1、I. .I.iI.!./.,NATiOUL ADVISORY COMhTiE FOR AERONAlilCSWAlrmm Iuw(m”r. ORIGINALLYISSUEDSeptember 1943 asRes whereas the other method is agraphical solution-for the same mathematical equation; Amethod is als”ooincluded for determining the vertical vari-ation of the neutral point. The combined horizont
2、al andvertical variation of the neutral point completely describesthe stick-fixed longitudinal stability of airplanes thathave large allowable center-of-gravity shifts.INTRODUCTION?The concept of the neutral oint has been treated inreferences 1 to 4, and its usefulness in the analysis ofstatic longi
3、tudinal stability, especially with regard tothe effect of power, has been proved. The determinationof the neutral point from flight data is discussed in ref-erence 3; whereas reference 4 presents the methods usedwithwind-tunnel date.The p-resent report offers two simplified methods ofdetermining the
4、 horizontal location of the neutral pointfrom wind-tunnel data plotted as pitchin-moment coeffi-cient Cm againet lift coefficient CL for severalstabilizer-setting tests with the elevator neutral: themethod applies equally well to tests made with variouselevator deflections with the stabilizer settin
5、g fixed. Amethod is presented for determining th”e vertical variationof the neutral point. The combined horizontal and verticalvariation completely describes the stick-fixed longitudinalstability of airplanes that have large allowable center-of-gravity shifts.Provided by IHSNot for ResaleNo reproduc
6、tion or networking permitted without license from IHS-,-,-/2.,. .The neutral point is defined as the location of thecenter of gravity of the airplane when the airplane istrimmed (Cm = O) and when the stick-fixed stability asmeasured by dC#dCL about the center of gravity, isneutral (2= 0)= Data obtai
7、nedfrom vind-tunnel testsare usually plotted aq Om against CL for several 6ta-bilizer settings at a specified center-of-gravity locatiop.The neutral point may readily be determined from thesedata provided the assumption is valid that the rate ofchange of the slope of the pitching-moment curve (about
8、 agiven e.g. and at a given lift coefficient) is constantwith stabilizer” setting it. !lhat this assumption is validis proved in appendix A, in which the slope of the taillift curve is assued to be constant, a condition whichusually holds up to the region near the stall of the tailsurface. If the da
9、ta are obtained for unstalled conditionsof the tail - which can be attained. by proper choice ofstabilizer settings - the neutral-point d6termiGations will Qbe valid. The symbols used. in this paper are defined as they occur in the text and are summarized in appendix B. .HORIZONTAL LOCA!?IOU OF NEU!
10、BALPOIIJ!IEetkod IConsider the two ar-oitrary curves of Cm against CLfor different stabilizer settings shown in figwre 1 and .suppose that the neutral point of the airplane is to bedetermined at some lift coefficient CL = 1.2. . It is appar-ent that, at CL = 1.2, the airplaG is untrimmed (Cm + 0)for
11、 both stabilizer se tin s7dcF: t5Rt , as is general forpower-on conditions, .dcm ; at CL = 1.2 depends upon,stabilizer settin . E$ea if m were zero, moreover, thevalue 02 (dCm/d,-”w :d :i:-ure 2, the neutral potnt is give in chrds forward orrrearward of t:ne center of gravity about which the data ar
12、egiven depending upon whether Cm/CL iq positive or negativeat thepoint of intersection,Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-4If more than two tabilizer curves are availa%le andthe values of!0dCm/dCL x against Cm/CL do not form astraight li
13、ne a in fig re 2, a curve must be faired throughthe poi ts to determine the intersection with the,line)dGm/dCL x = Cm/CL. In this case, the variation of taili.ftwit tail angle of attack is not linear. All the for-mulas presented herein, however, assume the usual aonditionthat all points fal on a str
14、aight line. 4,uIt has been shown that the neutral-point is the solutionof a set of simultaneous equations, which are represented inFigure 2 by the two straight lines. One line hast?:;.$?al -as the coordinates ofone point andas the coordinates of another point.quation of a line passing throughthese p
