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NckLI* vi ."' ARR No. LAJO5a i NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS JYARTIME REPORT ORIGINALLY ISSUED November 1944 as Advance Restricted Report L4JO5a EXPERIMETAL VERIFICATION OF THE RUDDERFREE STABILITY THEORY FOR AN AIRPLANE MODEL EQUIPPED WITH RUDDERS HAVING NEGATIVE FLOATING TENDENCY AND NEGLIGIBLE FRICTION I:By Marion 0. McKinney, Jr. and Bernard Maggin Langley Memorial Aeronautical Laboratory Langley Field, Va. UNIVERSITY OF FLORIDA I DOCUMENTS DEPARTMENT 120 MARSTON SCIENCE LIBRARY P.O. BOX 117011 WASHINGTON I NAQA WARTIME REPORTS are reprints Mf papers originally issued to provide rapid distribution of adv.uance research results to an authorized group requiring them for the war effort. They were pre 1t.wly held under a security status but are now unclassified. Some of these reports were not tech 4,taly edited. All have been reproduced without change in order to expedite general distribution. J" .'" ... . .. ... ..r;i .. . 1.. ... ,.:.... .. .. .. : N 4ll:..!.~i. :...I.. .. ,;~ k ';.~::.'i il ITACA ARP No. T4J059 NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS ADVANCE FRSTRICTED REPOr.T EXPERIi.,E1,TAL VERI TIC NATION OF THE RUDDERFREE STABILITY THEORY FOR AN ATF PLA"E MODEL EQUIPPED WITIH RUDDEES HA VI I:G ECATIVE FLOAT NG TEl DE ?!Y A [ITD IEGLI CI BL F I CTI ON By Far on 0. FcKinney, Jr. and Bernard i.iaggin SUir..RY An invest.iaMion has been rmade in the Langley free flight tunnel to obtain an experimental verification of the theoretical luddrrfrece stability characteristics of an airplane miLdel equipped with convent nal rudders having negative floating tendernits anrd negligible friction. The model used in the tests was equipped with a conventional single vertical tail having rudder area 0O percent of the vertical tail area. The model was tested both in fr3. fllrht and mr.ounted on a strut that allowed freedom only in :,'v. Yeasurements .fere 'made of the rvuddrrfree osci.liat ons following a disturbance in yaw. Tests were made with three different amounts of rudder aerodynamic balance and vith various values of mass, moment of inertia, and centerof_rcvi ty location of the rudder. lM'ost of the stability derivatives required for the theoretical calcilations v':r determined from force and frecoscillatton tests of t particular model tested. The theoretical analysis showed that the rudder free motions of an airplane consist largely of two oscillatory modes a longprFri od osci llston somewhat similar to the normal rudderlixed oscillation and a shortperiod oscillation introduced only when the rudder is set free. It was fund possible in the tests to create lateral instability of the rudderfree shortperiod mode by large values of rudder mass parameters even though the rudderfixed condition was highly stable. The results of the tests and calculations indicated that, for most presentday airplanes having rudders of negative floating tendency,the rudderfree stability 2 NACA ARR No. L1JO5a chvractcristics tray be ezamrined by simply considering the dynamic lateral stability using the value of the direct.iunalstability paiametear n for the rudderfree condition in the conventional controlsfixed lateral stabili y equations. Fnr very large airplanes having relatively high values of tne rudder mass parameters vw.th respect to the rudder aerodynamic parameters, ho',ever, analysis of the rudderfree stability should be ml3.e vi tn the complete equ'tians of notion. Good arree.nent between c:lculnte.d and measured rudderfree stability characteristIr. was obtained by use of the gnEral rudterfree stability theory, .n vhich four degrees of lateral freedom are considered. Then the assirnrtion is inide that the rolling motions alone or the lateral and rolling motions may be neglected in tLe onloulations of rudderfree stability, it is possible to piedi..t satisfacLorily the character istics of the lonperiod (Dutch roll type) rudderfree oscillation for e; rplancs only when the effectivedihedral angle is smrll. ''ith tnese s'implifing assumptions, however, sat1sfactory prdictlon of the shortperiod oscillation nme b.e obtained for any dihedral. Further simplification of the theory based on tie assumption that the rudder mo;.lent of inertia might te disregarded was found to be invtlid because this assumption made it impossible to cslculate the characteristics of the short period oscillations. I NTEODTUCTI O I SorIne military cirplcnes havs recently encountered dyaninc i nstahlic]jY in the ridderfree condition. Certain other airplanes live performed a rudderfree oscillation c.led ''na':ir:g" in which the airplane yaw and ru 3dr motions .re sn coupled as to maintainn a yawing oscilltirn of constant niplitut>. These pncnomena have bern th3 subject Df various Lhecretical investigations, and the f.ctors sff',ctlnj_ the ruiddrfree stability have been explored and iefin'd in Lhe tiveoreeical analysis of refer:nces 1 to ?. In reference 1 the .L.st corplete set of the three sets of equations of the rudderfr2e motion is developed. Th equations of reference 1, however, arc vary involved and rather unvieldy, and use of these equations to NACA ARR No. tLJO5a determine the rudderfree stability characteristics is consequently laborious. Suh equations are usually simplified by neglecting certain i :grees of freedom or certain parameters ani thus obtaining noproximate though satisfactorily accurate solutions. In reference 2, the equations were sirrollified by neglecting the rolling motions of the .irplane. In reference 5, vhich supersedes reference 2 for the rudder free theory, further simplification was obtained by neglecting siCevise motion a9s 'ell as rolling motion. An additional sirmlifying assumption of reference 3 is that the rudder moment of inertia r'i_.ht be neglected. It was realized thst these 3;r,.plified equations were not applicable throughout the entire rnnge of the variablz.s that could be obtained, but the rsultz were believed to bc, generally applicable to airplanes