PB No. UB21 NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS WARTIME REPORT ORIGINALLY ISSUED February 19'*-'*- as Restricted Bulletin lfB2l SOME NOTES ON THE DETERMINATICW OF THE STICK-FREE NEUTRAL POINT FROM WIND-TUNNEL DATA By Marvin Schiildenfrel Langley Memorial Aeronautical Laboratory Langley Field, Va. UNIVERSITY OF FLORIDA DOCUMENTS DEPARTMENT 120 MARSTON SCIENCE LIBRARY RO. BOX 11 7011 GAINESVILLE, FL 32611-7011 USA WASHINGTON NACA WARTIME REPORTS are reprints of papers originally issued to provide rapid distribution of advance research results to eui authorized group requiring them for the war effort. They were pre- viously held under a security status but are now unclassiiied. Some of these reports were not tech- nically edited. All have been reproduced without change in order to expedite general distribution. L - 251 \ Digitized by tine Internet Arcliive in 2011 witli funding from University of Florida, George A. Smathers Libraries with support from LYRASIS and the Sloan Foundation http://www.archive.org/details/somenote^ondeterOOIang n^ r-l NATIOPTAL ADVISOR^: CO'''!!TITTEE FOR AERONAOTTCS RE 8 TR IC T^: D BUL L":: TIN SCVIE NOTE'S ON ^IT^ DETFRMTNATIO'iJ OF T'^E 3TJCF-FP.EE F^UTRAL POINT FROI^ WIND-TUN~^EL DATA ^in By Marvin Schuldcnfrei STOSIARY The effect on static lon{-;it-aainal stability of freein*^' the elevator is shown to be similar to thxe effect of altering the slope of tne tall lift curve by a factor that depends upon the aerodyriarnic characteristics of the horizontal taJL surfaces. '['"'he stick-free neutral point may then be determined from stick-fixed data by taking account of the reduction of tail effectiveness. Two graphical niethocEs for determining the stick-free neutral point, which are extensions of the methods commonly used to determine the stick-fixed neutral point, are presented. A rna thematic al form.ula for computing the stick-free neutral point is also given. These methods ma^- bo applied to determine approxiiiiately the increase in tall slse necessai'y to shift the neutral point (with stick free or fixed) to any desired location on an air- plane havinr inadequate Icnr^ltudinal stability. 1 1 JTR ODUC T I ON The stick-fixed neutral p->ol!it vas defined in reference 1 as the center-of-gravlty location at which the stability, as measui'ed by the slope of the cur-ve of pltchlng-moraent coefficient Cj,-, plotted against lift coefficient Or, is neutral with the airplane trimmed. The conditions are stated mathematically as dCj^/dCL = 0, Ci-n - 0. This center-of-gravlty location is the limiting (most i^earward) location at -which varia- tion of trim speed v/lth elevator deflection 5q Is conventional (that is, up deflection of the elevator decreases trim speed and dowJi deflection of the elevator increases trim sneed). The condition thus defined is dSg/dCL = 0, \ Elevator deflection alone, however, does not neces- sarily determine the variation in stick force that will be felt by the pilot. The stick forces required to chanfje speed ar3 nade up of two components: that due to direct elevator deflection, and that due to the change in anf"le of attack at the tail when the attitude of the airplane changes in response to the control deflection. The stick-force variation vo! th respect to speed, conse- quently, depends upon both 6C^/&a^ and d C].y6 5© of the tail, where oCi /'^a^ is the rate cf change of elevator hinge -nor.ent coefficient with tail angle of attack and dC- /d6^ is the rate cf change of elevator hinge -moment coefficient with elevator deflection. The neutral point with the stick free (elevator free to flort) is related to that vdth the stick fixed, for tixe conditions to be met 'Aitii the stick free are, mathematically: dCj^/dCL = '■'> ^ri " ^> ^h = . The condition thirds defined is d6rp/dCj, = 0, where 5tp is the trim-tab deflection. 