M(kCi>^l'\l\ ACE No. lAEOl NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS WARTIME REPORT ORIGiNALLy rSSUED May 1914-4 as Advance Confidential Eeport lAEOl ABALYSIS OF AVAILABLE DATA ON TEE EFFECTIVEKESS OF AILERONS WITHOUT EXPOSED OVERHANG BALANCE By Rotert S. Svanson and Stewart M. Crandall Langley Memorial Aeronautical Laboratory Langley Field, Va. , ,,„,cncnv OF ^^^t^ ";:?;[ 326 n-rotiua^ NACA 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. L - 171 . f. 1 Digitized by the Internet Arclnive 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/analysisofavailaOOIang u^ jc i^- ^ . '^^cxj^ni^ MCA ACH No. ll[.'<:Ql C01\!FIDEIfriAL NATIONAL ADVISORY COiVD.^ITTEE FOR AERONAUTICS ADVANCE CONFIDENTIAL REPORT ANALYSIS OF AVAILABLE DATA ON THE EFFECTIVENESS OP AILERONS WITHOUT EXPOSED OVERHANG BALANCE By Robert S. Swanson and Stev.'art M. Crandall SU?/IMARY A considerable amount of tv/o- and three-dimensional data on the effectiveness of ailerons without exposed overhang balance has been collected and analyzed. The trends indicated by the analysis have been summarized in the form of a few approximate rules concerning the effec»-^ tiveness parameter Aa/A5 (at constant lift): Thickening and beveling the trailing edge (as measured by the tralling-edge angle pf) will generally reduce the effec- tiveness about 0.5 percent per degree of bevel for ailerons sealed at the hinge axis and about 0.6 percent per degree of bevel for unsealed ailerons. A 0.005c gap at the hinge axis usually reduces the effectiveness approximately 17 percent for flap chord ratios of 0.2. This percentage Increases as the flap chord ratio is reduced. The effec- tiveness is about lij. percent lower at aileron deflections of 20° than at aileron deflections of 10°. At large angles of attack (a = 10°) and for chord ratios of about 0.2, positively deflected ailerons are approximately 20 percent less effective than negatively deflected ailerons. The deflection of partial-span flaps has no consistent effect on the effectiveness. Increases in '/[ach number and forward movement of the transT.tion point decrease the aileron ef- fectiveness . No consistent deviation of the experimentally deter- mined values of static rolling moments from those values predicted by the lifting-line-theory method could be de- tected. Because the several factors neglected in the lifting-line theory apparently are fairly small and counteract one another, on the average, no additional correction need be applied. CONFIDE OTIAL 2 CONl^IDEMTIAL NACAACR IIo. Tj4l]01 niTRODUCTION A? a part cf the. ganeral lateral-control investi- gation by the. ':^hC.\, the large amount of two- and three- dimensional data on the rolling effectiveness of ailerons without exposed overhang balance is collected and ana- lyzed in the present paper. The main purpose of the analysis is to determine any fairly consistent variations in the effectiveness of these ailerons with the various design variables and criterions of similitude. Th':. secondary purpose of the analysis is to evaluate experimentally' the limitations of lifting-line theory ■■ i with regard to the estimation of aileron rolling moments from section data. SY^IBOLS C^ wing lift coefficient Cr maximum win':^; lift coefficient -^■"max c, section lift coefficient Cj wing rolling-m.oment coefficient a angle of attack, degrees 5 flap or aileron deflection, degrees b vving span y spar.'wise location y^ spanwise location of outboard end of aileron y^ spanwise location of Inboard end of aileron S wing area A aspect ratio \^~/^) X taper ratio, that is, fictitious chord at tip divided by chord at root MCA AOR^^o. rU'^Ol CO'^^ID^:>T^IAL c 1 M R a. m'inc chord at any section flop chord at any section aileron chord at any section airfoil tralling-edge angle, degrees Mach nijiiiher, ratio of free-s-creain velocity to velocity of so'-ind Reynolds nuznber slope of curve of section lift coefficient against angle of attack at constant 5 ^0 /a A a/A 5 (Aa/Ao); K sD.ope of curve of pection ll'^t coefficient against flap deflection at constant c section flap effectiveness -oarai-neter , that is, ab3oli:Lte value of ratio of equivalent change in angle of attach to angle of flap deflection measuj'ed at constant lift aileron effectiveness parameter, that is, ratio of equivalent change of angle of attack to angle of aileron deflection; suheorlpt 5 indicates that values are computed from tliree -dimensional test daisa by use of llftlng-line theory theoretical or experimental correction to llfting-llne-theory values of rolling moment R Aa/Ao) Ac /a 6 T 'Adnd-tuirinel turbulence factor Subscript 0=0° to ±10°, 5=0° to ±15°, or 5=0° to ±20°, etc., indicates range over which Aa/A5 or (Aa/A5)7 is evaluated. COI^TIDENTIAL C OW IDj i^ I AL N;.C a 4CP No . li+E 01 DATA Scop e The characteristics of the two-end three-dimensional models and the air-flow characteristics of the v;ind tun- nels in which the models were tested are sum^narized in tables I and II, respectively. The data as given in the orir:inal reports ("references 1 to 2[j.) were in many cases uncorrected for the effects of the jet boundaries or for model deflections. It was found essential to apply such corrections before the data could be correlated. Reduction and Presentation ' of Data Section dat a.