of that period. In order to obtain an rre'elin.nta l check of the general ,nd simlpll fed cquat.lons, an e:perirntal program is being conduct.aAd in 1he Langley rreeflight tunnel. The results of the first part of this piogrirr. are reported herein and are concerned with tre rudderfree dynamic 1 stability of a scale airplane modlel in gliding flight 7 equipped with rudders having insethinge balances and negligible friction. The rudderfree stability characteristics of the model were invest4ieted for varying snou nts of rudder aerodynamic and mass balance. The model was tested both in freefli'ht and mounted on a stiut t1ht allowed freedom only in yaw in order to determine experimentally the differences caused by neglect of the rolling and lateral motions of an airplane v.ith rudder free. In order that the results obtained by theory and experiment right be correlated, calculations wRere made of the theoretical rudderfrae stability of uhe model tested by equations. involving four degrees of freedom and by equations involving f,wer degrees of freedom. In addition, the rudderfree stability of th. model was calculated by an approximrate method that neglected all of the rudder parameters except those causing a reduc tion in the directionalstab4lity parameter C for the rudderfree condition. FACA ARR INo. LJO5a Various force, hingemoment, and freeoscillation tests wcre r..n in orde, to determine as many as possible of the stability derivatives required in the calculations of rudderfree stability. S..1BO LS S ,ing arca, square fe3t v freestre'am irspeed, feet per second 'b irg pspn, feet c vWi ny 3hcord, fest hb, srsn of rf..er, feet ni .',ss _' T.J r,,Ir&S mr. nass c f ru.i'j r, slu c 'v, rediius of ;.itin of mcdel ebouiL longitudinal (X) 1xic, fet radiu_ of ;rattlon of model about vertical (Z) aYs, f.et '"r radius of ,yretion of rudder about hinge axis, feet X., ri instance from center of gravity of rudder system to rlng r..xi; Fpositive 'hen certe1 of .raSvity is back of hinge, feet S distance frmr. mor'el enter r of gravity to rudder hin, e 11r: r t D !fferer til ri r.tr s di staiie traveled in rpsns (~t/b) P rcriod Df 'oscill nations, seconds T time rcu.i,ed fjr r.cttirns to decrease to onehalf am.plitule, seconds t ti'e, =.?onds NACA ARR No. LtJOa A, 9, C, D, E coefficients of stability quartic for rudderfixed lateral stability Al' 1, C1, 01 E1, Fr G,,Hi1 coefficients of stability septic for rudderfree lateral stability A2, B2, 2,D2,E2, F2 coefficients of stability quintic for rudderfree lateral stability A5, B3, C,D3, E coefficients of stability quartic for Srudderfree lateral stability A4, B,, C,, D), coefficients of stability cubic for rudderfree lateral stability S root of stability determinant (% = a' ib') ib' imaginary portion of complex root of stability quart c a' real root or real portion of a complex root of stability quartic q dynamic pressure, pounds per square foot pV2) p mass density of air, slug per cubic foot L r:odel relativedensity factor (m/gSb) ' rudder relativedensity factor (mr /Fbrcr ) cr rootmeansquare chord of rudder, feet a anale of attacV, radians unless otherwise defined p angle of sideslip, radians unless otherwise defined angle of roll, radianrs unless otherwise dEfined \ angle of yaw, radians unless otherwise defined 6 rudder angular deflection, radians unless other wise defined r flightpath angle, radians unless otherwise defined FACA ARR No. LiJO5a p rolling engul r velocity, radiens per second r yarinrg angular velocity, radlens per second v lateral component of velocity, feet per second (U ft\ L lift coefficient (M CD drag coefficient \ ' Cy lateralfore coeffic t (Lateral force qY C rollinrpo."ent coeffieenrt (Rolln: moment qSb laviIn.2 rioment ', ya'"in ~rom nt coeffi.i nt Zn n \ qSb .. Hings 'moment C irnre'orrent roeffTicient ( g = .I C rate of c.hasne of lateralforce coefficient with a angl' of sideslip (tCy/6p) r7 rrte of chang of rollinEmoment coefficient with S san]1.3 of sideslip 16C7/6) 07 rate of change of rollingmoment coefficient with rolling anrulorvelocity factor 0,7/_) C rte of change of rollingrmorent coefficient with Srb) .":zng nvularvel cit:. .t'f.ctor. /(6 r/6 Cn f'.te oi' ch'anre 3f' yevinTimormnt oefficient with rnile of ~'dslir 'OCn/~ ) NACA ARP No. L4JO5a , rate of change of a'virngmorent coefficient wiAh angle of yaw ( 1 Ci Cnp rate of change of yawirgTioment coefficient with p / ^ rolling canularvelocity factor 2 )n2 Cnr rats" of change of yawingmor.ent coefficient with / rb\ rowing arnul!arvelocity factor i6 /r C, rate of hinange of :/ya",ngmorrent coefficient with C rudder Lanulr deflection (6Cn/65) Ch[ rate of charge of rudder hinger.oment coefficient with angle of sideslip ('0,h/6 ) Cht rate of change of rudder hingemoment coefficient with angle of ya. Ch Chr rate of change of rudder hingemoment coefficient .'i th yavin Lng.ularvelocity factor 6 Ch,/') Ch6 rate of change of rludder hingerroment coefficient 'n ith rudder angular d r'lection (6Ch/665) Ch rate of chansige of rudder hingemoment coefficient with rudder anpularv. l.ociy factor CKh/ v /b APPARATUS The terts were rrun in the Langley frzeflight tunnel, a complete description of which is given in reference 4. The model used in the tests .was o modified 1/7scale model of a Fairchild XF2Kl airplane with its center of 8 NACA ARR No. L JO5a gravity located 25.0 percent of the mean aerodynamic chord. Figure 1 is a threeview drawing of the model. The mess and dirensional characteristics of the model are given in the following table: 'eight, pounds . .. . Radius of gyration, k foot ... Wing area, square feet . '1:ing span, feet . '"ing chord, foot . . Distance from airplane center of gravity to rudder hinge line, feet .. Height of rudder, foot . . Rootmeansquare 3hord of rudder, foot . S . 