'rl' s present paper shows how the third condition G}-. = may be taken into account as an extension to the methocis of determining the stick- fixed neutral point of reff-rence ] . For the purposes of this reoort it is assumed that ■^Ch/fboe and <^Oyi/<^ctt ^^^ constant at any particular lift coefficient being lnve;stigateQ regardless of the angle of attack at the tail or the elevator deflection, that tab der]ection has negligible effect on tail lift, and that the elevator is statically balanced. The other qi^.alif ications in the use of the methods are given in reference 1. The s^raibols used in this paper are defined as they occur in the text and are suriunarized in the anpendix. TAIL EFFECTIVE^TESS VIITH FREE ELEVATOR The pitching momenb contributed by the tail and the increment of stability contributed by the tail are seen to be directly proportional to the slope of the tail lift curve cC^ /oa^ from equations (17) and (l8), appendix A of reference 1. The relation betv/een the slope of the tail lift c-urve v;lth elevator fixed and the slope of the tail lift curve with elevator free may be found as folloivs; In general, with the elevator fixed, and at any dynamic [r\ pressure, CM I Ct, = 3 at + -r^5e (1) J-^t 6at 6og. ^ and the associated hinge -niorr.ent coefficient with elevator statically balanced is C = __iia, + —^5q + --^Qru (2) h Ar, . t A .=^ ^ A ,f, J- ' da^ ^ 65g " 6 5^ If the elevator is allowed to float, with a fixed triri- tab setting, the left-hand member of equation (?. ) may be equated to zero, whence 06 663 / Combining equations (1) and (5) yi£ld; Cl^ = 7r;-^a, - -x^i -^~- 4- -^i— i (k) [f equation (.'4) is differentiated -with respect to a^ , -t ""^h da. J t/f rjSg oat 6 0.^ 6^e (5) The ratio of (dCr /da^. )^ to dCT^/da4. is then x.^ t f -.■(-, Is) -— = 1 (6a) which raay be written as k = 1 - R (£b) where Cy lift coefficient cf korizontsl tail v/ith elevator ""t fir.ed C-r lift coefficient cf horizontal tail vrith elevator ^f free to float Cy, elevator hlnr-e-iaoriient coefficient ttj. angle of attack of tail with respect to relative v.-ind st tail L> 5y elevator deflection with reepeot to statllizer chord line 6^ tab deflection wi-G:^ respect to elevatoi' chora. line dOj rate of change of tail lift ccofficient with tail "'"^ angle of attack, elevator fixed 6 at 6Cj \rate of change of tail lift coefficient v;lth tail '"*"• I angle of attack, elevator free 6Ct rate of change of tall lift coefficient with . ""^' elevator deflection, a^ fixed 65q dCj. rats of charge of slave tor hln^e-DCinent corlT icient — •;— with tail angle of Rttai-'.i', elevator and tab fixed H ^^ I oCy, rate i^f charige of elevatoi-' hincro-ruomont coefficient ^"^ T~—^ wi'ch ele-'ator deflection, an^ie of Fttacl^ end '^'^'e tab fixed dCj^ rate of change of ele'^ator hinge-ri:oment coefficient -r:— -f'itY'. taj deflection, angle of attack and elevator T dei lection fxxfcc ''^C. ^ '^^ k elevator-free effectiveness factor R — A dC-J^a-^ 5cy^£e It may be seen frr'rn s -i'latlo/is (c) that the e.-^fective- ness of the tail v;ith elevator fr^ee in prodncing ].ift (and hence stability siiC p.loChin^; iixomont) is related to the eff ecti'-eress cf tiie tnxl with ele''''ator fixed by a factor k dependent upon tho asrcdynar.-'.ic characteristics of the bcri::;ontal tail az-^d elevator. Further^ it may be seen that this lector is inde;-)endem: of ol' e trim-tab setting, stabilizer setting, and dj-na.nic pre 3 sure at the tail, if the dynaiaic-pi'essure ratio is fairly unix'or.ri over the tail. The neu+-.rsl point vvith tbe stick free inay then be determined b^" rectifying data f r Tih conventional cests with elevator fix.