^fr(AL'l?^ ^/ AEE No. LkJ12 NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS a» WARTIME REPORT OmONALLY ISSUED November l^kk as Advance Restricted Report LhJ12 EFFECT OF HINCffi -MOMENT PARAMETERS ON ELE7AT0B STICK FORCES IN RAPID MANEUVERS By jxobert T. Jooes and Harry Greenberg Langley Memorial Aeronautical Laljoratory Langley Field, Va. UNIVERSITY OF FLORIDA DOCUMENTS DEPARTMENT 120 MARSTON SCIENCE LIBRARY P.O. BOX 117011 GAINESVILLE, FL 32611-7011 USA NACA T'*^ 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 - 185 <;:'• :■.-■£ a-.-. )l4 0^3 OH MCA ARR 'i-^lo, i4j12 NATIONAL ADVISORY COT!I'.IITT.«E FOR ^AERONAUTICS ADVANCE Rl^STRICTED R3P0RT JPFECT GP inilGS-fTCIvTENT PARAI.^TERS CN EIEV/^TOR STICK FORCES IN RAPID O.^EWERS By Robert T. Jonos and Earry Grsenberg SJ^a^RY ""he importance o.f tho ttisk fcrct psr unit normal acct^lcratlon as a criterion of lonjittidlnal stability and the cr:.tloal dependence of this gradient on elevator hin^o-raoniGnt parameters have beon shown in previous repoj.'ts. The p:'''erent repoi't continues, the investigation v/ith r:pecial reference to transient effects for m.aneuvers of short diirabion. The analysis nade shov/ed that different combinations of elevator parameters which ^^ive the same stick force per unit acceleration in turns .rrnve widely different force variations during the entries into and recoveries from steady turns and during maneuvers of short duration such as a'-irupt p'ull-ups. A comhiration of relatively larre negative values of the restoring tendency Cv^ and the floating tendency C]^ , approaching those of an unbalanced elevator, results in a stick force that is high during the 5nltial stage of a pr-'.iQ-up and then deci'eases, and may even reverse, as the acceleration is reduced at the end of the maneuver. The stick force per unit acceleration is greater for abrupt than for gradual c ont r 1 m.ov erne nt s . If the negative value of Cv, . is reduced so that the corresponding value of G, becomes slightly dosI- tlve, the reversal of force may be elim.inated and the force may be brought nearly In phase "with the acceleration. There is a limit to the pei-misslble reduction of the value of Cv, , however, because as Ov approaches zero the stick force per unit acceleration may become lov;er for abrupt than for gradual maneuvers and may thus lead to undesirably lov; stick forces at the beginning of the maneuver . NACA ARR No. i4J12 ijViTRODlTC^IOi^T The stick force per unit noiiral acceleration as meas^'ired in steady turns or pull-outs, which was proposed as a criterion of longitudinal handling in reference 1, is novif generally accf^pted as a La sic measure of longi- tudinr.l stability. The critical dependence of this stick- force gJ'adient en eluvator hinge -mouent pai'amoters and on mass unbalance of the control system was shown in reference 2. It was found that a given stick-force gradient can be obtained by any of a series of combina- tions of these parameters satisfying certain prescribed relations. F':.rther consideration of the problem and some recent fli'^ht experience, hovvever, have shov;n the need for inves- tigating the transient effects that occur during the change from steady unaccelerated flight to steady accel- erated flight, '^ef^e transient effects cause a difference between the stick-force gradients in a steady turn and in a maneuver of sho"!