NASA NACA-TM-630-1931 The steady spin《平稳旋转》.pdf

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1、.- -.-TE(HIHICAL EEMC)RANDUMSADVISORY COIMI7!TEE 2ORAERONAJJT1CSOC 630-.TEE STEADY SPIN- - icfi;a=gliding angle,wing chordleading edge,longitudinalnormal axis,later?.1axis,.Lo= rate of rotation about space vertical frl(1/s),; = u Cos q Cos pJ*_l JProvided by IHSNot for ResaleNo reproduction or netwo

2、rking permitted without license from IHS-,-,-IIH.A.”C!.A. Technical ;iemorandurITO.1630 3All rotations are positive when clockwise as seen inpositive direction of rotational axes,v (uI/s) = path velocity, :AT = L)n g (m/s) change i.npath velocity v dueto rotation Ql,P = -sjq (m) radius of helix,a(de

3、g.) = angle of attack 7)as defined in Figure 1(deg.) = angle of bankT(dego) = angle of yaw, formed by axes and gafter rotating about normal axis y,Act = 57e3arc tan !# (dego) change in a due.to rotation Clx.lift; in direction of lift axis yl,A(kg), ca=$j. ,.* K (kg), cm = J! drag; in opposite direct

4、ion to, pajh axS y,8 ,Q (kg), CQ = :+ cross wind force; perendicular tolift an.il.drag,17 (k), Cn = *- .= Ca cos a + cm ln a normal force;qin dire.,ctzonof normal a:isy,T (%) , = $! = Cw COS CL - Ca sin.(X tangentialforce; cppositc in directionto lor.itub,i,r.alaxis ,x,Ii oliLo(mkg) , %0 = fi aerody

5、namic moment about lead-ing etige,7Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.4/”sl:cvc. tor r.orzcrIt,., .mrodynamic moment about 1on-gitud.ianl axis ,%?Jd.loron Comont ifqo-u.tlongi-tudinal axis A$.*. q?rhLL (rnkg), IJ,sgyrosccpic mor,lenta“g

6、o-itp.or-P.:LI.axis ya71-.in direction to tho correGond-.*J-Ifa71Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-KOA.CQA, “Technical Uemorand-imUo. 630 5All control movements producing positive moments arepositive.Thisrenor$ attempts a comprehensive

7、survey of the.subject ofspinnigg, and constitutes an exte.nsivnandsupplement to Iuchsand opfs ltAerodynamik,llchapter IV,. .Several British reports (references 4 and 5) carrytilenotation that the angle of yaw is relatively small.inspinniigand rarely exceeds 20 The English have estab-lished the effec

8、t of side slip for the most necessarydata in the wind tunnel at angles of side slip T eofanbecomesvery pronounced at theusual angles of attack, while anairplane already inclines a-uitesteeply in ordinary curveflight. When LO= O, disappears.T6 compute the gyroscopic moments the rate of rota-tions w,

9、y and a)renecessary.-_Confol*ma31yto Figure 16, u does not become aPPre-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.,a71,Po the? Case of qcording to (9) while vtcndancy towar a fixed=vcosip*# .b. .+.uProvided by IHSNot for ResaleNo reproduction

10、or networking permitted without license from IHS-,-,-a71 N.A:G.A. Technical iIemorandumNo. 630 11.MKWith the nondimensionalK= inserted, we ob-gtain(Jx-.J3-)2-=-%=- Q (cos (pcos sin a + sin q cos avg (cos V cos V cos a - sin Y sin a),i which may be seen on Figure 20 in relation to a and q.The gyrosco

11、pic moments do not appear until the glidingangles a,revery high, and become very pronounced whenq- 85. .The aerodynamic moment, that is, where the moments akout the lateral axis are intalagce.) The equilibrium of the moments about the Iongi- .tudinal axis is expressed by(- K) = aerodynamic moment,ne

12、gative gyroscopic momentIL,. Qhe rotaticn Lox al)outthe pat-haxis induces wing. moments about the longitudinal ais ,exceeding by far any.* .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-12 IT.A.c.A. Tcchnicc.1IJemoran?.umNo. 530 ,.Theintegration cs

13、tir,atesthe aerodynamic “momcntsofthe wings att z.=-!”!-. 2In particular, cn (a + Aa, V + Av) hero signifiesthat Cn is =ffecte by and. by its cfforztadchangeFigure 22 affords %= aaist a “a “ “dt-hepossibility of positive aad negative wing moments,(the relevant poiaTh.eydisappear whet W=o *S may becz

14、illedouter zero voints , the u values pertinent for ymay be taken from thecurve of Figure 17 For S1OW rates.,.of rotations iilditi On, for“n 0,a 32, where only negative-.wing moments, and for a 140 and (?,.= only positive wing moments occur. AS cpandthereby Aa become larger, the positive noments bec

15、omejmore and more evanoscenij the zero points G and.H con-.(; tinue to come closer together and to assume still greatervalues,of a, until culy negative moments appear.,i: ,“With the gyroscopic noment KK eXpressed nondimen-! si.onally * :, ,fKI:.;:”f .,-v f;,?. ,g we have:.“.(J:#3) % = - %olt .owi.ng

