ARE No. L5PO6 NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS WARTIME REPORT ORIGINALLY ISSUED June 19^5 8-8 Advance Restricted Report L5FO6 WUro-TDMIffiL INVESTIGATION OF COHTROL-SUEFACE CHARACTERISTICS mi - MEDIUM AND LAROE AERODYNAMIC BALANCES OF TWO NOSE SHAPES AND A PLAIN OVERHANG USED WITH A .20 -AIRFOIL -CHORD FLAP ON AN NACA OOO9 AIRFOIL Bi John M. Riete and Elizabeth G. McKinney Lemgley Memorial Aeronautical Laboratory Langley Field, Va. Kj5»5T.f" •TSJCfJI*, NACA WASHINGTON NACA WARTIME REPORTS are reprints of papers originally issued to provide rapid distribution of advance research results to am 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 - 196 X Digitized by tlie Internet Arcliive in 2011 witli funding from University of Florida, George A. Smathers Libraries with support from LYRASIS and the Sloan Foundation http://www.archive.org/details/windtunninvestOO ^ACA ASK No. 15706 NATIONAL ADVISORY COI>I?IITTSE FOR AERONAUTICS ADVANCE RE3';:RTGT3D RETORT WIND-TUNNEL INVESTIGATION ON CONTROL- SURFaOE CHARACTERISTICS XXII - MEDIUN AND LARGE AERODYNANIC BALANCES OF TV;o' NOSE" SHitPES AND A PLAIN OVSRHAtIG USED v;iTH A 0.20-AIRF0IL-CNCRD FLAP ON AN NACii 0009 AIRFOIL 3y John M. Riebe and Elizabeth G. !'cKinney SUMMARY Elunt-no?.e ano elll-oticil-ncse overhangs of and 0.50 flap chord and a plain overhang on a flap having a chord of 0.20 airfoil chord have been tested in tv;o-dlnensional flow on an NACA 0CG9 airfoil. The results of the tests are presented as aerocynar.ic section characteristics for several flap deflections Viith the gap at the flap no.se sealed or ■i.nsealed. Tests were nade al?o to determine the effectiveness of a tab of 0.20 flap chord on the plain sealed 'flap and on a sealed flap having; an elliptical overhanr; of 0.35 flap chord. The pressure difference across the flap seal vi'as also deterr.ined for the plain sealed flap. The results indicated that the plain sealed, flap had the largest lift-curve slope, '-/hereas the slopes for the 0.50-f lap-chord overhangs were the sane as or sli£htly larger than for the 0.35-f lap-chord overhangs. A reduction in slope caused by unsealing the flap gap increased with balance chord. The change in lift coefficient v;ith flap deflection generally inci'eased vdien the gap was sealed ard v/''ien the balance nose shape v. as changed, tror.: elliptical to blurrc. Sealing the flap gap generally rt^ade the variation of flap hinge -noiTient coefficient v/ith angle of attack and with flap deflection more negative. Changing the nose shape fror. blunt to elliptical rr:ade the variation of the flap hinge-r.or.ent coefficlerit v;ith angle of attack more negative for the seal'od f^ao and more nositive NACA ARR No. L5P06 '" for the unsealed gap. At sma?.l flap deflections, the variation of flap hinge-;:ioinent coefficient with flap deflection -A'as more negabjve for the elllptical-nof^e than for the blunt-nose flap; at large deflections, however, this variation v/as more negative for the blunt- n3se flap. The change of flap hinge-moment coefficient with flap def].ection for the unsealed blunt-nose overhang had a larger variation v/ith balance chord than the change of flap hinge-ironent coefficient with angle of attack; for the sealed blunt-nose overhang, these vari- ations were about the sar.e in the range of balance chord from 0.35 to 0.50 flap chord. For the sealed and unsealed elliptical-nose overhangs, the change of flap hinge- moment coefficlem: with angle of attack had a larger vari- ation than the change of flap hinge-moment coefficient with flap deflection. INTRODTJCTTON The NACA :s conducting an extensive investigation to determine the characteristics of various t^Apes of flap arrange.ient suitable for use as control surfaces and to provide data for design purposes. The inveatigation, which '.vas m/-ide in the Langley 4- by 6-foot vertical tunnel, has included tests of modifications of flap profile, traillng-edge angle, gap size, flap nose shape, and balance chord; however, most of these tests have been made in two-dimensional flow with a flan having s chord 30 percent of the ajrfoi] chord (0.30c). Tne present tests ha\c extended the investigation of balance jhord and flap nose shape, which i/as reported in reference 1 for a 0.-40c flap, to a 0.20c flap. Data on the pressure across the flap nose seal and a method of applying these pressure data in the design of internal balances are presented. Tab datP- are presented for the plain flap and for a flap with aerodynarlc balance. SYMBOLS The coefficients and s:/mbols used in this paper are defined as follows; C7 airfoil section lift coefficient (l/qc) NACA ARR No. 15? 