BKUi MR No. 14-B23 NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS WARTIME REPORT ORIGINALLY ISSUED February 19^1)- as Advance Eestricted Eeport '+B23 DETEEMINATICW OF JET-BOUNDAEY CORRECTICNS TO COWLING-FLAP -OUTLET PRESSURES BY AN ELECTRICAL ANALOGY METHOD By S . Eatzof f and Robert S . Finn Langley Memorial Aeronautical Laboratory Langley Field, Va. UNIVERSlPi' OF FLORIDA DOCUMENTS DEPARTMENT 120 MARSTON SCIENCE LIBRARY RO. BOX 117011 GAINESVILLE, FL 32611-7011 USA NACA WASHINGTON NACA WARTIME REPORTS are reprints of papers originally issued to provide rapid distribution of advance research results to ain 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. L - 21^0 p3 fO'^^^ JO *^^ I L> IIATTOI'AL AD'^aSORY COMinTTEE FOR ArR0f''ATJTIC3 DETERMT!'TATION OP oET-BOT-NDAKY CORREGTIOUS TO COWLINO-FLAP-OUTIZT PRIISSIIRES 3Y AN ELECTRICAL-ANALOCY IIETKCD Ry S. Katzoff and Robert S. Finn SUMMARY In order to deterraliie jet-boiu:^aary con-ections to co\"linr-f lap-out ].et pressures, corrections to the ve- locities near a nowling-flap tip have been studied by an electrical-analogy method. The presence of the low-energy air leaving the flap opening v;as taken into account by so shaping the nacelle nodel that its cuter sxirface represented the strearn surface leaving the flap tip. Copper y;as found unsatisi'aocory for uso as electrode ■material. '^-ood accuracy v;as obtained v^ith cliroiniuiT!- platec^. copper for tank electi'odes snd platinurii v/ire for the solution contacts. An 8-percent velocity'- correction v/as found for a typical nacelle in the LYAL l6-foot higli-speed tunnel, corresponding to a correction of about 0.25 tiiTies free- stream dynamic pressure at the flap outlet. The results agreed appro.^:ir;iately with the corrections calculated by Lamb's r.iethod for an eq.\'lvalent souTce-sink ovoid. INTRODUCTIOl 3o:;ie uncertair'ty has existed rega"'-'ding uhe magnitude of the iet-boundar-; effect on the covi/iinr-f lap-outlet pressui-^es (and hence, on the available cooling precSiXt^es) in test? of air-cooled engine Installac:' ons in tlie Ll^IAL lb-foot high-speed tuniel. ':^he difficulty in analyait results not on^^;* fro!:i tlio threo -dimensional charae'*-er o:^ the f ] ow bi:t alro from tno presence of the lov;- energy nonpctential flow out oJ' tne flap opening. In order to obtain a practical solution of tho problem, the presence oi" the low-energy- air layer lae.y be taken into account by considering the nacelle radius to be increased by an amount eciual to the displacement thickness of this layex'. The potential flow about this new body, however, althoxigh perhaps amenable to analysis, is very difficult to dei'ive; and the results that r.iight be calculated for a simpler body like the KankJne ovoid (reference 1) were considered of questionable apnlica- bility. It was therefore considered e::nedis'nt to solve the problem in the electi'ical tank by use of the analogy between the flow of current and the potential flow of air. The method consisted of measuring; and comparing the flows about a given nacelle moiiel in four tanks (representing wind tunnels) of different size,, for the largest of which the. correcticn was so small tliat it could be adequately calculated by an anproximate method. The present paper presents risults on the jet- boundary corrections and a somewhat detailed discussion of some of the tecliniques involved. The existing literature on the subject is relatively unsatisfactory in this resnect. THEORY 0? ?.:ETH0D Electrical anala-^y .- The electrir^al analogy arises directly from the similarity of the differential equations for the irrotational flow of air and the differential equations for the flow of electric current in a loniform conducting medium. Both equations are Lanlacian: •7 2 0=0 where and 2 ere the velocity potential and the electric potential, respectively. It follows that, for similar boundaries and boundary conditions, the velocity of fluid flow is analogous to the electric current in both magnitude and direction, or inasmuch as . with uniform, conductivity of the redium the current is pro- portional to the voltage gradient, local velocity is directly