- The effectiveness parameter Aa/A5 is the section characteristic of flaps that determines their ability to provide rolling motion when installed as ailerons on an airplane, provided the analysis is based on aileron deflection rather than stick force. This parameter Aa/A6 is equal to the absolute value of the change in angle of attack necessary to neutralize the lift produced by a unit flap deflection. The effec- tiveness parameter was determined from the section data of references 1 to I5 by plotting a against 5 for a constant section lift coefficient c-, and measToring the slope (absolute value of slope used) of a straight line through 5=0° and 5 = 10° for the effectiveness at small flap deflections f Aa/A5) g-^o^^ ^qO and through 5=0° and 5 = 20° for the effectiveness at large flap deflections ( Aa/A5)g-oOtQ 20^ • ^^ -^^ often convenient in the analysis to consider the limiting case (ccj/c5)^ of da/65, which Is equivalent to -f: — — f— . For prac- ^Oc7yoa)5 tical purposes, the values of ( Aa/A5) q-qO^^ -j^qO are very nearly equal to the values of 6a/d5. St atic three-dimensional data .- In references 25 and 2Dare presented charts for estim.ating the rolling moment caused by aileron deflection. The charts were calculated from lifting-line theory for various wing and aileron plan forms f or a slope of the section lift ciorve of 0.099 per degree. The general method for using the COilPID^^^JTIAL Fa.CA AC?: "To. li^T^^Ol CO^JFIDC^TTIAL charts to determine the rolling-moment coefficient Cj is to evaliiats graphically the following integral across the aileron span; C^ ''b/a or C^ = 5— -^K /A£ d^ (lb) '' C.O99 J A5 a Vi'here Sq slope of section lift cjirve, joer degree K experimental or th3oretioal correction to lifting-line thcjory {to be evaluated) Aa/A5 experimental section lift effectiveness of aileron C^/a is determined from the charts of reference 25 or 26, and y Is measured along the -;ving span. If Aa/Ao is constant across the aileron, the integral Is equal to Aa/A5 times the difference between the end values of C-j/a. Fost of the models studied had ailerons of constant chord ratio and Aa/A5 thus was a constant. By in- serting experimental values of C^ and chart values of C-,/a in equation fla), ^— f~-] or its equlva- lent -2 — K-— - therefore could be evaluated. A few 0.099 A 5 erroneous values in references 25 and 26 were corrected and the cuTves were refaired to be similar to the known fairing for elliptical wings. By using section data to estimate aQ and Aa/A5, the value of X could be experimentally evaluated. If section data for evalu- ating aQ were not available, a was estimated by using the m.easured slope for the finite-span wing in the llfting-llne-theory formulas (reference 27) corrected for COI^FIDSOTIAL 6 CONFTDSMTIAL MCA.:.GRNo. LliEOl the edge velocity by the methods of reference 28. For these cases In which a^ could not "ue satisfactorily estimated, the data are presented as — ( — ) • 0.099 VA5/5 '^or the few cases in v;hich the aileron chord ratio was not constant across the aileron span, the integral of equation (la) was evaluated by usin^>5 the section data of figirre 1 to estimate the variation of Aa/Ao with Ca/c ; thus an effective average value of Ca/c, weighted according to the ability of each spanwise ai- leron section to produce rolling noment, was evaluated. DISCITSSION Effect of Viscosity From figiores 1 and 2, the effectiveness Aa/AS of sealed plain flaps and allurons with small trailing-edge angles is seen to be considerably less than the theo- retical values for thin airfoils. L':ost of the decrease in effectiveness may be attributed to the influence of viscosity. The effective surface or boundary of the airfoil is displaced from the actual siur-face by the amount of the so-called displacement thickness, which is the height of the mean ordinate of the velocity dis- tribution in the boundary layer. Because the shapes and thicknesses of boundary layers vary with pressure gradient, transition location, Reynolds number, Mach number, gap at hinge axis, etc., the effective airfoil shape varies with these factors. a The flap effectiveness Aa/A5 is less than the theoretical value because the rate of increase of the thickness of the boundary layer with flap deflection, v;hich results from the high adverse pressui'-e gradient behind the hinge axis, is usually greater than the rate of Increase of the boundary-layer thickness v/ith angle of attack. The slope (dci/dQ^ is therefore decrease more bjr viscosity than is fdcj/daV; Aa/A5 is thus decreased by viscosity. The larger the flap deflection, the smaller the effectiveness Aa/A5. The section data of figure 5 and the finite -span data of figure k. show d CONFIDiLiWIAL MCA^CRNo. L)4.T:01 COJJPIDEAiTIAL 7 that, at low angles of attack, the effectiveness at flap deflections of 20° is