1、. .llllIllllllllllllllllll1lllllllllliilllllllilllllll“.-”-:;: :.,- *:.-“.- =:”:;-*;*= ,3 Ii76 00071 4973 A , .-*6 !:A+$- NATIONAL ADVISORY COMMITTEEFOR AERONAUTICSTECHNICAL P40TIlNo. 1193EFFECT OF PRODUCT OF INERTIA ON LATERAL STABILITYBy Leonard SternfieldLangley Memorial Aeronautical LaboratoryLa
2、ngley Field, Va.WashingtonMarch 1947Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.*?a71 a11a15Aof theon theNATIONALADVISORYCOMMITTEEFOR AERONAUTICSTECHNICALNOTENO, 1193E(jT ()UTOFJNIA LATJrateof changeofyawtng-momentwithyawing-angular-velocityfact
3、or,dmping-in-rol.lderivatd.vejrateof changeofroll.ing-mnentcoefficientwithrolling-afla-V310cityfactor,rateof changeofyawing-momentcoefficientwithrolling-arqar-ve16cityfactor,yerradian (%/8$:)rateof changeofrolling-momentcoefficientwithyawing-w.guiar-veloci.tyfactor,perradian (ai*)rateof changeof lat
4、eral-fcrcecoefficientwitlnrolling-angular-velocityfactor,perradien(M$*)rateof changeof lateral-forcecoefficientwithyawing”angular-velocityfactorsperr.adlancy/a#WE secmdsdifferentialoperator (d/dtangleof swepba.ck,degreesangleof attackof rinci,ll.ongitudlna.laxisof airplane$positivewhenprincipalaxisi
5、s abceflightpath,degrees(seefig.1angleof flightpathtohorizontal,positivein a climb,degrees (seefig.l)apglebetweenrefereaceaxisendkorfzmtal:positivewhenreferenceaxisis abcv3horizent.a.1,degrees (seefig.1)-i“,.a71 a15a15 a15a15.,. .Provided by IHSNot for ResaleNo reproduction or networking permitted w
6、ithout license from IHS-,-,-TNNo. 1193 5Ranglebetweenreferenceaxisendprincipalaxis,positivewhen(seeRouthtSreferenceaxisis aboveprincipalaxis,degreesfig.1)discrimfnantEQUATIONSOFMOTICNThe linearj,zedeauatons of motion. referredto theaxesinfigure1, usedto calulatethespiral-andoscillatory-stabilityboun
7、dariesforanyflightcondition,are:Rolling%-_.i -1 :.-: .:;- .- - . . . . . _ . . .-pizo-xo) *-Cl, =osincosD2+CZ6D l. 1ILIzo COS2V + I ) I.x sin2qD2-C D*o $Sideslipping_,. “. .-I.I(Z. ) 1xsinqcosD2+Cn, l)-C0,-. $, n o,.Provided by IHSNot for ResaleNo reproduction or networking permitted without license
8、 from IHS-,-,-and.The symbols Ixa andprincipalaxesof theInclineds% an angleaboutthefliht-qathTNACATN NO- 1193=20 ra,presentthemoments ita aboutthe.airplane. Ifthe longitudinalprincipalaxtsis to theflightpath,themommts of Znertlacixis and theaxisnomal to the flj.p$htpathare:a71 a13a15.,m.8.,.Provided
9、 by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-JNACATNNoo 1193 7. .When ,f%oet is substituted,for , Vet for , ma poeht-for p in theequationswrittenin detemimnt form, k mustbe arootof theequationwhere.*Provided by IHSNot for ResaleNo reproduction or networki
10、ng permitted without license from IHS-,-,-NACA NO. 1193The conditionsnecessaryto obtatntheoscillatory-stabilitybounda are thatthecoefficientsA, B, C, and E mustbe positiveaadRouthsdiscrimi.nant,R = BCE - AE2 - B%, mustequalzero,TJm spiral.-stabilityboundaryisfmndby setting F = O. Thecompletelystalle
11、regionis thereforeboundedby thecurves R = Oand l!= O, whichareplottedas a functionof thedirectional-stabilityderivativeCnP and theeffective-dihedralderivativeCz sBStabilityDerivativesandMassCharacteristicsCalculationswere madeshowingtheeffectof theproduct-of-inertiatermson theoscillatory-s-taljility
12、boundaryfora hypotheticalsupersonicfighterairplane,an experimentalfighterairplane,anda model.flownin theLangleyfree-flighttunnel, The valuesof thestabilityderlativesandmasscharacteristicsof thetwoairplanesand themodelaregivenin table1, The con-tributionof thetailto thederivativesCn and CZr (seerefer