15、oint; is.(%32-G?.=sThe equation for th other line is.(5)(6)Equations (5) and (6) are solved simultaneously to obtainan expression for Cm/CL for neutral stability, which isthe equation for the Ustatic marginll specified in refer-ence 4. Substituting the eqresion for L ,fo.r .neutral stability in equa
16、tion (1) ieldso=x- (7).Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.5/0.3ar;-1d, whereo location of neutral point , chords behind leeding edgeof mean aerodnamic chord #Cml untrimmed pitching-moment coefficient at. CL f-or sta-bilizer setting 1 (m
17、easured from Cm = O)c uutrimmed pitching-moluent coefficient atla= CL for sta-bilizer setting 2 (measured from Cm.= O)()dCm slope of stabilizer curve-1 at CL (measured fromCL 1 horizontal)Method II . A After the neutral points have been located along ahorizontal line parallel to the thrust or refere
18、nce line,the next step is the determination of the vertical varia-tion of the neutral point.If the moments about the center of gravity are trans-ferred to a center of gravity y chords “below the orig-inal center of gravity, Cm ecomesc =mb c -1-Ccya (8)where subscript b denotes the pitching-moment co
19、efficientabout the lower center of gravity and subscript a, aboutthe upper center of gravity. ThenG%). = (!%)a + 2 ywhere the chord-force coefficientcc = c cog - cL sin or approximatelycc cD- CL :r$ir?-+?” :=Yl?rom fiure 4,andCm Cm2 1 - .,-1. dCm()cm - Cmp.2 =dcL cL - c ph%btracting gives(1 - .,.”-
20、. .-.”. .4: , ; f: : =- .!.: -7-. . . .-. ,-. . . . .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.(“JA (%d%)l: (CJCJ*slope of curve of Cm agaiustter of gravity at xnslope of stabilizer curve 1 atured from horizontal)slope of stabilizer curve 2 at
21、ured from horizontal)13CL for cen-. (meas-L (meas-Cm untrimmed pitching-moment coefficient at CL for.L stabilizer setting 1 (measured from Cm = O)Da untrimmed pitching-moment coefficient at CL for“ stabilizer setting 2 (measured .from Cm = O)Cilia pitching-momeqt coefficient at original center-of-gr
22、avity levOlfor ,a given set- of conditions (C%t,.c etc.) . .ms . . .Cmb c trs.nsferred vertically (with respect to horizon-s . :tal.“reference line of.model-).to a lower. . . center of gravity ”(d%ide$a fllOPe.Of curve a% Cya :“(dcfc.)b “ : “slope of curve at cmb . .c chord-force coefficient (CD cos
23、 ct- CL Sin )CD drag coefficient3 vertical center-of-gravity movement, chords downwardfrom original center of gravitya angle of attack of horizontal reference line of model,degreesq o angle of attack for zeno lift, degrees,/”L rate of change of drag coefficiet with liftcoefficientAx horizontal chang
24、e in neutral point for a verticalshift in center of gravity of Y chords, chords -Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-14 . .2c CLP coordinates of point of intersection of tangents .P to 8 series of stabilizer curves at a givencl .REFERENCE
25、 S1. Gates, S. B.: An Analysis of 5iatic Longitudinal Sta-bility in Relation to Zrirn and Control Force. Part I.Gliding. Rep, No. B.A. 1531, R.A.E., Apr. 1939.2. Gates, 5. B.: .An Analysis of Static Longitudinal Sta-bility in Relation to Trim and Control Force. Part 11. -Engine On. Rep. No. B.A. 154
26、9, R.A.E., Sept. 193% “3. Allen, Edmund T.; Flight Testing for Performance andStability. Jour. Aero. Sci., vol. 10, no. 1, Jan.1943, pp. 1-2.4. .4. Kayten, Gerald G.: Analysis of Wind-Tunnel Stabilityand Contrpl ?ests in Terms of Flying Qualities ofFull-Scale Airplane8. lT.U2.i,lN QL-?44c!?.Figure 3
27、.- Graphicalo .4 .8 1.2 1:6 2.0Lift cofficient, cLdeterminaion of horizontal location ofneutral point by intersection method. wProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-N/mCenter-of-gravitylocation,Pecent MJ.C. back of L.E. of lLA.C.I!I.20 246
28、28 32 B614 Neutral point from figure 2 at CL E 1.2*F* to Thrust+&z SineI +y4 I I i &=I -0.25+ I Y. -8 12 L_-1 $t16 1I,Figure 4.- LOCUH ofthat is,center-of-gravitylooations for neutral st&3tliiyJ 100us of neutral points.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-
