^Jfv^(\ I'M / ACE No. L4E10 NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS WARTIME REPORT ORIGINALLY ISSUED May I9UI+ as Advance Confidential Report lAElO ESTIMATIOW OF PRESSUEES ON COCKPIT CANOPIES, GUN TURRETS, BLISTERS, AND SIMILAR PROTUBERANCES By Ray H. Wright Langley Memorial Aeronautical Laboratory Langley Field, Va. NACA WASHINGTON NACA WARTIME REPORTS are reprints of papers originally issued to pro'/ide rapid distribution of advance research results to an authorized group requiring them for the war effort. They were pre- viously held under a security status but are now unclassified. Some of these reports were not tech- nically edited. All have been reproduced without change in order to expedite general distribution. 201 DOCUMENTS DEPARTMENI '^Uf^'-i^i^ NACA ACR ITo. LIikIO NATIOI^yAi:, ADVISORY COMIITTEE FOR AEROIJAUTTCS ADVAZJCI. COMTD^TTTIAL KEPORT SSTIMTI^>N OF PRESSURES OT: COC^'PIT CAA^OPJES, GUN TURRETS, BLISTERS, AT'-JD SPHLAR ^ROTUSERANCES By Ray H. 7:r:Lfc:-ht summar:^ Methods are described for 3s1: > ^'nating oressure dis- tribations over protuberances sacli as coci<'oit canopies, gun turrets, blisters, scoops, and sirrhtrn^ dorres. These methods are applied to the estivnation of the pres- sure distributions over spherical-cegmeiit and faired gun tvirrets and over the protuberances on the Brewster S32A-1 airplane. The effects of compressibility, interference, and flow senaration are discussed. It is shown that, by a corrbination of experiraent al dsta vi/i th theoretical methods, lirdting press'jras for use in deter- mining maximum loaf's Co-n in many cases be sG.ti sf actorlly estimated. >':uch sjsteratic experimentation is needed, however, to im.orove the accuracy of estim.ation. IFTRODUCTTO" The purpose of the present report is to describe methods by which pressures evnd hence loads on protuber- ances, such as cocVpit canopies, gun turrets, blisters, scoops, and sighting dom.es, mt:y be roughly estlm.ated. In particulai', the possr'bility of deterT'ining limiting values of the oressure coefficaont - valines which cannot be exceeded in oractice - is demonstrated. The investigation was initiated by a request from, the bureau of Aeronautics, I\'pvy Departm-ent, for load data on gun turrets. Ro aoplicable e.xperim.ontal data were available and, as the RACA testing facilities were already comm.itte-i to otlier investigations, it was decided to estimate the limiting loads. I/ethods generally useful in tl:e estimiation of loads on protuberances are described in the present report^ These methods are aoplied and, where possible, the CONFTDEIITIAL NACA ACR No. ikElO results are comcared -.vith experimental data. The methods are necessaril;/' only approximate. Fven If the potential f'lov oould be exactly calculated, the actual flov^- v;ou].d likely depart so vr^dely from the calculated flov as to rerder the results invalid. 7he exercise of judgment, based on experience, and the use of experi- ment in evaluating the effects of boundary layer, separa- tion, ooir'pressibP i t7y, interference, and departure of the shape from that for vhlch pressures can be computed are necessary in order to arrive at useful results. Although little opportunity for systematic experi- mentation is likely at presert, the study presented herein is being applied to turret shapes on particular airp.lane m.odels being investigated at LMAL with a viev/ toward improving the methods of estimation of pressures. SyivIBOLS p pressure V velocity P mass d'^r.sity q dynamic pressure, free stream: unless otherwise stated f-p^ ) r T?res3i-;re coefficient ; 1 \ "^ / M Mach number, fr=e stream unless other^viP€ stated AV velocity 1nci'em;'>nt Zi'-VVg vzli c^ity-increvrent coefficient V/A/q velocity coefficient f] -i- -~\ \ '-0/ Y ratio of specific heat at constant pressure to soecific hea it at con'^tsnt volum.e (— ^j x,y Cartesian coordinates CONriDENTIAL lUiCA ACR IIo. LI^EIO CONPIDENTI/ir, 3 7. , t complex variables Subscripts J 1 incorr-oressib], e or low speed in •un.'.listuroed stream 1 local Other syrrbolG are Introrluced and defined as needed. Insofar fs possible, tiae notations of the references are retained in the present report. For this reason, more thf.n one quantity Liay be desif-;nated by the safe s'yrabol or one quantity xr.s.ir be designated by niore than one syr.ibol . MSTIJODS FOR G.y:.C ELATION OF VELOCITtZS OVER PRO TUBER Al^GES Although the r^irolT-iie with its canop;} , turrets, blisters, and other protuberances is a comnlicated three-dimensional form about which even the potential fiov; cannot nov be corrputed, ari estimate of the pressures on the protuberances can be obtained. The airplane presents the [general aooearance of a win;/, fuselage, and tail with the orotube3^ances suoer'oo3-"d. These pi'^otubercnces are usually of small length relative to the length of the fuselage or to the chord of the wing and are very often quite thick in relation to their length. The load^j over these protuberances therefore are assumed to be determned largely by the shapes of the protuberances and to be miodified by the interference of the wing and fuselage. As an approximation that is usually valid vr.l33S the protuberance is located near the nose or in the wake of the body, the total velocity V is assumed to be equal to the sum. of the velocity over the protuberance v/ithout interference and the induced velocity increment AV due to the interfering bodies or, in coeffieienL form, V V o ^ (^ " ^^ (1) rrotaberanco alone '^"'interference CO?^FIDFI^TI/iL h COITFIDENTIAL NACA ACR No. LitElO Methods of 'determining the velocity inorement due to interf i^rence are given in the appendix of reference 1. In TT'any cases, the interference is sufficiently sn-all that it ir.sy be neglected. It is convenient and sufficiently accarate to s/^'plj the cor?pressibility correction to the pressure coeffi- cient GPtiTr.rjted for incGmpressibl;-: flow r . I (2) where V^/V,-, is the value of equation { ] 1 for incom- pressible flow. The pressure coefficient for com- pressible flow is the.i obtained frorn an approximation given by irrardtl in reference 2 as Pi r ( 3 ) /y - ^^^ where U is the stream Mach number. An approximatior that in specific Instances has been fo'^md to describe experimental results more accurately than f'randtl's method has been ^^Jven by von Ka'rman in reference 3 as P. a) 2 (1 + .A - M'^ \ Equation (5) is sufficiently accurate, however, for the estimations described herein. The pressure c*! s tributions obtained up to this point apply in potential flow-. The effects of departure from potential flov, wh'ch include development of the boundary layer on the surface forv;ard of the protuber- ance, separation nf the flo"?, v.hich occurs reg-alarly on the rear of blunt bodies, and interaction of these effects v'ith compressibility '^ust now' be estim^ated. Al- though the boundary layer and the joint and existence of separation ^if-ht be calculatcc: , at least for low speeds, by the m.ethods of references L and 5 (vith modification COFpiDENTTAL I:ACA ACR Yo. LliTlO CONFIDENTIAL of tho iroirientum equation for ths three-dl'cr'ensional flow) , no method 1s knowr: fo.'' calcv.la tin,;^ tho oorres7:ondln,g cres3J.res nor is ''ny tlieory available for ostiir.atlng t}ie Gomprea sibillty interaction. From the mea'^er e.7perinental datn svailrble^ these effects can be at least qualitatively estimated. (These data are presented and discussed in the section entitled "Applications.") In bi'ief, the procodure is as follows; (1) Est: mate the veloc-" ty-coef f icient distri- bution for :' ncoinpressible potential flow ovei- the pro- tuberance shape (2) FstirTuto the interference velocity coef- ficlentE for incoiiipresnicle potential flow (J) Add the coef f icr'ints obtained in steos (1) and {Z) as in equation (1) ''a) By use of stop (p), comp^ute the oressure coefficients for incoiapressible flow 'equation (2.'}) (5) Apply the compressibility correction (equation (J) or ( I4) '/ (6) Sstiinate the effects of departure from potential flow In practice, as aopea'^-s in the ezorriples , sone rriodif ioati on of this procedare ma/ be necessary. '^"'he rest of this section is ccncerr;ed largely with the determination of the velocity distribution with potential flow over soecific protuberance sh&pes v.ithout interference. n-ene r al ons i der at i on s Protuberances often appear as bodies that are approximately half of symimotrical forias cut by an Infinite Diane as indJcatod. in figare 1. The flow v/ithout the interference is then theoretically a ')n]"oxLmate to the corre spends" nr: l:alf of that over the coniolete body. In m.any cases the half-body aoprcaches the tv/o-dimensional form (airfoil); for 'vhi ch the pressure distribution is always calculable; then, as the pressure changes are larger In the two-dimensional than in the thi-ee- dim;ensional case, it is conservative to consider the COT^-^TDFNTIAr, CONFIDEIITIAL ITACA AOIl No. T,I|.riC flov" tv;o dimensional. In c^-lier oases the j^hepes nay approxinate 3lm.o?:.e three-dinicns Lonal f:irins, such ar, spheres and ni'olate or oblate spheroids for which the flov 18 kno\"n, and the corrasponling oressur-t- distribu- tions may be assu'^aed. [f the foiTTx of the body or half -body is such that the flow cannot be directly calculated, it :nay bo :ippro:d- mated by various devices. If the shapes of the front and rear ed.t5es of a orotuberance are different, inacn.uch as the flov; over one ed.-rce is often little affected t^y that over the other, it may bu porssible to compute the pr'-.ssure distributions over front and rear edges sepa- rately axid to join tlie distributions at the center. In sc-Te case3 a simole oody, for vhich the flow in three dimensions can be calculated, may be modified by s t-v<.