fhCAL^'jb ^ NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS WARTIME REPORT ORIGINALLY ISSUED Fe"bruBry 19^5 as Advance Confidential Eeport L5B01 liETERMrKATIOlT OF THE EFFECT OF HOEIZOHTAL-TAIL FLEXIBILITy on LOHGITUDIKAL COHTROL CHARACTERISTICS By S. M. Harmon Langley Memorial Aeronautical Laboratory Langley Field, Ta. 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 - 45 DOCUMENTS DEPARTMEN r Digitized by tine Internet Arcliive in 2011 witli funding from University of Florida, George A. Smathers Libraries with support from LYRASIS and the Sloan Foundation http://www.archive.org/details/determinationofeOOIang "7 1 a nif S3 NACA ACR No. L5B01 NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS ADVANCE CONFIDENTIAL REPORT DETERMINATION OF THE EFFECT OF HORIZONTAL-TAIL FLEXIBILITY ON LONGITUDINAL CONTROL CHARACTERISTICS By S. M. Harmon SUMMARY An Iteration method is given for determining the longitudinal control characteristics of a flexible horizontal tall. The method perialts factors such as the actual spanwise variation of elasticity and the aero- dynamic induction effects due to three-dimensional flow- to be accounted for to any degree of accuracy appropriate to a particular case. An analysis is included of the effects of horizontal- tail flexibility on the tall ef f ecti veness j the hinge- moment characteristics, and the control-force gradients in a dive ^'c^covery for two miOdern fighter airplanes. The effects of variations in speed, altitude, elevator stiffness, and center-of-gravity movements are considered. The results of these calculations for speeds below that at which critical compressibility effects 'Occur indicate for the tYiTo airplanes significant effects due to the tall flexibility. It appears that the location of the flexural axis of the stabilizer too far behind the aerodynamic center of the tail may cause excessive control forces in a dive recovery at high speeds. INTRODUCTION The design of tail structures for high-speed flight requires special consideration of the factors that CONFIDENTIAL NACA ACR No. L5B01 provide sufficient rigidity in torsion in order to ensure satisfactory control and maneuverability for the complete speed, range. Reference 1 presents an analytical treatment of the effect of horizontal- tail flexibility on longitudinal control characteristics. The analysis of reference 1 is based essentially on the assumption of a semirigid tail structure having a linear spanwise twist distribution and on tv/o-dimenslonal section force theory. The assuinptlon of a semirigid tail, however, does not provide for the establishment of the required equilibrium between the aerodynamic and elastic forces at every section; consequently there is, in general, no assurance of the extent to v/hlch the arbitrarily chosen twist distribution represents the distortion of the actual flexible tail. In addition, the lov/ aspect ratios commonly employed on tails produce sigriiflcant induced effects on the aerodynainic forces. It appears, therefore, that more reliable predictions of the control characteristics of a flexible tail could be obtained by taking account of the actual spanwise variation of elasticity and of the aerodynamic induction effects. The presenb paper presents a method for determiinlng the control characteristics of a flexible tall that takes account o^ factors, such as the actual spanwise variation of elasticity and the aerodynainic induced effects, to a degree of accuracy appropriate to any particular case. The method is based on an iteration procedure in which the effect of the tail flexibility is obtained by means of a series formed by the addition of the incremental effects resulting from each iteration. The rapidity of the convergence of thJ. s series depends on the degree of rigidity of the tall, and the increments for the higher-order iterations can usually be estimated from a knowledge of the values obtained from the preceding iterations . In order to Illustrate the iteration procedure and to indicate the magnitude of the effects of tail flexibility in some typical cases, the present investi- gation includes an analysis for tv/o modern fighter air- planes of the effect of horizontal-tail flexibility on the tall effectiveness, on the hinge-moment charac- teristics, and on the control-force gradients required in recovery from a dive. The results of these compu- tations are given for sea level and for an altitude of 50,000 feet for a speed range corresponding to Mach numbers ranging from to 0,72. CONFIDENTIAL NACA ACR No. L5B01 CONFIDENTIAL 5 SyTvlBOLS M pitching-moment contribution of tall about center of gravity of airplane, positive when airplane noses up, foot-pounds; Mach number when used to account for compressibility effects l^ tall length, measured from center of gravity of airplane to elastic axis of tall, feet e distance from aerodynamic center to flexural center at a section for the tall, positive when aerodynamic center Is ahead of flexural center, feet p air density, slugs per cubic foot V true airspeed, miles per hour q dynamic pressure, pounds per square foot 1.1.67)2 |v2" T total torque of tall, positive when stabilizer leading edge tends to nose upward (the dT derivative — — represents the torque per dr) unit span at a tall section), foot-pounds c wing chord, feet b span (of wing, unless otherwise indicated), feet S area (of wing unless otherwise indicated), square feet Cg root-mean- square elevator chord, measured behind hinge line, feet c^ mean aerodynamic chord of wing, feet y coordinate indicating fixed position along span from center line r) coordinate indicating variable position along span from center line CONFIDENTIAL 1; CONFIDENTIAL NACA ACR '^o . L5B01 A aspect ratio A' fictitious aspect ratio employed, in corrections fcr corripressitility effects (a^'/i-M"^ ) E ratio of semiperiraeter of ellipse to span of airfoil surface, priined to indicate fictitious Dlan form employed in corrections for compressibility effects 't two-dimensional lift-curve slope for tail c^ section lift coefficient for tail; -orimed to ^ refer to section lift coefficient of a fictitious plan form employed in corrections for com^pressibility effects a^_ geometric angle of attack of the tail, measured ""R from zero-lift line at section for assumed rigid tail 9 angular deflection of stabilizer due to tail flexibility, positive when leading edge moves upward, degrees a^ geometric angle of attack of tail, measured from zero-lift line at section for flexible tail, degrees (a^ + e^ 5j^ elevator deflection at section for assumed rigid tail, positive when trailing edge moves downward, degrees ^ angular deflection of elevator section due to elevator flexibility, positive when trailing edge moves downward, degrees 5 elevator deflection at section in flexible tail, degrees (5j^ + - 9) A5pj change in 5pj per unit change in normal acceleration in recovery from_ dive, degrees per g CONFIDENTIAL NACA ACR No. L5B01 CONFIDENTIAL 5 Aa^ change In a^ per unit change in ncrrrial acceleration in recovery from dive, degrees per g Pj-i^ change in elevator control force per unit change in normal acceleration, pounds per g acceleration of gravity, 32.2 feet per second o rate of change