approximately ll]. percent lower than the effectiveness at flap deflections of 10°. At high angles of attack, approximately the same reduction occurs (fig. 5)> except for the gap-unsealed condition in which little consistent reduction is in evidence. The effect of viscosity upon the aileron effec- tiveness depends markedly upon the pressure gradient. T The direction of the deflection of an aileron would be expected to have little effect at small angles of attack ■because the pressure distribution at 5 = 6° is very nearly the same on both surfaces. The data of figijre 6 verify this deduction. At high angles of attack, however, negative aileron deflections reduce the adverse pressure gradient whereas positive aileron deflections increase the adverse pressure gradient. A lower effectiveness thus m.ay be expected for positive aileron deflections. The data of figui^e 7 indicate that, at an angle of at- tack of 10° and for chord ratios of about 0.2, positively deflected ailerons are about 20 percent less effective than negatively deflected ailerons. This effect appears to increase with aileron chord ratio. The gap at the flap hinge axis allows the low-energy boundary- layer air to leak from the pressure side to the suction side of the airfoil. The boundary layer on the pressure side is thus thinned and on the suction side is further thickened with a resulting reduction of the lift increment. The effect of the gap on the lift-curve slope due to angle of attack (dci/da^ is fairly small, because the pressure difference across the hinge axis is small. The slope (p'^l/^^^n' ^^^ consequently Aa/A5, is considerably decreased, however, because the maxlm,um pressure difference due to flap deflection is usually located at the hinge axis. Pigixre 8 shows that a 0.005c gap at the hinge axis decreases the effectiveness about 17 percent for flap chord ratios of 0.2. This reduction appears to be larger for flaps of smaller chord. o A forward m.ovement of the transition point usually increases the thickness of the boundary layer and thus decreases the flap effectiveness Aa/A5. This effect is shown qualitatively in figure 9, in which data are pre- sented from tests v;ith and without the nose of the air.--'' foil roughened in order to fix transition. The position COI^IDSNTIAL '1 8 CO'^IDET^^IAL ILkCAACR ^o. lI+^OI of the trancition point on the unrou^hened airfoil v/as not deteriiiined. Some unpiiblished computations and ex- perimental data indicate that a reduction ct' about 2 percent in Aa/A5 for a forward transition movement of 0.1c may he expected with sealed plain flaps. The effects of viscosity are usually greater '.vith increased thickness and beveling of the airfoil trailing edge. The effect of transition movements and gaps thus are greater for airfoils with large tralling-edge angles 0. Gaps at the aileron hinge axis also Increase the loss in Aa/A6 that results from transition movements. The effect of beveling the trailing edge of the flap is presented in figure 9> iri which the effectiveness (Aa/A5) e_QO^Q T QO is shOMm as a function of the tralling- edge angle 0. Reductions of r.bout O.I4. percent per degree of bevel for sealed flaps and of about 1 percent per degree of bevel for ujtisealed flaps are indicated. The three-dimensional data of figure 10 shov; a decrease in aileron effectiveness of about O.3 percent per degree of bevel for sealed ailerons and approximately 0.6 percent per derrree of bevel for unsealed ailerons 10 . It should be noted that, un.der some particular con- ditions, viscosity may increase Aa/Ao to values even greater than those for the theoretical thin airfoil. The explanation for this rather astonishing fact is quite simple. The effectiveness parameter Aa/A5 is equal to the ratio of the lift-curve slopes -; ■ — r— . If vis- /. /-. \ \ '^^ /o cosity decreases foc^/oa^ more than it decreases (do-j/dd^ , the effec^biveness. parameter Aa/A5 is increased. For a few conditions, riiarkedly lov; lift- curve slopes (dci/ba^ occur over a small range of angle of attack a. Also, the slope ^■^CJ/6Q^ is less affected or is affected over a different range of a. Over a limited range of a, very large values of Aa/AS may therefore occur. A few cases in which this phenomenon has been observed are: (1) negatively deflected ailerons at large angles of attack near the stall, (2) so-called llnked-balance ailerons \?ith which a gap tliTough the v:ing occ\irs v/ell ahead of the hinge .axis and allows very low values of (icjyda)^, but has little effect on (dcj/d5) CONFIDEr?TIAL NACAACR i\To. IJjEOl COi\TFIDi]l'JTIAL near a = 0°, and (5) ailerons on low-drag airfoils with larje trailing-edge angles, which usually have a very large value of effectiveness Aa/AS near the angles of attack where the transition point suddenly shifts for- ward (near boundary of low-drag region) and causes a break in the curve of Cj against a. Effect of Compressibility Data on the effect of Mach nijraber on (Aa/Ao)g__^QO^ -jqO are shown in figure 11. The data are rather limited and subject to some doubt because It Is extremely difficult to determine accurately the wlnd- turxiel corrections at large values of Mach number. Cor- rections for model twist and deflections were applied to the data. Increasing the Mach number usually desire;- .