13、ence2) was includedPin thecharacteristicsof theexperimentalfighterairplaneand thefree-flight-tunnelmodelbutwasneglectedin thecalculationsofthehypotheticalwpersonicfighterairplane.RESULTSANDIXE3CUSS1ONThe results of the investigationarepresentedina seriesoffigureswhichshowtheoscillatory-and spiral-st
14、abilityboundariesas a htndbn of Cn and Cl . The solid Xlu O curvektnereasfor we caseinwhichtheprincipalaxisis inclinedbelowtheflightpath, IXZ= 0.00178, thestableregionisreduced.The experimentalfighterairplaneand thefree-flight-tunnelmodelweretestedinflightwiththeprincipalaxis inclined16and10,respect
15、ivelyabovetheflightpath. The 5.itialcalcu-lationsmadeon theassumptionthat In = O (thesolidcurvesinfigs.h and) indicatedthattheairplaneandmodelwould beunstableinflightfor-thecombinationof CnP and Cl denotedbys,.“.“-“,-the circled pointsinfigures4 and. Theflight-test”results,however,showedthattheexper
16、imentalfighterairplanewas stableand thefree-flight-tunnelmodelwasmarginallystable. Subsequentcalculationswhichincludedtheproduct-of-inertiatermsIndicatedthatthe R = O boundaryfor theexperimentalfighterairplaneincreasedthestableregionto includethecombinationof CnBand CZ testedinflightand thatthe R =
17、O boundaryfor theBfree-flght-tunnelmodelwas shiftedverycloseto themarginallystabletestpoint.In general,theinclinationof theprincipallongitudinalaxisabovetheflightyathcausesa stabilizingshiftin theoscillatory-stabilityboundarybut theextentof theshift”isa functionofotherairplaneparameterswhichare stil
18、ltobe investigated.Thesolidcurvesof figures2 to 5 maybe consideredtorepresentthe R = O boundaryfor theactualflightconditionsofan airplanewhichhasitsprincipallongitudinalaxisin linewiththeflightpath (Ixz= O) providedthewingsare setat an angleof incidenceto thefuselageto obtaintheliftcoefficientdesire
19、dforflight. The dashedcurveon eachfigurewould,therefore,representthe R = O boundaryfor thesameflightconditionsas thesolidcurvebutwiththewingssetat a differentangleof incidenceProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-sincetheyrincipalaxisis inc
20、linedto theprincipalaxisis inclinedabovetheflightNACATNNo. 1193fllghtpath. If thepath,theangleofincideicewhichcorrespondsto thedashedcurveis smallerthantheangleof incidencecorrespondingto thesolidcurve. If theprin.cialaxisis inclinedbelowtheflightpathlhoweverthewgincidenceislargerthanthewingincidenc
21、eof theairplaneinwhichtheprjncinalaxiscoincideswiththeflightpath. For e=plejthesolidcurveoffigure2 W the R = O boundaryforan airplanewiththewingssetat an angleof 17to thefuselageand theprincialaxisin linewiththeflightpatii;whereasthedashedcurve5s the R = O boundaryfor thesameairplanewiththewingsseta
22、t a 10angleof incidenceand theprincipalaxisinclined5shovetileflightpath, Infigure3, thewingincidenceiS7 forthesolidcurve,50 for thecaseot theprincipalaxisabovetheflightpath,amd9 for thecaseof theprincipalaxisbelowtheflightpath, The solidcurvesof figures4 ends are the R =0boundariesfor theatrpleneand
23、modeldesignedwitha wingincidenceof 16and10,resecti.vely;forbothcases the das d cmverepresentsan airplanewitha wingincidenceof 0 Thisinterpre-tationappliedto thesolidcurvesof figures4 and5 is onlyapproximatelytruesincetheangleof attackat thetailis zeroifthe wing is at 16 or 10incidenceend theprincipa
