AER No. L4I18 NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS WARTIME REPORT ORIGNALLY ISSUED Eeptemter l^k'■^ as Advance Restricted Report L4I1B analysis of factors affectdfg net lift i7jck}j>1ent attain;i3le with trail ing-edge split flaps on tailless airplanes By Marvin Pitkin and Bernard Margin Langley I^femorial Aeronautical Latoratory Langlej Field, Va. UNIVERSITr' OF FLORIDA DOCUMENTS DEPARTMENT 120 MARSTON SCIENCE LIBRARY P.O. BOX 11 7011 GAINESVILLE, PL 32611-7011 USA WASHINGTON NAC A 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 - l6k 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/det^s/analysisoffactorOOunit NACA ARR No. Ti;Tl3 MTIOML ADVISORY COrMITTEE FOR AERONAUTICS ADVANCE RESTRICTED REPORT ANALYSIS OF FACTORS APTSCTING lET LIFT INCRE^IEIW ATTAINABLE V/ITH TRAILIN'^-SDGE SPLIT FLAPS ON TAILLESS AIRFLAI3ES By Marvin Pitkin and. Psrnard Maggln SUMMARY An analysis has been made of factors affecting the net lift increment attainable v/ith tralling-edge split flaps on tailless airplanes. The flaps investigated in the analysis were designed to conbribute zero pitching moments about the wing aerod.ynamic center ^uliqu deflected. Calculations were made of the lift and pitching-moment characteristics of flaps of this type over a range of design conditions in v;hich svfeepback angle, aspecb I'atio, taper ratio, flap chord, and flap deflection were widely varied. In addition, calculations were i.iade to determine the effect of the various parameters upon the loss in lift incurred in trlimning the stability moments of a tailless airplane. A method is given for roughly esti- mating the maxlmixa lift coefficient of tailless airplanes. The results of the analysis indicated that asjject ratio a.nd sweepback angle were the principal parameters influencing the net lift increment attainable with the flaps on tailless airplanes in triiiiied flight. An increase of these para:neters allowed the use of larger- span flaps. Large values of both parameters were required to obtain si?-.able lift increments and to mlnii;iize the loss of lift caused by the longitudinal control sui'faces. In order to utilize fully the high-lift advantages associated with flaps on sv/ept-back wings, tne use of tip slots or washout will probably bo required to elir.inate the unde- sirable tip stalling and the accompanying stability losses caused by large angles of sweepback. The allowable flap span - and hence the net lift increase - of some wing conf igu.rations could be further increased by the addition of a trim flap located at the wing tips and deflected upward. 2 NACA ARR No. liillS Excessive wing taper v.-as shown to reduce the net lift Increment obtainable from flap systems, whereas increased flap chord and deflection increased the net lift increment . I^TTRODTJCTION The application of high-lift flaps to a tailless airplane requires a flap arrangement that produces only small pitching moments about the center of gravity of the airplane. Such an a.rrangement is necessary because the elevators on tailless airplanes operate on short moment aimis and thus produce relatively small pitching moments . The pitching mom.ents produced by flaps may be kept small by the use of a basic flap design that has a small section pitching mom.ent or by the use of partial-span flaps on v/ings with sweepback. Another miOthod of reducing the pitching m.om.ents of flaps is to cancel out the diving moments of one flap deflected downward (designated lift flap) by m.eans of a second flap deflected upward (desig- nated trim flap) and possessing a longer lever arm. An example of this method of obtaining Increased lift by means of such a multiple-flap system is shown by the con- ventional airplane in which the trim flap (elevator) possesses a m.omient arm from 10 to IS times as long as that of the wing lift flaps. I"ruch information is available on the section pitching moment and lift produced by various flap designs, and some work has been done on methods of computing complete- v;ing moments from section data although the data have not been directly applied to tailless airplanes. In the present report, the results of an analytical investigation are given for a wide range of v/lng and flap parameters. The effect of these param.eters upon the net lift increment obtainable from flaps en tailless airplanes in trlmraed flight has been treated. Conventional split flaps were chosen for the investigation because of their simplicity and because they produce relatively sm.all section pitching mom.ents for a given lift increase. Calculations were made ro determine the effect of sweepback, aspect ratio, taper ratio, flap chord, and flap deflection upon the lift^. increm.ent obtainable at a NAOA ARR No. lliJlS fixed angle of attack oy ir.eancj of flaps creating zero pitching moments aborit the wltig asrodynamic center. Addi- tional calculations viere ruade to determine the losses in lift resulting from the elevator deflections required to trim stability moments. A brief study was made of available empirical data concerning the effect of sv;eep- back and flaps uoon the maxir.iuni lil't orobable in trim:ned flight . The lift increments of different flap arrangements were determined by the method of reference 1 with a simple chord correction factor being applied. The pitching mom.ents were computed from a consideration of the incremental lift due to the action of the flaps at each spanwise section and the center of pressure of this incremental lift. This procedure is somewhat similar in basic principles to the method of reference 2. The accuracy of the present method was determined by calcu- lating by means of this m.ethod the lift and moment incre- ments of flaps on 10 different finite wing-flap combina- tions for which wind-tunnel data were available. SYMBOLS a angle of attack, degrees C-j^ lift coefficie -m Ct maximum lift coefficient ■■-Ynax Cy^ section lift coefficient Sect ion lift \ qc ■/ fCj "N maximum lift coefficient in trirnmed flight V ^maxytr AC-r Increment of lift coefficient C,^ pltching-moment coefficient ^' Pitching moment qcS c^ section pltching-moment coefficient / Section pitch ing i.io ment \ V qc2 7 [j. NAG A ARR No. lii-IlS AC-j^ increruent of pit chin^^ -moment coefficient q dynaiaic nressure / .