of section angle of attack with elevator deflection for constant lift at section for assuj.ied rigid tail 1 rate of change of section hinge-moment coef- ^6cj^y ficient vvith section lift coefficient for Sr constant elevator deflection for assumed rigid tail rate of change of section hinge-moment coef- ficient with section elevator deflection of assumed rigid tail in degrees for constant section lift •7 1 rate of change of section pitching -moment sP^R/p coefficient with section elevator deflection ^t of assumed rigid tail in degrees for constant section lift C-^ airplane lift coefficient a three-dimensional slope of lift curve for airplane rate of change of elevator deflection with airplane lift coefficient for trim for assumed rigid tall, degrees CONFIDENTIAL CONFIDENTIAL NAOA ACR No. LpBOl d e/do^^ rate of change of dov/nwash angle at tall v;ith v/ing angle of attack, degrees per degree -~=::=t=r coitiTDre s sl bi 11 ty correction factor, where Vl - M,2 M = Mach n"xmher / E/i + 2 \ B comiDressiblllCY correction factor f 1 ■^E'A' + 2/ Kg elevator gearing ratio, as obtained v/ith no load on tail, radians per foot Vv' airplane gross v^eight, pounds H total hinge moment on elevator, positive when leading edge tends to move upward, foot- pounds / H \ C>, elevator hinge -moment coefficient ( ~z~3 — \ \^^e^-^"ey 6 5r dC m rate of change of Cj.-^ with 5|^ as obtained for given movement of elevator control stick 'h rate of change of C^ with a^ over tail ^R C,^ pitchlng-momient coefficient due to tail about center of gravity of airplane (Nl/qSc^A rate of change of Cr^ with fip, as obtained for given movement of elevator control stick rate of change of Cyv, with a*- over tail 'Hp^ - m tf^ -r — - — ] rate of change of d-^ for given movemient of '^tj^ / elevator control stick with a-^ over tail. with Crr, CO m )nstant 1 — ^r— — 7r-r-^ ) CON^TDENTTAL KACA ACR No. L5B01 CONFIDENTIAL 7 t(y) total torque transniitted by the stabilizer section at station y, foot-pounds h(y) total hinge moment transmitted by elevator section at station y, foot-pounds ' r'bt/2 dh ^ — dr, C'TRq('n) coefficient of torsional rigiditj^ for ' t (r, ) stabilizer at station r) , equal to de /dv, ' where dO/d-q is the slope of the 9 curve at stablon x], pound-feet^ per degree '^TRo^'n) coefficient of torsional rigidity for elevator at station ri, equal to -^4^--, where dGf/d-n dp/dr, is slope of 0' curve at station x\, pound-feet2 per degree d^ dH rate of change of section elevator twist with total hinge moment on a loaded half of elevator surface q.z measured in etatic tests, degrees per foot-pound Subscripts: t tail w wing e elevator s stabilizer R refers to assumed rigid tail 0,1, 2, etc. numerical subscripts used to indicate the order of twist iteration CONFIDENTIAL 8 CONPIDSNTIAL NACA ACR No. L5B01 PRESENTATION OF METHOD Develonnent of Formulas The pitching moment cue to the tail ahout the center of gravity of an airplane, considered positive in the nose-up condition, is given hy the equation M = {-l^q I C7^c^ din I + T (1) czt^t ^•'' 7 where is the tail "itching moment about the flexural axis of the tail, assumed to he positive vv'hen the leading edge tends to move upward. In conventional airolanes, the value of T usually increases the elevator effectiveness niim.erically by about 5 percent. If the lifting- line theory of reference 2 is followed, the lift coefficient c^,^ in equation (1) is given as a function of the sDanwise coordinate m tne lorm cz^(7) = a+ A at A 5^ _ 65 R/( r.bt/2 1 / t-bt./2 ac7. ^c-i- y - qt. (2) in which, for the flexible tall. z ^R = .iS R f - The integral expression in equation (2) represents the induced downwash angle. The determination of the lift distribution by means of the lifting- line theory for an arbitrary angle -of -attack and chord distribution has received much attention, and numerous mxethods (references 2, ^, and Lj.) are available for obtaining the solution of equation (2) when the functions a^ and 5 are given. The basic consideration in the determination of the SDanwise twist distributions for the stabilizer and CONFIDENTIAL KACA ACR No .5B01 CO^JFIDENTIAL elevator, 9(y) and ^ij) , for use in equation (2) is the establishment, at every section, of equilibriuin "between the aerodynamic and the elastic forces acting on the tail structure. In the present analysis, 9 and are determined on the basis ^of the theory of pure torsion of tubes (references 5 ^■^'^ ^) • Other considerations relating to the torsional effects of the axial stresses induced by the restraints to the free warping of the sections of the stabilizer and elevator and to the effects of the bending of the ribs can oe accounted for by employing the oroper paraineters and following the procedure of successive approximations or iterations described herein under "Iteration Method." The ae airfoil sec contributed aerodynamic di stributio which acts unsyrametric contributes On the basi symmetrical across a se rodynamic tvi'i sting moment for a sj^mmetrical tion results from the lift distribution by the angle of attack, v^hich acts at the center of the section, and the lift n contributed by the elevator deflection, at its center of oressure. If the section is al, the lift distribution due to camber a further increm_ent to the twisting moment, s of the foregoing assumptions, if a section is used, the applied twisting moment ction dn of the tail is iT(Ti) qc^- ar] (5) In order to obtain the torsional moment on the stabilizer, the moment acting about the elevator hinges should be deducted from the total twisting mom^ent on the tail, because the elevator hinge moment is normally transmitted The apolied stabilizer , to the fuselage through the torque tube twisting m.oment across a section dx] of the therefore, is given by dt(ri) = dT(ri dh(iV ik) vifhere dh(rj) Is the elevator hinge mom.ent at the section r\ of width dri and dh(T^) f'^^h \^. /5 c + c- n 'It '^\^^l. qcg^ dr] (5) r-r^,T\TT-|-r-nT;^TyTr|ij ^^-|-^ 10 CONFIDENTIAL NACA ACR No. L5B01 The expression for cj in equations (3) and (5) is given in equation (2). The total torque transmitted by a stabilizer section y is t(y) = ^±&r] (6) Division of equation (Ij-) by d-\-] and substitution of the value obtained for dt/di-j in equation (6) gives i Vdrj di] ; ' where — ^ (ri) and — {q) are given in equations (^) dri dr| and (5), respectively. Similarly, the total elevator hinge moraent transmitted by a section y is nbt/2 h(y) = / f~firi (8) yy If the boundary condition that the tvv'lst Is zero at the root is assumed, the angles of twist for the stabilizer and elevator can be expressed in the form e(y) - / ^dn (9) 0(J) = / l^dr, (10) (/O "^ The torslonal-rigldlty coefficients for the stabilizer and elevator, respectively, are defined as CONFIDENTIAL NACA ACR No. L5B01 CONFIDENTIAL 11 ■■s d8/dri ^TR ^^\ ~ — 'ZT'/ — 'e where t(ri) and h(-p, ) refer to the total torque transmitted by a section ri . Substitution for da/dr] and d0/d.r] in equations (Q) and (10) results in e(y) = / .r^-^^dn (ii) CO ^TRs^'Oi where t(ri) and h(ri), corresponding to t{j) and h(y), are given by equations (7) and (8), respectively. Equations (2), (7), (8), (11)^ and (12) express, v;/ithin the limitations of the theory involved, the equilibrium conditions at each section between the aero- dynamic and elastic torques. vi'hen the aerodynamic, geometric, and structural parameters expressed in these equations have been determined, the three unknown variables 9, 0, and c^ remain. The simultaneous integral equations resulting from the required equilibrium condition generally involve complicated functions for the three unknown variables. In practical cases, however, it has been found convenient to determine the characteristics of the flexible tall by v/orking with the integral equations through a procedure of successive approximations based on an iteration -orocedure. Iteration Method The first approximation to the tail configuration is taken as the one corresponding to an assumed rigid tail; that is, G and )2f are both zero, and the elevator deflection 5 and geometric angle of attack of the tail a^ CONFIDENTIAL 12 C0NPIDE7TIAL NkCA ACR No. L5B01 at each section are equal, respect! vel;/, to 5p and '^to = Corresponding values of c^.