^d according to the factor given in eq^uations ( 6 ) . DETSRKlKATIOr 0? STICK-FHEIL KEUTRAL ?OIi'T !.:sthod 1 AssTjme that ccnvantlozial pitching-inoment curves of the forri shov/n in figure 1 have been obtained for a model v/ith elevator fixed. (These carves are for a fictitious airplane . ) ' It has been shown in refsronce 1 that, if (^Cj^/cICt') is plotted against G /C-i- for t\/o elevator (or stabilizer) settinp-s at a given C-r (fig. 2), the location of the center cf gravity for neutral stability is the point where (^^C.^n/'^'-'L) ^^ equal to (^j^/Cl? that is, the neutral point is the point of intersection betv/een a straight line connecting these two plotted points and a line having the equation fdC^/dCj\ = C^/C-^. In figVcre 2, the neutral point is given in choi'ds forward or rearward of the center of gravity about which the data are given, depending upon v;hethor C^,j/Cj is positive or negative at the point of intersection. The value of dO^/dC^ and C^jj/Ct for the tail-off curve is now plotted in figure 2; the values are taken at the same Gt as for the two elevator set- tings. For this example, Cy is selected as 1.2. Prom figure 2, it is apparent that the contribution of the tail to stability is the difference in ordinates between the tail-off and tail-on points plocted, v/hereas the contribution of the tail to pitching moment (plotted as Oyri/C-^) is the difference in abscissas. If, then/ the action of freeing the .ilevacor is represented by a decrease in tail effectiveness as has been shown, these values of the differences In ordinates and abscissas may be multiplied by the effectiveness factor k. The result obtained Is the equivalent of multiplying by k the length of the dashed lines a of figure 2. As an example in the use of this method, assuiiie that the following aerodynamic charactei'istics have been determined for the tail of the airplane of figure 1 (the methods for obtaining these characteristics v/ill be discussed later): ^C-^/ta.^ = -0.0012 dCj, /6a^ = 0.0630 6c>yd5Q = -0.00$0 dCj^ /do^ - 0.03^0 Then, from, equations (6), k = 1 - ■ = 0.80 -0.0012 0.03'; -0.0050 b.o68 7 and R = 0.20 which jndicates that the slope of the tail lift c.vrv3 with che elevator free is Ro pere^ent of that with the elevator fized. If this factor is applied to the dashed lines of figure 2, a new line is obtained; the intersection of i;his line ^vjth the line deteriiilnes the stick-ft'ee neutral point. F'rora figure 2, it ma7y- be seen tliat the stick-free neutral point is for- ward of the stick-fixed neutral pc int about O.OSl;- (or ').h,- percent) of the mean aerodyna^nic chord for this examole , Method II It has been shown in reference 1 that, if the tan- gents to t'.7o or more elevator (or stabilizer) cui^ves at a given lift coefficient are extended until they meet (fig. 3)> the slope of the line drawn fr'Q-ai this point of intersection through (Crn = 0, Ctj = 0) gives the loca- tion of the stick-fixed neutral point in cho^-'ds forward or rearwerd of the center--of- gravity location about which the data are coinp^ited. The principle.^ involved are the same as those used to obtain neutral points by the niethod o f f 1 gur e 2 . It can be shown that, if the tangent to the tail-off curve at the Cl undei' consideration is extended to a point having the same abscissa as the point oi' inter- section of the tangents to the elevator curves, the difference in ordinates of the two points b is pro- portional to the elevator- frje e'f'fectiveness lactoi' k (fig. 5). For the fixed-elevator condition, k ~ 1.0. V^Tith the elevator free, the vali.ie of ]<:. determines a new point through v.'hich to draw the line through •'-'111 ~ ^> ^L ~ ^^ ^'^ order to find the neutral point. For the examxple under consideration (fig. 5)> the dif- ference between stick-free and stick-fixed neutral points is again seen to be equal to ';..'.