1、,.-r. . .,.NATIONAL ADVISORY COMtilitt* FOR AERONAUORIGINALLY ISSUEDMarch194!jasESTIMMIOI?OFSIWK-FIKEDllmrRALPOINJ?SOFJmu?LAmsByMauriceD.WhiteL-y MemorialAeronauticalLaImratmyLameyField,Va.,.-.NACANACA WARTIMEREPORTSarereprintsofpapersoriginallyissuedtoproviderapiddistributionofadvanceresearchresult
2、stoanauthorisedgrouprequiringthemforthew= efEort.Theywerepre-viouslyheldunderasecuritystatusbutarenowunclassified.Someofthesereportswerenottech-nicallyedited.Allhavebeenreproducedwithoutchangeinordertoexpeditegenerdistribution.L-116 . . . . . . ., . .,-, , . . . .#Provided by IHSNot for ResaleNo rep
3、roduction or networking permitted without license from IHS-,-,-a a71NACA CB No. LCOlNATIONAL ADVISORY COM3i%TTiE*.” “ .*,. J“* FOR AERONAUTICSESTIMATION OF STICK.-FIXEDNEUTRAL POINTS OF AIRPLANESBy Maurice D, WhiteSUMMARYDw.A method is.given for calculating the stick-fixedneutral point of an airplan
4、e with propeller windmilling,flaps neutral, and landing gear retracted. This methoddiffers from those formerly used principally in theprocedure for estimating the effect of the windmillingpropeller. Comparison of the neutral,points predistedby this method with neutral points obtained In flighttests
5、indicates good agreement at low lift coefficients.The methods presented, In conjunction with the resultsgiven in NACA CB NQ. HOl lEffectof Power on the Stick-Fixed Neutral Points of SeveralSingle-EngineIlonoplanesas Determined in Flight,“ should be useful in estimatingthe stick-fixedneutral points o
6、f new designs for allflight conditions,Since the publication of reference 1, in which amethod was presented for predicting the static longitu-dinal stability of airplanes, additional flight data onthe longitudinal stability of airplanes have becomeavailable. Attempts to correlate these longitudinal-
7、stability data with the longitudinal-stabilitydata com-puted on the basis of reference 1 indicated that themethods of reference 1 were inadequate when applied tounconventional designs. A more rational method hastherefore been developed for computing the longitudinalstability of airplanes in terms of
8、 the stick-fixed neutralpoint, which yields results in good agreement with flightresults. This method differs from the method of refer-ence 1 chiefly in the procedure for estimating the effectson longitudinal stability of the windmilling propellerand of the fuselage and nacelles, although the differ
9、encesin change in longitudinal stability-due to the fuselage.W-.4 . *,w.,q z,:wingfuselagenaoellehorizontal tai1propellerpropeller normal foroedownwash due to propellerwing leading edge ,midchordpoint of lecal chordwing trailing edge. . .Provided by IHSNot for ResaleNo reproduction or networking per
10、mitted without license from IHS-,-,-4 NAOA CB Oo L5C01COMPUTATION OF NEUTRAL POINTThe neutral point of an airplane is defined as thecenter-of-gravitylocation at which the slope of the curveof airplane pitching-mmnent coefficient against lift coef-ficient d/dCL is zero. This airplane pitching-moments
11、lope is tb.eresultant of bhe.pttching-rnomentslopescontributedby the variousparts of the airplane, Inorder to predict the neutral point of an airplane, theestimated values of,“bCL due to the various parts ofthe a?.rplanemay b+ combined at each of several center-of-Sravj.tylocat$ons and the neutral p
12、oint may then beestablished as the center-of-gravityIocatfon at wh!chthe resultant value of ddCI, is zero. A procedureequivalent to this procedure for determining the neutralpotnt is illustrated in figure 1, where the valuesof bCCI, for the variousparts of the airplaneare plotted against center-of-g
13、ravitylocation. Thecenter-af-gravitylocation at which the total of thepositive values of ?lCdCL Is equal to the negative ofthe total of the negative values of /tiL - that is,at which dCm/dCL is equal to zero - is the neutralpointa71,Detailed procedures for calculating the valuesof bO CL due to the p
14、rincipal parts of the airplane -wing, fuselage, nacelles, horizontal tail, and propellers-are given herein, The methods apply best at low liftcoefficientswhere the airplane drag coefficientmay beconsidered not to vary with lift coefficient, theparameters involved in the calculationsare most nearlyli
15、near, and the effects of air-flow separation are at aminimum. The airplane was assumed to operate with pro-peller windmilling, flaps neutral, and lauding gearretracted. Negative changes in pitching-moment slope arestabilizhg and positive changes are destabilizing.%e values of Cm/ijCL for the individ