>" dimensional method to aoproxiinate a given shape. Such a .modification depends upon the assumption that a small local chanj;;© in the radius of a body of revolut'on produces a local tv/o-dimensional effect. As the radius r. of t'^e body of revolution becornes larger, this as subnotion becoirios more nearly correct. For exaii;rle, the p:^e?sa?^es over the lio of an open engine cowling e.poroach the oressures over an airfoLl with the profile shape of t]\e lip and with the sair.e effective an^le of attack. An example of an oblate spheroid modified to an-proach the shape of the f'-'^axson turret on the fjrev/ster SZ2.A-1 aii^-olsne is given in the section entitled " P:id lie a t i on s . " Tv-o-Dirtiensiont'.l Shapes Arbitrary foriris.- The two-dimensional potential flov past syiai-netf ical orofiles that correspond to given half-bod:^* OS can be obtained b;y the method of Theodorsen and Garrick (reference 6). In many cases, however, less laborious ir.ethods suffice. The graDhical method of Jones and Cohen ''i^eference 7) is v/ell suited to the computation of "ooter.tial flov; over UiUiips. Forn s fo r v-hi ch ^) oter.tiQl ilo-.v is knov/n .- In certain cases, 'bEe form o'r~tEe' pro t abe •'■anc e a" p r oache s that of some two-dimensional profile for which the pressure distribution or corresoonding velocity distriPution is alrerdy known and can be applied without much further CO input at-' en. Three such simple orofiles are the infinitely lon^^^ circular cylinder, the ellipse, and the GOWlDEr.TlATj NAG A AGP No. LliElO COF'^^IDEFTIAL 7 dou'bl'^-circule.r-aT'c ornfila. For the circular oy]inder moving rortia] to :'t.£- a;:is, tl^e velocity dis'cribu ti, on with ootentic.l flow is i-i ven ty 2Vq sin e (5) where 6 Ig the nolar angle measured from the stream cl i r e c 1. 1 n a. i d V -, i ? t }i e f o r v; a r d or s t x' e am v e 1 o c 1 1 j . The velocity dist_\ibutior; about the elliptic cylinder m.oving oar&llel to its inajor axis is ,£;iven 'by Zahri in reference o arid rnaj- he expressed in the form r"- (1 -^ / m r- ^ &r (6) where a semimajor aris b semiminor axis X d]*sta:ice along major axis from center The forv-ar.i t^ortion of a s /rra-ne t r J c r 1 airfoil shape v/ith zero lift can often be a-coroximated by an elllrse as jn figure l(cK "^f x is the distaxice from Jr.irjx the nose at vhich the maximam ordinate Yj-^ja- occurs, the 8'luivalent ellipse can usually be deteriiined from ^ii.ax The velocity distribution over t]:o for-J"ard portion of the airfoil r;cy then be ty'.cen the same as that on the ellipse. Anothir very useful siuape is the douole-circult-r- arc symmetry c8l a.ffoil, of v/hich the \r:per and lovi'er svrfoco profiles are arcs of the same circle. The C0!JFIDKJ1TI/;'. 8 CO Iodide rTiiUi kaca acr no. riiEio oonformal transf ornatlon Into a cir-cle is given by Gl'iuert in referariC^ '^ . Tho velocity distributions, obtained by -ootentipl theory, are given for different thicknesses by the rolid lines in .^Iguro cL. T'Mn bodies by s 1 o n e me t} lo d . - A simple anproxTuate t v.'o - dTmi-: n s i on £l method thalETIas proved extremely useful has been included in a publication by Goldstein (ref- eronce 10). This irethod, which j^ives the velocity distrioution ae &n integral function of the slope of a s2/mr"etrical profile, may be called the "slooe methocl." For the derlvrtion of the slope method, the following two simplifying as3urr.pt.lons nre nect.ssary: (1) Tne profile is sufficiently thin that the velocity is nov/here very different from streajn '.'■: velocity V^^ (2) The sloTo of the prof. lie is -everywhere small These aasum.pticns orsclude the e.x.istenc9 of stagnation points. The syrrjr;etrical profile xiiay be assumed to be re-oresented by a distribu.tlon of sources d^ydx along the chord c. The velocity increment 6(AV) at any point (Xq,:/.^) on the profile (fig. 5) due to the source elerrent — ^ dx nt x Js dx -- dx A(AV) - " (7) 2Trr Because the profile is thin, the velocity at (y.^y-^jr,) cannot be very different from the velocity st x,-,; thus, ^■^^ i(^v) ~ — ?^^: (S) 2^ (x - y.) o ' COIIT^ID^IITTTAL NACA ACR No. LiiElO COl^P'IDl- NTIAL The total iriCl"Liced velocity ther3fore is ,c '-Si ,. '0 -^^^ ^'o - ^-^^ (9) For- uro' t leng'th of the profile, the cross section at X Is 2y and, with 7 ~ V.^, the volu/ne flov-/ js approximstely eqaal to ^V^-^y. The voliime flo'w through any cross section, however, must be e^iusl to the total output of tne soai-ces upstroarri and, therefore, or ^ ~ ^V^y 'ivj, d-" With s utstltution of the value of d^/dx fr'O'm eqii.a- tion ''10) in equation d), the coefficient of the induced velocitry beccit:e3 7- ~ TT / y _ J; The lnte.p:rand in equation Cl) can be exorsssed ii-' trigonometric forn but, for the nresent purooses, the algebraic axpreasion is retained. The velocity coefficient is given by y A 7 ■' O '^ o If the slo-jo dy/dx in known as an a].r,obraic function of x, the velocity distribution ci;n usuall;/ be obtained v.lthout much tro\ible as a function of x . The integrand in equation (11) approaches J.r.i'inity or becomes indetonrinate at x ~ x , but the integral G01TIDi:i':TIaL 10 COITPIDSNTIAL K/'CA ACR No. Ll^ZlO is usually Tinite; tnc :nr'.n:.te positive and nog^.tive strlos cancel. '^f tr^e Integral approaches infinity at to. £iven point x^, a finite integral that yields a velocity Increment which approximately agree? v.-i th the actual flo-,v can urually be obtained for a slig-htlj different value of x^. 'T'he slope method is more useful than might be suopoped fron the restrictions '.nposed in the der^ va- tion. -Although the result?, are not exrct, they provide a reasonably good arDproxiniation even for rel::;tively thiclc forTis, esoocially over regions of the profile having smali slo e. T'he :'nethod is not applicaole in the viciinity of a sta.-n&tion ooint or \^here the slope dy/dx l3 large. This difficilty may, however, be circumv3nted. I'an-j urotuberanco shapes involve no very Ir.rge values of dy/dx and require no stagnation point. If a stagnation point does occur, the velocity distribution over the rest of the profile at some (iistance from the ncso r.ay be ap'-u'oximated provided the rounded nose or cail, \Mhich. involves infinite slope, is extended in a cusp cv otherv>;ise is slitjhtly altersd to prevent very large volues of dy/dx. A reasonably acc*iis;te velocity computation can be made if the slooo method is t^policd not to the given profile but to the shape ootained £s the amo\i.nts Ay by which the ordinate^ of the given nrofilo exceed those of a similar profile, such as ellipse or Joukowski air- foil, for \v'hich the velocity cistribuLion is knovvTi. The velocity increments are simoly superposed; that is, the required velocity distribution is the sum. of the velocity distribution on the simdlar profile and the Increment "^V found for the difference shrape. Thr :e-dimiensional Shanes R.sy be sli;j;htly rrodified in the same wa:/. Given nrotuberance profile shapes can often be approximated by the j-oxtaoositlon of a series of srcs for which t]ie slopes are .giver, a^ relatively sl-nple algePraic functions - for example, circular, elliptic, ard parabolic arcs. The iuduced-'velocity coeffi- cient AV/Vq miiiy then be obtained from, equation (11) by direct integration. T.iiz orocedurc yields approxi- m.atel7-r correct velocity distributions even though the curvature -^t the ^^unctions may be discontinuous. The slope should obviously be m:ude continuous; that is, the arcs should have the same slooe at the juncture. COWSJDEWT'^.M. IIAOA AGR No. iJjFIC COITIDErTI.'d". 11 A protuberance profila iriay have the approximate shape of a sirgle simple ar:;, such as the circular arc, in which case the velocltY distribution is easily calculated. Thus, in figure :.i, -^ = - tan e dx X = r sin 9 dy.: - r cos 9 di and equation (1-1) becomes V o ,/ _ sin 9 d 6 ,/ sin 9 - sin Q. '^-9, ■• 1 1 P"' - d9 f sin 9,^ ,o"l d3 sin 9 - sin -01 (15a) Integration and substitution of the limits give AV 1 = -<2G]_+ tan e^ V o /sin 9q tan -^ + cos g..^ - 1\ I 1 ! sin 9r, 't^"i 1 cos e^ - 1 ^Ogp sin 9^ tan ™ - cos 9^-, + 1 / ?(Vh) On [. ^ sin e„ tan -f-+ cos 9-, + 1 -! / ! V Jj for the velocity distribution as a function of 9,-,= COirFIDLNTIAJj 12 CONFIDENTIAL NACA ACR No. LUEIO From fi,c:ure [', , 6 = sin' d.V 6^ = sin -1 X o --" I- and ^ -p - hi CL from wli-i ch 9 = sir.-- Uk) \ -/ « 1 *^ c c Gq ^ sin"^ ■ — ■- (15) 1 ^ ^i?)' Substitution of equations (ik) and (I5) in equation (IJti) gives the lnduoe5-%"eloci ty coefficient AV/V^ as a function of the chord position x^/c and of the thick- ness ratio 2.^, v;here y^/" i^ pleasured from the center as shown. The vslocity increrient? for circule.r-arc profiles ranging in thicV'ness ratio from 0.1 to O.5 are shown ir figure 2, in which the results of the sloje method are oorrpared with tae results of the accurate conf ornal-transf orration :Tethod. In figure 2, x/c is COKFIDEKTTAL FACA Ac:^ ro. riixio Goi:FiD:^^yTiAL is center. Up to a thickness ratio of 0«2, the .slope method i-^lves a fair spr-'roxiTiation of the velocity dis- tributions over circular arcs. As was to be expected, the error is greater in regions of greater slope. The velocities at the center of the profile, v.'here the slope is zero, are apyjroicinate] y correct even for the 50-percent-thick profile . Thz''ec--Diriensional Shapes Methods available for the calculation of flov;p. in three dir.ensions are less- general than the corresponding tv?o-dirnensional nethods because, except in the special case of the ellipsoid v/lth three unequal axes, tliey apply only to bodies possessing axial s^Tiirietry, that is, to bodies of revolution. "any- protuberances are approximately axially 3^,n"-ir>ie trlcal, however, and the three-dir.ensional theory may prove useful in estimating velocity and corresponding nressure distributions in these cases. The sph ere.