-oV p den;-^ity of air, slugs pep cubic feet S wing area, square feet V true airspeed, feet per second b win^ span, except as clesl,[;;uatcd otherwise by subscript, feet c wing cborcl at any section, except as designated otherwise by fubacript, feet Cg root chord, feet c rue an wing chord, faet (S/b) c.p..o center of pressure of incremental lift load caused b;>. flap deflection, fraction of wing chord X distance from center of pressure to reference point, feet t/c airfoil thickness, fraction wing chord Aa ^ equivalent change in angle of attack for a given flap deflecbion, degrees A aspect ratio (b'^/s) A, taper ratio; ratio of tip chord of wing to root chord of v;ing A angle of sweepback of quarter-chord line, degrees Pj H theoretical factors that are functions of aspect ratio and taper ratio h static-margin factor (hC- (*S.s/«-) MCA Ar?R No. lUii8 5 x^ ^ distr.nce to aerodynaralc center cf wing from quarter chord of root section, feet c./lj. quarter-chord line 6 control-surface deflection, degrees a slope of lift curve, par degree (cC-^/da^ Subscripts • f flap L lift flap T trim flap e.g. about center of gravity a.c. about wing aercdynv.;;.ic center infinite aspect ratio theor pertaining to theoretical wing plan forms given in reference 1 max maximum 1 over flapped part of wiiig 2 over unflapped part of wing p ' longitudinal (pitch) control w unflapped finite wing bw basic wing with zero sweepback of quarter- chord line METHODS Calculation of Incremental Lift Caused by Flaps The increiaental lift caused by flap deflection st a constant angle of attack v;as obtained by Integration of the section incremental load distribution across the 6 MCA ARR Ko. li|Tl8 v;ing span. These span load distributions were calculated by the influence-linos -method described in reference 1. Inasmuch as the daba in reference 1 apply rigorously only to the wing shapes shown in that report, a chord correc- tion was applied to the span load distributions obtained from such data. No correction was applied to the span loading to account for the effect of sweepbaclc, however, because available data on the subject were inconclusive. The span loading was corrected for chord by multiplying the loading at each spanwise station of the wing shape most similar to that under consideration by the ratio of the chord of the wing under consideration to the chord of the wing shape of reference 1. The method of reference 1 gives the value of Incre- m.ental lift caused by flaps that create an effective change in angle of attack of 1 I'adian over the flapped parts of the wing. In order to convert such data to the incremental lift caused by a different flap deflection, the equivalent increment of angle of attack Aa for that deflection had to be found. For the present analysis, values of La were obtained from data for Vv'ings of infinite .span at a lift coefficient of 1.0, which corre- sponds to an angle of attack of 10^ for the average unflapped v/ing section. This value was chosen because the angle is far enough below the stall to yield con- sistent results and, at the same time, is in the high- lift range at v/hich flaps are utilized, A typical incre- m.ental span load distribution caused by flap deflection is presented in figure 1(a). The values of aa used in the analysis were obtained from reference 3 ^(^'- split flaps of various chords and are plotted against flap deflection in figure 2. The lift increm.ents of constant-chord flaps or arbitrary- chord distributions were calculated by use of a value of Aa based on the mean flap chord. Calculation of Pitching Moments Caused by Flaps The incremental pitching moiiients caused by the flaps were calculated by multiplying the incremental lift loads caused by flaps at each spanwise station by the corre- sponding moment arms - that is, the distance between the local center of pressure of the lift load and the moment axis, Graphical integration of the spanwise distributions of pitching moments thus obtained yielded the incremental pitching moments created by flap deflections. NACA ARR Fc. liillS 7 Calculation of centers of pressure of flap loads over flapped parts of win g.- Ths center of pressure of the incremental lift loads over the flapped parts of the v;ing c.p.|> was calculated from section data by the simple relation c.p.f = Tf '^'^ " °*^') ^ ^'^5 ''^' Equation (1) can be rigorously applied only to a finite wing that is equipped v.-ith full-span flaps for v;hich the local lift-ciu^ve slopes are equal to that of the vv'ing as a whole. This equation, however, was found to defir^e the center of pressuj?e of the flap load over any flapped part of the wing with satisfactory accuracy. Values of the lift -curve slope for wings of infinite aspect ratio a vary with airfoil thickness and were selected from the data of reference 2. Valiies of the lift-curve slope for finite wings a were calculated by the formula Fa^ (2) also presented in reference 2. The factor F, which is a correction factor involving aspect ratio and taper ratio, varies between 0.98 and 1.00. A value of O.99 vjas used in the present report. A study of df-.ta for the FACA 230-series airfoil (reference 5) indicated that the center of pressure of incremental flap loads on wings of infinite aspect ratio c.p.^ was independent of flao deflection but varied o somewhat with angle of attack and considerably with air- foil thickness and flap chord. All values of c.p.-, o were chosen at an angle of attack of 10°, the angle of attack ct which the lift increments were calculated. The effect of flap chord and airfoil thickness upon co.^ ■ -"o vjas determined from, the force-test data of reference 5 and is shown in figure 5» '^he variation of c.p.^- with -^o 8 NACA ARR No. Ti^Il8 flap chord, as calculated by IJf ting-line theory for wings of infinits aspect ratio, is also given In figure 5 for coiiiparison. 3y use of equation (1), calculations were niade to determine the center of pressure of the incremental flap loads over tlie flapped parts of the finite wing c.p.^. . I 1 Figure L^ presents the calculated variations of c.p.^ v/ith aspect ratio for split flaps of various chords on moderately thick ( l6 percent) airfoils. Agreeruent of these calculated values with availatle data for rectan- gular wings with fu]l-span flaps vvas fo\ind to be good. C enter of pr o s suro of i ncre:ne r.tal flap lo ads over unflappt'd parts of the wi ng . - The cent er - of -pr e s sur e distribution of the inoi'emenbal flap loads over the unf lapped parts of the v/ing C!«P'_fo "''^^ obtained from the pressure-distribution data of reference 6 that are shown In figiu^e 3» These data indicated that the value of c.p.^ msy be sat Isfactoril j calculated by equation (1) and that the spanwlse distribution of c.p.^^ may be simu- lated by a line faired between the C,l|9c station at the flap end to the 0.?5c station at a point O.JO^ from the flap end; the induced loads due to the flap may thereafter be considered to act along the O.