(. percent of the mean aor O'l-^-^nQxax c chor d . T'ethod III A mathemctical analysis to determine the shift in the neutral point due to freeing the elevator, which takes into account the variation of dynamic-pressiu'e 8 ratio at the tail, has been made in reference 2. The neutral--Doint shift has been shown to be ^^P " ^^P. - ^^P \ Pf ^datJ qo cicTTda V^ " da/ '^t / d— /dC. (7) , _,%, q.f /a. where n neutral-T^oint location, cbcrdc behind leading P edce of mean perodynamlc chord, stick fixed (:■: in reference 1) n„ neutral-point locaticn, chords behind leading edge of mean aerod^mamlc chord, stick free Anp shift in neut-'^a] point due to fi^eeing elevator C^Ff - -p) ^t increase in slope of tail lift curve due to ^6 at / dCL.X freeing elevator i-R-r — — ■ j \ °^t/ V tail volume f ^- — ) 3^ horizontal tall area 3 vving area l^ tail prm c" mean aerodynamic chord of wing q^ average d"namio pressure at tail coinpared with ~~~ free-stream dynamic pressure '^o 9 q,o rate of change of q^-Zo^Q with airjjlane C^ £^, slope of lift curve for coraplete airplane da d g rate of change of averare dovmwash angle at da tail v/ith airplane angle of attack If 'It/'^o ^^^^ ^^"^ constant value 1 fas for v/indrnilling conditions), equation (7) reduces to An^ = A^^ f-- (l-^) (8) P da^ AC-^/da \ da/ Inasmuch as (9) and d£ da _ "^^^t dCL/da dC^ then equation (7) becomes dCyvi da^ ^^ dlT dcT An^ ^- • (10) 1 '^t/^ o Cl where dC^ rate of change of pitching-morr'ent coefficient — — with stabil.izer angle, at any particular -■■t airplane C-r, elevator fixed 10 \ da^ rate of change of tail encrle of attack v;ith /l - 21\ Icient [- TT— j dC^ ainlrne lift coeffj rffiTHODS FOR DETSRMININCx TAIL CHARACTERISTICS AND FACTOR R Aerod^-ncmic characteristics, such £S c)Cj^/6a^ and dc^/^Sg, mentioned in the present paper (except i or dC^/di|- in equations (9) and ( 10)) were based on actual d\Taa.nic pressure at tlie tail. Thus these would be the values found in tests of ^n isolated tail siorface. In tests of a ccrrplete nodel, hov;ever, the dynamic pressur-e at the tail v;ill influence the hinge ;iior>:ent and lift produced per degree of elevator or stabilizer variation; and the dynanic pressure will vary, in general, v;ith airplane attitude. It is then necessary to determine the vali;e of the tail characteristics and K under conditions where ^t/^lo ^"^ ^'"^^ tail varies, as it would on the acttial sii'planc. The valu.e of the factor R has been shcv.n to be ■:: TT r rr — . Ta3 ratio -r r;— — IS inaeDendenu of the dynamic -pressure ratio. The value of -v— ^-7 may 6c^yo5e be determined from elevator and stabilizer tests by taking the ratio at any lift coefficient or finding the average at several lift coefficients of the airplane, if the hinge -moment-coeffici.ent variation is linear. Bv the same reasoning ^ is independent of It'^'lo ^^ 6Ci^/6at the tail if it is assuiried that ^t/lo -- fairly unlforiii over the tall span and, further, "^^L+-'''^e -^^ directly proportional to dCvj,/di^. Thus ^C^t^e _ 53v^ e 6Cj^_/6a^. dCjvj/dit rj 11 dCp./d5e and the ratio — , is constant at any ^^alue of airplane lift coefficient. If the actual values of dCh/dat and dC^/dCe (with respect to the actual ^^alae of the dyi.amic pressure at the tail) are desired f^^om wind-tunnel data obtained from tests of complete models, they may be found from the re.lationship d5g ~ qtAo exn and, similarly ^ = (^^h/^ ^t)exp ^^t ^tAo If the' values for dC-./dS^ and dCT./C.aj- are desired .; frcin vdnd-tunnel data, the follo'-.ring relations apply: ^ at qt^^ q o and, similarly. ^' ^e ^t DISCUSSIOM 0? ',l!.THCDS It may he ad-'^antagoous at this point to indicate the physical significance of the operations performed by these method? for finding the stick-free neutral point. 