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NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS WARTIME 'l REI PORT ORIGINALLY ISSUED February 1945 as Advance Confidential Report L5B01 DETERMINATION OF THE EFFECT OF HORIZOlTALTAIL FLEXIILITY ON LONGITUDDIAL CONTROL CHARACTERISTICS By S. M. Harmon Langley Memorial Aeronautical Laboratory Langley Field, Va. WASHINGTON NACA WARTIME REPORTS are reprints of papers originally issued to provide rapid distribution of advance research results to an authorized group requiring them for the war effort. They were pre viously held under a security status but are now unclassified. Some of these reports were not tech nically edited. All have been reproduced without change in order to expedite general distribution. DOCUMENTS DEPARTMENT L 45 Digitized by the Internet Archive in 2011 with funding from University of Florida, George A. Smathers Libraries with support from LYRASIS and the Sloan Foundation http://www.archive.org/details/determinationofe001ang 71 F ir S3 NACA ACR No. L5B01 IATIOFAL ADVISORY C'O[MITTEE FOR AERONAUTICS ADVANCE CD;7IDEUTIAL REPORT DETERP.I"ATIOIT OF THE EFFECT OF HORIZO'ITTALTAIL FLEXI ABILITY ;I! L)UGITUDIlTAL CONTROL CHARACTER ITICS By S. ,. Harmnon SWTP'ARY An iteration method is given for determining the longitudinal control characteristics of a flexible horizontal tail. The i:etho" oermtits factors such as the actual soasnmise variation of elasticity and the aero dynamic induction effects due to threedimensinal flow to be accounted for to any degree of accuracy appropriate to a particular case. An analysis is included of the effects cf horizontal tail flexibility on the tail effectiveness, the hinge moment characteristics, and the controlforce gradients in a r'ive r'c,very for two rr.ciern fighter airplanes. The effects of variations in speed, altitude, elevator stiffness, and centercfgrwavity riovemients are considered. The results of these calculations for speeds below that at which critical compressibility effects occur indicate for the t'.v airplanes significant effects due to the tail flexibility. It appears that the location of the flex:ural axis of the stabilizer too far behind the aerodynamic center of the tail may cause excessivCe control forces in a dive recovery at high speeds. INTRODUCTIAI The design of tail structures for highspesd flight requires special consideration of the factors that 2 CONFIDENTIAL NACA AUK NO. L.BU1 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 horizontaltail 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 twodimensional section force theory. The assumption 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 which the arbitrarily chosen twist distribution represents the distortion of the actual flexible tail. In addition, the low aspect ratios commonly employed on tails produce significant induced effects on the aerodynamic 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 present paper presents a method for determining the control characteristics of a flexible tail that takes account of factors, such as the actual spanwise variation of elasticity and the aerodynamic 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 this series depends on the degree of rigidity of the tail, and the increments for the higherorder 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 two modern fighter air planes of the effect of horizontaltail flexibility on the tail effectiveness, on the hingemoment charac teristics, and on the controlforce gradients required in recovery from a dive. The results of these compu tations are given for sea level and for an altitude of 30,000 feet for a speed range corresponding to Mach numbers ranging from 0 to 0,72. CONFIDENTIAL _^__1__1_____ _ r___l NACA ACR No. L5B01 CONFIDENTIAL 5 S'. B'DO LS MI p itchingmomient conLtribution of tail about center of gravity of airplane, positive when airplane noses up, footpounds: Mach number when used to account for cormpressibility effects it tail length, measured from center of gravity of airplane to elastic axis of tail, feet e distance from aerodynamic center to flex:ural center at a section for the tail, positive when aerodynamic center is ahead of flezural center, feet p air density, slugs per cubic foot V true airspeed, miles per hour q dynamic pressure, pounds per square foot (1.4`7)2 ] T total torque of tail, positive when stabilizer leading edge tends to nose upward (the dT derivative  represents the torque per unit span at a tail section), footoounds c wing chord, feet b span (of wing, unless otherwise indicated), feet S area (of wing unless otherwise indicated), square feet Ce rootmeansquare elevator chord, measured behind hinge line, feet cw mean aerodynamic chord of wing, feet y coordinate indicating fixed position along span from center line n coordinate indicating variable position along soan from center line CONFIDENTIAL NACA ACR No. L5B01 A aspect ratio A' fictitious aspect ratio employed in corrections for compressibility effects (A'VM2 E ratio of semiperimeter of ellipse to span of airfoil surface, primed to indicate fictitious plan form ti played in corrections for compressibility effects a twodimensional liftcurve slope for tail 0t cL section lift coefficient for tail; primed to t refer to section lift coefficient of a fictitious plan form employed in corrections for compressibility effects a+ geometric angle of attack of the tail, measured "R from zerolift line at section for assumed rigid tail e angular deflection of stabilizer due to tail flexibility, positive when leading edge moves upward, degrees at geometric angle of attack of tail, measured from zerolift line at section for flexible tail, degrees atR + 8) 6R 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 6 elevator deflection at section in flexible tail, degrees (6R + 0 0) AR. change in 6R per unit change in normal acceleration in recovery from dive, degrees per g CONFIDENTIAL CONFIDENTIAL NACA ACR No. L5BO1 change in Gt r, .per unit change in ncrrmal accelerawLion in recovry from dive, decrees oer g ('at 6 0 i'i C, cic chacii e in. elevat :r contr l force oer unit c2han e in noi,,ral accele 1 ration, p*u ..rLn.s per g acce leratio n i' gravity, v.2 feet oer second rate :f charge crf section anglc of attack ,.ith elevate :r deflection f.or constant lift at Eectiin ifr assued Fri id a il rate of chan je of section hinemomrient coef ficient with secti .n lift c:)efficient for constant elevator '"eflectijn for assumed ri id tail rate of chanh'e of section hinIemoment cef ficient ;..ith section elevator deflection of assumed rigid tail in degrees for constant section lift rate of charge of section .itchingirio:rent coefficient with section ele.ator deflection of assumed rigid tail in degrees for constant secti rin lif airplane lift coefficient threedimensio.nal slope of lift curve for airplane rate of change of eleat:r:' deflection with airplane lift coefficient for trim for assumed rigid tail, degrees CO:r FIDEl:iT AL " t  1 L CO1PFIDE!ITIAL , C 6 CONFIDENTIAL FACA ACR No. L5B01 dE/dcy rate of change of downwash angle at tail with wing angle of attack, degrees per degree 1 comoressibility correction factor, where VI M2 M^ = Mach number B compressibility correction factor +2 YE'A' + 2/ Ke elevator gearing ratio, as obtained with no load on tail, radians per foot VV airplane gross weight, pounds H total hinge moment on elevator, positive when leading edge tends to move upward, foot pounds / H \ Ch elevator hingemoment coefficient qebe e e 6Ch R rate of change of Ch with 6R as obtained for given movement of elevator control stick 6Ch rate of change of Ch with atR over tail StR Cm pitchingmoment coefficient due to tail about center of gravity of airplane (N/qSSc, 6Cm  rate of change of Cm with 5R, as obtained 6NR for given movement of elevator control stick Cm atR rate of change of C, with atR over tail 6 at R+5 R "tR 65a rate of change of BR for given movement of \ "aR/ elevator control stick with atR over tail, Cm iCm/ atR with. Cm constant  6 0m /00 CON1'TDF7TTT AL NACA ACR No. L5BO1 tty) total torque transmitted by the stabilizer section at st&tl.n y, footpounds (J bt/2 dit 9 h(y) total hinge moment transmitted b; elevator section st stiatiol y, footpounds dh CTR(') coefficient of torsinrial rigidity for t (r. ) stabi lizer at station q. equal to 6i/d,' wh ere d/di is t}iE slope of thie 0 curve at racT.on q, pondf et per d. ee CTRe(T) coeffIci e' of torsin ) rigid i  for levator at E t.on e,.u! l to u: ', "'here dA /d i3 3 o.. f c r.,e z tati:'rn q. pou.,fe tt rtner degree dGI  rate of change of actionn e.levator tf'i.t with dH tot l hin. e rn) r int t. a ioacl. d !A.l of ele:,tar, su.r1I' 2. es irieaisured in sa ,Etic te:zc, degrees ,er fotp:jund Subscripts t tail w 'jing e eleva tor s statilizer R refers to assumed rigid tail 0, 1,2, etc. numerical subscripts used to indicate the order of twist iteration CONPT DEiTIAL CONFI DEUITIAL NACA ACR No. L5B01 PRESENTATION OF :ETHOD Development of Formulas 7} pitching moment due to the tail about the center of gravity of an airplane, considered positive in the noseup condition, is given by the equation / bt/2 M = lltq / c7tct dr, + T (1) \ Jbt/2 / where T is the tail pitching moment about the flexural axis of the tail, assumed to be poltive when the leading edge tends to move upward. In conventional airplanes, the value of T usually increases the elevator effectiveness numerically by about 5 percent. If the liftingline theory of reference 2 is followed, the lift coefficient c.t in equation (1) is givsn as a function of the spanwise coordinate y in the form 2 c dc tct ] aibt/2 c clt(y) = aat I ~ 5 db (2) L /cZt bt/2  in which, for the flexible tail, t = tR + 9 6 a5 + e The integral expression in equation (2) represents the induced downwash angle. The determination of the lift distribution by means of the liftingline theory for an arbitrary angleofattack and chord distribution has received much attention, and numerous methods (references 2, 5, and 4) are available for obtaining the solution of equation (2) when the functions at and 6 are given. The basic consideration in the determination of the spanwise twist distributions for the stabilizer and CO:7;IDENTIAL CONFIMID)'TIAL NACA ACR No. L5B01 elevator, a(7) and Y(7), for use in equation (2) is the establishment, at every section, of equili briu between the aerocynai c and the elastic forces acting on the tsil structure. In the present analysis, 9 and are determined on nte bsiss of the theory of pure torsion of tubes (references 5 and 6 ). their r considerations relating to the torsional effects of the axial stresses induced by the restraints to the free ,.arpir of the sections of the stabilizer Aind eleator and to the effects of the bending of the ribs can ie accounted for by employing the proper par..aeters and following the procedure of successive appro:r.inations or iterations described herein under "Iteration .,thod.' The aerodynamic twisting mrncent fora s yaun trial airfoil section results from. the lift distribution contributed byr the an.le of a tt=ack. vitch .acts at the aerodynaic center of the section, and the lift distribution contributed by the elevator deflection, which acts at its center of pressure. If the section is unsymmetrical, the lift distribution due to camber contributes a further increment e o the twisting .,oment. On the basis of the foregoing assu.moti :ns, if a symmetrical secLion is used, the applied tviisting n:mTent across a section dn of the tail is c N dT (' ) + c 1 d 5) IR/,t In order to obtain the torsional Ir.ornent on the stabilizer, the moment acting about the elevator hinges should be deducted. from the total twisting rnmtoent on the tail, because the elevator hinge moment is normally transmitted to the fuselage through the torque tube. The applied twisting moment across a section dr of the stabilizer, therefore, is given by dt(n) = dT(I) dh(p) (4) where dh(r) is the elevator hinge mmr.ent at the section r of width dn and dh(r:)= Z + c i ( qcj jn (5) 11"?nr7Tp[TirPT AT. CO:PI DENTIAL NACA ACR No. L5BO1 The expression for cLt in equations (3) and (5) is given in equation (2). The total torque transmitted by a stabilizer section y is t(y) = bt/dd (6) Jy dn Division of equation (4) by dir and substitution of the value obtained for dt/did in equation (6) gives t) bt/2 1,f d ddT dh(\ where () and d (1) are given in equations (3) dnT dn and (5), respectively. Similarly, the total elevator hinge moment transmitted by a section y is hbt/2dh h(y) : Ti d8 If the boundary condition that the twist is zero at the root is assumed, the angles of twist for the stabilizer and elevator can be expressed in the form 0(Y) ILdr1 (9) ((y) d (10) Jo dr The torsionalrigidity coefficients for the stabilizer and elevator, respectively, are defined as COCiF'DENTIAL CONFIDENTIAL NACA ACR No. L5B01 CONFIDENTIAL 11 CTR ) tl ., d.