m^i\i-i\'^ ^ NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS WAllTIME REPORT ORIGINALLY ISSUED June 19M^ as Advance Confidential Report IA-F23 WUro-TDMEL mVESTIGATION OF CONTROL-SURFACE CHAEIACTERISTICS XIX - A DOUBLE FLAP WITH AN OVERHANG AND AN INTERKAL AERODYNAMIC BALANCE By Robert B. Liddell Langley Memorial Aeronautical Laboratory Langley Field, Va. ^' SiaiK"' "'■"T' ^ I WASHINGTON NACA WARTIME REPORTS are reprints of papers originally issued to provide 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. DOCUMENTS DEPARTMENT Digitized by tlie Internet Arcliive in 2011 with funding from University of Florida, George A. Smathers Libraries with support from LYRASIS and the Sloan Foundation http://www.archive.org/details/windtunnelinvlang -7^? 00911 ]\TACA ACR No. L^F23 NATIONAL ADVISJ?EY COn'ilTTEE FOE AERONAUTICS ADV/NCE COATT^'inECTIAi EEPORT l«.a"ND-Tl-K^-li;L IF'/ESTIIATTON OF CONTROL -ST'RFACF CHA^.ACTERISTICS XIX - A DO'JBLF IX AP V;ITH AN OVERHANG AND AN INTERNAL AERODYNAMIC BALANCE By Robert B. Liodell SUML^RY V.'inl- tunnel tests have been rr.ale in two-dimensional flovj to investigate the aerodynsrr.ic characteristics of a don.ble flap with an internal and an overhang balance. Three sizes of eech type of balance were tested v.lth three relative rates cf deflection of the t\vo flaps. An NACA 66-009 airfoil having a O.JO-airf oil-chord straight-contour forv.-ard fle.p and a 0.2C-airf oil-chord straight-contour rearvard flap v;t;s used. The test results indicated that a balanced double flap produced the sane lift as a single plain flap of the sarr;e chord and also produced highly balanced binge rroirents. High lifts and lor hinge -roir.ents were obtained with a do\ible-flap arrsngerrent if either an overhang or an internal balance having a chord 5^' percent of the flap chord vas incornorated on the forvrard flap. The overhang-balance flap shored a lorer value of the hlnge- Troir:ent gradient due to flap deflection than the intern- ally balanced flap. INTRODUCTION Previous work (reference 1} has chovm that greater lifts with lighter control forces could, be obtained D^/ the use of r Iain-flap siriall-chord control surfaces deflected to a large angle than by large-chord control surfaces v>;ith a siraller del lection range. The results of reference 1 also shored that two srnall-chord flaps deflected sir-ultaneously in the same direction v/ould be COFFIDST'TTAL NAG A AGR Wo. lI+FZJ combination that would give even better* lift and hinge- morient characteristics. Soma method of incorooratin^~; aerodynamic balance must be found, however, since the hinfre-moment forces of the plain flaps are much too large for these flaps to be used on high-speed airplanes. A double flap with various amounts of either over- hanrj; or internal balance and with different rates of deflection of the t^o flaps has been tested to find out v^hether the hingo moments could be reduced and the lift characteristics of a plain i'lan retained. A double- flap srrar.genent having somev/hat larger chords than those used in reference 1 was srlected in order to o';>tain greater lift, especially at lar.^e angles of attack v/ith fla^o deflections of o^oosite sirn. SYMBOLS '^he coefficients and the symbols used in this paper are defined as fellows; Cj airfoil section lift coefficient (l/qc) c^ airfoil section profile-drsg coefficient (d^^/qc) c airfoil section oitchin-r-moment coefficient V (m/qc2^^ Cy,^ section hinge-moment coefficient about forward- flag Divot ooint ?-, , shown in figure 1 Cj„ section hinge-moment coefficient about rearward- 2 flap pivot ooint p2> shewn in figure 1 dd- c^ control-stick (or ocdal) hinge-moment coeffi 's cient 6"'sAl^i V "* CONPIDEMTIAE TJACA ACR No. Li4-F25 COIMPTDEFTI AL v;".iere I airfoil secticn lift cIq airfoil secLJon orofile drar; m airfoil section oitching' mor.ierit abcut quarter- chord point of airfoil h-j f orv:'ard-fla;i secticn liiuge riornent about ?