06 3 c^ airfoil section profile-drag coefficient (dg/qc) Cm airfoil section pitching-momont coeffi- cient (m/qc^J C]^„ flap section hinge -moment coefficient fh^/qc^ / Cj-^ tab section hinge-moment coefficient (h^/qc.'^J Pf^ resultant pressure coefficient (- . " — -J where I airfoil section lift d-. airfoil section profile drag o m airfoil section pitching moment about quarter- chord point of airfoil; positive moment moves nose of airfoil up h^- flap section hinge moment about flap hinge axis; positive moment moves trailing edge down h^ tab section hinge moment about tab hinge axis; positive mioment moves trailing edge down c chord of basic airfoil vjith flap and tab neutral c^ flap chord from flap hinge axis to trailing edge c^ tab chord from tab hinge axis to trailing edge q free- stream dynairdc pressure p-r static pressure on lower surface of seal P-rj static pressure on upper surface of seal and c-^ balance chord Oq angle of attack for airfoil of infinite aspect ratio; positive when nose of airfoil moves up 4 NACA Aim xlo. ~I^Fp6 5f. flap deflection with respect to airfoil; posit when trailing edge is deflected down 6, ta'o deflection with respect to flap; positive v/hen trailing edg'e ic deflected down itive »sr = y^i c^,£. ■I ''a \ncr~. J ^■H "^^t ~ V65 CChA f'^t Ch-f = ^'^^^f = V^^ d cv. '"f^t = V"t 6ci.^ °0'°f The r.ubccripts outside the parentheses repr-esent the factors held constant during the msasureTTi.ent of the pararreters. ARR No. L5:-^06 APrARATUS AKD MODEL The tests were made in the Langley 4- by 6-foot vertical tunnel described in reference 2 and modified as described in reference 5. The model, Then mounted in the tunnel, completely spanned the test section exceot for ■^--inch clearance p-aps between the model and the tunnel walls. V'/lth this type of installation, two-dimensional flow is closely approximated and the section characteri,='tics of the airfoil, i]ap, and tab may be determined. The model was attached to the balaiice frame by torque tubes that extended through the sides of the tunnel. The angle of attack was set from outside the tunnel by rotating the torque tubes with an elecbrlc drive. Flap deflections were set by an electrical position inciicator, and tab deflec- tions v/ere set by a templet. The hinge moments of the flap were ricasured with a special torque-rod balance built into the model. Tab hinge moments wore m.easurod by an electrical strain gage installed in the model. For tests of tlie plain sealed flap, the pressure difference across the gap seal was measured on a manometer. The model (fig. 1), v;hich bad a chord of 2 feet and a span of 4 fee:t, was made of laminated mahogany (except for a steel tab), was aerodyno.mically smooth, and conformed to the NAGA 0009 profile (table I). It was equipped with a 0.20c flap and a G.20cf plain tab. The flap had a plain nor.e with a radius that was approxi- mately one-half the airfoil thickness at the flap hinge axis or was fitted v/ith 0.35c^ or 0.50Cf. blunt-nose or elliptical-nose aerodynam.lc balances. The el].ij)tical nose, the ordinates of v>rhich are given in table II, v^as a true el].ipso tangent to the airfoil contour at the flap hinge axis. Tlie radii shown in figure 1 determined the blunt and plain noses. The various nose blocks were interchangeable and v;ere fastened to the flap at the iiinge axis. In order to keep the -ap at the flap nose at 6,005c, blocks corresponding to each balance chord were attached to the airfoil j".'"t ahead of the balance. For the sealed- gap tests, airtight fabric ww-v fastened betv/een the flap nose and the airfoil. NACA ARR No. L5F05. The 0.20c£ tab had a nose radiu.^ approximately one-half the airfoil thnckness at the tab hin^e axis. The tab gap was 0.001c for al] the tests. TESTS A dynamic pressure of 15 pounds per square foot, which corresponds to a velocity of about 76 miles per hour at standard sea-level c:inditions , v;as used throughout the tests. The test Reynolds number was 1,430,000 and the. effective Reynolds number was approximately 2,760,000. (Effective Reynolds number = Test Reynolds nijimber >^ Turbulence factor. The turbulence factor for the Langley 4- by 6-foot vertical tunr:el is 1.93.) The Mach number for the tests v/as about 0.10. The maximum error in anp:le of attack anpears to be +0.S'^. It is estimated that the flap and tab deflec- tions v/ere set within ±0.2^. An experimentally determined tunnel correction was applied to the lift coefficient. In accordance with a theoretically derived analysis similar to that presented in reference 4 for finite-span models, the angle of attack and the hinge-moment coefficient were