^^c line . By use of the values thus obtained, the center-of-pressure distribution of incremental loads caused by flaps may be readily dotermined for any desired wing-flap config-aration. Figure 1(b) illustrates typical center-of-pressiore dis- tributions for constant -chord flaps. The pitching-ir.oment distributions obtained by use of such data in conjunction with the span loading are illustrated in figure 1(c). Accuracy of Methods In order to deteri.iine the ovei'-all acciiracy of the methods and data presented herein, the ircrei.iental flap lift and pitchlng-noment coefficients v/ere calculated for 10 finite wing-flap combinations for which wind- tunnel force-test data were available. The close agree- ment of calculated v/ith measiu'cd values is shown In figure 6. NAG A ARE No. li(.Il8 Lift Evaliiatlon under TrimrGd -Flight Conditions A certain percentage of the lift created by the liftinf^ STorfsces of an airplane is lost in trimmed flight owing to the action of the triiTimin£; surfaces in ■balancing- pitching moments. Such a Iofs of lift is considered herein to be divisible into two parts. The first part is the loss of lift that is encountered in trimming flap mom.ents; the second part is the loss encountered in tri:mjning the pitching moments created by the longitudinal stability of the airplane. These lift losses have been treated separately in the present analysis. Net lift increment caused by flaos . - If the basic- wing pitching moments e.t zero lift are neglected, the lift lost in trijimiing the flap mom.ents is caused by the triiTLming surfaces in balancing the flap moments about the wing aerodynamic center. The net gain in lift caused by flap deflection is, therefore, the lift increment caused by flap deflection minus the lift lost in trimming the .•'!'lap moments about the wing aerodynamic center. The net gain in lift caused by flaps in triinmed flight is therefore automatically obtained for the flaps that create zero pitching mioments about the wing aerodynamic center. All flap combinatioixs investigated in thjs analysis v^rere, for this reason, designed to create zero incremental pitching moments about the vving aerodynamic center . ^ov each design configuration investigated, the incremental lift of the flaps was obtained for a series of lift flaps of various spans e::tending outboard from the center line of the v.'ing and for a series of trim flaps extending inboard from the v.-ing tip. T'he location of the aerodynamic center for the wing shape under investigation was then determined from the follov/ing formula given in reference 2: ^a.c, = K^ ^^^ ^ ^.5) where H is a function of aspect ratio and taper and may bo obtained from reference 2. After the location of the wing aerodynamic center has been determined, the incremental pitching moments of 10 NACA ARR No. l1j.I18 ^^S the lift and trim flaps were calculated about tho v.'ln^ acred yiiar-iic center. Each lift flap was then luatohed with a triin flap so tnat the com'bined incr-eicental pitching inoir.ents of the two flaps were equal to zero. For some arrangements, a lift flpp existed that created no moments about the aerodynamic center. Tnis ty^^e of flap is referred to herein as a "self-trimm.inc; flap." The net lift increTient used to evaluixte a given flap system was then obtained- by deducting the lose in lift due to the trim flap from the lift increriient created by the corre- sponding lift flap. Equation (5) does not take account of the rearv\?ard shift of aerodynamic center caused by the shift of loading tov.'ard the wing tip as the ;ving is swept back. The data of reference 10 and unpublished force-test data from the MCA 19-foot pressvjpe tu.nnel indicate that this shift may be as large as 5 percent cf the mean aerodynamic chord. The results of the analysis are therefore believed to be somewhat conservative and sho\ild probably indicate net lift increments larger than those actually determined. Lift loss caused by lon .^i tudinal stability .- The lift lost by the longitudinal control surfaces in trimming stability moments is associated vixtli a pitching moment about the v/ing aerodynam^ic center equal and opposite bo hC-p , where h is the static -margin factor dC^ /dCj This loss is zero whan the longitudinal stability is zero (h = 0) and raay therefore be attributed to the airplane design rather than to tbe flap characteristics. Inasmuch as the longitudinal control sirrfaces of tailless airplanes are normally mounted at the wing tips, the data from the trim-flap calculations were used to obtain the lift lost by such controls for various sta- bility mcme nt s . ^CCPS OF CALCULATIONS All calculations made in the present analysis were based on values of flap effectiveness and the center of press-lire of the flap load obtained by averaging section force-test data for the NACA 230IH and NACA"'25C21 airfoils Tbe calculations are therefore most applicable to air- planes equipped with moderately thick" wing sections (about 16 percent) of the MA.CA 2^0 series. NACA iim No. lUii8 11 Calculations were made first of the net lift increases, at a constant angle of attack, caused by "■■ 0.30c flaps deflected 6o*-* and installed on a vdng with aspect ratio of 7.5, sv/eephacl-: angle of 20°, and taper ratio of O.25. Each of these wing and flap parameters was then varied independently of the others. The design parameters -.vere varied as follows: Svireepback an^le, degrees 10, 20, 50 Aspect ratio » . . . 6, 7«5j 10, I6 Taper ratio 0.2S, C.SO, 1.00 Flap chord, percent c 10, 20, JO, lj.0 Flap deflection, degrees to bO The lift loss caused by tri-n flaps of various spans was also calculated over the range of design parameters in order to porr.dt estimation of the lift lost by deflection of the longitudi;ial control surface. The maximum lift coefficient of a tailless airplane that incorporated the design I'eatures shown to be favort^ble for obtaining high lift was then estir.is.ted. RESULTS AND DI3CTT£SI0N The results of the analysis are presented in figures 7 to 14, which show the variation of the allowable flap span and the net lift increments due to flaps with each of the basic design parameters. A gain in the net lift increment obtained by the variation of one design parameter cannot be added directly to the gain obtained by the variation of another parameter because these gains were generally obtained by an extension in flap span. Two design changes, each of which permits an extension of a given flap equal to 0.[;.0b would not therefore necessarily permit an extension of 80 percent when acting together. Such changes would result in a larger allowable flap span, but the actual quantitative magnitude of the increase would have to be r^- calculated . Effect of FDap Chord Lift -flap chord .- The effect of increasing the chord of the lift ilap is shovm in figui^e 'J. Arrows and points are included as an aid in using the chart, and an example of the use of this flgiire follows? 12 NACA ARR ICo. ll;Il8 If the chord P.nd spar of a self-trinraing flap that fields /'ACt ^ =^ C.51 ars to be fcand, V ^f^.et point a Is first located on the net-lift scale and the arrow is followed to point b. Point b indicates that a lift-f].ap chord of 0.235c is required. Follc.ving the arrov>/s froin point b to ■"Doint c and then to point d indicates that the required flap extends over the inboard section a dlrtance equal to 0.20b. In a similar manner, the dlinensional characteristics of a multiple-flap S77stem may be obtained. For example, following the arrov/s from point a to points o, f, and g shows that the same net increiuental lift may be obtained from, a system consisting of a G.