16、ual partscomputed by the following methods are based on the valuesof dCL/dU for the wing alone. In order to determinethe actual value of bC#dCL based on the total lift ofthe airplane the values of d/bCL computedby thepresent methods should be multiplied by the ratio,.-.“. .“.Provided by IHSNot for R
17、esaleNo reproduction or networking permitted without license from IHS-,-,-r NACA CB NO, L5C01 5,This correction does not affect the location of theneltralpoint as dete:lminedby the pesent methods becauseat that center-of-ravity location the resultant valueOf dCm/dCIJ of zero would be unaffected by t
18、he correction,t-.-.,M.“.e methods described in the Present report are effective for predctln stick-ftxed neutral points at.low lift coefficientswith propeller windmilling, flapsneutral, and”landing gear retracted. Inasmuch as thestick-fixed neutral point generally remains fixed or .moves.back With i
19、ncreasing lift coefficient in this con-ditioh offliht (reference 2), the results obtained fromthe present methods will be conservative for the higher .liyt coefficients.The effectSofPoWeIon the neutral-point locationcannot at the present time be predicted by methods com-parable to those given herein
20、. 13ythe use of data givenin refeence 2, however, it should b6 possible to makereasonable preliminary estimates 02 the shift in stick-flxed neutral point due to power.A knowledge f the elevator hinc-moment character-istics is essential for determj.ningthe shift in neutral,potnt due to freeing the el
21、evatorP3.tchin-momentslope due to wing.- At a givencente=oavity location the value ofthe pitching- “moment slcpe due to the wing with flaps neutral(bCm/bCL)wianmerilly equal tthedist.nce betweenthe center of gravity and tl.ewing aerodynamic centerexpressed.as a fraction of the mean aerodynamic chord
22、.For the present purposes it has been fcund”satisfactoryto consider that the wing aerodynamic center Is locatedat a,erc.entaeor the mean aerodynamic chord equal tothe average of the percentages of the chords at which theaerodynard.ccenters of the root and tip airfoil sectionsare locatad. For center-
23、of-gravity locations behind thewing aerodynamic center, (%JU)lv is positive.,. ., ,. , . ,Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Pitthing-moment SIOpe due tc falsele-.to tinenacelles may be expressed by(1)The value of () dll” is calculated d
24、irectl by theq = f, nacmethods of reference 5. According to this method theIfdrUvalue of - -q f, nac may be conputefifrom(2)where the inteal is tkenalong thieenti.rlenh ofthe fuselage or nacelle.It is convenient in evaluating equation (2) todivide the fuselage or nacelle into finite sections.The fac
25、tor w2x is then calculated for each Scctton dzwtth average values of w and dp,ida used or each.section and, finally, the values o.? #w2Ax for allthe ssctions are totaled. ,The factor d/da represents the variation withangle oiattack of air-flow angle relative to the X-axisof the -fuselageor nacelle;
26、in the calculation of dida,it is assumed that fuselage - or nacelle - interferenceffect my Be inored.?letweenthe wim leadin,?edrband trailing edg,.where the flo follow; the wifigsfiface,d!3da is considered to be zero. 3ehind the winp trailinge the value of d/da is assumed to vary linearly from . ,-z
27、mo at the wing triling edge to (1 - %), at the tail.The discrepancy between the assumedlinearrariationand .-tha actual variation of d/da behind the wing willnormally he of little importance because, for conventionalProvided by IHSNot for ResaleNo reproduction or networking permitted without license
28、from IHS-,-,-a71BTACAC3 No. L5C01 7fuselage arrangements, this portion or the computedfuselage moment is only about 10 percent of the entirefuselage moment.Aheadof the wing,values of d/da are greater than1.0 because of the upwash induced by the wing; the variationof dda with distance from the wing l
29、eading edge isgiven in figure 2,.which is taken directly from reference 3. Figure 2(b)is used for all sections except the sectiondirectly aheed of the wing leading edge where values ofd/da rise sharply as the leadfng edge is approached.For this region an aerage integrated value of alp/da,x rld in de
30、termining alp/dainfigure 2(b) the valueof xl used in calculating the abscissa is the distance :from the wing lqading edge to the middle of the fuselage.-. section considered.The curves in figure 2 correspond to a wirqglift-. curve slope of 45per radian. In order to correct forothr values of the lift
