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fPr W'' L"I'. ACR No. L4E10O NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS ARTIME RIE PO ORIGINALLY ISSUED SMay 1944 as Advance Confidential Report L4E10 iERSTIATION OF PRESSURES ON COCKPIT CANOPIES, GUN 1,. TURRETS, BLISTERS, AND SIMILAR PROTUBERANCES ,!n :., By Ray H. Wright Langley Memorial Aeronautical Laboratory Langley Field, Va. .0 WASHINGTON CA WARTIME REPORTS are reprints of papers originally las ae research results to an authorized group requiring them f aulf hbed under a security status but are now unclassified. So al. edited, AU have been reproduced without change in ord L 201 S 2~i:n~w ,:.:.**.~..1r;, :'6~'~:L'.. ued to provide rapid distribution of or the war effort. They were pre me of these reports were not tech er to expedite general distribution. DOCUMENTS DEPARTMENT , 'a:/ r i ;'. ":,I.. " Fr"";... i, '". P * EN  * iii, ". F ,:'. .. ba:i:';;+ j ..: N. I :.:.. I, Q 0 . Z :...... ... NACA ACR ITo. LiJFlO NATIONAL ADVISORY COMMITTEE FOR PEROI.AUTT S ADVAiJ.C!. C 1 'T D .TI AL FORT ESTT'ATIriIl OF PRESSURES 0' COC'TTT CFT ES, TURrETS, LITSTEFPE, ATID S'Th.LAP ')nT"T3E;Tf.A"CE By e.ay H. Wright ST T .iA 1 '.. Methods are des ribed for ?st "st'.rn.: crressur,: di'  tribut,.,ns no er protu')er&nce..3 sach ,s acoc', t I3a1o. es, gun turrets, blisters, sco 'n:s, s['T!; ?., s. These meth:!rc are ac:.led to thas est'liati on of the :res sure distributions over sph ricaIceg.neit and failed gun turrets and o'.'er there nrotLuberanes o, the BrewsLer S 2A a1s ri.jnc. Th e efiie.t of comrrsessib ili 1 t, interference, and fl.o sena'ati n are ,J..s.cused., It is shown that by a corbL'. ati.n or :t r rerrct il dvta vi' th theoretical methods; liritirnc r:.s:u..rs for use in :"ter mining r'aximurm losiOs ~,n in r.any r!,ases Lie srti sf1s ct cril y estimated. "Lic.' s str.ti.c exIcr.mc itati n is ne'.ded, however, to rinor .ve the rccuracy of est j rat i:. T yTRODUCTTO.' Th: purnos.o of the pr:sent r':or't is to dz:s.r'oib methods by 'which pressures .rid .:.*.nce loads on 'tr.otu.r ances, such as co ;ir c.a op.es, iUn tuirrets, bl ters, scoos and ighting domes, my be r1or ; ntim... In particular r, t}: poss'bl 1itC1 of det rri 'in,; li"iti:. values of the ',rus.re co, ffccont values which cannot be exceeded in o:'acti:e is oem '7Inst"i'. The invest, ati :,n was initiated ;, a re'u:st from the &ureeu of Aeronauties, ,pvy Denartr'rt, for hai data on pun turrots. U:. qplictle e.erl'rnta. d.ta viere available an., as the I'AA testi.. facilities 'were already covmitte.d to other .nvesti.art:ns, it was decided to estinrate the limiting loads. Methods generally useful in the estimastinn of lo:.ds on protuberances are described in the present report, These methods are aoplied and, where )oss.t.ble, the 2 CONFIDENTIAL NACA ACR No. LrEIO results are compared with experimental data. The methods are necessarily only approximate. Even if the potential flow could be exactly calculated, the actual flow vromId likely depart so widely from the calculated flov as to reader the results invalid. The exercise of judgment, based on experience, and the use of experi ment in evaluating the effects of boundary layer, separa tion, compressilbi1ty, interference, and departure of the shape fro th'it for which pressures can be com..uted are necessary in oreer to arrive at useful results. Although little opportunity for systemrtlc exreri lentation is likely gt rresert, the study presented herein is be!r. as? ]ted to turret shaocs on particular sirFlane moccl]s oeing investigateed at LI4AL with a view toward improv.rin the methods of estimation of pressures. SYAi BOLS p p pressure V veloc. ty P rnsss d&rsity q dynamic pressure, free stream unless otherwise stated LP'?2) P pressure cnefficier.t \ q M. I.lach number, free stream unless otherwise stated &V velocity increment .0/V0 vclozit.yincreTrnt coefficient V/V0 velocity coefficient ] + Y ratio of specific heat at constant pressure to specific heat at constant volume ( x,y Cartesian coord!natEs CONFIDENTIAL NACA ACR No. lOE10 Z,t complex variables Subscripts: i incomoressible or lo:v speed o in undisturbed stream I local Other s;7rrtbol are ir.trdu:ced and defined as needed. Insofar Es 'oEsible, the notations of the references are retained in the o,rsent report. For tiLs reason, more thr.n one quanT'ty .isy be' des' asted by ':le sa..e s:.'rbol or one qusnt 'y. may be deslgnnted by more t a 1. one symbol. E'fTnDS 7rp1 *,.ALCU.LA'TTI."'. 0F1 V gC:Ts NV'E3 PEZT:SJBAJCLS Althou:zn thr ir3l'ne w'th its c on .,, t,.urret., blisters, and other pro'.'ier.nrices is a complicated threed inmensonal form about vwhicl even the potential flow cannot now be corruted, an esti.rs.te of thle pressures on the orotuberane. can be obtain.?d. the airp:ln 1 n. presents the ',:neral e:)c erane 'f Pa Wi.Ln.., fisE]C :e, and tail wi tn the nrotuberancev s'i.,roo3.o. LhesE protuberances ar.' usi:ally of snall lenth r:l:tive to the length of the fuselage o' to the cho'4 the ,:ing and are v,ry often qt..ite thick in elat'on. to their length. Th. oad.. oer tts_3 r rotu'beran3 strher.'er are assumed to be dttermLncd larrt.:l ty the s pes of the protuberances ari. t) be :r.odifiedr by the interfe.rnce of the wing and fuseleea. As an aoproximstlon that is usually vrlid t''r.?1.3. the .'ror.tbera&ie i3 2ccated near the nose or int the. wake 'f tre tody, the total velocity V is assured to be equal t3 'the s.It of the veloci, r" over the protuberanece vw.thout i nterferenic and the induced velocity increment Y7 due to th. interfering bodies or, in coefficient forwm., nc interfere /V\ / o V )rrotuberanco alone interfneence COYFIDLE'TI/AL COTFIDFNTIA5r U4 COIFITDEN TIAL NACA ACR No. LiElO Methods of determining the velocity increment due to interfrence are r.iven in the appendix of reference 1. Tn rany cases, the interference is sufficiently small that it may be neglettcd. It is ornvenient and sufficiently accurate to apply the o,'pressibility correction to the pressuree coeffi cient .p tim'ijted for incc.mprrss.ibl2 flo'. i = 1 (2) whe re I' /.', is the value of equation (]1 for incom pres]l ble flow. The pressure *.orfficier.t for c.m nressijle flv. is the., obtair.ed fro aen approximation given oy," Frardtl in referee:' 2 as F where i.B is the stream l%,.'L nur'oer. An approximation that in : ;.e.ific t..starces has 'be.n fo md to describe exFeri rnental result ts more accurat,:I,' than r'randtl's nethon has bcen A,,ven by von K.arnmn in reference 5 as PF. 1 (,. 2(,1 +,iimpi2 Equstior (5) is s,'ffi 3 ntlyv scf 1urat however, for the est'iiati cns des*r!iPed here in. Three r esur istriL .ut1 ns o obtained up to this point t apply in 'ot ntia flow. The effects of departure from 'otcntCal Ilov, w h'.h iclu.!e develo\rm nt of the boundary 1 a ;er on the .srface forvErd of the protuber ance, screariat'in . tlhe f]"i, 1*h.L.ih 2oLrs reularly on th, r'ar of blunt boz>s aind int:er t',n of these Stffcts with c.'p'res's i ;i lit; "tust now b) e;stirrm ted. Al thou.., thu: b ni vi laye r and thE r. o nt and cYistence of s tar.ation iFht c, ca].lul at(. at at ist for low creeds, b' t'? m.tno.ns r e. reUn.:: anO (,ith modification CO'FT DLNTI AL NACA ACR To, JtjFlO of the romentum c.lust'on fxr the threedim.rensi onal flow), *n.i rrme th,.d I s know: f o' coa 1,'1l 9 tin.., the ro re r .or 7 C.: * rress.ires nor is iny theory available for *stimattl.rji the con,pre 3 sibi 1 ty interaction. Fr,n t". r.',ea rn e:',er'inenta.l csal evai bl'e, tn sr. ef.fr;ts can be it least qualitative, l estrriater'.. (thes d stt re presented and discussed. in fhe section er.title'd "Angplicotions.") In brief, the .,r.cedure is 1s follows: '1) Est mate the' veloc t'seffit i ent di stri bution for lnco.npres u'.] e .te.tisl flow ove: th ro tuberar.ce slha.r ft) 1.t r'.t... t' int2"f' r : C , cit. coe  fici snts for. i cor:.r..: l :.*c.tet i; flow.' ( ) A.'0 tl'. o ff:"' . ts3 o' i".ln.,A st s (1) and '2) as n equ'ti, n fl L) (4) e us' n'" f sL'o ( c. r te th .re re coefficients for irc.i.niresstbls flow 'equation '.') i5) A'jply t zoi.pre.sibil i;, corre ti.on (equation (7) or iL,): ( 76) Eti.r te the effe'ts of deoat'_re f r.cr rotent ial flow Tir practice, ss n.e),es in the e:: C'.lev  ro i iation of this .rocedurc. n' ;' be neoessar . The rest of" this sector, s ccn.er.:'d ir:rel with the determination of the ve.ocit d istribiti..n vtith potential flow over soec fic ocotuL er e.nce sh t.s .. thut Snterfe r ence. General Consilersrt'.ons Protuberances often near as bodjes that ?rec aporoximatel.y half :.,: :.:y mrr', tricI fi f or.iins c, ,t b;, an infinite plane as indcoc tod in i,'ire 1. The fio.v .it"iI't the interference is then thle oit '.cal., a)8 ox i .m te to the c.orr'sa. ondirr half of tnat o'er tlc nr:.l ?te body.. In many cases the half'bx3i 3 ,rcechs t", t'. n,'l .m e.ional form fsairfo]il); for '.Shch the or srur distribution is alf;avs calculable: then, as the ,prcs s.3Uire chir.g.cs are larger in the twoci'nm.sionl thrn :n the three dimensional case, it Is *3.oserv3tiv? to c )nsider the CO~TPI DN'.TT T CONFI DEITIAL NACA ACR No. I4TF. flow t.'o dimensionril. In other cases the shapes nay a,)P"ro1xin.te simole threedimensional firms', such as s,)'.ertes and nrolate or oblate s)hIroids for which the f'lcv is ':no'."n, aend the corr3sponl.i.r:s Dressure, distribu t'.ons may be essu'::.ed. [f the form of the body or halfoody is such that the flow' cai.not be directly calculated, it mnay bz ':pproj. mated o var'oos ricvizes. .f the shapes of ihe front and r3ar e'.t's of a or..tuberance are; different, i;nn.uch as the flow u .r onz l., 1. i often little affected by that over the other, it un;y be nossibl2, to computer the prs.asure distribut,nrs ovor front and reor ed: .gs sppa rately arnd to join ti; distri"uti ns at the cnter. In scene case & s'r,ie jody, for which the flow in thr a d.m :rs .i ciw n Le c. iculite a;, o . mod' ied by F, two,dimen.s onl T..t3..d to aoE'toximate a iv.n shape. Such a rni fl ct n '..eoen'lis uor. the ussurption tihst a swell local ch'1.,e in t e radiu3 of a Uody of revolut'rn. p or'uc: s a Io E.I Lodim;nrsioniirl effect. As the rHclu: r .',f c':e L:y of revluten bO..sfa larger, this .ssu.,0tt .i. bec rnjs .nore nearly correct. For exxt.le, 1th, .: e s r'.2. .r'.r 1 the I 'n of' an coen en ino c .)i]. lnc on.roL'.c': the o'.ssures ov3e'r an a.' rfoL' with the coOlili 2h',e nf t;,e li,: end ".,' th tIhe sar:.e effective anle of atto.. Arn ::T I,, of an oblate sohertld i.)r li fie, Io tD .ro`fT' 1 he sh.l . cf thlt 'c.xson toirrct on the r.rce.!ster S'L2A1 Dirolsqne 1 s xi ven in the section entitled "Ao'.ic9tLns." T. oDT inr. i onl Shoes Arbitrarr foris. The t,:.',dim signal potential flow post sy.tr'caJ ,roi 1 le that correco)nd to !given hslfftod os c'.r, t obtain .n'd b:y the mtl thod of Theodorsen and& 'rri cl' f refer:nce :. Tri mwn casr=s, however, le.'s lr, ori.'ous n.thods 'iff icc. Thc granhlcal miethod of Jcnes rind ",hen f,'eference 71 is well suited to the co.nrutat:,.n of flte. tisl I ow v'.'er Lus. For'is for vh:ih not.er.til i lof' is known. In certain cases, ft. 6,::tm FlT' .? rct .F'be "ance a: oache that of some tA'o&d Sm.nslnal orf1le '.r wi'.ch the pressure d 1itr'l.'itton o"" correes ,ndQ n ~; .elo.1ry distri ution is already kz.ovn rd ''n rbe a'pt".e v.'1thout much furt,.er co;nriut. t't.n. Thre. such s nr)le or,fi.les are the inir, it.ely lon,, ci2n1lar cylinider, the ellipse, and the GCO 'i DYTTI AT, COI.FIDEINTIAL NACA .tCP No. LTi710 CO ITDL''TTAL 7 doublecir.'cul rnc ornf le. Fir the circ,... r c'yl in,'er movinT rormal to ; tE a:i?, t.e v 1oclt.y ris ributic.r 'ith notent '.: 1 flow is ,. v en by V = :V o sin e (5) where 0 is the o lc,' rn;nle me.,c: rel fror t'lhe stream direction ..Ad V: is the f." war* d or stret,r 1103.t . Thr v'1 0oc ty diQt' but' or. a:'.t the el 't i cyl!ini.eT v'nr :r. 111 to it: .i or ..i i n. 07 Zashi in r.efi reice cr2j ri;, ;:ei e:: s .d n t , .'r'm / 7 r 7: ,j I' + ( ' where a s .mili?.or :i s b s rrmiinr.or .I s x l sta.n.:oc :. rg cn r s: :1 :rIs C:l :a :r' ThF forrar.i r.ort, n r of a :.,. tr i "l I f LL L 'r :.e w th .zero lift c ni often be nr: ':rin r' L 1n 3.'t e as 1n igur"e 1 1l. 