1、AP_ No. _8B.l-;-jp,._=,_._-ttNATIONAL ADVISORY COMMITTEE FOR AERONAUTICSIIrlIRTIMI RI: Pi)RTORIGINALLY ISSUEDJune 1943 asA_va.nce Restricted ReRoz% 3F28EXPERIMENTAL DETERMINATION OF TEE YAWING MOMENT DVE TOYAWING CONYRIBUTED BY THE WING, FOSELAGE, AND!VERTICAL TAIL OF A MIDWING AIRPLANE MODELBy John
2、 P. Campbell and Ward O. MathewsLangley Memorial Aeronautical LaboratoryLangley Field, Va.WASHINGTONNACA WARTIME REPORTS are reprints of papers originally issued to provide rapid distribution ofadvance research results to an authorized group requiring them for the war effort. They were pre-viously h
3、eld under a security status but are now unclassified. Some of these reports were not tech-nically edited. All have been r_produced without change in order to expedite general distribution.L- 387:LProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Date D
4、uelILLibrary Bureau Cat. NO _1370IBb- ,Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-_TATIONAL ADVISORY COM.MITTEE FOR AER0_TAUTICSADVANCE BESTRICTED RI_PORTC0tOIEXPZRIMEISTAI, DETERMI_ATIOIT OF THE _AWI_TG MOMENT DgE TOYAWI_G C0_TPIBUTED BY THE II
5、NG_ FUSELAGE_ ANDVERTTCAL TAIL OF A M!DWING ATEPLANE MODELBy John P. Campbell and Ward 0, MathewsSuMM_RYValues of the lateral-stability derivative Cn r, therate of change of yawing-moment coefficient with yawingangular velocity, centributsd by the wing, the fuselage,and the vertical tail have boon 8
6、e_e_mined for a mldwingairplane mede_ by the free-oscillation mcthodoIt was found, that the values ,of Cnr contributed bythe vertical tall and by the profile drag of the wing were_n good agre_.zent with theory. The. damping contributedb;_“ the wing vaulted as the square of the lift coefficient,b,_t
7、the. actual values were some_,hat bower than those pre-dicted by ex_et_ng theory_ The value of Cnr contributedby the fuselage a_opoared to be n_gligibleAn empirical, formu.la is presented for obtaining anapproximate value of Cnr for a conventional midwing air-plane.Ii_TRODUCT IONIn calculating the !
8、a_cral stabi!i_y of an airplane,difficulty is often experienced in estimating values ofthe stability derivative Cnr, the rate of change ofyawingmoment coefficient with yawing angular velocity. Al-though theoretical methods for obtaining the value of Cn rcontributed by the vertical tail and the wing
9、are given inreferences i, 2, and 3_ little recent experimental workhas been done to determine values of this d_rivative. Inorder to provide experlmontal data on the contributions ofthe wing, the fuselage, and the vertical tall to Cnr,some measurement_ for a midwing airplane model have beenProvided b
10、y IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-2made in the NACA free_flight t_nnel. antula.r _-elocity par unit of rb/2Vfr orate of change of yawing.-moment coefficient withangle of ,_ideslJp (8Cn/38)lift coeif!cient (L/qS)lift coefficient of wing aloneincre
11、ment of lift coefficient due tc flapprofile-drag coefficient (Do/qS)profile-drag coefficient of wing aloneincrement of prof “_ _,_._-dra_ coefficient due to flapyaw_.ng-moment coefficient (NlqbS)yawing moment, foot-poundsrate of“ change of aerodynamic yawing moment _,jithyaving angular velocity (oJ.