0.73 475 0.66 ...07 0.667 0.185 The vertical tril of the model was a straighttaper surface with a ruldcr of the insethinge type. The area of the rudder behind tne inge line ,was 0O percent of the vertical tail area. Three different nose balances were attached t t.e rudder in order to vary the amount of aerorH'yna.mc balance. Sketches of these surfaces are given in figure 2. The rass characteristics of the rudder were varied by moving weights within the rudder or along a thin metal strip that prCtroded at the base of the ruoder trailing edge. The rudders were mounted on ball bearings to reduce friction to a minimum. The yaw stand .!sed in the tests was fixed to the tunnel floor nd allowed the model complete freedom in yaw but restrained it from rolling or sidewise motions. A ohotog:aoh of the model installed on the yaw stand is shovn as figure 3. TESTS Tots .,re imade to determine the period and damping of the rudienfre: latsral oscillations of die model during: fre.: ,ilnpg flight and vhen mounted on tha yaw stand. o ::Ls ':ere performed to determine the effect upon the ru'derfrie stability of eliminating only rolling motions. ITACA ABR No. li.7OSa Scooe of Tests The range of rudder aerodynamic and nass character istics covered in the tests is given in table I. The test range investiabt3d was obtained by altering the mass characterist'cr of the rudder by ard.ition of weights at various locations. In this manner the mass, center of gravity, and rdius of gyration of the rudder were varied si1.,ultan eo_ Ls7I This proced.1.re was followed for the rudder equipped with each of three different amounts of aerodynamic balance. All. tests v.ere run ?t a dyns.nic pressure of l.00 pour ns per square icot, "hih corresponded to an air speed of aooroximat ly I10 feet ,er second. The lift coef ficient was anproxiri ste l.f O.c. Flight Test Flight tests vwre made lor the nodel test conditions 1 to 5 anr; 10 to 15 n.f table T. These t ts were made by flying the test odel freely w;ithn.n the tunnel as explained in reference During a given fl] ht, a mchanisn, within the modp'l wa" so activated as to fr.e che rudder after an abrupt rudder deflection of saout 15. The rudderfree lateral oscillations resu.lting fr,r; the rudder disturbance werie recorded ty a n:cotioi..piture. cem7er:.. The, period and damipinj charaict .lti:s of t"he flight oscillations were obtain.d from th? rioti onrci ture record and w,:re corre lated with correzpor:ning re;ords from the :awstand tests and with calculated charect.ristics. Several runs were made at each test condition and showed a variation of period of aboui.t ? p9,rcent snd a v,.isti on of damping of less than 10 percent. Typic.i flight oscillations are shov.n in fi ure .LI f.r a state ccnti tion arnd in figure 1: b) Por in unstble cnr.. ti on, Ya'S tand Tets The yawstand tests v.wr marl5 for all test con ditions listed in table I. These tests ver nimade under conditions reprodu:?ing those considered in the analytical treatment of reference 5, in vhich the rolling and the lateral notion of the a' plane center of grsakty are neglected. For the yawstand tests, the model was attached to the stand and the rudder vas deflected 15'. At the given test airspeed, the rudder was abruptly released and the resulting oscillations were photographed by means FACA ARR No. 17JO5a of a motionpicture camera installed above the model. Record s of the period and damping of the sawing oscilla tions !were then obtained in the saine manner as for flight tests. Appro:ximatoly the same scatter of period and damping values was obtained in the yawstand tests as in the flight tests. Plots of representative yawing oscilla tions obtained from the yawstand tests are shown in fig ure h(a) for a stable condition and in figure L(b) for a neutrally stable condition. Yethod of Analyzing Test Data Stahili L theory Indicates that the rudderfree lateral osc' lations are composed of two sucerimposed oscillatory m'dceE, one of which has a shorter period than thr oth=1 The t..::t os.illations, however, after a short interval of tire r.'presented only one of these modes  the one that subsided later because of the Doriod or damping. Tn geinerl, the s;ti llty calculations showed that the shortoeriod mnrr? ardo,d to onehialf amolitude in roughly 1/50 the pe:;d of the other mo3e. Th3 test oscillations therefore r..pres3nted th longperiod mnode for most of the test conrit ions. iraszureimnt of Stability Derivatives The stalilit" eri vatives necessary for the calcula tions are oiven onr tsble II and were ootained by the following ?'roedure : The partial derivatives of yawing moi;'ent coefficient vith respect to angle of yaw and rudder deflect on, C3n, and were determined from force tpsts of the model on the sixcomnonent balance of the Langley fre:fli ht tunnel dscribed in refrcnce 5. 'The results of these tests are ore scented in figures 5 to 8. The hilinemo.rcnt derivatives d.ue to angle of yaw and rudoer r, fle 1.tion, ;h,,r nd 11, r'ere determined from hir, ero!ent tects of the model rudder, the data from which arc pretent.dL in i'gurps ? to 11. The rudder hingem:imnt d ri.vative due to yawing angular velocity Chr :a then calculated by the relationship 2 = 1 C1hr b Chj (1) IACA APRE No. LiJO5a The y:rnwinrmnomnt derivative due to y'win. angular velocity Cn, 'l ig. 12) ."s determined by the iree oscillation I3tliaod idcscribed irn reference 6, a id the rudder hingemrnment derivative due to rudder angular velocity C was similarly determined. The measured D5 values of the narameter ChD (0.02 6 for rudder 1 and 0.01.2.L for rulders 2 eand ) did not agre? vith the value of 0.1.2 as calculated :by tht n;etLiod presented in reference 7 eyceot that the frequency or the oscillation was neglected. The rcau.se of tnis discrepancy was not determined but is b'l.iev,.d to have been the high oscillstion frequency at which the. tests were run (about 6 cycl3s per scconrl at an airppced of .J.O feet per second). This f'Tequ.rncy orre: onded arpro\rl:.tje]y to the c]oculct d frequency of the rudd.er in the. ru."der fr,.ee tests of con1litions 1 to ': in tsble IT. "easuremrints indicated ttPft the fricti i n',1 drlqpin.l of the rudder wa~s ::bout onetenth of the air dam oi l,. T"i.s value was cons idered ne.l i;ibT'. a.ind no attempt :, :rade to irtr'oduce fri. tl in der v*t. 