NATIONAL ADVISORY COMMITTEE AERONAUTICS

Transcription

1 _ < NATONAL ADVSORY COMMTTEE FOR AERONAUTCS TECHNCAL NOTE 368"/ SOME WND-TUNNE L EXPERMENTS ON SNGLE -DEGREE -OF-FREEDOM FLUTTER OF ALERONS N THE HGH SUBSONC SPEED RANGE By Sherman A. Clevensn Langley Aernautical Labratry Langley _ield, Va. Washingtn June 1956

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3 NATONAL ADVSORY C_[[TTEE FOR AERONAUTCS TECHNCAL NOTE 3687 SOME WND-TUNNEL EXPERMENTS ON SNGLE-DEGREE-F-FREEDOM F_ OF ALERONS N THE HGH SUBSONC SPEED RANGE By Sherman A. Clevensn SUMMARY Results f wind-tunnel tests f _hree wing mdels with varius ailern cnfiguratins are presented. Density in the range f t slug per cubic ft has little effect n the initial amplitude r initial Mach number assciated with the ailern scillatins (buzz). Hwever, the frequencies decrease smewhat with decrease in density. The initial Mach number assciated with buzz decreases with increasing angle f attack, whereas mass balancing and changes in spring stiffness in these tests have little effect. ncreasing the ailern mass mment f inertia lwers the scillatin frequency. Placing the ailern at the wing tip delays the nset f buzz t a higher Mach number. There are experimental indicatins that the buzz range is limited t a range f Mach numbers abve the wing critical Mach number. A cmparisn f the results f the test data with tw previusly published empirical analyses is made. NTRODUCTON Great interest has been shwn in wing flutter which essentially invlves a single-degree-f-freedm flutter f ailerns n wings f high-speed airplanes (ref. i). This vibratry instability will be called buzz in this paper. Sme buzz tests have been cnducted at the Ames Aernautical Labratry in the 16-ft wind tunnel (refs. 2 and 3)- These tests were made with a full-scale partial-span wing and were limited t ne density cnditin. By use f the facilities f the 4_-ft 2 flutter research tunnel f the Langley Aernautical Labratry_ it was pssible t study effects f the density f the testing medium n this scillatin phenmenn and thus t determine sme effects f altitude. n additin, infrmatin was btained n the effects f changes in the inertia and spring stiffness f the ailern, f mass balancing, f angle f attack_ and f spanwise ailern lcatin (r tip-relief effect). isupersedes declassified NACA Research Memrandum L9B8 by Sherman A. Clevensn, 1949.

4 2 NACATN 9687 This paper presents the results f the analysis f the data btained frm three wing mdels with varius ailern cnfiguratins. t sls gives a cmparisn f the experimental results with the empirical analyses f references 3 and 4. SYMBOLS std r_ 2 mass-density parameter at standard air cnditins, rati f a mass f testing medium f diameter equal t chrd f wing t mass f wing, bth taken fr an equal length f span square f nndlmensinal radius f gyratin f wing abut its elastic axis a nndimensinal crdinate f axis f rtatin frm mldchrd x lcatin f center f gravity measured frm a 2 r_ square f reduced radius f gyratin f ailern referred t c reduced lcatin f center f gravity f ailern referred t c crdinate f ailern hinge axis plar mment f inertia f ailern abut its hinge line, slug-ft 2 per ft span gh, structural damping cefficients fh first bending natural frequency f wing, cps f uncupled first trsin frequency f wing relative t elastic axis, cps f_ natural frequency f ailern abut its hinge line, cps finit experimental frequency f ailern at nset f buzz, cps k spring cnstant f ailern hinges, ft-lb/radian

5 NACATN M Mach number M r theretical Mach number at which snic velcity is first attained n sectin f wing at zer lift Mch experimental Mach number at which wind tunnel chkes Minit experimental Mach number at which buzz is first bserved A g aspect rati f ne wing panel c_ P wing angle f attack, deg density f test medium, slugs/cu ft The fllwing sketch taken frm reference 5 shws the physical significance f the nndimensinal parameters tabulated in table. Leading Quarter edge chrd -i --i/ 2 Midchrd Trailing edge 1 r 2 c _ Axis f rtatin / c.g. f aile c.g. f en/tlre_l_wing 1 APPARATUS ANDMETHOD Mdels Fr this investigatin three basic wing frms were used: wing i, NACA 66,2-215 sectin_ wing 2, 2315 sectin; and wing 3, sectin.