12 \ Basically, it is desired to obtain tv/o or more curves of Cm plotted against Cj;, for the KiOdel with the elevator free to float, because, v;ith the controls free, an air- plane must fly with zero elevator hinge moment, flight speed or attitude can be changed only by varying either center-of-,p;ravlty location, trim-tab setting, or stab- ilizer incidence, for any particular airplane configiu-^a- tlon. Control-free flight may be reproduced in the wind tunnel by obtaining two or more pitching-rnonent curves with the elevator free with different trlra-tab settings (or stabilizer Incidences), and the neutral points with the stick I'ree may be found directly by the m.ethods of reference 1. This procedure r.isy also be used In flight to determine neutral points with elevatoi' free. . The air- plane may be flown with several center-of-gravlty loca- tions and the trim-tab settings required for trim may be determined throughout the speed range. Because an airplane can fly steadily only v/ith Cm - 0, the out-of- trim. pitching-moment ci^rves as obtained from wind-tunnel tests need not be determined. The neutral points may be determined directly as tb :; center-of -gravity locations at which the variation of tab angle required for trim does not change v.'ith speed (do.-^/dCT - 0)* Similar tests can be made with a vind-t'unnel model if the elevator is statically balanced and allc\^ed to float freely with the tab at various settings. The nltchlng-moment curves obtained m.ight then be handled in the manner described in reference 1 for the determination of stick-fixed neutral points. This method has been avoided, in general, because of the necessity for increasing the length of the test program but may be the onlyf satisfactory method to follow for models having nonlinear hinge -moment character- istics. By applying the m.ethods previously described it is possible to determine the stick-free characteristics graphically or mathematically from, the stick-fi;:ed characteristics, provided that the hinge moments of the elevator have been determined during the elevator-fixed tests made v.ith various stabiliser and elevator settings. .'.Ithough the lift characteristics of the tail of v/ind-tunnel models have been foTUid to represent fairly closely those of the tall of the actual airplane, the hinge m.oments have been found to be critically dependent 13 upon the acc-urate representation of the tail-surface dimensions, v;lth resnect to such details as pap, thick- ness, and trailing-edge angle. Further, the effect of scale may distort the r.iodel hinge -rr.oment characteristics even if the tail configiiraticn is rsproducod with the iTiaxi^iujn of accuracy. It 'las, consequently, been fotind desirable at times to test isolated tail surfaces of relatively large scale and to apply these data in con- junction Vifith sma]l-8cale complete -model data to estimations of flying qualities of the airplane. It is ' apparent that the aerodynamic characteristics of the large-scale tal^. surface with respect to stick-free stability may be represented to a fair degree of accuracy by determining the valn.e of the constant k. The effect of tho free-floating elevator on the location of the neutral point mjay then be found by the methods described if the tail-fuselage interference effects are approximated. The effects of tail-fuselage interference have not been subjected to rational analysis. Some approach to the Interference effect maj?' be made by testing the large- scale tf'il siorface in the presence of a stub fuselage, for conventional airp.lanes, or in the presence of stub booms, for tv«in-boom airplanes. If such tests are not possible, the effect must be estimated. The effectiveness of a tail surface as m.easured by the slope of the tail lift curve v;ith elevator fixed may prove to be different in the tests of a large-scale tail model from that obtal?ied from tests of a small-scale complete model. In this case the effects may be taken into recount and the wind-tunnel results corrected graph- ically by considering that the difference is due to an increase in the factor k , or mathematically by the use of equation (7) where A-r — '-- is the increase or decrease oat in *^CL4./<^at obtained fro;n tests of the large-scale