* dr j CT e Iri  where t (n)l : h r,) refer t: the tot&l torque transmitted by a section rn. S. ubsti turtio.n for d 'd and d60idrl in equations (9) and (10) results in S ti t fl .Z) = 1 t r dq (11) ,, /"y ) ;oJ(.e ') =e1 (12) where t(n) and h(j) correP ; nding t:: t (,) and hi ) are given by equations (7) anc. (3) r esrectively;. Equations (2), 7), ( ill) .nd 112) express, within the lirrmitations .f the theory involved, the equilibriumr cnCritions at each sectLion between the aero dynamic and ela stic torques. .,Ihen the aer,'dnamti c, georrmetric, and structural paraie ter.s e:.x:1ressed in these equations have been determined, the tiwee u.il:n:wn variable, s n, l0, and c>t remain. The s irL.ltane :us integr al equations resulting froci the required eq,.io 1 ibrirum co ndition generally involve c i:I.licated funrctio ns for the three u.n!rno,'n variables, In practical cases, iowever, it has been f:u.nd convenient to determinee the cnaracteriis"tics of the flexible tail by worzling v.,ith the integral equations t':ro.igh a procedure of successive approximations based on an iteration procedure. I te ration ii .. tho, The first ancro.ximation to the tail configuration is taken as the one corresponding to an assumed rigid tail; that is, 6 and g are both zero, and the elevator deflection c and geometric angle of attack of the tail at COFIJTDEITIAL NACA ACR No. L5B01 at each section are equal, respectively, to 6R and atR Corresponding values of c7t0(y) are then determined from equation (2). Substitution of these values of cLtO(Y) dT dh in equations (3) and (5) gives (9) and (rj), and dn dur the functions t0(y), h0(y), B1(y), and fl(y) can be determined, respectively, from equations (7), (5), (11), and (12). The values thus determined for 81 and rl can then be employed in turn to determine, successively, new increments in the cl., 0, and / distributions. The series resulting from the addition of the successive increments permit the determination of tie control charac teristics for the flexible tail. The general procedure for determining the elevator effectiveness of the flexible tail is as 'cllwevi: Assume, as a first approximation, that the geometric angle of attack at(y) is equal to zero and the elevator deflection 6(y) is equal to 6R. Compute c t0() from equation (2). Obtain values for dT/dr and dh/di~ at several spanwise stations from equations (3) and (5), respectively, with 5(y) = 6R and ctb(y) = cZ,(y). Integrate equations (7) and (8) to obtain, respectively, t0(y) and h0(y). Substitute the values of t0(y) and ho(y) corresponding to t0(o) and hb(~I) into equations (11) and (12), respectively, and obtain el(Y) and '1(y) as a first approximation to the twist distributions. For the second iteration (first twist iteration), assume that 6(y) = /1(Y) 81(Y) and that at(y) = 01(y) and compute the corresponding c0t7 distribution frcm equation (2). The substitutions and integration in equations (3), (5), (7), (8), (11), and (12) with 6 = 1 61 and ct = ct in the manner described for the previous iteration then provide the second twist increments 02(Y) and 2(7y) For the next iteration, assume 0(y) = 12(Y) 02(y) and at(y) = 82(y) and obtain,as described previously, the third twist increments, 93(y) and p3(y). This iteration procedure is continued until the increments for ct, 6, and / become negligible. CONFIDENTIAL NACA ACR No. L5B01 The foregoing procedure for obtaining the distri butions cit, 0, and is surmrnar.ized in the following table, which gives the variables employed in each iteration: order of twist " teration 0 1 2 Variable  o a Si E0; i e;. I I tLI 0 U 2 C t 0 1 In applications of the method ,f iteration, it will be found that in minany cases various anproxim.tiion s may be employed quite advantageously. Tithus for the first and second iterations, the equivalent geometric angleof attack distribution can often oe approximated by uniform and linear distributions, respectively, sa that the c I distribution rmay be obtained directly fr:.i, the data of reference 7. which gives results for a wide range of taper ratios including the low aspect ratios commonly employed on tails. In other cases, an ap:proximnation to the cbt distribution can be obtained rapidly by the method given in reference ". The 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 twist of the succeeding iteration permits, 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 succeeding iterations will depend on the similarity for the two iterations of the distributions of torque. (See equa tions (11) and (12).) Because the shapes of the torque and hingemoment distributions t(y) and h(y) (equations (7) and (8)) for a particular tail are usually not very sensitive to the spanwise variations of 9 and X, the shapes of the twist distributions tend to resemble the corresponding twist distributions COIFITDEIITIAL CONFIDENTIAL NACA ACR No. L5B01 that initiated them. In these cases, therefore, the twist distributions for a higherorder iteration may be estimated 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 8n(y) = 8n2 S reference station A similar procedure may be followed to estimate the increments in $ and cit for the higherorder iterations. The foregoing iteration procedure leads to series of the form cLt = ct0 + citl + cLt2 + ct3 + S= 0 + e1 + e2 + 3 + S= 0 + 1 + $2 + + From the formulas derived in the preceding section, the quantities cLtl, 81, and 01 will be noted to contain the dynamic pressure q as a factor; cLt2, 82, and $2, which are dependent on the corresponding values obtained in the preceding iteration, contain q2; and so on. The lift coefficient and twist at a section may each be represented, therefore, by a power seriesin q. The coefficients of these series, which depend on the various aerodynamic, 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 follows: CONFIDEi!TIAL CONFIDENTIAL NACA ACR ;l. L5B01 CONFIDENTIAL 15 f ib where the ni irieri cal sub crinots reier to the orcer of the twist it erat i on ad In = 2t t i ) + h : ( See equation: (7 and ) njci ?i n 1.1 t:;.a be written := i.:, + [ + + .