31、-curve slope the values given bythe curves are incres.sedor reduced in direct retio tothe lift-curve”slope.An additional factor accounting for the eff?ctofthe fuselage or nacelle on the wing becomos importantwhen the width of the fuselsge or nacelle is not uniformalong the wing chord, According to r
32、eference 3 this factor is computed by(3)-9A.When the pl.m form of the body shows 10CQ1 protu-berances in width directly ahead of the wing leading edgethe application of equstions (2) and (3) Is believed toresult in exwzgeratad velutisof the destabilizing efiect.For such cases, reduction of the incre
33、ment due to theprotuberance ob.tainedby calculating the factors withand without lienrotuberancb) by ens-half appears toresult in more nearly correct values This correction,. .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-8 liACACB 0. L5C01?wh.fch i
34、s based on ver scant data, is subject to modifi-.cation as mere data are obtained,?urveF for estimatins the wl.w liit-curveS3.0J3 dCE,/da as a functton of aspect ratio are Civen infiyura 5. These CUPVeS were o-otaj.nedfrom the ex.presionend at-l-m:e.smct ratios.were corrected,The various terms in eq
35、uation (4) are calculated asfollows:q.t-.q A value of O.$1is used fcr the conditicn ofVrlP.dm.ii?!.infqpropeller.acwt 3CytCurves for the evaluation f 3G are civcrIinfiqures 3 and k.g Valu9s of Cda at the tafl nay be estimated fromthe charts of reference . 4shorter empiricalm.ethdfor determining dE/d
36、a at the tail,based on thesficharts,is given in rfel?l1.UNCLASSIFIEDw.-.- .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-,. .r. .,1. 11.“-. ,1.NACA CB No. L5c01 9For conventionaldue to Wne horizontaltail l.ocat.onsthe value of C.,Provided by IHSNot
37、 for ResaleNo reproduction or networking permitted without license from IHS-,-,-;of 20 given in figure 2 of reference 6. Thisfisnme presents data for a Eanilton StandardX155-6 mro-pellerat a value of Tc/“ equal tozero and a side-force factor (defined inrefqrence6) of 80.7. For-conveniencethevalues g
38、iven in this figure for a propellerbl.afleangle of 20 are tabulated as follows:PropellerTwo-bladeThree-bladeFo-l -TrDthat whenthe propeller claractersilcsar; known theproper values of sid.e-lorcefactor and bladeE.ngleshould be used in reference $ to deter-A value of xl that correspondsofthe propelle
39、r is used.figure 2(b),to the plane .For moneller locations ahead of the center ofavh” te%Ue of Cm/jCL due ta tk roelkr narlfor:e iz positive. .IT.eadded dOwnwash over the horfzOntal tail relaltinfrom the normal force on the propeller contributes a?urtherchare in pitchin.g-momeitslope.that is LlssI.l
40、mGato be given by“ (%$(2)$)$!. da tLINclAwFm. g“;lanesymbol + (I-t)of wing, olhord area, tailOr tail from wing dia- fiom Whg len$h width(eq ft)(ft)Awnacellemeter,a.c. too;:% “. # .*.1“ . .=iTABLE II.- ESTTMATED VALUES OF CCL AND Winsk-pm $! ?:Estirnatevalues of j.ncrementin pitching- .-.aerodawfcAir
41、plane center!faction 1 0.2.42 .24i$,2-6.2385 .2z/3.6 .2o33.128 .0 L - .018 .016 -.210 .36.090 e039 - .017 .012 -.158 ;3 a71 34.108 a71 037 - .013 .014 -.1 2i 2 :3$.113 a71 020 .025 .009 .01z-.1 2 a71“1 52 ,041 :1: .015 .02I ?-.291 .3 i:32.OuL.015z.016 .019 -.1 R .;2J* .o,o .0 8 a71 022 .020 -.2 . “J
42、., , -,.7 “ inProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-“,.a71a13a13a15a15. .NACA CB./8./6./4.72./0Q.; -.2$?-./?8,.30:32.3iN-O.L5C01 . Fig. 1-(%=l-u-u “nliTiONAL ADVISORr.24 .28 .32 .36 .40 .44Ceder of gravity froction EFigure .l.-lVodrdon of p
43、rocedure for dehrmjnhy aeufro/ pohfor +Ypicu/ a/rp/a0e. .UNCLASSIFIED.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-. . ,NACA CB NO. L5C01-,#;.-. .x,z-.u$)fo.use wi+h04 fudby decfiiwwcAYu of wA9 exepf .sec7%o/7Udoceti+toI F/gur8 4. correction for d
44、CN/da & horizon al foi WIend p/bfe.x (DO/O from reference 4.)per rudk7t7.*It-.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA CB NOO L5C01 Fig. 5UNCLASSIFIED,&I:& &tl-. -T=4$= .4 a71+e w=+I 2 4&we!3 6 7a-?-.“*,. +“ 1#-“-.frJz%41+&.&d -+14 15a9&.
45、 &L. .13 16 HAIMML AOVIMRVCOMMITW FOR Amo!mlflmtested.UtIICLASStFIED -Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-#NACA CB NO. L5C01. Fig. 61#,*4.6w“a71.LM?U2MSSlFiEB46:.42 /#/ / /38 /t34/d/ /30 /4/ aRw5mEm26 rUNCMSSFIEDb. .- .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-