■=: -:■? creases Aa/A5. Prom figure 11, It may be seen that an increase in Mach number from 0.2 to O.i^S reduces the effectiveness about 7 percent. The simple theory of Glauert and Prandtl indicates no effect of Mach number on Aa/A5 because (dc^/6a^^ and (6ci/6d^ are ass-umed to be increased equally by compressibility. Experimental data indicate, however, that ^^c^/^aV is usually increased a little more and (bcj/f^o^ a little less than the Glauert-Prandtl relation would account for. The explanation appears to be related to the. thickening of the boundary layer and the transition changes that have been observed at high Mach numbers. It is believed, therefore, that below the critical speed the main effect of compressibility j-i upon Aa/A5 is to Increase the effects of viscosity. Corrections to Lifting-Line Theory The limitations of lifting-line theory for the esti- mation of aileron hinge-moment characteristics from section data v;ere discussed in.reference 28. The aspect- ratio corrections to the hinge "moment determined from lifting-line theory were shovm to be inadequate whereas, for the cases in v/hich lifting-surface-theory calcula- tions (reference 28) are available, the aspect-ratio cor- rections to the hinge moment determined from^ lifting- surface theory are shov.n to be satisfactory. The large COI'lPIBETvlTIAL 10 CONFIDE iNfTIAL MCaaCR Nc. l1|.^01 difforence between the results of tht two theories may be illustrated by the fact that the ai"7ect~ratio cor- rections to the slope of the c-orve of Linge moment against angle of attack determined I'roii: lil'tin^-surface theory are about twice as grear as the corrections determined from lifting- line theory. The aspect-ratio corrections to the slope of the lift curve against anglj of attack (references 2Q and ^0) for iTiodei'ate aspect ratio as determined by the lifting- line and lifting-surface theories differ by only about 7 or 8 percent. The aspect-ratio coi^rectlons to the daiiiping moments of elliptical vings rotating about the lateral plane of symiiietry as determined by the two tl:ec- ries also differ by only about 7 or 8 percent (unpub- lished correctfon determined by the methods of refer- ence 30). The difference bstv/een bhe two aspect-ratio corrections to the slope of the lift curve against flap deflection is about 3 to If pei'cent, which is only about one-half as much as that for the slope of the lift curve against angle of attack. This difference exists primarily because the distance to the three-':iuart3r- chord point (point for best measure of effective angle of" attack of v:ing) from the center of load that results from aileron deflection is roughly one -half the distance to the three-quarter-chord po5nt from, the center of load that results from changes in angle of attack. The ef- fective length of the trailing vortices thus is less for the load that results from, flap deflection. It might therefore be expected that the aspect-ratio correction to the static aileron rolling moments determined from lifting-surface theory would be of the sam.e order, 3 to Ij. percent greater than the value determined from lifting-line theory. In any case, the afleron rolling moments debei-mined from lifting-line theory should be xnuch closer tc the experim.ental values than the aileron hinge moments would be. It may be seen that the section data (fig. 1) and the finite-span data vath the lifting-line-theory aspect- ratio corrections applied (fig. 2.) are in fairly/ good agreem.ent. Although there is considerable scatter, the curve faired through the section data represents very well the finite-span data, especially for aileron chord ratios of 0.2 or less. (See fig. 2.) An experimental evaluation of the over-all -*ispect-rstio corrv^ctions shows, on the average, no serious discrepancies (exceeding 10 percent) with the lifting-line-theory valiies; that is, coKTPrn'^rPT'iAT, ^ NAOAACR '}-^o. lIlEOI C0.WFIDE?1TIAL 11 (Aa/i5)T on the averas;e, K = ^ = 1.0. The 3 or 14. percent Aa/A6 Increase in the aspect-ratio correction that might be expected fro'n a qualitative study of lifting-surface theory (actual numei-ical values have not yet been calcu- lated) may either be masked by the scatter of the data In figures 1 or 2 or may be coimteracted by three- dimensional boundary- layer effects or by the effect of the vertical location of the trailing-vortex sheet (ref- erences 28 and 31) . Lifting-line theory indicates no change in aileron effectiveness vath deflection of partial- span flaps. Some effect might be expected because of cross flow; hov/ever, figui^e 12 shows that the deflection of partial- span flaps generally has no consistent effect on aileron effectiveness . The available data on the effect of sv^eep and taper (figs. 13 and 1I4.) show that, insofar as aileron rolling moments are concerned, no large corrections