the results of tests run by other organizations and in most cases shows be-tter test aoearacy, 1Thi report presents curves of pressure ooefficients., lift coefficients, drag coefficients and center of pressure versu&s angle of attack for 200 cone as calculated from pressure data obtained from wind tunnel tests. L

L ENGINEERING RESEARCH INSTITUTE Pa-e ___ IM~B.5 __ [ UNIVERSITY OF MICHIGAN S ybol: A frontal a.rea of model Ab area of base of model CD DRAG frag coefficient q0 A CDb Ab C p P - pnrssure oosfficie.5nt CL - LIFT lift o teffioitent qo A C.~P center of pressure 1 length of cone model M x Mach nwaber Pb - base static pressure P0, free stream static pressure Pg: cone surfae statio pressure o s free stream dynamic pressure x axial station measured from tip of cone I, II, III, IV and V - numerals indicating meridian. planes at 0~, 45~, 9Q0 13s5 and 580~ respectiv'i CQck? J^

I ENGINEERING RESEARCH INSTJITT"I I l......'......UNIVERSITY OF MICHIGAN _ - Di ous; s m. The raodi-1 used in the vind tunnel is shoenm in plan visw in Figure 1I Tt i s. 200 stainless steel cone eqtipp3e wit.. 18 pressure orifices *0226"0 in di amet r.. e The copper orfi.ce tthi adinc tledng hrough the sting and Supp'rftin.',' seo" tor is 0f- t i uts?..; dia.z.e'ttr a'id.022. iside diia m*W i T'i zcdtl is hIn ^i yd o s noznth e finisr ',ts rpossibla. Se.. o..- tL o rii,cs:;suppli.d.useful.ata. - one orif ie was pluwg di a.d c.n:.uldk. no)t Lbe c:leo.red, KRa'3ings w"e.e tak.en at a:.p.1les.of' atack c F,^ppr:x. "..a..l. ( ~ 4 t 0~ te rodel Irt*t 18 ane'.rea tings tak:t1 at e.c. proximn^atel' 0~, 4~ atid ~ i#3 to ochck +th<, s i... iii,try ~6 BtS A,...~... ~,. -,.. u A.. of result, Al - rxns >mzre iade at a M.'. nM.. uutbr" of 3.,93. A Scb> hLiereil r1t-cgraph was taken of each rn, A -. plumb line war used to; create a werttior1l refer nce lin e Wv.s~ ey*isrr, i n saca Sohli.e n pho t;' g o rtpt* iTh. a ue.l 1,.g;le c f a. ttac K s r8 'ead fr^..-e -ctogr.h * A typi o4al totnc'i,-.r.i.::~,-'.1 tgatS-; s; t lc- 'e i m.hlieren photogmxph shc; tnvg; the xnocil at,.ppr.:ximately- 10 tn. gle of.tta..ck is shown as Figre. 2 'Nco photorp he s of t1he manier tI.k re o taeo takeno f r anoil of a'ttsac!k. T-hee 'bhc'togrsapns r'.tcr-d 'the pr4'ssv.reo data whi.c ia reduced to in. e t.fU!'w:sr.s.reJo d istr:i bbut i,. o ver the srf:ace o f: the mnode l A ty piJal r:.c'rne-e;:r?ba nk 'trioBraTli goT.i the reai.nt at + 10~ appears ini Figure 2, Tlhe first tlu'eCe tluiud le'v Is of f>v Ulbe t irou'pS represent orifi.ce meritdiax& pla.ns. i/, ans II r ^.ivct1.ly 'ht4 last level three tubes reprsents basn oressw'm orifices, Th,-e toheoretical. e;..-thodC': u. erid i-o *>.tesmiene tha pressure dist.ributtiox.n at'.oro, e~.:~-l. 15:'" att-a ck are th':, o 1f ih n 'r^.rical intfc; ra"tJon me thod of Taylor and M!-ac.o1 in Ke;f2s'.:r.ncs I and the i.ha, riz td,t-.thod o' Refrence 2. As is r asonable to expa act th h-e ioanla-ris o.n betwieni experiments satd theoretio al L