analogous to local voltage gradient. The 3 boundary cor.dlticns for tri^'se tosts are reer': ly (1) the flow Is tuiiform and parallel to the axis at larf-e dis- tances upstream and dovnstream i'roiTi the bod';/, and (2) there is no velocity coriponent normal to the body or f'le tunnel wa].l. For the electrical tank, the first condition ir satisfied by rising a tank of sulficient lengtji, with electrodes coriipletolx covering the ends of the tank and at right englus to the tank axis. The second condition is satisfied by usinr; insulcting material for the body and for the tank vmlls . '''hq or7ir of r aodel-nacelle degi ^;n. - The flov; of cooling air throur'i an air-couDed ergincs canxiot be simulated by - what night appear as ar obvious analogy - the flov- of electric current through a hJ.gh-resistance membrane in the nacelle rriOdal. Such an internal resistance \).'culd result only in a flow as shovn in figure 1(a), quite unlike the true flov- (fig. 1(b)), beea^ise a discontinuity in total pressure, such as exists at the edge of the coollng-alr layer, cannot be represented in the elec- trical tanl:. The model was therefore extended to a continuation of the flap (fig. 2) in order that the flow of current pbout this region might represent the I'low of the external air in the neighborhood of the flap exit. In order that the flow near the cov.'l entrance might be simulated, a passage was provided along the model axis of such area that the current flowing into the entrance corresponded to the cooling-air flow. The net cross- sectloral arec of the model at every station thus corresponds to the cross-sectional area of the engine nacelle plus the displacement area of its surrounding low-energy air; that is, the am.o-ont by which the outer streamlines are displaced outward as a result of tbe reduced velocities in the inner layers. ■because of the jet-boundary effects on the an.ovdit cf internal flov; and on external pressures, the design of the model shoulci o'^obably not be exactly the ■^ame ^'or all four tanks. Inasmuch as no means of determining these variations wf.s available and a tost showed ■^••hat a PO-pj-'-'cent blocking of the interna] passage ciue^d rnly a O.T percent incrra"je in external gradient, the :..atter Vifas not further c.gv^ I'icved. h For best ruprescntatloii of the external flov/, the model should not taper to r.cro cress section but should continue indefinitely dOvvnc.treaji vvlth a Cx'-osp-seutioia], area equal to che di^placeiaent area of the v/eke : where A'" displacement area of wake D na?,e].le drag q^ free-streaiT' d^mamic pressiire The rear cross section of the model 'vas accordingly made lar^re enough to correspond, by this equation, to the large drag coefficient? iTier-iStrred for flap-open conditions. The len-rth of the model, hov;e\;er, was for pi-accical purposes only four times itr diameter. AlthoU;Th the model was somewhat too short to reprer,ent effectively a model of infinite length, the error involvtjd vas estimated to be S'Tiall. Basis for oomputing iot-boup.dary correction . - The suction in the flap opening" is as3u:Tiod to be determined by the velocity of the flow ovc^r the flap tip, according to the eq\iation p - -% = ¥(\' - "') or (1) vnere p free -stream stat:lc prossuro p local static pressm-'e V free-stream airspeed V local ar'.rspGod p dencity P pres£'ui''9 coefr^cisnt and the jet-bcundary o.fTect on 2xlt pross-orss is accord- ingly fcirsuir.er' to dtrend only on the jet-boundary effect on tad velocities in this re<;:ion. T c As bas already been nou'='d, the local velocity corr^ spends to the Icoa], voltage :~radient, anc the ratio V/ corresponds to the ratio of tbe voltage gradient along the model in the region of the flap tir) to the voltage gradient in the "free atreaiii" ahead of the inodel. From corapariscns of the V/V^ "^atics thvs fui^nd in the dif- ferent tanks, the jet-bovxidary coi-rections in the srraller tanks are found relative to the correction in the largest tank, which can be obtained accurately by a simple calcu- lati or±. APPARATUS AND fSVJlODS Tanks . - Fouj? semi cylindrical tanks rere used, all about jO inches long, with diameters of 5*5 inches, 8 inche'^, 11 inches, and l'.3.S inoaes, respectively. The tanks were made of cellu.loid sheets curved to fit into heav;^/ "'/ooden forms and sealed together '.v"ith acetone. A sketch of the 8-inch tank is shown in fig-ore J. ^^a-^elle riodel.