^ub lift flap and a C.20b trim flap, both of O.ljc". The data presented in figure 7 show that an increase in flap chord on a tailless airplane causes an almost linear increase in the net lift increment due to the flaps. Although this lift increase is caused largely by the increase in Aa that accompanies an Increase in flap chord, this action is further reinforced by the forward shift of the center of pressure of flap loads with increased flap chord. This oenter-of -pressure change allows extension of the flap span for a given flap pitching moment and hence Increases the net lift attainable in trimmed flight . The data of figure 7 sl-i-ow also that the addition of .trim flaps to the outboard wing sections permits an extension of the allowable lift-flap span and results in increased net lift increm.ents for a given pitching moment. The increase in lift with a given increase in flaj) chord is more pronounced for the multiple -flap systems because of the greater allowable span of the lift flaps. A mu].tinle-f lap system occupies more span for a given lift Increment, hovi/ever, than a self-triiianing flap and conse- quently leaves less span for lateral and longitudinal control surfaces. Tr i m - f 1 a p cli or d . - The effect of varying the chords of the trim flaps required to trim a series of constant- chord lilt flaps is shown in figure S. These data show that varying the trim-flap chord had no appreciable effect upon the net lift produced by a multiple-flap system but that the principal effect was to decrease the required trim-flap span as the trim-flap chord was increased. NACA ARR No. LkllS 15 The variation of trim-flap choi''d had no effect on the iiet D.ift oroduced bj?- a multiple-flap system, because the rearward shift in center of pressure of the local flap loads with decreasing flap chord was offset by the decrease in moment arm that resulted from the required increase in trim-flap span. Varying the trim-flap chord thus caused little or no variation in the effective moment arr.- of trira flaps for a given pitching moment; the lift lost by these flaps therefore was, for practical purposes, independent of flap chord. If the primary con- sideration is the span available for control surfaces, lar^e-chord trim flaps would generally be desirable. The data of figure 8 indicate that, for the wing conditions specified, a lift flap of 0.21-3b is self- triniminf., , Flap spans smaller than 0.21'3b create stalling mojnents and consequently I'equire trim flaps that are deflected dowfnward. Effect of Flap Deflection The effect of flap deflection upon the net lift increments produced by flaps is a function only of the resulting increase in angle of attack Aa because the center of pressure of flap loads was found to be almost independent of flap deflection. The variation of net lift increment with flap deflection is shown in figure 9* These data indicate that the largest practicable flap deflection should bo used. For split flaps on thin to moderately thick wings, however, there is little increase in Aa and hence in net lift for deflections greater than 600. Effect of Sweepback The results of the calculations made for a range of sweepback angles from 10° to 5^° are shown in figure 10. Arrangements of self-trimming flaps are not possible for a wing of zero sv/eopback, because the resultant centroid of flap loads v/ould act behind the v;ing aerodynamic center and would not satisfy the requirements of zero pitching moment, Sweepback of the v/ing, hov/ever, so shifts the wing aerodynamic center and the vving sections that the lift-flap centroids of incremental load move forv^ard IS 1)4- NACA ARR No, Ll^.IlS relative to the wing aerodynamic center and trim-fls.p ceiitroids ■ move rearvvard. As the 3-,;eepback an^:le is incres^ed, therefore, one angle is reached at '.vhich the center of pressure of flap loncis at the v;ing center line acts at the same fore-and-aft location as the wing aerodynamic center, Tlals sweepbacl: angle is the minim\im an^le at which self-trir^Kiing flaps may be employed. For the particular win(- vsecl in the calculations shov/n in figure 10, this minimum sweepback angle was ll|.5'^. Further increase in Svvecpback an/rls allov/s the use of larger-span self-triHir.^in,[; flaps and results in sizable not lift coef- ficients. The folD-CV/in.f- values taken from figure 10 illustrate the rapid riL^c of net lift coefficient with s w e p b 1 c ]■: e ng 1 c : oweepback angle, (deg) M c t lift inc r c ..s c , V / ne t Alloi/able spun for sulf-ti'imming flap (percent b) 1,'l.S 1^ ' 13 20 2S 50 .19 8 16 22 11 These values do not include consideration of the effect of sweepback on the stalling and hence on the maximum lift characteristics of an airplane. The results presented in figure 10 i net lift Incremients larger than those att self- trimming flaps may be obtained by co flaps with ti'im flaps located at the tips if the sv/eepback angle is small. Use of flap systemis provides the means of obtain ments from. tra3 ling-edge flaps for sv/eepb the minimum angle i'or self-triiruriinr flaps flap system, ho'.vcver, provider a smaller per unit span utilised by the flaps than flap. ndicate that ainable from up ling the lift - particiilarly these multiple- ing lift inc re - ack angles below , A multiple - lift increase the E e 1 f ~ t r i ;:nn i n p The lift Increase due to increase in allowable flap span with increased sweepback angle is not all gain inas- much as an increase in r.v/eepback angle also reduces the lift-curve alope and shiJits the wing stiUl to the wing tips. The theoretical i-inalysis of reference 11 indicates NAG A ARH No. L' ill 8 15 that the loss In lift-cu^ve slo^^c varies approximatGly as the cosine- of the angle of sv/'3^..pbac;k. As a rough approxi- mation, the maxinrorR lift coefficient of a wing also Vv'as assmned to vary as tho cosine r..L the anglo of 3\voepback. Figure 11 presents available wind-tunnel forc3-test data concerning tho reduction of C,- due to sweepback "max angle. In addition to reducing maximum lift, vvins-tip stalling may also produce undesirable lon^jitudinal and lateral .