6 4 NACA TN 3687 Because the purpse f the investigatin was t study the buzz phenmenn, thege wings were made f cnvenient materials f sufficient stiffness t eliminate ther types f flutter. Wlng i was cnstructed f bismuthtln ally with a dural insert (fig. 1). On ts lwer surface at ailern midspan were three pressure rifices at 35, 5, and 65 percent wing chrd which were cnnected t three pressure cells. Prvisin was made t add a spanwlse extensin at the wing tip (wings 1B and 1C). Figure 2 shws the wlng munted in the tunnel with thls spanwise additin. Wing 1A was the basic cnfiguratin wlth r withut tufts n its upper and lwer surfaces. Wlng 2 was f dural cnstructin having the same plan frm as wing l, but with different airfil sectin. Wlng 3 (fig. 3) was f dural cnstructin and had a smaller chrd and larger span than wings 1 and 2. The ailerns were f spruce r balsa cnstructin (with spanwlse laminatins) wlth dural blcks at the ends fr munting (fig. 4). Fr the purpse f mass balancing fr sme tests, the leading edges f the ailerns were cut away and replaced with bismuth-tln ally. All ailern chrds were 2 percent f the wlng chrds. These ailerns were munted t the wings with steel spring hinges (fig. 4). Sme tests were als made n a furth wing, cnstructed whlly f spruce wlth a pln-hinged ailern. Wing 4 had an NACA 65-9 sectin, 12-inch chrd, 1 17_-inch span wlth a 6-1nch ailern span lcated 2 inches inbard f the wlng tlp. A llst f the wlng parameters is presented in table. Tunnel The tests were cnducted in the Langley 4_-ft flutter research 2 tunnel which is f the clsed-thrat single-return type emplying air r Fren-12 (having a sund speed f 51 ft per sec at 15 C) at pressures varying frm 4 inches t 3 inches mercury abslute. The experimental chking Mach numbers Mch fr the wings were as fllws: fr wlng A,.851; fr wings B and C,.831; 1r wing ; fr wing 3,.816; and fr wing 4,.917. Reynlds numbers culd be varied frm i 16 t n all cases, the test wing was munted in a rigid base as a cantilever beam frm the tp f the tunnel (fig. 2). nstrumentatin All wlng mdels had bending and trsin strain gages near their bases. Fr measuring ailern deflectin, wings, 23 and 3 had strain gages n each hinge f each ailern. Wing 4 had a type f inductin psitin indicatr attached t its ailern

7 NACATN Wing i had three _yn,_u_icelectrical pressure cells cnnected t three rifices in the wing. Wing 2 had within it an electrmagnetic eddy-current damper fr the ailern (similar in principle t the standard watt-hur meter). All strain-gage circuits, pressure cells, and psitin indicatrs were cnnected t amplifiers and a carrier system. The electrical impulses were recrded n a 14 channel recrding scillgraph. Fr visual bservatins f shck frmatins and shck waves, a shadwgraphsystem emplyiug a 1-watt pint-surce light was utilized. Tke _unnel test sectin was painted black except fr the tp which was p_nted white. The light surce was belw the mdel and directed alne the wing span tward the tp f the tunnel. RESULTS AND DSCUSSON Experimental data are presented in table and als in figures 5 t 12. The effect f density n the nset f the scillatin is given in figures 5 and 6. t can be seen that buzz starts with relatively small _mplitude (apprximately 2 ttal displacement). The initlalmach number _s relatively independent f density. Wings 1A and 1B have essentially cnstant frequency, but there is seen a tendency fr a decrease in frequency with decrease in density. Wings 2 and 3 shw a mre definite decrease f frequency fr decreasing density. A small decrease f frequency with density has been predicted in reference 4. n figure 5, an indicatin f the tip relief effect is given. There is a definite _nd_catin that the Mach number assciated with the initiatin f buzz with the ailern near the wing tip (wing 1A) is higher than the initial Mach number f the wing with the ailern inbard (wing 1B). The hi_ler Mach number attained is prbably due t the higher critical Mach number in the neighbrhd f the ailern due t wing tip relief. This result is in accrd with the experimental trends presented in reference 3. Figure 6 gives the data fr wing 2, which it may be recalled has an NACA 2315 sectin. Cmparisn f these results with thse in figtu_e 5 (thse referring t wing 2 with similar plan frm but with an NACA 66,2-215 sectin) shws that buzz ccurs n the 2315 sectin at a higher Mach number. This is apparently a wing shape effect. Figure 6 als shws that the buzz frequency may pssibly be a range f frequencies at least fr this case. Hwever, this rapid change in frequency may be caused by instabilities f flw in the tunnel near tunnel chking

