KB Ko. Ll>.E23 \ NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS WARTIME REPORT ORIGINALLY ISSUED Eestrlcted Bulletin LUE23 M ADTCMATICALLY VARIABLE COHTROL LTRKACJE AHD ITS EFFECT OK THE LATERAL -COHTROL CHARACTERISTICS OF A HIGH-SPEED FIGHTER AIRPLAHE By Harry E. Murray and Clarence L. GiUls Langley Meanorial Aeronautical Latoratory Langley Field, Ya. 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. ^ - 65 DOCUMENTS DEPARTMENT Digitized by the Internet Arcliive in 2011 with funding from University of Florida, George A. Smathers Libraries with support from LYRASIS and the Sloan Foundation http://www.archive.org/details/automaticallyYarOOIang I. > ITACA RB No. L4B23 NATIONAL ADVISORY COr/ETITT':': FOR AERONAUTICS R'^STRJCTRD SITLIETIN AN AUTOMATICALLY VARIABLE CONTROL LINKAGE AND ITS EFFECT ON TPIE LATSRi^L-CONTRCL CHARACTERISTICS OP A HIGH-SPEED FIGHTER AIRPLANE By Harry E. Murray and Clarence L. Gillis SUMI.IARY An analysis and a preliminary design were made for a control linJ-are that varies automatically with dynamic pressure. This device can provide greater lateral con- trol than a fixed control linkage at all but one airspeed v/ithout additional aerodynamic balance. The mechanical construction should nresent no unusual problems and both the weight and volumie of the device appear sufficiently small for use in single-seat fighter airplanes as -.veil as in large machines. INTRODUCTION The m.echanical advantage of aileron control systems in fighter airplanes has necessarily been a compromise between the control requirements at high and at lov; speeds; the airplane has therefore had its optimum control charac- teristics occurring in the mdddle speed range. In contrast with such a comprom.ise, the critical control conditions occur at minimum speed, when the airplane is close to the groiond and probably poorly trirmied, and at high speed tmder fighting conditions. It is consequently desirable that the control characteristics of fighter airplanes be made more nearly optimum throughout the speed range. If the optimum control at any speed is to be realized, it is necessary that the m.ech.anical advantage of the con- trol system be varied automatically v/ith si^eed without perceptible ]ag and independent of' stick force, stick position, and normal acceleration. The nresent paner presents an estimate of the lateral-control characteristics NACA RE No. L4E22 of an airplane equipped v;ith a variable control linkage capable of such a variation in mechanical advantage. A preliminary design for the device is incliided. Although the rjresent analysis deals only with lateral control, oor.ewhat similar problems exist in longitudinal and directional control; and the variable control linkage can probably be e."pectad to render a similar improvement v;hen apolied to the elevator or rudde r . SYIffiOLS q dynamic pressure A area of dynamic-pres-^^i^re piston F force en dynamic -pre seiire piston (qA) X linear displaconant of dynamic -pressure piston I number of effective coils of spring on dynam.ic- pres5;ure niston L length of stick from pivot to push-rod link Fq ;orelcad on spring of dynam.ic -T.-iressi5re piston Lq length of sticlc belo'.v pivot when F = F^ d diameter of wire of which spring is wound D diameter of helical spring J torsional modulus of elasticity of spring wire 6 aileron dG.ilecticn, degrees ^^s Qg stick deflection, degrees control-system inechanical advantage 5 Ig stick length F stick force NAG A RB No. L4E23 -^ p rolling angular velocity, radians per second (plotted in degrees per second to conform with ■usual practices) b ST)an of airplane wing V forv;ard velocity, feet per second wing-tip helix angle of air-olane in roll, radians pb 2V Cy rolling -moment coefficient Cj rate of change of rclling-moiaent coefficient ^ v;ith aileron deflection Ct rate of change of rolling-moment coefficient v,'ith j-— 2V C>^ hinge -moment coefficient Cv, rate of change of hinge-m.oment coefficient ^ with aileron deflection bg^ aileron span Cg^ aileron root-mean-square chord p density of air, I'Ovnd-seconds^ ner foot kg spring constant per coil of helical spring Ap presf3ure difference across dynamic-pressure piston C]_,C2,C3 constants used in determination of spring characteristics Kq.,. K-^rj constants used in determination of lateral- control characteristics Basic assihiptions iiND conditions for the analysis. The analysis of the effect of the variable control linkage is made on the basis of the following assumptions: (1) The