24、laxiscoincideswiththelineofflight;whereasthecalculationsincludetheeffectof thetailat em angleof attackof 1.6 and10on thestabilityderivativesC% and Ct a71rA comparisonof thesolidemddashedcurvesin eachfigureclearlyindicatestheincreasein theoscillatory-stabilityregf.cmfor an airplanedesi.gnedwitha wing
25、setat 0 incidence,therebynecessitatingtheinclinationof theprincipalaxisabovetheflightpathto otitainthedesiredliftcoefficient.CCNCLUD3NREMARKSThe results.oftheamlysi.smadeto investigatetheeffectof theproductof inertiaon thelateraltabilitybowbries emphasl.zethenecessityof includingtheproductf-inertiat
26、ermsinthe lateralequationsofmotionto determinethe lateralstabilityof an airplane.The calculationsIndicatethatthe inclinationof theprincipallongitudinalaxisabovetheflightpathcausesa stabilizingshiftinthe oscillatory-stabilityboundary.LangleyMemorialAeronauticalLaboratoryNationalAdviwxcyC?ommitteeforA
27、eronautics&ngleyFfeld, Va.8August13, 1946,. .*.-:Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-. NAC,ATNNO. 3.193. nJ. REFERENCES.1. Zimmerman,CharlesH,: An Analysisof LateralStabilityinPower-OffFl,ightwithChartsforUse inDesign, NACARep.No. 99, 1.9
28、37,2. Bamher,MillardJ,: Effectof SomePresent-DayAirplaneDesignWends onRequirementsforLateralStability,NACATN No. ?314,gt$,3. Bryant,L. W., and.l?ugsley,A, G.? TheLateralStabilityofHighlyLoaded.Aeroplanes,R,& M*No* 1.840) BritishA.R.Cm,1938a71Provided by IHSNot for ResaleNo reproduction or networking
29、 permitted without license from IHS-,-,-12 NACA TN No. 1193 .,TABLWISIWILITYDERIVATIVESMD MASSCHUWTESISTICSUSED STABILITYCALCULATIHypotheticaleuperamicExpe*talrghtera-laneFrea-flit-tunnel!ncdofighter airplanecondition Lending Oruimlng Landing Landing?4/s,Ib/eqft 80 80 35 1.85b,ft. 20 20 34 3&0,slugs
30、/cuft 0.00238 0.0002 0.Ou.23a o.0023E,ec 264 1465 173 44% 1 0.372 1 OAP 54 620 13 6,33kXO,ft 2.02 2.02 5,28 0.51so,l-t 9.64 9.6b 8.03 1.29CZP,perrdlan -o.lsq -0.197 -0.3 -0.17CZ,perraWm 0.25 0.0929 0.25-0.04c 0.142-0.o%znr p(tail) B(tail)P,perradan -0.0198 -0.00732-0.029-0.04C%(tail) -0.0406-0.099cB
31、(tail)c,Pm radian -1.47C -1.47Cr % (tail) ?3(tail)O.086- 0.twl -0.0131- 1.2Cp(tall)%(m):Yp,k= radian o 0 0 0Jyr,perradian o 0 0 0+B, Per radian-1.33cnp(tall)-1.33c%(tai1) .oJ3 .2a34(tii1) ,-13.o4- 1.76cnp(mi11k13gee:e, -0.25-0.25 -0.02 0,deg o 0 0 -9,deg 60 63 35 42NATIOMLADVISORYcmQ1lEEFORAEsommc9P
32、rovided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-* NACA TN No. 1193 Fig. 1. %,-.,J.,/+zNATIONAL ADVISORYCOMMITTEE FOR AERONAUTICS“. .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-0f= o-,0+ -.08 -./3 -
33、./6Stohle/1-.20-. _ 4%2 LrRZO,omI/t!uwy-+QbIII+yhowdary=OJ8pwu/-s+ibi!/fy boundary-24 -.28 732NATIONAL ADVISORYEffec7t Ye - dihea(rul derl w+l ve C2P CoNmmm mmuncs:36!23a71. .-.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.,?“. ,.+,b, ,0.TQ=L7?=0I
34、. . . -.0076 z . (90/ 78 2Q= ascllatoty-tibdjtyboum?iwyD -af&+v #,rTiiTT ,T,T T +?=LJ-.04figure 3. La#era/- stblty bowxtorjes for cruJsIng flgh f for hypotetcal Supersonm fighter oqplme. wProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-a71 a15h. -.,.
35、 &.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.4.20X5f =0Ji42 T/6 720 :24 :32 :36NATIONAL ADVISORYEffec+l ve. dihedral der I vu +1ve Czp CONMTTEERIRAERDWWCSF/gu re $. La+erol - jabjlify boundaries for Iand/ngflgh+ for free- flgh+- tunnel model.2!w1-.ylu-lProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-