8 6 NACATN 3687 Mach number r by large nnlinear flw effects. Figure 7 is a sanlple scillgraph recrd f wing 2 shwing the frequency variatin frm 87 thrugh 17 cycles per secnd in less than.3 secnds f time. Figure 8 (wing 3, sectin, 8-inch chrd) shws that /'r a cnstant density cnditin, the ailern buzz frequency and amplitude increase with an increase in Mach number. Fr this case, a range scillatins was btained. At a Mach number f.81, there were indicatins that the shck psitin was n the rear part f the ailern and the scillatin stpped abruptly. Even thugh this phenmenn ccurred clse t tunnel chking Mach number, this wuld indicate that buzz ccurs in a range f Mach numbers. This is in agreement with statements in references 2 and 4. The angle f attack was varied n wing 1A, and the results pltted in figure 9- t is seen that the Mach number assciated with initial buzz drps ff with increasing angle f attack. As indicated by the tw sets f data pints in figure 9, the lw amplitude nnperidic scillatry mtin appears t precede a larger amplitude sinusidal mtin f the ailern. Small changes f ailern natural frequency had n appreciable effect n buzz characteristics. Changing the spring cnstant f the ailern hinge did nt affect the frequency f scillatins (f_. lo) btained previusly. The effect f changing the mment f _nertia f the ailern is indicated in figure ii. There can be seen a tendency fr buzz frequency t decrease with increasing ailern mment f inertia. This is als shwn in figure 9(a) f reference 4. n the curse f testing, it was determined that mass balancing had little effect n the frequency r initial Mach number f buzz. By bserving initial frmatin f the shck waves n al] the w_ngs tested in Fren-12, it was nted that buzz cnsistently ccurred shrt]4 after a shck wave culd be seen. The use f tufts n the wings made it pssible t bserve the flw separatin at apprximately the shcck-wavc psitin. The rapid scillatin f the shck psitin culd be seen as a blur. The pressure scillatins culd be recrded by using dynamic pressure cells r pickups fr wing 1. Hwever, due t the time lag f pressure prpagatin frm the wing rifice t the pressure cell, n exact relatinship culd be determined between the ailern displacement and the psitin f the shck wave. Pressure variatins at the 35-, 5-, and 65-percent-chrd statins were recrded by using dynamic electrical pressure pickups. Figure 12 is a reprductin f the scillgraph recrd f the pressure scillatin f wing C (with a balsa ailern). This pressure variatin i pprximately 49 punds per square ft and ccurs at s frequency f 85 cycles per secnd at the 65 percent statin fr M =.85. The ailern

9 NACA TN scillatin ccurs at the same frequency. The ther tw pressure pickups shw relatively small pressure variatins. Visual bservatins placed the shck wave at apprximately the 65-percent-chrd statin. The electrmagnetic damper installed in wing 2 gave n psitive results. At zer airspeed, the maximum damping, when applied, was.41 ft-punds per radian per secnd. During buzz, this amunt f damping (equivalent t aprrximately five times that f the riginal system) had n effect in changing either the frequency r the magnitude f the scillatin. An attempt was made t btain buzz with a relatively thin airfil. Cnsequently, wing 4 (NACA 65-9) was used. Hwever, fr a density cnditin f "p =.34 with an unbalanced ailern n wing 4, wingailern flutter develped at M =.488. With a balanced ailern n wing 4, wing bending-trsin flutter develped at M =.895. Thus, n buzz data were btained with this wing. An empirical methd f determining buzz frequencies is presented in reference 2 and an example f this methd is given in appendix A. The methd utilizes an aerdynamic frequency parameter which is then mdified in sme systematic manner t determine a buzz frequency. The aerdynamic frequencies fr wings 1B, 2, and 3 were respectively 112, 75, and 94 cycles per secnd frm which the buzz frequencies were determined t be 56, 38, and 48 cycles per secnd. These frequencies were based n the velcity f sund in the testing medium, Fren-12. f these frequencies were determined by using the speed f sund in air instead f the velcity f sund in Fren-12, the aerdynamic frequencies wuld be 22 and 145 fr wings 1B and 2, and the crrespnding buzz frequencies wuld be ll and 74. Reference t table ll shws that this empirical methd is in better agreement with the experimental results fr air than fr Fren-12. n this same reference, a criterin was suggested fr the preventin f buzz, namely, a sufficiently high ailern mment f inertia t make the ailern natural frequency less than ne-half the aerdynamic frequency. Fr the wing-ailern cmbinatins tested, this criterin was apparently satisfied by a large margin and yet did nt prevent buzz. n reference 4, a hysteresis mechanism is suggested t determine buzz frequency, Mach number and the amunt f damping necessary t prevent buzz. The prcedure used is t assume the damping and restring aerdynamic frces and mments lag the velcities and displacements, in particular, because f flw separatin. t was fund by the use f this analysis (see example in appendix B) that the ailerns f wings B, 2, and 3 shuld have exhibited buzz respectively in a range f Mach numbers f.71 thrugh.85,.7 t.81, and.71 t.82;