airplane has a rigid wing and control system « IIACA RB No. L4E23 (2) The aileron hr'.ngs-inorr.snt characteristics are linear v/ith both deflection and angle of attack (3) The aileron effectiveness is constant The first assumption is strictly true only for low speeds, and the second and third hold for small aileron de flec- tions j however, the accuracy is sufficient to rive a preliminary prediction of the effect of the variable linkage . The effect of the variable linkage on an airplane having the geometric characteristics and performance of the P-51, which v;as chosen as a representative fighter airplane, was studied. The slope of the dynamic hinge - moment ciirve Cv, and the ratio — ^ for the P-.51 alr- 5 Ct, plane were estimated to be the follo'.vlngt = 0.0G25 radian per dep;ree All computations were made siibject to the following geom.etric characteristics of the P-51 airplane: IV in g J Area, square feet , 2c 5. 75 Span, feet 37.03 Root chord, inches 103.99 Tip chord, inches 50.00 Taper ratio 0.45 A-spect ratio c.315 Aileron: Area, square feet ^ 6.70 Span, feet 6.95 Chord, percent wing chord 13.7 Deflection, degrees , ±25 Distance from center line to oxxttoard end, semi span 0.965 Distance from center lino to inboard end, semispan 0.510 Root-mean-square chord, square foot 0,923 NACA RB No. L4E23 Stick: Travel, inches at top <• 18 Length, inchss 22 Total deflection, degrees 45 SFFECT OF VARIABLE LINKAGE ON LATERAL -CONTROL CHARACTERISTICS OF a HIGH-SPEED FIGHTER AIRPLaITE In order that the control sj^-stem of an airplane be at an optimum mechanical advantage, the maximum allowable stick force should always occur at the maximijjn stick deflection. If such a condition is to exist throughout a range of spesd and atmospheric density, the mechanical advantage of the control system must vary directly as the square root of the dynamic pressure. Equations for determination of lateral-control charac- teristics of an airplane eqiiipned v/ith a fixed control linkage and the optimum variable control linkage have bean derived by the usual method and are presented in aopendix A for the conditions of no limitations and the limitations of maxim\im stick deflection, stick force, and aileron deflection. Formulas for the constants involved in these equations are also presented. The lateral-control characteristics shown in figures 1 and 2 were obtained from these equations. The estir.ated lateral-control characteristics for a oO-pound stick force at full stick deflection of a high-speed fighter equipped with a variable linkage are shown in figure 1. For comparison, these characteristics of the same airplane equipped with a fixed control linkage such that the maxim^um rolling angular velocity occurs at about 0.8VV,ax ^^e ^lIso given. Because the average maximum, force exerted by pilots appears to be approxim.ately 50 pounds, the estimation was made on this basis; however, a 50-pound stick force is not developed on the part of the curves v/here aileron movement is limited by maximum aileron deflection. From figure 1 it can be seen that the variable control linkage provides more lateral control than the fixed control linkage at all but one airspeed at any altitude. The effect of a variation of the stick force exerted by the pilot rather than of altitude is shown in fig- ure 2, v/hich presents la.teral-control characteristics NACA RB No. L4E23 similar to those of figure 1. When this stick force is greater than 50 pounds, figure 2 shov;s hoth the rolling velocity and the helix angle to he Independent of stick force on the variable control linkage. Siinilarly, the loads on the wing and ailerons resulting from ailaron deflection are independent of stick forces greater than 50 pounds at any speed. With a fixed control linkage the wlnr and ailerons are designed to sustain some naximum load, which corre- sponds to a certain constant ntick force and, at high speed, to a stick deflection less than rnaxiin\im. If the ailerons tend to overbalance at high speeds or if the strength of the pilot is excessive, deflections and loads beyond desirfn values will occur with this systein. Vi/hen the automatically variable linkage is used, the maximuj^i possible aileron deflection decreases v;ith speed and is determined not by a stop at the aileron but by maximum stick deflection. This maximum stick deflection then corresponds, for any speed, to a definite load which caiinot be exceeded regardless of the strength of the pilot or any tendency of the ailerons to over- balance . PRELlKlrlARY DESIGN OF h DEVICi TO ACCOMPLISH THE REQUIRED LINKAGE VaRIaTION A mechanism for electricallj?