- The simplest body of revolution is the spl-icre, for v/hich the velocity distribution is given by 4- - 1«5 sin 9 (15^ ^0 where the anrle 9 is measured along any meridian starting from, the strer>m or flight dlrectjon. The oblate s pher oid .- A tody of revolution resembling a gun turret is tno oblate spheroid obtained by revolving the ellipse about its minor axisr Motion in the direc- tion of a m.aior axis of the ellinse as shown in figure 5 corresponds to that of the gun turret. The potential is given by Lap;b (reference 11) in term.s of the elliptic- cylindrical coordinates I, [!., and oo. At the surface of the oblate spheroid, ' I = l^ and ^q is given by .^^=^ (17) b a ■ i 1 - (^"^ where a and b are the semimiajor and ser.iminor axes, respectively, of the corresponding ellipse. From^ the CONFIDENTIAL 14 COHFIDEKTIAL NACA fl.CR No. li^ZlO potential, the vslccity distributions at the surface relative to the body may be derived. Around the rin in the YZ-plane (lire 1, fig. E) /1^\ = L sin 0) (18) V^"/rim where L = _- ^-11 ^ ^ (19) to-' + 2 - to(to^ + l)cot"l ^3 and 00 is the anrle with the plane containing the direc- tion of flow and the polar axis as shown in figure 5 and i? related to the distance a].ong the Y-axis measured from the center by y/a = cos U) The velocitv over the top in the XT-pl^ne (line 2, fip. 5) is /,r N ft '' + 1 \ ■ 1/2 ^\T- (20) v'^k=o " '\i^'- + ^y v;here T.\e velocit;^ rxrosF the raeridian lying in the XZl-plane (line 3) is (rj-) , = L (21) :Tr/2 which, for a f^iven thirhness ratio b/a, is constant; COTTIDIZ^-^TIAL NACA ACR No. L1|.E10 CONFIDENTIAL 15 that is, the velocity at the siarface across the meridian perpendicular to the motion of an ohlate spheroid moving normal to its polar axis is constant. Although velocity distri'outions along other lines on the surface may be obtained, those given by equations (l8), (20), ai:id (21) are of greatest Interest and are most simply derived. The prola te spheroid.- A related body, for which the velocity distribution is more easily obtained than for the oblate spheroid, is the prolate spheroid moving parallel to its polar axis. The velocity distribution at the surface along any meridian as given by Sahm (reference 8) may be expressed as I = (1 + k,), / -A^^— : (22) where K = - 1 + e I — e log 1 -r- e e 1 - e2 where the eccentricity 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 samo v/ay 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 bhe equivalent prolate spheroid. CONFIDENTIAL l6 COITPIDEl-ITIAL NACA ACR No. LliElO 3o''^y of re v ol ut Io n i-epres en ted, b y axi al Fouroe (i ir^t rl .j\.Tt: on. - Tl7^ \e'l'ocity distrx but! oh about a bocy of FevoIatZon w^ th flow parallel to the axis can bs obtained' by the luethod of von* Ka'rman (reference 1>), providec the body can be reprasented by a distribution of sources and sinks .Tdong the axis. This rethod is useful for a very regular body for which the shaoe of the r.eridiar. profile can be [.iven by only a few ordinate s. If the rreridian profile is irregular, the rrothod ir tedious and pei-haps impossib] e. It is described in detail in reference 12. 3odv of revolution reor'^sented by doublet distri- bution a] on,:; l 7 1 .;; uo rn"' al t o flow . - 'The c i r cul e.r c yl i nd e r projeccfnf? rrom a' plane surface A-A (fig. 6) is considered a half -body of which trie other half is shown by dashed lines. At the plane of syr;irr;etry /.-A, the velocity must lie parallel to thi= plane anr tangential to i;he surface of the cylinder. At other planes, cros' velocities occur and reduce the peaks; the .-r.axim'Jiri velocity changes consequently occur st the plans A-A, except possibly over the sharp corners st the ends for which the velocity d istributj ens cannot be computed. By a iT^thod described o^r von Ka'r.r/'in (reference 12), the part of the polar axis occupied by the cylinder is covered i'-;ith a doublet of r.or.ent per unit len^jth equal to that obtained if the cylln.der v/ere infinite in length. The end?; of the cylinder corresponding to this mathe- matical device are rounded rather than plane bs shovn; the influence of the rounded ends on the velocity dis- tribution at the plane A-A must be srrall, however, and the ends of actual gun turrets are irore llk'^ly to be rov.nded than plane. The pressure distributions in planes parallel to the plane A-A generally are similar, but the peaks are lower as the end of the cylinder is approached except that, in the re.'.ion of small radius of curvature nea;-- a blunt end, high peaks may occur. The velocity at the su.rface of the cylinder in tlw plane A-A is ,-- ^ (1 + cos 9) sin {25) ^o where is the polar angle measured from the plane containing the flow direction rnd the polar axis, 6 is ONFIDENTIAL ITACA AC? ITo. IL.EIO COi:P'IDI;:rTI.\L I7 the a:a£,:] e ."^hcwn in figure 6 for vhicli 3 0£ V is the radius of the cylindet", . aR'3. I is the lenj^th, of its projection fro:->i the surface. /in example for which r is not constant is treated lifter. Tne method Is de.'^crihed in i-eference 12. .j ocy of revolution by _ir!ethod of 7f:plan.- A.. Incthod' has recently been developed 'by '■^aplan'Ti'ef 'Srence I3) by which the ootentisl flow about any body of revolution moving in the direction of its.^inlsr a:^J.s may be calcu- lated tc any desired. degree of ' approxlMation. By this method, the flov; is obtained v;ith orthogonal ■ curvi linear coordinates for v./hich t?:e surface of the body itself is a constant. Tne coordinate systera,' v,'h:Jch is different for each body, is obta-^.ne'i by means of the conforrtial ti'sns format ion ai ap s,z z = Z + C-, + -- 'h -=■ -I- -^- + . , . (2u) Z Z2 z3 . '1 n -i* which transforms the circles p = Constant and the n radial lines £, = Constant in tho plane Z = Re 'e Into the corre spondin,^ orthogonal coordinate lines in the z-''0-ane,' where -,1 - is the ivieridian pi-cfile of the bociy of revolution. The potential is ip.ven as a series of terrr.s involving the Le;3:erdro funccions F' n and where Ke .-a ^ = £ + iri P = (1 + e)a COI'iFIDENTIAL NACA ACR No.- Ll+ElO CONFIDEl:TIAri 19 and a is a cons tart depsncling on the size cf the body. On the profile (t) = 0) , equation (25) becomes r. + iY- = f 1 + e) a( cos| - i sin E ) + ( cos I + ± sin £) + c-| - e-,afG0s !,+ ! sin^) e„a(cos 2c + i sin 2£,) - e^a^cos 5c. + i sin 3|) (26) The first two terns of equation (26) r^ive the elliose > - = 11 + e + — cos i; a ( 1 + ey a 1 + € - 1 + e sin I > (27) and the remaining terms give Ax C-, - £]_ cos i - Co "03 Lii - 1-, cos 5 1 - e, s'nS- €. s:n2£- f_ sinJS. > (28) The coefficients e, , Cp , and e_ m.a/ be so determined as to yield a slight modification of the ellipse approximating a given m.eridian profile. i^or a small m.odif icatiori of the ordinates, the abscissa x/a is only slightly changed and, as an approximation, the required m.odlf Ication Ay/a m.ay therefore be determ^lned at the values of x/a for the ellipse. The ellipse to be used as a basis for the approximation should be so CONFIDEKT'^AL 20 COITFIDEriTIAL KACA ACR No. lliElO chosen that the rcjquired irod.:. i'icaticn is as small as possible. The vxlre of € oorrospondlng to a given thickiiess ratio 3/-A, whera B i^ the minor axis and A the major axis, is obtained from equation (27). Thus, ll) , _ B _ \-/:7 iax A " fr.\ .T?ax ^L 1 + c 1 + c + + c 1 + e and solution I'or c c-ives V 1 - t _ 1 (29) Ail exairiole v;ill clarlf;/ the method. In figure 7(^) is shown a meridian profile to be aporoximated. The ellipse with • e = 0.20, also shov-n in figure 7> ''■S determ.ined to be a satisfactory basic r.^rof^le for the approximation. The required modification of the ellipse is shown in figure 7(e)' For convenience in this modification, the values of -0,1 sin |, -0.1 sin 2g, and -0.1 sin 5^ are plotted against x/a as ccTTouted from equation (27). It is seen from fig- ures 7(1^) t'^ 7'<^) with equation (23^ that e, chan^^es the thickness of the profile while the symr.etry is re- tained, €o oroduces an asymi'-netry forward and rearward, and e^ increases the ordinate at tbe ends while the : center is deoressed. Inasm.uch as the main adjustm.ent required is th^3 introduction of asymmetry (fig. 7(3)), ^2 v.\ust be given some value. It is seen that a value of e = 0.1 accounts for a large part of the modifica- tion required. Further adjustment requires tlie eleva- tion of both ends while the center remains unaffected. CONFIDErJTIAL NACA ACR No. lIlEIO CONFIDEWTI/i 21 If one-half the el'jvation is accomplished with e and one-half with (.-,, the desired modification is achieved. ? Because the required ele^'&tion Ay/a 1^^ -O.O5, the values of these coefficients are e^ = 0.025 S = 0-^25 The resulting coordinates frora equations (27) and (28), shown as the first approximation in fi(i;\ire "Jia.) , are therefore + 0.025 j sin ^ - 0.1 sin 2| - O.O25 sin 5£ The failure of the first aporoj^imation near the nose of the given profile is due largely to the reduction in x/a produced, by c^. it is further evident that the forward part of the profile is mors nearly approxi- iTiated if the value of e^ ^-^ reduced from 0.10 to O.O7 and if the effect of e^ -^ reducing the value of x/a at the nose is neutralized b^/ giving c-, the \"alue 0.07a. The recultinp' profile, which is a satisfactory approxi- mation to the given profile, is sliov.n as the second approximation in figure 7'^)' -^ still better approxi- mation is obtained if the value of c-] is increased to O.lOa. The whole forward part of the given profile is then very closely a^iprox'' mated, and subs ti tutioii of the values 0.20 ep = 0.07 e^ = e^ = 0.025 ^1 - 0.10a COKFIDIiJ^TIAL 22 C0IsTID3NTI/iL KACA ACH V.o . lLEIO in equation ( c.'