L ENGINEERING RESEARCH INSTITUTE Page _ iVLB5_-,5 UNIVERSITY OF MICHIGAN 5 results is fairly close onsidering the fact that the Taylor and Macooll theory neglects visoosity and the linearized theory neglects both viscoty and the ocourance of a finite shock wave. The results of an approximation method given in efaerence 3 was used to compare with experimental results at angles of attack. The comparison shows fair agreement between the lift and drag coefficients, This method also neglects viscosity which has its effect on pressure distribution through increasing the effective included cone angle. This method also assumes corncal flow. Figure 4 shows pressure coefficient plotted versus axial station for every meridian plane at zero angle of attack. 'he theoretical results and experimental results compare farorably when consideration is made of the following factors contributing towards any deviation: 1. No account of the boundry layer or visoous effects is taken by the'theoretical calculations. The boundary layer tends to increase the effective cone angle. 2. The linearized method takes no account of either viscosity or a finite shook wave. This theory gives reasonable results for small cone anrgles only 3* The numerical integration values as tabulated in Reference 1 were extrapolated to give values at Mach number 1.93* This leads to a slight error in results, 4 Alithough extreme care was taken in fabricating the model, some deviations will occur in the geometry of the model with a corresponding effect on pressure readings. 5. Some test secon loity flution loity fluctuation is unavoidable which contributes slightly to inaccuracis in experimental resultsa

ENGINEERING RESEARCH INSTITU'TE Page ~~~~EM3-s5 __ UNIVERSITY OF MICHIGAN 6 6. The method employed to set the angles of attack was not an accurate one Reading the angle ferom a photograph gives limited accuracy.?. Some undetected roll and yaw -of the model may have ocoured while the rune were being made. This leads to errors in the pressure readings. The experimental results plotted in Figure 4 agree with the theory of existance of a coniocal flw field at zero angle of attack. This is Pubstaitiated by the existance within experimental aoouracy of a oonstant pressure coefficient for each meridian plane over the surface at zero angle of attack. References 4 and 5 reported. similar results for slightly lower Mach numbers Figure.r 5, 6, 7, 8 and 9 present plots of pressure coefficient versus axial distance for fivme seridian planes atc angles of attack of + 2~, ~ 4., t ~oj + 6, and + 10~. The experimental points are connected by a solid line while the mean values of pressure ooeffticent for each meridian plano ars repremsnted by a straight broken line. Figures 5 and 6 for - 2~ and ~ 4~ shows tha.t within experimental accuracy '1the pressure coeffioients for each axial statioa of a meridian plane does not deviate rery much from a oonstant value. This indioates that the flow field has not departed far from conical flow at these smell angleso Since the linearized theocry presumes the conrial field to be preserved at small angles of attack the theoretical resul-t of the linearized theory and experiment should be fairlyr close* The method outlined in referenoe 3 also asswes — the conial. f'ield to be prmserved at smnall angles of attack, and it rill be shown later that results of this mathod compare favorsbly witoh tosjt results* -i I — ---- —

I ENGINEERING RESEARCH INSTITUTE Page ______ B>5 ______5 _UNIVERSITY OF MICHIGAN 7 The lines in Figures 5, 6, 7, 8 an1, 9 representing a consta-Ft fe;an oressure coefficient for each meridian rlAe^ wero used in. the graphical integration detV.rmining the lift, drag and moraent of the modell. This prooedure omploying a constsnt pressure c.oefficieant for asach nteridian plane was adopted because it was shown that at the small angles of atta'ck (2f and 40) thi s condit-ion approximately existed and for the higher angles the deviation from this condition was not much more thaa the acourxoy limits of test data. It is thoughtt that the calculations based on this assumption will yield i'early correot values of lift aid drag coefficient while the error in moment will incras6 as anglt5 of attaok incrsoasse Figures '7, 8, and 9 showing pressure coefficient for -So, - ~ and t 100 tend to indicate that at thess angles the conical flow field no longer exists. No trend in pressure ooefficient along a meridian plane seems to exist other than the fkact -t1hat it seeis -t1o bea iighest in the region of the t-ip Tests reportxed in iRferences A and 5 also found t'hi tyke of beharvior in pressure c oefficien.It although the scatter of tst points was much greater because of mors dTviations of test coditions. It is seen,, however, that the values of oresiore coefficient do not depart far from a mean value at angles of attack as high as 10~ which.indiates that the flow ficldl has not departed very far from a conical flow.fildv It oan be seen that -the pressurO ooofficients represonting mroidian plane II at 450 are less than those represerting tmeridian plarn I at 0~0 This so tewhat startling result was not fotund in the tests reported by References 4 and 5 and may be exrlained by the possibility of someI roll and yaw of the model, being present a-t the,time of these rums Tie tests for plane I ware run with -the iiod1el at poitive angles of attack while those of plane II were run at negative angles. If the.model wss not sy~metrioally aligned with the stream the behavior 'as shown in Figu'es