arc to be applied to lifting-line theory for the effects of taper and sweep. For wings of low taper (large values of \), it appears that the aileron effectiveness is slightly greater if the wing is swept forward. CONCLUDING REi\5ARES The trends indicated by the analysis of available data on the effectiveness of ailerons without exposed overhang balance nave been summ.arized in the form of a fev; approxim.ate rules concerning the effectiveness parameter Aa/A5 (at constant lift): Thickening and beveling the trailing edge (as measured by the trailing- edge angle ^) v/ill generally reduce the effectiveness about 0.3 percent per degree of bevel for ailerons sealed at the hinge axis and about 0.6 percent per degree of bevel for unsealed ailerons. A 0.005c gap at the hinge axis usually reduces the effectiveness about I7 percent for flap chord ratios of 0.2. This percentage increases as the fla-n chord ratio is reduced. The effectiveness is about ll; percent lower at aileron deflections of '20° than at aileron deflections of 10°. At large angles u>- 01" attack ■ (a ~ 10°) and for chord ratios of about 0.2, positively deflected ailerons are about 20 percent less COWIDST.it lAL 12 C01WlD!uliTlAL TACk \CR No. LI4EOI effective than negatively del'lected ailerons. The de- flection of partial-GpEn flaps has no consistsnt effect on the eff'ectlvcness . Increases in Mach nurr.fcer and for- ward niovement of the transitio:! point decrease the aileron effectiveness. Vo consistent correction to the lifting-line-theory method of estimating aileron rollin^j moments could be detected. Because the several factors ns.r^lected in lifting-13ne theory apparently are fairly sr.all end counteract one another, on the average, no additional coi'rection need be applied. Langley Llemorlal Aorcrautical Laboratcry, National Advisory Committee foi' Aeronautics, Langley Field, Va . , COMFID'ilJTIAL MCAACRATo. Li;E01 CONFIDENTIAL 15 RE.F£1^.ENC3S 1. Street, William G., and Ames, Milton B. , Jr.: PrescTore-Distributlon Investigation of an N.A.C.A. 0009 Airfoil with a 50-Percent-Chord Plain Flap and" Three Tabs. NACA . TN No. 73l|., 1939. 2. Ames, Milton E., Jr., and Sears, Richard I.: Pressure-Distribution Investigation of an N.A.C.A. 0009 Airfoil with an 80-Percent-Chord Plain Flap and' Three Tabs. NACA TN No. 76I, 19iiO. 3. Ames, Milton B. , Jr., and Sears, Richard I.: Pressure-Distribution Investigation of an N.A.C.A. 0009 Airfoil with a 30-Percent-Chord Plain Flap and Three Tabs. NACA TN No. 759, 19i|0. I4.. Sears, Richard I.: ^"ind-Tunnel Investigation of Control-Surface Characteristics. I - Effect of Gap on the Aerodynamic Characteristics of an NACA 0009 Airfoil with a pO- Per cent -Chord Plain Flap. NACA ARR , June I9I+I. 5. Jones, Robert T., and Ames, Milton B., Jr.: Wind- Tunnel Investigation of Control-Surface Charac- teristics. V - The Use of a Beveled Trailing Edge to Reduce the Hinge Moment of a Control Surface. NACA ARR, March 19i|2. 6. Sears, Richard I., and Liddell, Robert B.: Wind- Tunnel Investigation of Control-Surface Charac- teristics. VI - A 30-Psrcent-Chord Plain Flap on the MCA 0015 Airfoil. NACA ARR, June 19l|2 . 7. Crlllis, Clarence L. , and Lockwood, Vernard E. : Wind- Tunnel Investigation of Control-Surface Charac- teristics. XIII - Various Flap Overhangs Used with a 30-Percent-Chord Flap on an NACA 66-OO9 Airfoil. NACA ACR No. 3G20, 19i4-3 • 8. Sears, Richard I., and Koggard, H. Page, Jr.: Wind- Tunnel Investigation of Control-Surface Charac- teristics. XI - Various Large Overhang and Internal-Type Aerodynamic Balances for a Straight- Contour Flap on the NACA OOI5 Airfoil. NACA. ARR, Jan. 19[|.3. CONFIDEPITIAL ik CCRFIDECTIAL !TACA ACi; No. liiEOl 9. Purser, Paul E., and Hlefce, Jchn M. : vrind-Tunnel Investigation of Control-Surface Characteristics. XV - Various Contour Iwodif icafcions of a O.JG- Airf oil-Chord Plain Plao on an lUCA 66(2l5)-0li| Airfoil. ITACA ACH rJo.^$L20, 191^3. 10. 'Venzlnger, Carl J., and Delano, James 3.: press-ore Distribution over an N.A.C.A. 25012 Airfoil with a Slotted and a Plain Flan. :TaCA Rep. No. 633, 1938. 11. "Venzinger, Cerl J., and Harris, Thomas A.: Vjind- Tannel Investigation of an N.A.C.A. 23012 Airfoil with Various Arrangements of Slotted Flaps. NACA Rep. No. 66^, I939,. 12. Cran3, Robert M. , and Holtzclaw, Ralph Vv.: Wind- Tunnel Investigation of Ail.eronr: on s. Low-Drag Airfoil. I - The Effect of Aileron Profile. FACA ACR No. I+A-I4, 19^'+. • 15. Denacl, H. G., and Bird, J. B.: '"ind-Tunnel Tests of Ailerons at Various Speeds. II - Ailerons of 0.20 Airfoil Chord and True Contour v'ith O.6O Ailercn-Ch'>rd ?^ealed Internal Balance on the NACA 66,2-216 Airfoil. NACA ACR No. 5Fl8, 19ii3. ll\.. Davidson. ^Illton, and Turner, Harold R., Jr . r Tests of an NACA 66,2-2l6, a = 0~. 6 Airfoil Section with 'a Slotted and Plain Flap. NftCA ACR No. 3J05, 19^5 • 15. Rogallo, F. M. : Collection of Balanced-Aileron Test Data. NACA ACR' No. 1^-All, 194l<-. 