corrected for the effect of streamiline curvature Induced by the tunnel walls. The increments of drag coefficient are believed to be reasonably independent of tunnel effect, although the absolute value is subject to an unknown correction. Inaccuracies in model construction and assembly of inter- changeable blocks probably caused the small flap hinge mom.ent at a^, = 0*^ and 6^ = 0''^ . A summary of iniormation for convenience in locating the data for the various m.odel configurations is presented in table III. RESULTS AMD DISCUSSION Lift The lift-coefficient curves for the plain flap and for the flaps with various overhangs are given in figures 2 NACA AKR No. L5F06 to 11 for the flap ga-nr; both sealed and unsealed. These curves were nonlinear at larfe flap deflections. The flaps vv'ith elliptical-nose overhangs generally developed lift to larger flap deflections than those v.nth t)]-unt- no ^ e ove rhangs . Parameter values obtained from figures 2 to 11 are surirr^ara zed in table IV. The variations with balance chord of the lift parameters C7 , c; . , and Qc are ^ ^a' ''Of' 5f given in figure 12. Wj.th tie gaps sealed and unsralod, the plain flap had the largest values of the slope of the lift curve c^ , v.'hereas the values of c^ for the 0.50C|> overhangs were the same as or larger than for the 0.35cr. overhangs. This variation was simjlar for the 0.40c flap (reference 1) . A red\iction in c, caused by unsealing the gap increased with balance chord. The valiie nf c-, . was usually lara-er for the blunt than for the ell:!ptical nose. Except for the flap ?.'ith the 0.£Ocf blunt-nose overhang, sealing the gap increased Sf The flap lift effectiveness paraiueter ag^ decreased as the balance chord increased, except for the flap v«ith the unsealed blunt-nose overhang, and v.;as usually larger for the blunt-nose than for the elliptical-nose overhang. Sealing the gap increased og for the elliptical-nose overhang and the plain flap but generally decreased it for the blunt-nose overhang. The values of a^^^ given in table IV and figure 12 were ineasurcQ over a snail flap deflection range at c^ - and therefore are mainly useful as a comparison of the various configurations tested. Hinge Moment The curves of flap hinge-moment coefficient as a function of angle of attach at constant flap deflections are presented in figures 2 to 11 for the plain flap and for the flaps with various overhangs. No appreciable flap oscillations were noticed throughout the flap deflection range tested, although such oscillations occurred on the 0.40c flap (reference 1) . 8 IIACA ARE No. LSPO'^- The hinse-moment parar.eterr Cv, ,^ and c^^ presented, in table IV and pdotted apalnst balance chord in figure 13 indicate that the O.SOcf blunt-nose over- hanr was overbalanced (c\~,,., was oocitive\ and had a positive C];i^ for the gap sealed and un?ealed. (Value.-^ ^^ on of c-^^ v;ere determined at a^ = and at 6^ = C and values of c-^,^ were determined at a^ = and small flap deflections.) The C.£Oc flap v;as found to be overbalanced for conditions siinilar to tho'?e for which the 0.40c flap tested on the same airfoil (reference 1) had been overbalanced. For the flap with the O.SOCf^ overhan'i, c-.f^ could be made negative by 1 -J' '"-Of the use of a tab deflected in the sarrie direction as the flap. The 0.50cv:> elliptical-nose overhang, v.-ith sealed and unsealed gap, had a positive C]^,. at 6^ = O'"' ; at lar:y;er flap deflection?;, hov-"ever, -an increase in angle of attack or flap deflection generally gave a negative increment of hlnge-monent coefficient (figs. 10 and 11) . For the 0.50Cf blunt-nose overhang, flap deflections up to approximately 15'^ r.s-ve xjositive incre- ments of hinge-moment coefficient; changing the flap to larger deflections gave negative increments. Figure 13 indicates that, for the unhealed tlunt- nose overhang, C]-,^ had a lare'er variation with i5f balance chord than Cv,.p ; for the sealed blunt-nose ■''la overhang, the variations of Ci-„ and c-, were about a ''-^5f the same in the ranfre of balance chord from- 0.3£c f to O.bQCp. For the sealed and unsealed elliptical-nose overhangs, c^. had a larger variation than cv,^ . " ^'^a '°f Changing the nose shape from blunt to elliptical made c-^ more negative for the sev.led gap and more positive for the unsealed gap. Changing the nose shape from blunt to eliictical also made Cv„ m.ore negative at small flap deflections and less negative at large flap deflections. NACA AR.R No. L5F06 Sealing the gap at the flap nose generally made c-^^ and Ci. more negative, ^ ^ a Since the aspect-ratio corrections for streamline curvature are always positive (reference 5) and since the hinge-moment parameters are very small and the signs are critical for several of the flaps vjith overhangs, the slopes m.ay change from negative to positive and produce an overbalanced flap on a finite-span wing. Becau"e the hinge-mom.ent parameters shown in table IV represent the slopes of the curves at 5f - 0'"* and a = O'^' these parameters should be used miainly as an indication of the relative merits of the different flap nose shapes. Because the tabulated slopes are valid for only a small range, the curves of hinge-moment coefficient should be used, rather than the tabulated parameters, in the calcu- of a control s.urface. P i t c h i ng M om:e nt Values of the pitching-moment oarameters [''cv>, "l 5f 64- and /c„, \ are shov/n in table IV and indicate the position of th,e aerodynamic center with respect to the 0.25( point. When the lift was varied by changing the angle of attack at 5f = 0^, the aerodynam.ic center for the plain sealed flap was located at the 0.26c point; the aerodynamic center for the balanced flap v;fith sealed gap, I'egardless of balance chord or nose shape, was near the 0.24c point. The effect of unsealing the gap was to move the aerodynam.ic center 0.01c forward. The centcr-of-lift positions due to flap deflections up to approyi:!iately 15^ are given in the follov;ing table: 10 NACA ARR No. L5F06 \ Center-of -llf t position caused b?/ flap deflection (percent c) Gap 0.35c£- overhang 0.50Cf. overhang Plain overhang ; Blunt 'Elliptical nose j nose Blunt nose Elliptical nose Sealed. 0.005c 46 46 45 44 44 47 44 43 46 50 This table indicates that the was the same for the plain fl sealed or unsealed. The effe of Increasing the balance cho of-lift position due to flap blunt-nose and rearward on th The center-of-lift position c a function of the aspect rati moves rearward as the aspect center-of-lift position ap whether the gap was ct of unsealing the gap or rd was to move the center- deflection forward on the e elliptical-nose flap. au?ed by flap deflection is (references 5 and 6) and ratio decreases. Drag Because of an undetermined tunnel correction, the measured values of drag canr.ot be considered abf overhang. The effectiveness of the tab in cnanglng the flap hinge moment decreased v/ith tab deflection. A comparison of figures 3 and 16 with figure 15 showed that the tab effectiveness generally was the same whether th.£ flap was at 0'^ or deflected. Pressure Difference across Plain-Flap Seal The variation of resultant pressure coefficient across the plain-flap nose seal with angle of attack at constant flap deflections is shown in figure 19, ' The change in resultant pressure coefficient with angle of attack .^ — 11) was found to increase with flap deflection. -^ The data of figure 19 can be used with those of figure 3 to determine the flap section hlnge-morjient coefficient at a given angle of attack and flap def 1 ec- tion for a 0.20c flap with an internal balance on an ITACi 0009 airfoil. It can be shown that {'ehf)j3 = chf + FrK (1) Vihere /c^-,A section hinge -mo?iient coefficient for flap with V -^/IB internal balance 12 NACA ARR xTo. L5PCS c--..^-, section hj.nge-mo-nor.t coefficient for plain flap with pap sealeol, obtained from figure 3 P-3 resultant crersur-e coefficient, oVjtained Irorn fi.-^ure 19 / o •c_^'\2 , \c^ /■ constant, obtained fro- figure 20 * - ' t seriithickne5?s at h3n~e a::is Cvj' balance chord plu? ore-half .^ap width The hinge -moment nararreters ci-,^ and Ci^ deter- ■-a '-f6f mined froR-; flap hinge -moment coefficients obtained by equation (1) are plotted in figure 13 for internal balances of various chords. CONCLUSIONS Blunt-nore and elliptical-no.^e overhangs of 35 and 50 percent flap chord fo.3£Cf and 0,50c£.) and a plain overhang: on a flap having a chord 20 percent of the air- foil chord (0.£0c) have been tef^ted in tvifo-dimensicnal flov; on an NACA 0009 airfoil. A liirited investigation was also r.ade of the cnarac ceri ,<:'ticE of a O.idOc^ plain tab The results of the tepts indicated the follo-./ing con- clusions: 1. The slope of the lift curve was largest for the plain sealed flap, whereas the slope? for the O.SOcx. overhangs were the same as or sliP"htly larger than for the C.35cf overhangs. A reduction in slope caused by unsealin.g the gap increa-^ed wj th balance chord. 2. The variation of lift coefficient with flap deflection generally inci'cased when the gap vv'as sealed and when the nose was changed from elliptical to blunt. 3. The flap lift ef f ecti^.'cness pararieter ag^ generally decreased when the overhang chord was increased and was usually ' larger for the bl'ont-nose than for the elliptical-n,-)se overhang. Sealing the gap increased a5„ NACA ARR No. L5F06 ir5 for the Dlain fl^ap and for the elllptic.al-no.'