'r l:itc the ~_ l.iaticns. Four runs vaer? re1.3 with er:;; rtrdder and tnr scatter o1 vali s .of 0' was le s. th:'.i 10 percent. The rartil *eriv't 've 'f the rollrn'm:rent *:oef f cient with re.sct to the rolling veloc'ity parsiametr 7 was d trined fr.,r, th? charts of P reference S. The deri .'ciLt ivs ,7 and C were r no c.rermlnred from the forimnlas riven in rerferen3e , *A;LCJ LA.TITO CS Scope Calculations were mide of the damiping and period of the ruddl.rfree lateral O.)scilli ti on1 ,of the mndel for the range of eir.milne arl rudaer parameters given in table I. These zal!uleti ons were made by equations that provided f',ur de'..rees rf freedom as well as the fewer degrees of freeoi. whi,h re.ulted from the nelct of rolling or the negle2t of rollins and lateral motions. Other cl..ul.tti3n wenre made to determine the effect of v:ry.:n_ th: effe ati ver!hedr:1 parae;rt.:r upon the rudder rfree sta bil; ty h r act' r stics. NACA ARR No. L4J05a Method The customary methods of stability calculation (outlined in reference 5) were employed in the present investigation. The equations of motion were set up, rendered nondimrensional, and so treated as to obtain the stability equations defining the period and damping of the lateralstability modes. Equations of motion. The nondimensional equations of motion used in the calculations are given in the following paragraphs. The equations used for the rudderfixed condition are (2 D Cy 1F + CL) + (2 + C. tan 0)1 = 0 C0 0+ 2j D2 + (L D) =0 > (2) (C + ( C 0 + 2 ) D2 nc D O j 0 Equations (2) yield the familiar lateralstability equations of the form Ak4 + B + CO2 + DX + E = 0 (3) The general equations of motion for the rudder free condition four degrees of freedom) are NACA ARR toT. LlTJJOr5 SL DC ) ~+ C + V L t ' Do + .. i, l = n (c1nS 1 + Q Cnlp + 2D Cr Q.r = 0  !r \ 1) rr + +  Et uations o) 7L. I 1 ' l t r : ts' li t ecuatiLcns ': th.. cr. A+ + + t ( )1 For tih ruddrfree ii tion, .l nr ling ic neglected i thiee (eiees of fr .l' .r), tr: r irs.ti, r Cs c e (2D CyF + (2pir)' = 0 + [2 2 I  2n r 'o ) /  .r b 7.h [ V r h ' L+ , " r h 2 +~ ~ F~C ;r ^D r b0+^ ^'/'4 +_ L.^ h ' 14 NACA ARR No. LLJO5a Equations (6) yield stability equations of the form A2,5 + Bp' + Ck3 + D2\2 + E2% + F2 = 0 (7) When the rolling rrotion and the lateral motion of the center of gravity are neglected (two degrees of freedom), the equations are r 2 L . ,. +2 ( 0 1'8) 2Lb D + 24r C D C C i r / r'i b + LPr. h5 2 Db D = Equations "E) yield stability equations of the form / + B. + C + DL + E = 0 (9) Tf, In. asd,'itJon to neglect of rolling and lateral rotLj n cf the center of gravity, the rudder moment of inerta is al.o neglected, the equations are D nr D C (Cn6)6 = 0 / >(10) K 7 D2 rD C c + Ch D Ch = 0 b2 (2 L. NACA ARR No. Li 05a 15 Equations (10) yield s*abil'ty eqution. of the fcrT A + E2.2 + C + D = 0 Deterrmiinaton of feriold end 'rmp3'nt o'f 'i_',:_ 1 oscilltiion". The ro's of equao'n r i ], 7 (T, 7, TT, and (111 ar) cf th form, a or 1 .. + b' Tile roots are us id in Ic..e follo;. n eq..'.. ti oni t,: d 'etLr mine the period nd the t i.? to d.,' to onehrol ample i tude: ? = '12) and 1 o ; ., 5 , a _ T T A T ) R .L T 3 A ;' C ;," T ,, *r0 . The results of the test. n3 n 1'.: 1 lti ln. r : r.: rnted in table II, vhi h list the crt r : . :i. fe r c i :. . : l t tne time to rha p to oneha f l" p11 i tti e i,:r 3r cl, o, iL ti .in inrestijated. Tr:e Cr'ec ro cal of the ti"e: to d ,: n D J.n  half amplitude was .ch sen t v lu.:tc t'. d, p] i ; this value is di ic t :rat.L than a!, iiv':rs r':re3st; 'e the degre..of stoa lit;. .e 1: ivi vt ':91u'j * f t i.e rciprocal of the ti.e t to drro to oneh:ialf a'li t' c r.ef : fr to t.. time to increase to iouole a.':l.i t:.'G Cor.rel ti ton of rest s cnd .' neral 2 :ua tirons Calcillat; n s. 'Tr7e vtsQ .. J t.i. ';ti On.: r..1 ad v 1 th the general eq.a~t ions o1 r.otLon i nd:i e : t LTt t t:'ott.ons of an airplane vi th r drid.r f'r.: c;a, st of two aperic r.di,3 m"?des (convergences or di'.er ..,ncez) 'ni two o. cill.tor/ nmories, one of which ;is_ ofI ci trl d 2 to 10 timLS t.iL othicr. As shcwn by' t'h re ult '.reseated in table II,the23 calculations indicated thct, as Ion,: as tl, rudder radius FACA ARR No. J4J05& of gyration nnd mass unbalance ware small (conditions 1 to 9), the shortperiod mode was very heavily damped and, consequently, the characteristics of the more lightly damped longeri d mode determined the nature of the rudderfree oscillations. Table II Indicates also that the characteristics of the longperiod mode were only slightly affected by the rudder parameters as long as the rudder mass parameters were low (conditions 1 to 9). rhlien the radius of gyration and the mass unbalance of the rudder were larre (conditions 10 to 15), the calculated period of the shortperiod mode increased considerably and the d.'moing decreased. At high negative floating ratios ;conditions 12 and 15), the calculations indicated that the destabi li zing effect of high rudder radius of :,ration sand rrps unbalance was sufficient to cause Icteral in;: tc&c I ty. SlL tLs.t. T)ic results of the flight tests are presPlited in tro]e TI. Tn.se data indicate that,for low values of the rudde' r :.llss naramoters (conditions 1 to 9). the less '"" pe and hence thbe apparent mode had a neris)' of ftout 1.5 seconds, w.hirh corresponded to that calulaterd cfr the lnioeriod mcde. For high values of the rurddr mEss paraw:ters (conditions 10 to 15), either the long or th short eriod mode was the less damped of the two rod3es end rence determined the characteristics of the apparent r.:otion, dependint uoon the magnitude of the r,.lddcer &erodrinamn'c parar' ttr Cp and Ch. For the condition of h1ih rudder aerodyn,,mric parameters (condi tions 10 arid 11 the longperiod mode was the loss damped. Condition 12, however, showedV the shortperiod mods to be the less da.pec at som.;,.'hst lower values of the rudder rnass parameters