- varying the stick mechanical advantage and a control unit for relating the mechanical advantage to the dynamic pressure according to the characteristics of tho spring located in back of the dynamic -pressure piston are shown schomatically in figure 3. This control unit supplies power to a reversible direct-current motor through the breaker points which are moved, by moans of a flexible cable, a distance proportional to the linear displacement of the variable link. Such an electrical system (fig. 3) for varying the control linkage has no extremely delicate or complicated parts and should operate quite reliably without perceptible lag, as does a sinillar but more complicated mechanism for varying the pitch of constant-speed propellers. The prescure cell shown in figure 3 v/as mounted with its axis parallel to the latei^al axis of the airplane in NAG A RB No. L4E23 ordsr that the effect of inertia forces resulting from normal and longitudinal accelerations might be elimlnatedi It is conceivable that such a device might hunt, in which case a brake could easily be installed as indicated in figxire 3. If this mechanism is to produce a variation in mechanical advantage directly proportional to the square root of the dynamic pressiire, the length of the lever arm L (fig. 4) of the aileron push-rod link must vary inversely as the square root of the dynamic pressure. The dynamic-pressure piston must thus move according to the following relation, which is developed in appendix B: (1) ;c, - x)2 In order that such a force-deflection relation shall exist with the constant-diameter-coil spring shown in figure 3, the num.ber of coils in the spring must vary vifith deflection as follows: kgX (Cg - X)^ (2) If the relations shown in figure 4 between the constants and variables involved in the link systemx are used, the constants of eqixations (1) and (2) can be evaluated, as jxplained in appendix B. Physically, such a variation in the number of effective coils of a spring can be achieved v/ith a constant-diam.a ter helical spring by variation of the helix p.nrle a:iong the length in order that the coils of the spring will gradually fall against each other as the spring is compressed; the effective numbei^ of coils are thereby decreased according to the relation given. Typical curves of the force caid the shortening characteilstics of the spring fulfilling these relations are shown in figure 5. Although onlj the constant-diameter helical spring was considered in this analysis, the same characteristics can be obtained from any one of several other spring; ^o . No special power sunply is required by either the miotor or the control unit; hence, it has been estimated 8 II AC A RB ITo. L4E23 that the entire device can be installed in a high-speed fighter for an additional weight of about 10 pounds. If, however, the power supply failed or the mechanism became damaged by gunfire, the pilot might conceivably be left in the high mechanical-advantage range without sufficient aileron deflection to make a safe landing. A manual method of operation may therefore be required in case of an TV-e additional lateral control made available by the variable linkage will result in an additional wing torsional load v/hich increases with speed. If, at speeds near terminal velocity, the additional loads become vndesirably large they can be reduced by reducing the stiffness factors of the dynamic- pressure spring and, consequently, the available aileron deflections corresponding to these speeds. Because of the im-Drovement in lateral control indicated by t^e analysis and of the simplicity of the required mechanism, it is suggested that the autc- raaticallv variable control linkage be tested in fli^;ht CCNGLUSIOKS From an analytical investigation of the effects of a variable control linkage on the lateral-control characteristics of a fighter airplane and from a preliminary design of this device, the following conclusions are indicated: 1. The automatically variable control linkage can provide miore lateral control than a fixed linkage at all but one airspeed without additional aerodynamic balance . 