^t duration such as a pull-up. The pvrpose o'T' the present report is to investigate the variation of elevator stic'; force and normal accel- eration during the transition i'^^-'^-^vi 1 preceding the steady turn and also during tui'ns or pull-ups of short duration. The effect of combinations of hinge-moment parameters is considered, each com.binatlon is chosen to give the same stick-force gradient in a steady m.aneaiver . Tim.o histories of the stick force and normal acceleration are found fcr predetermined variations of elevator deflec- tion„ An attempt is made to explain and to suggest a remedy for the large variations of stick force with time observed during pall-ups of short diu^atlon on different ali'planes in flight. A previous analysis, somewhat similar to the present one, was made in Snglaiid (refer- ence 3) but Included a sm-aller range of hinge-moment parameters . SM30LS A asf^ect ratio of wing o wing span mCk ARR No. i4J12 ^ H .q^e^e. 0^ elevator hin^e-irionert coefficient Cl airplane lift coefficient fii^:^^ 1 C.^ pitchlnf:-moinent coefficient about airplane center / Pitch! lip- moment \ of ir'ravitv ' ^' ' qSc c wing chord Cq elevator chord D differential operator (d/ds) P g stick f or c e , p ound s ri. . Pc, cases representing particular combinations ^ of hinge -moment parameters P stick-force gradient in ma:aei;.vers g acceleration of gravity H hinge moment; positive when tends to lower elevator Hq m.ass miom.ent of elevator control system about elevator hinge ° positive when tends to lower elevator '-J i^ c. ■ ■' ^. ^ ky radius of gyration of airplane about Y-axis l-^ tail length, half-chords m m.ass of airplane n norm.al acceleration per g of airplane due to curvature of flight path; accelerometer reading minus com.ponent of gravity force q dynamrlc pressure S \-jln.a area [[. NACA ARR No. lJ+Jl2 Sp elevator area s distance traveled, half-choi-'ds (2Vt/c) T period of elevator motion t t ir.ie u independent variable used in Duhamel's integral V volccil^v 7.^ ... dirtance "bstr/een center of r^ravit-"- and aerodynamic center; nopitive when stable 'a .0 dCVd:: de.flectlcn of elsvator per unit movei-nent of stick, radians per foot 0. ancle of attack, rad<.ians a^ angle of attack at tail, radians 5 deflection of elevator; positive downward 6 anjrle of pitch of airplane /v. root Q-^ 5:tability equ3.'cion ^jL airplane-density parameter (ir/pSb) p nass density of air Subscript • rra.x '-■lay Iwxm p Sub-script?! a. Da, D'a, af^. D9, 5, and Do indicate '-■ -'w derivatives; for exariple , CL, ., = . A dot over a s^nrnbol indicates differentiation with respect to time. I.IETROD OP ANALYSIS The following arsumptions are made in the present analysis ; NACA ARR No. L]+J].2 fl) Variation in forv/ard speed is negligiiDle (2) Stability derivatives rre constant; that If., any possitle nonlinearlty of coefficients is negligible (5) l-iffecte of power are negligible rJ^J Fffects of control -system r.icment of inertia are negligible ( '3 ) Cont^^o] -system mass unbalance is all located at airplane center of gravity The equations of motion of an airplane subjected to a prescribed elevator motion can be obtained from, refer- ence 2. If forward speed is assumed constant, there are three equations of rnotion. The first two equations determine the motion of the airplane if the control motion is specified. T]ie third equation determines the hinge -moment coef ■^icienb , which depends on the motion of the control surface and the ai]:>plane. These equations are ^ +ZAitD;a 2 / 2A.a D8 (1) ('^^a + ^ in- Da '"^D^n n2)< c,,,p3-2VkY'i>)ue -S' (2' (Ch„ * (=hDa'' - ^F " '''"r>2a'^] " * (S^X * ^■) ^' * f "6 * '''^Ks'^Y "^^ <" Equations (1) and (2) are used to solve for a in terms of 5. Ihe sol-ution can be expressed in determinant form, as a 5 -2Apa m; CLa 2 + 2Ai',D h^a "■ ^^Da^ -^ C,,.2^ir -2A U ^mce 2HtikY2D ik) MCA ARR No. li4.Jl2 If c Is flvsn as a function of tine, the solution for a Is found b;^ the method of operational calculus as fo].lows: Fir.ot a is found for a unit change in ^. This solution is o'-^tained from FfD) = _5 -2At-Cjj-._ V X s + mg /_ >^ F'(>.) P(0) (5) wh ?rr- F(P) ir the aeteriiiinant riven In equation (1;) and X represents the roots or F(D) = 0. The solution fOx^ a ^touation (5)) may be denoted by a(s). The value of c for a p:lven variation of o is then gix'^en b y Dui arae 1 ' s Int e gr a 1 , .vh 1 chic = a(s) 5(C) i- / a(s - u) 5'Cu) du ■^.y a slTiilar procedui'e D9 can be found for a pre- scribed variation of 6. The angl3 of actacl<: at the tail can then be found from a+ oa+ Cg -a + 7.