-^-pfy) are then determined frori equation (2). Substitution of these values of ^Itn^^^ d'^ ■ dh X "^ in equations (5) 8.^-<^ (5) gives — ^(•q) and — ^(r,), and d-q dri the functions tQ(7), ho(y), 6]_(y), and /liy) can be determined, respectively, from equations (7), {■:•), (H), and (12). The values thus determined for 9 ]_ and y^-^ can then be employed in turn to determine, successively, nev; increments in the cjj., 9, and j^ distributions. The series resulting from the addition of the successive Increments perrndt the determination of the control charac- teristics for the flexible tail. The general procedure for determining the elevator effectiveness of the flexible tall is as f cllowi : Ass^ome, as a first aoproximatlon, that the geometric angle of attack ^tij) is equal to zero and the elevacor deflection 5(y) is equal to 5p^ . Compute c^^ (y) from, equation (2). Obtain values for dT/dri and dh/dt-) at several spanwise stations from: equations (3) and (5)) resoectively, with 5(y) = 5p and ci^(y) = C7.^^(y). Integrate equations (7) and (8) to obtain, respectively, to(y) and ho(y). Substitute the values of tQ(7/) and hQ(y) corresoonding to tQ(i-)) and ho(ri) into equations (11) and (12), respectively, and obtain ^j^ij) and ^lij) as a first approximation to the twist distributions. For the second iteration (first twist iteration), assume that 6(y) = j2'i(y) - 9q(y) and that at(v) = 9](y) and com.pute the corresponding cj, t^ distribution from equation (2). The substitutions and integrations in equations (5), (5), (7), (8), (11)3 and (12) with 5 = j^q - 9 1 and c-;,^ = ^^+i ^-^ ^'^^ manner described for the previous iteration then provide the second twist incremients B^ij) and ^^(y). For the next iteration, ass.jm.e 5(y) = ^2^7) ~ 82(7) ^^^<^ '^t(y) - 82(y) ^^■'^ obtain, as described previously, the third twist increments, 93(y) and '^'7^{j) . This iteration procedure is continued until the Increments for cj^, 9, and ^ become negligible. CONFIDENTIAL NAG A ACR No. L5B01 CONFIDENTIAL 15 The foregoing procedure for obtaining the distri- butions ci-^, 6, and Is summarized in the follov;ing table, which gives the variables employed in each iteration: i'~~~~^--.___j3rder of tv/lst "~~~-~-~-J,^ r a 1 1 n 1 2 3 Variable ~~---^____^ e 61 02 83 ^1 ^2 ^3 ^t 91 ! 62 63 5 5r (01 - 6i) (0p_ - 02) (^3 - Bj)! ^H 1 itj In applications of be found that in many ca employed quite advantage second iterations, the e attack distribution can and linear distributions cj^ distribution may be of reference "J, v;hlch gi taper ratios including t employed on tails. In o cjt distribution can be given in reference 8. The the method of iteration, it will ses various approximations may be onslj . Thus, for the first and quivalent geometric angle-of- often be approximated by uniform , respectively, so that the obtained directly from the data ves results for a v/lde range of he low aspect ratios commonly ther cases, an approximation to the obtained rapidly by the m.ethod xj-i^ fact that the method of iteration is based on a procedure in which the twist obtained from each iteration Is used to Initiate the torque and the tv/lst of the succeeding iteration permilts, in many cases, a rapid estimation of the twist distributions for the higher- order Iterations. Thus, inasmuch as the twist for a given torque distribution is directly proportional to the magnitude of the torque, it follows that the propor tionality of the twists obtained at a section in iterations will depend on the similarity for the iterations of the distributions of torque. (See tions (11) and (12).) Because the shapes of the and hinge-moment distributions t(y) and h(y) (equations (7) and (8)) for a particular tail are usually not very sensitive to the spanwlse variations of 6 and 0, the shapes of the twist distributions tend to resemble the corresponding twist distributions CONFIDENTIAL succeeding two equa- torque 11^ CONFIDENTIAL NACA ACR No. L5B01 that initiated them. In these cases, therefore, the twist distributions for a higher-order Iteration n.ay he estiraated from a knowledge of the values obtained in the preceding iteration by taking the ratio of the twists for two consecutive Iterations at any suitable reference station. The twist 8 at any station for the iteration of order n is then given by h-ii-j) = (Qn- A2 'n-2 reference station A similar procedure may be follovved to estimate the increments in and cj, for the higher-order iterations . The foregoing iteration procedure leads to series of the form 6 = 00 + 6;^ + 02 + 9;. + . . . = ^Q + 0-^_ + 02 + ^3 + ' ' • From the formulas derived in the -oreceding section, the e quantities cz,^ , B]_, and the dynamic pressure q as 01 will be noted to a factor; cz,^„, 02, contain and 02_, The cit2' which are dependent on the corresponding values obtained in the preceding iteration, contain q2; and so on lift coefficient and twist at a section may each be represented, therefore, by a power series in q. The coefficients of these series, v/hlch depend on the various aerodynam.lc, geometric, and structural parameters, in general vary with speed because of modifications in the aerodynamic characteristics of the tail introduced principally through the effects of compressibility. By the application of these iteration procedures, the elevator contribution to the pitching moment about the airplane center of gravity is obtained from equation (1) as follov/s: CONFIDENTIAL JnTacA ACR IIo. L5B01 CONFIDENTIAL 15 F = ■^b^/2 y-bt/2 ^2 where tlie nu'merlcal subscriots refer to the order of the tii equations (7) tviflst Iteration and Tn = 2rtj-^(0) + Yi-^^{0)~\ . (See md ( S ) . ) E M = Mn + M quatlon ( IJ ) may he written iLz + (1^) The elevator reversal speed is obtained from the value of the dynamic pressure q that makes the right- hand side of equation (iL.) equal to zero. In a similar manner, the elevator hinge moment for the flexible tail may be obtained as H Ho + Ki + H2 + (15) where Hn = 2hn(0) An iteration procedure similar to that described for the elevator effectiveness may be followed to determine the effect of angle of attack of the tail and expressions for M and H similar in form, to equations (llj-) and (15) will be obtained. The