-itPbility chai-acteris tics , Some feature that would eliminate or reduce the effects of the -.Ying-tip stalling should therefore be incorporated in the design of the -.ving. Wing- tip slots or Vifasaout has already proved to be beneficial in tnis respect.' ihe results of reference I5 indicate that as much as 50 percent of the lift loss due zo swuepback m.ay be ^""ecovered by washout. Part of the lift loss due to s^reepback will probably be recovered on most tailless airplanes, inasmuch as some washout is usually used. Effect of Aspect Ratio Results of tJie aspect-ratio calculations are pre- sented in figure 1,2 and indicate tliat si2:al;le net lift increments cannot bo obtained, even for wings v/ith large S'veepback angles', "'hen the aspect ratio is small (less than 5)« Incrtasinp; the aspect rscio above 5 resulted in a rapid increase in the allowable flap span. At high aspect rat-.ios (about 10), lift increments comparable with those for conventional airplanes wer calculated for tailless airplanes. These trends are illustrated in the follovving table: A \ Vnet Allowable span for s e 1 f - 1 r iirmilng flap (percent c ) ^•5 6.0 8,0 10.0 12.0 11., .18 1.00 1.10 Q 29 The results of figu.re 12 shov/ also that the efficiency of the trim fla.p in neutralizing pitching momtnts '.vlthout l6 NACA ARR Nc. L1^I18 VLndue loss In lift decreases with increased aspect ratio and that use of this flap syster.i is not virarranted at high aspect ratios. For hi^-h aspect ratios, the single seli'- trirniuing f].ap occupies almost all or all the span that can be allov/ed for flaps without reducing the span neces- sary for lateral control and, as previously shown, the self-trimrnlng flap yields higher lift increments than the inulxiipj.e-flap system of equal span. The aspect-ratio calculations explain the diffi- culties encountered in trj-ing to obtain high lifts on tailless fighter airplanes. In an investigation in the NACii free-flight tunnel (unpublished data) of .a model of a taillasc fighter ailrplano with aspect ratio of 5*1 ^^'^ v/ith sv;eepback angles of 2[;° and ^^P , a maximura increase in the net incremental maximuin lift coefficient of only 0.11 v/as obtained v/ith the best of a large variety of flap systems operating under trimmed-f light conditions. The present calcu3acions show that a lift increment nine times this value would be obtained for a similar airplane having t^vice the aspect ratio. Trailing-edge-f lap lift increm.ents approaching those of flapped conventional airplanes thus seem to be obtainable only on tailless airplanes of fairly high aspect ratio. The results of the aspect-ratio calculations can be explained by consideration of the action of increased aspect ratio upon the aerodynamic center of a sv;ept-back v.'ing. As previously shown by equation (y) , the fore-and- aft location of the wing aerodynsinic center is defined by the relation x^ ^ = Hb tan A. For a given v;ing area, an increase in aspect ratio increases both H £md b and consequently results in a rearward shift in the wing aerodynr.:ri.ic center. This action results in a reduction of the diving iriomxents created by flaps aiid hence allows extension of the lift-flap spans for a given pitching moment. This fact explains the rapid increase in net lift incrym:\nt with increased, aspect ratio. The moment arms of the outboard sections are similarly reduced «/ith increase in aspect ratio and a greater lift loss is thereby incurred for a' given required trirroning momeiit. Inspection of fiie formula x^ = Hb tan A a.c . ^ indicates that the largest effect of aspect ratio occurs when the sv;eepback angle is large. High lifts are most readily attained, therefore, for relatively large values of both aspect ratio and sv/aepback angle. NACA ARR No. ill II 8 I7 Effect of Taper Ratio Results of taper -ratio calculations are presented in figure 15, which shows that an increase in taper ratio allows a sizable increase in the net lift increments of self-trliniriing flaps only when the taper ratio is initially small. For values of taper ratio higher than 0.5> the gain in net lift increment with increased taper ratio is negligible. For the airplane investigated, increasing the taper ratio from O.25 to O.5O Increased from O.I4.2 to 0,66 the allowable net lift increment obtainable by self-triirrning flaps. A iurther increase in taper ratio to 1.0 increased the net lift increment to only O.7O. The resTilts of figure 15 also show a successive decrease in triia-flap efficiency as the taper ratio is increased from small values to 0.3« Above O.5, however, a slight gain in the trim-flap efficiency is afforded by increased taper ratio. This value seems to indicate the point at which the direct effect of increasing the tip chord offsets the decreased mom.ents of the outboard sections caused by the shift of the aerodynamic center. An increase in taper ratio results in a rearward shift of the wing aerodynamic center. It would thus be expected that, as the taper ratio is increased, the flap moments would be reduced and, therefore, that self- trimming flaps of larger span could be used. Increasing the taoer ratio of a given v/ing, hov;ever, causes also a reduction in the chords of the inboard sections and an increase in the chords of the outboard sections. The gain in lift -flap span allowable, due to the aerodynamic - center movement with increased taper ratio, is thus Increasingly opposed by the decreasing chord of the inboard sections. In a similar manner, the decrease in trim.-flap efficiency caused by shortened moment arm.s with increased taper ratio is offset by the increase in chord of the outboard sections. In addition to the favorable effect of moderate ' taper ratio (about O.5) upon the lift produced by flaps on tailless airplanes, further advantages are realized by taper ratios of this order. The wing-tip stalling characteristics are more satisfactory for moderately tapered wings than for highly tapered y\rings. Moderately tapered designs therefore allow use of larger angles of sweepbacl" before sizable losses in lift are incurred. Reference 17, in addition, shovi's that moderately tapered wing designs (taper ratio between 0.55 to O.S) are structurally most efficient. 18 MCA ARR i:o. iJillS Lift Loss in Cbtainin,? Longitudinal Trim The celculations made to d the para.neters on the lift and i sties 01 the trim flaps are al of the lift loss incurred in ba mouients of the airplane. The e trim.-flap chord are presented i that no appreciable cb.anp;e in 1 the trim-flap chord for a given of the effect of taper rc/cio al effect on the lift Iocs due to The effect of taper ratio on th trimming a moment of 0,10 about of a win£ witli sweepfcach angle of 7«5 is shown in the followln eternine the effect of pitching-moment character- po applicable to the study lancing the stability ffects of varying the n figure 8, v/hich shows ift occurs vvith varying pitching moment. A study so indicated that this trim v.'ould be negligible, e lift losc incurred in the aerodynamic center of 20'^-' and aspect ratio g table: (fieg) ± 0.25 .50 1.00 -0.25 -.21 -.18 1 The effects of aspect ratio and sweopback on the lift loss resulting irom the additional trim, required for longitudinal control are summarized in figure lli. data indicate thab large values of aspect ratio and pweopbac''.: angle are required zo minimize the lift loss "'■^"^ ^-' '" ' -.