16、toWith anwe Mivo:” .,.,.,. ,., . ,;,.,.,.$, “.the lack of e.xpcrinentaldc.ta, a71rudder momont, constant for any a,.15cl.cci,dcd.l:?li$gkcr; thus the abscissa of the curves nust besljfc,.paalg%,downward an upvard, respectively,.;,.IT,.,The“dr,ming”nonents cf the fusolago and of the cti-cnl tail grou

17、p, iriduccdby rctation xisj they may in fact hocouc just as high as the,7iII:fioments .L, k,nd oven surpass then at large N.,. *.,.,. Hith6rto“ovr st72adefiaed the ValUCS for u and cpat which the forcos and ts about tilethree body axeswerd in equilibrium, as exhibited in I?igure26 for thespdd$ticase

18、 of Q and pS = 0 with q plottedagainst k,” disregarding the damping c,ausedby he fuse-lage and by the vertical tail unit. Curve a ccmprisesthose values of G and $ for which, tf W = O, al1forces hcting o,tke airplane me in equilibrium and,since “thefiomontsnust r.lso be in equilibrium if the spinii i

19、o “?estea?ly, Where fall czrvcs of the moiilentequilib-rium must start cn this curve a. The 3 curves divulgethe.dquilibrium of the moments about,the later.1,:.xisfiifhtherespective elevator moments.,.,., ;., “,“.flslong ,cesrotation w vomains small, ief3e,for rol-c.tively small q as shoun in Niguro

20、17, t“norenro practi-,20,), so that, for acaliy no gyrosccpic nomonts (see fig.itik$f.el”elc,tcrmonent,these about the lateral ccti;sareineiilibriumfor those values cf,rofora.llc”,to ;ct.,.,.,-, .,!. ,., . Consequctitl”y, curve bz .i$Ll,S,$Ghcdwnyirgmoments of tho fuscl.ngoand tho vertical control s

21、-irfe.ccsarc disrogardode TheSOd.arpingmoncnts nay beconc conparativcly large, thus rMz-ing a nomont oquilibriun.posible oaly for ,asnail angloof attack.”A glance at Figi.rc 26 discloses the fact that currcs, d and e, even when disregarding the damping nomcntsof the fuselage and of the vertical tail

22、 surfaces, neverintersect in one single poiat if no coiltrol movement oc-cur sa71 The result is that as far as concerns the,A 35, astead”spin is impossible with,outcontrol displac-ementsaa71.,“Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-IT.A.C.A,

23、 TGchnical ldemoraadumNo* 630 17.However, it is quite possible to force such an in-tersection point as, for instance, Y a slight negativeelevator displacement pH=- 3 which yields point E.Any steady curve flight is possible depending on thechosen control novement - at least, for comparatively lowangl

24、es of attack. However, at very high angles CL, say,near point l?, the b, a and e curves most probably:never meet in one poiu.t;outsince the curves are soclose together, and there prevails at least an almostperfect balance of forces and moments, we shall designatesuch,as Approaching steadytlspin-When

25、 the possible curve flight is very steep and therespective angle of attack is above that for maximunlift, we ordinarily speak of ltspinningfand we distin-guish tilelfsteepllfrom tilelflatrrspin, according towhether the.angle of attack is near tfi.atfor maximum liftn or very large.The tendency of an

26、airplane to spin depends on thea71 mass distribution, the shape of the wing structure, the. position of the center of gravity, the area of the ex-posed fuselage and the vertical tail group and its dis-tance from the normal axis,.Hopf (reference 2) has already pointed out (seereference 1, cnapter IV)

27、 that the mass distribution pre-dicts the magnitude of tle gyroscopic moments (Jx - Jy)w O. the brun parallel to the ordinate axisca less pronounced de-If it were possibleJY it wOda theo-aiiygyroscopic mo-and c curves wouldFor very smallJg -Jy the b curves would not deflect to the rightuntil ery hig

28、h gliding angles were reached outwouldthen deflect that nuch sharper, and become % - 90Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-$8 N,A.C.,:Tchnical Memorandum N*,630,.?for,higher a,. thus moying a considerable distance-awayfromthe other ,d. an

29、d ,? curves. ,.:,. , , .,The result would be that at smal J”- $Y curvi-linear flight would be impossible for angles OF attackabove those attainable,in level flight but not as yetbelonging to a flat,spin.Thus it becomes apparent that spinning may be prev-ented more or less completely, at least for an

30、 averagerange of a, by judicious mass d.istributi.on,We have seen that sj”la,cqmqntupward)., - ., ,% =“m”OOIOf “ “f downward) .,8.s*.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-IT4.c.A. Technical l)ernorantumNo. 630 . 19.,.*+.#% = ()$nddouble gyr

31、oscopic mor!ient,I autorotation cane.otsot in.Wk.enwe introduco an aileron monent I . ,.a71.,Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-*.a71Figures 33 and 34 (l*eforonces7and 9), .nlsotnkeilfrom a British reports apply to t“eomcateqliliriulstou