|^ D9 The normal acceleration, v/hich is considered positive up.^ard, is proportional to the change in angle of attack a and IS p-iven by eg 2Atx ^'■ The value of the stick force can be obtained by substituting the derived values cf a and D9 and the given value of 5 in the hin3C-;-..oinent eqiiation (eiuation (3)). The relation between the stick force and Ci^ is sir.iply - 1 -2 d5 Fg = 3pv-s c^a, - 2 e eh. .ax The assujiied variatio^-jn^ elevator deflection with time is ilD.ustrated in fir^e 1 an3 can be represented analyti- cally bv 5 = 6. maxV 2 CO 2^.^ s -^t] NAG A ARR No. IJ|J12 7 T'lie cnlculat: ons vere made for a pursuit airplane for five cliiTersnt combinations ot the hinge-mornent parameters Cu , d-, , and h; for three different dura- tions of the rraneuver T; and for three different center- of-T;:^avity locations. These five different combinations of the hinp;c-moment naraineters were selected to give, for one center-of-gravity locauion, the same stick-force {gradient In a steedy tiirn, es determined by the formula for stick-force gradient in a gradual pull-up or steady turn f^lven in reference 2, which is p _ .. . ^ ^ _ _ -|. Yi ^ 4- dx\ Cr ^^De Ct C^„ Cm, The locus of points in the Ch Cv-, ^ plane corre- spon'lirg to a ^^alue of the stick-force gradient of 5 pounds per g and a center-of-gravity location 75- percent chord aheaa of the aerodynamic center is shown in figure 2 for a mass-balanced and also for a m.ass-unbalanced elevator. The aiiiount of unbalance corresponding to the line marlred h = 5 '■''•■ould reqi-iro a pull of IS pounds on the control stick for balance. The five points marked F-^, . . . Fc represent the combinations of the hinge -moment parameters used in the calculations. ^T^ffiHICAL VALUES USED IF AFALYSIS The fo] lowing param.eters were used in the analysis: ^La • • • ^-5 'fJ- •■ - 12 . 5 A 6 Cra^ -0.5I,lS, -0.195, or -0.0li.6I^ x^^^_^ 0.075c, 0.0[^2c, or O.Clc ^^Da • ""-^ S^a '5.2 %e • • " -''-' 8 ¥kCk ARR No. La .712 kv, lialf -chorda Cn.5 1.5 6.6 Z-j-^, ha] f-r.l.crd.s dC/l:;, radian of elavator raotion per J-'oot of stick travel C.5 a O.SliiO^, '6.220- Da '^Do h ^di ■lQ.55Ch -1 The ■^ollo':-lr!g direnHions ard dar.bity v^era assu-aed: c, feet •e» • ^ , .1- .ecu W^ J u.- ^U CtJ. C I ^ ^ O , . • • .-. * • p, slug/cu ft; at altitude of 10, COO fest . . . . 7 . . . . 2 . ... 50 . 0.00176 The foregoing airplane derivatives are for an air- plane havlii£'- a wing loading of .^C pounds per square foot. Five ccfoinetloaE of hinge -mc-nent parameters selected to gi'/e a stick-force gradient of 5 pounds per g in-, a steady pull-up vj'uen the ceater-of-gravit^ location is 7~ P'Srcenk chox'd ahead of the aerodynamic center (see fig. 2) are as iollows : Caee ^n % h ?1 n -0.1 -0,2;0 ^2 -,065 .0.59 ""h -.1 -.0^5 R ' 1.65 All these valu.es were used in co.lculatin-" the variation in stick force durinr a ,aaneuver for x^ „ = O.O7S0, Por qualitative co-.