-, h^, control-stick (or pedal) hinge norient {h-]_ c chord of basic airfoil with both flaps neutral C"! f crward-flar- chord with rearward flap neutral C2 rearward-flap chord q dynamic pre rj. sure (IJ lb/-q ^'^■) and c-]^ chord of balance a^ anf;le of attack for airfoil of infinite aspect rat: o 5-, forward-flap deflection with res'^ect to airfoil, degrees 5p rearward-fla\) deflection with respect to forward ■" flap, de.ri'ee3 6 rearward-flap deflection with respect to airfoil, d.errees (see fip. ^O; referred to as "total flap deflection"' (h^ + 5o) 66^ C0I'FI"OI"'TIAL [}. COKFTDFITTIAL TAG A ACR No. LIj-F25 <=>> a \ •? For cotnoarison, all slope valiies are measured at an anrle of attack and a flap deflection of 0"' and therefore apply to only a very linited portion of the data. APPARATUS, r^OD~L, AUD TnlSTS The tests were rrade in the IliCA I4.- b^r 6-foot vertical tunnel (reference 2) nodified as discvissed in reference 5« The 2-foot-chord by [|.-f oot-span model v;as made of lami- nated mahogany, except for the front flap which was steel. The airfoil conform.ed to the IJACA 66-OO9 airfoil contour forv/ard of the f orv;ard-f lap hinge axis and to a straight- line contour behind this hin^e axis. The model was pro- vided with a O.JOc forward flap and a 0.20c rearward flap. Figure 1 s'-^ows the method xised to connect the flaps to each other and to the airfoil . '""h-e rearv;ard flap v/as coiinected to the forward flap by a mechanism that allowed the rearward flap to deflect one, ty;o, or three times as fast as the forward flap; that is, d52/d5]_ equals either 1, 2, or 5* "^^e forward flap was provided with three interchangeable blunt-ncse overhang balances and three interchan;reable internal balances having chords 25, I4.O , and 50 percent of the forward-flap chord. The arrangements tested and pertinent model dimensions are shown in figure 2. COKFIDEPTIAL NACA ACH No. lIiF25 COLIFIDEiMTIAL The double-flap arrangement te!_:ied is in reality a flao with a Isr^e leading tab. The tab could have been linked to rhe airfcil with a single cress-link connec- ticn. "The riodel was i.isde v/ith the linkage system shown in figure T, however, and it should be noted that points P, and "p^ are t}ic acttial flap oivot ocints <:>n the rrodel and that the aerodynair.ic characteristics are the sane as for a O.JOc flap '/.'Ith a 0.20c leadj.ng tab. The rearward-flap defZ.ectlon and the rate of deflection (riechanlcal advantage of rearward flap over forward flap) can be obtained analytically. If x and Y are as indicated in fieure 1, sin 5^ - — sin 5 (1 ) V ana X cos 6 )^ y cos ^-2 (2) The departure of rearward-flap deflection anc of rate of rearward-flap deflection from linearity with forward- flap deflection, as calculated from equations (1) and (2), is indicated in figure J for each linkage arrange- ment tested. It may be noted that a linear rate of rearward-flap deflection, and hence a constant value of d5-)/d5]L' throughout the deflection range was d5o obtained only when — r^ - 1; that is, vihen ;: = v. It J. r^ O ■^ may also be noted that y. that :: = yj for d5-, c6. = 3 dO^ — o md The airfoil model v/hen iiiounted in the tunnel com- pletely spanned the tost section, "'ith this type of installation, tv/o-dimensional flO'// is approximated and section characteristics of the model can be determ.ined, The tests were made at a dynamic pressure of 13 pounds pel' square foot, which corresponds to an air velocity of about 71 xniles per hour at standard sea-level condi- tions. The test Reynolds number was approxi- mately 1,310,000. (T^ffective Reynolds' num.be r = Test CONFIDENTIAL COITFIDELTTTAL NAG A ACR No. LiiF25 Reynolds number > Turbulence factor. The turbulence fac- tor or tiie NAGA ii- by 6-foot vertical tunnel is 1.93' ) With the Internally balanced arrangements, the gap between the forward flap and the cover plates was O.OO^c. The gap between the rec.rward flap and the cover plates on the forward flap varied with flap deflection. In all cases, for both internal and overhang balances, the gaps at the nose of the balance on the forward flap siid the gap between the forward and rearward flaps v^ere sealed with thin sheet rubber. An experimentally; determined tunnel correct apolied to the lift. The angle of attack and hi were corrected for streaTnllne curvature of the f is induced by the tunnel walls. The nethod used mine these corr'=ctions . is analysis of reference h. sirnilar to the an undeterninedt as follows'; tunnel Values of 'rection. arag The data the o ret are sub c- O.Q65 -- 0.007 i a. a X + 0.21 t U, 7,T cz we r ) ion nge lap to ical ject e CO was momen t s that deter- to rrected wnere Ch Ch = Chn^ +- O.OTJc^.