tendency noted previously vi/'ith regard to the similarity in the respective distributions for 9, p', and cj. for the higher-order iterations will lectd in many cases to considerable simplification in the Iteration procedure for determining the effect of tail flexibility on the pitching mioment K and the hinge m.om.ent E. The increments in M and E for the higher- order iterations can tnerefore be obtained in these cases by mieans of the follom'ing relationships: 'n ^n-1^ lii (16) n-d E n Hn-1^ (1?) CONFIDENTIAL l6 CONFIDENTIAL NACA ACK No. L5B01 The forces and resulting twists on the tall structure are directly prooor tior.al to the tall angle of attaclc and the eleA/ator deflection corresponding to the values that would he obtained in an as3uir:ed rigid structure or to a-}-,^ and 5^^ respectively. (See table III.) The diff ei'entiatlon of ejuations (li^) and (15) v/ith respect to atn and 6-^ and convei'sion to the nondlmensional form gives, therefore, for the flexible tail the ijarameters Q^r' ^^tp 6'5r' ^'^t. "R Corrections for CoLipressitility Inasmuch as the aerodynamic charteristics of the tail are affected to an imnortant extent by compressi- bility, the effects of compressibility must be considered in predictions for the control characteristics of the tail. In the absence of experiraental data, the following corrections for compressibility, based on the theory of small perturbations, which is discussed in more detail in reference 9» are swiimarized for the paramieter-s involved in the present analysis. These correccions may be applied at speeds below that at which the critical comT)ressibility effects occur or up to a Mach number of approxim.ately O.bO in conventional airplanes. The span- load distribution in a compressible flow should be computed on the basis of a fictitious aspect ratio equal to the true aspect ratio, reduced by the factor vl - 11^, and the resulting values of cj, obtained for this red. uced f ictitious aspect ratio should be multiplied by l/vl - M^. Thus, if the primes denote values obtained for the fictitious airplane. At' -At\/l - m2 and ^^t' ■" 1l - m2 CONFIDENTIAL NACA ACR Fo. L5301 CONFIDENTIAL 1? The values for the narameters and as obtained from low-speed data should be multiplied by the factor l/^l - m2. The slope of the lift-coefficient curve in three- dimensional Incompressible flow is corrected for compressibility by multiplying it by the factor B = SAt + 2 E'At' + 2 in which the sy^ibols E and E' represent the potential- flow correction for chord effect in incompressible and compressible flow, respectively. This correction applies specifically to elliptical plan forms but is approximately correct for other plan forms. In incompressible flow, E Is the ratio of the semiperimeter of the ellipse to the span of the airfoil, as indicated in reference 10. In compressible flow, the ratio E' is that for the fictitious elliptical tail of span b-t and aspect ratio At ' • The derivative de/da,/ for compressible flo?/ is com.puted on the basis of a fictitious tail length equal /■I ^ to the true tail length increased by the factor l/yl - M'^^, and the fictitious aspect ratios for the wing and tail equal to the true aspect ratios reduced by the factor h - m2. APPLICATION OP METHOD Data for Calculations Calculations were made by the foregoing procedure of iterations for the effect of tail flexibility on the longitudinal control characteristics for two modern fighter airplanes designated airplanes A and B in order to illustrate the method and to obtain quantitative results for some typical cases. The comoutations v;ere made, for both airplanes, of the tail effectiveness, the hinge-moment characteristics, and the control-force gradients required in recovery from dives at sea level and at an altitude of 50,000 feet. CONFIDENTIAL l3 CONFIDENTIAL TTACa aCR No. L5B01 Figures 1 and 2 show the plan foriTis and dimensions of the horizontal tails for airclanes A and B, respectively. These figures also give the location of the flexural axis as determined from stabilizer torsional- rlgidltj?- tests ir.ade In connecclon virith the present investigation. The tor sional-rigldity tests for air- plane A were made by the Langley Flight Research Division and for airplane 3 "by the Langley Aircraft Loads Division. Both the stabilizer and the elevator for airplane .4. are metal covered, v.'hereas airplane B has a metal-covered stabilizer and a fabric- covered elevator. The aerodyneimic paramieters for the two airplanes were based on low-speed data corrected for compressibility effects, essentially as described orevlously. The basic data employed in the calciilatioiiSj the source from which these data were obtained, and the compressibility corrections applied are given in tables I and II, Average values along the scan were as sunned for the par-ta'.eters K' \ which vvere obtained on the ^H ^ "-^5 R basis of estimates for cCyyt Ot> and 6C>y6a-^ from lo'vV-speed flight data. In the computations, the aero- dynamic centers of the tail sections were assui^ied to be at the quarter-chord ooints of the sections. The tall-stiffness data for the calculations were obtained from flexibility tests made on the stabilizer and elevator of the full-size airplanes. In order to clarify the relationship of the f iexlbillty-test results to actual flight conditions, the procedure for the determilnatlon of the stiffness data is described herein in som.e detail. The stabilizer tests were m.ade by applying a concentrated torslons.1 couple at a section near one tip of the stabilizer and measuring the torsional deflections at several stations along the span vi'ith reference to a station on the unloaded half of the stabilizer. The elevator- flexibility tests were made by loading bags containing lead shot or sand on one-half of the elevator along a line one -third of tne chord behind the Mnge viflth the elevator locked in position. The spanwlse loading on the elevator surface corresponded approximately to a uniform distribution. The deflections of the elevator on the loaded side were m.easured at CONFIDENTIAL IIACA ACR No= L53C1 CON_^IDENTIAL 19 several stations with respect to a reference station taken on the unloaded half of the elevator. Tests v»ere also performed on one rib of the elevator of airplane B at a station about k . 5 feet from the fuselage center line to obtain the effect on the distortion along the chord of a chordwise loading that simulated a triangular distribution more closely than the one Just described (load concentrated at one- third of chord behind hinge). In these tests, measurements vvere taken of, the deflections at very small intervals along the chord (5 dial gages for an 11-inch chord). The results indicated that with both types of loading the distortions along the chord were equal and that the deflections along the chord followed a straight line. It was assumed, therefore, that the measured angular deflection due to the elevator flexibility could be considered as an equivalent change in elsvator deflection with no change in the camber of the elevator surface. The tail-stiffness data for airplane A are shown in figure 3. The results for the stabilizer given in this figure are based on a concentrated torque of 833 foot- pounds applied to the right half of the stabilizer at a station 6. 