?e overhang hut generally decreased it for the blunt-nose overhanr. 4. Sealin'j the gep at the flap nose r.iade tlie varia- tion oi" flap hinge-moment coefficient with anfrle of attack more negative; changing the nose shape frora blunt to elliptical made this variation more negative for the sealed gap and .nore pocitivc for the unsealed gap. 5. The variation of flap hinge-moment coefficient with flap defloctioa wa.s generally more negative with a sealed gap than with an unsealed gap. Changing the nose shape frora blunt to elliptical made this variation more negative at sm.all flap deflections and less negative at large flap def } ectloi.s. C. llie change of flap hinge-moment coefficient with flap deflection, for the unsealed blunt-nose overnang, had a larger variation with balance chord, than the change of flap hinge-mcm.ent coefficient with angle of attack; for the sealed blunt-no3e overhang, these variations v\?ere about the same in the , range of balance chord frora 0,55c.r. to O.^Ocj-. For the ."=;ealed and unsealed elliotical-none overhangs, thu change of flap hinge-m-oment coefficient with angle of attack had a larger variation than the change of flap hinge-moment coefficient with flap -Geflection 7, For all conditions, uxisealing the gap m.oved the aerodynamic center forward- about 1 percent airfoil chord. Unsealing the gap or increasing the balance chord moved the ceater-of -iif t position due to flap deflection forv/ai'd for the blunt -nose and rearvirard for the elliptical-nose flap. 8, The tab was slightly more effective in changing the lift and the flap hinge mom.ent on the plain flap than on the flap v/ith 0,35Cf elliptical-nose overhang. Langley !?emorial Aeronautical Laboratory Rational Advisory Committee for Aeronautics Langley Field, Va. 14 MAC A ARR No. L5F06 REFERENCES 1. Riebe, John '•'., and Church, 03 eta: Wind-Tunnel Investigation of Control-Surface Characteristics. XXI - Medium ai.d Large Aerodynanlc Balances of Two Nose Shapes and a Plain Overhang Used with a 0.40-Airf oil-Chord Flao on an NAGA 0009 Airfoil. KACA ARR No. L5C01, 1945^. 2. uenzlnger, Carl J., and Karris, Thomas A.: The Vertical Vaind Tunnel of the National Advisory Comr^iittee for Aeronautics. NAGA Rep. No. 387, 1931. 3. Sears, Richard I., and Gillis, Clarence L. : Wind- Tunnel Investigation of Control-Surface Charac- teristics. VIII - A Large Aerod;^mamic Balance of Two Nose Shapes Used vn'.th a 30-percent-Chord Flap on an NACA 0015 Airfoil. NAGA ARR, July 1942. 4. Swanson, Robert S., and Toll, Thonas A.: Jet-Eoundary Corrections for Reflection-Plane Models in Rectan- gular Wind Tunnels. NACA ARR Nc . 3E22, 1943. 5. Swanson, Robert S., and Gillis, Clarence L. ; Limi- tations of Lifting-Line Theory for Esti>ration of Aileron Hinge -'i'loment Characteristics. NACA CB No. 3L02, 1943, 6. Anes, Ml. 1 ton B., Jr., and Sears, Richard I,: Determi- nation of Control-Surface Characteristics from NACA Plain-Flap and Tab Data. NACA Rep. No. 721, 1941. 7. Ames, Milton B., Jr.: Wind-Tiinnel Investigation of Control-Surface Characteristics. Ill - A Small Aerodynamic Balance of Various Nose Shapes Used with a 30-Percent-Chord Flap on an NACA 0009 Air- foil. KACn ARR, Aug. 1941. I'TACA ARrl No. I,5F05 15 TABLE I ORDIN^.TES FOR NACA 0009 AIF:FOIL [stations and ordlnates in percent a,lrfo3M chord] Station Upper surface Lov;er surface | 1 1 1.25 1 . 42 -1.42 2 , 5 1,9S -1.96 £^. 2.67 -2.67 7.5 o . Ic -3.15 10 3.51 -3.51 15 4.01 -4.01 20 -1 ^ r\ ■ -4.30 25 ■;.46 -4.46 30 4.50 -4.50 40 4.35 -4.35 50 3.97 -3.07 60 3 . 42 -3.42 70 2.75 SO 1,97 - 1 . 97 ■ 90 1 . 09 -1.09 95 .60 -.60 100 (.10) (-.10) 100 ■ L.E. radiuf^: .89 NATICKiiL ADVISORY CO:SiITTEE FOR AERONAUTICS \ NAG A ARIl Ho. L&i^OCT TABLE II ORDIKATES FOR 0.35Cf. AND 0.';0c^ ELLIPTICAL-NOSE OVERHANCrS [Stations measured from forward end of overhang; stations and ordinates r^ieasured In percent airfoil chord] 1 ! 0.35c p overhang 1 0.50c-f overhang station Ordinate Station Ordinate .03 .21 .03 .21 .12 .42 .15 .42 ,18 .62 .36 .50 .83 .65 .33 .81 1.04 1. 05 1.04 1.22 1.25 1.58 1.25 1.75 1.46 1.46 2.48 1.67 3 . 17 1.67 2.85 1.75 3 . 63 1.75 3.30 1 . 33 4 . 18 1.33 3.90 1.92 4.67 1.92 4 . 92 2.00 5 . 86 2.00 5.67 2.02 6.70 2.04 6.42 2.00 7.67 2 .06 7.00 1.97 8.64 2.04 9.48 2.00 10 . 00 1.97 NATIONAL ADVISORY COMMITTEE FOR AERONaNTICS NAG A ARR IIo. LE?03 H H E^ .r~i. ■ o o o o Ci, oj ■qw ,Q nJ -iJ 9*^ ^ ii -p .■-H w ^r-J t--i :1 p-l r-H t/^ f-1. 1^ e-1 ■■ r; t^ €■.} o * o 1 — ' Hi CI: h-i P. u. oj i' H r-1 O iV-t o o H-1 1.