'f '. t ? .' :ti.c? rr.": the n  st ': i h l 'i? ,.xi r'.. or :,.st: :3 a: .:3' rs, th e 1 1 ' n c1,,l ,ir a ll.,, b ...et ?r..:i t d ,r I 2. A 7 The veloc it: r" s r't. on ,v 1 f:.'."rd .rt : f the Ji. .oi. r.Sy thr n br t:.';: t : E .,' ..: :', t ..e .Ain th :r v r:r : tf.1i s.t.i, i2 ; t. d.o'u lL  .' r arc s;rT et. 1 c i. ft f "'io.i h. : Jn o.v;:' r surface or.fill s aTe ires 11 It? r..:r.? i2 . %  Co' !D: 'TTI T? 8 CONFIDENTIAL NACA ACR No. LE.10O conformal transforratton into a circle is given by Gli.uert in refers", ". The velocity distributions, obt.ine 1 y notentlpl theory, are given for different th'.ckneases by th: trolid llnes in figure 2. Thin bodies by s!one method. A simnnle anproxirate twodThrsfn.l a eT Thod ThaT ha oroved extremely useful has been included in a publication by 9oldstein (ref erenrce 10). This Tethijd, which g.ivss ti.e veioci.ty distriou.tion ar in intitral funrctI*'n of the slope of a symretr.ical orcfile, ma;., be c:411ad the "sloi' method." For the dertvrtlon of the slope method, the following two si.fnnlifyj r. 7 2ssu.t.oL.s nrec narecssqry: (1) T.i' rrofile .s sL'ff i intly thin that the vclocit., is ov.h ccre vr; di.C'ii r..nt from store am velocity .V (2) Tho slo" of the profile is suvrywhere small There assunmotions oreclvue the existence of etsgnation points. The s~nrctric'al orfile rmny bo assumed to be reresented by a dl rtr' .)ut' n of sources d),/dx along tne chord The velor'ity Hicrenent f(&V) at any pci.nt (xon.t) *.p the profile (fij. 5) due tp the source eler ent dx it x is dx d x A(Av.) = (7) 2nw Because the nrof.le is thin, the velocity at (xo,y,) cinr.ot bLe very differ.nt fi o, the veloc" t at x,,; thus, a(AV) O __2r. (8) fl CO TID ITTIAL NACA ACR No. T4lElO COIT0ID.TIAL 9 TThe total induced velocity therefore is A d7 rr (7y, ') For unit len,_th of the profile, the cross secti n at x is 2;y 9ad, with 7 = V.), the volum,,e flow is apoproximatel: eiLiql to 2Vov The volur.e flow through any cross section, however, must ibe e i.l t.: the total output of t.:. sou,.ces unstr,ea. a.d, t.,erefore, or =2. 10) With sutstit..tTon of the value ..' d,/.ix f:'oir, eq a tion lOC) i: equatio L ), the .cneffi cent of the indued velocity becn:mea /V 1.. dx .' / 9X y, "h u C j5 vj d The interra'iid .i c'qu tion (1 ) ar be eF) r S? i r. tri gonomretrLc forr: bit, for rhs nrses.t Ui'j2Es, thre algebraic :7.res'. ,n i . r tair.ed. The v loc it r coefficient is 4, 'n c: S= I +  le ) V V 0 1 T.f the slo'j dy/'ix in. knorn as an al., ,.braiL; function of x, the vclor:2. L t',' d'i'tricuti.on c.,ri uv_uallv b' obtained vithout much trouble lc a function of x . The integ.rand :.n tquiti.a '11) a arircahis ..i intty or b.eccmes Indsterr.in'tc at x >.,, but t'. integral C' *ITIF TD.TI ALr NACA ACR No. iC410 is usually fI.nte; thn innfi'n'te positive and neg".tve strio. can.el f the Integral approaches infinity at Spv1 aen ':.'Mi.t x,,, a finit integral that yleld.s a vol.oi. T ncrement wi.lch approximately egreer with the vctuial flon can nuually be obtained for a slightl different vlu9 of xx. ihe sl.pe method is mere useful than might be supposed frir the restrictions .m.posed in the der'va t,'on. Although the results are not ex.r.ct, thej provide a reasonably g)d4 eoproimation even for relatively thick forns, eso.ci alli; over reions of the orof3le having small slo c. The ethod is not aoplicaole in the vc :1nty of a st 'tat'on ..int or ..:hrc the Flooe Cdy/ i. lare. This d'ffic ltt ma.7, however, be ci r', v r nted. I'ny nrotuber..iLc. ChPl es "nvDlve no very l ir v values nf n .' /dx arn reqUire no !t.agnation point. Tf a t.'.r.naton onlnt does occur, t"le vlo'o.ty distritutior over the rest of the profile at somr distance from thr. nc s nPay be Dax',oxini.ted jroviiled. the roundoa n c or coil, 'hlih. ivo..ves l .finiCte? lone, :.s exterd l 'n a c':) cr ot.eilelse is sli '.i tly altered to prcvLant veir; tr,2 v.nla' of r '/d.: A rescrnabl': SaE .: st c volci ..ty .n.iputat o en can be made 1f the sloo:. rre tr d '3 lt.0:'. not t to the given "rofit 1. b'ut to ti,'. shEt . ojutain. Es the anamonts j.y b Wh. c t.e ord r.at "' rf i'. i /e'! 'fil : cx ed those of a .sir'11e profile, vrch as .ii3.se or Ju$.,owski air f,il, for :'hi.h t'.e velocity distrit.iLon i? known. The vcloity inacre.e.:t. a,e slmnly n3perPosed; that is, the required vel.oclit, distributl .n is the sum of the velocity .ettrtbuttr.n on the ,".imil ar orofle and the incrOement .V found .fcr the d fer'rtce snpe. '.hr' edimensi nSal sh'..nes ri n7 be sl.hti: rodi.l"ed 'n the same way. r'Ven r'rotuler'ane ,rofile ..haces can often be asrT r .'.ated b t !. jaxta.I t1 Tn of s er.ehs )f zIcs for which thic slor es are river. a, relritively si.npile alga:,'raic fu!:ct'.'.is :or xe: rp.).Le, c rc'ular, ellipti3, and rir.bol .c T'fe ... duaeie 1 oci t7 oeffi. clent &AV/.1, '.' then he nobtsin7d fror eqastion (11) b; direct *. tegr'.tion. r.liz r.ced.ir ds anproxi m"ately correct v,0lo03t:' distributions even th',ugh the curvature it the .'ur.t'.onn.s r:y 0e dis.IcotInuous. The slooe should obvi.us.v be rude continuous; that is, the arcs ab.uld hal;s the s're loD. aj th juicture. COrTDT "FTT AT., COTJIDENTIAL NA A ACR No. 1).! TI. A r rotubcrance ornifi 1 maiy have the approximate hape. of a smicl.? imlole ar, such as the i rcular arc, in vihich case the velocltj distribution 13is easily calculasLpd. Thus, in figure L,  = tan 6 dx x = r sin @ , = r cos 9 ,9 and equation (11) becomes 41 r1 AV _ TY sin 0 dO sin 9 sin 0H sin e .in a ( a) Integration nd si.ibstit.utMon of the limits give / D1 ssin i tan + co a 1\ AV 1 n_ V 7T291+ tan 1Fe (1 lb) o sin 9, tan  Ons 9 + 1 t 1 / I sin 9o tan +' cs + for the velocity di str'bution as a f.function of 6, CO FIDL 1 TI I 1 1 p 91 = de + sin 9 U,"8 COITIDEETIAL NACA ACR No. LrEl0 From figure L, 8, = sin  2r 6 = sin 2 (21 1 xo 1 = r2 _ r h) 2 c2 h + r = j. from w}. ch 9! = s'n1 Ssn1 o ~r 1V 1xn h 1 + C Substitution cf equations (1i1.) and (15Y) In equation (13b) gives the Indu.;e1velcity coeffi.cient AVP/' as a function of the chorl osition xo/c and of the thick nees ratio C, Tv:hEre xo/3 is measured from the center as shourn. The velocity inzrements for circulerarc profiles ra.ing in thicnres9 ratio from D.1 to 3.5 are shcwrn ir figL.re 2, in whi:h the results of the slope method are omrrarer' with tn? resilts o)f the accurate conforraltransfor action methc.c. In figure 2, x/c is measured from tn end of the ir..'ile rather than from the CO FTDENTIAL and (1s.) (15) CONFIDF NTIAL NACA A C. Tc. 11.710 center. Up to a thic'es? ratio of 0.2, the slopr. method CiveF L. fair sp roxiration of the velocity, dis tributions over circula. arcs. As was to be expDcted, the error is greater in regions of greater slope. The velocities at the center of the profile, v.here the slope is zero, are appro:1r.at.] y correct even fcr the 50percentthick profile. ThreD.:lenrsional Shanes Iletbods availbtle for the calculation of flo,.ws in three dir.en ions are ler& gec.er.al + hn tic. corCre'po.dingi twodimensional :ethod" because, e:'C'e i thtf s..r i'6 l case of the e li.:,.cid ".' th three u.e ). ] z7 t ,y apply onl, to bo .s poss.es :i.ng a:,1i l s'r.i*).r1:,, th.t iS, tn bodies of revolution. ;'i.;7.prot.uberavice: are approximately axi'lly s:rne trial, however, ard tihe threedirenssioral theory rr.a/' grove useful ir: esti.1, ti:ng velocityT and corresp.oidir nr essiie di.tibu tionz i these cases. The sphre. The Zitmple.t bod;. of revolution is tae sphere, for which the velo.'.: r di? trib'hit n is givEr Ib = o.? in 0 (16' where the anrle 3 i r:'easurcd alonr an. m'. r dian ste.rtinf fror the stream or flight di.eetion. The o') lte "Dphr.id. A todI of revoljticn r' r, F cling a guun turret ? t'er oblate spher3 .'.. o:bti'n r!ed .y "c 1 v1ing the ellipse about Its n'".nor axisr. '.Motion .n the direc tlon of a ma 'or a.:s :f the E llinse as 'shown in f i ire 5 correspond toC thr'L o the C'LU turret. T' r, o t, al is given by Larn.b referencee 11) in tecre of Ith ellitic cylindrical coo.1irates pi., and w, At the anrface of the cblate spheroid, = :o and r iz give, by b 1 where a and b are the set.ir.a ir n.d renir i.'nor Exe , respectively, of the corres:,ondin( ellip.Fe. F'roan the COFIl EITT/ .L CO')I.FID"'TIAL NACA ACE No. LIO10 potential, the vlccitv distributions at the reative to th.e bod; uay be derived. P'urface Around the rim in the TLplane (line 1, fig. E) (oV\ \/rilm = L sin (w (18) (19) to + 2 to(o + 1)cot1 o ind w is t'P rrncrle v.'th the plane containing thr direc tion .of flow and '.he nDoar alis as shnwn in figure and ir related to t'e dist:.ce alonr: the Yaris i!easured from the center b:' y/a = cos ) The velocit'r over the tnp in the XY)plnne (line 2, fig. 5) is (V S)Lo f + + (20) where 1 II V \a I The velocitT vcrosF the Mieridian X)plane (line .) is  T. \' v r/2 lyinrr in the (21) which, for a gFven t.':ness rrati b/a, is constant; CO TTI DE"TT 'L where CO1FIDE'rTIAL NACA ACR No. LIE10 that is, the velocity at the surface across the meridian perpendicular to the motion of an oblate spheroid moving normal to its polar axis is constant. Although velocity distributions along other lies on the surface may be obtained, those given by equations (18), (20), and (21) are of greatest interest and are most simply derived. The prolate spheroid. A related body, for which the velocity distribution is more easily obtained than for the oblate spheroid, is the prola.te spheroid moving parallel to its polar axis. The velocity distribution at the surface along any meridian as given by Zahm (reference 8) may oe expressed as V (1 + ka) (22) o x2 b x2 a Y + ( a (a where 1+ e loge e 2e a 1 + e 2e loge  1 e 1 e2 where the eccentricity e = (T and a and b are the semimajor and semiminor axes of the corresponding ellipse. The equivalent prolate spheroid can be employed to approximate the forward portion of a body of revolution in exactly the same way in which the ellipse was used to approximate the forward portion of a symmetrical airfoil. (See fig. 1.) The velocity distribution over the forward portion of the body of revolution may then be considered the same as that over the corresponding portion of Lhe equivalent prolate spheroid. COiIFIDENTIAL CONFIDENTIAL NACA ACR No. L4E1O Bory of revolution represented by axial source ditrirton.. TLi: elo "city .distr.ibution 8aout a body of revol'tlon w'th flow oirallel to the Paxs can be obtained by the iiMethod of ":onk'rm. an (reference 1), provides the body can be r eprzsented by a distribution of sources and sinks :.1cYrr Lte sxis. This method is useful for a very r',:ul:]r body for which the shaDe of the reridiar. profile an ce ',iven by only a few ordinates. If the Treridian prfile is irregular, the Tethod ir tedious ar.d perhaps Imrnossible. It Ls described in detail in reference 12. ody of revoilit in recrp'sented by doublet distri oution aton, 7yi ; ..r a to flo w. The circule.r .cylinder projeceLr, from a lanT surface AA (fig. 6) is considered a halflbody of "ic h ihe other hilf Is rhown by dashed lines. At the plane of sy etry AA, the velocity :r,..st lie rarl:l to thr plunr an tan',ential to the surfac' cf thrn cyli 'nder. At other plinres, crosl vcloc!ties o'cur fr.d reduce the r:,' 's; the :rTaximun veloc'iy changes consiuerntly occur st the plane AA, ;eit fsLL'ly o.'er t share. irners at the ends for which the velocity distribut.cens cannot be comp.ted. By a r:t.lod describhc o von I'.a'r.."i (reference 12), the part of the C.c.la .3 occu.yd o' the cylAl.er .s co.vered v ith. d. 