50 feet from, the fuselage center line, and the data for the elevator are based on a total hinge moment of S5.3 foot-oounds distributed on the right half of the elevator in the manner described previously. The tail-stiffness data for airplane 3 are shown in figure I4.. The results for the stabilizer given in this figure are based on a concentrated, torque of 'jOO foot- pounds applied to the left half of the stabilizer at a station 5-92 feet from the fuselage center line, and the elevator data in figure Ij. are based on a total hinge moment of 60 foot-pounds distributed on the right half of the elevator in the manner described previously. Procedure for Calculations With the aid of the foregoing data, the soanwise distributions for ^l-t) 9> 3-^d were determined for several iterations. The ci. distributions were obtained by the usual m.ethods based on lifting-line theory. In the computations, the stabilizers for the two aii'planes were ass'umed to act in torsion similarly to tubes so that CONFIDENTIAL 20 CONFIDENTIAL NACA ACR No. L5B01 the distributions of stabilizer twist resulting from the aerodynamic forces were calculated by means of equations (7) and. (11) by use of the stabilizer torsional- rigidity coefficients shown in figures 5 ^-J^d. [{.. Because the results of the elevator-flexibility tests for both airplanes indicated the probability that the static loads on the elevator did not act in pure torsion (see figs. 5 and k for d'^/dli near root and tip sections), it was believed nractical in the present investigation to modify the method described previously for determining 0. The tvvist distributions due to elevator flexibility were obtained, therefore, by multiplying the total hinge moment acting on each half of the elevator by the rigidity factors — (y) shown in figures 5 and i;. This method dH for determining the elevator tv^/ist is strictly correct only if the loading on the elevator surface in the static tests simulated the loading in flight. For the present investigation, hov/ever, the error from this source is not expected to be important. Some computations with different assiomed elevator flexibilities, which are discussed in the section entitled "Results and Discussion", Indicate that the calculated results are not sensitive to reasonable variations in the elevator flexibility. The increments for cj, , 9, and that were obtained in the various iterations were used to compute the pitching moment about the airplane center of gravity M by means of equations (13) and (lli) and to compute the elevator hinge moment H by means of the corresponding equation (15)- The results for M and H were then converted into the nondimensicnal form as the derivatives 60^/6 at^, oCm/^Sp^, dC]2/6atn, and 6Ch/d5f^. The details of the computations for determining dC-^/bd-^ and dCh/66R for airplane B for a Mach number of 0.60 at sea level are shown in table III. The change in control force per unit change in norm„al acceleration in recovery from a dive vifas computed by means of the following formula: 6Cv, ^C ,^ 2, ^n = It^-^Sr + 7— ^at^)Kgqce% (l8) ^R .65^ ^ da^ CONFIDENTIAL NACA ACR No . L5B01 CONFIDENTIAL Zl where Aor and Aa-^^p refer to the changes in 5r and at-, per unit change in normal acceleration in terms of g and where Ke is the elevator gearing ratio. In equation (l8) A5r W 6C. m 6 5r 1 - d€ da^ ^bO,, 6C,,,,^ V^^tR O^tr + 28,6i^pg( d.5 R ,^^t R, r G™ (19) and A at-, R (20) In equation (19) the tv^o terms on the right-hand side enclosed in the brackets represent the part of A5r required to trim the airolane, and the third term represents the part of A5r required to balance the effects of rotation of the tail during the steadjr ohase of the iDltching motion. In these equations, 6C]^d5R, •'^6r N 6Ch/'^6atj^, 6Cm/6 5R, c^CmA^atR, and are tne 'm values for the flexible tail obtained by the iteration procedure. If values for these paraineters for the assurned rigid tall are used in equations (l8), (19) > and (20), the control-force gradient for the rigid tail ti ve is obtained. The values for the deriva- for airplanes A and B vifere based en flight results at an indicated airsoeed of aoproxi- /c]5r\ mately 200 miles oer-hour. A value of ( tttt- 1 equal dC ^k CONFIDENTIAL 22 CONFIDENTIAL NACA ACR No. L^BOl to -5.20 was obtained for airolane A based on a center- of-gravity location of 23 percent of the mean aerodynamic chord" whereas a value of -5.26 was obtained for air- plane B based on a center-of -gravltjr location of 29.5 percent of the mean aerodynamic chord. The effect on Fn and F^p of movements of the airplane center of gravity was Investigated by assum.ing different values for de The variation of with soeed as determ.ined by da^v means of the theoretical compressibility corrections noted previously, in conjunction with the design charts of reference 11, indicated a negligible change in this parameter up to a Mach number of 0.60. It was therefore considered sufficiently accurate in the present compu- tations to assume constant values for de/day^f. The /dop^\ values for -\ , however, were corrected for com-oressi- billty effects by multiplying the low-speed value by the factor 1/B corresponding to an average between the wing and tall. RESULTS AND DISCUSSION The results of the calculations are presented in table III and in figures 5 to 9 • Table III shov/s the results obtained for the various iterations in determining dCni/65R and oCh/c^Sp for airplane B at a Mach number of O.6O at sea level. Figure 5 shows the spanwise variation of tail angle of attack at and elevator deflection 5 resulting from an application of the elevator control equivalent to unit deflection for the assumed rigid tall, as obtained from table III. Figures 6 to 9 show tiie effects of horizontal-tail flexibility on the longitudinal control characteristics for airplanes A and B for a range of true airspeeds from to 550 miles v>er hour at sea level and from to I|.90 miles per hour at an altitude of JO.'OOO feet. This range of true airs-oeed corresponds to a Mach number range from to O.72. The speed for each altitude corresponding to a Mach num.ber of O.6O, which represents CONFIDENTIAL NASA ACR INC. L5B01 CONI^IDENTIAL 25 the limit for which the theoretical compressibility corrections employed in the present computations are believed to be reliable, is indicated on figures 6 to 9* The results for the Mach numbers higher than O.60 are included in the figures in order to give an indication of the trend of the flexibility effects. The results of the comput,ations for a Mach number of O.6O at sea level are summarized for both airplanes in table IV. Table III indicates that the convergence of the iteration procedure is very rapid. This convergence, as indicated for dCi-ii/6 5T^ and 6Civ''d6j^ for airplane B,, is typical for the other parameters in the flexible tail for both airplanes Thus, if the contribution obtained for each successive iteration is expressed as. a ratio of that obtained for the zeroth-order twist iteration. ^Cm/c5.R 6Chf./6 6R = 1 - 0.501 +0.0727 - 0.0167 +Oo0038Ii. = 0.759 1 - 0.2^1 +0.0557 - 0.0151 +0.00506 = 0.805 >{2.1) The subsequent comparison lllust twist iterations required by the regu iteration in order to determine the 1 characteristics for a flexible tail, from table III as given by equations three regular twist iterations, will results obtained by the use of one an iterations, respectively, in conjunct relationships given by equations ( 16 ) estimating ¥.