16. Rogallo, F. r. , and Purser, Paul E.: Wind-Tunnel InvestifZatlon of 20-Percent-Chord Plain and, Frise Ailerons on an N/'.CA 25012 Airfoil. NACA ARR, 17. Rogallo, F. I"., and Schuldenfrei, Marvin: Vjlnd- Tunnel Investigation of a plain and a Slot-Lip Aileron ^^n a '7ing with a Full-Span Flap Consisting of an Inboard Powler and an Outboard Slotted Flap. NACA . ARR, June 19:^1. CGNFTDFl^^TAL FACAACRNo. t4E01 COFFIDE^jTIAL 15 18. Welck, Fred E . , and 'il'enzinser , Carl J.: 'A'lnd-Tunnel Research Ccmparing Lateral Control Devices, Particularly at High Angles of Attack. I - Ordinary Ailerons on Rectangular Wings. NACA Rep. No. kl9, 1952. 19. VJeick, Fred E., and Shortal, Joseph A.: Wind-Tunnel Research- Comparing Lateral Control Devices, Particularly at High Angles of Attack. V - Spoilers and Ailerons on Rectangular Wings. NACA Rep. No. 1^-59, 1932. 20. YJeicK, Fred E., and Shortal, Joseph A.: Wind-Tunnel Research Comparing Lateral Control Devices, Par- ticularly at High Angles of Attack. VIII. Straight and Skewed Ailerons on \iVlngs with Rounded Tips. NACA TN No. i+Ji5 , 1953- 21. Welck, FreA E., and Wenzinger, Carl J.; Wind-Tunnel Research CoTnparing Lateral Control Devices, Par- ticularly at High Angles of Attack. IX. Tapered V>iings v^ith Ordinary Ailerons. NACA TN No. kk9 , 1933. 22. Wenzinger, Carl J.; ■Vlnd -Tunnel Investigation of Tanered ''Ings with Ordinary Ailerons and Partial- Span Split Flaps. NACA Rep. No. 611, 1937- 23. Wenzinger, Carl J., and Ames, Milton B., Jr.: Wind- Tunnel Investigation of Rectangular and Tapered N.A.C.A, 23012 'V'lngs wi-ch Plain Ailerons and FliII- Span Split Flaps. NACA. TN No. 6bl, 1953. 2i|. Irving, H. B., and Bat son, A. S.: A Comparison of Aileron Control on Tapered Wings with Straight Leading Ed£:e and Straight Trailing Edge. R. & M. No. 1837, British A.R.C., 1938. 25. Welck, Fred E., and Jones, Robert T.: Re'sume' and Analysis of N.A.C.A. Lateral Control Research. NACA Rep. No. 605, 1937- 26. Pearson, Henry A., and Jones, Robert T.: Theoretical Stability and Control Characteristics of Wings vvith Various Amounts of Taper and Twist. NACA Rep. No. 635, 1938. COJJFIDEJJTIAL l6 CONFIDENTIAL NACA ACR No. 1J4EOI 27. Anderson, Raymond P.; Deterr.iination of the Charac- teristics of Tarjered iA'ln:^s . NaCA Rep. No. 572, 1956. 28. Svanson, Robert S., and Glllis, Clarence L.: Limi- tations of Lifting-Line Theory for Estimation of Aileron Einge -Foment Characteristics. NACA C3 No. 5L02, l^k5- 29. Cohen, Loris: A Method for Determiniiig the Camber and Twist of a Surface to Saoport a Given Distri- bution of Lift. NACA TN No. 835, 19i;2 . 30. Jones, Robert T.: Theoretical Correction for the Lift of Elliptic -Vings . Jo^or . Aero. Sci . , vol. 9> no. 1, Nov. 191+1, pp. 3-10. 51, Bollay, Willia:n: A Non-linear 'A'ing Theory and its Application to Rectangular 'A'ings of Sm.all Aspect Ratio. Z.f.a.M.M., Ed. I9, Heft 1, Feb. 1939, pp. 21-55. 52. Jacobs, Eastmian N., Abbott, Ira K., and Davidson, ?"ilton: Supolement (loose-leaf) to NACA Advance Confidential Report, Preliminary Low-Drag-Airfoil and Flap Data from Tests at Large Reynolds Niiiiibers and Low Turbulence, NACA, March 19'4-2 . C0?'1FIDEATTIAL NACA ACR No. L4E01 CONFIDENTIAL 17 TABLE T.- SUPPLEMENTARY INFORMATION REGARDING TESTS OP TWO-DIMENSIONAL MODELS Model Basic airfoil Type of flap Air-flow characteristics n 3 .H U 22 Desig- nation Sym- bol r M B 1 o NACA 0009 Plain 1.95 0.08 1 to 5 2a + NACA 0015 Plain 1.95 0.10 I.I4. X 10^ 6 2b /^ NACA 0015 Internally balanced, straight contour 1.93 0.10 l.k X 10^ 8 3 X NACA 23012 Plain 1.60 0.11 2.2 X 10^ 10,11 k D NACA 66(2xl5)-009 Plain, straight contour 1.95 0.10 1.1+ X 10^ 5 O NACA 66-009 Plain 1.95 0.11 l.k X 10^ 7 6 A NACA low drag Internally balanced Approach- ing 1.00 0.17 2.5 X 10^ 15 7 V NACA 66{2:!cl5)-2l6, a = 0.6 Internally balanced Approach- ing 1.00 0.18 5.3 X 10^ 15 8 l> NACA 66f2xi5)-ii6, a = 0.6 Internally balanced Approach- ing 1.00 O.lU 6.0 X 10^ 15 9 < NACA compromise low drag Plain • Approach- ing 1.00 13.0 X 10^ 10 V NACA low drag Internally balanced Approach- ing 1.00 O.llj. 6.0 X 10^ 15 11 ^ NACA 65^1+20) -521 (approx.) Internally balanced Approach- ing 1.00 8.0 X 10^ 12 t^' *NACA 66(2l5)-2l6, a = 0.6 Internally balanced Approach- ing 1.00 0.20 to 0.i;8 2.8 X 10^ to , 6.8 X in6 13 15 b- *NACA 66(215)-2l6, a = 0.6 Plain Approach- ing 1.00 O.II+ 5.8 X 10^ 12 Ik A NACA 66(2i5)-oiij. Plain 1.93 0.09 1.2 X 10^ 9 15 a NACA 66,2-216, a = 0.6 Plain Approach- ing 1.00 , 6.0 X 10^ 11+ This designation has been changed from the form In which It appears In reference to the form described on p. 21a of reference 52. CONFIDENTIAL NACA ACR No. L4E01 18 < 1—1 Q O 03U3J9J8J ; ir\ U> l/> ir\ paqctiqud ' -* H rH *-« o vO NO o v£> vO vO vO vO o O o o o O 4-> B n n X K X )( X X CrrH O-iH^O (T-rH^ O-r^^O OnI^^O C^.H^i> C^r-lsO "T^o 1 *J (. O rHO rH r-IO <-* <-*0 r-t rndr^ r-l O rH r-l O r^ r^dr^ 3£ II II II 11 II II U II II II II II II II II II 11 II II II II KEV KSV KSV. kkV KEK « = v. a:x\. ■0^ C *J 1 av. CO ■ o ^ c a c— m. .