'icl t of' . '..t .cr rnit l=inoth equal to tr'at obta'r.s .: thn yltiider 're infinite in length. The erncir of the c. 5iJ..:r 2orrespo)ns ir.. to rt.s Tjathe mtical ,,v'ce 9sr ru.deid r?ether then lsne bs shovn; th. irifluenc of t're rou.ndel cndrs .n the velocity dis trl',.tior. *it the ,'ar? Af rorust z Esall, hDwever, and the cndq of actuall g._n turrets ar: !=rn likly to 'be rox.;nded than p!en =. T'.e .russur. distributions in pl ..nes parallel tL the u. ane AA g. neraIly ane sim illar, but thr r~. k. are lov.sr ss th'. eind of t!"e cvl.irder Is a;.,.roa ,i ex,?cpt thvt, in thc. r. .ion of snall radius o:[ e.',rvatur? nea. a blunt :nd, high poeks mry ozcurr. The velocity at the ~u.rf'ce cf the cylinder in the plEne AA is (1 + cos 9) sin $ (25) where is t }e .,nlr aile measured from the plane containrng the flov: dircctin rnd Lte polar axis, 0 is C '.)TF I DE 'WTI AL, CO ITTFIDENTIAL IlACA ACF Nt'. LLE lO the an, ] e shown in figure 6 for v'hich o 9 =  / r + 72 r is the radius of the cylinder, and Z Is the length of its orjjection fro.r the surface. An exzr',:le 1fr which r is not constant is treated l1:ter. TIn: method is described in reference 12. ..ody of revolut'on by r'eiod ocf 31A. A. n th d hes rc.eentyv be de7 lootid .y "api "ef rerce 13) by which the no t.ent 'l fLou shout : b iy f revolJ.t ' miovin; in the d'ri section of "ts nlar ) o. I. mI,. be cs3 u lated to any iesIred. de ree of Ar prox :,at ,y this method, tne flo7 "s 3otsined vwith crt'iogonal j urv linear coordirnates for "'f'h su.rfac of h"c ny><. tsf is s a constant. 'L e cr ,.'or tei nate s. tc1, v'si r: is di ifer'2r.t for each bod', is ojta'aed n i:amns of ths confo .al. transformation z = Z + C +  + + ... (2L.) which tran,sforms the ?irles n = Constant n.d the n i i radisi lin=s s = C.nsstant in the la:"e 1 = P into C.he corres jodin I orthogocrial coordinated lines in the z!ane, v.e:e q = 0 is th ;.oi1crin : i,. of the bocy of rc vo 'tioln. Tnh. pot_nt a l is n . :v. a s2 ri of t.rn.s in'ol ng th'. L .nrd.t fun cions F and and the constants P .'.n .*.en .g i n the ser les ii. e u1tion t' ). The d r, ovation .f the nc :.e'Lzar;, f 'icti jr.s h es be extended in ref3rfnce 15 only far noi 1t. 10 t ccowit of the ter.r. a," Z in equ't 'on ._ ). If ndd,. t nl terms are necessa.3, to des .rtbe the ie.ri.rda.i profile to a suffiiie.:t degree f Prox] mat ._!i, the Lor resoLc'i functions :uct 'e ,.erived. The ',,eth:xd of J.i S vatirn is described in drateil in rfference 13. F'".er tri:ms of e',uvt lt.i (2.'.) arc required as the profile i, r.ore rerinrir and more nearly q '..,',.ates t'r. llL "e. Pcr irreg'.u r CO" FI DT.'TAIT CONFIDE 'TI.J, NACA ACR No. L4E10 bodies, additional terms are required and the labor necessary to calculate the flow is greatly increased. The practical utility of the method is therefore much greater for regular bodies such as airship shapes, fuselages, or nacelles than for irregular shapes. For such regular bodies, the labor required is not excessive. Approximate thin body. A thinbody method appli cable to bodies of revolution and corresponding to the slope method in two dimensions has been suggested by Munk (reference iL, p. 269). An attempt to use this method indicated that, with usual fineness ratios (less than 10), the accuracy was insufficient for estimating induced velocities over protuberances. proximatee body of revolution for use with method of Kaplan. If the transformation (21.) is known (it can always be obtained by the method given in reference 6) and if the given meridian profile can be sufficiently well approximated by the first three or four terms of this transformation, the flow about a body of revolution moving in the direction of the polar axis rmay be cal culated by Vaolan's method with no more labor than is required by the thinurofile method. The potential flow thus calculated is the potential flow about the body that corresponds to the terms retained in equation (24). If the given body of revolution does not depart too greatly from an clliose, the required transformation may be approximated by a method of superposition. The series of equation (24) can be written in the form z = x + ly a2 EIa (cfa Cp93a = Z + a + 2  ... (25) Z 1 Z z2 Z5 where r7= vei = + iT P = (1 + E)a CO NFID NTIAL CONFIDENTIAL NACA ACR No. rhrlO CONFIDENTIAL 19 and a is a constant depending on the size of the body. On the profile (r] = 0), equation (25) becomes x + iy = (1 + E)a(cost i sin ) +  (cos + i sin E) o 0 1 +  + c la(cos ( + i sI.n ) E2 acos 2, + 1 sin 22) cza'cos Uc + i sin (5) (26) The first two terms of equation (26) give the elliose 1 + E +  cos s a + " L (27) +  s in a I + I and the remaining terms give Ax I '= c: c! Cs 3' e2 cos 2 ez 0os 5 ... a L E2 co s f (28) = El sn ! E sn 2r E sin 53 .. The coefficients C'q E, and C, maj be so determined as to yield a slight modification of the ellipse approximating a jiven meridian Drofile. ror a small modification of the ordinates, the absclssa x/a is only slightly changed and, as an approximation, the required modification Ay/a may therefore be determined at the values of x/a for the ellipse. The ellipse to be used as a basis for the approximation should be so CO NF I DENTT AL 20 CONFIDENTIAL MACA ACR No. LE10O chosen that the required zrod!fication is as small as possibl. The vlve of corraspondtng to a given thickness ratio 3//, when b is the minor axis and A the mnjor axis, is obtained from equation (27). Thus, AB max A f 1 1 + c  1 + c 1 + +  1 + E and solution for rc gves + t < = 1 7!29) V1 t An eearle will clarif:y the method. In figure' 7(a) is Ehorn i meridian profile to be ao')roxim.ated. The ellipse w "th e = 0.?, also sho,wn in figure 7, S' determined to be a satisfactory basic r.rof~le for the a:oro>.i'ation. The required modifi cation of the ellI os i' s *h\shown in figure 7(e). For convenience in tiIs modificati.n, the values of 0.1 sin , 0.1 sin 2", and '.1 gin 5. are plottrcd against x/a as cc.r,uted frr. equation (27). Tt is seen frorm fIg ores 7(D) to 7(d) with eqluation (23' that cE changes the thikc'ess of the .rDf!le while the symmetry is re ta" ned, c2 ruciu.,.' an asy.r.ctry forward and rearward, anr c z increases the ordinate at Lhe ends while the center is deoress.,d. Tn:.sn.uch as the main adjustment required Is the !ntroductlon of asymmetry (fig. 7(e)), cE2 irust be given s'rmie value. It is seen that a value of 2 = 0.1 accounts for a large part of the modifica tion required. Further adjustment requires the eleva tion of both enCd: wnilc the center remains unaffected. CONFIDE NTI AL NACA ACE No. LLElO CONFIDEiNTIAL 21 If onehalf the elevation is accomplished with c and onehalf with e the desired modification is achieved. Because the required elevation Ay/a is 0.05, the values of these coefficients are c1 = 0.025 E = D.325 I The resulting coordinates from equations (27) and (28), shown as the first approximation in figure 7(a), are there fore S= (1.2 +  0.02 cos 0.1 cos 2E 0.025 cos 3 a 1.2  = (.2 + 0.325 sin 0.1 sin 2( 0.025 sin 7. a 1.2  The failure of the first apnroximation near the nose of the ,iven profile is due largely to the reduction in x/a produced by c2. It is further evident that the forward nart of the profile is more nearly aporoxi mated if the value of E2 is reduced from 3.10 to 0.07 and if the effect of 2 in reduc.irng the value of x/a at the nose is neutralized by giving c1 the value O.07a. The resulting, profile, which is a satisfactory approxi mation to the giver, orofile, is shion as the second approximation in figure 7(a). A still better approxi mation is obtained if the vadie of ci is increased to 0.lOa. The whole forward part of the given profile is then very closely anproxiniated, and substitution of the. values c = 0.20 E2 = 0.07 E = ez = 0.025 cI = O.lOa CONFIDESNTI AL NACA ACR No. LlE10 in equation (25) r.'.ves the required traneforination 0.r'fa2 0.130,a O.OL)2a_ z = + 3.1a +   .OL Z Z2 Z5 from which the flov may be calculated without great difficulty b): the eth.) of reference 13. Alth:urh tre ,or:A.wrata method yields the potential flow su.ut a sh,.' s..st J"flferent frorr the given pro file, it is t:.3',eral quite rstisf!.ctory for use in estimatir: lor.. a t ap. r orm.ate shaoe is likely to show sl.irht bi'u ns 'here none oC nr. the govern orofile, but tn. es'iin' r "resure d'strlbution is )orservative in tb'qt it an:.ws i:;'rs;r nr .: ure rationsios then would be ol.t ired for a ,i.ore re.i.i.Lr oofile. On account of .mran'facturrin irre gL..itjie,, the's conservstismr ma, be desira'jL. nv: thr r'r o'. E body, m.orevr, the actual fior alwayss ::rts ar.e .3 less from t.e ooten tial f?.ov arid '11tl .i.:*s ir, .3'uracy7 n.:. therefore be expected frro an; .zisl lil.re of the atprr:.lnmacion in that region. T.z? ret':c .' e'..] oye. sho.Id not be ascu.edi tre ?..me I.s a 'it l hsrnonic analysis. COrres.3cr'itn., b'ics in two and t, ;reed r;e.onnl fl ovs. s .' T Th :I T 'Ti1 _on bo t v.  dimnesinal PLh.3 is .cn:rn, h r3';h estir.etio. of the veloctr distri 0o1in nbcut ty.e bocy of revolution of which it is the m rid 1an or:ifile m1'y be obta tried from the rsn of velo3 ties in thi edlmensl..ral flow tc those in ftlwr lr.?:n.ioia&.l fl.': ebault corres roonl.in;: tbii..s. The velo.31ty dlstr'but lns about the corresnor.ning bodies  elliptlcal o1'rin.e.rs and orolate o.herjic:s with motion psralle' to the :r.ajor i;.Fs r.ve been cu c'alated L. eqv.torf l r ) .nr (2 respe tivel;, a:d hae been plc'tte.' for c.n.:,3 Ison Ir. fiure L ) SIrm. arli, in figure C[ b), the It ,', t',, rtric ti'i.ons obtqLred for aprovo2r(itely ct'c rlarnare :odces of revlution by the C. thod of a '.en r.:.e o:. ' .i t 'the ve o1 ty dic tributions ov',.t ne iresour.'inr t '.irienea icnal sha Pe Tn i Urr :" is th. .st::.ce fror: che nose of the brd :r.d 1 i4: 4t length. D. vision f u':..n ., by eu t.'tcn (o) ivCes for the ell:'':s? a,d arol t., soh rnid CC !T DE:TT AL CO NTPIL ENTIAL NACA ACR No. LLF10 VSD 1 + ka Vb AO V2D 1 + a where 3D indicates threedimensional flow and 2D two dimensional flow about corresponding bodies. Tnasmuch as kg is a function of the thickness ratio b/a of the corresponding ellipse, equation (30) shows trat the velocity distribution about a prolte spheroid is a ccnltsa,t times the velocity distribution about the ellipse which is its meridian profile. The constant V2D given by equation (50) is plotted in figure ) as a V 2D function of the thickness ratio d/Z. This relation suggests the pnssioility of usir.n the corresponding two dinensi)nal 3hape to des'ipn a body of revolution sir..ilar to the prelate suheroid with a gI ';en velocity dis tri b.ition. V7 The velocity ratio  is not enerally constant '2D along the length, however, as ray be seen from fig ure 9(b). Ini particular, the velocity over the tail of a threedimensional body dpoerts less from streak velocity than the veloity ov.:r the tail of the corre sponding airfoil: the ratio therefore increases '2D and exceeds unity as the trailing edge is so:jroached. Tt is nevertheless reasonable to saopose that figure c could be used to estimate the velocities on bodies of revolutiLon over tne parts of the meridian profile that are roughly elliot'cal in sh.:e. The following methods are suggested as alternative.: (1) Fit an equivalent elliose to the profile as in figure 1. 'With the thickness rsti fi this ellipse, find the corresponding velocity ratio from fig 2D ure 9. COIjFIDrTTTIAL CONFIDENTIAL NACA AC No. L)4E10 (2) Assume that the corresoonding ellipse is the one which has the sa rre peak velocity as occurs on the profile. Prom equation (6), the corre0oondiz.E th'.ck nesc rFtic d/,,Z or b/a then is b V.ax t =b 1 (31) a V0 VD which witP figure gives the velocity ratio 7. "2D As a tes& of the method, the velocity ratios VSD , wh:ch "ere constant alon, tnc length for the 2D elliptical profile: tjt gc'.n:erally wvriable, were com put.ed for several :,airs of correspondin:.p, haoes. The variation along the length I is given in figure 10, V5 in which the values of for the equivalent ellipses 2D obtained by 'r,ethod (l) are s'ihon for conmri son. 