^ and Hv^ for the t'vvis higher order than one and two, re spec use of one regular twist iteration. rates the number of lar procedure of ongitudinal control The results obtained (21), which utilized be compared with d two regular twiat ion with the and (17) for t iterations of tively. Thus, by 6 Cj^/6 5|^ 6Ch/6 5R 6ChRA^6R = 1 - 0.501 + 0.0905 - 0.0272 + 0.0081s = 0.771 = 1 - 0.2)4.1 + 0.0581 - o.oiiiO +0.00558 = 0.306 > (22) CONFIDENTIAL 2li CONFIDENTIAI NACA ACR No. L5B01 By use of tv^^o regular twist iterations. = 1 - 0.301 + 0.0727 - 0.0176 + o.ooi;25 = 0.759 dC^_ .fi 5k ^Cr^fit^ = 1-0.21^1+0.0557-0.0129 + 0.00300 = 0.805 ^ (25) The comparison of the results shown in equations (22) v;ith those given ty equations (21) indicates that the use of one regular twist iteration in conjunction "vvlth the simple relationships given hy equations (16) and (17) is sufficient to deterraine the effect of tail flexibility to an accuracy of the order of oercent . Figures 6 and 7 show for airplanes A and B, respectively, the ratio of the tail effectiveness and hinge-moment paramieters as obtained in the actual fle:K.ible tail to those obtained for the assumed rigid tall. These figijires indicate, for the complete range of airspeeds for both airplanes, that the parameters 6C-i/6 5p, ^^a/^^t-a> dCh/^^ri, 3.nd ^C-'cJ^o.^-r> are reduced nuinerically because of the tail flexibility and tnat the Daram.eters — ] are increased numerically because of this and 6 Crn /i 5r factor. The numerical reduction in dCy^Jd^-^ caused by tail flexibility is due to the fact that the center of pressure of the lift resulting from the elevator deflection is behind the flexural axis (see figs. 1 and 2 for f lexural-axis locations) and the resulting torsional mom^ent twists the stabilizer in a manner that reduces the tail lift. The numerical reduction in dC^Jbbx^ is also due to the negative value of dCh/^5p^> vjhich causes the elevator to twist and thus to reduce the elevator deflection. CONFIDENTIAL NACA ACR 1^0. L5B01 CONFIDENTIAL 25 The numerical reduction in ^Cm/'^Q-tD due to tail flexibility resulted because the location of the flexural axis of the stabilizer is ahead of the aerodynamic center and because the value of ^Ch/<^citp is negative. The respective numerical reduction in the values for 6Ch/d5H and cCh/'^'citij due to the tail flexibility resulted principally from the fact that each of these parameters for the rigid tail is negative and the elevator twist therefore numerically reduces the hinge moment in each case. The forward position of the stabilizer flexural axis relative to the center of pressure of the lift contributed by the elevator tended, however, to increase numerically the value of 6Ch/65f^ due to the stabilizer twist (5 is increased by -9); similarly, the location of the flexural axis of the stabilizer ahead of its aerodynamic center tended to increase numerically the value for dCh/'i'O.tp^ • Figures 6 and 7 indicate that, in general, the effects of tail flexibility vary vvith speed and altitude approximately as the dynamic pressure - modified, of course, by the relative compressibility effects. This variation with speed and altitude results from the raoid convergence of the nower series in q, which causes the terms in q of higher order than unity to be compara- tively small. In some cases, however, at very high speeds (see figs. 7(b) and 8, for — and F^/Fno respectively), the effects of the terms in q of higher power than unity become comparatively significant. Computations were made to estimate the effect on the parameters shown in figures 6 and 7 of increasing the elevator stiffness at each section by 12.5 percent of the average elevator stiffness. The results of these computations indicated that, for a Mach number of 0.60 at sea level, the ratios of the parameters ^Cm/^Sp, 6Cii/65R, and dCh/6atp to the corresponding ratios for the assumed rigid tail would be increased in the order of 2.5 percent as compared with those shown in figures 6 and 7 J and the corresponding ratio for ^Cra/i^CLto v/ould be Increased by less than 1 percent; whereas, at 30,000 feet for the sam.e Mach number, the effect of the CONFIDENTIAL 26 C0:MPIDSNTIAL NACA AGR No. L5E01 Increased elevator stiffness would be about O.lj.0 of the corresponding foregoing effects indicated at sea level. It call be noted from figures 6 and 7 that, provided critical compressibility effects do. not appear, elevator revei'sal for both airplanes A and 3 does not occur up to a speed corresponding to a Kach nuraber of O.72, Figures 8 and 9 present a coi;-:parison of the control- force gradients in recovery from dives as obtained for the actual flexible tail and as3u;med rigid tail. It should be noted in these figures that the required motions of the elevator control stick per unit g are not necessarily equal for the flexible and assiimed rigid tails, Figiire 8 gives the results for airplane A at sea level and at an altitude of yO,QOO foet. This figure shovvs the variation with airspeed of P^ and the ratio Pj-^/pj^ for values of (- — --] in incompressible ^R (^ \^%) n R flow of -3.2 and -I.60. These values of -5.2 and -1,60 correspond, respectively, to conter-of-gravity locations at 28 percent and approximately 51 percent cf the mean aerodynamic chord. Figure 8 sho\-/s that flo::ibility of the tail increases the control-force e;radient and that this increase for a Mach number of 0.60 amounts to 12 percent at sea level and 5 '5 percent at 50,000 feet altitude. This figure also shov/s that a rearward movement of the center of gravity of approximately 5 percent of the mean aerodynamic chord causes a small reduction in the ratio F /F . The results for the airplane B at /d6\ sea level and at altitude for values of | -7™ I iri Incompressible flow of -5.26 and -6,00 are presented in figure 9« These values of -5*26 and -6.00 correspond, respectively, to center-of-gravity locatioris at 29.5 percent and approximately 25 percent of the mean aerodynamic chord. The figure shov;s, for airplane B for a range of airspeeds at the altitudes considered, a small increase in the control-force gradient due to tail flexibility?