( The elevtc.r r..er.,l se.e Z .;, :taine fr: mr the value *' the n.amlc pressure q .i.t *:ez the riht hand si e :f e:iuati.:on (li. e:ual to er:. In a s' i ile r manner the elev..tc'r in e mo.,ernt f':or the fle 1 ble tail be .:bt ne.d as H = E + l: + 2 + (15) where Hn =h( n ') .n iteration ':rtcedure .n:.:..mL 1 t: th1 t eescri o ed for the elevator effectiveness a I. I::e f. lo ed t:. det.er.iin the effect o:f angle of attack ,of tlie tail ..id e:::re ssi :ns for i.i nd H similar in form' t:. equ ti:ons (1 1) and (15 i will te o btaine d. The tendency noted. e..:us l, v. it regard to the similarity in the respective distributons for 9, ;, and" c for the highercrdier i tereti on?_s tiil le.ad in many c "ae t. cons ier e ] e sir.',plificHt ion in the iteration pr ocedure for deter innLec the effect of t.il flex;:i'oility on the citching rrmo.ment I1: and tae hi ge im:.ent H. The i ncre.reents in .and I: f:r the higher order Lterations can tnerefo're be obtained in these cases b, means of the following r! f 1t i rlnshi ps : E .(16) Sin r. H =  (17) Li i ) C IFIDElTTIAL CnCa ACR No. L5B01 The forces and resulting twists on the tail structure are directly proportional to the tail angle of attack and the elevator deflection corresponding to the values that would be obtained in an assumed rigid structure or to atR and 5R, respectively. (See table III.) The differentiation of equations (1),) and (15) with respect to UtR and 5R and conversion to the nondimensional form gives, therefore, for the flexible tail the parameters 6Cm 6Cm 6Ch 6Ch C Cm, I, and . 6 R' E tR 65R atR Corrections for Compressibility Inasmuch as the aerodynamic charteristics of the tail are affected to an important extent by compressi bility, the effects of compressibility must be considered in predictions for the control characteristics of the tail. In the absence of experimental data, the following corrections for compressibility, based on the theory of small perturbations, which is discussed in more detail in reference 9, are summarized for the parameters involved in the present analysis. These corrections may be applied at speeds below that at which the critical compressibility effects occur or up to a Mach number of approximately 0.60 in conventional airplanes. The spanload distribution in a cmnoressible flow should be computed on the basis of a fictitious aspect ratio equal to the true aspect ratio, reduced by the factor l 2, and the resulting values of clt obtained for this reduced fictitious aspect ratio should be multiplied by 1/ T.2. Thus, if the primes denote values obtained for the fictitious airplane, At' =A M2 and ct' ill I2 C 't ': CONFIDENTIAL CONFIDENTIAL NACA ACR No. L5B01 The values for the parameters z and tc) % R/ z ,I as obtained from lowspeed data should be multiplied by the factor 1/ .2 The slope cf the liftcoefficient curve in three dimensional incompressible flow is corrected for compressibility by multiplying it by the factor EAt + 2 B : tE'vt, + e in which the symbols Z and E' r.eur jesnt the potential flow correction for chord effect in inco.ipressible and comoressible flow, respectively. This correction applies specifically to elliptical plan forrs but is approximately correct for other plan forms. In incorpressible flow, E is the ratio of the semniperimeter 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 bt and aspect ratio At'. The derivative rd/daw for compressible flow is computed on the basis of a fictitious tail length equal to the true tail length increased by the factor 1/V M,1 and the fictitious aspect ratios for the wing and tail equal to the true aspect ratios reduced by the factor I . APILICATIOH OF 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 t, order to illustrate the method and to obtain quantitative results for some typical cases. The computations were made, for both airplanes, of the tail effectiveness, the hingemoment characteristics, and the controlforce gradients required in recovery from Jives at sea level and at an altitude of 50,000 feet. CONFIDENTIAL CONFIDENTIAL NACA ACR No. L5B01 Figures 1 and 2 show the plan forms and dimensions of the horizontal tails for airplanes A and B, respectively. These figures also give the location of the flexural axis as determined from stabilizer torsional rigidity tests made in connection with the present investigation. The torsionalrigidity tests for air plane A were made by the Langley Flight Research Division and for airplane B by the Langley Aircraft Loads Division. Both the stabilizer and the elevator for airplane A are metal covered, whereas airplane B has a metalcovered stabilizer and a fabriccovered elevator. The aerodynrnamic parameters for the two airplanes were based on lowspeed data corrected for compressibility effects, essentially as described previously, ?'' basic data employed in the calculations, the source from which these data were obtained, and the c :.,:essibility corrections aoplied are given in tables I and TI, Average values along the span were assured for the parameters and I which were obtained on the basis of estimates for C/Ch~5R and C j/actR from lowspeed flight data. In the computations, the aero dynamic centers of the tail sections were assumed to be at the quarterchord points of the sections. The tailstiffness data for the calculations were obtained from flexibility tests made on the stabilizer and elevator of the fullsize airplanes. In order to clarify the relationship of the flexibilitytest results to actual flight conditions, the procedure for the determination of the stiffness data is described herein in some detail. The stabilizer tests were made by applying a concentrated torsional couple at a section near one tip of the stabilizer and mnesuring the torsional deflections at several stations along the span with reference to a station on the unloaded half of the stabilizer. The elevatorflexibility tests were made by loading bags containing lead shot or sand on onehalf of the elevator along a line onethird of the chord behind the hinge with the elevator locked in position. Ir spanwise loading on the elevator surface corresponded approximately to a uniform distribution. T. deflections of the elevator on the loaded side were measured at CONI!DEITI AL COITFIDENTIAL ITACA ACR No. L5B01 several stations with resC ect co a reference station ta::en onL the unlc added half of che elev atr. Tests were als:, performed on one rib of the elevator of airplane B at a station at:out .5 feet from the fuselagi e centter line to obtain the effect on the di tortion 1alo ng the chard of a c hord i se loading that simulated a triangular distribution nore closelyr thE.n the one just descriLed (o ad mrncertated at onethird of chord behind hin2er e Iii tne e tests, r' asr.er:enr' ts ..ere taken of the deflecti.n t vetr;i sill intervals alone the chord (5 dial a:es for an 11 i.ichi chord). The results indicated that v1ith botr h ty es of loading the distortions :ai. ng the chord. 