32、t path axis x, about which the rotation Ox oc-currodo,., ,Wing gap, stagger, d.ccalageand ai.orondisplacement“di!feetin general a chango in rriuttualinterference? honco,in r.u.torotation.,. Iicrease.Mffect of elevator displacement iilsteep an?.flatSpin: , It is generlly conceded that any control dis

33、place-ment ina steep spin effects an immediate and powerfuldisturbance of the provailin flight attitude, but thatall co:troldisplacements are oiviously ineffective in aflat spin. Pushing tho control stick fOrmard is the bestmecns, if any, to recover frorrithe spin, These factswwoo very well with o-o

34、-rcalcuation$For tho stocp spin .curvos b, d and o in Figurp .2,6,reveal distinctly Opi*Osscdintersections which prevailfor well-defined control displaccrmnts only; t-hocurvesfor the,corresponding COntrO diSlaCementS CLre$ mOre-ovcr$ ftir ap2rt.In a flat spin the conditions are different, Dis-tinct

35、intersections on tho throo curves b, d and e aremost likely :ltogcthorprecluded; the curves for all con-trol di,splacoments are very closo togctierSo in order to prosago the manner, and roorc,partic-ulnrly, tho timo interval during which the mornontarilyproscnt fligpt attitudo is cnangea, wo made se

36、veral cal-culations on unsteady flight. Wo limited ourselves tothe effect of a positive f310vator riisplacemcit(pushig);onto in a stcop, perfectly steady spin) thoin a flat!“approaching steady” spin - (E antiF on Figuro 26)tProvided by IHSNot for ResaleNo reproduction or networking permitted without

37、 license from IHS-,-,-,*24 N.A.C.A.Technical Memorandum No, 6S0We ?.efinedthe two fligk.tsas follows:. -.- -1-_, - -.7 r s - “! a v T fiunlberQ v u of Psi $q Ps,turns. . .-Steep 7Co_! then we introduced an additional elevator mo-Flcnt h!H= + 0.0021, which corresponds to a pH :=-I-100elevator displac

38、ement at small a. !lM.swas used to dis-turb the lnorfectllas WGII as the Ilapproachingparfectllnosition o eauilfbrium in the steady sad in the flat.“pin,Numerically integrated in 1/20 and l/0 second in-tervals, the differential equations revealed the datagraphed in Pigures 35 to 37=1a71a15In a steep

39、 spin a push on the control stick effectsan instantaneous and powerful chap.gein flight attitude.Theangle of attack, in particular, promptly assumes anormai range, and the rate of rotation w drops veryqu.ickly (13cferece 10.) Iia flat spin the effect of IIpushingflis altogetherdifferent- The Gradual

40、 and semingly periodic chauge inangle of attack is strikingg An equally periodic changein all other variables is bound up withit, so that theairplane, if at all able, would ass,ume%aother and$ aboveall, normal attitude of flicht only very slowly. Thefact.that pilots who went into a flat spin unintei

41、tional-ly were able to get out of it again,by alteriatinglypushing and pulling in the tc-myoof the ensuing vibra-tions.,seems to bear out our contention,.,.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-N.A,C,A. Technical Memorandum Nb630 25.I.,. .

42、. Concllis ionWith the object of f,wrtherclarifying the problemofspinning, andto stipplementand ex”tendthe data in Fuchsand Hopfls l!Aerodynamiks1!Chapter IV (reference 1), theequilibrium of the forces andmoments acting on an air-plane is discussqd in the light of the mqst recent testdata. Convinced

43、 that in a spin the flight attitudo byonly small angles of yaw is more or less completelysteacly,the study is primarily devoted to an investiga-tion of steady spin with no side Slip. At small CL,wholly arbitrary and perfectly steady spins may beforced, depending on tho type of control ,displacements

44、.But at largo a only very steep and only “approachingstcadyltspins aro possible, no matter what tho controldisplacements,A steep curve flight for which, in dlditio-n,theanglo of.attack oxceods even that for maximum lift, isgenerally cailedIspinlland we dis”tingizishthb IIstcopspiniffrom tho Iflatspi

45、nfaccording to whothor the an-gle of attack is near to that for maximumlift or verylarge. ,.From the desi:nerlspoint of view, thespinning ten-dency of an air:planecan bematerially lowe%ed by:1) Wing shape: a continuous rise of the Cn curveagainst a valid for each”wing crosssectionp“aralleltothesymme

46、trical plane. Even if not altogether*unavoidable, the Cnmax silo”uldnotoccur until very high an”g,lesof attackhave bpenreachcd.,and should,only he “solarge that thedrop in the cn curio is as small as possible,for high valuo$”of ct.”2) Mass distribution: inertia moment Jxabout thelongitudinal axis an

47、d inertia moment- Jy about,the normal axis should be as nearly alike aspossible. .3).Pqsition of t,ho,contcra71of gravity of tho air-,plane: should ,he cxt.rer:clyfar forward.4) Corroct shapo “ofrear ,etidof fuselage and of ver-tical tail group: the sides of t“hefuselage, par-ticularly at the rear end, as well as the area ofthe vertical tail group should be as large as Pos-sible and be exosedto the :tirstream in all di-rectionsProvided by IHSNot for ResaleNo reproduction o