^^oarison, case F-, may be taken to represent a normal elevator with a fairly high trailing MCA ARR Fo. lhjl2 9 tendency end a rnoHerate aRionnt of blunt-nose inset-hinge balance. The characteriptics of F2 °^ ^^ could be achiev^.d by the use of a sharp-nose inset-hinge balance, a horn balance, or a beveled trailing edge; Fji, coiribines a laV'-'-.e emonnt of inset-hinge balance with a bob-.veight at the control stick; Ft- is the case in which the stick force is due entirely to the bobweight. Two more-rearward center-of-gravicy locations (^a,,c. ~ 0.0^2c and C.Olc) were also assumed, and the stick force in maneuvers was worked out for cases '^n , ?v , and Fr . RESULTS Cujrves of stick force and normal acceleration for a varying elevator deflection are shovai in figi-ires 3, I4-, and 5 i"or T = '-|., 2, and 1 seconds, respectively, for 7 = i|00 miles per hour, and for x^^^^^ = 0.075c. In these curves, the stick force for ■P]_ ' reaches a maximum value before the pea]-: accelera-!-ion 3?:d reverses dlrectioii in the 'latter part of the cycle. Thio effect becomes inor'^ rron' >unced as the d-iratic a of ::ie r.oneuver becomes shorter. The curves for F2 > ''''5> ''^'b s £^^'~->--- I'h shov; a progre csi'/ely smaller phase difference between the stick force nnd the acceleration. The stick-force curve for ■'^1, is ■"i.ost nearlA'' in phase wjth bhe acceleration curve . The effect of center-of -gravity location on the stlck-iorce gradient in stead^'^ turns or pull-ups can be shown m diagrams of the type of figure 2. Figure 6, foi' exaiaple, shows that the "maneu.ver point'' (e.g. loca- tion for zero stick force per g) for case F-j is Ij.,? percent chord ahead of the aerodynamic center (point v.here Cj^ =0). For center-of-gravity locations 0. behind the maneuver point, the stu.ck-f orce gradient for case P-|_ is negative. The stick forces for Pz and Pc , hovi'ever, are unaffected by center-of-gravity location. The tim.e histories of the stick forces in a 2-second maneuver for the cases shown in figure 6 for x„ ^ =0.0lj.2c and O.OT'c are plotted in figures 7 ^-^^^l 8. In figure 7> the stick force corresponding to F-i (e.g. at mianeuver point) 10 .^lACA ARE No. I4JI2 is poaltive at .f3.rsc and then ve-'^ersep. and becomes nega- tive. The riiaxl;':Tuir valines of the positive and negative forcsr. are ar-pr'oxl^Tiately equal. As the center of gravity is ■.noved cchind the iiianeuvei- point for F-^ (fig. 8), the negative '^larirrr.iin lo:"cc is rveatev than the positive; this increase •vorld be eriDected since a nef;-ative force is required to hold the ajr plane in a steady turn. The stick forcrs for Fx end Pc; remain positive. The ele/Rtor deflection required to produce a f "tl-© desired stick force for steady turns is achievea through the action of C-^ alone. All curves for F2 vtfculd. have the same magnitude for any djaration of T>,anou*>;3-':' and would be in phase v:ith the fclev^?^.t or -de flection ciirve but for the conti-:buticn of Oh^^. The effect of C^^c. increases v/ith the rabidity of uhe elevator movement and causes a phase shii't in the force curve relative to the elevator deflection, which results in a slight increar^e in the maximum, value for the shortest i.if:neuver. A slight pu.sb force near the end of the maneuver is produced by Cii 5-. Figure 10 shows that in case Fp the m.aximum force per unit maxim.um accelera- tion increases as the maneuver is shortened although net so much as in case Fn . -I. The balance is achieved in case Fz through action o^ ^■h.r- aloxio. In this case, the maximum stick force NACA ARR Fo. tJ+J12 I5 attri"'outed to Ou If' nearly in phase v/ith the accel- ^^t eration and, consequently, the maxlmioin value occurs after inaxirium elevator deflection v/hen the elevatoi' is being moved back to its criminal 'oosition. The forces at the beginning of the maneuver are consequently smaller than in cases F-^ and F^ &nd may be too small for satis- factor^r handling qualities. The effect of Gy. is to decrease the maxir.um force by an increasing amount as tbe mareuvur becomes shorb^r. 