'ethod '2) would l.ve quite similar vali.e.. or bodies of revolution vwit., rerii "an profiless rouahl7 similar to .D tnose for which tih values of re Iaown, these V2D values mir b.e used to obt.tin velocity estimates rnmre nearly cox rect than can be obtained by ase of the elliptical profiles alone. Relations similar to equa tion (30) can also be obtained for the o'.,late soheroid, tut th!.r an)nlicatinr is less benara! than for the elongated bodis. The elliiscid vith three nr.eqa.l a::es. A .;ro tuberance shane nor' rossessin:. axia] sy;a'netry a flatten.d blister, frr instance m'y be anproxImated by an ellipsold wvth three unequal axes. The necessary elliition!F c ordinates and the potaItial. are g ven .:nd exalIinod in reference 1j. on psges 2513'2. The mathe ,m.atical :o.xrlnxity is such that, in mianj cases, a less accurate a.pzroxicmat'cn by meins of the simpler body of revolution is "r.:ferred. CroTPFIDENTIAL CONFPIDEETIAL ITACA ACR No. L.FIO Estimation by Comparison Comparison of the shace for which pressures are required with a somewhat similar shaoe for which the pressure distribution has been experimentally deter mined should prove very satisfactory if sufficiently extensive sstematic experimentation had been com pleted for the most part, hnv.ev.r", only sattered data are available. The only existing syster:atic investigation of pres sure distributions over protuberances at high speeds is that for windshields and cockpit canopies given in ref erence 1. If a given shape arioxi 'sat.s ne of the shapes tested, the corresponding pressure distribution may be assumed. If a shape lies between t'wo of those? tested, its pressue distribution may also be assuned to lie between the to measured, rYovided no critical change in flow occurs for examle, separation or com pressibility burble,. Tf the anony has no tail of its ownbut is fired directly into the fuselage (as in the case of the PLO airplane), the pressure distribution over the forward part may be assumed independent of that over the tail and may be faired into that for the fuselage. In comparing canopies, the angle between the nose section and the hood is assumed an important variable because, for the small radii of curvature often found at the junc ture between these two sections, the theoretical ores sures, which are large negatively, are not attained; it therefore seems reason.ble to suppose that the peal negative pressure coefficients are determined largely by the angle through which the stream must turn. These assumptions have not been thoroughly and systematically tested but, when applied to the estimation of the pres sure distribution about the coceM,!it canopy of the FlOD airplane, gave results in substantial agreement with measurements subsequently obtained in the M.ACA Sfoot highspeed tunnel unpublishedd). The results of experiment may also be used to esti mate the difference in pressure distributions between nearly similar bodies when the theoretical pressure distri bution can be calculated for one of the bodies. Few data suitable for this pur;ose are available, however. COFFIDENTI AL COFIPTDE TTALT, NACA ACR No. LUE10 Experimental data used for comparison may include interference and corprossibility effects: in this case, the difference in these effects must be estimated and a suitable adjustment applied. APPLI CATIONS In this section of the present report, certain of the methods described in the preceding section are applied to the estimation of pressures over various protaberances, for some of vwhih experimental pressure distributions are available for comparison. These and other experimental data are analyzed to determine how the methods should be applied and what modifications and adjustments are re quired to bring the estimated pressures into agreement with the experimental values. Examples aRrtin turret. complete lowspeed pressure distribution data for the "artin turret cn a model of the North American B25 fuselage are given in refer ence 15. The location of this turret on the fuselage is showrr in figure 11(i). The pressure distributions are compared in figure 12 with the calculated values for the sphere and for the oblate spheroid with thick ness ratio b/a = 0.67. The theoretical estimation of the velocity dis tribution about this turret is oarticularly simple. The shape is that of a body of revolution almost ellip tical in cross section end may therefore be represented by an oblate spheroid moving normal to its oolar axis. The formulas for the velocity distribution over the top of the body in the direction of motion, across the top of the tody in a :lane peroundicular to the direction of motion, and aroundd the rim of such a body are given in the setion entitled "Metnods." The interference from the fuselage should be small and, except for oound ary layer and separation effects, tha agreement between estimated and nmeasur3d values should therefore be good. 7igur! 12 shows that the estimated negative pressure peak, n particular, is alirost exactly' the same as the value obtained fror the measured pressures. Over the top of the turr3t In a .lane oero. ndlcular to the direc tion of motion, the theory indicates a constant pressure CO NIDENTIAL CONFIDENTIAL NACA ACR No. LhElO and the measured values show alrost constant pressure. Failure to reach stagnation pressure in front of the turret is due to the boundary layer developed over the fuselage; behind the turret, where the pressure coeffi cient approaches ze.o, stagnation pressure Is not attained owing to separation. Inasmuch as the pressures were measured at low speeds, no allowance has been made for compressibility effects. A rough estimation could be obtained by multiplying all pressure coefficients F by the factor 1/1  Turret A. The two locations.of turret A on the fuselage ar shown In figure 11(o). Its shape and di.r.ens'ons are given in figure 15. Pressure measure ments on this turret are given in reference t16 and are plotted for comparison v.ith estimated values in fig ure i1.. Turret A is a spherical segment in form and is large comp.ar2d with +he fuselage, having only slightly smaller radius than tht fusege radius. About a third of the radius is projected above the fuselage. The turret is located back on the fuselage where the interference cannot b.' large. TI cons deration nf this geometrical configuration, "t is esti'rated that the pressure peal's cannot be greater in absolute valu: than would occur on thc sphere and that, because '.f tht interference of the fuselage and the development of the boundary layer along its surface, tha peaks nre probably lower. The change with M.ach number u. to = 0.70 is assured insufficient to cause the prcssvre coefficients to exceed in absilute val ie thos.e calculated for th, sphere by the potential theory. The tLeoretical pres sure distribution for the sphere, as obtained from equation (16) with equation (2), is shown as the solid line in figure iL. A velocity distribution of approximately the correct shape but w.th peaks higher than actually occur is obtained by applying the twodimensional theory to the circular arcs over the top and side of the turret. The distri bution of induced velocities, from which the pressure distribution is calculated by equations (2) and (12), can be obtained by interpolation for the proper thick ness in figure 2. In this nase, the velocity incre ments corresponding to the more accurate method of nntrqnVrprT AT CONFIDENTIAL ITACA ACn N:%. LE10O conformrl transformation from a circle are used. The pressure distributic.is obtained by this method for the L5percenttlick circular arc on the top and for the approximately 27nercentthick circular arc on the side are shovrT in figure 1L. The pressure on the rear of the body departs from the estimated values but, without the experimental data shown, the limits could hardly be fixed more closely than 0.h5 for the circular cylinder (from unpublished data obtained in the 'ACA 3foot highspeed tunnel) and 0..6 for the sohere (reference 17); however, a value close to zero would seem likely. Turret B. Turret B is described in reference 16. Its locaton cn the fuselage is shown in figure 11(c) and the shape and dlm3nsions are oiven in figure 15. A pressure distribution over the central profile (line 1, fig. 15), with peaks larger than are expected in prac tice, may be comnnuted by the t'rodimensional slooe method. The integral indicated in equation (11) is made up of three narts, designated integrals I, II, and ITI, that corresoond tU the three divisions of the profile shown in figure 16. The integral I extending frcm x = 3 to x = 2.03 inches is obtained from equa tion (1) with the upper limit equal to 0 and the lower limit equal to G. Tntegration and substitution of limits give C' IT DE TTI AL CON"TDENTTAL NACA AC' fro. TE1, CONFIDErITIAL A 0 0 I D t t cr  c c + r r' C. 0 C CD * i I1? *r I!  r c? Cr ) 1 C3 cEl C) .. 01 ,I,2 ^ 29 ,4* 0) I ':' r 0 r AT 4 3. CL C5 r a) 1 C , I r ; 441 J 0> 4.1 C 0o I D NTI A . 30 CCNFIDENTIAL ITACA ACR No. L4E1O C o A C SC LIE 4 ",j , I C a. II1 + 1 N rj 11 '4 'J . Se 0 0 _  ' r ., i) C' 0  CO 4  X' ,  c 1 rco ,, . C 0   >l I II C4 ,.r 0 CO 0 C) o r1 D '0 C . 04 CC 4C3 e on ct  .4' ui (p O n o0 CL * ' OO c 3 OC.^3.r COIID 'T'T AT NACA ACR FNo. T.4EIo Cr'NFIDENTTAL 51 The integral ITT from x = L.79 inches to x = 3.16 inches as obt:rined from equati.rlr I11) viith uoper and lower limits of 3.16 and 4.79, respecti""aly, and 'ith dy/dx = O0.S3Lq Is 3.16 Then, for : < 6.1. inches, 4 TI + ITT T T "0 and, for x > 6.L6 inches, AV I = T(a) + IT + ITT "0 Calculated values hae been converted to pressure coef ficients, and th.e resulting di tri buti.n has been plotted as the solid 1ine irn f.ure 10. The cocffi ciei'E t.:n octair nel nrre c,onsidered linitinf values and i a. ue.' h.::f f '.! etlr h.,h in ats i te vlue to elliw 1 coi )rssi.o'i" t: effects u) to a "ach number of 2.73 ind remain concerv;tive. From the calculated tv.'odirlensinml veloci t:. dis tribution, the velo,.t.ies abo it the corresnoond:in. body of revol't.on wre e imat ed b'" the r.tij of velocities in threedimensionri fl t.i to those in twv...irr.ensional flow as ,ven for ellilses and nrolate sbiherols.c in fi, ._ure 9. Th 2or.e.32andJ nuTIg ,jresszui coefficients ar? ThoAn as the dashed urve in fi.'ure 16. The shape of this turret is batveen the twodii.ens ioni! ha:,e and the body of revolution and, c'nseq.iitly, h.e measured pressures lie betweEn the estimated values for the pro file and the values estimated for the body of revolution. Cockoit canopy nd gun turret ,n Erewster SB2A1 air plane. Thie s apes an. lo3l a lons of the cockF it canony and gun turrets on the fuselage of the E.rewster SB2A1 airplane are shown in figure 17. Two alternative gun turrets have been suggested for this air.ilane. The top CTFIDZ'NTIA' KACA ACR No. L4EIC. shane of the "axson turret approxjr ates an oblate spheroid moving normal to the polar axis. The other turret is spherical in shane. The tneoret4cal velocity distributions are computed first for the turret shapes alone without interference. The meridian profile of the 'axson turret is shown ,ith pertinert dimensions in figure 1S. Tnas.r.uch' as the shape Is symmetrical, the pressure distribution is symmretrical from front to back and only onehalf the half profile neeO be considered. The axes of figure I1 are arranged to correspond with those of fi'gura r. The turret profile is seen to be only slightly different front the ellipse with thickness ratio b/a = 0.67. The difference is shown as the shortdash line plotted along the yax!s. This dif ference can te approx!msted by a circular arc; and the turret profile shapo thus can be more nearly aporoximated by adding to the ellipse in the region indicated the half thickness of the double circular arc of thickness ratio t = 0. 