-H .H T3 a« o O o ■9 a ■H c t< "§ 1 T3 O C d o — ^a" a o - c o K\ K\ fTi K^ fO\ m Boo S"3 o o o o O o S"£ .H r-< r-l O V B«-< 3 B o o o d o o o H O CO (7^ nj 0^ ir\ ON ITS < if vO -a Er o r-< • o O d d d o d d u-4 vO sO c- vO c- ^ a |(\j J- g. o c^ O r- g^ i-°|> a^ o\ o^ OS CTN ON d d d d O d d .H O o 8. o O a ON 35 |nj J- ON CTv o- t-- ■?!> Co -S ^ -* J- -j i^^ d d d d o d 6 OJ r^ ►f\ K^ rrv s o d o o d d d ^ K\ rr\ fC K^ IfN o rg IN ry cy fy iTN < r-i ^o \D •^ ^ vD lA \ii ^^ ^O -o sO VO r-l «U3 rH O rHO ^o rHO rtO iTk . D. < 4 ' ■< JLr^ <-^rH 1 • <;Lr; •<>l.r4 ^ty K < . o OlT* O U^ d ir« Ulf\ OlfS oco u ^ = s " j II S3S. ^ "i" 2 « z - ^ m vO « =§& lO vO vO ^ ^JD to C 1 A A A A i- l\ o / \ / \ / \ / \ / \ / ' \ / / \ / \ / \ / \ / \ / \ / ^ / \ / \ / \ / \ / \ / \ / I / \ / \ / \ / \ / \ / \ / © / \ / \ / \ / \ / \ / \ / \ m / \ T' TT -f--4- A^A / \ A A — u — C / \ /\ /\ A l\ /\ /\ — f- + -* — /\ /\ Nai^ o / \ / \ / \ \ /\ / \ / \ A f\ / \ / \ / "n t. / \ / \ / \ \ / \ / \ / \ \ 1 /\ / \ / \ / 1 o / \ / \ / \ \ / \ / \ / \ / \ / \ / \ / \ / ~i — +— 1— / \ / \ \ / \ / \ / \ / \ / \ / \ / \ / \ /^ / Vj \ / V \ / Vi \ / \ / \ / \J \ / 1 ffl Mr^ h~~^-A K-^-A h ^A h-^LA h ^A ^ / n / \ /^^\ / \ / ^^\ / \ / « / / / \ / \ / \ / \ / \ / / 1 \ / \ / \ / \ / \ / \ / »H / ^ — ^\ / \ / \ / \ / \ / \ / ft / \ / \ \ \ \ \ F- /, , 1, ,\ /, ,\ /, A 1 U— 1- r r — -J ^ — 1 1 y y e — i — 1 1 \ J \ J \ J \ J / o 1 \ 1 / \ / 1 \ II / «-( ' H H H H \ M 1 / c • ^] u 1 U n /I u SI •^ H \ 1 I '/ \ '/ \ 1 1 ff n ^ n 1 '/ 1 I / \ 1 / \ 1 1 .V / a, 1 I // / / 1 1-1 ,/ I 11 I // \ ll \ 1 1 \ 11 / o ■a ? U I y I y I 1 I y I 1/ : c KJj \ y \ y V J* V V V if L _iJ s ^—f ^^— ^ ^—ff T rH o t b O o o o 6 •a M 1 c w o m x> „ ■V o o i-i t* lA n o vXl v£l S43 ^> o O O o ■-0 >4 o W *^ ^ o o o O n iH >-l <-| T* X X X X *H U X X K 1 c jm JCO irs<-i ^o ^ _»o iTtp^ (**> ITVO"^ mo^ OrH^ ino^o u-\o^ l^So^ H>rjd^ II II II II II II II II II II II II 11 II II It II U II II II KSV- (CSV KaV K31V (csiV- a:sK anil- C *) TJ , 1 at-. 3f C 1 O M 5 a-a fot rr\ 1 fr\ ^ •M i-H ^ o O 1 O o • « i-H c L. C5 M 12 I i ( o O • 1 O o 3£ ■a D O. V iTv Ip. \r\ ir\ tf\ ir\ -H Q > m ^ O o O O o o o 4J - O fl iH rt »-i p4 H O 3 e J n O o d o o o ^ lf\ K^ S 8 ?> s » ^ r-l O o rg iH »-t »H o O d d d d d d .J^ ^ ^ ^ 8 8 Q S §§ -1> O cr. crv O O o ON ss o o 9 rH Jd ^^ Q 'i 2:- crv o o o OS ^1^ En o 5- NO ? ?. o d d n < S s s 8 8 o o ^ d d d iH M iH d < in m m 8 8 o o o lA lA m J- j A t^ l^^ • iTv . lA . t\J K OJ K CM K < . o < . o < . O o. 003 t. OOD (- 0<0 (h ■*:o a A « I c bOO X) o ■O m J3 OJ CO CO a^ o I — I O NACA ACR No. L4E01 20 E-i Q I — I O O eousjojoj 1 ' peUSTTQi^ 1 eocrv tt? c» CO rg IN fg « -£> vO ^ ^o ■^ ^o vO 0^ I-* rH X * X X X X X 1-4 t* V4 C iTN^ io KXrH^O ^<-;-* ^Or^-* sO .H.^- ^r^^ vo^_d- ^OrH_lt 3£ INOr^ r^ doM ddrH GOr^ ddr^ ddr^ J3 II II II II II II U II II II II II II II II 11 II II CEV Kav tc^\- cceV. (cxV (CSV (CXV *i Ti a^ u> « O'^ c afl r- t^ t— p- t^ r- r^r^^ ON Qs ON CTs cr\ a- a « c t. t! 000 i d d • " e • Ck« tr» M nj 1 ^ • > MM 1 Sv.§ • • » 1 u ■ ' d > § fcr\ ?. a 8 rg -^ rg rt f\i ni -J- d d d -1^ 8 § 8 8 ag ^?|> O^ is s a -1 as d rH ■-< .H «-• i-i .-H & 5 s 1 9. s d d d d d d f< rg J- 8 8 s s S d '^ ■^ '^ d 8 ■* ff\ c-^ so V43 vO sO vO ^o 0. *-i H y rH C 1. -Sa ■o ►^ X [« w !m >H tt i « t i :SS rH « m • 9 m 4-t iH < ^ ^ k: cc c ^ / / / / / / / / / / / / / 4J / / / / / / / / / / / / / I 1 / / / / c / / / — Tt] / / /, / \ / / / u / I / / / 1 €> ~k:7r — V "*"■ — / / / -eJ — /v_Ly\ , ><, / / f-N^ » MM ' / ^ / / , rn ■3 W N^ "/y / \ 1 1 / ft / / / / ' t< /, ,1 U H /, Li — (- M 1- /, -* — V- 1 1 1 ' ^ 1 1 r- •^ i p ^ 1 p -t ; T -I r r 1 I 1 _ / ^ / / ' u -^ 9 7 ; tJ r4 •/ i 1 0-. //? 1 n 1 n / ^ « u -^ 1 1 ' — M 1 / E 1 1 ' r4 J3 A <7 V V ti c;^ -N to 1 c wo r* rl fl m >3 « A m t' ^ OJ !!1 f>J SS ■M J rg AJ < I— I El Z o o u NACA ACP No. L4E01 21 I — I O c:i 03U9J9J0J .H (M S! »rv paMBTiqnj ■^J Ol ■j Kj OJ tM nj n vO •J3 ^o ^o NO NO NO n .-< rH O-H X X X jj ^ X X r^ (4 <^ © •-i iH .-1 (H 1 -»J ^rH J- ^.^.-^ ^ r^_d- ^'^-^ nO^ J NO.-«-:t vO .-i^O ^S 00-^ 00-^ O-"! 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II II II II II II II II II q::£K CCS£ t- ai^V KE V keV IKi^ (CSV C *J ■d QVi U3 O-H t— r- r- 1- [— -HrH -O Q. a> ON cr. cr- C7S cr- 1 " c t. c [ •d *-( D. i ' d ' B ■■ Tl BOO a © ry fvi OJ ■^ n > 1 1 ^ t> a) r-< ««-. 3 © Ul 1 1 1 1 (J ^ ITN rr\ t- p. ^ u^ ITS KN J- f\J CM J OJ -=t i-( d 6 d ol-Q* 8 8 S CO 8 c c >'l> ON ON o- c -• rH r^ M d d .-i KN UN l-H _.lc J- r- 03 5^ ^l> in r- sD lTn NO ^ d f< c 8 § ■-• ■-I --1 rH 8 < ^ >wO •ji NO NO NO nO E-< .^ c Oi -1 -i >' >-■ ^ >-■ t" t« 4-, *J iS « ^ •s u OJ ^ % 1-1 0) ^ (d a •< ^ 4J K ce C / / / / h / / / / / / / / ID / / / / I \ c / / / / / + 1 / u 1 / / — f-- / / V y / ,N-^ V^ d / — t- + — 1-^, i- + - — (- + - r^ ^ y* / / rw 1 / ^4^ / ^ / T / / / / 1 / t*> / / E- M V- / -V-1- /, , M V- _^ !__ M iJ 1 \ ''/ \ ^1 \ / — i p 1 p - 1 T— - 1 |- \ j' / c \ ff \ ■'/ \ lJ c \ / \ / Cli \ / \ , / V \ ■/ / T3 VJ/ 1 V M^ l^__^/ ^'' \ .--^ -( cS* p^ K -F a ^ ^ a 1 ii ton -O j3 a] N% K- K^ 1.-N i,-\ .J3 a> 9; -vj -^ .