^.F denotes an;y hinge -moment coefficient, cj -f is the tunnel lift coefficient produced oy deflection of the flap (arbitrarily taken at a^^ - -8°), the subscript T denotes a value from the tunnel, and K and stants that are functions of balance arram rmi F are con- ;nts and are given in the following table: ^ i d5;[^/Q0^-~..,^_^ Y. 0.^5 o.Lo 0.50 1 2 3 -0.68 -.72 -.76 o.ooS 0.C07 .009 0.006 . 00 5 .011 RESULTS Lift and hinge-moment characteristics are presented in figures 1; to I5 for each of the arrangements of ror.T^DENTIAL EACA ACR Fo. lLlPZJ C0K:^TDENTIAL 7 brlanoecl double flap tested. Fj.tc.h?lii^— Tr.o"".ent character- istics are c.lso presented in sorie of these figures for the balsnce arrangements having lift and hinge -moment characteristics that were considered reasonably satis- f factory. The ef fectivenesr? and hinge-roiT"3nt parameters in table 1 are based on total flap deflection. The hinge moirexits, as measured about the forward-flap pivot r-, , v;er8 transferred to the rearward-flap pivot t2_- The hinge -m.oment and effectiveness parameters thus are compar- able for the various arrangements tested, regardless of the relative ratvi of deflection between the forward and re arward f 1 ap s . DISCUSSION Lift The slopes of tht' lift cv.rver are in agreemeiit v/ith those measured from previous tests of the NAGA 66-009 air- foil 'reference 5'« ^-^ large positive flap deflections for large negative angles of attac^^, Ct become? vei-j great regardless of balance type, size, or relative rates of deflection 01 the two flaxes. This effect is character- istic of small-chord llaps. The shapes of som.e of the lift curves at hifh flap deflections are sim.ilar to those of reference 5- The overhang balance would protrude w-'ll into the air stream, at high flap deflectioiis and thus cause alr-f]ow separation. Tlie lilt effectiveness o.g^ decreases somewhat with increase in d52/d52 for all tjpes and sizea of balance tested (table I). The decrease In effect ivr^ness may be accounted for by the fact that the forward flap has a greater effectiveness than the rearward flap and as d62/'^5l increases the forward-flap deflection decreases for a given total deflection 5-^. The more effective flap thus moves m.ore slowly and the less effective flap moves faster. The effectiveness of the comibinatlon shoi.ild therefore decrease. The decrease in a^^, with increase in d5p/d5] is clearly evident in figure 16, which shows airfoil section lift coefficient against total flap deflection as obtained from, figure 5« Tlie similarity of the slopes shovi'n in fig- ure 16 in-^icates that the lift of these double-flap com- binations is more nearly a function of the total flap CONFIDENTIAL 8 COI'IFIDEIITIAL I'ACA AC.R Ko . l1|.F23 defleotion than of either of the separate flap deflections. For comparison, the lift coefficient of the 0.20c double plain flap reported in i-eference 1 has been plotted in figure l6'. Even though a different airfoil section was used, smaller-chord flaps produce less lift than the large- chord flap for positive flap deflections at zero r.nd negative angles of attack - an attitude critical for a horizontal tail. The sr.sll-chord flap, however, produces even greater lifts than the large-chord flap at high positive angles of attach - an attitude usually critical foi^ a rudder. i^igure lb indicates that the flap with an Internal balance and the flap Y;ith an overhang balance ha've about the same lift at the san-e flap deflection and at a^ = O'^, although the flap with overhang balance shows Just slifhtly greater lift. Data for the O.JOc plain flap of reference 5 ^^'^ also presented in figure l6 and the similarity of the lift characteristics and those of the Q.JOc double flap should be noted. Hinge Tv'ioment The hinge -moment coefficients of the arrange'rents of balanced double flap tested shov;ed little change with angle of attack in the region of lov¥ angle of attack (figs. h. to 1^). The curves are typical of most low-drag airfoils tested at lov' scale, however, in that they rapidly become increasingly nonlinear beyond a^ = ±6°. A nefi-ative value for cvj is indicated for all of the arrangem.ents except the O.5OG-. overhanT balance with dS^ = 1, for which Cho was about zero (table I). The flaps with a O.UOct^ or a 0.50c-j_ overhang balance tended to have a more positive value of c%-, than the flaps with an internal