than those of condition 11, and condition 15 ave an unstable shortperiod oscillation for even lower values of rudder mass parameters. Comomaris .n of theoretical and calculated results. Tho tests conf. rred the results predicted by the theory inasmuch ss an unstable lateral oscillation was obtained for test condr.iti n 1. The quantitative correlation of measured valupe of period and daTrping with corresponding values calculated by the use of the general euattions is shon in figure 15. The.. data show that the agreement between measured anr' calculated values of period was excellent for ill conditions tested. This agreement was also shown In the correlation between measured and calcu lated values of dumping eycert for conditions 12 and 15. iNJACA A"? Yo. L .JO 5 10 For conditions 1.2 andi 15, the aclcul..tion indicated & larger ce.;ree of i': nstA ility thiur. t'ut e:.i,ou; nteired .' th; te"ts, This sppre't rdi s rcpJ;..:;, as exp : flne L' furchor c'.lculat. :ns *"h.i';i sho;.rdL t 1nt ti: rud lrfc stao'" litvy was 2.1 ti' al ., d. pe dnrt aon r "'e rul: :r' :s :. characteriS tics 3 for. tihse test conJ ti on The r sc. . of the 'fu11her rsl l. tuiat ins ar' P v n in "E'. e il ., Ehow thst +he d..;re o n:st aci i t v e r.. g'i t :r: i n r ,t conli tion 1' woa 7n 2 cted 'c..y t'U.,r to ':.e.c r t r.:  what srall.er values of nSF luLr]1 e i t th.1" Ls .'orz the test. An .her r, sI 1 :1: :ti l tA: dt.' .r  ancy h1etwoen to: ts r.c t.i=c.r ....r ;:,v.'1.tiro s 1.2 eand 1_ is tlit thn a'tus.] .:iCe ni F.,r Ltter lo"' fr c'ency condition' J nwi, "'.t Tha; he..r. ,i r n r! rh ,*s n ,.: in the calci i t ons En c..:: rn d T i hi h r ? 1: ...r. 'ents 'lore nf'or,, tic is r. . r:.I to 1.: r r.'ire t':,1 effect of frequency ol te: o. 1i, t nr. on thi s jpra tcr. Physical inter :r,'etct n. 'r, r:epr tn eF:xpl'L in :.ore clearly the physical t s t T .' ttc.:, lor.' anj short..riod modes of tie rur'derf iee nscil t ; ns, .Jd 1 tion.l ".oi lations iv.ere mec'e of tr.e ia.derfre : : i .: rfi. stability character.'istic ove'r i. ras,e of Lih i '1.l In this wv'ry, itW v s r.s l.e o cs :.ve ar.lyt call t ch nige of literal st tbill ', :L ....., i s_ I hen th.3 r.'.. er was 'ree. A comniaris n of th, T.r s.l3 t? f t ': trudTi' fi cx and ruJderfrae c lo1.] S t. ns i '"'L Le t'; t tL z'.o't period mode of thte rul rj' fre. t.sc'. liatli on hm' r'o '"v 'nte r part in r.iriderf' ixr fl :ht s .,e T, :. < ition 1,. Ths mode, t eefore 's 3 n nantir.!y n . ; Lr, create. d th3 new' d'J g" e f i" ed I a'. 'c"" r the rtuddt.r wa'S fr3?d n i rc l', r"n r Js1 .' Ss t' 1 lati on of th. mdeuider out its 'vn i i tie. T: '.l  lat i.ns 'also shov;e t'h.t t ; i~ya t:eri st: t " th. sho.3rtpe iod mO were m. v ..lt ua.i in.i' : '. t o the effective dih '.irs .:i 3t r c v ri .t n o" ti calb ulat3,d val'.i s i a.,xr o' .i. 1.. ?Z. ;. ..:.'  period o .ill at n f.:'jr n. ,i lt '. th .'. 'l av . diher.ri. l no.rs: .t r i: o ;'e ':1 P" 1 / T .' c ._. _7 L c .03o .c.7. j  .12 .'.7 l. t .i .16 .0o7 I 5 NACA ARR No. L4JO5a The additional calculations indicated that the characteristics of the longperiod mode of rudderfree oscillations varied with the effectivedihedral pora:neter 0. in a manner similar to the variation of the rudderfixed oscillations with this parameter. The results of these calculations are presented in figures 15 and 16 and indicate that the characteristics of the longperio'd rode for the rudderfree condition were of the same order as th:.se of the rudderfixed oscillation but were of lower damninn and higher period. Inasmuch as frtein rudders of negative floating tendencies is known to decrease the directionalstability parameter Cn und a decrease in this factor is known to decrease the dsaDnpDig and to increase the period of the lateral oscilltion (references 10 and 11), the longperiod mode of the rudderfree oscillations appears to be a modifica tion of the fariliar Dutch roll oscillation normally encountered in controlkfixed flight. The characteristics of the longFprloc rudderfree mode may then be concluded to be largely drpendrnt. upon tnei same parameters as the rudderfixed osc'llttory mode. For airplanes having rudders of n.Egative floating tendency, then, instability of the longperio. ru.dderfree mnde should occur at smaller values of effective dihedral than for the corresponding rudderflxId condition. Correlation of Tests and Simplified Equations 'reclect of rudder psrarreters. Inasmuch as most presentda,' eirpolnez have low values of rudder mass parameters, the longperiod rrode is the predominant factor affecting the rudlerfrec stability character ist!cs for Eiroplnes having rudders of negative floating tendency. Consideration of tne rudder mass parameters would therefore not seeir necessary for these airplanes. An anproximste scljtion for the rudderfree stability has been obtained .by simply considering the controlsfixed dynamic lsteralstability equations (2), in which the value of I' for the rudderfiee condition is used. Calcul.stions were made for the test conditions by this epporcixiate method, and tht period aid damping results are presented in table 11 and, for condition 7, as points on figured 15 and 16. The value of Cn for NACA APR No. L4JO5a the rudderfrse condition was calculated by the follov.inz relation fromr reference 1. Ch C n ni n C  C  'J(rudder free) rudderr fixed, h5 "b The values of period and darping obtained with this method are in good asreeiment ith the values calculated by the general equaticns for test conditionss 1 to 9. For conditions 10 and 11 the sorrelstimn is rather poor, as was expected, because of the high values of rudder mas. psarm.eters at these two contittions. Because tle approxintr, e r.thod cannot predict a shortperiod oszil laLio., this method failed completely' to predict the imports'..t features of the rudderfree mot,.ns for con ditions 12 anid 1, for which the snortzeriod oscillation v, :b.t ncutraliv darned. These calculations indicate T' . .thruh the predictions ,ielled by the approximate .I.L:3.d are 