^ i.,:J r.) f-^l • C5 o r^'r Xi +i •H ^ r-i •r-l O • 1 f-l •» 1 -' •y-i ,.;j in in LO LC- ! bO 1— r-i ,— 1 r-i 1—1 rH tH &, •\ "^ ♦v •> •■ -. o H CD !> CO C\i to -^1 U.) ^ £:- CO C) rH rH rH r-H rH 1 i ! t:j o o o ! 1 ;'-' , — ^ |^^^ CJ Kj ' 1 05 ^-■U i 1 f^' (D o o O O o O o o o O o o o I 1 'O ■p -p -p ■iJ V ^ 1 O O I i o 1 t-O o o lO lO i-O Lf3 in o in O oo i !^ ,-— ^ fO [O Ci C>1 C-J CJ CJ CO w OJ rj CQ ct! M i fn CD C) T) O C o o o o o o o o c^ •"(J J_) -iJ -u -p -p -p 4-5 -p -P -1- -P 4J ^ •^ — ! O O i i c o o o CJ o o o o o o :=i- 1 a O XJ O Ti o Tj o Tj O -I? 'd t:> ^J tj l/j o iO ^ u: G •H •H C C 'H •H •r-1 03 -P -P -p -P J..J ^; ■4J -P a P-,- -P ■p ft M. Pi ?H f^ c •rH •H C f-.; -H •H •H 0) r< d rH ( — i :3 ;3 r-! 1 — i r-J > rH rH rH rH (— i •-i r-i r-H rH o ^ ^ CD (P ^ ^ QJ CD o tp --M UJ id to a r-1 r-l • • • • • • ■ • r-; . rH . Ph M-t o o O O o o o o PhCJ Ph CO o M Fh >-l 1— ' -*H ^H fj o-' Ci M .Qi > l-cl i-:i •t:; -h: K n o -i: CiH C-J w Pi W f;H L-( -M R ►-;- h-l 1^— * »-=^ 1=:^. O r,-) \ NACA ARR No. L5F06 18 TABLE IV PARAMETER VALUES FOR 0.20c FLAP WITH PLAIN, 0.35Cf-, AND O.SOCf. OVERHANGS ON NACA 0009 AIRFOIL [slopes taken at ao = 0° and 6^ = 0°] Parajneter 0.35cj. overhang 0.50c. overhang Plain overhang Blunt nose Elliptical no se Blunt nose Elliptical nose Gap sealed Gap 0.005c Gap sealed Gap 0.005c Gap sealed Gap 0.005c Gap sealed Gap 0.005c Gap sealed Gap 0.005c M ^''<^. 0.102 0.096 0.096 0.087 0.097 0.086 0.100 0.090 0.098 0.086 (■"''') ^'-L^. .052 .042 .044 .043 .047 .032 .046 .049 .040 .030 -.51 -.44 -.46 -.49 -.48 -.37 -.46 -.54 -.40 -,34 /dchA -.0050 -.0025 - . 0022 -.0006 -.0046 .0008 .0017 .0039 .0012 .0048 -.0122 -.0097 -.0020 -.0022 - .0044 - . 0023 0026 .0064 -.0012 -.0012 .0135 .0104 .0230 .0103 .0232 .0070 .0167 .0133 .0136 -.206 -.207 -.200 -.192 -.194 -.223 -.191 -.176 -.210 -.247 NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS \ NACA ARR No. L5F06 Fig. 1 ^ § 0) o UJ CD O % c:5 Co ^ ■C; <^ to I t I ^ ^ ^ " s P 5 -8 q \ NACA ARR No. L5F06 Fig. 2 I I I W 14 1.2 10 .3 .6 .4 -z -A- ^ -6 ■:d -1.0 -I.Z -ZO -16 -IZ -6 -4^ 4 S Angle of atfacAjOCo j deg F/ffi/re <2 -/leroc/(^/7a/??/c secf/on characferist/c^ of an /f/ICA 0009 o/rfo// y\//f/? a O 20c p/o/n f/ap. r/ap gap, 0.005c; fab,O.ZOCf; fab gap,0.00/c; ^f ^ • NATIONAL ADVISORY COMMITTEE FOt AEDON/tUTICS NACA ARR No. L5F06 Fig. 2 Cone. •^ ^^ ^ ^ -/ 5§ :^ <0 ^1 .08 .04- -.04- -.08 ■^^ ^ ^ -/^ ^ Q 5 . -.16 i-^ -.zo <:: t^ r. •'^ ^ ^ ^ .^ -z^ ^S ^ V -.Z8 ^ "o a -3Z < -.36 -.40 -.44- -ZO -16 -IZ -8 -^ 4 8 /Z /6 Angle of attach, a^ , deg Fjgure Z .-Concluded. NATIONAL ADVISORY COMMITTEE F0« AEDONiUTICS \ NACA ARR No. L5F06 Fig. 3 i.e 14 /£ 1.0 .6' .^^ 7^ 4 ^ ^^ ^) .^ .'d ^ s:^ • Si V -z to -4 t X -e -d -1.0 'I.Z 1 f ^ A ^A\ A v/ M f\tt / i/' r A V / R [ / w / 1 A I F/ V / / ^ ^( A w / 1 ; / (i T 1 — . Y// \\ ^ \ / 3C ^/ r / / / 1 V 25 jj 1 \i / 1 r c ',(7^ Y / I > ^ '^\ I V / / y] (/ J / / < f / h J / / 1 f / / (/ (deg) - 6 ° 10 ^ 16 - ZO o 2t5 - 30 / I / / / / i t 1 / ^ // / f / / s / ''k V / / f\ \ A / / / 1 / < ^ f / / / \ / f / / \ / / / \ Y / \ A ; V / -zo 12. 16 ■le -/£ -6 -4 4- Q Ang/e of attack ^cCofleg F/^are 3 .- /lerodgnomc sect/ on choracferistJcd of an A^/lCf) 000 9 oirfo// i^/f/? a O.20c p/ain f/ap. Flap gap sealed- fob^O.ZO Cf, fab gap, OOOIc-, 6^-0". NATIONAL ADVISORY COMMITTEE FO* AEDONAUTICS \ NACA ARR No. L5F06 Fig. 3 Cone. So 5: ?5 ^ -ZO -16 -IZ -6 Angle of ot^ackyOOo, deq national advisory ^ -, ^ "^ ^ ' •J rnuuiTTFr FOt UBONIUTIC /-/gure J rConc/uded. COMMITTEE FM AUONAUTICS NACA ARR No. L5F06 Fig. 4 I I I /.4 /.2 W .8 \ /// / ¥ t A A ¥ / ^ / // A / \ M f / 1 ^ 6 A V / V / 'deq) / v V / / i A 1/ / / / L t 1/ / / ~?.o / / ( / \ N . ^ ■■ J> L) v / \ '// ' 'U / / V / V / y / 5 b / / . ! (decj) ° 10 ^ 15 - zo o Z6' A if / A \^ / V / / / / .i / / / ,/ / i V H / ; ' / / r .S iV / / / / \ \/ / / / \ \f / / / ^ / / \ / / a ^J / .6 4 .2 -4 -.6 -8 -1-0 -iz -ZO -16 -IZ -8 'A- 4- 6 /2 16 An^Je of attack ^cco y d<^S F/aure 4. - /lerodt^namic section choracter/st/cs ofoA7///ICA 0009 o/rfo/7 /4^/rA a O.ZOc f/ap ho^//7^ a O.SScyp oyerhongr py/f/? blunt no6e.Flap gap, O.OOSc; tab, O.ZOcf, ta,b gap, 0. 00/ c- 6^ = 0". NATIONAL ADVISORY COMMITTEE FO* AERONAUTICS \ NACA ARR No. L5F06 Fig. 4 Cone, f>» 5^ V: C ^ ■■^ *o ^ ^ ^ c; $ ^ «^ '^ 'O ,<:i is ^ ^ I (J ^J - -ZO -16 -IZ -Q -"h ^ 8 IZ 16 Angle of attach , cKq , deg Figure 4.- Concluded. NATIONAL ADVISORY COMMITTEE F0« AIROHAUTICS X NACA ARR No. L5F06 Fig, 5 I I I /4 /.2 1.0 .8 .6 .4 .Z 'Z r4 ■76 -w -I.Z 16 -ZO -le -/^ -8-4 4 8 y4ng/e of atfacA :,cx:^ , deg F/'gure 5 .