balance of equal chord. The value of '^h-j becomes zero and sometii-ies positive at flap deflec- °- o tions other than for m.ost of the arrangem.ents tested. At large positive flap deflections and large negative angles of attack, the hinge-moment coefficients change rapidly from a large negative value to almost zero at large negative lifts. This rapid change in hinge -moment coefficient occurs in the same lift range and at the same large flap deflection for which the slope of the lift curve COm^IDENTIAL ITACA AC- No. lI|.F25 COKFIDEKTI/iL becomes excessively steep. This rapid change of the hinge -inoKient coefficient anight cause reversal of control- surface force but, in any case, the force required to reti'rn the control surfFce to neutral sliould be relatively sriall . Of the arrangements tested, the double flap with either a O.5OC-, internal or a C.50c-| overhang balance has values of c-,,^ lov; enough to warrant its consideration i. for an airplane tail control surface. The overhang balance had a lov/er value of Ci_„ than the internal balance. The value remains fairly constant up to large flap deflections for the more usable arrangements. The balanced double flap and the linked-balance flap are shovvn scheria tically in figure 17, which indi- cates that a linked-balance arrangement may be con- sidered a balanced double flap having coincident forward and rearv/ard flaps. By Tising the equations (see fig. I7) 5^ + 5p = 5^ md dS^ T dS^, " 1 . ''2 do, it is thus possible to compare the linked-balance flap and balanced double flap on the basis of rate of flap deflection dS-, /dS^ . The variation of the hinge-moment parameters x'.'ith rate of flap deflection is shown in figure l3. Also included for com.parison are the curves for a O.JOc flao with a 0.50c-j_ linked overhang balance (reference 5)- An examination of figure 18 indicates that c, varies ^? a very little with the rate of deflection whereas Cu is affected to a m.uch greater extent. For the particular an-'angement tested, the paramieters for the balanced CONFIDENTIAL 10 CONFIDEFTIAL ?TACA ACR Fo. l1,'F23 douole flap are smaller than thos'3 for the flap with the linked overhang balance. The stick hinge -moment coefficients for the balanced double flap with a O.^Oc-, balance are shov;n in figure 19 as a function of lift coefficient at three angles of attack. The characteristics of the linked-balance flap (reference 5)' ^ ^-J^c flap having conventional overhang balance (reference &), and a 0.20c double plain flap (reference 1) sre also included in figure 19 for con- parison. The control stick v/as assumed to be limited to a m.ayimi.un deflection of ?0°. "T^he total flap deflection was approximately 3^° for all of the arrangements e>:cept the double plain flap for which it was 60^. B^'- limiting the total flap deflection as indicated, the curves are nearly equal with respect to maximum lift. The curves of figure 19 therefore take into account the m.echanical advantage of the system and extrapolation to a higher lift coefficient would not be valid unless the slope is increased. The curve for the aouble plain flap, presented in figure 19(a), was taken directly from refsrenca 1 for dSo = 1 and the hinge-mom.ent coefficients were based on dS^ a O.^Oc flap. Because this particular double plain flap had a total' flap deflection of 60°, a higher lift coef-^ ficient was obtained at a^ c h or d v;a s s ome v.'ha t shorter ficient was obtained at a^ - even thou^^h the flap Causing t>ie r-'^arv.'-ard flap to move increasingly faster than the forward flap generally increased the stick hinge -moment coefficient for any narticular value of lift coefficient. The reverse was true with regard to the dotjble plain flap I'eported in reference 1. This apparent discrepancy might be explained in the following manner! The decrease in hinge moment with increase in the value of d62/^^] for the double plain flap is indicative of an inci-easinrly better camber for the air- foil, ^y incorporating a balance that is attached to the forward flap, however, the for-.vard flap would move more slowly as the rste of flan deflection d5o/d5-, increased and therefore" the balance v/ould be loss effec- tive for the same totsl flep deflection. The curves of figure 19(b) indicate that»the linked-balance flap has higher hinge mom.ents and lower maximum lift