-.... - -. ■.;;r>j_-|, requirements. 'hese ; suiting fro/a the additional The data of figure I/4. inay be applied to trim, controls using different choi'ds or deflections or to control surfc-ces other than the plain split flap, if the centroid of in^'remer.tal flap load is located at approximptely the samo chordv.'ise station as that of the split flap. An incror.xcntal anrle of -- --0-- -- -ittack Aa = S.Ii."-^ was used to miake the oalcu].ations required for figure ll;. . In order to convert the data of I'lgure ll; to other flap cnords, flap deflections, or airfoil sections, the scales of the graphs can be m/aitiplied by the ratio of incremental angles of attack . MCA AHR, No. lliIlS 19 Estir.iation of T.Iaximum lift Co^afficlent of Flapped Tailless Airplanes in Trirjned Flight Diirin^ the course of the investigation, it was recognized that the data obtained in the analytical and empirical studies could be employed to give an indication of the raaximutn lift coefficient attainable, with tralling- edge split flaps on tailless airnlanes. The maximu-n lift coefficient of a tailless airplane in tr ironed flight with flaps deflected iviay bo expressed in sur.imary forra as (Cj ^ = fCj ^ + LCr ^ - Losses V -^max^^^ >v HnaxJ^j ^f The lift losses of a tailless airplane may be con- sidered to originate from three sources - the loss due to the longitudinal control surface, the loss in maximum lift Induced by sweopback, and the loss due to change of wing stalling characteristics when the flaps and longi- tudinal control sur-face are deflected. The first two sources have already been discussed. The loss due to trim is given in figure 11+, and the loss induced by sweepback can be assumed to vary roughly as the cosine of the angle of sweepback. The change in stalling char- acteristics of a wing, when the flaps and longitudinal control surface are deflected, may change the angle of attack at which the maximum lift occurs and may change also the characteristics of the nonlinear portion of the lift curve. These effects may cause the increase in maximum lift produced by flaps to vary from the value of the lift increase produced by flaps at a wing angle of attack of 10°. Because stall prediction is uncertain and because of the complex nature of the problem, no attempt has been m.ade in the present investigation to analyze accurately the factors affecting the flapped-wing stall. A statistical study, ho'A'ever, was made concerning the ratio of incremental maximum lift coefficient pro- duced by flaps ' ('ACx "^ to the increm.ental lift coeff i- ^ -^^max cient produced by flaps at an angle of attack of 10° MCt ,^ . These data were obtained from available wind-tunnel force-test data and are presented in figure I5. 20 NA.CA ARR No. iJillS Thcjr-e data Indicate that a T'lLio of (1\Ct A /(^•^jA ^r, of 0,9 "joiild be a good mean value. An indication of ths maxir.-.um trim ].ift coefficient can now bs obtained from the relationship rC- \ = /Ot +0.9 ACy A COS A - ACt ()+) where l\Cj corresponds to the lift lost by a control P surface that yields a pitchlng-mo-iient coefficient about the aerodynamic center equal to h /'Cr \ and ma-^r be 'v -^max^'tp obtained from figure I.'l. It chould be noted that ACt is a function of fC-r \ f-^-i^*^ hence equation {14.) has V max y^p to be solved by the tr ial-aad-error method . High-Lift Design for Tailless Airplanes The present analysis has indicated that by proper design a tailless airplane may obtain majjcim^'ajn lift coef- ficients comnarablo v;ith those of conventional aircraft. A design that combines the features shown by the present rerults to be favorable for achieving high values of ma::imum lift coefficient is shown in figure lb. VJith this design, ^t is estimated that a maximum lift coeffi- cient of 2.0 in trimjnsd flight with a 5-P®rcent static margin may be obtained. CONCLUSIONS The conclusions drawn from an analysis of factors affecti?ig the net lift increment obtainable from trailing- edj;e split flaps on taillecs airplanes in triirtmed flight follow: 1. The maximum lift coefficient of tailless airplanes may be of the order of 2.C or greater for reasonably large vali;es of aspect ratio (10) and sweepback angle (20°). Low values of aspect ratio (5) ^.nd sweepback angle (10°) NACA ARR Ko. iJ-iIlS 21 will, lii-idt the Increirental lift obtained with flaps to sr.all values rnd vi/ill also rerailt in e::cessive lift losses due to lonsltudinsl control. 2. The highest net lift Increruents will be obtained from flaps oii wing desi£;n3 that allow nse of single inboai'd £elf-tri:rmung lift flaps v;hich occupy all the wing span not taken up by other control surfpces. 3. '^o-' v.'ing designs that limit the span of the inboara self-trlra;dng lift f]ap to a fraction of the span other\;ise allowable, furtner increases in not lift mey be obtained by usg of a multiple -flap system con- sisting of an inboard lift flap deflected downward and an oxitboard tri^ flap deflected lapward. i|. Excessive taper will reduce the net lift obtainable from flaps on tailless airplanes. Taper ratios of O.5 or greater are roconmendcd for tailless-airplane designs. 5. Increased flap chord ana deflection will lead to increased net lift increments due to flaps. 6. For wing-tip elevators, aspect ratio and sweep- back are the controlling factors in minimizing the lift loss for obtaining trim of a given pitching m.oment. Taper ratio and elevator chord have little effect on the trim loss. Langle3'- Memorial Aeronautical Laboratory ]»'at.lo--i.^l Adviriory Committee for Aeronautics Laiig lo y 5' i e Id , Va . , 22 ^lACA ARR Ko. li].Il8 REFEREIIGSS 1. Pearson, Henry A., and Jones, Robert T.: Theoretical Stability and Control Cl'iaracterl sties of ".-lingjs with Various Amounts of Tauer and Twist. NACA Rep. No. 65s, 1938. 2. Pearson, TTenry A., and Anderson, Raymond F. : Calcu- lation of the Aerodynamic Cnaracterl sties of Tapered Wings with Partis l-S-c.8n Flaps. IIACn Rep. No. 665, 1959. ^, Wenzinger, Carl J., and Harris, Thomas A.: 'Vind- Tur^r.el Investigation of K.A.C.A. 25012, 23021, and 25050 Airfoils with Various Sizes of Solit Flap. NACA Rep. No. 668, 1^59. 1;. "enzinger, Carl J.: Vvind-Tunnol Investigation of Ordinary and Split Flaps on Airfoils of Different Profile. NACA^Rep. No. 55lj., 193 6. 5. Weick, Fred. E., and Harris, Thomas A.? The Aerodynamic Characteristics of a Model •■■ing Having a Split Flap Deflected Downward and Moved to the Roar. NACA TN No. [(.22, 1932. 6. Wenzingsr, Carl J., and Harris, Thomas A.: Pressure Distribution over a Rectangular Airfoil with a Partial-Span Split Flap. NACA Rep. No. 57I, I936. 7. 'Veich, Fred E., and Sanders, Rohert : Aerodynaraic Tests of a Lov; Aspect Ratio Tapered '.7 ing with Various Flaps, for Use on Tailless Airplanes. NACA TN No. 14.65, 1933. 