1L. The corresponding velocity ratio VVIo is obtained by directly superposing the increments aV/Vo, as found for the circular arc b. interpolation in fig ure 2, on the values ( = over the elliptical oro file r.f the oblate snheroid. ""ith b/a = 0.67, equa tion (17) gives [.3 = D.91 end the velocity ratio over the elliotical section in the xyplane is given by equation (20) for values of *,. The cormoutation form is indicated in the i V/V for 9 ,/a Ioblate soheroid following table: AV/V, for 1loercent rcircular arc 0 t1.00, 0 0 .23 .98 .LO 0 .O .71 1.1 .1' t. 1 6o 1.24 .1. ^o0 .1,. 1. 2 .ot oo I.51 1.5o o 1.00 0 1.0 3 CC .J T77 NTT AI 1.00 .Gk .56 .57 .74 .95 .02 .93 COi'FTDI 'ITIAL NACA ACR No. ..10 COVNFIDFNTTL 55 The velocity increments AV/Vo obtained by the twvo dimensional method are likely to be somewhat large, and some small adjustment in the corresoonein pressure coef ficients must therefore be made. The pressure coefft cients with these and other adjustments to be discussed later are plotted along the turret line 1, fig. 19). Around the circular rim of the turret, velocities somewhat higher than those aoaut the rin. of the oblate spheroid may be expected beca.Ase cf the departure of the turret from the true spheroiral shi.ne and because of interference from the cylindrical sides of the turret extending down onto the fuselage. For use in the esti mation, the velocity :.rrundr the A1.rm of the oblate spheroid is computed. 'i,,ith ) 0. 1, the velocity distribution ('1/ 0) is obtained from equation (1.) as a function of (L and is sho'."n in the following table: y/a = cosw V/r.  (deg) i \o 0 1.0' 0 1.00 10 .98 .211 20 .9. .L7 .73 50 .37 .52 ,) .77 .. : .21 5C .64 1.06 .12 6Q .50 1.29 .ILL o .17 .7 .3 9c o 1.5 .7 Again because of symmetry, this pressure distribution holds for negative values of y/a:. that is, for w between 99 and l!08. For the soherical turret, shown .; profile i, figure 23, the theoretical velocity distribution over the merid sn lying in the olane with the forward velocity was calculated from equation (16), and the pressure coeffi cients were obtained 'y equation '2'. The values of y/a are obtained from y/a = cos 0, vrhere again y is taken in the direction of motion. C3FI 'J TA. 'T A' NACA ACP. No. L4ElO For the cockpit canopy, the pressures over the nose and the general pressure distribution forward of sta tion 121 'figs. 17, 1, and 29) were estimated from the data for the L.5 windshield given in figure 22 of ref erence 1. The an'le between the nose piece and the hood v'as 4c' for the SB2A1 windshield as compared with 4'.S for the O35c win.dshield; otherwise, the two wind shields appeared similar. The data for a Vach rumber of about 0.70 were used, but the negative pressure peak was elevated slightly to allow for conservatism in regard to the somewhat sharper nnse angle of the SB2A1 wind shield. The use o2 this pressure distribution involves the assum: tion that the difference between wing and fuse lase interference in th two cases airnlane and model tested) ir negligible. This assumption is reasonable because the wing and. fussalge cannt differ greatly in the two cases and because the interference velocities are relatively small. The burin in the oressuredistribution curve about station L2 is intended to represent the slight discon tinult;, at the rear of the sliding natch cover. The dimensional data available do not errit the exact determination of the shaipe of the offset and, even if the share werae known, the calculated pressure distribution would be of questi'ratle accuracy. The magnitude of the bwiu above thu general pressure distribution was taken instead from the recu.lts of tests of a cockoit canopy similar to tiat of the S32A1 airplane. The theoretical pressure distributions for the turret shapes are modified by interference, for which certain assumotions must be made. The turret is too close to the canooy and too large in relation to it for a read%. estimate to he made of the effect of the canopy on the turret oresrures: because the canopy is situated entirely ahead of the turret, however, the assumption can safely be mrade that the nnly effect of the canopy is to lo',er the velocities ovr the turret. The shope of the f.,sla., in thc r.s.rion of the turret is such that the incLucad veloeities must be small a:ud in addition it may b. Ess:m.rvd th!it, because tre 'in.f is ahead of and not very close to the turret, tno induced velocities due to the wing tend to be canceled by the: induced velocities from the canopy. Tnat thee assumptions are reasonable is indicated by figure .2 of reference 1, in which the pres sure coefficler.ts bclhind the windshield rith the tail an in! the presence of 'K.Lng a:.d fuselage approach zero. If the ccnopy of the S32A1 airplane were faired out with a sirilir tail in the rea.r, minreover, the turret CCI:JFTO NTT AT. CONFIDENTIAL NACA ACR No. LLElO would appear very similar to the halfsphere or half spheroid on the tail. The flow over the part of the gun turret not thereby covered should be affected only slightly by extending the canopy straight back to the turret. The pressures over the top (line 1, figs. 19 and 20) have accordingly been taken as those over the modified spheroid and sphere, respectively, for which the theoretical distributions are given in the first part of this section. Over the section indicated by line 3 in fig ures 17, 19, and 20, either turret contour is charac terized by a circulararc profile of about 50percent thickness ratio superposed on the surface of the fuse lage. Figure 2 gives the velocity distribution, which may be used with equation (2) to calculate the pres sure distribution. Over the rim (line 2, figs. 17, 19, and 20), the velocities must lie somewhere between those over the side (line 5) and those over the top (line 1). They are therefore taken to lie between the theoretical velocities over the rim of the oblate srheroid and those estimated for line 7, and the peak is assumed to be about the same as the theoretical peak for the sphere. The resulting curve Is quite similar to that for the sphere and is taken to be the same for both turrets. The pressures at line L. must be determined largely by guess, because the contour itself is only slightly disturbed by the presence of the gun turret. The dis turbance at line 5 must influence the velocities, however, and it therefore seemed reasonable to assume induced velocities onehalf those at line 5. The corresponding pressure coefficients have been so calculated. Behind the turret, because of separation, complete pressure recovery as indicated by the theoretical dis tributions is not attained. The pressure recovery shown in figures 19 and 20 Is based on the tests of reference 15. The pressures on the rear of the circu lar cylinder and on the rear of the sphere are shown for comparison in figures ]Q and 20C and art considered limiting values for low and moderate Mach numbers. ro adjustment of the pressure peaks has been made for the effect of compressibility because, for such blunt bodies, at least up to a Mach number of 0.70, the CONFIDENTIAL CONFIDENTIAL F".CA A.CR No. LLE10 conservatism of the nethods used is assumed sufficient to cover the changes. Compressibility may, however, cause the separation noint to move forward and uhus lower the regat've peas arind decrease the pressure oshind the turrets. The negative pressure p3al:s therefore ra; be brandened backward, and some account of this effect has been tak:n in broadening the peaks in figures 1' and 20. Tn no cae, however, at least up to a '"ash nu:nber of 0.70, can the pressuree on the rear of the turret decrease below the negative pressure oeak that v:ould be obtained in potential flow at the sane r'ach number. The negative pressure :.eal' in figures l and 20 is th'.s indicated as the limit of the oressure or. the rear of the turrets. The development of the burdery layer over the canory ahead of the turr';t and separation in the rear tend to prevent either positive or negative pea&s in the pressure c1istributiin from being as great as predicted; in this respect, the estiration is therefore connservative. Average vRlaes of pressures obtained over the gun turret of thI 3rewster X3b2Al tirnlane in flight at soaedfs below 22; miles ,or hour unpublishedd) are ore sented for comparison in figure 1. F)r obtainincr loads, the estimation cmPriares satisfactorily with the measured values though, for the to) of the turret, it aPoears to be unconservative. Frni.. the data available, however, the turret on the XS32A1 airplane appears to pr,.ject h.hher above the canopy than was assumed in the estimations and larger pressure peaks miriht therefore be expected. The irregularities in the measured pres sure distribution may be caused by the ribs and other irregularities on the surface. Severe separation is indicated behind this turret, where the pressure recovery is little greater than that behind the circular cylinder. Lower qun turret on Douglas XS32D1 airilane, As a furtTer examTe that involves the method f ditribu tion of doublets along the axis of a body of revolution movin, normal to Its axis, tne pressure distribution ove:r the lower gun turret of the Douglas XS32E1 air 'lane is estimated. The form and location of this gun turret are shown in figure 21. The pressure distribu tion over the central orofile (line 1, figs. 21 and 22) is obtained and the distributions over other lines from front to back cre assumed.to ba. quite similar. or a shave that does not differ too greatly from a body of revolution, this ass': motion is reasonable and has in other cases been found to agree wll with experiment. (S., reference 1, for instance.) C"N IDENTT AT C 'NFIDFNTTAL N.",CA ACR To. LLE1 C The turret was divided for comroutational ourooses into front and rear Jarts. The pressures were assumed to be the sqme as if the turret were a halftody on a plane containing th3 surface of the fuselage imme..diately forward of and to the rear of the turret, with a stream velocity parsels1 to the olenc. As sho3mP in figure 25, the forward part of the turret profMl. can be opproxi mated bS an arc of the parabola o 0.7 x1  I cI Vith substitution of the slooe / = l.7Lh 1.L,..C d( x/c) c in equation (11), th' velocity ,istribution A V 1 "o 1.L38 3.7L. 1.,l8 10le '  shown in figure 25 s easily obtained. The rear of the turret was apor..xi.mated by a quarterbody of revolution v'ith polar axis normal to the stream in the horizontal direction and with symmetry to the rirht and to the left. Velocity distribution was cor.uted by the method of distri'.uting doublets along the polar axis normal to the flow. (See ref erence 12.1 The cross section normal to the stream, the central profile that is the ap.oroxiration to the rear part of line 1 along the stream direction, and the re quired dirensions are shown in figure 2L. The doublets of constant strength are indicated oy the short, heavy lines along the axis; and, from equation (5) of refer ence 12, the potential for one doublet is = i (cos 9" cos 9') cos ' hTrr CO'PF7TD1TTI 4L COr' FT DNTTrTiL NACA ACF. N.. LhElO By symmetry, the velocity on the surface at 1 = 0 must lie along the central profile (fig. 24(b)) in the plane of the stream velocity. Because the largest and smallest velocities on the body occur along this profile,this distri bution is of greatest interest. The velocity due to one doublet, the i doublet, is AV = L _o = .