than the CONFIDErTIiilj NACA ACR No. LliF23 CONFIDENTIAL 11 balanced double flao -.vith = O.5O. Fro:^ this ccm- T parison, a leading tab sorr.ewhet shorter than the flap chord causes a smaller hinge r.oment for a given lift than a l.OOc-, leading tab (linked overhang balance). Tliis fact mipht be explained by th.e more gradual curvature of the air, the smaller peak presar.res at the hinge axis, and a snaller adverse ;Dressure gradient, v/ith a conse- quenti^.l later separation of flow, for the balanced double flap than for the llnkecl-balance flap. Unpublished results, hov/ever, indicate that, for a leading tab v/ith a chord a little shorter than 5'^ percent of the flap chord, the hinge-monents increased at a more rapid rate than the lift v/hen the tab was deflected with the elevator. The arrangement is therefore unsatisfactory. All available data indicate that some intermediate chord v/ould be the optimum for the tab rather ■clian a very small or a very large chord. liVhetiier tlie tab chord used in the tests reported herein is the optlmiam is still indeterminate. There are not enough data available, ho--ever, to deter- mine the cptim.um chord for a large leading tab and further tests are recommended to provide the data neces- sary for finding the cptimium. flap chords and deflection rates. The curves of a conventional overhang balance that 'would be well balanced at small flap deflections are shown for comparison in figure I9 . The advantages of a double-flap arrangement are evident. Flap oscillation was noted for tv;o arrangements of balanced double flap over a portion of the range tested. Ail ranges in which ti^is osciDlaticn of the flap occurred are shov;n by dashed lines in the hin~e-riOn:ent curves of figures Ii. to 15. '-his oscillation v;as similar to that reported in reference S. Drag Increment of airfoil section profile-drag coefficient caused by flap deflection against total flao deflection at a^ - 0° is presented in figure 20 for all arran.'3;e- ments tested. For small total flap deflections (under 20'='), the type of bslance bad little effect on the oroflle-drag coefficient for all arrangements tested. At large total flap deflections, however, the flsp -.vith an overhang balance had m.ore drag than with an internal balance. This result seems reasonable because an overhan;: balance GONFIDEITTTAL CONFIDENTIAL NACA AGR No. LtiF. -Z'' tends to induce air-flov: separation at high deflections v/ith a consequential increase in drag. At large flap deflections, the drag decreases with an increase In 0^2 /dS-, . The increnient cf airfoil section profile-drag coefficient caused by flap deflection is shov/n as a function of section lift coefficient In figure 21, in which figures lo and 20 have been combined and, replotted. The relative positions of the internal-balance cur^ves are an indication of f^ie amount of separation occurring over the double-f?.ap combinations. The upper surface is not broken by the protrusion of a balance that would precipitate separation, as is the case with an overhang balance . It is evident thai;, in tlie region of higher lift, the resultant camber of the airfoil i.vhen don/do-, is increased tends to produce a pressure gradient over the airfoil v/hichi induces a later and less pronounced separa- tion than v;hen the flaps move at the sr-me rate. Ccm.- parison of the drag plotted against lift for the short- chord double plain flap of reference 1 and the longer- chord internally balanced doul/le flap of the present report indicates that the profile-drag coefficient for any particular lift coefficient was gener'ally some- what higher for the double -flap arrangement v/itli' the short chord. Pitching Moiiier.t The pitching-moment curA^es are linear for small flap deflections but change rapidly -.vith angle of attack at large flap deflections. The rapid decrease in pitching moment coefficient at negative angles of attack and large'' positive flap deflections in the same region in which values of hinge moment and lift change rapidly is char- acteristic of small-chord flaps. Pitching-moment para- meters, mieasured from the data of figures 'I4. to 15 and from, some data not shown in these figures, are given in table i. '^hese values are an indication of the'locaticns cf the centers of lift caused by angle cf attack and by flap deflection. COmTDEFTI/J. NAG A ACR Fo. lU?23 COIIFIDEI'TIAL 15 CONCLUSIONS The results of tests of an NACA 06-OO9 airfoil with a O.