- T\e nacelle iiodel (fig. 2) / > in diameter, wras cut from a Micarta cylinder and given several coats of spar varnish. Its size, in proportion to the 6-incii tank, corresponded to a typical nacelle in the Li'AL l6-fcot nigh-speed tunnel. In order to treasure the potentials near the flap opening, six s.uall con.tact3 m&'Ae of flattened ii c . 2ii platinum wire, were brought tripough the .3urfa::e, about 0.?- incb. apart, along 'x meridian. Ib'xing the contacts on the uiodel :i. t-.:' z way is rrucb rj^ore accur ^ '. -- , for the present piirpoio, tr: 'j. U3irg -i r'--vaple s:. ' .nal contact. Tu3 platin"T.i. A'lves wort. 3jlc.',-Ted '."o '.). j^',3v leads, which ware bro";..gbt oc.t tnrcugn a s-ia..,] g hu.£ & tube into wnicb chey vvDr'- sealed with paraffin to insure that no :iiotion ol' tno ext3.-ral leads could be irnparted to the contacts. The model \,as susoended from a triangular board that re^tt-'d on top of the tank; thrt:e leveling- screws were used to adjvi£.t bhc holght and inclination cf the nacell'5 nodsl bO chat it vould be exactly hfill' iminersed in the tan!:. Blectr?cal circ uit.- The circuit, which is essen- tially a v/heetstore bridge, is shovm in figure li. When the bridge is bj^lf.ncsd, as !nc?loated by silerce in the headphones, the voltaf^c at the contact is ^:iven b;;,- the relation A^oltage at contact - volca^:e at left elect r ode ^ " ]. Voltage bstreen electrodes R-, + V.o All voltage diffcrencos between pcirs of adjacent contacts are thus ft electrodes are thus found rc-latl/e to ti:e voltage between the end A variable capacitance across ono cf uhe resistance arms was ixitroduced to balance the strry circuit and solution capacitances. In order to avoid excessive dieljctrlc losses, only mica and air condensers were used. Altno'igb absolutely osrential for getting a reading, the capacitenco v;as at no time large enough to affect the Impedance of its circiit, that> is, to make inaccurate the use of the simple resistance ratio in the preceding equation. The bridge was fed by a ^^-\'J3.tt pov^-er oscillator, operated, for most of tbe t-osts at lOOC cycles. The headnhcne-B vere, for high sensitivity, selected to have a high impedance (20,000 ohms) comparable with the impedance of the circuit. Tbe tv.o 10,000-ohjri resistance boxes were calibrated to 0.1 ohrn. "lectrod es . - Previous workers (for example, see references 2, 3, and k) with the rr.ethod of electrical analogy have used electrodes of copper, brass, oi* alumi- num. Few difficulties in the use of these metals have been reported, although the necessity for frequent polishing of the electrodes and for the use of acid in the solutions has been notod. In the present study, some atte.apts were made to v.se copper for tlie end elec- trodes and for the contact v.'ires; however, the readings were I'oun.d to dril't at ] arge and irregular rates and the copper surfaces quickly lost tho^ir polish. Satisfactory- results were obtained vith chrouixum-plated copper sheets for the end electrodes and platinurr. wires for the con- tacts. Even with these metals, so.ne slow di'ift vvas almost slwavs observed, but the potentials of the platinum contacts always drifted up or dcvm together: the cause of the drift vvss therei^ore probably elsewhere;, occasioned either by chemical action at the end elec- trodes or by ternperatiu-^e or concentration var-iations. ^^iith regsrd to electrode material, it is of interest to note that copper was lon.n; sp;o discarded for m.easure- ments of the conductivity of solution'?. Platinized platinura is used almost exclu.Tively for such measixreiTients , although smooth platinum h«3 been used successfully for solutions of low ccnd^ictivity and the less noble metals, silver and nickel, have been found reasonably satisfactory for less precise worV: . Distance standard .