^) gives the required transf orination z = Z + J.lOa + '■ — - ^ Z 2 73 from which the flov iray be calculated without great diff lenity by the rethod of referonce IJ. Although the enproj^lrrate method yields the potential flow about a zlr.s.'jn soirowhat J: f f erent from the given pro- file, it is oor.sicered quite satisf&ctory for use in estimatirg lords. The approj-Jmate slnape is likely to show slight bu^nos v'hera none occur on the given profile, but the resulting pressure distribution is conservative in that it shows larger pr6Sj;ure variations than wo\''ld be ootained for a ir.ore regular profile. On account of rr.anuf acturing irregularities, this conservatism maj- be desirable. Over the re£.r of & body, moreover, the actual riojv always departs ,a^ve or less fro^ the poten- tial flov;, and little loss in accuracy raay therefore be expected from any crrall failure of the approximation in that region. Tne irethod hei>e e^nployed should not be asEurred the osme as a r:ir,-pl3 har:nonic analysis. Cor re snord in^v b-^lies in two - and three -G'r.ie'i3ional flows . - TI'~-he velocity drs'cricutlon about a two- dinenslonal shar).3 i? Iciown, a rough estimation of the velocity distriba'-ion about the body of i-evolution of v;hich it is the meridian orofile mc.y be obtained from the ratio of velocities in three-dlrrenslonal flow to those in two-diinenslonal flov; ebout corresoonding bodies. The velocity distributions about the corresoor.ding bodies - elliptical cylinders and prolate spheroids v/ith motion parallel to the major a>.es - have been calculated bj equations fb) . L^SIO confonnrl trans forrr.ati'^'n frorri a circle are used. The pressure dlstributic.is obtained by this rrethod for the Ii5"P'5^'^crt- thick circular arc on the too and for the approxiiTiately 27-'^ercont-thick circular arc on the side are shovTi in figure lit. The ores sure 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.i45 ^or the circular cylinder ^ from unpuolished data obtainec? in the NACA 0-foot high-speed tunnel) and 0.16 for the sohere (reference I?); however, a value close to zero would seem likely. T- Arre t U .- Turret E is described jn reference lb. Its Ibca^on en the fuselage is shown in figure 11(c) and the shape and dlmonsions are j^lven in figure 1^. A pressiire di st-^ibution over the central profile (linel, fi£;. 15) » with peaks larger than are expected in prac- tice, may be co^nouted by the t')"o-dimensional slooe method. The integral indicated in equation (11) Is m.ade up of three nart?., cesi^J.nated integrals I, II, aiid III, that correspond to the three divisions of the profile shown in figure 16. The inteti,ral I extending from X = to x = 2.88 inches is obtained from equa- tion (1$) with the upper limit equal to and the lower limJ.t equal to 9- . Integration and substitution of limits pive COF'IDZFTIAw IT AC A AC:?^ ITo. lUeI COIJFIDEITTIAL O CO I O i ai Vi fH + I 11 M 4) 0) -d c 0) ct; rH d p> •H 1 Ch CD r-\ o ?-, o 1 rH ■•o CD CD O CD Q) & C OJ ^ •H a Q »s C. =H .a 1— 1 1 r- CO <^ (7^ o .—1 ^, ^^ TZi nH '.Ti o H CD -P CO 1 d f: Cl •H ».— i -p m ^ ^ 1 • •• 0"J c6 ^ ^ Oj M ,-|\ r; o m 1 C3 c: CD 1 GJ vO •I-' ;> ] rH • • .H o I r-o, CD CO CO bO -^1 ■03 • a 1 a H CO ^-O •vi) o •H *-< I rH"\ C! -P 1 ^>. •H cd >7J .^^ _^ 01 K s: f-H -p bO r-\ II II CD 1 p. P r; rH r-H 05 (-1 CTJ CD o CD -P •^ L ^ i a^ t:! C fn C^ •H w C3 rH n X -p C~ CD rH O ^ p •H CD O r-' t/5 OJ V. m 3 C\J •H d) r^ ^^2 f^ pi r> A CC Ph + > CD -P rH CD Cd CD X' 0) 1 -P ~v Jh -■1 p o ro P-. CD G O CD II 03 ,o (- COF'FIDIIFTIA' 50 CCNFIDEETIAL IIACA ACR No. lI+BIO CO a.-' x: o A •H r ^ c crN«-i o- • CO J 4-3 O 1 ^ ^ --^^ 1 II E > / CD \ ^ C OJ OJ 1 ti 1 o d '' 1 -^ C^ ilj ?H M + 1 \J .H 0) : S-; p. rH rH -1 •■H CD C 00 CO CD :3 . 1 1 >> 1 1 r\) rH ■•■v ^, ^'^^ II -P > ^ ^. ^ .H c rj X r -P CO 3 1 + +3 o -P 4^ .r-l O i-H r-^ ;:: g G ■Ai OJ (D 01 CD 73 O CD 5 (D t. ■P C \ f^ )-« X" n / -P O X. y^ hOX> ^ c: o -. __._—- — — 1 Tl 0) !>s oi d to nH .H rt rH 0) M 1 1 rH M t\J .rH CD CO ^- -p .H h CO II u Ph (D H! (D C CT" M ^ Pm -P (D M ^ o vO •H CO oj X OJ II OJ O CD ra CONFIDEFTIAT-.. MCA ACR No, TJilEIO COKFID^NTTAT. 51 The integral III frcm x = k.79 incheG to X = 0.16 Inches as obtained froTn equation (11) with upper and lower limit3 of 3.l6 and q..79> rsspec tlvel.y , and ^jith dy/dx = -O.35L.9 is T-r-T = ^13ii2 . „,. -^ - 4-7^ "^ S.li X - _) . J. o Then, for ;: < b.L.S inches, + TI + TII and, for x > 6.L& inches. AV , , -- = 1(a) + II + ITT Calculated values ha", e been converted to -oressure coef- ficients, £iv6. the r'isulting distribution has been plot-^ed as the solid line in fi^^ure lo. The coeffi- cien-':& taon ootained ere considered liirdtin^, values and i--e a;'sumeJ £uf f _•' ciently hiji-b in absolute value to sllovj .f r^ cOiT'oressiDil J ty effects uo to a ''ach number of 0.']0 and remain conservative. From the calculated two-dinensionel velocity dis- tribution, the velo:;i '.ies abo at the corresoonding body of revolution v/ere estimated by the ratio of velocities in three-dimensional flow to those in tv;o-dimensional flov7 as gT ven for ellipses and prolate soheroids in figure 9" The corresponding pressuT-e coefficients are shown as the dashed curve In figure I6. The shape of this turret is betv.-een the two-dimensional shape and the body of revolution and, consequently, the measured pressures lie between the estim.ated values for the pro- file and the values estimated for the body of revolution. Coc'^pit canooy ." "i.d g un t u rre t on Frew s te r SE2 A-1 air- pl a neT~~The s rii"T?"e"s ~a"hd~"l o c a t i ons r"~che cockoit canoioy and" gun turrets on the fuselage of the Brewster SB2A-1 airplane are shown in figure 17. Tvi/o alternative gun turrets have been suggested for this air.Tlane. The top COIvTFTDZNTIA", 52 COixFIDli TIAT. NAG A ACR No. Li;7ilG shape of the ''"axson turret approicnr ates an o'.^late spheroid moving normal to the polar a;-:is. The other turret is spherlca] in shaoe. The theoretical velocity distributions are computed first for the turret shapes slone vitliout interference. The meridian profile of the "''axson turret is show-n ^vith r>ertinent dimensions in figure iS. Inasmuch as the shape is s^'Tnmetrical , the pressure dl? tribiition is s;T,iiret-^'.cal from front to bad: and only one-half the half profile need be considered. The axes of fip^ure' It are arran^^ed to correspond vith thoss of figure The turret nrofile is seen to be only slightly different from the ellipse with thickness ratio b/a = 0.6?. The difference is shown as the short-ciash line plotted alori^ the y-axis. This dif- ference can be approxlm.ated by a circular arc; and the turret profile shape thus can be m.ors nearly approximated by adding to the ellipse in the region indicated the half thickness of the double circular arc of thickness ratio t = O.lli. The corresponding velocity ratio vAq is obtained by directly superposing the increments AV/V , as found for the circular arc b.v inter-colation in fi.«j- ure Z, on the values f-f— over the ellic^tical oro- b/a = \' Vco=0 file of the oblate snherold. 'Vi th tion ("17) pives to - 0.91 and the velocity the elliptical section in the xy-plane is gi equation (20) for values of -^l . The comout is indicated in the following table; .07, equa- ratio over ven 05- ation form |i jV/Vg for! ,'/a oblate ! AV/V.^ for li^-oercent spheroid; ci rcular arc Y/V^ P = 1 1 .h^ .80 1 17 1 .52 1 .59 1 .50 1 • 3b 1 ■ 3^ & •15 .oe . . 00 ■ 71+ .95 ■ .02 ..93; CCivTTu?NTTAI NACA i\CR No, COFFIDEKTIaL 55 The velocity increwents AAZ/Vq obtained by the tv-o- diinensional method are likely to be soirewhat lar'ge, and soine sir^all adjustment in the corresoonc'ln3 pressure coef- ficients "must therefore be made. The pressure coeffi- cients v'ith these and other adjuptments to be discussed later are plotted along the turret (line 1, fig. 19)' Around the circular rirn of ibe turret, velocities somev/hat higher than those about the rini of the oblate spheroid may be expected because of the deoarture of the turret from the true spheroidal shape and because of interference from, the cylindrical sides of the turret extending down onto the fusela(3e. For use in the esti- m.ation, the velocity -^ircjnd the r: m of the oblate spheroid is computed. ^"/ith i ,^ ~ 0.91, the velocity di s t ributi on f 7/^^. ) . as a function of table: ni . is obtained from equation (lo) ° rim (jc and is shov;n in the following Again because of s^rmmetry, this pressure distribution holds for negative values of y/a, that is, for co between 90'^^ and l&O'^. For the spherical turret, shown in profile in figure 20, the theoretical velocity distribution over the meridian lyi.ng in the olane vith the forward velocity -.vas calculated from equation (l6) , and the pressure coeffi- cients were obtained by equation '^ The values of y/a are obtained from y/a - cos 9, where again y is taken in the direction of motion. CONI ^ IvT'i^T "^^ HTIA' $i| CGNFIDEKTIAI. NACA ACR No. lI+EIC For the cockpit canopy, the pressures over the nose and the general pressure distribution for'vard oT sta- tion 121 'figs. 17, l^^', and 21) were estiriated from the data for the u-ij-5 windshield given in figure 22 of ref- erence 1. The antrie bebveen the nose piece and the hood vas Up'~' for the SE2A-1 windshield as compared with i;3° for the 8-I1-5 windshield; otherwise, the two wind- shields appeared slriilar. The data for a ■■'ach rumber of atout 0.70 \"ere used, out tne negative pressure peek was elevated slightly to allov; for ocnservatlsi-n in regard to the soraewhat sharper nose angle of the S52A-1 v/ind- shield. The use of this pressure distribution involves the assumption that the difference betwejn v/lng and fuse- lage interferonce in the two cases (airplane and rriodul tested) is negligible. This fcissumpticn Is reasonable because the wing and fuselage cannot differ greatly in the two cases and because the interference velocities ere relatively small. The bumo in the press\ire-distributlon curve about station \\Pi is intended to represent the slight discon- tinuity at the rear of the sliding iiatch cover. The dimensional data available do not oertrit the exact detprraination of the shape of the offset and, even if the shape v;ere known, the calculated pressure distribution would be of questionable accuracy. The magnitude of the bomp above thu general oressure distribution v.