surface over that obtained from tests of the sm.all-scale complete model. Also the size of the tail surface needed to shift the stick-fixed neutral point to any desired location may be determined approximately by considering a larger sui^face as having an increased effectiveness and solving graphically or by equation (7) again. Langloy Memorial Aeronautical Laboratory, relational Advisory Committee for Aeronautics, Langley Field, Va . Ik APPEroiX SYi'IEOLS Cjy, pitchinp-moirient coefficient Ci lift coefficient Ct lift coefficient of aoi- j.zo^-itr.l tajl, elevator ^ fixed. lift coefficD'ent of horizontal tail, elevator f free to float -x 'H C^ elevator 'h.in£':e-mor:ient coefficient a^ angle of attack of tail with respect to relative wind at ta:j 1 6g elevator de'''lechicp vuith respect to stabilizer chord lino (positive v.-ith "".E. dovm) 6rp tab deflection with, respect to elevator chord line (po.sitive vath T.E, down) ^^Lt — rate of change of tail lift coeff.'cient with °^t tail angle of attach, elevator fixed l-T — -J rate of change of tail lift coefficient with V ^t/f tail an3:le of attack, elevator .free > ^^Lt -r rate of chan^^-e of tail lift coefficient with ^^3 elevator deflection, a^ fixed r — — rate o.f chanre o:^ elevator nin.re-norr.ent coef- ^ *^t ficient with tall angle of attack, elevator and tab fixed ^;—- rate of change of elev:.tcr hing-e -mcn^ent cosf- " e ficiont with elevator deflection, ar.,f^le of attack and tab fixed 15 ^ rate oT change of elevator hango-rioirent coef- ° ^T fie lent with tab deflection, angle of attack and elevator deflection fixed ^ k o].evator-free effectiveness factor (1 - R) I 1-1 R = X original centtr-of-r;ravity location about which data are given, chords behind leading edge of mean aerodynaTnic chord n neutral-point location, chords behind leading edge of mean aerodynamic chord, stick fixed (Xq in reference 1) n^ neutral-point location, chords behind leading ^ edge of mean aerod77nar.:ic chord, stick free An shift in neutral point due to freeing elevator A-^ increa.^e in slope of troM lift curve due to cat / 6Ci freeing elevator l-tW I V S^ horizontal tail area S wing area l-t tail arm c" mean aerodynamic chord of vv'lng ii. angle of incidence of staciliiier (stabilizer setting) with respect to horizontal reference line of model (positive with T.L. down) q-t average dynajtiic pressure at tall compared with "~~ free-stream dynamic pressure 16 — - rate of change ox ^f -o with airplane Cr da d£ da dCm \ slops cf lift curve foi' complete airplane rate of change of average downwash angle at tail with airplane angle of attack rate ol' change of pitGhing-raon:ent coefficient t with stahiii^OA^ Gng;le at any particular airplane Ct,, elevator fixed dCm — — rate of change of pitching-moment coefficient ^^Q with elevator angle at any particular airplane C-r , Stabilizer angle fixed da+. rate of change of tall anz-^le of attack with aC^ '^ A - ^A airplane lift coefficient I da \ Subscripts ; 1,2 elevator settings X referred to center of gravity about which data are presented exp experimental values 1? RSPERENCES 1. Schuldcnfrel, Marvin: Some Fotss on the Determination [rx of tlie Stick-f^lxed ■Teutral Point from Vjlnd-Tunnel 7 Data. FACA as Nc . 3120, Sept. 1943. 2. Gf-tes, S. B. : An Analysis of Static Lnnt^itudinal Stability in Relation to Trim and Control force. Part II.' En-^^lne On. Rep. No. B.A. 15i;.9, R.A.E., Stpt.'l959. \ NACA Fig. 1 H LPs I -p a >, g" •H O > tJ fH to csi O trH ^1 .-. ■P o • o (D C • 4^ -H t:5 - c a) -4J ^1 + f^ -C o o ,e! o o o •H .■^ Q •H n 6 o u 1) o O j O o ^0 ':^TisTOTjjsoo ^uoraom-.'^uiqcq.ij o o [in N NACA Fig. 2 \ iTACA ^0 'q.u3iox^j900 ^uauiom-SuxT:[O^T;£ M f\3 r-H O Fig. q - — \ UNIVERSITY OF FLORIDA 3 1262 08106 489 N. UNIVERSITY OF FLORIDA DOCUMENTS DEPARTMENT 1 20 MARSTON SCIENCE LIBRARY '''•O. BOX 117011 GAINESVILLE, FL 3261 1-7011 USA