- As a primnry distance standard for the determination of the free-stream potential gra- dient in the solution, the instrument Ehcv.m in figure 5 was used. It has a platinum contact attached to a sliding arm which can be moved precise distances of 1 inch and Z inches along the tank, by means of carefully ground spacers. A more convenient secondary standard, calibi-'ated against the primary standard, Vv'as made of a pair of platinum contacts suspended from the arms of an Inverted glass "J (fig. 6). The potential gradient as determined with these standards was nearly 1 percent less than the ratio of the potential difference b3t'A-een the end electrodes to the distance between the end electrodes. The difference was tentatively ascribed to the knovm tendency of the end electrodes to act as series capacitances, wherein polar- ization sets rp a counter - voltage analogous to that set up b^'- a charged condenser. An effort v/as made to eliminate the capacitance effect by using higher ^^re- quencies, since such an effect shou.ld decrease with the inverse square of the frequency; however, the gradient was fonx.d to rise almost linearl;/ with frequency, with a total gradient increase of 0.6 percent in the range from 1000 cycles to "SOOC cycles (the highest frequency that was distinctly audible). 8 Series inductances were also tried (Tig. 7)> O- such magnitude that the effective electrode capacitances could be balanced (thPt is, a ip-axirrium gradient could be foriTid) with a frequency in the neighborhood cf 1000 c^ycles. Inasinuch as the inductances had appreciable resistances relative to th^ tank resistance, a direct solution of the circiut shov.n is not possible; the potentials could be calculated, however, by sii-ultaneous solution of the equations of balance with and withonc an avuciliary resist- ance in the circuit. Two different values (5*^0 chms and 1300 chms) of this aioyiliary resistance were tried and both gave the saire result. Th? s result, however, was identical with that originally neasui-ed at 1000 cycles. Since the effective olectroc'e capacitance is tmis appar- ently not clearly defined or at leas'c is aiscciated with other effects that could not be identified, no further effort was made to establish the gradient in terns of the total applied voltage and the distance bet-.veen elec- trodes, and the gradient determined with the sliding arm v/as taken as correct. Electrolyte .- Solutions containing about 0.005 to 0.010 percent sodiiEn chloride in distilled water vrere used as electrolyte in the tanks. 'luch sr-aller concen- trations still permitted sharp readings but v;3re avoided because of the relatively largo local concentration variations that might i-esult from the solution of traces of conducting natter from the varnish or frc;-n the air. Much larger concentrations were also avoided in order to minimize polarization at the electrodes. Tap water was not used because it was found to precipitate considerable amoimts of material on standing. Local variations of temperature, '.mich could produce lai'ge local variations In i-eslstance, v/ere minimized by covering the tanks, keeping them in a thermally insulated wooden box, and stirring the solutions frequently. V'hen the drift was large or wben stirring caused appreciable changes in the readings, the readings were discarded. Test procedur- e.- The tank was filled with solution to slightly below the level of the diameter (allowing for the displacement volume of the model) and then care- fully leveled until the potential -radient as determined with the standard was uniform along the length of the tank. The model was thin lowered into the solution and its height and level carefully adjusted ^juitil it was just half imnersed. The adjustment was facilit!