-as taken Instead from, the recults of tests of a cockpit canopy similar to that of the 332 A-1 airplane. The theoretical pressure distributions for the turret shapes are raodified by interference, for which certain assumptions must be made. The turret is too close to the canopy and too large in relation to it for a read;, estimate to be m.ade of the effect of the canopy on the turret oressures; because the canopy is situated entirely ahead of the turret, however, the assumption can safely be made that the i^nly effect of the canopy is to lower the velocities over the turret. The shape of the fuselage in the region of the turret is such that the induced velocities must be sr.all and in addition it m.ay be assam<--d that, because the ■A"ing is ahead of and not very close to the turret, the induced velocities due to the wing tend to be canceled by the induced velocities from the canopy. That these assu:r.ptions are reasonable is indicated by figure 22 of reference 1, in which the pres- sui'e coefficients, behind the windshield with the tall and in the presence of wing and fuselage approach zero. If the canopy of the SB2A-1 airplane were faired out with a similar tail in the rear, moi-eovei", the turret CONFTD^MTJAL NACA ACR No. lUeIO CONFTDEKTIAL 35 v/ould appear very sirrllar to the half-sphere or half- spheroid on the tail. The flow over the part of the gun turret not thereby covered should be affected only slightly b7f 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, respectlA^ely , for which the theoretical distributions are given in the first part of this section. Over the section indicated by line 3 ^^^ fig- ures 17j 19> s^^d 20, either turret contour is charac- terized by a circulai-arc profile of about ^'^-percent thickness ratio superposed on the surface of the fuse- lage. Figure 2 gives the velocity distribution, v;hich may be used v;ith equation (2) to calculate the pres- sure distribution. Over the rim (line 2, figs. 1?, 19, and 20), the velocities must lie s-om.e\i'here betv.'een those over the side (line J) and these over the top (line 1). They are therefore taken to lie beti;;een the theoretical velocities over the rim. of the oblate spheroid and those estimated for line 5, and the peak is assum.ed to be about the same as the theoretical peak for the sphere. The resulting curve is quite sim.ilar to that for the sphere and is taken to be the sam.e for both turrets . The pressures at line k 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 one-half 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 com.parison in figures 3 9 and 20 and are considered limiting values for low and moderate Mach numbers. r'o adjustment of the pressure peaks has been miade for the effect of compressibility because, for such blunt bodies, at least up to a Mach num.ber of 0.70* the CONFIDENTIAL 36 CONFIDFT'ITTAL r.'.CA ACR Wo. lLeIO conservatism of the nethods used is assuried sufficient to cover the changes. OoF^preosibill ty may, however, cause the separation point to move forv/ard and i.hus lower the negative peaVs and decrease the pressure oehind the turrets. The negative pressure peaks therefore ma;; be broadened backward, and some account of this effect has been taken in "oroader.mg the peaks in figures 1? and 20. In no cac-e, hovover, st least up to a ''ach nuinoer of O.'JO, can the oressure on the rear of the turret decrease below the negative oressure peak that v;ould be obtained in potential flow at the same T.«ach number. The negative pressure ceak in figures IQ and 20 is thr.s indicated as the limit of the oressure on the rear of the turrets. The development of the boundary layer o'ver the canopy ahead of the turret and seoaratlon in the rear tend to nrevent either oositive or negative pea'-^s in the pressure distribution fron being as great as predicced; in this resoect, the estiration is therefore conservative. Average values of pressures obtained over the gun turret of the 3re\vster XSb2A-l ?.irolane in flight at sooeds below 22^ miles oar hour (unnublished) are ore- sented for comparison in figure 19. For obtaining loads, the estiiration compares satisfactorily with the measured values though, for the top of the turret, it appears to be unconservative . Froi.-: the data available, however, the tiu-ret on the X332A-1 airplane appears to pr^-^ject hasher above the canopy than was assumed in the estimations and larger oressure peaks might therefore be expected. The irregularities in the measured pres- sure distribution may be caused by the ribs and other irre polarities on the surface. Severe separation is indicated behind this turret, where the pressure recovery is little greater than that behind the circular cylinder. Lo wer gun tur ret on Douglas XS3-2D-lairola ne. - As a fur'EFer exampTe that involves "the method of distribu- tion of doublets along the axis of a body of revolution moving norm.al to Its axis, the pressure distribution over the lower gun turret of the Douglas XS3-2D-1 air- T)lane is estimated. The form and location of this gun turret are shown in figure 21. The pressure distribu- tion over the central profile (line 1, figs. 21 and 22) Is obtained and the distributions over other lines from front to back ere assumed. to be quite similar. ^or a shat)e that does not differ too greatly from a body of revolution, this assumption is reasonable and has in other cases been fo-und to agree v/ell vith experiment. (See reference 1, for instance.) confidf:ntiat, NAG A ACR ^■^o. LU^IC COFFi^DEKTTaL 37 The turret v>?c,s divided for computational ourposes into front and rear jarts. The pressures were assumed to be the spme as if the tui^ret were a half-tody on a plane containing the surface of the fuselage i^ranediately forward of and to the rear of the turret, with a strs-im veloc? ty parallel to the plans. As shown in figure 25, the forv.-ard part of the turret profile can he approxi- mated hj an arc of the parabola ^- o.7hh. ^(i - ^) C ' ' c \ c/ V 1 th substitution of the slope <^ ( y/c ) d{y:/c) = o.Yli - 1 . Uub— in equation (11), th^-- velocity distribution AV ^ 1 (, . 7k, log shovm in figure 23 is easily obtaineci The rear of the turret v.'as ap-^roximate quarter-body of revolution with polar axis the stream in the horizontal direction and to the rirht and to the left. Velocity di was computed by the m.ethod of distributing along the polar axis normal to the flov. erence 12. ) The cross section normal to t the central profile that is the approximati. part of line 1 along the stream direction, quired dimensions are shoy/n in figure 2ij.. of constant strength ere indicated oy the s lines along the axis; and, from, equation f^ ence 12, the potential for one doublet is d by a normal to w i t h s ymm.e try stributi on doublets (See ref- he s t re am , on to the rear and the re- The doublets hort , heavy ) of refer- - -^ (cos 6'' - cos 9') cos ^ lirrr GOI^FIDEFTI AL 58 CONFTDFFTIAT NACA AO^ r~ LIjEIO 3y symmetry, the velocity on the surface at 1=0 must lie along the central profile (fig. 2ii(b)) in the plane of the stream velocity. Because the largest and smallest velocities on the body occur along this profile, this distri' button is of greatest interest. The velocity due to one doublet, the i doublet, is AV, fees 9^" - cos 9. '; sin Reference 12 shows that as an approximation the doublet intensity jji^ can be v.-ritter. ti. = 2rr^2v^.^ The velocity increments AV. are oarallel and, with the substitution for a^ , can be added to give (cos 9j^ ' - cos 9j_'') sin ^ The com.-oonent of the stream velocity V,^ in the direction of the profile is Vq sin and the total velocity is therefore '\m^ cos 9,. ' - cos 9 . " ) sin ^ From the dim.ensions given in fijure 2L, the com- putation of fiV/Vp is indicated as follows: COyFTDEFTTAL KACA AOR No, LiiFlO COKFIDHNTIAL 39 & co: cus 9." fees 9j ' - cos 9,- ") -3 -2 .1 J- 1 C . 5j.7 • 779 loOOO l.OOQ 1.000 .77'^ • 5^7 :S 0.717 )°2 J.C5 ,11.5 -.1L.5 -,li03 0.502 . Loj .il>5 -0-2 -.717 o.oJ'^U .290 .2S8 .1II7 .oJ.jk / (f^) X^-'^ -i' " ^'^^ ^^"'^ ^ I.1S7 The velocity is therefcr-3 •which seems reasonable in comoarison with the value 1.5 sin for the sphere. The oosition along the streain direction x at which the velocity occurs is obtained v.'lth sm 5f. From the velocity iiistributions thus calculated for the front and rear portions of the turret, the corresoonding oressure distributions were obtained by equation (2) and were then joined at the center to give the solid line in figure 22. Some adjustment of pres- sures v/as necessary to effect this junction. pressure (line 2, fig T^or the turret in the guns-absam position, the distribution over the cylindrical surface 21) was estimated by assuming a circular cylinder projecting from, a wall. The dimensions are such that cos 9 = 0.1'52. Substitution of this value in equation (23) gives the velocity on the surface of the C3'"lindrical gun tarret near the fuselage. The pressures are thereby determined and are shown as the dashed l:.ne in figure 22. GOrriDFNTIAL iiO CONFTDFNTTi.L TAC^ ACP No. Li|El ,o The remarks conoernina; the ef facts of irterference, boundary 3.ayer, and sep-^ration on the SB2 4-1 turret also apoly to the XS3-2D-1 turret. lor the reasons discussed in reference to the SB2A-1 airplane, no compressibilitj correction has been applied. The turret does not project from the fuselage so Ter as v^as Pss'u^ied in the calcula- tions. }-or this reason, the estiirated pressures should be riiore conservative than voald otherwise have been the case. iJo exoer5inentel data are ava:^'lable for comparison. Analysis and Discussion The agreement oetv.sen estir^cted r.nd measured pres- sures generally is better than had been oxpected and it apr)e?rs that, if allo-'ance is i.inde foi' tne effects of interference and separation, calculations based en the potential -flow theory .