2. l»/hen tbe automatically variable control linkage is used, the design loads can be made to occur at maximum stick deflection, which corresponds to a constant stick force within the limit of the pilot's strength. Further aileron deflection with a corresponding overloading of the str^jcture cannot therefore result from excessive nilot strength or a tendency of ■:he ailerons to over- balance at high speeds. NACA RB Fo. L4E23 5. A manual method cf operation may 'be reqi.ilred. in the Link- variation Tiechanis^ in case of a power failure or mechanical difficulties. [(.. The revice has no extremely delicate or com- plicated parts, should operate without perceptible lag, and probably can be installed in a high-speed fighter airplane for an additional weight of about 10 poLinds. SUGGESTION FOR FUTURE RESEARCH Inasmuch as the conclusions indicate that definite improvements in lateral control may be expected from the use of a variable control linkage, it is recommended that such a unit be constructed, Installed in an air- nlane, and tested in flight. Langley Memorial Aeronautical Laboratory, National Advisory CoMmlttee for Aeronautics, Langley Field, Va . 10 NAG A RB wo. L4E23 APPENDIX A LATERAL-C ONTROL CHARACTERISTICS The basic fonriulas for con:puting the lateral-control characteristics may be conveniently tabulated as follo-.vs: Lateral- control character- is tics 1 No iSs = Gg limitations j ™^- t Fs = Fs S = Omax Fixed control linkage; 5/9 = K^ pb 2V P D 2 Kj5 KgSV P 2 2-7' K.^V "10 %2/f'^ ^^13/2'^ Pv v2 K17V Variable control linkage; 5/83 = Ko/Vq " s Db 2V P ^^^' v'1 K-i_6 K7 ^^10 K12/V/I -13/ /I Kl5V\/| ^^16 KivV The constnnts Kq , , , K-j_y may be evaluated from the following relation Kq constant depending % - c 2 ^■^2 = fcKi ^% = upon aileron-stick linkage ^^10^2 ^1^0^ ^max "13 = "^ K2Ko9s„,_ %. = K55 Jl. - 2 Is '^h5^aCa ^0 \o = max K7 - KsKo^Sjnax K K. 'max lO^^l 12 '^5 15 - ^^5"max ^^17 = K25jnax NACA R3 No. L4^23 11 APPENDIX B DSTllRMINATION OF CONSTANTS FOR SPRING E'^JJATIONS From fifTure 4 it can be seen that L = Lq - CiX If the mechanical advantage is to vary directly as the square root of the dynamic presstire, however, the follov'ing condition must be true: vq and, therefore. = Lq - CiX F = qA v/he re C2 = c (Co - X)2 ^o ^3 = \^ A For a helical spring F = (y)x + F, where From these conditions I = or k^,X{Cp - X)2 -y. O <-> ^3 - Po^Cg - X)2 12 IIACA RB No. L4E2: Figure 5 shows a typical curve of I plotted against X and a c or I'-es ponding curve of P plotted against X for the following numerical values of the constants : C2 - 4 C3 =. 4 Figure 5 represents no particular setup, however, and is given only as an example, because Co, C3, and kg will depend upon the dimensions of the device designed and the properties of the spring. NACA RB No. L4E23 Fig. 1 fOU 1 Altitude \6C (ft) / y -"N \ •l -10,000 / / V f 1 -\nnnn / / / \j \ "53 r"^ V > / / ^ V \ \--. / / -- A ^ 4^ ^ V -^ v\ 9. wo Q> 5k 0^80 > / V \Kzo,opo \ 1 / y / "v. ^^ \ -0 / y / -^ \ \ ^^ V y ^ ^, '-\0,000 "^ rn / • y / r - _^ ol 60 / ^ / -0 40 y c X .14- NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS s. .12 \ ^ \ \ \ s \ \ ,10 \ \, \ N. \ / raon 0- 7 N \ \ ^ "v \^ / -JO.OOC ^-ll |/ .06 -- — — — . — - — — - — ;^ ^ V ^ ^N. -4 cOn 1 N ^ \ ^ f \ .rui .06 \ \. ^ ^ ^^ ^ i TT 4 -- ^ \ ^ r~- ^^ .04 ^ ^ / - ^ ^^ '-i; ^- Vanabie linKaq 2_ -c -^ .^ "^ ^ .02 — -^ — Fixed \inkaqe. f r 1 1 , ■~ - - — 1 m m )0 31 X) 4C lo 5l )0 True a/opeed; mph Figure 1.- Lateral -control c/iaracteri5tic5 of a hign- speed fignter airplane fia/inq fixed and variab/e linkages at three altitudes w/th a maximum ^tick force of 50 pounds. Fig. 2 NACA RB No. L4E23 4-> O O Q) c o I4C (lb, 60 I2C ;— / / V r / \ V I -5-0 ■60 100 / r A y \ ^r / / \ i \ — :^ ^ 80 / / y \ \, K^ — > 40 50 ^ ^ / / / ^ I "^ -^ "~~~^ ^ 60 / X '^ ^ >-., ^ ^~ ^_ / / Ua __ J """* — -— — , ~^_ 40 / y c I 1 — ■■ - \ \, 12 \ s, \ \^ \ \ \, .10 \ \ N Ob) 60 5C 40 N N ~\ 05 N, \, \> ^ \ \ ^ / 06 ■V. > N \ '^ s u —J — \ N ^^■■-^ — 1 04 '^ V ^ -— ■^ ■~~. .^ — /^ o — Vauable linkage -Fixed linkage , 1 1 1 1 ■^ -^ ^ 02 IC ^L \o 3C )0 4< X) 5i )0 True airspeed, mph NATIONAL ADVISORY noMMlTTEE FOR AERONAUTICS Figure 2 -Lateral -control characteristics of a hiqh-speed fighter airplane having fixed and variable linkages at tea level with three stick forces. Max innum stick deflection occurs with the variaDie linkage \A/r\en F^'SO pounC5. NACA RB No. L4E23 Fig. 3 to o Fig. 4 NACA RB No. L4E23 /— z3^-<7'-N ^- c^-^ mt. ^f/'ck ^fi'ck n/'voi- To a/'/eroO'^z:^ L L NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS. o/s'/'on anc/ y-h& /acafion c?f fh& \/cfr/a6/G //nA. NACA RB No. L4E23 Fig. / a 3 ^ "3^ ' 2 7 ' S UNIVERSITY OF FLORIDA 3 1262 08105 057 6 UNiV/ERsir/ OF FLORIDA GAINESVILLE, FL 32611-7011 USA