8. Neely, Robert H.: v^'ind-Tunnel Tests of Two Tapered ■■•I'ings v.'ith Straight Trailing Edges and with Constant- Chord Center Sections of Different Spans. NACA ARR, March 19.'j.3 . 9. Wenzinger, Carl J.: '.'ind Tunnel Investigation cf Tapered VJings with Ordinary Ailerons and Partial- Span Split Flaps. NAOA Rep. No. 61I, 1957. 10. Anderso.a, Pa^^Tnond F. ; Determination of the Character- istics of" Tapered T/ings. NACA Rep. No. 572, 1936. NACA A:^ No. lI^IlS 25 11. >!utterperl, William: The Calculation of Span Load Distributions on Swept-Back Wings . NACA TN No. &3h , 19lf.l . 12. T^ouse, Rufus 0., and '.Vallace, Arthur R.: ■"ind- Tunnel Investiration of Effect of Intei-^ference on Lateral- Stability Characteristics of Four ITACA 23012 Wings, an Elliptical and a Circular Fuselage, and Vertical Fins. FACA Rep. No. 705, I9I1I. 13. Rossell, H. "., and Brand, C. L.: Sv;ept Back^Vings. Part Viiij Reports on "".'ind Tunnel Experiments in Aerod;rnamlcs. Smithsonian I'isc. Coll., vol. 62, no. I, 1916, pp. 55-73. 1!;. Knight, Montgomery, and Noyes, Richard"/.; Snan-Load Distribution as a Factor in Stability in Roll. NACA Rep. No. 395, 1951- 15. Anderson, Raymond F. : The Experimental and Calculated Characteristics of 22 Taoered Wings. FACA Rep. No. 627, I93&. 16. Villiams, D. K., and Halliday, A. S-: Experiments on Swept-Back and Swept-Porward Aerofoils. R. & M. No. Iii91, British A.R.C., 1933. 17. Anderson, Raymond P.: A Oojiparisoii of Several Tapered Wino-s Designed to Avoid Tip Stalling. NACA TN No. 713, 1959. 18. '7all3ce, Rudolf: Investigation of full-Scale Split Tr ailing-Edge V/ing Flaps with Various Chords and Hinge Locations. 'NACA Rep. No. 539, 1935. 19. Jacobs, Eastman N., Finkerton, Robert M., and Greenberg, Harry: Tests of Related Porv/ard-Camber Airfoils in the Variable-Density '.^ind Tunnel. NACA Reo. No. 61c, 1937. NACA ARR No. L4I18 Fig, I s u ?^1 d Gain IncremenkiJ ///7 due -6 //// f/ajD IncremenfaJ //// dae h fr/m f/ap F^rcent semiopon I.OS5 (a) Typical incremenfoJ span Jood di^nbution caused d/ f/op c/ef/ecfion. Aerod/na/nic cenier Tr/m/jt2p 0) TypiooJ ^panmx center- of - pressure, distnbuf/on of /ncrementoJ /ood due to f/aps. O IL) 10, ^1< 1^- ^« Diving moment Jncrementd pitdiinq moment due to lift fJop /ncrementoJ p/ thing moment due to fr/m flap StaJ/inn moment NATIONAL ADVISORY CO'.:VITTEE FOR AERONAUTICS (c) TypicoJ jncremenioJ nncynent c//3fr/duf/on due to f/a/DS. ffgure /.' Soimple f/ft^ cenfer- of -pressure, and pi tcn/ng-nxynent distr/t>ut/on5 cJue to part/at- span f/ops on a .^lA/epf- fxtcH wing. NACA ARR No. L4I18 Fig. 2 ; - — ... 1 1 . . nz t. . — 5- 1 9 1 "k -- — o< .4. \i^ 1 ! ^ X D IS 11 \m ! uJ ' V; — So O + s — 1 UJ ,^ ^ — HAOA 23012 — NAOA 23021 1 i V}> s , >1Q r I ^ 1 \ S^ g "<3 1^ — ^ \ 1 \ 4 t \ I 1 */1 1 \ \ \ d 5 1 \ \\ \ . ' 1 (S L ,^ \ \ \ V \ \ \ \ — — 5^ T , \ 1 t / \ IP > i !-■ N. \ \ \ ^ 1 — — " V ' ^ \ \ \ N^ \ i \ \ s \ \ y^ 1 \ \ \ ^ ^ \ \ \ \ V \ L \ \ a 1 ^ \ \, s ' \ \ \ 1 y- ,s 1^ \ s \ \ 1 ri 1 \. i /' !^ \ 1 1 \ \ V W < ^- -- -♦. \ N V' s \^ > 1^ ,\\ \ O "^ N \ \ \ * La. \ V ^ > S \, \, \\ )^ \^ !^- 1 1 s i s S,^ J\ !\ \ \ i? ^ 1 ^ 1^^'^- }— ^ f y s^ \ 1 L \^\ \ \ •^ * \ ^1 ^\ ^N. \ i\ !8 '^ \ \^ \^^ k ^ N, ^^ \ c^ ^ ^ \ sK^ V ^ -ii ^ \ ^ vVv^ v\ .!l ?^ ^ \^ ?n\^ J 1 \ 1 !? >5^ fV ^v Vv i "^j (I1 \Vv 1 ^ 1 v^ ! 1 ^ ^ 1 1 f\ J ! "S 1 k <2 «; tl ^ — — ■j '*■ 5 K r 'v s ^ -1 V/ '^ f\ Z ?^ ^Z ^ v^ s >^ \ . ^ /^ Aa \ \ V -- -- ^ 4 d \ s N ^ r ^ 4*^ f- \ N > "■• ~~H t- _ ^ °(^ n X § \ ^ *N \ "^ ^ s S •v \ ' ^ ,4 o \ V } s ^ *¥( J * ,,[ 1 ^ ■ \ y/ V 'A ^ 17 Oi. 'P. J N s ?^ s i' •M — — Vrt rthi. 'Ot 1 -ff 1/ n <: ^ ■s ^ fn \fi n<7- Uf ~>fi f, 'A nf V S: VI ^ ■J 's S 1 f s V C ? •f. ^ > 1 ^ f >J c ~K ^^ ^ C ^ % a r- /.I, J $ H ">; NAT ONA. Al iVlSC ERO RV lAU t& ^^ O i\ :oM LEF OR/ £ * n c ^ ^( } / 1 p, ? ,? 9 4 •? A n 6 ^/ r?/ ) r„ V V? A ^ / JO T, ?/" '/ r — — Fi P?/' r<^ . I ^t ^M -:/ 4 ^/J 7/ ■ ; "?a — • o d 5 s ■♦■*-* lf> J 1 1 I ^ .^ \^' 1 1 '■ ^ — — — 1 ^ >> ■ U O H * •< • t-o ^:? H >^ 606B OJ OJ 3 5 1 n";i IS £ g E^ ,g;^ •V T^ — g I ^ — — — / 1 T' — S "0 ^ « ^ c N I ^ s ^ 1 " £ 5^ II — to o jd ♦» o d • o ah 51 20 20 20 Ae Indloatad 20 1 1 ^ e, ^ ,v 1 ■ / / ^ V 1s — — — ( 1 1 8 ^. , 1 ^^ CO, -^ ( «c II O + X DO / Qo 1 \ / J J^ y. *0 VJ C' •^ 1 / / — -^ < iv! ^ ^ St < \ / r^ 5? k j '^ y / L- ■* y y z^' ^ ^r 1 X / y c C 1 — — ^7^ ^:l k° — 1^^ \ V V — St ^ ^ 1 1 J*' 1 «^ 'i -- — Q f ■8 k^ •« h <> > '» c^ 4 c ) > 1- i <, ■) V ■v :> ^\ >< ■) ".< '>. "^ J: '^ h 1 i! cj / ^l -f--L 1 1 -* >(. ''W^-' -u 7W~ ':z ut vo c/c //^ /i>. \io 707/ w 01 li 's>uy< / y< ^ ' 1 1 1 1 NACA ARR No. L4I18 Fig. 1 ■ 1 r- n K r^ r!^ VJ s i y] ^ I S^ ^ — .N (^ ^S V -■^ "^vi >1 i« S! y — C -^ "^ ll « f) § •^ ^■3 ^ i ^^ i^ v r; — -- ^o' .1'^ »cv r>l rx' — ^ ^ ^ - 5 ^^ ^ «^ ;>^^ ^ ^} "^ VJ 1"^ ._ _a. L s 9i 1 — V, ^ " — (^ ^ 1 S> : 1 ^. ^ ) s; -i^"^ ^ -1 fe ,■ ii ' ^ i <^i ^ II % -^ $ k 1 \ k 't> Vn w^ ■^ / ?a ^ "* K — ^ / ^o ' 1 ;^ §^ ^. *^ ■— 9 — ' ^ ^ k ^. ^ s =§ ^^ j / IP nH '^ ^ ,A '^ ■ 1 ^ '^s; V J\ K "-J •i ^ ~ . ^ ^^ ^ 1 f ■i v ^ 1 L r — ^ ^ ■^ ^ 1 ^ , ^. -V (^ f^ k' ' Qi e ^ o ^'^ Q 5^^ ) 1 ' H ^ ^■^ ^ 1 Q S- ^■f^ c^s> >^ 1 'r 15 _c ^ \1 >^^ ^ 1 (\ "n § i^ "?:] - - r ^ >^ ) ^>^ -f ^ '\ ^ ^ 5^ \ > ^^^ ^ i -i r — \ c ^^ ■^ i 1^ t *; t *^ ^5 :.i ^ 1 ^ ^ fs 91 c; — Q ^ — i^ \ '^^ ^S ^ ^^ S^ =2. ::5 I '-? n i i - Q S ^ ^ i ci . ^'■^ t k >^ "S ,'v: ^ lo ^ > 'H k ^^ ^ 1 1 ,ji < 'N ^^ ^, ^ ^ i ^ ^ ".^ « J ^ 1 1 \ II ii rs; i;^ :$^ 1 ■^ c- ^ V 1 < -> NsT- ^ ^ \' •< C; r ^ ^ l 3^ <; -> $g S' c ^' ,, \ 5ik . ^i s HI) (n ^S '^ ^ 5$^ ^ J K \ >^ — ^ ^ § 1 ^^ J-l ?^ ^ ^ V ^^ 1 • ?$ ?$ ^ \ ^ r% r> C? c :) \ 3" I) I, r f^A^ ^t '- J^ ■L 'f '>- /■;(, O I 70 /> "' — ^- c ^' 1 \ > 1 1 1 l^' 1 1 '^ 1 1 I 1 1 r ^ I' ^■y [j ■ 7^ u\ I/;? n 7' '^- 'y^ D £\ >u M .._ _. NACA ARR No. L4I18 Fig. NACA ARR No. L4I18 Fig. 7 _ n "n - 1 1 k .. ■ . .' ""'f *! 1 r\ " 't ' ' L J ^4 /h • ■::t vi I ■fr r v^ a. ? / ^ ;t^; ^ ± / \ / -■i v^ ^ h / / y > > ;ip s ^ ^- A y — £ r-^ ■. ■ ? / / /^ 1 '.■t V ^ * y ^ y ^ *A J / 'y / y . '"^ -s > f y 1 / ^ 'y •- 1 1 "M / •\ ^ r 1 .1 . c ) 1 " ( 1 l\ 1 ? ,? 9 4 n A n ^ 9 ' ' : 1 li ff -^ in "^ 1 <:/? V ^ f 1 f n ?/ ''1t\ '/? 1- r; 1 1 >i •\ 1 '- (. 1 !i^ f ■f\ h i/ h . \^ N " 'r / - '' ' . r\ \N \] V s -'" ci :::i- t"' i ^ ^ 0( \ N, N ■^ — 1 -- ^ y^ /^ ) ^ -/' a N Sk 1 1 ~^ , ^ y ^ ^ "*t ? \ "^ - - - _ y y __ ^< 1 -; i:- \ N •N t: ' t ^ ■ --,> y y N"i ^ J M n 9" K ■ * s^ -- ^ \y ,3 4i J s >" ■; ■ ■:■ ■"" ■ ^ ^ r-" y >i > X ; f ■<^ *■ * , ■~ T — - - ^ ^ y 'u r*- • f r> K O J ^^ w= ' - — - j. - ■ "1 ^ <3 r\ ;•:-_; ■ ^ c u ' wn m H vno iY ■ - s' - J 0M_ II7T EFtaA m pun cs " ;■-: ^ r " 'r ^ l\ "l<1 ■-- . ; --t A KJ ■ -■ .' - , 1 ■ ;f B Of r^ Ti ff ~ 1 TA '0 i- -7< ^ -a nr ) 7f J? 3. Z2 52 _i2 1£ 1} u ■ -|t^ }p ir (5. U £ -iti fr irk- H 7/ < Yi n f A Cn = A \: . ' )^ o_ / ?J rfi — i^( r 1^ C'f ^7. ■" ' i\ r ''/ i r NACA ARR No. L4I18 Fig. 8 -1 •> .t > _ i_ ( h - Hi, -< -— 5C 'fy r i . ^ -« k s .