~ (cos ei" cos 98,) sin S ro ~6 hrorr Reference 12 shows that as an approximation the doublet intensity VI can be written 91 = 2Tr i2V The velocity increments AVi are parallel and, with the substitution for .i, can be added to give AV_ 1 sin Vo 2 \r) (cos ei' cos ei ) sin The component of the stream velocity V, in the direction of the profile is Vo sin $ and the total velocity is therefore = 1 + 43) (cos 01' cos Qi" sin # From the dimensions given in figure 24, the com putation of AV/Vo is indicated as follows: CONFTDFTTAT, CONFTDFNTIAL NACA ACR No, L 0FlO The velocity is therefore ( + sin = 1.9 sin 9 which seems reasonable in comn'rison v.ith the value 1.5 sin $ for the sohere. The nosttion along the stream direction x at which the velocity occurs is obtained with sin 9. ro From the velocity distributions thus calculated for the front and rear portionss of the turret, the corres9ondinz pressure distributions were obtained by equation (2) and were then joined at the center to give the solid line in figure 22. S'me adjustment of pres sures was necessary to effect this junction. For the turret in the gunsasear. osc'iDn, the pressure distribution over the cylindrical surface (line 2, fig. 21) was estimated by assurming a circular cylinder projecting, from a wall. The dimensions are such that cos G = ).).52. Substitat:on of this value in equation (25) gives the velocity on the surface of the cylindrical gun t .rret near the fuselge. The pressures are thereby determined and are shown as the dashed line in figure 22. CON YIDENTIAL COrIFIDENTTAL NACA ACP No. L4ElO The remarks concerning the effects of interference, boundary layer, and separation on the SB2A1 turret also apoly to the XSB2D1 turret. For the reasons discussed in reference to the SB2A1 airplane, no compressibility correction has been applied. The turret does not project from the fuselage so far as was ess'uned in the calcula tions. Focr this reason, the estimated pressures should be more conservative than woald otherwise have been the case. !n exoerSmentsl data are available for comparison. Analysis and Discussion The agreement oetv.men estimrnted and measured pres sures generally is better than had been expected and it &?ooe?rs that, if alloance is made for the effects of interference and separation, calculations based on the potertialflow theory Jve a satlsfactor indication of tho rmiximwur loads. The qgreenert is good for the martinn and !,'axson turrets, v'iisn approach forms for which the potential flow can be accurately calculated. In other cases, the ac".,al oressures way denart widely from the theoretical values. Tna reasons for this divergence from the calculated values which are connected with departure of the shares from those assumed, with com oressibility effects, rvth interference, and ,ith sepa ration and other boundarylayer effects are now dis cussed. The experimental data available are analyzed and comrnared w,.th theoretical values to deterimne, at least qualitatvely, the modifications that should be made to calculated pressure distributions in order to aoroxiate more closely the actual values. The appli cation of pressure distributions to the estimation of loads is briefly considered. The following additional figures are introduced: Pressure data obtained in the NTACA Sfoot high speed tunnel 'unpublished) on approximately hemispherical turrets at different locations on a fuselage are shown in figure 25. The orifices at which these pressure data were obtained were located at the tops of turrets C, D, and E anid at Ql.e side of turret C, where velocities approaching the maximum should occur. The variation of rezsure coefficient P with stream "ac91 number M! is compared with the heoretical variation given by the factor / _2". In figures 25 to 27, the curve of critical pressure Doefficient Pcr that is, the CONTIDENTI AL CONFIDE'NTI.L I,.kCA ACP No. LrE10 pressure coeffiident corres"ondinp outside the bounc.sr; Plyer to thie attinr.r.ent of the loal speed of sound  is shown to indicate the critical speecs of the turrets. The critical Mach nu;.mber '.1 Is the I'ach number at which the pressurecoefficient curve intersects the Spcurve. Figure 26 shows a comparison between the pressures at the top of two sphericalse,iment turrets A and E, both in the forward location of turret A as shownr: in figure 11ib) and projecting different portions of the radius above the fuselage. These pressures are conrmared. w'th the th?o retical pressures for the sphere including the variation with Mach number i.veln by the factor 1 S1 .2. A com r arison is given ir, fLcure 27 between ires sure coefficients at various pos'. tons on the fired turret 2. of referenc 16 and those .:n a tnciker faired turret F, both in the locsti.n of turret 3 showni in figure llc). The vr.riauton ."' Lh ..ach number is sho,',n and co opared with the theoretic'.,l aviationn. Figure 2'3, for "hich the data ar,. taken from ref erence 1, shc:r.s the pressure change ', th ;.:ach number at four different points on wirdshiilds rerresrtVnp bodies of three different types; the 511, which has blant tail; the 75', which is characterized by a sharp corner at the nose and ty a lonj, faired til; and the X1, which is well strea:nl ined. Departure frcm for.s for "'h:ch potential flow can be calculated.j The shape of a protuberance is usually such that the potent l flow cannot be exactly computed. ExperimenL is therefore needed to determine the effect of *.stevatic departure frcm forns for which the poten tial flox is calculable, such as variation in segment of a sphere from the halfbody or variation in thickness of a body. The effect of these variations is indicated in figures 26 and 27. The pressures vary qualitatively as might have been expected; that is, larger peaks are obtained for thicker bodies. The data are insufficient, however, to define any quantitative relations. CONF DEITTT AL CCNFIDj'.TIAL NACA ACR No. L4EIO Figures 25 and 26 Indicate that, unless considerable inter ference is present, the limiting pressure on a spherical segment less than a hemisphere may be taken as that on the sphere. CoinressLilIty;. The effect of comaressibility on the pressure &oefTf'7ents over protuberances cannot be accurately estiu'at3d although a qualitative estimate of the nature of the change of pressure with 'ach numoer may ce obtained. "Th theoretical variation shorn in equations (5) and QL) and derived in referenceso2 and 3, respectively, strictly applies only to potential flow. The actual variation ay be greater or lose than the theoretical v.ariat'on and ra.; even be ooposite in siLn. For protuberances, !'hich ti re usually influenced by bo'"nd.arlayer developmrnt forward of the protuberance and by sep:aration of tje flow, the theory is less uze ful than for a.rfo'ls, for which the flow generally aroroaches more ne.rl the potential. As snown in fig ures 1i, 16, and 25 to 21.3, the peak negative pressures general% increase rith "ach number more rapidly on well faired bodies located on the forward part of the wing or fuselan than on blunt bodies located near the tail. A detailed eyannation of the exnerrimental data available indicates how and why the roes'sure coefficients in dif ferent positions on protuberances char,1e with e'ach number. On the lowcambered turret A of figure l4, the peak pressures change with '"ach number anzrroxir;ately as pre dicted b:T the ,qlauertPrandtl theor'. At the rear of such a body, the oressures decrease because of an increase in severity of seoarsti.in a comprecssibility effect that has beer observed in other tests (unpublished). The compressibility effects on the faired. turret a of fig ur. 1a are, similar to those on turret A, except that for turret "' the positive pressuar coefficient at the rear, which should theoretically have increased, was maintained constant by the slight separation of the flow or thickenhing of the bcrndary layer. The effective change in shaac c f the form was apparently sufficient to cause a slight c'ecrease in the negative pressure coefficient at th.e 5inch station. Fi ure 25 shows different comressibility effects on the ~essires at tr *op and side of approximately hericoh'erical turrets that deorend on interference and the bounDrirylayer c(evalopment ahead of the turret. CONP FNT T AL CONFI DE:TI iJ. TNACA ACR Fo. LLEFI"' Turret C is subject t considerable interference front. the windshield ju3t downstrearii. This interference dec reses the "elocities and nrevenc? th.= increase 1i. neativa pressure e coEfficient v ith "ach nrurrber that would other wise occur. Turret L, on the other hand, is placed in a region in which the inteeferenc m be xoec ted to increase the veploctit s 6 am the incrcass vith :'ach number of the top negative pre.;sure c.effcient 9poroxi mates the th oreticl] inreasz up to tre critical snctd, after which it increases shar i:: fhr :a s.):rt ",. nulMnber range. Turret E, whichc h is lo.ted far bock on ti1e fuse lage and therefore subject to c.ns i.rsa:, interierc.ce from the boundary I ,er, shcws sm1 1 2.hsn:1. in th,. ares  sure coefficient wLIh p'ah r! number. The turrets of f gure 26 were located in r:,ion in which the boundary layer on the.f.selage must ha:'r been very thin. TIn ad11tion, considerable inLeferrence was possible; the possible effect of interference i' increasing the change of :.ressur'e ceffent ':,ith ach number is discussed in reference 1. The neak nPe.atL.ve pressure coefficient on the appro 'x. matel:: hersph.r c.l turret D increased ,;ith "ach nur.be: about ac 2 ordin. to theory un to the c] tical speed and ,ore r;soidly there after. The incre se on the lowercotr'bered turret A approximates the theoretical increase. The comoressib'iity effect on the pressuress of turret 3 has already been noted in figure 27. The variation of the roakt native c.resur_ .oefficients ac.oears to asree closely vith the the. retical vri nation. For the thicker turret , the .eoart ion should be more severe; this fpct is probably be rtlSs n that the ores sure coefficient at the to in.rea':s less raaidly with r'rach number than the thery iandicates. Farther back on the turret, the change in efifetive shee due to separation produces a large decreass in negative .res sure coefficient as the I'ach number is increased. Tbs effect of ?omorcssibllit: .,n pressuree coeff: ci nts at points on bo._ics of three different t.,ces (from reference 1) is shown in fijuar 23. T'or the wellstreamlined XI body, the pressures at oIrnts b and d agree with the theoretical change vith "ach number: at point a, t'.e peak increases more rapidly than the theoretical values; and, at point c, the effect of thickening boundary layer in decreasing. the pressure is seen. On the 75L body which has a COU' TDFNTT Al. 00 FTiDE TLT, NnCA '.CR No. L4E1O wellfaired tail end a sharp corner between the wind shield and the hood, the pressure at point d agrees with Lhe theoretical variation, the pressure at noint c show., the effect of thickening boundary layer, and the negative pressure coefficients at points a and b a short distance behind Lhe ooint of separation decrease before they rErt to r'se wiNh 'ach number. On the 311 body, whi'h has a blunt tail, the pressures at pointss b and 1 change about as theoretically predicted, the pres sure at Dint a sorrewhat aherd of the separation point fails for the most po"'t to decrease as fast as indicated by the theory, one the nresure at poInt c on thu tail :ecreases greatly behind the ":oint at which separation probably occurs. The effect on pressure coefficients of change in "'ach number is seen to be different for different points and for diffeent bodies. For roughly similar shares In similar locations, the ccrres.onding varia tions with Vach number may be assumed. The effect of compressibility cn the pressures over a orotuberance obv3..usly deends on the Feynolds number of the ,rouberance anc of the body on which it is placed, inasmuch as the type of flow must be a func tion of the reynolds number. Comr.ressibility effects also depend cn the relative size of the protuberance in relation to the body n which it ".s placed, because interference and boundarylayer effects are different for different relative dimensions. From the experimental data, the following principles that are useful in a qualitative estimation