-vi r-J rM -^J ^J Ci c 1 Q I — I En. O o NACA ACR No. L4E01 22 I — I Q O a gSU9J9J3^ peqsiiqnd ^ -J- Tj i ^ n o ^0 ■£) ■jj vO -J3 o O c *j o O k « O -J X rJ t. X Vi a> ^^~^ t^U-N [--U~s p-tr> r^Lr\ 1 4J vO^vD rHO ^ O r^O <- o O 1 -p (. a m « V* 3 woe « o o 1 1 1 t o r> o o O ?- \ o ITS u~> ITN i) --; ^M rvj -^i 'M " o o d d d o o Q o o 8 O t r\j o o o O B o o o o o 0«4 r-< o Q o o o 3° o o" d s 6 s o o < o o 8 8 o R s. o r\j J -^ tN ^ r^ d ° d d d o o < o c r»i OJ rvj OJ -J3 ^ t^ t- t^ t^ o- e- ry rvi CO GO CD C3 ^ c o o K^ »Ov rrv -^ O O --« CM ry ^ 4-> bi b. t! fe. t. U •< < 5S s^ s < •< ■* < BS E m Ed K a: «j o o cc C /I A /I /I /I !\ o / / / / 1 M / / I / / / o m / 1 / / / / c / / |J / / / / o / 1 / / / t. / / / / o / / / / / / / / / / a) / \J^ 1^ / J / ^ ^ / 1 h) / / / fri H V-l i } Ll L M 4—1 / S -1 T- VI T r- — ^ \ ^ |- c^ , / \ o , / \ § \ // j \ L ff \ ■■- \ 1- j j 1 \ a. \ '/ j j \ \ i-H \ '/ \ 1 \ . o \ , T3 1 \ // \ O 1 \ 1 ^ // \ 1 ff 1 ^ '' ' I ^ Q cr o <[ ^ A cl 1 c r wo £i vO r— M". I — I td Q O NACA ACR No. L4E01 CONFIDENTIAL Fig. fc I I: dlio <| <3 m m (D C > O '■>-> On c o •rl O c CO 1 1 1 Theoretical ^' s / y ^ <" / 'i/ !> -^ y 1 1 Exnertmental / y '^Y [> / / ^ ^^^ / A" / \a 1 / / ^ i / y / / ¥ / y // / (a) 5 range from 0° to 10°. 1 — .6 r hec )re tic ,al -^ .-1 r^ l/^ y /^ \ /J ( / ^ / V y 1 / V / / ^ p < .2 J / / / f / / / 3 n 1/ .1+ .1 .2 .3 Flap chord ratio, C£./c (b) 5 range fVom 0° to 20°. 'Igvire l.- Variation of section flap effectiveness with flap chord ratio for small Mach rumbers and a small range of tralling-edge angle, j& sealed; c, = 0. (Symbols designating two-dimensional models are Identified in table I.) CONFIDENTIAL NaCA ACR No. L4E01 CONFIDENTIAL Fig^ o o r-t O 4-> O o r^ I II o hCv IS > O O '" \^ ^ "*, IX y' 3^ "K y 1)1 1 Exner Imental i^ / ^ •r_0 1 section data / / / i / / A > / / ^ 2 -7^ K / // • /^ . / (a) Gaps sealed. 1 M 6 ,-- -'f ^ "^ '^5 • 1 1 t0] hr / /^ r b >' / / / 2 ^ (V / / r\ / .1 .2 .5 Aileron chord ratio, Cg^/c (b) Gaps unsealed. Figure 2.- Variation of aileron effectiveness with aileron chord ratio for small Jiach numbers and a small range of trailing-edge angle. a« 0°. (Symbols designating three-dimensional models are identified in table II.) CONFIDENTIAL I NACA ACR No. L4E01 Figs. 3,4 S \ -4 J*- \. ^ c* 3 \^ -0 Qx <^ \ \ p. cs \ \ \ \ ^ \ ^ \ » (uvj oDu_u 'aseusA-noBjjB uoasxTT 2; Ed Q (—1 6h Z o < I— I E-i is Ed P I — I Z o u O •p o o CM II ■O •t> KS ct 'ayo n n ^l< o c, « ON 0) o ON > rl at o . . •o o 4> o . e (n Id *H u. «-l -p at rH 41 o O .H Tl o nA «H r ^ ^ »H O c o C c rH O o *^ b 0) a o .H rA ti rH Ti 01 iH ■< u< dl 6 1: o R o 1 3 <4 j- e « w & s \ \ o o \ o o\^ o ^ %\ o \, o. iH o o \ . o o '>^ O P. 00 CM ''-' C O o o o «H O O P< a 31 C 1-1 o •P c o o o ■P tj o o « -^ n P. «H eg O r-i a O iH oOT 0^00=9 /gv' — )'geeueA"[H09jj9 d^tJ uof^oas (4 Q D. s ■2 o a u d to, t. 4 rH » of ^ «-l o e OS n c y o c (. o > 0) b rS IS 4^ g ^ rH O d ■H o! ^ ^ A o a> 0) c > ■H c o ■U o a 01 •H tu h *l iH 01 c H- < o o 1 ot > VO ^ I \ r- — \ ^ "^d ^ f> O" "to- \ c c Jh -d -d c O O OCl © «rH O ^ ^ z a ^ ^ r O + > \ N o o o r-i o o o i bO C d ti o \ ^ \ ^t \ " o + \ \ C \ o \ G \ \ CO o o J3 4i <5| o o 4-1 -d d ■d C d 03 < 1 — I O I — I O edsS poxBse tm« — 'eeeuaAHoejje d«ij uof^oes U d d Q. 0) B to 6 C o -H • 4J \ ts c l^\ uJ ^ ^ ^^ y d- cf q \ \ \ \ g o5l-°^oO=9 ''fSl 66o'o , " to- o s o cr\ • •H »^ d (-1 4J -U o o ^ \ • o \ d t^H f-H s^ -K V ^ s a> 0] C ■« liH V ■kA<: ■o A \ o ^ c U "^ a '='s c > EQ o c d -u t1 -M rH o a -H c d o © \ ^ \ a> > \ c O -t) n d ■^ to (. (D ^ o »H d C •H O. O G vO CM O o d 1 o • > © -H essusAtq 09JJ9 uoa9iTV fc, n 5) S. NACA ACR No. L4E01 Figs, 9,10 f 1 f -L A ix '1 / / if i-. / 1 3 i n o o (S o o o o o o Cd Q o0TOi^0I-=9p^ ■(^) 'Be9ueAT?09jj9 uojBXTV ■SI. >. « M at C 1 T^ o u to rH n c ^ a! a r-l ^ o at O +i c at *3 •H ;< Ol > < t-H Q CO O a f^) ee9U9Af308jja dsij uonoes to NACA ACR No. L4E01 Figs. 11,12 \ > n § "H *i O 9> r-* Id c o « rH «-l 0] 4) > s> a) \ 1^ Cf \ ■A t?P \^ \ \ \ \ pe^osj^isj sdBtJ UBdB-iBT*JwJ mT* o5t?o?oO=9 rj ■(S) 660*0 'ssauaAT^losjjg aojexTV A h « rH o . » ^ M (0 O c o ' res' •H 4^ ■^ ^ v£) clltO V • •^al-'d 0) o »-l ^ 4) (T\ o o > •H •H 4J U m •H c\J o 3 . • ^ +j o Fh < '. n 1 C\J iH « rH « 4J ca a as 3> < I— ( El Q I— < O o X <~t t^ M t f- o, o IfN O to OJ u^ o o 4J O O J c • • — o o # > F« ^ J 4 S ^"^ N -* 4^ c ■n i-H O C 00 A 1 0) c\i -^ iH O 1 hJ 0) . < a. (u HH ^■i . Eh CM 3 O S w o m -H -a -J Q 1-3 rH O HH 0) c fc to >) •- 2; o c o 13 d o O td ff) ■H J3 •J (-1 Ct) o oo o o O D O < c tiO *H n © oj o rH C O (d X) Q. a cQ -d ?» I © OS o \ agged parti defle y Cb \ \ \ \ II \ \ er 4\ <3, \ \ \ o pjBaaoj :)daMS eSaiji joj ►J < I — I en td Q o o '(I?) 66o'o 'es9ueATrj08jje uoasfiV 60^ aj o u ■a o o o o o r\j ^ i-t r\j o o o o ■P -P 4^ 4^ o o o o O D O <] o, < td Q I — I O O I « \ Ugged parti defle i * u o «-. ■p o. o CD \ ^\ &. a n CT \c \ \^ <1 \ \ \ \ \ HI B > u r-l o K>« ^ O n *i n « 00 c <\i O tc (. 0) o » O O © CO » • d CO o o n x) II •ri c o. ^ a o OJ .* O XI ^3 P. « 1 O rt • c o cii:^ 4^ 4^ o <7> 00 <11 O 0) <\J O rvi rH f> 0] c •d 0) II o o u a C >< V > 4J 5 d (. »