'T'he discontinuity in the h'v ciarve (and also in the F[, and Fr curves) for the l--second maneuver results from the disappearance of the C-u ccranonent at the com-oletlon of the elevator motion. Figure 10 shov/s that the maximum force per unit maxirirom acceleration for case F^^ decreases as the m.aneuver is shortened; this effect is primarily a result of the action of O-, , . For case Fi , the stick force for steady turns is achieved mainlv bv a balance of necative Cv, and bobvirelght effects. As a result of the large mass unbalance required, the maxim-'om force in the 1-second maneuver occur 2 at the end of the elevator motion. The stick force is achieved solely through the action of mass unbalance, or a bobv^eight, in case Fr . Compu- tations have been made for only the 1-second maneuver. The action of the bobvfeight, as previoiisly m.entioned, is similar to that of Ca but for a slight phase shift. ^t The phase shift for a maneuver of short duration is suffi- cient to reduce the adverse influence of Ov, . This case Vifould show a slightly/ greater decrease of maximum force per unit maximum, acceleration than case P^ v;ith decreased duration of the maneuver. The change of ?tick force with center -of-gravity location for case F-^, shown in figures 7 and S, is caused by the greater angular response of the airplane to a given elevator deflection that occurs with reduced stability. The greater response changes the balance between the Ci-, and Oh ^ cor.iponents . If the stick li.L NACA ARR No. i4J12 .force Is independent of '^'n~> ^^ ^^ cares Ft and Pc , t\ie f'nvrn. of the stlclc-forco curves is unchanged by varia- tion 01' the cent-jr-of-^ravity location. Fig\.ire 11 shovis that the variation cf maximum foi'-oe por unit maximum uccelorat ion in a r-apid maneuver vrith center-ef-gravity Iccation ■becomes less as the value of (V is reduced. The adjustment of the elevator parameters so that the 3t:'_ck forces for steady turns ar3 directly nropor- tional to the normal acceleration produced and independent of center-oi'-rravity location is generally conceded to be desirdhle. It appears possible from the analysis to accomplish these ccnditiom by maVing the stick forces denend primarily on % or on a bobv.'el.^ht, provided the entrance and. recovery are made slowly. It is not defi- nitel-'T l-nc'/n who Lher this condloion o'*^ strict propor- tionality is desired in maneuver.? of short duration. In these cases, however, \;hen the entry and recovery are of necessity rppid, strict proportionality bebween stick force rnd acceloraticn sppears iiapossible because cf the action of Cv . Accoi'din-^ to firur?.- 10, a stick-force (gradient that l-s independent of diiration of m.aneuver but varies som.e\vbat wp' th center-of -^rravity location can be obtained for a care intermediate between ?£ ^^^'^•'- ^5 • This case would correspond to a certain amount of nega- tive Cv and positive Cy and would also z-'esult in -'5 ^^at higher stick forces at the start of the maneuver. A bob-.veight that increases the stick forces can be substi- tuted for the nositlve Cy, ^t CONCLUDING RE!iARKS A si-all stick-force gradient in steady turns can be obtaiiied vjith fairly large negative values of the restoring tendency Cy^ and the floating tendency C-^ , approaching tho-re of an unbalanced elevstor. Although suitable for slow m-ane\^vers, this combination of parameters leads to a high initial value followed by a reversal of the stick force in abrupt maneuvers. This difficulty can be avoided and the stick force can De made to follow FACA ARR ITo. l1^,T12 I5 closely in phass with the aii-pl^^^^ noriripl acceleration dui'in^- toth abrupt and slow maneuvers Toy decreasing the value of C}^ and by making Cj-^ ^ slightly positive. If Cy^ is made zero, the stick-force gradient depends entirely on a positive value of