of the change of pressure coefficient with "'ach number may be derived: '1) Over the greater part of wellfaired bodies that are not too thicv and are relatively free from boundarylayer and velocity interference from other bodies, the theoretical change of pressure coefficient with ;"ach number may be assir.ed. The factor 1 1 expresses the change with sufficient accuracy. The negative pressure peaks may be assumed ts increase somewhat more rapidly than this factor indicates. CONFT DENTAL CONFTIrNTTIAL 1';\CA ACR To. LTL, 0O CCNFIDENTI AL (2) Separation of the flow, which re ulsrl., occurs from the rear of blunt forms such as the sDhere and the circular cylinder and to a less degree fror less blunt bodies, Is likely to becoi..e more severe with in crease in I'ach number. The res.'ltinyg change in the effective sha)e of the body ma.y roriuce an increase (as compared with the tn nreteal decrease of the :ressure coefficients near the be.;ining of the se'aratd rei.ion and a decrease m.orenregati.ve proesseire o.effic Lents near the tail. Fvu n on mo derately thin faired bodies, somthing of this effect may a:,..ear" whereas, on tod es with short tails, a larae decr.a&se in the negative ores sure coefficients just forward of the tail and a con siderable increase in the negative Dressure coeffi,ents at the rear may oscur. (3) Tnterference that increases the veloc'Lties is likely to cause a further inrease in negative pressure e coefficiernts 'i th "ach number, whereas interference that decreases the veocities " liely: to ha,e he opposite effect. (1.) Tf any considerable a.rt of the protuberance lies within the bouncdsry layer nrodI ced on the body for ward of the procuberance, the chobtn: in pressure coeffi cient ,with Vach number is likely" t, be different fror the change that would oc:ur if no boundary layer existed. The pressure peaaks may be smaller and seOaratin effects ma'.a be introduced. (5) If a critical Reynolds num.iber occurs ,'ithi_. the !,ach number rsn.e or if a considerable change in pressure coefficient with Peynolds number is otherwise to be expected, the resulting effect on the change in pressure coefficient with ?ach number musL be accounted for. The foregoing discussion hilds for "'ach n;unbers less than the critical. Above the critical "'sch number, still less is known about the pressures to be expected. outside the region of suersonic speeds, the pressure change is much the same as at subcritical ;"ach numbers. The supersonic region commonly coreads rear ward as the '"ach nume..?r is increased, and the negative pressure oeak usually increases and broadens toward the rear. As the shoc'c wave develops with its large un favorable pressure gradient, seoration is likely to occur and produce the pressure changes already discussed. COF'T DENTI AL h16 CONFIDENTIAL NACA ACRT No. LLE10 The negative pressure coefficients cannot in any case continue indefinitely to increase with 1iech number, and a tendency to decrease at the highest Mach numbers is already apparent Ir. sare of the curves in figures 25 and 26. An absolute Jliilt imposed by the condition that the local static pressure be zero is given oy (P)ma The experimental data available indi cate a limit less then given by this relation. Up to a iach numoer of C0.70, however, the changes in pressure coefficients likely to be encountered on protuberances may be estimated by the methods herein presented. Tn order to estimate with quantitative accuracy the effect of compresslbility on the pressure distribu tions over protubersices, extensive systematic experi mentation Is necessary. Interference. ror cases in which the interference cannot eV expressed by slmnly adding in the induced velocities due to the interferin, bodies, an estiratton at least qualitatively correct may still be obtained. It is reasonably certain, for instance, that a canopy in front of a .un turret can have only the effect of reducing the velocities and thereby the pressure peaks. Figure 25 illustrates the difference in Znter ference effects for turrets in different locations on the fuselage &nd for different angles of attack of the wing and fuselage. Turret C is subject to a reduction in velocity due to the hump in the fuselage immediately behind it and, n addition, the accompanying unfavorable pressure gradient ray be expected to precipitate earlier separation than would otherwise occur. As seen in fig ure 25, the negative pressure coeflfiients on the top of turret C were much valler than on turret D, which was located in a region of .increased velocity due to both wing and fuselage. Turret E is so located that the velocity interference should be small but, with most of the fuselage forward of the turret, the boundary layer interference must have been considerable. The negative pressure coefficients are only moderately large. The change in pressure coefficient with angle of attack is aopreciable. A rough estimate of the interference could be obtained by adding the induced velocities due to the win;g and fuselage as in reference 1. CONFIDENTIAL 'ACA, ACR N0o. T, 10 The velocity interference on the central part of  fuselage commonly amounts to about = 0.10. A rouh' estimate of the induced velocity'. c.An 'e obtained b fitting an equivalent prolate spheroid to the fuselage as described in the section entitled "reth:c's" an.d in reference 1. The wing . s approximate ely a twod.i nsional form and thus may cause relatively large tu.terferin velocities, If a protuberance is located n.esr the velocity peak on a *...tng, tl.erefore, tnc. ress,'res m:. be widely different fr'..i those on the sra ,r,'tu,.bartnce not subject to the interference: in pddit.i'n, 4Lhe c.aroe in pressure with change in 'ach number or vin_ an le of attack mra:. be large. Tt may be necessLry in some cascs to determine the interference effect of a nrotubOerasnce on tha loads over surrounding surfaces. The induced velo Lties enerally decrease very raidly wit 'h inrease i.n distance fr Mi the surface. The decrease of the 'e: velo ity incre:rent is shown for a win' and for oro.late steroids in fi: ures 56 and 57, reso,.,tively:, of reference 1. The methods given in the &p.pen'x of' Teference 1 can te used to estimate the interference die to a orot.iberance. If an equivalent orolate soheri'1 can b, fitted to the protuberance, the maximum. interfere.nme %elocities can be estimated fro,.r figure '7 of' ref" r',ce 1. If f'ore detailed information is needed, however, a veloicTy contour chart sucl as that of figure .r of r.eer nc: 1 can De cre:ared for a 'ody r.rox.in trinl the orotube rance in shane. For simp)Ic haoes, such as thc sphere or oblate soheroid, vv:lo'i.tty: c),tour.s r '.ssil., obtained from the potential theory. A':itt'L nal exoerirnnt is needed to permit very accurate cstimstcs of the effects of interference. Surface Irregul.ariti3s. The theretical pressure e distributions are calculated for smnth bodies, but in practice the surface is usually oro'er. by ribs, joints, waves, or other irregularities; as a result, oea'.s and valleys appear in the pressuredistricution curve. Such an irregular )pressure distribution is Liven by the experimental data shown in figure 1'. The irost obvious surface irregularities in this case were the ribs of the turret. Estimated ,c.ressure distributions should be made sufficiently conservative to allow for the effects of these irregularities. COITFTDFNTI AL CO FITDE].1TT.'!J, FACA ACP No. LLE10 Separation and Dress'ire behind a protuberance. ost prcEFT eranc are sufTfcTlenly Etat tHef tail that the flow fails to some extent to follow the sur face. Thic sen&rstion of the flow is aggravated by the boundarN layer develoood on the surface forward cf the protuberance "iith the result that separation becomes more severe as the protuberance is placed far ther beck from the noe of the fuselage or other body on which i.t is s!tuatd. Although separation dops not usually increase the severity of the leads, it greatly increases the drag of the protuberance and shov.ld therefore be prevented by a firing if conveniently nissible. In the case of gun turrets, a r.3thod that might be used while the advantages of 3vr.me'rical turrets are retained i, to install r:trsctable fairinns behind the turrets. The effect of fairing on separation is sh.wn in a coim ,arison of the ":xper'"icntal data given In figures 12, .l, 16, and 1). The use of faired turrets appears to give little advanteae over symmretrical turrets unless the fairing is suffic'ert to orwvent anr.y considerable separation. If the flow becomes unsyr. retrical when the turret is rotated from the stowed position, local loads may be substantially Increased. If sharp corners are thus exoosed, the pressurs may be impos sible to estimate and the neak negative pressures may become very high. At share outside corners, the flw searates either completely or swith a bubble sbout which the flow later closes in. A method of estimatingM the pressures near sharn corners has been sugested in the section entitled "Estimation by Comoarlson." Tt is point3d out in ref erence 1 .n ages 12 and 15 that outside corners with radii of curvstures leEs than a'nrxiuatel 25 percent of the height of the orotuberance may be considered shar.'. Separation changes the eff)ctiv': shape of a body In such a ,,ay that th.. pressure nea's influenced by the se~'artion are reduced and the oressure on the rear of the original form is decreased. At the roar cf the fsir.=d turnet of fir..re 16. therefore, the pressure coefficient is posi ie; whereas, on the rear of the more severe turret Df figure li,, for which a greater pressure recovery; is irdicated, se,'aration has reduced the pressure coeffic ent to zero. behind the still C'Or TDFNTT AT CONF IDFITTA. T, FACA ACR No. LL.ElO more severe forms of figuress 12 and '1, the pressure coefficients at the rear are naga&tive. Frori, t.ese exoerimental data and irom the kCnown vpales of the pressure coefficient on the rear atf spheres ar. cir cular cylinders, a rough eatimare c.f the Drcssires behind protuberances cerr be madre; but it 1 evident that, in order to judge accurately whether sepaation will occur and vbat .iressures will then exist, much systematic experimenio'tion is required. The effect of iorpressibility in rrcipitating or increasing the severity of separation has already been noted. Estimation of loids. From the pressure distribu tions, estimated or measured, the lo.Id.s can be determined provided the internal lressuras are known. The internalpressure coefficient may be :osL.ive if the pro tuberence is vented to a highoress're region, as about the nose or tall of the fuselage, but Is more likel to be negative because leaks regul.arly occur to the low pressure region "'n which a prj:tuoera.ice is usually placed, such as leaks around the sliding canopy, through other craci's, or through holes .n the surface. Because the external pressures var; with anle of ttack or the positions of the leaks change with ancle of ;.un turret, the internal pressures also var:. Since negative pressure coefficients uo to P = O.LC often accur on a fuselage similar ne .~ures m:n be expected in.'ide canopies or guai turre.s. In lows ed t& ts of the GrunTr.an XTBF1 airnlare unpublishedi), for example, internalpressure 3oefficients of 0.15 were found in the canony vhil e, in the .'mmetr.cal s''rt 'n turret tested., t.h orcssur: cofficient varied fror 0.02 to 0.11 depending on the angular position of the turret and angle of attack of the airplane: similarly, in the unsyrmmretrical Grumman turret with which the air plane was originally equipped, the internalpressure coefficient varied between 0 and 0.06. For the Brewster XSB2A1 air)lano in flight funoublished), internal pressures in the gun turret varied from P = 0.20 to P = 0.32 inside the ccckoit canopy of the SP2A)4 airplane, very low pressure coefficients of 0.530 to 0.LO were found. Because of differences in leakage, the internal oressures are likely to be differ ent from time to tire, even for the same airplane, unless the COITTDEF'TITAL SCO NF IDENTI AL NACA ACP No. LLElO enclosures are sealed. It is evident that, because of low internal prsssureq, jettison may be impossible even if a orotuberance is dei.ignind to be released. An increase of internal pressure could be realized by venting to the tail of the fuselage. CONCLUSIONS 1. By the meth'bs given in the present report, pressure distributions can be estimated for use in cal culating loads. 