- /leroc/y/yamic } / / 7 /\ A / / / \ \ / / } 1 / /J / ■ % / / / 7 / r /j M / ^ / / / / V ^ ; h \\ / / / V / / k \ / -z -4 -.6 -1.0 -I.Z -ZO -16 'IZ -8-4 4 8 II 16 Ang/e of aftacA, oco , d'e^ F/gare 6 .-Aero $ 4 % KS ^ .a. •^ ^ k^ A> V^ t2 (^1 s -4 ^ A - X :6 -6 -1.0 -1.2 -ZO -16 -la -8 -4 4 8 1^ 16 y4ng/(? of attack, cc^ , cit^Q F/(^ur£> 7. - /4eroc/i/r?am/c section choracten6t/cs of an A^AC/I 0009 oirfo/7 kv/ft? a 0.20c f/op tioy//?g a 0.36cf oi^er/iang tv/Y/? el/ipt/co/ nose. Flap gap sealed; fab,O.ZOcf^fab gap^O.OOIc -, S^^^O"". NATIONAL ADVISORY COMMITTEE FM AEDONAUTICS \ NACA ARR No. L5F06 Fig. 7 Cone. 5^ 5 -16 -IZ -8 -4 4 8 /^ /1nq/e of oftfofck :, oOo ; <^^g F/^c/re 7. - Concluded . NATIONAL ADVISORY COMMITTEE FM AEDONAUTICS \ NACA ARR No. L5F06 Fig. 8 1.4 12 1.0 0- .s % ■^ .6 \, % 4 ^ ^ k .2 -* 1 i:: ^ ^ -2 .\ N t -4 .^ \ _ NATIONAL ADVISORY COMMITTEE FO* AEDONAUTICS /' \ / A ^ A^ f, /s\ /; (/ Y / \ 1 y- /J '/ r \ / / // / } 1 / A / / / ^ / / f/ / ,^ / '' / <2( i / / / 7(7 A ') 1 / A ^ ) / / A ( / 7 f/ / / J A h / 1 P k ' J (deg) o - 6 - 10 > 16 - 20 o 25 A r \ ' / f / \ . / / / s l/ h '/ / k \/ ^ / / 1 / / 1 / / / X 1 \^ ' f / / \ . / / / f / \ / / \/ V 6 rS ~I.O -1.2 -20 -16 -12 -8 -4 4 S 12 16 An^Ie of aifocAjOCo yC/egf r/gare 8 .~/^erocfi//7amic ^ .08 ^^ .04^ -.04 -W £; -OS o 1 ^» .^ .6 Ss ^) c> .4 \) ^ Z ^ .§ •f: ^,> ^ -cL N 1 r4 .V .> X '6 -8 -1.0 -i.a // \ /, r \ } V / > \ V^ i / / \ /. / / \ / ' h ' . / V \ \i / / / // \ V 1 r '/ / / / /A \ V \a / / / (deQ) -?o /; \ p 1 I } '\ 1 / 1 \ / ' c ^ I — \ N. V ~l ^J V ^ 1 / \ ^ // m { / s^ A / / i, ,/ p G / / h /' ^ "^ / / / 1 / ° 10 - 15 ^ 2.0 / / 1 / / / / h E ./ (^ / / t H / / \ V / V \ / ^ ' -zo -16 -/a -3-4 4 s /e le Ang/e of affo'cA: _^cCo yolec^ F/'qure 9 —y^ero diy/iam/c s<^ct/o.'7 charade t/si'/cs of an A^/\C/I 0009 crirfoJ/ m//'/-/? qO.^Oc/'/o'p hoi//ng cf O.SOc^ ot^er/?^/?^ i/v/f/? /:)/unt no6e.F/ap gap sealed} f ah, O.ZOcf-, fab gap, 0.00 /c; S^=0°. NATIONAL ADVISORY COMMITTEE FM AERONtUTICS \ NACA ARR No. L5F06 Fig. 9 Cone, II -^5 I -I rZ ■IZ .08 04 (i. ^1 -04 Co *^ -OS ./2 -16 -.^0 rw% \ l< 0, s rrO- n \ o-o — ^ — ( — ^ 5 *! 1 i : i — ' > A-^ \ ^ w /^, ^- P \ I ^— -c— t , 15, 0==^^'^^'^ V ^ ^. [Zi _^ id eg) ° ^ - 5 ° /^ ^ IS - 20 ] 1 1 1 (deq) \. £j J p ■ I; Ac * 1 h^ ^ M I~— 1 — L 5 ^ ^ ^ K ~-^ — ^ h^ rv , — ' n i ^ \ 0. ^ ^ r \ \ \ \ \ \ \, \. k H \ \ V -) \ \ \ \ O \ \ \ \ \ \ \ ^ N Jk K N -^ N ' — ' \ \ S V -£4 -ZO ~I6 -/2 -8 -4 4 8 IZ An^Je of crtfocM, cco :, de^ r/^c/re 3. - Concluded . 16 NATIONAL ADVISORY COMMITTEE FM AERONtUTICS \ NACA ARR No. L5F06 Fig. 10 O •40 u O /2 1.0 .& .4- Z -4 -6 -.6 -1.0 -20 IB. /6 -lib -/Z -0-4 ^ Q Angle of attack, oc^^ deg Figure /O. - Aerodi^r?a/7?/c sect/' on chariycfer/sf/cs of or? A^/)C/I 0009 ajr/b/7 h^/t^/? a O.^Ocf/ap hc/y/'/i^ (7 O. 60c^ oi/er/7a'/7(j lA/Zf/i e///pt/co/ nose. Flap gap, 0.005c; fab, 0.2.0 Cf, fab gap, O.OOfc ; 6^= 0°. NATIONAL ADVISORY COMMITTEE FM AEDONAUTICS NACA ARR No. L5F06 Fig. 10 Cone. -ZO -16 -/Z -8 -4 4 8 IZ 16 Ang/e of attack, oc^ , deg Figure 10. - Concluded. NATIONAL ADVISORY COMMITTEE F0« AERONAUTICS \ NACA ARR No. L5F06 Fig. 1] .0 I 1 — [— L4 <^ / ?^ \ I.Z / / / \ r/ / / A / \ 1.0 /. y\ ^ / / \ A / / / J i 1 .8 s y/ / / / / y / f / 5 .6 A / / a 1 / I \ / / / ^ \ y y / 21 u \l / / / .2 / 1 1 / / ^ / ^ 7 9 (/ > / / K /, / J f X / / / / (deg) e Q - s ° /O - 16 ' ZO -z / f i / / ^ / 1 / h / -4 / / / r /, / V 7* 1 / / / / -.6 ^ s/ ) / / L / t / / / / -6 f / / \ / / / -1.0 1 ^V ? / \ / -1 c \ 'ZO '16 -la -8-4 4 6 JZ 16 y^nqJe of otfackjcc^jdeg F/gare II . - /^erocft^nam/c sect/o/? character/sf/c^ of ar? /V/ICA 0009 a/rfo/'/ 14^/t/? cr0.20cf/ap hai^//7q a O.SOc^ o^er/?<7/?^ ^/t/? e/l/pf/cal nose, flap gap sealed; fab, O.ZOcf, fab gap, O.OOIc; 6^=0°, NATIONAL ADVISORY COMMITTEE FM AEDONtUTICS ■x NACA ARR No. L5F06 Fig. 11 Cone. I <3. <13 <0 •^ k I I ^ o Of ieq (c 1 v-o- 3 \ M /\ fi c T — \ \ s — i r — ^ n \ -./ V ^ — r — r" JO. r ] — ^ ^ \ vJ — ^ i — \ — ( r— 1 % lb. -- ^-^ [^ -z V^ -\ •^ 7 - 5 -10 >/5' v20 c M 1 fripn) r vo 1 5- —] ;> X < > — J.. 4- F>rfl -M c| ^ F^ U=^ _r 1— ^ 1 — r p ), 1 — ' d^ *^J ^^ c -i V "^ M K h k -06 N % 5- \ \ V \ -It \ N > ill \ \ !• -.16 \ \, \^ '^? -20 ^ ^ ? V \ -r>4 \ -2^ -/6 -/£ -5 -f f 8 Angle of affach , a^ , de^ IZ 16 ^/gare // .-Conc/aded . NATIONAL ADVISORY CONMITTEE F0« AERONtUTICS NACA ARR No. L5F06 Fig. 12 .1/0 NATIONAL ADVISORY COMMITTtE FM AERONAUTICS .100 £ , C ~~~- ^t ^ .090 •^ •\. ^ - --- f^- 1 I .060 .050 G ^ ^- ,^ ' ^ -^ ^^ > .040 C — — — jrt f=^ \^ .030 k.-__ __ o Blunt nose ^ Ellipf/cal nose .020 -.30 Sealed gap 0.005c aao I J 1 , ^' c ^ ^ -50 ~^:^ =— =c -— ^ (^ ( ) c ~~~~'-- "^ ' o J .^ .3 4- .5 "^69 Figure 12. .