'er.. e el iu anO t iat tie deflect ins along toe chord follor i . a strsaint litn. It vas assumed, th r'fore, that the i.ea u .ud an.;ular deflection due to tti' leatjor il .: bi iiity c. uld be considered as an e.Aquivalet chran.s in el '.;.'tcr dIeflction with no change in the canTIL r of the elev/at.r sur face. The tailstiffness daci fo'r air. i:sne A are shtorn in figure 5. The results f'r the stai;:i.liaer give in this figure are based on a cncrentrrited torque of f'3 foot pounds applied :. the ri.zht half of the staliliLer at a station 6.5 0 feet from the Lfu.elae c:'enter line, and the data for the elevator are based on a total hine rm;iicoent of 3.3 foot..unds distributed on the right half of the elevator in the manner descriced previously. The tailstiffriess data for ailrlane 3 are shown in figure 4. The results or the stabilizer given in this figure are based on a concentrated torque of 50 foot pounds :applied to the left half of tile staliiizer at a station 5.92 feet from the fuselage center line, and the elevator data in figure L? are based on a total hinge moment of 60 footpDunds distributed on the right half of the elevator in the manner described, previously. Procedure for Calculations With the aid of the foregoirng dates, the srcanwise distributions for clt, U, and 9' were detsermlined for several iterations. The clt distributions were obtained by the usual methods based on liftinglin= theory. Tn the comoucations, the stabilizers for the two airplanes were assumed to act in torsion similarly to tubes so that C'9PIIDEiNTIAL CO'lII DEITIAL NACA ACR No. L5BO1 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 3 and 4. Because the results of the elevatorflexibility tests for both airplanes indicated the probability that the static loads on the elevator did not act in pure torsion (see figs. "3 and 4 for d9/dH near root and tip sections), it was believed practical in the present investigation to modify the method described previously for determining '. The twist 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 dZ(y) shown in figures 3 and 4. This method dH for determining the elevator twist is strictly correct only if the loading on the elevator surface in the static tests simulated the loading in flight. For the present investigation, however, the error from this source is not expected to be important. Some computations with different assumed 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 ct, 0, and V 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 (15) and (14) 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 nondimensional form as the derivatives 6Cm/6atR, 6Cm/65R, 6Ch/6atR, and 6Ch/6R. The details of the computations for determining 6Cm/66R and 6Ch/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 normal acceleration in recovery from a dive was computed by means of the following formula: Fn = a6 R + at  tRKee2b (18) (6,5R 5atR R) CONFIDE ITIAL CONFIDENTIAL NACA ACR No. L5B01 CONFIDENTIAL 21 where CpR snd AatR refer to the changes in bR and at Fer unit change in normal acceleration in terms of g and ,here Kf is the elevator gearing rati., In d 1 Wp I1 (C.n L&6R = r t j q T tR IR 7FLR + Lt (19) and La = + 2.oZt (20) r 4,a \ %, In equation ('7) the tw terms on the' righthand side enclosed in thne brack:ets represent the oprt 'of ., required to trim the airaolare, and the third term represents the part of ti'R required to balance the effects of rotation of the tail during the steady chliSe of the Ditching motion. In the.e equations, 'hLJ/. R, "Ch/}'ct, CCin 6R, R' ~AQtR, and (J, are the h ' citR, 'C.Un..' L5 R.m' t values for the flexible tail ,btained by the iteration procedure. If values for these parameters for the assumed rigid tail are used in equations (18), (19), and (20), the ccntr lforce gradient for the rigid tail FnR is obtained. The values for the driva 5R tive I ) for airplanes A and B were based on d" L/R flight results at an indicated airspeed of aoproxi mately 200 miles cer hour. A value of L equal (dc^L COniFTDEITTIAL NACA ACR No. L5BOl to 5.20 was obtained for airplane A based on a center ofgravity location of 28 percent of the mean aerodynamic chord; whereas a value of 3.26 was obtained for air plane B based on a centerofgravity location of 29.5 percent of the mean aerodynamic chord. The effect on Fn and FnR of movements of the airplane center of gravity was investigated by assuming different values for dR . dCL R dE The variation of  with speed as determined by daw 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/daw. The /dR\ values for however, were corrected for compressi bility effects by multiplying the lowspeed value by the factor 1/B corresponding to an average between the wing and tail. RESULTS AND DISCUSSION The results of the calculations are presented in table III and in figures 5 to 9. Table III shows the results obtained for the various iterations in determining 6Cm/66R and 6Ch/o6R for airplane B at a Mach number of 0.60 at sea level. Figure 5 shows the spanwise variation of tail angle of attack at and elevator deflection 6 resulting from an application of the elevator control equivalent to unit deflection for the assumed rigid tail, as obtained from table !II. Figures 6 to 9 show tie effects of horizontaltail flexibility on the longitudinal control characteristics for airplanes A and B for a range of true airspeeds from 0 to 550 miles per hour at sea level and friomi 0 to 490 miles per hour at an altitude of 30,000 feet. This range of true