^j-ve a satisfactory indication of tho msximurr loads. The f^greenert is good for the 'ai-tin and Faxson turrets, viiicn approach forms for which the potential flow can bs a':;curately calculated. In other cases, the act^ial of^essures iray depart widely from the theoretical values. Tne reasons for this divergence from the calculated values - which are connected ■'jvith departure cf the shares from those assumed, v;ith com- pressibili tj:' effects, with Interference, and ".■1th sepa- ration and other boundary-layer effects - are now dis- cussed. The experimental data available are analyzed and com-oared vith theoretical values to determine, at least qualitatively, the modifications that should be made to calculated pres-^ure distributions in order tr approximate m.ore closely the actual values. The appli- cation of pressure nistributions to the estimation of loads is briefly considered. The following- additional figures are introduce -f: Pressure data obtained in the "TACA 8-foot high- speed tunnel 'unpublished^ on ar)pro:Mimately hem.i spherical turrets at different locations on a fuselage are shov/n In figure 25 • The orifices at which these pressure data were obtained were located at t^.e tops of turrets C, D, and E and at ^he side of turret C, where velocities approachTng tho Tiiaxim:um should occur. The variation of pressure coefficient P with stream, "ac'; number !! is compared with the heoretical variation ^^^iven by the factor —-zz ^ , ■ . In figures 2^ to 2", the curve of /= 1 - ^/T^ critical pressure coefficient P^,^, - that is, the CONFJDEITTIAL ACH No. Ll+ElO CONFIDENTIAL kl pressure coefficient corra spending outside the 'boundar:/ Isyer to the attainrnent of the loc&l speed of sound - is sho'."n to indicate the critical speeds of the turrets. The critical Mach nuri.ber ^:1^^ is the i.!ach nurifoer at v^hich the pressure-coefficient curve intersects the P^^-curve.' Figure 26 shovs a comparison between the pressures at the top of two spherical-seginent turrets A and D, both in tlie forward location of turret A as sho^n in figure ll^b) and projecting different portions of the radius above the fuselage. These pressures are compared with the theo- retical pressures for the sphere including the variation i,"dth Mach nuirber given by the factor • /l j^:2 - ( be twee n pres- A comparison is given in figure sure coef f -^ ci ents at various positions on the faired turret E. of reference l6 and those on a thicker faired turret F, both in the location of turret B shown in figure ll''c'i. The variation v:i th I'.Iach number is shown and compared with the theoretical variation. Figure 23, for which the data are taken from ref- erence 1, shows the pressure change with i'.lach number at four different points on vnindshlelds representing bodies of three different types; the J-l-i, which has a blunt tail: the 7~3-k, which is characterised "oj a sharp corner at the nose and by a long, faired t'^til : and the X-1 , v;hich is well streamlined. De'Parture from f orms fo r v;h- ch potential flow can be calculated .- The~s'hape of s protuberance is usually such that the potential flow cannot be exactly computed. Experiment is therefore needed to determine the effect of systematic departure from forms for which the poten- tial flov; is calculable, such as variation in sep.m.ent of a sphere from the half-body or variation in thickness of a body. The effect of these variations is indicated in figures 26 and 27- The oressures 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. CONFIDENTIAL k2 COHFIDENTT'.'J. NaCA ACFc No. 1,14.210 Figures 25 and 26 indicate that, unless considerable inter- ference is present, the liTniting pressure on a spherical se.'tment less than a hemisphere r.ay be ta>.CA '.OR No. lUEIC v-ell-f aired tail end a sharp corner betveen tVie v/ird- shield and the liood, the pressure at point d agrees with the theoretical variation, the oressure at noint c showrj the effect of thi cleaning boundary* layer, and the negative pressure coefficients at points a and b a short distince behind the oolnt of separation decrease before they ettrt to rise wi ch ••'ach mimber. On the 3~1~1 body, v'hich has a blunt tail, the pressures at ooints b and d change about as theoretically predicted, the pres- sure at point a soirewhat alier.d of the separation point fails for tiie mnst prrt to decrea.^e as fast as indicated by the theory, nnc? the pres.'^ure at point c on thu tall decreases greatly behind the point at which separation probably occurs. The effect on pressure coefficients of change in ^■'ach number is seen to be different for different ooints end for dif ferment bodies. For roughly similar shaoes in sirrdlar locations, the ccrresnonding varia- tions v'ith T>'ach number may be assur.ed. The effect of compressibility en the pressures over a orotube ranee obvic>u3ly depends on the Reynolds n\iF-ber of the protuberance and of the body on which it is placed, inasmuch as the t;;v-pe of flow must be a func- tion of the Reynolds number. Compressibility effects also depend on the relative size of the protuberar:ce in relation to the body on which it is placed, because Interference and boundary-layer effects are different for different relative dimensions. From the exoerimental data, the following principles that are useful in a qualitative esti:rxation of the change of pressure coefficient with ■■•'ach number may be derived: (1) Over the ^''-''^'^'t'Sr part of well-faired bod:es that are not too thick and are relatively free fror.i boundary -layer and velocity interference from other bodies, the theoretical change of pressure coefficient with ^-"ach n'omber mey be ass'aned. The factor 1 ., .. —r exoresses the chan?;e with sufficient accuracy. The negative pressure peaks may be ass^omed to increase somewhat more rapidly than this factor indicates. CONFIDENTIAL •iCft AOR 7>To. lUeio confidential k5 (2) Ceparation of the flow, which ^e^.ularl7r occurs froxn the veer of blunt forns - such as the sphere and the circular cylinder - and to a less degree fror. less blunt bodies. Is li>ely to becone more severe with in- crease in ''Tach number. The resulting"; change in the effective shape of the body may x^roduce an increase (as compared with the tn.. "^retical decrease"! of the pressure coefficients near the beginning of the separated region and a decrease 'more-negative pressure coefficients) near the tail. Fv^.r- on moderately thin faired bodies, somethinp; of this effect mav ao-oear-; whereas, on bodies with short tails, a large decrease in the negative pres- sure coefficients just forvrard of the tail and a con- siderable increase in the negative pressure coefficients at the rear may occur. (3) Interference that increases the velocities is likely to cause a further increase in negative pressure coefficients with '"ach number, whereas interference that decreases the velocities is likely to have the opoosite effect. (jj.) If any considerable part of the protuberance lies within the bouiidar;/ la^/er nroduced on the body for- ward of the protuberance, the chcnge in pressure coeffi- cient with Tv'^ach number is likely to be different from the change that would occur if no boundary layer existed. The pressure peaks may be sm_aller and separation effects may be introduced. (5) If a critical Reynolds number occurs within the Fach number range or if a considerable change in pressure coefficient with Reynolds num.ber is otherwise to be exnected, the resulting effect on the change in presEu.re coefficient with T^ach number m^ust be accounted for. The foregoing discussion holds for '"ach n-rmbers less than the critical. Above the critical '"ach number, still less is known about the pressures to be expected. Outside the region of supersonic ^speeds , the pressure change is much the sam.e as at subcritical yach num.bers. The supersonic region commonly spreads rear- ward as the '-'ach namler is increased, and the negative pressure oeak usually increases and broadens toward the rear, Ks, the shoe'-: wave develops with its large un- favorpble pressure gradient, sepc?i'ation is likely to occur and produce the pressure changes already discussed. COFF fDENTIAL ho CONFIDENTIAL NACA AC?. No. lUfI The negative pressure coefficients cannot in any case continue indefinitely to increase with Llach numbei-*, and a tendency to decrease at the highest Mach nur.bers is already apoarent in some of the curves in flfrures 25 and 26. An absolute lirat irrposec? by the condition that the local static pressure be sero is given oy 2 (-F)w,„ = • '^^e exToerimertal data available indi- ^ 'max ^ cate a limit less than given by this relation. Up to a ^ach numoer of O.JQ, howover, the changes in pressure coefficients likely to be encountered on protuberances may be estimated by the methods herein presented. In order to estimate with quantitative accuracy the effect of compressibility on ■•"he pressure distribu- tions ever protuberances, extensive systematic experi- mentation is necessary. Interference . - '^or cases in which the interff^rence cannot be expressed by simoly adding in the induced velocities due to the interfering bodies, an estiiration at least qualitatively?- correct may still be obtained. It is reasonably certain, for instance, that a canopy in front of a gun turret can have only the effect of reducing the velocities and ther^^^by the pressure peaks. Figure 25 illustrates the difference in inter- ference effects for turrets in different locations on the fuselage and for different angles of attack of the wing and fuselage. Turret C is subject to a reduction in velocity due to the hum.p in the fuselage immediately behind it and, in addition, the accompanying unfavorable pressure gradient may be expected to precipitate earlier separation than v.