12、_/3r)rate of change of frictional yawing moment with yaw-ing angular velocity (SN/3r)frate of change of aerodynamic yawing moment with an-ofProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-D-o3+i)IkLDoqSr.bbfV3rate of change of restoring moment of tor
13、sion springwlth angle of yalelift9 pouzdsprofile drag, pounds dynamic pressure, pound_ per squar_ feet (+lo_r_w_.ng area, +(_usre feetyawing angular ve.ocity,-radians per secondwing span, feet-flap span, feetairspee secondsperiod of y.uwing oscillation, secondsasy:,6ct ratiotaper ratio (ratio of tip
14、 chord to root chord)distance from center of gravity to rudder hinge line,feetyawing moment of In_rtia, slug-feet squareProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-4METHODThe equation of mo_ien of a system hsviug freedom onlyin yaw can be express
15、ed, to a close first approximation, as) ( o (l_The yawing motion of the system represented by thisequation can be expressed by an equation of the form= e-at (A _in bt + B cos bt)which represents a damped havnonic oscillation where therabio of the ma_-imum amplitudes of successive oscillations_s_Imcx
16、, -at= e_m_ X 0The value of a, the logari, thz_ic decrement or the dampingfactor, can he detezmined fror:; the experimentally recordedangles of ya_agair_ct h_r_e by. means of this relationshipwhich_ when tr_nsposod, glve:_log _n_ax - log “_maxt (2)tThe damping derivative expressed in terms of the da
17、mp-ing faotor isIT r + l._r f = _2Iza (3)and the damping derivative due to friction is_Trf = -2Iza f (_)Combining equations (3) and (4) _JvesITr =-21Z (a - af)or, in nondimonsiohal form_41J (a - af)Cnr = .(5)Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IH
18、S-,-,-5The period of the yawing oscillation expressed interms of the coefficients of equation (1) isCOIW21T_N r + Nr s N_j + kTz)(6)The effect of friction on the period is negligible. Atz3ro airspeed, _rhen N r and _T_ become zero, equation(6) reduces toorT24IZI z - kT2 (7)4TT 2By substituting in eq
19、uation (7) the value of T atzero airspeed, the yswing moment of inortla IZ can beobtained for use in equation (5).it should be noted that the restoring moment of thetorsion spring k affects the period of the oscillation(equation (6)but does not affect the damping (equation(3). It is pos3ib_e_ theref
20、ore, to adjust the period toany desired va.ue without affecting the measurement ofCnr APPARATUS AND PROCEDUREThe investigation was carried out in the NACA free-flight tunnel with the apparatus shown in figure 1. Theupper portion of the strut to which the model is attachedis mounted in ball bearings
21、and is free to rotate withinthe fixed base. The model is therefore fr_e to yaw but isrestrained in roll and pi_cho The movable portion of thestrut is hinged to permit adjustments in the angle of at-tack of the model being tested.A torsion spring connecting the fixed and movableportions of the strut
22、provides the additional restoring mo-ment necessary for obtaining short-period yawing oscilla-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-tlons. It is important that the period of theoscilla-tions be fsirly shoi“t to insure a well-deflned oscilla
23、tionenvelope and therefore to permit an accurate measurementof damping.The airplane model used in th_ tests.ls shown in fig-ures 1 and 2. Th3 _;_ng of the medial had an aspect ratioof 6_7 and a tater ratio of 0.40, a_d w_. equipped _Ithpartial-span split flaps deflected 60. T_o verticalu _ intails,
24、s_o_n figure 2, were used on the model Themodel was mounted on the strut with its center of gravityon the axis of rotation.The recto_ngular wing use% in the investigation had anaspcct ratio of 6 _na an _Tr_ 0 # _elcas_nE _t, and recording theresulting oscillation_ _ith a mo_,ion-picture -_amera moun
25、t-ed on top of _he ta_inel.The .,$riction of the system was determln_d from testsat zero airspeed with the models replaced by flat l,._adwelgh_s on long rods. These weights were adjusted tb sim-ulate the ya_ing m.om_nts of in ertfa of the models and werealined _,_ith the plane of rotatien to gi_o ne
26、gigible airdamping, Im _ests of the ai_plane model at zero a-irspeedwith vertical tail removed, essentially th_ same dampingwas o_ta.i_ed a,_ in the f_iction teethe _. appeared, there-fore, thht a tail-of, _ run at zero aifspo-,_d could be satis-factorll_ used to repiace the speci_,i frict_e:_u test
27、s w_thbead welghts.The peaks of the oscillations recorded by the camerawere _ead from the film _ecord and plotted against time.The zzatural logarithms of the faired _eaks were then plot-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-7q9!ted against
28、time and the slopes of the re_ultlng straightlines were graphic%l _epresentation_ of the logarithmicdecrements a and af_ The numerical values for a andaf were determined from the slopes by eq_._ation (2) andthese values were subsbtuted in equation (5) to obtainCn r .Lift and drag coeffcients and yaw