Cv^ and is ^t unaffected by the location of the airplane center of gravity. In this condition, howe"/er, the stick force roqulrGd to initiate a maneuver may be ixndesirably light. In order to prevent undesirably light stick forces at the beginning of a maneuver, a small negative C]^, must be retained. The use of a bobweight in the elevator control system has an effect similar to that of increasing C^^ although, in rapid maneii.ver s , there are slight phase differences in the sticL--force variations. Langley Femorial Aeronaiitical Laboratory National Advisory Committee for A.ercnautics Langley Field, Va. ^t l6 NACA ARR No. 1J4.JI2 REPSREr^CES 1. r-ilruth, n. R.: Requirements for SP-tisfactory Flying ''l,us,lities 01' Airolanss. NACA ACR, Aoril l^lil . (Class5f ication changed to Restricted Oct. I9U5.) 2. Groenberp, Harry, and Sternfiold, Leonard: A Theoretical Investigation o.f Longitudinal Suability of Airplanes vrith Free Cumtrolr Includin-f^ Effect of Friction in Control Syctem. NACA ARR No. I4.BOI, 19liJ4.. J). Ij"^', \V . ; Control Forces during Recovery frora Dive. J.A.C. Paper No. 69, British R.A.S., April 19i4.1. NACA ARR No. L4J12 Fig. 1 y / i I ^^^^ r '•■ I (f\ ' 3 ¥■ ' i :» ■ J ^^ o ■ C ^x"^ C i Ll o u y ^ / • ■ :^ E / t^ ^ K ^ Of] C! OS to cK C o *^ ■u o CB • r-i m Vi ^ o n rH O C -p e( at > Q « .d f-» -p 4> c o > s ^ o « O « 03 to «H 9 *UOf^OQTJ»P JO(}»A»IS -<- rwa^ NACA ARR No. L4J12 Fig. 2 t^; <<^^ ^ ■ flpr ^ H^ ^ ,y /' X ^..- ®=^ y ^ V^ /^ ^ . , A y y ^ NATK NAL AJVlbUK ■ FOR ^ERONZ UTiCS .2 .1 -.1 -.2 -,5 -.[;. -.5 -.2 -.1 Restoring tendency, Cj^ o C -d c ,, / \ m u F'l I / R tick for lb CO \\ / • , ^Y \ CO k ' / / / ^'^ \ \ \^ \ / / 'A / / \^ /// \ \ N V / ^ 1.6 /' \ ^ / z' > / c o ~y ccelerat • 00 1 \ / \ -P 0) « O t3 r-t « O o O -i ^ N, ^ -^ \ ^ / \ 20 / r \ ^ 16 A \ \ 1 ' \ 12 / r z \ 8 / / \ // / ^ ^J__. / , — 1+ '/ y^^ _ -Vis \ \ ^ 5 ----- // / ^ '-^ '^' ~* '^^ ^^ — — N \ ■V. //.^ \ ^ ^- '^ ■> ■ — =■ i,r \ "^ _^'' ^ ^ -1+ V \ ^ ^ / / A \ / / .<^ / \ \ / .8 / ^, / \ / V / \ \ .1+ / \ / / c NAT lONAL £E FOI ADVISC AEROl RY lAUTIC! S, .^ y ■ ■ X X .2 •U 1.0 1.2 .6 .8 Time, t, 3ec Figure 5.- Stick force and normal acceleration due to rapid elevator motion. T = 1 second; V = I4.OO miles per hour; ^a.c.= 0.075c. l.ll NACA ARR No. L4J12 Fig. 6 -.5 ".I4. -.5 -.2 -.1 Restoring tendency, Cv, o o a (D -tj » « o -d t-t (D « •d a « o O rH '+ o rt bO c o •H +» 0) « O O d »4 o -8 1.2 .8 ^ -^ -\ ^ ^ ^ N ,r N, 1 / \ — / - \ \ F. / /' \ V ' !j - N / 1 * / J' \ ^- S. N /- / \ I "v^ ^^^ ~-^-.= \ y \ / \ r- ^ \ / / / "n K y / \ / \ 1 \ \ / 1 > \, / :OMMI TIONAI TEE f ADVII )R AER ORY )NAUTI ;s \ K^ ^ / V - — ___ 12 3 Time, t, sec Figure 7.- Stick force and normal acceleration due to rapid elevator motion. T = 2 seconds; V = l+OO miles per hour; *a.c.= 0.0U2c. NACA ARR No. L4J12 Fig. 8 o ^ J" o a ■p o cd .H to > 4J 4) 4> O T> rH « o t> £> o ^ u •H •P CO bO c o •H ■P 0) c 1-1 o o o d o -1 ■ ^^^ ^ ~-~^ -^ 1+ y ' " ' \ /5 / f '/■■ / \ V •^ N /-^ ■=^ = ''.^j:^^__^ ■ — ^ ^^ ^ -k y \ / -8 \ \ / \_ / -12 ~T^ ' / /'" \ 1.2 / \ .8 / \ \ A / \ ^J / N COMM ;tiona nEE F . ADVt 3RAEfi 50RY ONAUT cs ^ n ^^ -— -^ Time, t, sec Figure 8.- Stick force and normal acceleration due to rapid elevator motion. T = 2 seconds; V = 1+00 miles per hour; NACA ARR No. L4J12 Fig. 9 2k 20 16 12 o O U <0 K\ C\J G O •H OS o o to CO vO xway/^^s OJ o -H O ■P J3 OS u iH O O Ot ^ (4 a. « fi o •H O K J- § II *i > P n • -d u a © o i:^ o a> O CO o U CM O ^ II .i«! Eh O >H ■P • in fi O G *-< 3 -p H a •H O K O Vi -P O "H > fi d ^ & p I OS ^ •H O I -P c o o at > si (D -P ^ UNIVERSITY OF FLORIDA 3 1262 08106 511 1 UNIVERSITY OF FLORIDA nr„-. If ■'■NpfS DEPARTMENT i 2 .TON SCIENCE LIBRARY pB/bOX 117011 C3AINESVIU^. FL 32611-7011 USA / |i