=ted "by means of marks on the model showin£- the position of the hori- zontal meridian. Care wa^ also taken to center the model laterally. Measurements of the potentials ab the six contacts were lap.de in order and repeated in reverse order. The set of readings v/as repeated several Limes. Tne free- stream g-radlent was measured, with the m.odel in place, at a point some distance in front of the model. The value of the free-stream gradient was considerably less than that measured with the model removed because of the increased resistance oJ' the pas3a£;e around the model. The field of the model itself cau.sed a negli£^iblc cor- rection to this free -stream frradient. The uniformity of the gradient along the tank was checked after removal of the model. Precision . - "^he sonsibivlty of the bridge v;;as very hD gh; the resistance boxes could generally be set to 0.1 olim, cori'esponding to about O.OS percent of the potential dilTeronce between adjacent pairs of contacts on the model. The accuracy of a given set of readings, however, is con^niderably less than the sensitivity of the bridge, as indicated by the ■^act that independent tests (involving repetition of the entire procedur-e) could give results differing by as much as O.J percent; and irregularities of the same order appeared in the wall corrections derived from the potential difference measured between the five d3 x'f ei''ont pairs of adjacent contacts . Inasmuch as the wall effect is obtained by comparing the potential differences measured in the largest tank with the potential differences measured in each of the other tanks and since few independent sets of readings were taken, the results might contain twice the inac- curacy of each set. If a further error of perhaps 0.1 percent is allowed in the estimation of the wall effect in the largest tank, a toisal error of about 1 percent appears to be possible in the correction de- rived for each pair of adjacent contacts. That the errors will tend to be additive is, hov/ever, unlikely; and the average of the corrections for the five different pairs of contacts will, in any case, nave considerably better than 1 percent accuracy. 10 Actual fradient.T. on the moiel are kno'wi cnly v.'lt-iin 2 to 3 percent because the distance? b&twaen the model contacts could not b3 reesu'^td or, in iTct, r'denbllleJ to within O.CO5 inch. The wall correction is deter.riined only I'ron? the ratios ^r the £;Tadlpnts ?nd is tharcfore not iffectad by ineccu^ecies in the distances between the ncdel contacts. R5;SDLT?. /5ND riSGTjSSION Hrperiiiiental veloc it y oorr^cti cii.- Curves oT the jet -hour da:>^y correction to the voiccitics in the neigh- borhood of the flap, found by co..ir)£.rintT thJ potential differences betwt:er adjpcenc pairs of contacts meoisiired in the different tantio, aro thc-.vn in figvjre G. The average jet-boundPi-y-coi rection curve is shov/n in fifure 0. '7'he lov^est point of these c\un-3s - that is, the correction for the largest tank - v/c.s coinputed theoretically by the methods indicated in the follov-in^r oaragro.ph . C or-parison v n° th t heoretical correcti on_ . - I. a:nb (reference 1^ shov/ed how to ccmDute the flov; about a Hankine ovoid in a cylindrical tank. These methods were used to provide the correction for the l-^^rf-ost tahlc, and also to compare the experirrental results vdth those that could have been p-"edicted for an ovoid of roughly the same dirnensions . Ihe lor^.itudinal aisbribution of cross-sectional area for the nac3l2e model is sho-.m in figure 10, tof'ethor with the distribution for the assijuaed equivalent ovoid, vhich had the sazae maximu'n cross section, a sor..ewhat greater volume, and a somewhat Siiiallei' length. {Pn ovoid v5 th uhe sa^e maxlKiun cross section and length v:ould have had an excessive voluire and a compror.iise of this type v/as considered most rea- sonable.) The computations were i.^ade for point 3 on the ovoid, the longitudinal distance of vhich frora the upstream focus is O.I7 times the distance betv.-een foci, or O.5G times the liiaximum diameter . The results have been plotted together -vith the experimental results in figure 5* -he agreement ic within practical acc-jracy over the entire range. The agreeinent , however, depended to some extent on the location of point D. If the point had been chosen at the mjddlo of the ovoid Instead of near the end, the correction for the smallest tank would 11 have been 52 percent instead of 2J_^ percent, or one-third higher; for the larger tanlcs, however, the relative difference v/ould have been somewhat less. Application .