29、ing-moment coeffi,-clents due to sideslip were determined by tests on thesix.-component balance iu the tunnel for use in correlat-i:ag the measured valves of Cnr with the _heoretical de-rivat lye s oTH._ORET ICAL D_kP.:T_ DERIVAT r.FESThe value of C_jr for a complete airplane may be as-sumed to be m
30、ade up of d.roctly additive contributions of “the vertical tail, “,._ing_ _nd fuselage, if interference ef-fect_ are neglected; that is,Cnr = A_,.r(tail_ + ,jUnr + AOn_ _ ; (wing) r(fuselage)It can be s_;owu that the contribution of the vorticaltail iAc_._ (s)For a wing without flspsACn .r(,ri_g) =
31、KoCDo + K“CLSimple _ntegration for Y _i_.idst(o = -0 “ 2 4. 2h/Va!,.!e s fo,“_,hich may be relorese_itcd by bhe cqua.tionK., :-0o0SI (! A-. 6 - ._, 13 2.5 /The valueK_ are g_ven in figure 13 of reference 2_(o)-.O.OJ is for a rectangu.ar _.,.ingof aspectProvided by IHSNot for ResaleNo reproduction or
32、 networking permitted without license from IHS-,-,-8ratio 6.0. G!auert, in reference I, gives a value of-0.024 for tills condition,For a wing wi_b partial-apsn flaps extended, theprofile-drag term KoCDo becomeswhereKoCD = _ToCD _ KfACDo (II)o ow fbf4 - 3 - (I - A)b2 + 2A,(12)and the i1_duced-drag te
33、rm K_CL s takes the formKICL 2 = KICLw 2 f._+ Ksf_.CL CLw + K3AC L (13)fValues for K i and K 3 are given in figures 12 and13 of reference 2, but the value for K2 _ s not given inthis referenc_ and is a!_parently not available from othersources. Inasmuch as ACnr(wing)_ for the flaps-.extendedconditio
34、n cannot be computed without the value of K_, ita_pears dc.sirabe to pre_are adiitional charts for thisfactor,Calculations of reference 5 indicate that the theoret-ical value of Cnr(fusel_ge)_ is zero for fuselages thatare elipsoidal in shape.RESULTS A_iD DISCUSS!OITContribution of Vortical Tail to
35、Cn rValue_ of Cnr f_,r the complete mode! with partial-span flaps extended are given in figure 3 as a function ofvertical-tail _ize. Values of _,rhoreas reference1 predicted a vslue of -0_C24 and reference 2, a value ofProvided by IHSNot for ResaleNo reproduction or networking permitted without lice
36、nse from IHS-,-,-I0-0.03. It anpears that the va!uo of -0.031 given by ref-erence 2 and used in equation (lO) is too arge and shouldbe re!laced by-0.02,0.The varlat_on of u;_or wSth lift coefficient for thewing with partial-_pan flaps eztended (fig. 4) differedfrom the variation wi_h flaps retrac_ed
37、 in _hat the mini-mtlm value of Car _;as obtained ._t ._ am%l! positive llftcoefficient rather than at zero !ift_ This result, whichis also indicated b_T equatioa (i3), is d_le to the factthat at zero lift the cent;at flapped section is developingpositive !_ft, the tip section is developing negative
38、 lift,and both are contributing to C_nr, In%smuch as no calcu-lated value for the const_%nt K_ was av_,_ilable, no corre-lation of the theoretical and experirzental variation ofovalues, v “;s found to be -0,007 or“_o 0 ,024-0.29, Equation (9) yielas 0,33 as the theoretical valuefor K o for a reetanu
39、lar wing. it a0pears that the cal-culated and bhe experimentally determined values of K oare in fairly good agreement.With the partial-span flaps deflected on the rectangu-lar wing, the val_ie of Cnr due to profil, e drag can be ob-tained from the value of Car at the lift coefficientgiven by the fla
40、p. For the _:ing tested, the flap gave anincrement of lift coefficient of 060. From figuro 4 at alift coefficient of 0_60 the value of Cn r was -0.017.Combinin_E equations (ll) and (I3) and eliminating t_rmscontaining CLw , because CL w = 0 st CL = 0.60, givesCn_ = KoCi) + KfACDo- ow fVt_O03-qProvid
41、ed by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Ii(o!The valu_ KoO,D wss -0,007 from the wlng-alone test;oW_,gD was 0.080 from force tests; Kf was -0.072 fromofequation (1.2); and 3 was-0,0092 from reference 2,for a v oFi_o.re 3.- Variation of lampiu_ it,
42、yaw _,_th vertieai-tail effoctive-hess _,._d,i._ai,-ola:_e_,model; _!,_-PSextelle:ll CL = 1.0.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-_Tco_0CoI_
43、.12 -_-.I006 +,04 . ,0I4-.-+. L_rI!-J l- _. d.lt .I/I!I!1 f-liirplnne molel _lIIIII. IIIt i 1f-+i/ z_- i-,._7_I- . I-o- I !I!IItif- . Ii i _._,4 o8 i,_o i._,$Lift coefficient, CI:_.0Figure _.- “i,%rlation of Isc_pin_ in -v“s.v_v_Gth lift coefficient._laps extenlc!; ve-tical tail remove-l,Provided by
44、 IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-coLoINACA,14.12.i0 .,O8-C_.:r.O6Fig. 5 04-.O20 Experg_ental value s-(o.oo7+o,o_o cL2) _. _ -(o.oo7,o.o2-_ cL_)(ref,
45、 1).(0.007+0.031 CL _)(ref. 2)i !.liiII._.U.!.q-!,7-!-/-.t i ; L_L i! | , I i l /iil1 1 , /t1 l _ t t , i I ! / i. l t- +i. i _-f-7 . ,7“. 1./ I ! _/ V ,r!/ I i i/ /I _,-_ 1 -4_i -_:.z_i_,z_i-4. T i I i, i I,f i |J i i ; il / ; /i I i t 7 _+11 ! |I I , +L i _ . _ i“ -1- . /i I,i i/. i/T i4.-, 4-l-z-
46、/-/-i _. -,. , .I, ! J .,.iX , , I . II / I. “!./! i ! i L.t. I- _ .7-/ . I r . P _- fI t _ I././_t ! , i J.-_.-_-.-I-.-ti-.%_ b“ .tI I t I . _. _i_ _;-.,. t ! _ I0 ,4. .8 1.2 I.S 2.0Lift coefficient, CLFigure 5,- Variation of lampi_ in yaw _,itl_lift coefficient.Rectangula.r wingl flaps retracted.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-