^ 0, /(\ 1 S^ s .<] '> ^ ^ '' \ S N s. N - - ^ ^ N s N rs ^ n ) ■J V' ^ ^ \ s. "Sj * Cs i .'^ \ s s_ .i ? ^ +» I z' /" \ ^ V 'H^ / S s^ 4\ ? - - - ' ^ '- 1 ■ } ' ?: - / ^ - -■ - ~ S» s / , ^ V /' ; J ■» / c \ ^ A 7 ?'" ) J 9 4 7 4 .6 - ;- a Jl i^ £ }7,? '1 oc in t>f H /— 06 '/: 1£ a L. ii - : / ■\ t It'-' - (\ ) j s^' / / 41 ) — •- !^ 1 - \ / •^ A y /"" - i •- \ \ \i \ '" J^ i r\ rf _ V Plj _^ rff - -f <1\ \ N. N V \ ~ O U — J r % 1 \ s ^ ' ' \ \ - ^ ^ - \ s \ ;'_:_ ^ 4 o 1 S 1 ^^ \u-- c 4 U > \ V ' fi- ^ > I \ it: V ^ ■ \ \ v:- n a /\ > \ tr- \P • s5 u \ --V ^ \ ♦t^-" r- : . \^ c ,^ e /^ ^ £ 1^ o U \ -.t n.'- ::ji ) - — t'nr: 7 o . Hi: / J " «/m 1NA Al 'm fY ■- 1 m )rn| ifORft ao! m 1 cs [^ - — — a 70 rr if /J? 5^ <2 1^ K7 7^^/ "i/^/ i 1 in 7f\ -^/n a. t. 1 \n it A 0)" in 9 _ \fr y? Y^- r. = < 7/ ;,v. A ^'.?, ?! } = 7 ?, f'j / -( i\?. r, f ,.^ ^<'i M \o a '^t '.C .= . / 4 V ' \ ^J NACA ARR No. L4I18 Fig. 9 NACA ARR No. L4I18 Fig. 10 — 1 — n r ife ^ ■ ^/ r\ />, P V.1 ' f. ly. '•'\ V/ :\- ^ ~'^^ b 1 ^ ■ . ■ - \ ^ -• ^ Hv > 7 \ ^ 1- --' — s .(. J ■ \ \ \ y y y r ^ /( ? \ \ f^ .^ '' ^ — — v ■ \ \ ^ x' x^ ^ i . r, X / ^ ' ^ 5 J. > :• t . _' '■ X / N y f' y •>♦, ■ / / \ 5> y , s . r /' / ,^ K, ^ ^ 4 / / ^ / ^^ ^ ^ <■ / / / - ^ / /* y / t / ^ / ,^ / y ■ 1 ^ / ' / , . $ lit • ■ /] f / V-X s '^ 1 ^ I ■ ' "s ■) ( c / 1 A 1 ^ ? 1 ? f, n /, *) i^ i '^ — P' 4 «?, <=>, •?, ) i ' ■ Si^ ''<°i y h ir H ?/' > A — ■*^ \ ^ J > r '!< 1 ' \ t] ^ ■ ■ \ \ ; ^ 1 ^ S s — — -vl ? 1 n > ^ ^ -^ N, . ■" •z i) 1 ^ •< ^ 's >^ ^^ s vJ ■> ^ V >^ ^ <: ' "v *^ / / f "> --, --. ^^ i'j c if r\ ^ N y\ ■^ -■ -1 ^ 1" \ *? u V L ) ^ / y / '^ . ^ "--ij ^ c . ^ 1 / / ^ ".-' V J "" . ( 1 / / / / ■V '- , ^ ^ ■ fi lO /( )- / / / ~-> -, . 1 ^ J 2l 9- / / •^ 1 -4 ,^ •?- / ^ s- " ^ Q r\ a J NAT) \m H mo lY OM^trn Ef )RA [ROT m re ■ 9. Tii^ r(° 1 9 F/ 7^ r/ -?/ 5"<^ '«'< ]rx y? 7/ r f7( b r, ^i /r r.t ?=, TiV ?r / \ ^ — — ?- 2: f/ & % ) or T, a 1 f £ i^ V^ ^ L_ ^1 ■J J Z & _J 42 -it '5 = ^ ; C-r 6 J ^ 1^ _C '^ D lsJ il ** U '.C f\ f,r 6^ i( V )• ■■1 >i ''l f T _ 1- ■,v '\ ' ' • 1 NACA ARR No. L4I18 Fig. 11 J 1 ! 1 LI 1 1. :h — — !-■-' ■"■■■F I ! i- rrm r : ■ ■— "" -! .-■:^ m • • s ?i3g33»a:s i 1 'it"*" :.J — . '-i :^ — £2 oo-*oooooo — — — __ _ — - — - — -_-. — . — ^- _ _ — -rrr ^ — — ' — ; — — — — — . — 1^ •* n ■ ^ '1:1 ifi ' S 1 g p :_] rfri << toocvjoointno - i . ^ - i:i - ^ , ■'K) .- i 1 51 1 ? C\J .^0(DC0^J OJOi 4,- - , ~s > • ■■i - M i^ Jl ■ ^ ■ ; •] ■■■^T \ \, ■■ i\y ^ 1 . ,^ s J I ■- — - ^ ofxaOO^ r- \ \ ^ % _ ^ \ ' i, c Ss s b : : ;, § VJ,^ i^ \ r.' ,■ > ^ ^ ^ \ '\i -^ SO s -^ H '"i^ • — r V -'- h § s^ 'N s ■ h i^ 1- T-^ ^ ^'^ / s r A <;^ > '_'- N ?^ ^■^ \ / i J ^ \ ^ < > 1 : ^^~ J s vS ^^ f-l \ v>;;. ^c; \ V'l > -^ " \, s s ' \ vl f 1 r ^ i \ ^ V ,v ^ :- \ <^i !h ' - \ ^ N ;■ : ■ f Sr h \ »1 . , if — 1. " \ /\\ L) \ 1 Si ^- r-.. (-■ ■:..'- ■ ..ft -- — 1 Hj = J: -.-; \ K — \ ( ■ ( )\ 1 *J ■v - — 5^ |5 r> u- ■< ^ 5^ \ ^ - c ^ ri ^i ' «? ' ■"■ J ' J - 27S> c/ a~ x^ Ui ^ T ~i U "1 7C If. 77 V ^ i ■•:- t' Ui'>. y , :? V -•- 1 1 NACA ARR No. L4I18 Fig. 12 "^ / n ■ / C J ' -^ s- Ss: ^ J ^ ^ i^ j> ■. - 1 fj^ ( ri ^ ^ ^ i ^ / U "~ : : >" ■ y f A y :.-r- ];- ^ y ' .-'■- A M / ■ ''-'' >. ■^ ■ ■ /^ / V ) 1 K/ ' t / j:; .(. J A ■ , . . . '/ t ^^ r 5? / / / ; f b "" * y / — — ^ ^ . - ■ V • J f x > ■ V /^ ^ / / - / / ''-' '{" . . " V-' Q^' ! ■ 'I /^ / V 1 / - ■ ;'' ■ : ?^ 9„ \n — t -* /, / 1 / - _T y^ ^^ 4 t / o A Nil nnti II invi nov Vi, . ^ CO Ml to. fQR AEI ym m ; V L / /?; ' ) 'H T;"' r- ^ — __ — — ^ — . — rl __ _ T — _ _^ -i — — — — — — — — — — -> n — — — h-^ — r^ iL = ~ dk X — — • — — __ — — — — ^'^ I, U l( ) \ ■ \ ' s \—\ \ S3 1 2 :;i. ■ ^ \ tj > ji o . \ N \ s. ;:- N r' 'f u .. 3 o V \ s " V N - : J ' ■^ n^ ?' n^ '? r 'H °r, f nf ^\ ~p ?^ i- m\ y^ on n\ ■?/ fOi \n ?/; ^ f)} -; ni iif /■ :o. ■°-1 M nf n)t c rk / / ■/;'- // "7/ 1 ,5 Of 7/", 7f r i' Y7f \u // 5 ;;t ff irn- ■f, ^'7, 9 t '/> If '^51 A ^' >-l = ( \ '6 0^- K '": ^ _ r. ,; \'!\ « r. Ar, 3 0< V, _,/■ ^,1 r, ^6 .c n I' 6( p* '' A J w/^ . . ^-7 'l 1/ V NACA ARR No. L4I18 Fig. 13 — ^ ? 1 1 r\ ^ O ;._i ^ _, I) ' // 3 ; s * 1 r :- ^ i \ -1= <) C r .L 1 __ -i :r- Z. — ' ^ P r7 ' — -^ __ =s= f- _ - - -- - -^^ J ^^ s — — ^ -_ . — — ' -~" — : : .^ .4 ■'T : $ ■) i / fl-^ 'i\il ( ? 1 f. i ( '-> / \ i ' - :':!! n in f^t rr 7f 'O A t t •\ T (. ) ■'C " t --- ~K n r\ - ^^ i vj k ^4 i/\ 1 ^ 4 r\ N \ ^-~. i r^ . 1 4 u N ^ =- - ^-| <: K.*. < -. . "^ ^~~ ■v k -~~, ~^ ~ - ' ■ -^ -- ^^ i\ 1 "'.|. S f: /~\ ^ ■^ ■^ -^ ? o u -*- ^ ■^ - ^ ."if. ■ ^ ~" P ^ X s. -^ N .4 ^ ^ ' \ s >-- - •v \ ^ ^ K' \ \ - ' T- - ., :■ ^ ^ ^' —- — -- — — - "" tV -i; / 1 i^ #»< . ^_ r= - — ^'--1 b c 5 ■^ ^ ~ " '^ [ - ^ ■ NA noN HI lOVf riRY -e^ \ CO IMI^ TEE FOR AEIi )NAI ■TICS k 5 ' — :i .-- ^^ ^sS 1 '■' 4s Of r,\ (. ^1 ^^ 'f> V r/ f :■,::. j'- 1 -:j A- 'f, n (7i f 11 -"t S- sl :§ . ._„ —^ ,, — . — " ■ — ^ — ■n ^ — — — — - — ft r~ ,■ :? — ^ y -- r- — =1^ :;^ J 7' — — — — ?7 — — — — — — — /^ ') ;? (^ ■ l-P ' 1 91 ;, .^ A — # ^5 P ; 1^::: - ■ / ^= . , S ?1 ■ - / \ b^ ■^ > I'l . ^/^ -> ^ t' t .i^ / T --} \^ 5^ -^ ^ . --- -^ k _-j . —- i; , ' N : ^ ^t^ ;=• -— — — ^ -J . - - - ■ /■ 1 r r« f^- =r — ~l C ^ .(■ ?, .''> f ,r; ^ ■^ =? ./< 7 7^ n} \rr >/, ,^ 'i-< :/? 'n Q ■/7 ?(7 (?/ ?/ (^ :^^ \^ 9^ :/(< '/?■ / V/' OL /?* n. <7, 1-. ) . ^ '^ c. // \ r- -■ / ' ■" '^ as. V7i 1\ 1/1 -_ 7^ ^n n( |7 1 1/ ')(* \ft 'ffl ih -y^ /Q H- — - ^n \>n 7 ^ >y/ r, =(r >r. ■cV «< r A 2 IT "i ^' 1 / _ J NACA ARR No. L4I18 Fig. 15 -- ii —L 1 jL _L I _i _L _J. "t __L =L J. =L J. i -i =£ -t iL -4~ 4::x:i A 5—1: =i =L J -L-i-- — — — — Caae Airfoil section bf (fraction b) Of (percent o) «f (deg) X Referenoe 1 2 3 5 6 Clark X ^ 0.5 .7 1.0 .5 .7 >- 1.0 ■ 15 J 60 6 /0.2 .2 .6 I .6 f ' — — -- — 7 8 9 10 11 HACA 22 eerlee 0.82 1 20 C 10 20 ■ 40 60 6 1.0 18 l 75 J '- 12 13 14 15 16 17 18 NACA 23009 k 20 75 6 1.0 19 NACA 43009 NAOA 63009 NAOA 23012 NACA 43012 HACA 23015 NACA 23021 . 1.0 J a3.9 820 «21 NACA 23012 0.60 20 60 6 0.33 12 — — ._ ^ *Wliig-fu8elage combination: fuselage, circular; eweepbaci angle, 4,75°; high wing, mldwlng, and low wing, respectively, represented. — — — 1 1 1 1 1 1 '1 1 1 1 "1 1 — / y\ c ) h 5- - — — 1 1(0 -■■ s'^ ( ■s h: V /( KJ c ) C )^ V \ (1 ^' r ^ -' Is ) y 1 ■ 1 ' - r /•\ -- c A ^0/f vr)i '/Tt:?'^'^ 7 /(3l /^ ) /'\ 5 '" 1 ( U 1 K '-.t 0^ 1 ,c ) 1 "'l' ^rn ^ ( 1 <. J _.i.. \ V ^_ ^ i ' _ 1 — 1 i-H — — — ^ 9- \J_ ^ i ^ 1 / i 1/ ? /^ ^i-; ) _ — 2- i ._. rTr? >"<^ 1 "*"' ; 1 NATION \»ltTEE FOR Km AER ■fm — - — - 1 - 1 - [- ! 1 1 CO 4 JNAJITIC- n^j rA / T A \>nhr 7K\irj ' \n /-l^/O/ at //r y ^ 7f = 30f 7iifJ<; '(3, % I 1 ! '7/'5-._j 1 lu/A^i 2,! /,^^/L 1 i 1 l- 1 I 1 i 1 1 "t"] NACA ARR No. L4I18 Fig. 16 « II II II 'I 'I 1' ^ ^ -; v.-^^^^ ^ ^ R !^ I "^ ^ UNIVERSITY OF FLORIDA 'IB2 08106 450 2 UNIVERSITY OF FLORIDA DOCUMENTS DEPARTMENT 120 MARSTON SCIENCE LIBRARY RO. BOX 117011 GAINESVILLE. FL 32611-7011 USA X*