- Variaf Ion of a info 1 1 section lift parannelers with overhang on /VAC A 0009 a/rfo/f. F/op, 0.^0c -, f/ap gap, sea lee/ and 0.005c ■ Tad ,O.^Oc^ } fo^ gap ,0.00/c ) 6f =0° ■ \ NACA ARR No. L5F06 Fig. 13 :§ — <^ o^ Ni ^ ■^1 W ^ ^-s o a •*- Si ^ Ct o- ^ ^ >^ ^^ V ^ k I si ^ ^ ^ I \ NACA ARR No. L5F06 Fig. 14 I 8 f I I .06- .04 .OZ I „^ -.OZ I Sealed gap Q^OOBc gap ) 1 ^'/ / a" /., ^ ) ^ A / / ^0 iV ^ x- r / i > (deg) -8 o A 3 '1? i/ ^ '" r^ / o^ ^ y ^ '2^ > - ^'1 ,-^ ^ -^ '6/ / ■^H 22 r^ r-^ -' " / / :i___ ■ -? -- . _j -o- _- ^>< p- — 1 ' _J 4 8 12. 16 ZO Z4- Z8 3Z F/ap def/ect'ioh,S^ ,deg F/^ure 14- .- Incremenf of o/r/b/7 sect/o/i profi/e-dra^ coeff/c/enf caused bu def/ecf/on of a 0.2,0c pltyin f/^ r^ -a A ^ r^ "^c: =«b :r:_. ! ^ rfr^ V- t=V^ 4 8 12 16 2(9 2A 26 F/op def/ecfion jSf ,deg Figure /5'.-Tncre/7?ent of o/'rfo// ••^ '2 o ■§ .08 -.08 r/6 T2f -32 .-/lO c XJ -S6 -12 -30 -M '20 Figure 16 fK 16 -12 -& -^ b 4 6 /2 16 ngle of attack:, ccoj deg Corit/nued. NATIONAL ADVISORY COMMITTEE FM AEMMAUTICS \ NACA ARR No. L5F06 Fig. 16 Cone, m m r\ Q> \ -M -OS ^ 5: -1? % ^ -16 ^ (b -20 v>^ -^ ^ -.24 ^ ■^^ '2d *.) ,^ •o t32 ^ l§ -3b (d r \ r3d q < — — - 1^3 \' S-, r^ ,^ 1 JM __^jj ^ b \ \ >. ^-^ ^ U^ ^^ ^ r \: N N l^ X r^ H ) ^— ) hv m r^ "" \ T % ^ ^ <\) to rd N N t -4 ^ -.6 -8 -1.0 NATIONAL ADVISORY COMMITTtt fM AEHOMAUTIC! (deg. 7, Y f 1 ' / / Z 0/^ 1 f 7 / \ 2 1 / p r/ -x / 7 1 f 1 /, V / \ 0/ / / / i / / / r/ h / 1 1 / i ly / / r 1 1 M / / / / / I y / > / ft y / o/ P •i / 1/ If A f / I / / / / ) ^ / / f / / ' / / s L 1 / / / / / /f / / i t F H / / •> 1 ^4 /c / / t / } ' (c/eg) « ^ 10 - ZO ; ' 1 / / / / ^ R // / / V y f / ■? / / \ f f / I \ / \ / -ZO '16 -IE -8-4 4 6 /^ 16 /fng/e of attack ,oCo:, ^^^ F/hure 17 .-/leroc/i^na/v/c sect ion choracfer/st/C6 (p/ a/7 /V/^CA 0009 oirfoil w/fh a O.ZOc f/ap hay//7g a 0.3Jc^ oi^er/iang ^y/th e/f/pt/caf nose and 0*ZOCf p/o/n tad w/th 2^ = ^/ F/ap gap sea/ed -, tab gap, 0. 001 c. ^ \ NACA ARR No. L5F06 Fig. 17 Cont. '16 -12. -S -4 4 S /Ing/e of c/ftock^cco ydeg Figure 17 .- Co/it in ued. l^ 16 NATIONAL ADVISORY COMMITTEE FO* AEDONAUTKS \ NACA ARR No. L5F06 Fig. 17 Cone. +4 ■1 '^ .08 «: •5j .04 « 0) u ■^ -.04 ^ .§ -16 ^ ^ -^o ■$ ^ -.Z4 -Z8 -dZ ^r (a t 'eg ) V G ■^ — c J \ 1 J 1 ^ / f N _ t H Y " t % ^">r ^t >. dSjdbf ____ / / ^ 10 \ \ ' T X 1^ ^ \ 1^_^ r - \ V V \ t ^ ^ \ 5/ ^deg) B 10 ^ZO N \ \ V ^-i y ^ '- — _, r— f — 1^ \ -ZO -16 ~IZ -6 '4 4 S /Z 16 /in^/e of (T/fcyckyCCoyde^ Figure 17 .-Conc/ude d. National advisory committee fo* aekonautics \ NACA ARR No. L5F06 Fig. 18 NATIONAL ADVISORY CONMITTEE FO* AEMMAUTICS /f 11 1.0 <0 8 «\ K. .6 \ <0 c ft- V 0) c^ "o Z ^ s> ^ § -F \ -K <0 ^ -^ \ -^ -6 V. -£ i.O -IZ /, fa ^ // ^ f) 1 d / / I\ 3 V/ / b // 1/ ^ f/ i i t ?^ /, Jo • /// w '0 %/, V / Ik / 1 7 / A / p j '// / A M {/ / A h (deg) o -10 < 30 f k \A i / h / / \ ■^ A h i^ ^ f / \ ; \ / -10 -16 -II -8 -1- "f- 8 II 16 Angle of attack , oCq, deg F/gare /S- -Aeroa/ynom/c sect /on c/ioracfer/sf/cs of A/ACA 0009 o/rfo// w/fh 0.20c p/o/n f/op hav/ng O-^OCf p/o/n tod. r/op gop,sea/ed ifob Qop , 0.00/c ; 6f = O"". \ NACA ARR No. L5F06 Fig. 18 Cont, ./ •>c <0 5^-^ ^ ? •^ ^J ^c /O/l effi -I •^ Q ^ ^ "^ ^ .08 irfo/ mo/TJ .0^ X -Of •^ i^^ -.06 ^ ^ ^ -.11 k ^ ^ ^ 1^ -16 "\ -v ^ "^ c: •5 ,^ -10 > <^ -Zf '^ O — { ^V-1 > — \ ) — ^n \-* _^ FT— S ) m rr; ti p — 3 3-D- ^\ M^ 71 r T Vi=i *= t=^ !f= *= ? \ \ ^^ c ' >^, 1 M k, St (c/eg) 1 ( f\ >>, f ^ ^ \ N N I N V Q V \ k. \ N li k f — ^ 1 \ 's S T '■— ( r^ ^ 5-^ ^i \ \ N V ^ ^ \ \ k r 3 V N , ^ ^ (deg) o Q - 10 V ?n < 1 hH ^J '^ -^s. s k K ^/^ V \ v^ / S. \ s \ \ <3 =,0 -ZO -16 -12 -8-40^8 Angle of attack , a^, deg 12 16 figure id . - Continued. NATIONAL ADVISORY COMMITTEE FM AEDONAUTICS NACA ARR No. L5F06 Fig. 18 Cone, i I I f$ .08 M -M -08 -.IZ -16 -zo -24 6 1 r (degj o G /O - ZO <30 6t (c/eg) - \ \ -^ i ^J ^ \^ M h~~^ R r \ □ ^ v Y ^ ^^ //) ^ ip^ 1 J i \ --~£ ^^ i^ r — "* jfO^ ^ ^ v^ \, ^^ \ '"-> \ N s. \ «, \ / r ^ \ W / / \ •\ ^ >i y \ h !9 -zo -16 -IZ -8-4-0 4-8 Ang/e of attack , ao, deg r/gure /8 -Concluded. IZ 16 NATIONAL ADVISORY COMMITTEE FO* AEMMAUTICS \ NACA ARR No. L5F06 Fig. 19 Q* O s }; to I to /.2 J ^ ~~~^ K^ r ir\ <5; V A H — 1 y. s •u f l.U ^} ^ / ^ J .3 1 • li / /« r M <* "^ J-E (^^ y^ A .1 i^ .6 % / 7^ ^ ^ m /" i-r* ^ Sr-^ s V / > w > / 4 / ■^ / ,^ X ideq) - - 6 ^ 10 ^ 15 - ZO o 2.5 • T H ^/ 1 / 3^ 3-^ o / > ^ ^ .c. M / y h^ p r^ n i f /^ u y^ u / ) r ' -z 1 ,^ /^ 1 ^ ^ ' -.f / 6 1 ^ ' ' > ^VvW -X, flc-— r I \ \] \ \ Wi 1 .-■ ■ ■ ■ en N y ^ \ ctk'-'-v '^c ci^^pinjfc 3 1262 08106 452 8 yK.r rrcjqrTY OF FLORIDA C £\iT3 DEPARTMEMT 120 N-^ARSTON SCIENCE UBRARY pro. BOX 117011 GAINESVILLE. FL 32611-7011 USA X It '•l 1