-oulc otherwise occur. As seen in fig- ure 25, the negative pressure coefficients on the top of tu-"ret -were, m.uch ?i allei' than on turret D, v/hich was located in a region of increased velocity due to both v;lng and fuselage. Turret E is so located that the velocity Interference should be small but, \K±th 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 appreciable. A rough estimate of the interference could be obtained by adding the induced velocities due to the wing and fuselage as in reference 1. COFFIDE-TTIAL TAC/: AGE Fo. Lli.^10 COFFIDI^IITIAL I4.7 The velocity interference on the central part of a A"' fuselage coinironly amounts to about — - 0.10. A rou.'.:h V . "^ estimate of the induced velocity can be obtained by fitting- an equivalent prolate spheroid to the fuselage as described in the section entitled "T'ethods" and in reference 1. mv [■he wing is approximately a two-dimensional form and thixs m.ay cause relatively large iiiterfering velocities. If a protuberance is located ?::ear the velocity peak on a -iving, therefore, the pressures may be- widely different from those on the sarre protuberance not subject to the interference: in addition, the change in pressure with change in Iv'ach number or v;ing angle of attack ma-; be lar£.e. o^ It ma^? be necessary in some cases to determine the interference effect oi' a nrotuberance on the loads over surroiinding surfaces. The induced velocities generally decrease very rapidly with increase in distance from, the surface. The decrease of the -oeav velocity Increrrent is 3hov;n for a wing and for prolate spheroids in fig- ures 56 and 37> respectively, of reference 1. The methods given in the appendix of leference 1 can be u.sed to estimate the interference due to a orotuberance. If an equivalent prolate snheroid can be fitted to the protuberance, the maximum, interference velocities can be estimated from figure 57 '^■^' reference 1. If more detailed information is needed, however, a velocity- contour chart such as that of figure 35 ^-^ reference 1 can be creoared for a body app^oxim^atlng the protube- rance in Shane. For si.mple shapes, such as the sphere or oblate soheroid, v-docity contours are easily obtained from the potential theory. Additional experiment is needed to permit very accurate cstimiates of the effects of interference. Surface irregularities.- The theoretical pressure dis tribut^.'orri are c al cul at e^d for smiooth bodis.^, but in practice the surface is usually broken by ribs, joints, waves, or other irregularities; as a result, oeaks and valleys appear in the presaure-di stribution curve. Such an irregular pressure distribution is {;;,iven by the ex-oerimental data shown in figure 1^. The most obvious surface irregularities in this case were the ribs of the turret. Estimated oressure distributions should be made sufficiently consorvative to allow for the effects of these irregularities. GOllFTDEKTTAL U.Q COlv'FTDEliTTAT. NACA ACR Ko. LiiElO Sepa ration ar.d -pressure be hind a protu ber ance. - Tost p re t'TJer anTelT are PuTf.-.cTintly 'blm^t' at' the tail that the flow fails to some extent to follow the sur- face. This senarstlon of the flow is aggravated by the boundary la^z-er 'jl'3veloDorl on the siirface forward cf the protuberance "/ith the result that separation becomes more severe as the protuberance is placed far- ther beck froir the no^e of the fuselage or other body on which it is sltuat -d. Altho^igh separation does not usually Increase the severity of the Icadr , it greatly increases the drag of the protuberance and should therefore be prevented by a fairing if conveniently possible. In the case of gi.in turi'ets, a ir.3thod t?iat miuht be used while the advantages of syr.me'' rical turrets are retained 's to install retractable faii-in^is behind the turrets. The effect of fairing on separation is shown in a com- parison of the experimental data given in fii;;ures 12, ill, 16, and 19. Th.;; use of faired turrets appears to give little advantage over syn-iinetrical turrets unless the fairing is sufficient to prevent any considerable separation. If the flow becomes unsyr.imetrical when the turret is rotated from the stowed position, local loads may be substantially increased. If sharp corners are thus exposed, the pressures may be impos- sible to estimate and the oeaV: negative pressures may become very high. At sharo outside corners, the flow separates either completely or with a bubble about which the flow later closes in. A method of estimating the pressures near sharo corners has been suggested in the section entitled "Estimation by Comoarison. " It is pointed out in ref- erence 1 on oages 12 and IJ that outside corners with radii of curvatures less than apnroxi-ratel" 25 percent of the heij^ht of the orotuberanca m.ay be considered sharp. Separation changes the effective shape of a body in such a vay that th.^ pressure oea'-fs influenced by the separation are reduced and the pressure on the rear of the original form, is decreased. At the rear cf the faired turret of figure 16, therefore , the oressure coefficient is posi+^ive; whereas, on the rear of the m.ore severe turret of figure l/i, for which a greater pressure recovery Is indicated, separation has reduced the pressure coeffic. ent to zero. ' Behind the still COFFTDFNTIAT. No. LL.FIC CCKFID2NTIAL I1.9 more severe forms of /'Igures 12 and .L"^, the pressure coefficient?^ at the rear are n^3p^ative. Fror.i tLese e:>'perlTrental data and from the known vslaes of the pressure coe:fflcient on the rear cf spheres and cir- cular cylip.cers, a rough estimate of the res sure s behind protuberances c^n be made; but it Ir. evident that, in order to Judge accurately whether separation vdll occur and v;hat :.)7''£ssures will then exist, much systeifatic experimentation is required. The effect of ^ornpressibil Lty in crscipitat ing or increasing the sever"! Ly of separation has already been noted. E sti'^iation of lopd s.- From the pressure distribu- tions, estirratjd or measured, the loads can be determined provided the internal pressures are known. The inteiTial-pressure coefficient may be positive if the pro- tuberance is vented to a high-pressure region, as about the nose or tail of the fuselage, but is more likelj to be negative because leaks regulai'ly occur to the low- pressure region :'.n v;hi ch a protuberance is usually placed, such as leaks aro'Jind the sliding canopy, through othei'' cracks, or through holes in the surface. Because the external pressures vary with angle of attack or the positions of the leaks change with angle of gun turret, the internal pressures also vary. Since negative pre,; .sure coefficients up to P =^ -O.LO often occur on a fuselag; , similar r)""essures may be expected inside canopies or gun turrets. In low-speed tests of the Grumman XT3F-1 airolane (unpublished), for example, internal-pressure coefficients of -O.I5 were found in the canooy V'hile, in the s;^mimetrical T'artin turret tested, the pressure coefficient varied, from -0.02 to -0.11 depending on the angular position of the turret and angle of attack of the airplane; similarly, in the unsymm.etrical Grumman turret with which the air- plane was originally equipped, the internal -pressure coefficient varied between and -0.06. For the Brewster XSB2A-1 airolano in flight ''unoublished) , internal pressures in the gun turret varied from P = -0.20 to P = -O.3O; inside the cockpit canopy of the SB2A-i4 airplane, very low pressure coefficients of -0.30 to -O.iiO were found. Because of differences in leakage, the Internal orsssures are likely to be differ- ent from tim.e to time, even for the same airplane, unless the OOITFTDEFTTAL 50 CCNFTDFNTJAL NAG A AGP No. lIlEIO enclosures are seale^'. It is evident that, because of low internal pressure??. Jettison inay be impossible even if a protuberance is derignad to be released. An Increase of internr.l pressure could be realized by ventimi to the tail of the fuselage. ■•t:. CCNGLTTSIOrlS 1. By the inethods 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 ootential-flovs' theory give a satisfactory indication of the maximum pressures to be expected. 5. For shaoes about which the potential flcv is not exactly calculable, the oressures may be estimated by various aoproximate methods presented or by com- parison v^'ith exoeriment. k. Compressibility and interference effects and the effects of deoarture from, potential flow, including separation, 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 the external-pressure dis- tributior must be known. 6. Further experimental investigation is needed to determine the effects of interference, compressibility, separation, and systematic changes in form. Langley t'emor^ al Aeronautical Laboratory, Matlonal Advisory Committee for Aeronautics, T",angley Field, Va. CONFIDENTIAL NACA ACR No. lIlFIO CONFTDUKTI AL 51 RTPZHEKCES 1, Delano, Jaires B. _ and Wright, Ray H. t Investigation of Dras and iressure Distribution of ■Windshields at High Speeds. NACA ARK, Jan. 19ii2. 2, frandtl, L. : General Considerations on the Flov/ of Conpres'sible Fluids, NACA Ti'.l No. 8C5, 1956. 5. von Fa^rmari, Th. : Compressibility Effects in Aercdynairics . Jour. Aero. 3oi., vol. 8, no. Q, July 19)il, pp. 557-356 = h- von Doenhoff, Albert E. : A Method of Rapidly Esti- mating the Position of the Laminar Separation Point. NACA TN No. 67I , 1953. 5. von Doenhoff, Albert E. , and-Tetervin, Neal: Determination of General Relations for the Behavior of Turbulent Boundary Layers. NACA ACR No. 5G15 , 19l:.5. 6. Theodorsen, T. , and G&rriokj I.E,; General Potential Theory' of Arbitrary ^ring Sections. NACA Rep. No. bf^Z , 1935. 