I ENGINEERING RESEARCH INSTITUTE Page 8:~,'iB- ___ UNIVERSITY OF MICHIGAN 5, 6, and 7 may conceivably hae occurred. However, it is difficult to explain why the pressure should be lower at plane II than at plane I at positive an.gles of attack unless sowX other flow deviation ocurred. It is tthought that this maniifestatioln is an additional indication of the departur of the flow field fro m exact conical flow conditions Figure 10 gives values of drag anld lift coefficient versus angle of attack. The value of drag coefficient determained experimentally compares favorably in magnitude and trend with those values determined with the approximation rmethod of Reference 3 and with the magnitude of the numerical integratioln method of Reference 2. Reference 2 considers the value of the drag ooefficie-nt as being constant for small angles of attack. Experiment showed tha. drag coefficient was approximately constant up to 40 angle of attaeck which is the region considered by Reference 2. The experimental drag coefficieant is higher than theoretical because of the orission. by the theory of consideration of the effects of viscositys Lift coefficientas show in Figure 10 were somnewhat lower than theory as was to be expectedo Theo deviation from theory was greater at higher angles where the viscous effects not considered by theory begin to take a grebter effect on thet pressure distribution. However, the slope of the lift ourv- wa s-iowmi to remain constant as is predicted by theory. The location of' the center of pressure is presented in Figure 11 These values were determined by making Lse of the moment oalculations using the constant mean pressure coefficients. These values are not correct; in ragnitude because of this approximation and are only indicative of the trend of ooenter of pressure looationl The theoratical constant looation pdredicted by the linearized theory is shown to be in error by this data. 16 _ -------

ENGINEERING RESEARCH INSTiITUTE Page F&]B-5 ' UNIVERSITY OF MICHIGAN g The value of base drag cosfficient for zero angle of attaek was c&lculated by using the value of base pressure registered by the orifices on the bae* of the model. This experimental value oompared favorably with values reported in Referonoe 10 found for tests run under similar conditions at a slightly lower Mach number but at the saeB eynolds number. (Since the bass pressure is largely affeoCtd by the bounda.ry layer condition ovr the model which in turn is a function of the Reynolds number these valuee should ooripar favorably even though the Maoh number differs slightly*) The two values are shown below. Cone Test Refereane 10 |)CDp.152.14 to.16 This result seorvs to indicate that probably very little deviation from normal test conditions occurred during the cone tests*

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ENGINEERING RESEARCH INSTITrTE i ae.l.l.B5 5 ' UNIVERSITY OF MICHIGAN - 21 l o. ".perso nic FlowF of Air Around Cones%, MT-TR-1* t2 "Linearized Supersonic Flow 'round Yawed Bodies of Revolution", By R. Sauer, Curtivseff-right Corporation, Translation CGD-620. 3. "Method of Determining Lift, Drag and Pitching Moment of Inclined Cones at Supersonic Speeds"%!IT-Meteor-UAC-3. 4* "Pressure Survoy on Cones in the Two-Dimensional, 1.73 M Free Jet at F.G*S." Applied Physios Laboratory, Johns Hopkins University CF-716-N. 5. "Bxperimental Determination of Pressure on the Surface of a Cone in a Supersonic Streams' Applied Physiocs Laboratory, Johwns Hopkins University CF-530-N. 60 "Air Pressure on a Cone Moving at High Speeds", By Go I* Taylor and J. W, Maccoil. 7.* "Resistance of Slender Bodies Moving with Supersonic Velocities with Special Reference to Projectiles", by Theodore Von Karman and Norton B. Moore, American Society of Mechanieal Engineers, June 1932. 8'. "Supersonic Flow Around Yawing Cones", MIT-TR-3 9. "Supersonic Flow of an Inolined Body of Revolution"^ by H. S. Tsien, Journal of Aeronautical Scienee, Volume 5, 1937, 10. "Ebcporimental Investigation of the Effeote of Support Interference of the Drag of Bodies o Revolution at a aoh Number of 1*6"t National Advisory Committee on Aeronautics RM A81305*

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