airspeed corresponds to a Mach number range from 0 to 0.72. The speed for each altitude corresponding to a Mach number of 0.60, which represents CONFIDENTIAL CONFIDENTIAL NASA ACR No. L5B03 the limit for which the theoretical compressibility corrections employed in tne present corrputations are believed to be reliable, is indicated, on figures o to '. The resI.lt for the M"ach numbers higher than 0.i0 are included in the figures in order to ive an indication of the trend of the flex.ibility effects. The results of the coimDutations for a ach nrier of 0.60 st sea level are summ.rari ed for both airclIan? s in tale IV. Table III indica es that tlhe c.,'onv.egence of the iteratiocn procedure is very raniid. This con"ergence, as indicated for rCI/; 5:. and C.i% R for airplane ., is tt:y"ic il for the other pir:niete in thle flex;1 ible tail for both airolane. Thus, ii tn1 conributiocn Otctained for each successive iter nation is ex.r::sed a: a ratio of that obtained for the Lerothorder twist iteration, r'iC,,/ 5F R S1 0.301 +0.0727 0.017 +U 0.008 $ 0.7 ' rr.FR '. .'"'r SCh/ci. c oC I .", ".;ol 0= 0.2411 0 0.0101 F D 0.;3u The subsequent comrpari :son illustrates the number of twist iterations required by the regular procedure of iteration in order to determine the longitudinal control characteristics f:or a flexible tail. The results obtained from table III as given by equations ('21), whic'n utilized three regular twist iterations, will be compared with results obtained by the use of one and t.%o regular twist iterations, respectively, in conjunction with the relationship s given by equa ,ions ( 6) and ,17) for estimating .. n and Hn f:r the twist iterations of higher order than one and two, rspectively. Thus, by use of one regular twist iteration, = 1 o.01 + 0.0905 0.0272 + 0.0081, = 0.771 o rr,/. R 22) 6C h/5R = 1 0.241 + 0.0581 0.o01o +0.00558 = 0.3o6 bC hR/, R C r FI DIIT i AL COITFIDENTIAL NACA ACR No. L5B01 By use of two regular twist iterations, 1 0.301+0.0727 0.0176+0.00425 = 0.759 (23) =1 0.21 +0.0557 .0129.+0.00300 = 0.805 6ChiR/6 The comparison of the results shown in equations (22) with those given by equations (21) indicates that the use of one regular twist iteration in conjunction with the simple relationships given by equations (16) and (17) is sufficient to determine the effect of tail flexibility to an accuracy of the order of 1 percent. Figures 6 and 7 show for airplanes A and B, respectively, the ratio of the tail effectiveness and hingemoment parameters as obtained in the actual flexible tail to those obtained for the assumed rigid tail. These figures indicate, for the complete range of airspeeds for both airplanes, that the parameters 6Cm/66R, 6Cm/6~tR' 6Ch/66R, and 6Ch/ atR are reduced numerically because of the tail flexibility and that the parameters VatR 6Ch/6 R and are increased numerically because of this 6Cm/6 R factor. The numerical reduction in 6Cm/66R 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 flexuralaxis locations) and the resulting torsional moment twists the stabilizer in a manner that reduces the tail lift. The numerical reduction in 6Cm/66R is also due to the negative value of 6Ch/I6R, which causes the elevator to twist and thus to reduce the elevator deflection. CONFI DENTAL CONFIDENTIAL NACA ACR No. L5B01 The numerical reduction in 6Cm/6atR 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 6Ch/datp is negative. The respective numerical reduction in the values for cCa/6', and 6Ch/ atR 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/c0,R due to the stabilizer twist (6 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 Ci/,at., Figures 6 and 7 indicate that, in _ener&l, the effects of tail flexibility vary with 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 raid convergence of the oower 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 e 6 Ch/i atR soeeds see figs. 7(b) and 3, for and FnFn,, ( 6ChR/o atR 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 Cmin/'6R, 6Cjh/6pR, and Ch/I6atR 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, and the corresponding ratio for 6Cm/IatR would be increased by less than 1 percent; whereas, at 50,000 feet for the same Mach number, the effect of the CONFIDENTIAL CONFIDENTIAL MACA ACR No. L5B01 increased elevator stiffness would be about 0.40 of the corresponding foregoing effects indicated at sea level. It can be noted from figures 6 and 7 that, provided critical compressibility effects do.not appear, elevator reversal for both airplanes A and B does not occur up to a speed corresponding to a ,'ach number of 0.72. Figures 8 and 9 present a comparison of the control force gradients in recovery from dives as obtained for the actual flexible tail and assumed 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 assumed rigid tails. Figure 8 gives the results for airplane A at sea level and at ani altitude of 30,000 feet. This figure shows the variation with airspeed of Fn and the /d6 ratio Fn/FnR for values of R in incompressible flow of 3.2 and 1.60. These values of 5.2 and 1.60 correspond, respectively, to cen.terofgravity locations at 28 percent and approximately 31 percent of the mean aerodynamic chord. Figure 8 shows that flexibility of the tail increases the controlforce gradient and that this increase for a Mach number of 0.60 amounts to 12 percent at sea level and 3.5 percent at 50,000 feet altitude. This figure also shows that a rearward movement of the canter of gravity of approximately 3 percent of the mean aerodynamic chord causes a small reduction in the ratio F / The results for the airplane B at sea level and at altitude for values of  R in incompressible flow of 3.26 and 6.00 are presented in figure 9. These values of 5.26 and 6.00 correspond, respectively, to centerofgravity locations at 29.5 percent and approximately 25 percent of the mean aerodynamic chord. The figure shows, 'or airplane B for a ran'. of airspeeds at the altitudes considered, a small increase in the controlforce gradient due to tail flexibility, or approximately onehalf of that indicated in figure 8 for airplane A. Figure 9 also shows that a forward movemrn:n of the center of gravity of approximately 't.5 percent of the mean aerodvinamic chord causes a small increase in the ratio Fn/FnR. CONFIDENTIAL