7^ Jones, Robert T. , and Cohen, Doris: A Graphical Method of Deterinining Pressure Distribution in Two -Dimensional Flow.' NACA Rep. No. 722, 19^1. 8. Zahi;j. A. P.: Flow and Drag lorraulas for Simole Quadrics. NAC ,-. Rep. No. 255, 1927 , 9. Glauert, H. : A Generalised Tyoe of Joukowski Aerofoil. R. 5'- TvV No. 911, British A.R. C, 192ij,. 10. Goldstein, S. : A Theory of Aerofoils of Small ThicknesvS. Fart I. Velocity Distributions for Sjirmetrical Aerofoils. 58014., Ae . 1976 (revised), British A.R.C., IV'ay ih , i9ii2. 11. Lamb, Horace: Hydrodynamics. Sixth ed., Cambridge Univ. Press, 1952, pars. I07 and 109, pp. li;i.2-l[^6. 12. von Karrr.a'n, Th. : Calculation of Pressure Distri- bution on Airship Hulls. NACA TM No. yjk, 1950. CONFIDENTIAL 52 CONFIDENTIAL NACA ACH No. Li^ElO 15^ Kaplan, Cerl: On a New J.fethod for Calculating the lotentlal p] ow past a Body of Revolution. TTACA AP.R, July 19ii2. lli. Munk, 119.7. M. : Fluid Ivleohanics , Ft. II. Vol. I of /.erod;,nnPTnio T\eory, div. C,W. P'. Durand , ed. , Juliu.3 Springer (Berlin), I93I.'.. Fluid iiolion vith Arcial Syn^metry, ch. V, sec. 6, p. ^^9. Ellipsoid with Three Unequal Axes, ch. VIII, sees. 1-5, pp. 293-502. 15. Young, D. T. , and Davis, E. L. : Drag and Pressure Distribution of Gun Turrets on a Model of the B-23 Fuselage. Five-Foot '"'ind Tunnel Test No. JCiC. A.C.T.F. No. i'753, !.'ateriel Cominand, Army Air Forces, April 10, 19ii2. 16. y.attson. Axel T. ; Tests of a Large Spherical Turret and a r'cdif^ed Turret on a Tynical Bomber Fuselage. KACA aRR, Oct. lQii2. 17. Fluid '.iotion Panel of the Aeronautical Research Cor^Tii^tee and Others: Modern Developments in Fluid DynaiTiics. Vols. I and II. S, Goldstein, ed., Oxford it the Clarendon Press, 1938- COKFTDENTTAI, NAPA ACR No. L4E10 Fig. 1 \ «0 « ^0 Q. I. • V ^1 ?> i« ■£ «. «^l :i .-jf NACA ACR Nc. L4E10 Fig. ?. ■ ^ r-i ■'^ u k ^ > yy f/ ^ f^ / / /Eu^ ^/ •Si u .^ u 1 .s ■B 1 ■B 1 / ^ Jf u : 1 //I / '/ 'nil >i / //^ H ll / 1 f/^ jl Z Ui ^ ~^' 1 1- l-_ «i; Jl I ii ; 1 ^ f 1 y r V 1 ^. (/ 7 1 — 1 wi 1 N , _j K, — N • l_L "i \ O fl ^j ^ • O II ■x CJ) ^ ^ >» V" ^ So to \ I \\ \ \ 1 \V \ ] 1 I v \ \\ — \ \} CONFIDENTIA \' v^ \\ \ M \ \ v\ \\u \ \ "^^V \ ^ "^ N N, \\ n; i^ \ V *^ i^ ^ \v ^ ^ fr^a k'<^ k. ==3— ^ 00 I Q) «0 vo t ^) M A/a7 ''4.UBIOI^J.SOD ^U3UJ3JOU/-^^IOO/3/] S (0 D I o :j • o C •I .<0iJ :^ •I ^-y ^- ^//.' * Ol s in Z€ 1 ijtjt JKSQJ TO tSllip 1 1 1 1 ■»«£ 1 -Tel CONFIDENTIAL NATIONAL ADVISORY COMMITTEE FOIl AERONAUTICS. -Z.0 -1.6 -i.z -a -.'f- o ■a I.z. /.6 Z.O 2.4- F'/pure 7. - Defefminafi'on of Me complex -function fon fhe con formal -frans-formaHon of a circle info a pro-file approxifnahhg fhe meridian .section of a foody of rei^oluffon - NACA ACR No. L4E10 Fii o ••^ u z.o 1.6 1.2. .6 -t 1 :oN FiDENriAL 1 t O.I .1 -A -^ ■^ ^ r, .6 3 1 r- ■ — - "-v ^ / .8 A ^ \- — --' ■ " '■ ~^— -- ' " / .^ 4. Jf^ _'^r_ — — — — — — — '~^. iy^ ^ ?^ // . '^ .- -4- — — — — — — .~T T ^- y ^ 1 V. T\A/o dimensional Three dimen ziona / >l 1 1 1 1 1 1 1 M 1 \ {a) Ellipfic0l cylinders cine/ trtoridian profiles of prolai-e Spheroids . z.o NATIONAL ADVISORY COMMITTEE F0« AEBON«UTICS. '(t>) Appraximare cincu/ar-arc bymmefrical airfoils ai-)d meridian profiles of bodies of revolQfion ■ I I I I I I I I I I ' I i I r!i!*J'-!r(!-!\! ri/ii I .4- .5 .6 .7 .8 I.O F^ig<-ire &.- Cornparison of cctlcula-f-ed \/e/ocii-y d 1st rihuf fans oi/en -f-i^o - d"rtens7on<3/ ShapBS v^ith those oi^er -the correspond I'n^ bodi&% of re^^a/uf/on. NACA ACR No. L4E1C Fig. 9 CONFIDENTIAL /.o \/zo .9 £ .7 •"o \ 1 1 i NATIONAL 1 1 ADVISORY 1 1 \ \ ( :ommittee for aeronautics. \ \ \ s. s N ■^ ^ ■^ ,^ "^ - ^ ___ ■ c ;UI* JMl JLI ^n, \i .2 .^ .6 .a /.o figure 9.~ Ratio of ve/octffes on protafe spheroicfs to fhose on correspof^c/f'ng eiiipi-t'c. cy/thcfers . NACA ACR No. L4E10 Fig. 10 /.2 /./ i.o .8 £qcii\/c3lertf ellipse "n \ \ \ \ \ I r Circu/ar-arc. profile T/nic/^ c .0 c I .0 I I.o .8 Tmj i^n Ukt^^i #-«#" ^ji:ia 1 1 1 1 1 1 \ £,< cf/l - 0.37S J_J se \ \ ^ \ 3 _^ -' _ — ■ — — — " " ' V -^=-= -=^- -r^ — — - ■ — — - — — — • - .A — — — — 1 — (b) JoukowsKi approximately SytnmefHcal profi/ej t = o.z?7 (preference 13) - I.O .6 Laminar --ftov^ prof Tie Equivalent ellipse ^ d/l = o.37_ CGf^FiDLi^TlAL NATrONAL AbVrSORY COMMITTEE FOt AERONAUTICS. (c) Laminar - flovv pro file • t =■ O- 266 J .Z .-^ .5 .6 .7 .3 .S /.O F'tgure lO .- Varfafion of the ratio of i/e/ocifies in three -dimens/onal to fhoze in f^/vo-dimen-^ional flow o\^er several bodies and -i-heir ec^ui^a/ent &!/ I'pses . NACA ACR No. L4E10 Fig. 11 x// = 0.6 J 9 CONFIDENTIAL (a) Mar-^/n -turret. O n^ x/2 ^0.590 mmni. (c) Tar ret S. NATIONAL ADVISORY CQNFiDENTIAL committee for aeronautics. Figure- I /.^ Locations of the Martin turret ctnd turreis A and B on tuseicK^e . NACA ACR No. L4F10 Fig. 12 (■s/laf-t/n ft^rnar CONFIDENTIAL oh/ctta ^phUKoid 6/' _ ^ y / ^ / \ s •-^-^ ■%- - X -- ' / -^ ^~ — s ^ ^ ^~ \ X --y.^ X /^- ^0 ¥ i c ^ .y + / // / \^ / / 5 \ <" u /< / N ^ N & *-H D / // \\ \ (A //; / \ K^. 1 \ \l / \ \ c .5 l.Z y \\ 1 f \ CG^^F^ULmJAL N COM ATIONAL AOVIS( MITTEE FOn AERON 3RY AUTICS. i -> , / . 4 2 • « 5 ,« ^ • « J- .4 » , 7 .i 9 ,J ? / o ^t F'i^urs 12.. — C:o'-r>pi3rj5on oT tnea sQrisd prassures> on ■fhs ^icjrtt'n t!~trr>sT (reference IS) u^ii-h calculated vaJues on an equiva/^ni" oblate, -spheroid and on a sphere. NACA ACR No. L4E10 Fie. 13 CONFIDENTIAL /?e la ti ve i^i'nd Top Front- CONFIDENTIAL NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS. r igu.re 13.— ~Tu.rret A d&tcLils. NACA ACR No. L4E10 Fig. 14 Line / (iop) Line 2. (side) CONFIDENTIAL '1,6 'I.Z -.a -.4- .4- .8 I.Z 1.6 Theory for A / » ^ ■ Sphere / \ / — Circular arc ^ f o V ov^r top- / ■"-^ A // / / A \ \ V \,r- Circular ore. -t // / -j- 1 \ > ^ c jvef • S/c 1e. n i 1 1 1 < \ \ :\ V 1 1 t 1 1 \ \ \ 1 1 1 A/fe asu rtffl' of \ \ \ "1 ,2 8.6" fuselage \ \ 1 sfotion^ line. 1 Cfop). \ \ 1 1 / o 0.22. \ 1 / > 1 1 ( + .70 Mi sasi jred at i ',7.S « fuse /age station ■ Line 1 (top) iS/f Line 2 Cs ide. 1 0. 22 o .70 tUNf IDEM riAL NATIONAL ADVISORY COMMITTEE FOn AERONAUTICS. 1 1 1 1 1 z -4- e a lo Distance from edgBj /n- 12 F'igure Z-^.— Connporlson of nfeasur^d pressures on turret /\ of reference /£ i/vifh theoretical pressures on sphere and circular arcs. nf >os/V orta / V e/o< =,/y d, •5/r. hui 1 r 7 - o / z 3-^5 ^ ^ N I" I t I o K NACA ACR No. L4E10 Fig. 19 c^ r ®i ©^ r1 T C .O I I d ^ iv; / c r^ h 4- »0 1 :« § "^ ^ 1 R t a> If n $ s c/) ( ^ '' c G c 1 o \ □9 X c if < ^ Z UJ 8 y ^ t5~ — — — - f _,•-' 1 ^^ V' >■ QO 1 (r / ^ \ / %, 1 m j 51 / i ' 1 1 1 1 'C 3 1 1 (U h— 1 1 ~o -z. 1 ■ 1 •\ C3 1 1 LJ- U- 1 ^ o o 1 N CJ CJ / / / C 1 / / 1 ^.* y (D \ { 7 \ Q) \ C y \ \ 1 1 3 1 / 1 1 1 ; 8 ° ° 1 / / 1 1 1 s ui ^ / ___,- ■^ , £ ^c ^,„— -— l- g Q ft s^ - — -^ --^ — -^ =^ ==-= «V-- 1 ^ ^y. ~ i::::^ •^ ■- y ) t> J Q 3 ^; ; c > ^ h. <0 ■5^ 5!^ « NACA ACR No. L4E10 Fig. 20 5 u Q U »^5 .v>- C .O <-/ :^UdlOI^J.SOD BJn^^B^cJ Iv ■Si NACA ACR No. L4E10 Fig. 21 CD T* Q S^ QQ CO X CO o Q C o s I I • c^ cu NACA ACR No. L4E10 Fig. 22 ^iai'ion <^9^ CONFIDENTfAL Turret profile line I a CLjIindrical side of turret in guns — abeam position ^ line Z. CONFIDENriAL NATIONAL ADVISORY COMMITTEE FOn AERONAUTICS. Figure ZZ.— Esflnnated pressure distri bution about ioiAier gun turrat of Doug/as X5B-2D- 1 airplane . A^ 555 0.70. NACA ACR No. L4E10 Fig. 23 § CO O O V) 0) (U H^ .c (U -^ V ^^ ■K s: c n QJ s. ,0 CL ^^ 4^ <=)J Q) J s. s^ -L :i K t- ■< "^ Z Ul O ji <*) o 0> <0 o "ON 8 ro M ^ -Q 4!^^ •%. P| n 1^ b^ 5^ 5.0 (hi: ' i ^.-Q Q)-> U ^.«0 ^^ -krj^- '^S? "k «< <0 ^ o**i« •5; 1 H^ • ^^ .§»*|o 1^^ '-J- Id < ,n^l« N ^ NACA ACR No. L4E10 Fig. 24 "^ >• V :^ .c >-^ > c Ss -J / V /^ ■ c H > a o > < -1 < z o !5 z to t- Z s UJ < 1 Ui Ui t- Z Z •o 5t1:'" o S-S ^ C §&n 1 ''.^ -J' < 1 — 1 to O Q> 1 1 c ^ >5S 2 r tvj «) 'S 1x1 Q I — 1 >J >■ ^ \A •*> •0 • V 00. Ct. /'s V c 0% 2 O o \ y^ O II / / f N 0< « / ^^-y* ^ / •r •i*. "S / ^« / §>^ ^/ ■^^ S-0 ^ ^1 / II t5 • 1^ < 1 — t E-H Cd Q t— 4 co w. ^? •*) V s^^ oV Cr. 0-S '1 \ K.7 V \ r ' ^>^ O o |-s I \\^ \ II \ v^" N 1 ik \ \ \. \ 'o \ ^\ c 1 \ V fl^^ .^ ^ \ >*> 5 -0» "^ ~--\j 1 s NACA ACR No. L4E10 Fig. 25 Turret C CONFIDENTIAL D o -ZO -l,& -1.6 -/A -/■Z -1.0 » _ \Q .6 -Z A 1 / / Theo ry 1 ^or s-bhet-es 1 / J /.-' .ir^ V // • A ■ -^r \ / 1 ___^ -J^'Jl •1 — "' ^+^ "* \ / J. — — "' .^-' ^ -Per H .+-' , '^ 1 .'■^."J! -'' "V Jl^M^ ^ ^ """ X "4^ #A 7 ^^^"^ 1 \ \'K { -o _ O-p /—- — O "" , -' "^ ■ \ \ itw " " o_- — 7S-t 9 \ Tu f^n j/ -rr^ C J fop + C, fop X E, fop a c, s/de _^/ i , 1 ■0 TT — — « — 1 — e — -^ oi \ 1 . 1 .il_ __ ~ s- — n _ 1 (r 5 ; NATIONAL ADVISORY COMMITTEE FOB AEDOHAUTICS.' - — CONFIDENTIAL 1 1 1 >6 .6 tAach number, Af flqure Z5- Pressures on similar gun turre on the fuselage. .8 ts in different locations NACA ACR No. L4E10 Fig. 26 I.Q20 ' uselogi •I '1.8 ^ ia/^ CONFIDENTIAL Front /■^ -1.6 \ \ /.' \/ y 1 V*. ^ ' ^ ^ y \ -/.^ . 'JTJI t" ' -^ \ -/.2 - - __H -—- " ' ~I.O c 1 \ r^ 3 ^ \ 7 \ -.8 ='cr- -.6 -.^ e Turret A (rmfsrence /£>}. ^; )- -.2 -■A" . »//-/v;*y /• COI'iPIDEr 1 ITIAL NATIONAl COMMITTEE F 1 ADVIS » AERO ORY NtUTICS .2 .3 .4- .5- Figure 2G.— Pressures on -top of -ti/vo spherica/ furr&-ts shoi/^/ng e-ff&cT of re/at/Ve projeci- ion above, fha fuselage . 3o-f'h turrets /oca fed of 2.4.9 perczenf fuselage length frotn nose . — A F , near -top (from unpublished daia) F , near back & , at fop (reference I6) B, at side B. of X/l = 0-6I 8, at X/l = 0.86 CONFIDENTIAL .2 .3 ■^ l\/\ach number, M. .5 .7 Figure 2 7.- Comparison of pressures on finfo &freatn/ine turrets of different fhicHness rafio showing different cotnpres^ibi/i^^ effects. NACA ACR No. L4E10 Fig. 28 a h x-i /\ — ^«^^ ^^ Zr A <^ "^ -A 4 /f/////m k ■^ i -I.t V N 1 \ // 1 a - ~\ / Q-.<5 \ \ ^^■ ^' / 1. Q> -C >.6 Mi T — — -'-' ^- ^ X ' L _ _ - y- -0 ■4 _- -^ r^ __^^-— - ^ yfrr M^ u _ 1 — - D ". — ■^ I »-.2 -O.c ._ .— — " J — \ll-M^ ■ . . — 1 ~ -- - ::r> d- — 1