-, or approximately one -half of that indicated in figure 8 for airplane A. Figure 9 also shows that a forward movement of the center of gravity of approximately ij..5 percent of the mean aerodynamic chord causes a small increase in the ratio PnAnR- COKPIDSNTIAL NACA ACR No. L5B01 CONFIDENTIAL ZJ An examination of equations (l8), ( 19 ) > s^nd (20) indicates that the control-force gradient in a dive recovery may be Influenced to an important extent by the aerodynamic parameters ^ r^ , oGj^/oatD, and oCrti/oato. dCn-^oSR " " The results of the present analysis show for both air- planes A and B that the first two of these parameters are affected by tail flexibility in a manner to increase P^; whereas c)Cm/^citR is affected by this factor in a manner to reduce Pn- As noted previously, the numerical reduction in 6Cin/^citR obtained in the present computations for airplanes A and Bis caused principally by the location of the flexural axis of the stabilizer ahead of its aerodynamic center and by the negative value of dCh/da-tp,. In order to obtain an indication of the Importance of the change in '^ Cm/'^ CLtp due to tail flexibility for the control-force gradient in a dive recovery, computations were made for the two airplanes in oCyn o Cjnp which it was assumed that = —, vi?hich is roughly equivalent in the present case to a rearward movement of the flexural axis back to the aerodynamic center. These computations indicated, for a Mach number of O.6O at sea level, that in the case of airplane A the ratio Pn/^no would be Increased from 1.12 to 1.26, and in the case of airplane B this ratio would be increased from 1.0,5 to 1.075' 0^ the basis of the present analysis it appears, therefore, that the location of the flexural axis of the stabilizer too far behind the aerodynam.lc center of the tail, could cause excessive control forces in a dive recovery at high speeds. CONCLUSIONS An iteration method for determ.lnlng the effect of tall flexibility on the longitudinal control charac- teristics of airplanes was applied to two modern fighter airplanes and was found to provide a practical procedure for the determination of these effects. CONPIDENTIAL as CONFIDENTIAL ITACA ACR No. L5301 The results of calculations to deter'Tiine the effect of ';ail flexibility on the lon^itucjlnal control charac- teristics for two fighter airplanes Indicate that the longitudinal control characteristics are affected to a significant extent at high speeds cy this factor. The following conclusions apply to at speeds below that at which critlcaj. compressibility effects occur; ■J 1. The magnitude of the tall-f lexiDility effects, in general, varied approximately as the dynamic pressure - modified, of course, by the relative compressibility effects. In some cases at very high speeds, however, the effects of the terms containing the djmam.ic pressure of powers greater than unity becaiie cohiparatively significant. 2. Tail flexibility v;a.fi fcond to reduce significantly the rates of change of pitching moment and hinge moment with elevator deflection and tail angle of attack, 3. The control-force gradients in a dive recovery wei'e increased because of tail flexibility. •li.. Rearward movements of the airplane center of gravity tended to decrease the effects of the tail flexibility en the control-force gradient" whereas forv:ard moveinents of the airplane center of gravity tended to Increase the magnitude of these effects. 5. The location of the flexural axis of the stabilizer relative to the aerodynamic center of the tail is an l:;iportu.nt design consideration with regard to the. magnittide of the tall-f lexibilit^f effects. The location of the flexural axis of the stabilizer too far behind the aerodynamic center could cause excessive control forces in a dive recover^T at high speeds. Langley Memorial Aeronautical Laboratory Fational Advisory Comm.ittee for Aeronautics Langle^r Field, Va. CONFIDENTIAL NACA ACR No . L5B01 CONFIDENTIAL 29 REFERENCES 1. Collar, A. R,, and Grinstead, F.: The Effect of Structural Flexibility of Tallplane, Elevator, and Fuselage of Longitudinal Control and Stability. Rep. No. S. M. E. 522?, Britl sh R . A.E. , Sept. 19ii2, and Addendum, Rep. No. S. M. E. 3227a. Oct. 191+2. 2. Glauert, H.: The Elements of Aerofoil and Airscrev/ Theory. Cambridge Univ. Press, I926 . 5. Pearson, H. A.: Span Load Distribution for Tapered Vlflngs with Partial-Span Flaps. NACA Rep. Wo. 585, 1937. ij-. Hildebrand, Francis B.: A Least-Squares Procedure for the Solution of the Lifting-Line Integral Equation. NACA TN No. 925, 19l|i;. 5. Trayer, George W., and March H. W.: The Torsion of Members Having Sections Common in Aircraft Construction. NACA Rep. No. ^3k, 1950. 6. Timoshenko, S.: Theory of Elasticity. First ed. McGraw-Hill Book Co., Inc., I93I1-. 7. Anderson, Raymond P.: Determination of the Charac- teristics of Tapered Wings. NACA Rep. No. 572, 1936. 8. ■ Schrenk, 0.: A Simple Approximation Method for Obtaining the Spanwise Lift Distribution. NACA TM No. 9i+8, 19^0. 9. Goldstein, S., and Young, A. D.: The Linear Perturbation Theory of Compressible Flow, with Applications to Wind-Tunnel Interference. 6865, Ae. 2262, F.M. 601, British A. R.C., July 6, 19^3. 10. Jones, Robert T.: Correction of the Lifting-Line Theory for the Effect of the Chord. NACA TN No. 817, 19^1. 11. Silverstein, Abe, and Katzoff, S. : Design Charts for Predicting Downwash Angles and Wake Charac- teristics behind Plain and Flapped Wings. NACA Rep. No. 61+8, 1939. CONFIDENTIAL 50 CONFIDENTIAL NACA ACR No. L5301 12. Ames, Milton B. , Jr . ^ and Sears, Richard I.; Determination of Control-Surface Characteristics from NACA Plain-Flap and Tab Data. NACA Rep. No. 721, I9I+I. CONFIDENTIAL NACA ACR No. L5B01 CONFIDENTIAL 31 TABLE I n»TA FOR CALCnLATIONS - PHYSICAL AUD OEOMETRIC CHARACTERISTICS [pBt* rurnlabed by maDuTaotur^rJ Airplane Weight, W (lb) *lng area, 3 (eq ft) Wing aspect ratio Kean aero- dynamic chord of wing, c, (ft) Tall area, St (nq ft) Elevator span, b. (•q ft) Root mean chord or elevator, <^e (ft) Tall length, h (ft) "e (radlan/rt) A E 12,000 7,660 300 256 5-55 5.815 7.28 6.64 55 lH.l 16 15.2 1.19 l.Ol 21.1, 15.5 0.66 .57 TABLE II DATA FOR CALOULATIOHS - AERODyNAMIC PARAHBTERS Parameter Value In incompressible flow Source of data Correction for compressibility All-plane A (6V'*»r)c,^ •-0.0086 Reference 12 Multiply by —i—r Vl-1«2 "0 0.095 Assumed Do. (a=h/«»R),j^ -0.00686 Unpublished data baaed on dCh/iOtp = -0. 00218 and dCh/4BR ' -0.00804 to. (i>Ch/dcit)^ -0.0552 Nona (6at^/aSR) a-0.66 Reference 12 None dt/do. 0.50 Reference 11 Assumed constant 0.077 Reference 7 Multiply by B («r/-=l}b -3.2 Baaed on unpublished data for e.g. at 28 percent K.A.C. Multiply by l/B; average for wing and '11 Airplane B (*'=m/^^),j^ b-0.0091 Reference 12 ^1-m2 ^o 0.095 Assumed Do. (*Ch/'^6R),j^ -0.00605 Estimated from unpublished flight data bused on eCh/6citR = -0.000511 and 4Cji/M[j = -0.00655 to. (6Ch/^c,,)^^ -0.00825 None (^-t„/^»R)_^^^ b-0.59 Reference 12 None d./do. 0.50 Reference 11 Assuned constant a 0.077 Reference 7 Multiply by B (d8R/''=L)R -5.26 Estimated from unpublished flight data for e.g. at 29.5 percent H.A.C. Multiply by l/B; average for wing and tali ^Value given Is for a section at U.5 ft. sectlona . Average constant values were used. from fuselage center lino; appropriate values ^ere used for other CONFIDENTIAL NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS NACA ACR No. L5B01 32 < t — I Ed Q O 'Ot'D to ff "-L" ■pIcO »i„- :; r0.hfNM-\i-vj ry O CO 0_:Jr\/_d'f\] 1 rH .-\J OJ KS-d" J- I ^tO lTno cr\0 I T\0 rTirH r-I lTx ) •^ C~<0'-( J-Vj I OO O -H ,-l,-i 1 O O O OO O t 1-1 OnoJ lOcO CTv (~— f\] ro,.£> LPir<^ 8N~,^0 CTmH r-vj OO O ■-t'-i O O O O O I O OvD^O O I ) 1-1 O u~^f^J -H I rrvrriOi v-i i i .. I I P I KMTsi-y r-l iHCO I ONCruXl Oj iM in I r-*J3 i/>-J n-vrvj I mD _d- (N CfNC— '-O O f\l O rH K\vO .H O O O OO -H ■MJOMrsO J- o o o o OO HI c f •U- /l^ OJ [— tp>a"0 iM 1 "^O^OXDCO rr\ I -;±_d-u^r^O O I O OO O-H rH I _d-0 ir\0 0^0 1 ff\0 K\rH i-H in I vO (XO iH J3 rH OOO O O rH CT^O (\1 iJ>LnK\ OrHrH rH rHr^ O O O O O o ■? .