2. Tf allowance ir trade for the effects of inter ference and separation, calculations based on the ootentialflov: theory give a satisfactory indication of the maximum pressures to be expected. 5. For shares abnut which the potential flow.' is not exactly calculate, the pressures may be estimated by various ionroxirrate methods presented or by coan oarison v ith exoer'mrent. J. Com'ress'iblit v and interferrice effects and the effects f deoarture from potential flow, including seoara*ion, can be estimated by a combination of theoretical methods presented and by comparison with experiment. 5. In order to estimate the loads, the pressure inside the body as well as t.he externaloressure dis tribut or Ii'.st be known. 6. hurtrer erperirental investigation is needed to determine the effects of interference, zompressibility, separation, nrid systeirmtic chnges in form. Lanley remor ral Aeronautical Laboratory, nationall Advisory Corrmittee for Aeronautics, Tangle.; Field, Va. CONTTDENTIAL CONFTDFTTTAL TTACA ACR No. LLFlO REFERE ':CE S 1. Delano, James 3. and Vright, Ray H. : Investigation of rras and pressure Distribution of '.indshi.lIds at Eigh Speeds. i!ACA ARE, Jan. 19L2, 2. Frandtl, I.: General Considerations on thE Flow of Compressible Fluids. NACA Tk.. Io. S., 1956. 5. von FKarmarn, Th. : Compressibility Effects in Aercdynaymics. Jour. Aro. 3Ei. vol. 8, no. 9, .Tuly 19)1,, pp. 537556. L. von Doenhoff, i: ert E. : A :.!thod of Fa[cdly Esti mating the Fosition of the Larinar Separation Point. TA>A T. No. 671, lQ3i 5. von Doenhoff, Albert F. and . terv'n, Neal: Determination of Li.',ner.cl Eel'ati ons for the 3Bhavior of Turoulecnt boundary L.yers. i!ACA PCR i1o. 301, 6. Theodorsen, T., and CarricI':, I.E.. 'General potential Theory of Arbitrary r'"I,: Sections. NCA Rep. I:o. l2, 1955. 7. Jones, Robert T. and Cohen, DWris; A Gra.hicnl Yiethod of DeLermni1ng Pressure Distribbution in TwoDimensional Fl'7v. V' ,CA Re.. o,. 722, Ill. 8. Zahn. A.F.. Flow and Drag Irmulas for Simule Qundric?. IJAC.. Pep. Pi. 253, 1927. 9, Claniert, H.: A Ceneralised Tyue of Joukowski Aerofoil. P. & r. No. 911, British .. R.C. ].12L.. 10. 33ldstein, S.: A Theory of .erofoils of Small Thickness. Fart T. Velocity Distributions for Syrrmetrical .erofoils. 58dL, .e. 1976 ('revised), British ... .C., M'ay 1 4, 1 . 11. Lamb, Horace: Hydrodynamics. Sixth ed.,Cafribridge Univ. Press, 19532, pars. 107 and 10, pp. 1'214.6 12. von F'rr'ia'n, Th. : Calculation of pressure Distri oution on '.irship Hulls. P3A. TM 1;;o. 574, 190. COITT DENTI AL CO1fTT DEUTITAL NACA ACR No. LElO 15. 1Kaplsn, Carl: On a New Method for Calculating the lotentlal F)ow past a Body of Revolution. NACA ARR, July 19Lo2. 1L. Munk, p.ax M. Fluid mechanics, Pt. II. Vol. I of /..rdim.nemi T'.eory, div. C, W. F. Durand, ed., Juli..: 2,'nger (Berlin), I09 . Fluid ;;,oLjon with Axial Syrmetry, ch. V, sec. 6, p. _( . Ellipsold with Three Unequal Axes, ch. VIII, ses.. 15, pp. 293502. 15. Yonur., D. "'., and Devis, E. L.: Drag and Pressure Dist iitr.tn of Gun Turrets on a Model of the B25 Tuselage. FiveFoot "ind Tunnel Test No. 30C. A.C.T.P. 1o. 1753, ..aterlel Command, Army Air Forces, A,.ril 10, 19i2. 16. 2atts)n, Axel T.: Tests of a Large Spherical Turret and a Podfo_ ed Turret on a Typical Bomber Fuselage. IVO.CA nRR, Oct. 1Qi2. 17. Fluid "ntion Panel of the Aeronautical Research Com.1tee and Others: Modern Developments in ludl, Dynernics. 'Vols. I and II. S. Goldstein, ed., Oxford 6t the Clarendon Press, 1938. CONFIDENTIAL CONFIDENTIT AL NAfA ACR No. L4E10 UbU IrS \ IL 'I 40 oQ00h Do LU / e^S / Qg Cl) * \ ii U' 04 8^ I I I I I I I I I / / *s c C.s .0 "^ C 0 .0 it *  L bO 0 0 0 10 t 1  s>.* I 40 D.U S.5 *W A. 1z Fig. 1 NACA ACR Nc. L4F10 %0 u * t rv *~ u 00 0 3.* .0.0 LI 1 0 aO I I" oA/IV '.4et8J:eo:.o wau!4oooe Fig. !9 NACA ACR No. L4F10 CONFIDENTIAL dv Vo \_S 0lpe dx Souce disribwtion Calong a x y /oe dy NATIONAL ADVISORY dx. COMMITTEE FOR AERONAUTICS. CONFIDENTIAL Fi'gure 3. Slope method for CONFIDENTIAL CONFIDENIIAL Figure 4. Circulararc profile . veloc'ify c/lcula fi/n NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS. Figs. 3,4 NACA ACR No. L4E10 Fig. 5 N x 00 .. o 0 I 5  II 0 0 / \ \ ^ (Uo '.c 0 ^ S.b D <"* Xb  ^ 1  NACA ACR No. L4E10 CONFIDENTIAL V . 7 i / Po laP r CONFIDENTIAL NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS. Figutr 6, Circular cly/inder of fi,'ife lehgth ,from 7 s a rfqce. I I ax is . Fig. 6 I I \ ! I i f 6?ojectiny NACA ACR No. L4EIO .2 (a) (b) o./ sin h .4 I~ ~ ~ ~ ~~~4    ^^     *  (C) 0.I 6in 2 f  (d) 0./I in 3 . AmountL ao be odded to eclipse 0  0.i Sin 2  1 I I 1 I f  ,CONFIDENTIAL l I ] I .. .. .. . I __ I 2.0 NA IINAL ADVISORY COMMITTEE FOR AERONAUTICS. #* .8 /.2. /. 2.0 2.4 /.6 1.2 8 . O0 2s/a Figure 7. Deferminaf'lon of Ohe complex functi'oi for Mhe coaormna/o/ freisfaorma'ion of a circle infto a profi//e pproxii/ing the meridian section of a body of revol/rOtn  CONFIDENTIAL I  SA/eridian profile Ellipse  Fir.s* approximation econcd cpproxi/m ftibn I I I i i I I I .2 .2 .2 .2 2 AV 0 4? .2 Ir n n. . Fig. ? NACA ACR No. L4F10 2.0 t CONFIDENTrAL t 0.1 = .. 0.4^ZI 1.6 3,  , " Two dimensional 4 Three d,'mensionr/l 0.4 ( ) Ellipficql cylinder3 and rneridian iro file  of prolate Spheroid,5. 0 o I I_ _ii _I___ ___ 2.0 u 1T 1.6 .4 1 1. 1I IV NATIONAL ADVISORY "Two dmens ional "  ' Three d imenSionc Il .4 (b) Approximale circulararc syrnmefrical airfo;/15 ar meridian profiles of bodies oP revolution  .. I, ,,_I I I IL ,II I U IU NLd f iAL L 0 ./ .2 .3 .4 .5 .6 .7 .8 .9 F'i0ure 8. Corparisonr of calcu/loaed ve/oci/y aisfributions over #two dimensional shapes wifh those over the correspondcti' bodies of revolution. Fig. 8 NACA ACR No. L4E10 CONFIDENTIAL ( ^ ) CONFIDENTIAL .4 I I ~ I I I NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS. .8 Figure 9. Ratio oa velocities on probate spheroic/s *o those on correspoinacig. ellipi'c cy/'nder's. Fig. 9 /.c V3D V2 20 .8 .2 1.0  1\11 III I Ill O . 61 NACA ACR No. L4E10 (a) Circular arc profiles. (b) Joukowaki approximately symmrefrical profile; S=0.277 (reference 13) . uI Lmiarnirflaow profT/e I I I I I l EWuivalen', e //ipse ,' r" d /1 = 0.37  / / NATxONAL ADVISORY COMMITTEE FOR AERONAUTICS. ,. ri^r. ._____ _(c) Lamia fa pro file. t =.6 ./ .2 .3 .4 .6 .6 .7 .8 .9 '.o Vi .6 Ftywre /0o. V/at'afion of /he ratio of ve/ocifies it, three dirnersionaia to those ifp twodcimei.sional flow over sever/l bodies drcd +heir eyui'valenrt ellipses. Fig. 10 NACA ACR No. L4E10 CONFIDENTIAL (a) Mar in 6u.rret. (b) Turret A in tivo loccxltons. z/? = 0.590 (c) Tu rre B3. CONFiDENTIAL NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS. Figure Marin //. Loco'bons of the furre and #urreit A aon B on fs e /age. Fig. 11 X/1 = O. S90 NACA ACR No. L4F10 Af o f Err t CONFIDENTIAL Re/ofive wind \ 5ide Fronat /Mfeasured Oblaot spheroaid 6/ = O. 0.67 RelaTive . I Top ca/cr/afec/ o Around rism, line /. + Over central meridian  In direction of 1fl/o". line 2. x Over cenra/ meridan  norm/al o direction of f/oV, line 3. Figure 12. C.znpQrisoin of mea sured pressures on the AR/arfi' tfrre r referencee /5) tvifh calculated values on @n equival/ena oblate sphero;id and on a sphere. Fig. 12 NACA ACR No. L4E10 Relative incd Top Front 5Side CONF!DENTiAL NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS. ' Turret A det//As. Fig. 13 F igure /3. NACA ACR No. L4E10 L/'ne / (Cbp) ,'ne / (Ao). CONFIDENTIAL / Line 2 (s/e). '",, / Theory for 1.2  sphere / \ / Circular Orc, over fop. F Circula/r arc,_ / \ o over s$ie. 1 JMeasured oft___ 4 x 1 28.6" fuse/oge s ation, lie I /f (op). I o o. 22 + .70 1.2. Measured of 67.8 L.2 fuselage station . Line I (top) At Line 2 (side) S/0.22 o ,70 ^ 1I6IA NATIONAL ADVISORY I IU~NE IIAL COMaMITTEE FO EoWM cs 0 z. 4. 6 8 /0 12 Distance from edge, in Fl'gure /14. Comparison of measured pressures on turret A of reference /6 vwo'v# theoretico/ pressures on sphere and circular arcs. a = J". Fig. 14 NACA ACR No. L4E10 CONFIDENTIAL Re/c five wind_ Top CONFIDENTIAL 5/de NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS. I Turret Fig. 15 D de' /5 s. 11Igu, re NACA ACR No. L4E10 \I . Fig. 16 CONFIDENTIAL . /= 0.3319 J1 I 2ZZT /.6   /.2 .\  .8" 0 + o / I o oA Meo5aswrdc/ at 67.8 ,1 fu.se/loe afaion, c=3. ' 46 Top S lde n. orifices orifices NATIONAL ADVISORY o 0. 22 COMMITTEE FO AERONAUTICS \ _+ .67 a ]CONFIDENTIAL _ Calculoated by slope method wo dim enaionaI.   Estimafed for body of revo/utiorpi from fwodcriensiomna/ ve/ocify disbribuifon. I l I I I I I I I I I 1 I l I 0 / 2 3 .Distance from 4 5 6 7 a /ecft'np9 edge., r. Figure 16. Comparison of es /,'faecf Wii; meoasuredc pressures over tc'rret B owT reference /6 . NACA ACR No. L4E10 I a 'a C I i 9 j o  D \ L :;  \ c iA42 *_i qj qj^^^ ^ ^ ">   I '. S J i, Fig. 17 NACA ACR No. L4E10 C. C) Fig. 18 'S 4) O, I '3 2. O B Iz NACA ACR No. L4E10 Fig. 19 oLl I..e mu A. /~~ i, ^ s \ i '1 ^ra ^~I Ub a 5/ :3 /:z %6l Sas gnA u OM Nj a 00 o .1 ^ "^j ..^ o I ^^ ["00 Nz z s i oit Ilk) I'I. io lb ^ // ' 1r g Ii I l ''/o '*SA TT^> ^ t ^^ <"Coi NACA ACR No. L4E10 Fig. 20 / A / ; IN' Ii . I: .9 .NACA ACR No. L4E1O it ,Ls Fig. 21 000 I a I ci, I 01 4Z It I.. Aml^ q) kL NACA ACR No. L4E10  CONFIDENTIAL  I____ / // // /I \ NNv \ \ \ LJ /1" T // /I _________ _____________  op of turrets lind e /. jcli'ndrical side of ft ^ * z *.. irret n i guns a eom position, one 2. CONFIDENT TIAL NATIONAL ADVISORY COMMITTEE F0A AERONAUTICS. I Figure 22. Esdimated pressure distribution about lowerr gun turrer of Doug/os XSB2D/ airp/one. /v7l = 0.70. Fig. 22 NACA ACR No. L4E10 Fig. 23 __ \ 0 0 \o  I  \ 0 __ 8 \ 0 S\ 0 0  II C. 0 4 0.?  / I N S  I a< 1 1 1 _ogo NACA ACR No. L4E10 rw) C 'It N I I 0 c (0 00 a a jCjC 4z "I tc 10 s 'ItC k1. E k C 0 43 1 q) 0 . a t0 C 0 9. QO 49. U? aS 'I gS 0 j 0 1 Zai 0 a zz 0 E Za Ld3 ii 4j z; 0 U Fig. 24 0 b 0 T. eE LD 63 le jS S.0 a k lo IL 0 194 *0 Ito t 0 St. cO't CL *R"y s0 S.. 0b ti Co *0 NACA ACR No. L4E10 CONFIDENTIAL Alach number, M Figure5. Pressures on similar yvn furrets in different locations on the fuselage. Fig. 25 NACA ACR No. L4E10  1.0   I  7 __ __ _   e Turret A freaerence /6J. ' ^ + Turret D (unpublished dato). Theory for sphere P = ' .2   C CUFIDE,'nTIAL NATIONAL ADVISORY i I COMMITTEE F AFAomAUtICs . / .2 .3 .4  Mach number, /. .6 .7 Figure 26. Pressures on top of two spherical turrets shoAwing effect of re/otive project tion above Mhe fuselage. Both turrets located ao 24.9 perceet fuselage length from nose. tt = 3". I. _. m m Fig. 26 NACA ACR No. L4E10 Turref Side CONFIDENTIAL Front 0 heor   .2 .  * Tu etr NATIONAL ADVISORY COMMITTEE Fu AErONAUTICS .4 o  F, near top (frome unpublished data) + F, near back x  f a fop (reference 16)  .6  8. at sio.de  S ...  at x/1 = 0.61 CONFIDENTIAL 0 .1 .2 .3 .4 .5 .6 .7 .8 Mach number, 14 Figure 27. Comparison of pressures on two .sream/ine furreft.s of different thfickness ratio .shovvrng different compressibili ty effects. Fig. 27 NACA ACR No. L4E10 Winds field 7 3 4  311 CONFIDENTIAL < d jb c I CONFIDENTIAL j I. .2. 3 .4 .5 .6 .7 .8 A4Qch number, AI Figure 28. Pressure change wvd/ Acach Imrnber at points on three windashields from reference /. Point locations and corresponding pressures are indicate.f by the /lefters a b c anc cf. I A) . 0 S. * (0) S Fig. 28 UNIVERSITY OF FLORIDA I, 'L Ii' UWLY I, I ~  6~. ,K IA ..% IY 4 1 A I 