'rd st low values of the rud.j'er mass rarEmete.rs, i 'more com Srl'e analysis is necessary at high values of tle3 ruddcrr m sss parsireters. FNe'.ret of rolslinz otion. The s]i.r.xlifis&tion obtained by ne p c .. n rolling r': oion ',a; ,s !nv:esti.: cL.. ed for the zlrsen :. report by cor:pai ng; the results ,, btaiLned by the :., 1. equo tinr wv.th chose obtained b. eqiauations !" i' LL.' i'n r'llin. equal ion 6). The ,I. I . of period S .... .i for the test con ti on. as I.''iilated by erL. .s ticA (6) are presented in ttble II. In figure 17 the crrsacteristi .s of the shortpericd rro.e obtained by this method are compared ith thoe calculated by the generall equations. The correlation o" the characteristics of both t'e lon.: and s"hortperiod m'iod:es cr iculated by the modified equations with those obti ned rom flight tests or from cJicula~tons by the general a uati Ins is fair except for r...'itioTr's 10 :nd 11. This fact !nj.cht indi aL'e that trh s lifl fi ,d rh.orr.y ,i' es ",oor ccrr itin for the case of nnri.:'"i.trl stability of the shortperi.o mode when the Dpr.cd o.o the iong and chortperod modes i73 nearly eq'... . Equoi.tion (6 show tiEt nEglcct of rolling eliminates all of e d']ivativos ini. lvrng rolling mome,?t as well as tbos invo:>lin rollIng motions. The effect of C. NACA APR :'o. IrJO5a on the lateral stability cannot, therefore, be predicted by this si.mplified method. The effect of dihedral on the longoeriod mode is to reduce both the period and the da!ping, as is shown in figures 15 and 16. For dihedral angles less than 5 C < 0.06 however, neglect of rolling in the equations gives conservative results,because these equations indicate less damping than the general equations for low values of rudder mass parameters (conditions 1 to 9). This result is obtained mainly because with low dihedral the rolling component of the, motion is small, The effect on the stability of neglect of rolling with rudder fixed ha: also been investigated. The results of these calculations are given in table II under condition 1L. and show reasonably good agreement with th3 results obtained by the general theory for the rudder ftLed condition. This agreement is further proof that, for low values of d.hedril, rolling ray be neglected in making thest calculations. On the other hand, for air plane? having hiph dihedral and large values of relative densi ty nd radli of [.ration, the longperiod oscilla tion might become unstable, as shown in references 10 and 11. The neglect of rollinE for these conditions would invalidate the results for the condition with the rudder either free or fixed. ;eglect of rolling and lateral motion. In the theoretical analysis of rudderfree stability published In reference 5, the equations were further simplified by necleting lateral notion of the airplane center of gravity as well as the rolling motions. These simplified equations also predicted a longperiod and a shortperiod oscillation. Tests of the model in the rudderfree condition were reads on th: yaw stand in order to reproduce the theoretical assumptions made in reference 5 (freedom in saw about the i. rplane Zuais and freedom of the rudder about its hinge lin3). The results of those tests are presented in table IT an1 indicate tLat,for low values of the rudder mass p.rsa~eters (conditions 1 to 'Q), the lon7period mode was the less damped &nd hcnco determined the characteristics of the apparent motion. For higher values of the rudder mass parameters (conditions 10 to 15), either the long or shortperiod mode was the less damped, depending upon the magnitude of the rudder aerodynamic NACA ARR No. IJ1JO0a '1 parameters. For conditions 10 and 11, the long;p e r in mode was the less dariped ::Jhereas for condliri ')i 12 .nd 1, neutral damping of the shortperiod rode *vis o':.tCini at lower values of the rudder mass oaraneters. Tt ma" be of interest to note th.t i: unobli s': cata from y;awst.ar.. test, mede. a nic' v'l. s of ':' ssZ unbalance of the :':d.dde tChn thhan hc' r;: nt.d h':.n, rn unstable shortciod os.i.latic: ,,a, ...t.t'.r.?i. Thi' unstab'; oscillaori n could be st te,' L t." v'r'; s'.r ll disturt;nce and vo ulo r n.creas. in rl..i tdfie until it became a constarta rpli tuide oss llaticn of fOsoat +1'0 yaw. The results of col. ul;tion. .rade by ,ti 11r,n, the equations of reft'r'encc 5 are listed. n tsblie ITT nd hEve been compared in fiTure 1j to meas..red values obtained from the ypwst.rnd tests. The rieta piseiited in liu.re 18 show that the equations of ref3rr.nce 5 closely predicted the rudderfree dL.ta octa*ne.d in th'e ,swstand 'ests for stable condi ti onrr L: '. the rerersl theor,,, how/ev: r, the simplified c.,unt2. ons r reJF cted,] insa i lit.:; cf .th short period oscillati c u:c c I _w:r v'alu,s of r.Li!.kl E mr'I.s a r ml terms than did the yawstand lests. A comparison of thi i,v,.; t.nd and fr.eflight t:.t results shows that the elirrinstiton of the rclling and lateral motions results in roe,,'hat '.oner perilo' t'nd less damning than is obtar.ed in flight, :.s !oloin as the longper:iod ercillatc.r. Is '"he controllin. I :er in' th~ atarent moti n I; f lit.'.. '..;n the cher?ter' .t :.s of the. shecpc ond c.i .. l 1'icln ar asoprent in fi .ht, tes~tS o.' the yAv:' s .: c gtve': nearl. y I t' t't r:.:' with rT cse frojn ,g t : s. a. '!:e cst iri ; t for smerll efIee+.i. 'eirL' an l.es ie let of the roiling and. lateral rictiuon. ie's c.ot ,er 'F 1:*_; "arlue;r for tl.e longer~ri.od, rui:.derfre cs 11sill o'n arnd r. rate values for thn ,I rt .... tn 1i.ticn Li... i .t co:,irrr the zn, ..ni n drs.'