- According to equation (1), the cor- rection to the pressure coei'ficient follo'.vs from 1 - Ptimnel _ (^Ao) f.innel 1 - Pfree air ^^^''o^^fpee air For example, where for a typical nacel]e in the l6-foot tunnel (velocity correction = 1.08) a pressure coefficient of -0,75 is observed, the corrected pressure coefficient is -O.5O, as given by the equation ■^ "free air The pressure coefficients for the model are showii in fl.g^ire 11 for the two smallest tanks and for the free- air condition. For the free -air condition, the suction Indicated for the region of the flap tip seems about normal . COFCLTJSIOI'IS Jet-boundary corrections to cowling-flap-outlet pressures have been studied by an electrical-analogy methoc''., and the corrections found have been presented as a function of the ratio of '.vlnd-tunnel diameter to effective nacelle diameter. The correction in the LMAL 16-foot high-speed tunnel for a typical 5-fcot nacelle v/ith 12-inch-chord flaps extended 30° is about O.25 times the free-stream d^mariic pressure. Comparison of the results witii theoretical values for a source-sinl?: ovoid in a circular t'urmel showed approximate arreement. 12 It was found that accwracy in the electrical tank roq^uires that only the noo2er inetels he used for the electrodes. Wire contacts fcr pr chins; tuo solution ■potentials should he of olatinuiii. Langley Memorial Aeronautical Lahoratorv, National Advisory Co:mittec for ner cnai'.t ics , Langley Fieia , Va. IiSF3il3NC3S 1. Lamh, H.: On the Effect of the Walls of an iSxperiiaen- tal Tank on tne Pesistance of a Iiodel. R.« M. lf/'ons o/' p/of/nu/n confacfs. Figure 3. - 5k€fch of 8-inch +ank NACA Fiqs.4.7 I — e 4^iv^W&: /f. i»i, riD q)^ -J=^^W^ JbojceSj 0-/0,000 ofy/ns. C J \/ar-/ah/e ccyooc/tance 0-000/5 mfd /^/gur^ 4.- ^MuftTMuh of Clirct//f ^ Ma^wwi^- ^. > L ^Vv^W^ ^4 /ooo o/jms Z^ a/y /nc/cjc/or ^<6ou/- /v-eyty^/Tcy of osc///cr/or crarre/?/' /'/oiti' //? /a^A:- ^^ /^/^{/re 7.- cr/r-cu/-/' /or e///rj/na/jo/7 of ^r/'o^s c/cre fo yooA:^/-/£ar^e>A NACA Fiqs 5,6 •MCA 1.24 1.20 '— I I I F- trt C) (-4 ^^ 0) +' S tQ § 0) +J (iJ fH rt tH •H S >> •H Tu:inel dianiater Sffective uscdl.le diPnieter (a) Contacts 1 and 2. Jigare 8.- Wall effect on mean velocity betvjeen adjacent pairs of contacts. IIACA ?i£-. eir 1.28 1.24 1.20^ t- rt (J iH .■^ a> +J n C3 3 O +5 f') t^ f-1 tH •H t--n •H •P •H >» CJ 4-> O •1 H 1-1 O 'JJ O !:> rH (U > 1.15-- o 1.12- 1.08 1.04 1 1 1 i i o— i 1 ! „. 1 ! 1 1 i f 1 i 1 1 ... 1 ! 1 1 i ! 1 1 1 i 1 \ \ \ 1 1 . . 1 i ' \ 1 i ! ! 1 \ \ \ r "• " — 1 -^ r '1 i i i ! \ \ \ 1 i i ! \ \ i 1 1 1 ! 1 1 \ \ S .. . . 1 i i i . . 1 ! 1 1 \ q i i \ \ '\ 1 . , i. \ \ i i .-_ ^^ 1 1 i 1 1 __ 1 _J _ 1 t 2 3 4 i Tunnel diam : ter 5 6 1.00. (b) Contacts 2 and 3. Elfsctive nacelle diameter figure 8.- Continued. ITACA r. 8c S Cfi (II r-i fH C +J r; CO « fS a) 4^ 0, f-i R Cm •H c: >;< •H 4-> •H >. C) +' O ■rH 1— i C/ (U o > 1— 1 <1) > 1 o 1 1 1.24 1 ! 1 h 1 1.20 i 1 t 1 1 1.15' ^ \\ 1 1 1 t^ ' — i . \ _L 1 .._ 1 1 1 ]2i ! i \ , 1 ,a _^_. ! 1 i i 1.08- 1 i.o4 i 4- - - -_V.-,. _l i 1 \ 1— . -i U-r% 1 1 1 i \ 1 I 1 i ^ ■>^- "^^^ i _. ... J Xi 1.00] £, 3 ^ 3 ■^ 5 5 Trjinel .iiarr.eter iiffective nacelle aiameter (c) 3ontaclE 5 and 4. V- ~-^-\-rP' R ... Cmti "iie':^ TACA Tie. 8d 1.28 1.24 1.20 1.15 t^ 1.12 o o 1.08 1.04 1 • 9 ■ 1 ! 1 ! 1 1 ' ■ ■ 1 ■ ■ i i i 1 1 j r --1 ! . L. ' 1 L. . ! I i i 1 1 1 i \ 1 ! 1 i ! 1 \ 1 N 1 ■ ' I * \ ^ ■ i i , 1 \ ^ ^ "\ 1 ! i ! 1 1 ^^ ^ 1 2 t 5 z : 5 6 1.00 (d) Contacts 4 an.;? 5. Tunnel diameter Effect-iva nacelle diameter Figure 8.- Continued. FACA ]?i ig. Be .-rt 'D r-t S-1 (U -fJ r; 03 c f-i 0} +-> 0) ^ c •+H •H C >» ■H -t- ■ H !>^ Ci -(J O • H r-l O Tunnel iicimeter Sffective nacelle diameter (e) Contacts 5 and 6, Jifc-are 8,- Conclude i. JfACA 0) ■:i) V; -I -* .--I .) ^ •I- ' -I > 1.28 1.24- 1.20 1.16 1.12 — l.OB 1.04 1.00 Erf&c:i/e .lO.cJla di'in.atcr Pif-nxre 9.- Moan wall effect on velociuies in region of ccv;l-flap tip, and corres-.pjndj.ng thecretic-'J-l correction for point B of the ovoid of ■Jiizo.TB 10. lACA S'is. 10 4J c '\, 1- w > •r- 7i C !-i J •4^ (n « SOJf! c, o •H PL, += • •H Tb &.'. -H c o o > 1^ o 1 o 0) •H ITACA Fig. 11 +3 Q) 1-1 p! O r-i «H O o 0) P! CO 0) !^ ?l CO ca