$0-airfoi] -chord straight-contour double flap having an overheng and an internal balance of various chords and several rates of deflection for tiiP two flaps indicated the following conclusions: 1. The balanced double flap produced lifts about equal to a single plain flao of the sane chord and at the sane tine produced closely balanced hinge moments. 2. Hich lifts and low hinge moments were obtained with a double -flap arrangement if either an overhang or an internal balance having a chord 50 percent of the flap chord was incorporated on the forward flap. The data also indicated that, for the arrangements tested, the forward and rearvard fls\ps should deflect at about the same relative rate. 5. The relative rate of deflection of the two flaps had a large effect on the hinge moment duo to flap deflec- tion and a small effect on the hinre rnom.ent due to angle of attack:. 'l. The flap having an overhang balance showed a lower value of the hinge -moment gradient due to flap deflection than the Internally balanced flap. 5. The rapid change in hir.ge-moment coefficient at large flap deflections and angles of attack of opposite sign m^ay cause reversal of control-surface force; however, a relatively small force should be required to return the control surface to neutral. 6. A double-flap arrangement incorporating an aerodynamic balance is a ver^r prom.ising arrangem^ent . Inasr.uch as this double flap is merely a largo leading tab, its incorporation on the tail of an airolene should not present any particularl;/ difficult problem. There GOl^TIDEFTIAL ik COlvPIDEITTTZ-iL KACA ACR Fo. L^FZ^ are not enough data available, however, to determine the optimuin chord for a large leading tab and further te-sts are necessary to find the optimurri flap chords and deflec- tion rates. Langley Memorial Aeronautical Laboratory, National Advisory ComiTiittee for Aeronautics Langley Field, Va. CONFIDENTIAL NACA AGP. Fo. lh,F2^ CO?IFIDEFti AL REP^.EITCES Sears, Richard I., ard Purser, Paul 5.: 'Vlnd-Tunnel Irvestigaticn of Contrcl-3urface Characteristics. XIV - ITACA 0009 Airfoil with a 20-Fercent-Chord Double T^iain Flap. NACA ARR Nc . 5F29 , 19''4.5 . 2. Wenzinger, Carl J., pnd Harris, Thomas A.: The Vertical 'Vind Tunr.el of the liationel A.dvisory Corrjnittee for Asrcnautics. IIACA Rep. !Io. 587, IC'Jl. 3. Sears, Richard I., and lloc.^B.rcl, V. Page, Jr.: '.Vind- 'T'unnel Investigation of Control-Surface Character- istics. II - A Lrrge Aerodynamic Balance of Various Nose Shapes with a JO-Percent-Chord Flap on an V.^Ck 0009 Airfoil. NACA ARR , kn^. 191x1. ij.. Swanson, Robert S., and Tell, Thornas A.: Jet- BoT.mdary Corrections for Reflection-Plane Models in Rectangular '.Vind Tunnels. NACA ARR IIo . 3F22 , loi|5 . 5. Sears, Richard I., and Liddell, Robert 3.: 'Vind- Tunnel Investigation of Control -Surf ace Character- istics. X'/III - A Linked Overhang Aerodynamic Balance. NACA ACR No. 1;B28, ISkk- 6. Gillis, Clarence L., and Lockwood, Vernard F.: '.Vind- Tunnel Investigation of Control-Surface Character- istics. XIII - Various Flao Overhangs Used with a 3G-percent-Chord Flap on an NACA 66-OO9 Airfoil NACA ACR No. 5G20, 19i;5. CONFIDENTIAI, ^•fACA ACR ITo. lI.'F25 CONFTDEFTIAL TABLE I INPORMATICN CONCERNING ARRawGEJ.IENTS OF BhTA^CZD DOUBLE FLnP TESTED 16 Cv^/Cl d5^ ^^•a Kjrv J- '"5fTl ^0. e-^)a, Figure IntRrnal bal.nce o.sc 1 0.099 -O.^I. -O.COIO -0.0028 -0.19V 0.011 u .30 p .096 -.^0 -.0011 -.0057 -.190 .021 .50 5 .092 -.1].7 -.0010 -.OOlik -.195 .017 6 .kO 1 .100 -.0020 -.00^5 -.18k .013 7 .,'iO 9 .095 -.0020 -.005]^. -.}Q1 .008 8 .2^ -t- .100 -.".5 -.0029 -.0068 -.185 .007 / Overhang balance o.so 1 0.099 -0.50 0.0000 -0.0021 -0.193 0.005 10 .50 2 .098 -.iic: -.0001; -.003? -.213 .Oil! 11 .50 7 ^ .101 -.1+8 -.0006 -.0014.1 -.213 .006 12 .ko \ .098 -.57 -.0016 -.005I; -.190 .015 13 .14.0 2 .09? -.52 -.0015 -.0051 -.197 .015 ll^ .25 1 .10? - ^-,- -.0050 -.007I;. -.192 .006 15 NATIOKAL ADVISORY COIi'R-iITTEE FOR AERON/lUTICS COl'JFIDENTTAL NACA ACR No. L4F23 Fig, -J < O o §1 lAA/^vA^yvA^ Si I ^ I I I I I I '^^'^^VAyxAyvJ NACA ACR No. L4F23 CONFIDENTIAL Fig-. 2a Data in figure S 7 8 6s, CONFIDENTIAL (a) Internal balances. 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