CONFIDENTIAL IT ACA ACR IPo. LSBOl1 An e::amr. nation of equations (18), (10), and (20) indicates that the controlforce gradient in a dive recovery ,as.y be influenced to an iimnDortant extent by the C },/j s, aerod'namic Cparam eters  C I and 6 The results of the present anaiy.is show for both air planes A and B that the first two of these paraneteirs are affected by, tail fle:ibi lity in a manner to increase Fn; whereas 6Ci6/',att is affected by this factor in a manner to reduce Fn. As noted previously, the numerical reduction in 'Cm/,'atp obtained in the present comvputa aions for airplanes A and B is caused principally by the 1,cartion of the flexural exis of the stabilizer ahed of itr aerodynamic cnter and Lb' the nes eti e value of C h/C, att. In order to obtain an indication cf the importance of the change in oCrnm//"Ct due to tail flexibility for the c:rtr.olf:,rce gradient in a dive recovery, comoutations were made f.or the two airplanes in which it was assumed that  = which is roughly octR ',tR 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 0..60 at sea level, that in the case of airplane A the ratio F,'/FnR would be increased, from 1.12 to 1.26, and in the case of airplane B this ratio vould be increased from 1.0' to 1.075. On the basis of the present analysis it appears, therefore, that the location of the flexural axis of the stabilizer too far behind the aerodynamic center of the tail, could cause excessive control forces in a dive recov.ry at high speeds. COiC LUSI 0.TS An iteration method for determining the effect of tail 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. CONFIDENTIAL COITFIDEI'TTAL 28 CO;0'I,2:'T. AL :TA.A ACR No. L5B01 The results of calculations to determine the effect of tail flexibility on the longitudinal control charac teristics for two fighter airplanes indicate that the longitudinal control characteristics are affected to a significant extent at high szeed.s by this factor. The follc. ng conclusions apply to results for these airplanes at speeds below that at which critical compressibility effects occur: 1. The magnitude of the ta lflexibility effects, in general, varied approximately as the d:.r.c pressure  modified, of course, by the relative compressibility effects. In some cases at very high speeds, however, the effects of the terms containing, the dynamic pressure of powers ,grater than unity becalie co.mpaaratively significant. 2. Tail flexibility was found to reduce significantly the rates of change of pit'hir_.; moment and hinge moment with elevator deflection and tail angle of attack. 3. The controlforce gradients in a dive recovery were increased because of tail flexibility. 14. Rearward movemients of the airplane center of gravity tended to decrease the effects of the tail flexibility on the controlforce gradient; whereas forward movements of the airplane center of gravity tended to increase the agnitude of these effects. 5. The location of the flexural axis of the stabilizer relative to the aerodynamic center of the tail is an important design consideration with regard to the. magnitude of the tailflexibility effects. The location of the flexural axis of the stabilizer too far behind the aerodynxamic canter could cause excessive control forces in a dive recovery at high speeds. Langley Memorial Aeronautical Laboratory National Advisory Committee for Aeronautics Langley Field, Va. CC' F :D: T I'A NACA ACR No. L5B01 REFERENCES 1. Collar, A. R., and Grinstead, F.: The Effect of Structural Flexibility of Tailplane, Elevator, and Fuselage of Longitudinal Control and Stability. Rep. No. S. M. E. 5227, British R.A.E., Sept. l192, and Addendum, Rep. No. S. M. E. 3227a. Oct. 19L2. 2. Glauert, H.: The Elements of Aerofoil and Airscrew Theory. Cambridge Univ. Press, 1926. 3. Pearson, H. A.: Span Load Distribution for Tapered Wings with PartialSpan Flaps. NACA Rep. No. 535, 1937. 4. Hildebrand, Francis B.: A LeastSquares Procedure for the Solution of the LiftingLine Integral Equation. NACA TN No. 925, 1954. 5. Trayer, George W., and March H. WV.: The Torsion of Members Having Sections Common in Aircraft Construction. IACA Rep. No. 35, 1950. 6. Timoshenko, S.: Theory of Elasticity. First ed. McGrawHill Book Co., Inc., 1934. 7. Anderson, Ray:mond F.: Determination of the Charac teristics of Tapered Wings. iJACA Rep. No. 572, 1956. 8. Schrenk, 0.: A Simple Approximation Method for Obtaining the Spanwise Lift Distribution. NACA TM No. 918, 1940. 9. Goldstein, S., and Young, A. D.: The Linear Perturbation Theory of Compressible Flow, with Applications to WindTunnel Interference. 6865, Ae. 2262, F.M. 601, British A.R.C., July 6, 1953. 10. Jones, Robert T.: Correction of the LiftingLine Theory for the Effect of the Chord. NACA TN No. 817, 1941. 11. Silverstein, Abe, and Katzoff, S.: Design Charts for Predicting Downwash Angles and Wake Charac teristics behind Plain and Flapped Wings. NACA Rep. No. 648, 1939. CO NFIDENT IAL CONFIDENTIAL TACA ACR No. L5B01 12. Ames, Milton B., Jr., and Sears, Richard I.: Determination of ControlSurface Characteristics from NACA PlainFlap and Tab Data. NACA Rep. No. 721, 1941. CONFIDENTIAL CONFIDENTIAL NACA ACR No. L5BO1 CONFIDENTIAL TABLE I DArA PR CALUrLATroNs PHYSICAL IAD GEOIETIR C CHRALcruIsrics [Date furnlmbed by manufatourer] Ie I t. *l I re Tall Eleeator r.ek ratill Airplane area n ynamic ire.. apan, c atord length a *lrplrne i '3 a e: o : be e ^  ri J n/ ( t) tlb) ratio cnord :r c Lb ar t t a.4, 1t) n, r. (q rt) (a, fI) alr) it) ift) 'r A 12,000 300 5.55 7.28 55 16 1.19 21.4 0.66 B 7.660 256 5.815 6.6. 1.1.1 15.2 1.01 15.5 .57 IABLE II DATA FOR CALCOLATrOBS IAROYrTfN1lC PARAMIBRS alue in .,rretiorn tor Parameter Ir.cu pr ees le Source or data rlI com prer an L Ltyv Altiplane A c'O r'Rctit M0.0086 Reference lI Multiply by  ao 0 ..9) Asaumed Do. b6ch d'R I 0.00686 Linpubllised data based 3n Do. t d Cb/oot = 0.00218 and i6ch, cit,' 0.0O 2 dCh 6b = 0.00804 None (at/AI 'R )o.66 .Rferenee 12 Bone dr do 0.50 Reference 11 Assumed cnatant 0.077 reference 7 Multiply Dy B (.dB dCLR Based on unnuorllbad data Mu.ltipL by 1. B: ('dR dCL' R for c.g. at 28 percent M.A.C. averede for wing and *11 Airplane B (m/6 O.0091OO Reference 12 Multiply by  ct 1/_M5 o 0.09 Assumed Do. (ch."6r.' 0.060b5 ELstlated frrm unpublianed DO. ''Lt fli ht JaLt Eb.sed on .C 6tR = 0.000511 and   Sc" '"c I' R 0.00625 "r, dci = 0.u06b5 one 'tR RR) t 0.5c, beferernrce 1Ie None a( ao .'0 Referir.:e 11 Aa Lied constant Referernc 7 Eattmatea from .npucrllahed rllArt a.ta for c.g. at ).5 percbret .A.C. Multiply by B Multiply by I/a; a&erage for wing and talA NATIONAL ADVISORY OlMMIiTEE POR AERONAUTICS aVal.e giAven to f3r a sectin at L.5 ft. from fu3elg6e center line: appropriate veluas ere used for otber sec tions. Average *:onatranTr valj were used. CONFIDENTIAL NACA ACR No. L5BO1 42  7 It .. L_ " i, : c  I I "iK 4.1 *j= I  =*1.' l^ j S  '2 i i, c I :,' : . Cfl  . i' g i'' . f* _ i i i . ~'. 