. f .he an ': ".c.l in.zsta nation c:,'ra r. n ni : the If_' t f L : er..:l, that th: characteristics of tie ;':,r'teri od mde ',are relat.'velv iniener..de t of ui: r.1, :hich s a :asic rolling derivative. The data of qbSie IT indicate that the si.nlified theory of reference 5, '.iich ne !. zt: ryollirn and lateral motion, predicted the charLcteristis of 'he shortoperiod mode iust as well as dd the enp:3l ti.heor, and that use of the simplified theory r.a! therefore jstified in this respect. NACA ABR No. LLJO5a Nerglect of rolling, lateral motion, and rudder moment of inertia. A further assumption suggested in reference 5 is that the moment of inertia of the rudder, in add5t.ion to rolling and lateral motion, night be disregorded in the calculation of rudderfree stability. The results rf calculations made with the rudder moment of inertia neglected are presented in tabl3 II and indicate that, for airplanes with small amounts of effective d'hedril, application of the theory gives a rcasonchly :ccure.te orediction of ths rudderfree stability chsract ristics as long as the lorngpri jod oscillation .s t.3 c !*tr ll' r factor in the aopp;,'a.nt motion. For corit: ';3 '" which the sho:rtpetc oscillation is the le s Jd''". 1 :td hj.,ev':r, the S. .j'c'm : n r!iS m t be con s ier ,' .. ', in i f r r' ?. .": of ,::. ve floating te n:' r 3, ,.'.s e the c a .. LL' l ion; 1 r..j2 i e tT.at, when the ru.'.; m ricnent of ir: rti a is 1 .i.:l1z 'd, the short peri.jr mrode is replaced. by a tea'ially dLrrped convergence. COIC LUSIOi.IS The fnl]ownIng conclusions were dr'vri "roT an inv'sti.":tior. in three ticr'le: fr:r;fli'.t tunnel of the rudde; '.re.l. stab.L. ty ,.sra'scter1 ti .s of an airplane nmod'1 l ~ou;i p dr1 v.'th n ..'.'rerr'.e cf n llat 'l floating tend~n:!ies .,d !ibin.n ne.lirible3 ricoion: 1 F)r Tm st rre~e t % : , ,ir r,].n, :onsiieration of the r''".' r :' .'s pc.ra t .t rs ~ :i , ' ari: in an analysis of tTr h" 'fr stul r''" :". tC L,.< : Th .se ch9:' r. .s OP .: '. .i' .y >. nsidering tht ... *.ter I sxto' i t: ,', b07 u.ing the value of the i :r.'r t c. Zl il Ly :J cio!,m,: r Cn for the radder free ccr' IL t io.n ii. the converttlonal control fixed lateral stability ec uat ors. 2. An. l..:, of th ruri .erfr' stiabi lty of airplanes having re i .r ,' ,.. v'alC *f t, h? r:' .dder mass parare ters wl:t reco t t he rur '"e )rrd', .amic parameters (such 3s vould be enci,_.unterc in T.ry large airplanes) should be made rith the conri lete equations of motion for the rudoecrfr.ee cor,nitirn. J. The rA.derfree stability+ characteristics of the model tested were saLisfactorily calculated when all four fACA APR ITo. LIJOCS degrees of lateral fre.dornm .ere consilercd in the cal.u 1Eti on0. L. The roludl rf rre .sh r..ct r st icr of t} :m' '.el tteted were predicted fftirl: well whn rollin mori :ns or rolling ard later s! notinrs ,ere ne;e. :1 ct.d in t_ calculations Tnsta.br ty 01 tn ru] ..rf r: : t D t: ,, 1 ty e oscllt 11 .at on, how ve oC ld n t be : r A! a t.d ., this metrhcd. 5. Larg. sm irnt nf r.i':.er c:.s b.lan'. 0 use d an unstable shortp riod ra'..erfl, e eilll: jt on 'or the model tested. 6. The ,:qsracter'istic. of thl hortp3riod occil lation are found to ba ''n.j,Dend nt of tihe airlJ.ane effective dihedral and Lver.3 ratizsftoril]y or'edictcd for the model ter~ted by either the general stability eluastLins in which all f'cur degrees of ] E,t 3l fr ef.doin re considered or by the mo'":' field stucbi.lit.; equ:; tons i.n .i!.ch ,.ther the effects of rolling rmtions s91'le1 or of r'llin tions and lateral motionris of the ai'rl.nei center of cr' vi. t' are neglected. 7 T1.hen the rudder , nor..ent .oF in nrti: was neglcted in the calculations, t'ie cho3r~.teristic cf the short period ruddarfre osci 1 Lti ons f or ruderrs havinn negative floating t.er.Ji .r i coall .rot n pr :'ict :d. Langley Memorial Aeronasut ic l L'bor.topr" Fat. onal Advi sory Cornrit t e for Ae'onr.a tit ? Lsngle',y 'eid, V. NACA ARR No. LJJO5a PREFEBENTC ES 1. Bryant, L. '., ,nd Gandy, P. W. G.: An Investigation of the Lateral Stability of Aeroplanes with Rudder Free. L504, S. P C. 1007, British N.P.L., Dec. 18, 2. Jones, Rooert T., and Cohen, Doris: An Analysis of the Stabillty of sn Airplane with Free Controls. IACA TFep. In. 700, 1941. 5. Greenberg, Harry, and Sternfield, Leonard: A Theoretical TInvestigation of the Lateral Osa4llations of an Airplane firLh Free Rudder vith Special Reference to the Effect of Friotion. lIACA ARR, March 1945. !. Shortal, Joscp l .., and Osterhout, Clayton J.: Pre liminary Stability and Contrcl Tests in the NACA Freer'li hlt 1.ind ..Tunnl. and Correlatln with FullScale light Tests. I.ACA T!T ro. o10, 1941. 5. Shoital, .Toseoh A., tand Draper, John V.: FreeFlight Tt'nn3l Investigation of th3 Effect of the Fuselage Length and the Aspect Ratio and Size of the Vertical Til o1 Lateral Srab lity and Control. NACA APR U7o. 5D17, IC'5. ,. Campbell John P., and ?.athe s, Ward 0.: Ex'erimental Determination of the Yarin,.3 Yorrnt Due to Yawing Contributed by the Wing, Fuselsae, and Vertical T.il of a 'id ding Airplane "odel. NACA ARR No. 5F28, 1943. 7. Theodorsen, T:lodor: *eneral Theory of Aerodynamic Lnstnbility and the ie.chan1sr. of Flutter. 1 ACA Rep. dor. .17, 155. 8. Pearson, Henry A., and Tones, Rc.bert T.: Theoretical Stabi.lity and Cjntrol Characteristics of Wings with Various Armounrts of Taper and Tw' st. :ACA Rep. 3. Friaber, :illar, J.; Effect of Some FresentDay Airplane DesPigr Trendi on Feq'tirements for Lateral Stability. ITAC A TIT No. clh, 19 1. NACA ARR No. L4JO5a 25 10. Campbell, John P., and Seacord, Charles L., Jr.: Effect of Wing Loading and Altitude on Lateral Stability and Control Characteristics of an Airplane as Determined by Tests of a Model in the FreeFlight Tunnel. NACA ARR No. 3F25, 1943. 11. Campbell, John P., and Seacord, Charles L., Jr.: The Effect of Nass Distribution on the Lateral Stability and Control Characteristics of an Airplane as Determined by Tests of a Model in the FreeFlight Tunnel. NACA AFR No. 3H31, 1945. L.\ rt S L c. r1 \ 1 rs N N1 LU1 0 LC OJ Lr Lf, r F C ,C r co r , r\, . 0 o 0o 0 O 0 0,k j r CJ 0 O0 0C 0 0 0 ,  0 ) 0 0 00000 000 00000 00000 000C C o)J \,D L., fP. L', L \ Lr L, r 0j 0 L C :, C .0 C L C1 T J C3 CJ i J C 1 (11 Lil l.r 'J [^ o0 :3 c C 0 0 C, r. (J rr,( C C 0 0 0 '_ 0 '. 0 0 0 O C a 0 0 i [ Z L. 1 , 1 0 r 0  [ , ' L L." r l c, 1z I Z , pr ,' p. r ,4 Q S 4 !i 0 C0 0 C 0 i' E rN 0 0 0 0 r00 r. r o .oo . o S I l I I I I* I I , r 0 1 "" ,"' 0 I .. . r. 0 o' ". ..  