• ■• .• .• .• r-^OM3 c— CO t~- C'JO-if ry-d-oj rH c\)(\j N^w3--J O I I t I 1 •-< t— iH O C~W3 COCTviHvO ixv-^ rHrH njr\J «^^r^ ^\^ ffilo _:J-fO,rr\KMN C\J O CM O iM -cN3 t\j ^ -^■mc^ry cr-co i ~ H rocoJ-ro, • H rH rH (\] OJ I O O O O O O I ^-d _jO LOO cr\0 I rOiO N^iiH ,H ir\ I •^ [XO rH IT^^ i OO O rHrHrH 1 O O O O O O 1 ^a]«f CD \'0 rH -HsO OJ IJ~irH -,d--D o i-y r— t\J O rH JvO r-(M iM iM rH I _ J^rH^t-J-CTx I O mo rH r^ ti~V I O O O^rH ^-ON I vOJi-iJ CT" C~-^ O ^^COOsOCO^O I CM O rH fOi-X) I-* I OO O OO rH I /k _H-rH O rHTH CO 3^0 rH t-O^ry O O O OOO O O O OOO cMr-mcTio cy ' u'MriCT'coco m t J--:* mc— o O I O O O O iH rH I tH r- ir-.-^ ^ c~- ■ £--cocQ I T: O O O O O I o o >HC3 E < 02: t/lO NACA ACR No. L5B01 33 « :3 1-3 CO Eh O o . 1 ^ < M »-H < Eh ti :^ '«. Cd ffi Q H tr. 2 g U5 o < ft. o ja « o H C o c -%J> o ■o o o 1 1 1 I<3 -H t~- c n (D a cf 1 ^ g 4J nj o II II o *• 3! VO t- n o =1o« =^o« ■4J i-i rH ^ 3 o o *} L J -H C o a c rH OQ .. *> •> 4-1 n 2 1 ■p ■(-> 0) o o vO o i iH 3 3 t^ Jd o Q n •u o* CO o- o ■p 3 c o a> CO d o O «-( rH ■o 1 1 ^ .H o «-i o IM > o o o d (» II II O (. »< (. o n « ■o « K 1 o O. ^ § II s II ^• o E a1o« § ^« o V '^ t bO & & + + 1 to 5 i s'^ » bT > ro S o > W O <5 <: i-PO O H eg < I — I E-i Cd Q O U NACA ACR No. L5B01 CONFIDENTIAL 3I^ TASLS IV-- COMPARISON OF EFFECT OF EORIZONTAL-TAIL FLEXIBILITY ON LONGITUDINAL CO':'TROL CHARACTERISTICS FOR AIRPLANES A MD B AT A MACE FJM3ER OF O.bO AT SEA LEVEL parameter ratio Airplane A Airplane 3 6Cny/6at^ 6CrriR/6atj^ Cmr 6ChR/65^ 6Ch/6at R 6Chj^/6at^^ 6Ch^5R_ 6Cm/^6R I^n p. n R 0.79 • 97 1.22 .91 .9k 1.15 1.12 0.76 .98 1.50 .80 .96 1.06 1.06 NATIONAL ADVISORY COMIv'ITTEE FOR ivERONAlJTICS CONFIDENTIAL NACA ACR No. L5B01 Figs. 1,2 Ci/^ I me. F/e-xura/ axis 3.6 Z NATIONM. ADVISORY COMMinEE FOR AERONAUTICS o Location of test points CONFIDENTIAL Figure /.'Tlan form of ta/l sem/span shouuing siah/lizer and elei/otor cf/mens/or^s. A irp /a n& A-, honzorrbol tail area, S3- stpuare feet-, e/eyaior area^ zz spoor e. fee6) bo/ance areo^ /j.s percenl of e/ei^o-tor arisa. CONFIDENTIAL Fuse /oga ^ l.42\ 6.60 ZJl NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS s' Locai/on of test points F/gure 2.~Phn form of tail sem/spar? shoiiiing stabilizer ana/ elevator d/ mens ions. Airplane. 3 j horizontal tail arsa^ 4/./ spaare feei^ elevator area, 13.0s' spuore feet; balance area J 0.2'^ spuare feet, confidential NACA ACR No. L5B01 Fig. of I Z 3 4 S 6 Distance from iai/ cenie.rline^ft F/^u re 3.- (Experimental data for flexi bi liic^ horizontal toil. Airplane A . Data from tests made, bu Lona/eij F/i^hi 7fe search Division. NACA ACR No. L5B01 Fig. 4 So CO NFIDI NTIAl ■ 016 .^ " — ^ 01? A J I ^ 00& ^ jy ^ Or- 004 H = 60 ft-l b Ho 1) .s .3 .2 .1 \ \ / \ C.,^ L ci/i oini of op //cat/an con ctn- 'aied torout V ^ "^ J / o1 ir ^ & ^ / of 500 ft-l b [\j / \ s / / 1 com ATIONAL ITTEE FO flDVISOf ! AERON Y lUTICS ^ ^ jy -^ -^ ( ;ONFI )ENTI AL ZO MO 16 12 3 4 O I 2 J 4 S , 6 1 Distance from iai/ center f/ne^ ft F/gure 4-.- <^x per/ mental data for flexihilitc^ of horizor7tal tail . Airplane B.Data from tests no ode. bt/ Lang/eiJ Aircraft Loads Di^/sian. NACA ACR No. L5B01 Fig. 5 10 ( ^.. CCNFIDl :ntia L ^ "■ 6-&^^0'e^ ^5 — — — j L^ -- ^ 6 -^ ^ .2 ac, .-e-. i -^ t ) ^ ( NATK OMMITTE INAL AD EfORA /ISORY ;ronaut CS _______ ^ CO NFIDE NTTAl i 'JZ -OS -.M o ^ O / Z 3 4 S 6 Dtsianc^ frann fa// ceyiier /rne. f/ F/gure Sr Disinbuiion of iail Gfn^/e of a/fack O'^o^ ekvahr cjef/eciion in a -flexible, ^ail resuffm^ fronn an apph- caiion of I he elevator co/rtrol ei^uivdfe/ni: to un/t defleci/o/1 for the osso/rneef r/giJ toif. Airplane^ Bj f\f^och numher,0.60cit sea fe.vef^6f^-l^-OCj-=Of^. NACA ACR No. L5B01 Fig. 6a 1.4 1.2 1.0 C0NFI1>ENTI \\. / ' / ^ r^ ^ _ — 'Tl - -h"' in .^ i -0 1 . 1- — ~~~\ \ CO -0 10 ^- ^ - — — : 1- -^ .5 A\iiiude ^ [> K. \ .6 --- 3aooo \ *] Indicoies limitlh^ speed for Luh/ch ca/cc/Iaied compress/ bddtf correc-^'ons pre he/ieved relial/e 4 .2 n CO >JFIDE NTIAI C( NATIO MMITTEE lAL ADV FOR AEI SORy ONAUTIC S IOC 600 200 300 400 SOO True airspeed^ mp/7 0) Effect/ \/eness parameiers. Figure. 6.-Effect of horizontal -tail flexibility Oh lon^itudi nal-control parameters. Airplane f\. NACA ACR No. L5B01 Fig. 6b =^1^ 1.4 13 KD /.o CO fflDE vITIAl y ^ k" rt -4 - /.o 3 -=^l — K^ ^^"■^ 15^ S^ O 10 ^" ^^ ^~: h - ,-- A latitude (ft) Sea let^eJ — - 3QO0O ^ s <-i Jndicaies limiiing speed ' -for ujhich co/cu/a{:e.d compress/biliiij correct ions are be/ie-veJ relialile: .4- 2 n CGI IFIDE] JTIAL COI NATION (MinEE IL ADVIi ■OR AERI DRY INAUTIC5 100 zoo 300 400 SOO Tra& airspee d ,m ph (b) Hinge- moment f:^ram&iers. Figure. 6.-Conc/uded . 600 NACA ACR No. L5B01 Fig. 7a -^ .^ 1.6 ^1.4- 1.2 1.0 CONI IDEN1 ■lAL / / J 1 ^ ■^ -^ _______ r^ rrT _- " V' ^ "0 < 1 1^ '^ — =i — \ J ■^ <7> *« ^'^ o 1.0 " — - - — - - — - _< 1--. .& MiiiuJe (ft) Sea level - — 30,000 ^ \ \ ^^ v^ ^ .6 \ f] Tndicaies limiiing jpeed for which calcu/aied conypressih/liit/ aorreciions are be lie\/ed reliab I& .4 .2 n CONF DENl lAL CO NATION IMITTEE U. ADV)" FOR AER ORY )NAUTICi 100 600 ZOO 300 WO SOO True airspeedj/T) p h ^) Effectiveness parameieKS. F/^ar3 7- Effect of honzontal-tail flexibility on longitudinal- control parameters. f\\rplone B. NACA ACR No. L5B01 Fig. 7b 1.0 CONFIDENTLU. ^ L — "^ « ^ -fi^ "0 1.0 .& /.o .& .6 .2 ---^ ^ - — - -' AliduJe (ft) Sea level 3Q000 i K \ ^ *1 IrxJicaies limding spe&J for uih/ch ca/culaiecJ compress lb iliiy corrections are. he/i&ved reliabla- c ONFII KNTI, iL CO* NATION IMinEE IL ADVI! OR AER ORY INAUTIC! o zoo 200 JOO 400 SOO True airspeedj/n p h (b) Hinge- moment parameters. Figure. 7 - Conc/ac/ed. 600 NACA ACR No. L5B01 Fig. 8a, b 1.41 I.3C I/O /JO ccInfiiIientIial I I I I Fn for f/e-Xi/ile. iai/ Fp^ for rigid tai/ 1 ZnJicoies ///n/iing spe&d for u-'hich co/cu/atea compressi hiliiy corrections are he/ieved reliakle- _j,2 Indicates \/afueyS -'■^ for (jSp/dCi) in incompressihle flow "Nmupr --3.2 -1.6 £oa •^ ? iTIA . ,— — ■/.6 O >/00 200 300 dOO SOO True a/r^peedj mp/} /a) At sea /ei/e/. /OO 200 300 400 SOO Frae airspee-d^m p/i (b) At a/iiiude of jqOOO fee t. F/gure S.-Fffect of /ionzonia/-iciil flexiiii/iiij on e/evator Contro/- force qrad/ents /n recoveri/ from dives. Airp/ane- A. NACA ACR No. L5B01 Fig. 9a, b I St F^ 1 1 1 for fle.x/blfi. f ai/ 16 />,- for naic/ -tai/ CONFI DENTIAL 14- -&.oa / y IZ ^Y ^- -^ - -^ -<= ^ ^-^ 10 ^^ <:- -3.2^ ^.' Q * V- .^^ -^^ '^' r 6 < , <^ ^-3.t£^ -— ' "^ ^ Z n m 1.06 ^ Ind/caies limiiing speed for wh/ch ca/cu/aied compressiM/ii/ corrections ore he/ laved reliatile. 1 r — I \ — —6VO Irdicaie vo/uas ~ ' for^6)(/dCj in incompressible flow -6.00 /OO ZOO 300 400 . SOD True o/rspe&djrriph 6f)fitsea/ei/e/. CCNFEENTAL O N COMM mONA fTfFF «RY ,j ■6.0C 326 * ^ -^' AL :==: -^ '^~ /OO ^00 300 400 soo TVue a/rspe-e-d^ mph (b) Aio/iiiude of 30,000 feet. F/^ure f.- Effect of horizonta J -tai/ flexibility on elei^aior conirol- force ^rac//en£s in reco\^ery from di^e.. Airplane, B. UNIVERSITY OF FLORIDA 3 1262 08104 943 8 U^We^llY OF FLORIDA OOCUME^JTS DEPARTMENT GAINESVILLE. FL 32611-7011 USA