11 "' 5V "7 .'  1 "** "" .3 "^ I I I ] I~ u ^ ;;" '' I:' " Si ..' 1 ? **i I ; :o.r :. _ =. i i  r .7 ~. ,:~. , ** r c. *? ,' ....4 #A 7 ....r c.?'.^ .' r : ; : i ,r I . 0 .) ., I ,_3 , j ,i. ji. :. .* . .. r,r : ' : , :, *_<,_ :i P: 1 i~C~ ' O' T 'i i i I .4 . i: S,. + 4 4 ,' : 1_________ i i i . IC'' " , '.4 ?N .44.. 1 {'7.=. ....j4  *Ii ..~ 23.14 C _, I  7''. _ .. i'r^n =1 u :, ,:, J ,,= ,I ST .1'14  1LI I  II  I  I. L Ir r l.(.4c,. a 4 1* 4" *= r~ u> .S. c. *.. ~* . 1 r * c* r . NACA ACR No. L5B01 0 a r( 0 0 u I oi el 4 0 \o o 0 0 o 1S F r. m Ir oa u S a 0 0 C o 3o a o I I I, I ,, g a^ I f1o0 C,.,fr  I __ L CO p O LN a o ip ao 0 >0 0 C II + o + B CC K 1 s 1< 0 0 0 0 + A 0 + (N + U)1 , ~ r i ID' r  o 1* 0 > 0. o o 0 r 0 E UO I o 0. U) 1 o o 0 C, ' NACA ACR No. L5B01 CONFIDENTIAL 34 T AB' IV. COMPAlRIS 'i OF EFFECT OF iCHRII.'IITALTAI FJE' ..FI.;I .T '. i GIT JDIpi L R 0 ROLC CHARACTERISTICS FOR AIRP'L.AIE.3 A AI, AT' A .'A.!: 1' P.41BEFR c'F 0.o0 AT ;EA E"'L FPgra'reter ratio Airplu A Alirpl1 9r 5 6rm /SR ,. 0. 6',I F/t_, IJ ''U i & ri/... /.t 'm/r at, tm tR i.iF/C iR 6 Ch .) 1 .8 0 / , ,' t C a i 1 I ' 6Ch /'HR Iin *; R 1.15 1.o5 .CR/ FR B J 1.12 ..Oo ,'ATITOIIAL ADVISORY CO.T ITTEE FOR AERONAUTICS CONF IDEI:T rA; NACA ACR No. L5B01 CONFIDENTIAL 362' I ~1 f/ useaye, t / '_ CeC/~ lne ' F/e ura/ oxis NATIONAL ADVI:ljRI COMMiITEE FOR AiiONAUTICS o Location of test points CONFIDENTIAL Fiure / Plan form of ta'/ sem,'aDon showing siab/lizer and e/evotor c//menr5,vs. A irp/'a ne A; hor/zonlo/ to// area, ss square feet; e/e vaor area, zz spoore feel ba/once area, 7. percent of elevoaor areo. ONFIDENTUAL NATIONAL ADVISORY o Local/or of test points comi FOR AERONAunTCS gure 2. Plan form of to/a sem/spon sho/wng stabi//zer and elevator d/mens/ons. A rp/lne B; horizontal toll orea, 4.1/ spare feet elevo or rea oS 1305 puore feet;bA/ance area, 0.24 Spoare feet. NFcomEN AL Figs. 1,2 NACA ACR No. L5B01 9 W iS uj i 0 .6 k .* I3 20 x 03 /6 6.Q 6 ,; 2 3 4 5 6 7 Dis5 ance from eaI/ ce.7er Ikne, ft F/are 3.xperirne nta data for f/lexb,','/ of /o.'zon.al Co.r. o Airane A. Dati from Je ts Tr ade. by, L. F, ,Fsearch ,i/son.. 7?L i/  CO FIDEI TL4L _ H = 3.3 P1h_ Fig. 3 /J/I.~ 0.0 2   NACA ACR.No. L5B01 Q n I. 4 n Zt K K^ K CC FDINTIA. .0/216 .00 0 .0 4   .5  20 x O " PonTR oi .4 __ __ Cr avo!.ecatan i/ S', /I ct con cn traded lfar, O f / of t5 fZ./ .J_ 7___^  1 .3\ / .2  6 _ / ArIONAL ADY'i,0i f / COM IITE F0 AEO O UII CS ./  / __  . ,''4 O O __NFI ENTI 0 0 2 3 4 6 7 D5/sance from taol cerner Ine, ft F.'re 4.(cxper/mental cata for flexiblily of horizontal tal/. .A .p/ane 8. ODaLa from tests rnad y L iorl.ey Aircraft Loaos D/ls/ton. Fig. 4 NACA ACR No. L5B01 12 ic d0 NATI NAL ADVISORY / OMMITTIE FOR AIUQONAUTICS I CoNFDENTIA I IO S / 2 3 4 5 6 Didsonce From fAol conerl/hen Figure . D,slrbuon of lod en y /e o aooc oa'a'ce/evor def/eclion in a lexible Zoll resul,/tng omr an opp/ colon of lte e levador control elu'va/en, to a~n defledton for he assumed rigid lo/. Airplane B. Mach num ber.60ol sea /eve/l;, =/ o.Xf=0? Fig. 5 NACA ACR No. L5BO1 S(ONFniENTI \L /.4 /. / S.0 .____ ____ __ ,:1: tO .8 6 .2 0 FI Atlude ' Sea le"e/ 1 Indicates .md,/ny speed for /h'chA ca/cu/oaed comroressibilAt correcticrns are be,eved relmaie NAli AL A DVSORf CONFIDEJNTIAL. C(MuMirlI FRAE Al ONAuTIC 0 /OC 200 J00 400 True o'rspeed rqnph 500 600 () Effect/veness porarmetiers. Fyore 6.Effeci of norizonaa/la/l flexbilbty on7 /onlllud/ a/contrc/ parameters. Airplane A. Fig. 6a NACA ACR No. L5B01 Ik ^*a *o .6 .6 1 .4 .2 0 i 4 Altitude Sea e ve/ SIndca/tes I/mitfln speed for which cau/caoled comnoress'h ibi correct ons are beheved rehlail~e. NfAION L ADVI ORf COl FDEITLAL r.o MITTi OR A UTICS ,300 9 /00 2906 ,rue aorspeed, mph i) Hinaemoment ,.jrometers. Fgure 6. Conwc/ded. 200 500 600 Fig. 6b NACA ACR No. L5B01 I, L.LL /. ,jQz K^ /. ^  'Jk^ / CONT [DEN 'IAL 6 / 2 / g   3 Aii tude (ft) .., 4 Sea level ... 30,000 \ i Ind/COtes h ,mtn speed for which ca,'cu/atcd compressit/dyf corrections are belie ved relaole NATIO IL ADI O y CONF DEN1 AL ____ CO IIiTEE FOR AER IAUnl 0 /00 Zoo 300 400 5 True airspeed, /r o n '00 600 l) Effect/veness parameters Fgure 7Effecd of horizontaltall f/exlblity on /on /otdlna/ control parameters.Airplone B. h  Fig. 7a NACA ACR No. L5B01 1u 0 U 1L0 1 ___ [~~ ___ [or ijET4i L*7I~~L~ '.1 *' .6 U . .2 (9  Sea /evel   3,000 < I diAcates /imbrrt, spede for which calculaed compress.,bil y correcrons ore be/leved rel/ale/ NATION L AD; R, Ot )NFilENTn,L COarinM t OR t B NTAUTI 0 /00 900 J0' 400 fOO0 600 True air.speed,mph (o) Hinge mornent parameters. Figure 7 Conc/lded. Fig. 7b NACA ACR No. L5B01 SI I d 'i1ENT4L I I I  ., for f/,x ''e ~t/l S tFor r,'od ctal 0 O I O sj^ s3 t r 1 ^J 0 10 200 300 40 True airspeed, mph :ONf IDE 500 24 Z6 O/ I 8   0__ I ndicales /imIna speed  for ,h1ch co/cu/loeo  compressi hbily corrections are believed re /able /13. J.2 Indicadoes values 1.6 r (ddCi in_ i/ ncomrresshle flow  1.6 /1 Z2O 300 400 SOO 7re aorspeed,. n.ph a') At sea /eve/. tb) A.t solitude of 3q0Od fee t. F/gure 8.Effect of horizonot/ta/l flexibl/dlt on e/evoaor contro/force grad/ents in recovery from dives. 4irp/ane A. rA   13.2 IT1A .__ ___ a=*"=^ if ' ^ 1^ Fig. 8a,b NACA ACR No. L5B01 14 /0 o  6 S  t"=== : / _ Fig. 9a,b 0 /00 200 JO 400 5~ 0 /00 200 300 400 SJO True o rupeed, mph T7ru airspeed, n ph A)At se /e ve/. (b) Af doflude of 30,000 feet. F/yure Effec of horizonlo/lal/ flexiblity on elevator contro/force yrad/ents in recovery from dive. Airplane B. UNIVERSITY OF FLORIDA ' 'RSIy CF FLORIDA CDOJCUMENTS DEPARTMENT 120 tAPRSTOQI SCIENCE LIBRARY PO. BOX 117011 GA;NESViLLE, FL 326117011 USA 