C I' l l IIII IllI I C c r j i 1 * *T 0 ^ i *; 0 J0 ,0 o t_  N". r' r CL Cl oD Io \ I c 01 (N 1 01 C1 OJ (1 (C\l OJ CU c r i O' c' , ,4 r  C 0 I l A l T   : i 'J C\J C J ClC, 1 0 n cA J 0 r *t C. 0 o0 C ' r 0o C I I II I I I I C r, ~ ~3I o o c.. IT t *J Ci ;i Cli 0 r i l 0 Q. r 0 C 1I I I 10 I 1 1 I I I I l) 0 11 iI 0 E. V I F Ct Er; U NCJ N Nr.r , rlJ pC NACA ARR Fo. L4JO5a  o0 C 1 o 0 I I II II ,. x.n 0 U wo U U u) V I V II II u 0 40 C . . 0 0 I I II II CJ Ll s r r 0 II II CJ 1. ^\* I r' Cu COJ I"" C 01 II S1 KP<  0 0 I II II .nP ' C C rr  L.% C L, CD C '7 ro C(J ..$ rI r r r' *1 NACA ARR No. L4JO5a TABLE II. COMPARISON OF PERIOD AND DAMPINO FPOM FLIOBT AND YAWSTAND TESTS AND CAiCULATTONS Tests Caloulations Rolling, Rolling sldealip, Rudder Teat General Rolling and and conditions Flight Yaw stand theory neglected sidealip moment of parameters neglected Inertle neglectedb neglected Iongperiod asollation S Period, P 1.72 1.80 1.69 1.6 1.66 1.6 1.60 Daping, 1/T 1.17 .90 1.12 .a .92 .9 _1.39 Period. P 1.61 1.78 1.60 1.60 1.6 1.6E 1.60 S Damping, 1T 1.09 .90 1.10 1.27 .8 1.5q Period, P 1.48 1.66 1.40 1.70 1.60 1.61 1.60 SDmping, 1/T 1.06 1.00 1.10 1.32 .98 1.00 1.5, Period, P  1.69 1.60 1.70 1.68 1.68 1.60 a ping, f/T  .90 1.)8 1.26 .95 .9) 1.59 Period. P : 1.65 1.56 1.60 1.6 1.66 1.60 5 Damping, 1/T  .90 1.59 1.30 .9 .96 l.9 6 Period P  1.62 1.6 1.60 1.62 1.62 1.60 Damping, 1/T  1.00 1.1 1.26 .99 .99 1.59 Period, P  1.86 1.7" 1.80 1.83 1.82 1.71 7 eping, 1/T  .0n 1.5 1.20 .88 .88 1.59 Period, P  1.79 1.65 1.7 178 1.77 1.74 8 mping, 1/T  .90 1.55 1.2 .92 .99 1.9 Period, P  1.72 1.55 1.60 1.7 1.72 1.74 mping, 1  1.00 1.30 1.30 .97 .97 1.9 Period, P I.50 1.60 1.20 1 1.9 1.50 1.60 10 amplng. 1/T .90 1.05 .92 1.5 1.05 1.U1 1.9 Perloa, P 1.15 1.50 1.05 1.20 1.1 1.60 11 Daping, 1/T .8 1.20 .90 1.5 1 1.50 1.59 Period, P   0.96 0.99 1.06 1.16 1.60 2 Damping, 1/?   5.50 5.80 3.85 1.74 1.35 Period, P   0.7 0.98 1.1= 1.2 1.74 1 Dmping, 1/   5.22 5.19 5. 1.60 1.9 Period, P  1.56 l.0 1.66 1.50   I Dping, 1/T . 1.00 1.87 1.L4 1.05   Shortperlod oselllatiln Period, P   0.16  0.15 Damping, 1/T   5.66  4.92 L00 Perl.od, P .  0.09 0.09 0.08 2 Damping, 1/T   15.15 14.55 1.1 6 5L8 Perlol, P   0.20 0.1 0.12  5 Deainng, 1/T   4.45 5.L0 .l6 570 Period, P   0.10 0.10 0.10  4 Demping, 1/T  32.50 50.80 52.50 152 Period, P   0.10 0.10 0.10  5 Damping, 1/T   52.50 .80 52.20 1l7 Period, P   0.10 0.10 0.10  6 Dmilng,   52.50 50.80 52.20 LI1 Period, P   0.12 0.12 0.le  7 Damping, 1/   2.50 50.80 32.0O 99 Period, P   0.1 0.15 0.1  8 Damping, 1/T   2.50 50.80 52.20 9, Period, P   0.15 0.15  neping, 1/T   52.50 50.80 52.20 88 Period, P  0.80 0. 0.6 10 Dampingp. T   1.90 .88 .76 322 SPeriod, P   0.87 0. 0.51  11 Damp ng, 1/? . 1.56 **. F7 U278 Period, P 0.83 0.888 8 .0.81 0.90  12 ampl ng, 1/T .10 .00 5.51 2.75 1.52 71 Peri o, P 0.92 0.90 0.86 0.92 0 . 15 Damping, 1/T .15 .00 2.76 2.19 . 4 65 _ Period, P    1 Dmping, 1      P and T liven in seconds. bApproximate method, all rudder prameters neglected except those affecting C . NArTONAL ADVISORY COMMITTEE POP AEROBADTICS i 1 ii J NACA ARR No. L4JO5a FJgure /. Three view drawing of /te modified scole model of the fairchild XRZP? Qirpltne. Fig. 1 NACA ARR No. L4JO5a Rudder / Rudder Rudder 3 Sections AA Rudder area Balaece Rudder In percent inpercnt vert/ca/to/ rudder oreO oreo / 40 0 2 40 3f 3 40 3" NATIONAL ADVISORY COMMITTEE FOR AERONAUTI F/gure Z. . 5Jetch of rudders used / f/Ae ruadderfreQ stab ly d nveestigafbon in the laingley freef/'gAt tunAe/. Fig. 2 NACA ARR No. L4JO5a Fig. 3 V rA *4 t o O4 C4G a) 64 00 H 0 EU 00 I C uO O a aE 10 o  ed  e co I Cd 0d Q) 00 E W .4 a, 0 Cd cd :3 X ho a, 3 H Cd Cd E aj C a, 'i Li~ ~ei. Cr d ii~uH NACA ARR No. L4J05a .1 C) rQ, I LAZ cO M 0 c o 69p ( ) o'M/o a/6uv Fig. 4a NACA ARR No. L4J05a Fig. 4b ..  CO 00 a EE 1o R ', 
nl$  f^ ^r ^  6 ^^ ^ ^ 6& 16'/ zr 0o a/6t/v NACA ARE No. L4JO5a 0 1).3 $ 0 0 8 /2 of cf/acAr,) odeg Pilchn rmomnt coeff,/enl/, Cr f/gure J. Aerodynam/c Cho,7cter/stIcs of the mooe/ used n the freef//ghttunne//nvest/gat/ion of rudder free st6//ty. Ar?9/e C /I _ Co Fig. E SNACA ARR No. L4JO5a Ang/e of yogw, Y, deg F/lure 6. Ruf/dder efferveness fAr rudaor /. Fig. 6a NACA ARR No. L4JO5a > .2 0 .c0 I S.01 I 0 E (Z Fig. 6b 0 0 /0 An/le of yaw, W, de9 Fi ure 6. Cancladed. NACA ARR No. L4JO5a Fig. 7a .05 0 O 1 S  1 SA 1/0 S 15 0  30 .0> O^ X20 .0 /^^ u^ g  ^ Ul \ i \ ( ' <  \ Figure 7 Rudder effect/venes or ruodder 2. NACA ARR No. L4JO5a Fig. 7b 3 .2_  / S  __ (dog)5 d  l3 0 2 _9_ _______ .3 20 ___ 625 a3 1Ivo~ 96 .03 /3 0 05E) flgare 7. Conclarkd. NACA ARR No. L4JO5a 02 01 .02 03 D4 f/qure 8. Rudder effec/veness for rudder 3. Fig. 8a NACA ARR ho. L4JO5a Fig. 8b 01O Ch 0 "N '9 ,; 0 c Q I I I I I I 11111. I I II 3 ua/lfDijao a3o}_/OJia/T7 NACA ARR No. L4JO5a Figs. 9,10 S I Is I" ,_ *     .. S 00 N 0NOs  ^^~  T a ^0^ %Y ',uaiPiq9 os ,tuau/oWwabuiH C O ^'b S ^e II __ I NACA ARR No. L4J0O5a Figs. 11,12 __I j_ _ 1,  . % a 0 0 4 _____ 8 al oZ' '. 00_~ 'Ii Q .  "/,.,,' fall/u.W ,' NACA ARR No. L4JO5a Fig. 13 y^ 0 9 /i '/Ipo/j1dp pffolngly S     0 NACA ARR No. L4JO5a 2 \0 Al\asured __ ____ ___ ____ (fconodf/an / 2   NATION L ADVISORY COMMITTEE OR AER NAUTIC 03 o ./ .2 .3 .4 .s Pudder certerofo/p raty /xcohto ,//. 7gqure /I. Co'npor/son of calcu/fed aCnd measured dampn9 o/f the shortper/od ruddeP/o e aro//tan. Fig. 14 NACA ARR No. L4JO5a Figs. 15,16 sas/, /N badwcLd C 20s 'G( 'POO'ld 'A.L 0 I. N 0 O OU I u* glil Bf 68^ $z ^^1~ ^^ NACA ARR No. L4JO5a o OQ N 0 S99 's'fu /OJ, 6Ual/69u 'pO/J 6uio /o o' CUO r 6wuol 6U/lpal(7 / 'uI cciUs 7 $" 8 b d, il Fig. 17 lql NACA ARR No. L4JO5a 3s"' rd Ppo/.j,, paO/inalo3D (nj /Q '6 /ot: 'q// '6u/11aP Qj 0Z a o to Fig. 18 lZ p/fO/n /Oo "1 'I I i > I UNIVERSITY OF FLORIDA 3 1262 08106559 0 UNIVERSITY OF FLORIDA DOCUMENTS DEPARTMENT 120 MARSTON SCIENCE LIBRARY P.O. BOc. 117011 GAINESVILLE, FL 326117011 USA Ai ":h 
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