10 8 NACATN 9687 at ranges f buzz frequencies respectively f 44 t 7, 23 t 78, and 39 t 55 cycles per secnd (fr a tunnel density f.29 slug per cubic ft). The analysis als shwedthat it wuld take damping fr the three wings mentined respectively equivalent t.95 t.126,.154 t O, and.472 t pund-feet per radian per secnd per ft span t prevent the scillatin. The damping inherent in the hinges f the ailerns f these three wing cmbinatins were respectively 7.72 X i-5, 8.44 X 1r5 (41. x 1-5 with the eddy-current damper in peratin) and 6.15 x lo-5 pund-feet per radian per secnd per ft span. The ailerns f these three wings did scillate but at substantially higher frequencies (see table ) than thse predicted, namely in the ranges f 65 t ll, 55 t 13, and 7 t ll5 cycles per secnd, respectively. The crrespnding Mach number ranges were.72 t.851,.8 t.853, and.75 t.81. The frequency test data were btained by using Fren-h9 as the testing medium. n rder t btain further insight n the phenmenn,tw runs were madewith air as the testing medium. Fr wing 2, apprximstely the samefrequencies and Mach numbers were btained in air as were btained by using Fren-12 at the same density. Hwever, fr wing 1B the frequency was cnsiderably higher (table ). By applying the analysis f reference 4 t the data pints in air, it was seen that the analysis predicted the scillatin at the samemach numberswith a slightly higher frequency than that predicted previusly (table ). Unfrtunately the experiments were nt as clear cut as ne wuld llke them t be, and the separatin phenmenain air and Fren-12 were nt fully investigated. Thus, althugh this analysis predicts buzz Just abve wing critical Mach number and at lwer frequencies than thse btained experimentally, it is nt whlly incnsistent with the experimental results f these tests. An ver-all cmparisn is fund in table. CONCLUDNG REMAREB Results presented fr these wings shwthat density f the testing medium in the range f.8 X 1-2 t._8 X 1-2 slug per cubic ft has little effect n the initial magnitude and initial Mach number f buzz. The buzz frequency decreases smewhatwith decrease in density. The Mach number crrespnding t the initial wing angle f attack is increased. buzz decreases as the Mass balancing the ailern apparently had n effect n buzz; whereas increasing the ailern mass mmentf inertia tended t lwer the scillatin frequency. Changesf the spring stiffness f the ailern

11 NACATN hinges in these tests had n effect n buzz. Placing the ailern at the wing tip delays buzz t a higher Machnumber. There was an indicatin that a sufficient increase in Mach number t bring the shck-wave psitin t the rear part f the ailern dampsut the buzz; this implies that buzz exists nly in a range f Mach numbers abve the wing critical Mach number. A cmparisn f the experimental results was madewith empirical analyses f tw references. This cmparisn shwednly qualitative agreement. Refinements bth in analysis and experimentatin are desirable. Langley Aernautical Labratry; Natinal Advisry Cmmittee fr Aernautics, Langley Field, Va., February i, 1949

12 i NACATN 3687 APPENDX A EXAMPLE OF THE EMPRCAL METHOD OF DETERMNNG BUZZ FREQUENCY FROM REFERENCE 2 This methd assumed that flutter with ne degree f freedm can result frm a time lag in the changes f flw abut a wing. This time is determined as t = K2d a(l - M) where t time d distance frm trailing edge t shck M free-stream Mach number a velcity f sund K factr t accunt fr any additinal time and estimated t equal 2 By inverting t, a frequency is determined as fllws: f a : a(1 - _) 4d where f aerdynamic frequency a The phase difference is determined as fllws:

13 NACATN 3687 ii where phase difference between hinge mment and ailern psitin f single degree f freedm flutter frequency The predicted cnditin fr preventing steady flutter is where C damping cefficient < Ccr 2-_ equivalent spring cnstant <ZO2) mass mment f inertia f the ailern A variatin f the hinge mment with ailern angle : 2_f tan _' : C_ K m - _ 2 Since _' = <i - _a)36, the determinatin f f is f K m is smaller than _ 2, f is between.5f a and.75fa, and when Km is greater than _ 2, f is between.75f a and fa"

14 12 NACATN 3687 By applying the parameters f wing ia, f = a(l - M) = plo(l -.71 ) = a 4d 4 X.333 i12 cps Km = Z_2 = ]2 x x -5 i(9_i.5) 2 = Ccr = 2_- q = C =.25C r =.25 x x x lo -4 C =.5 x.154 =.77 x 1-3 Therefre, / = f _ l]2_tan-i.77 x i-3_ 2_ 36 \ i.18 - e.339 x 1-4 and is slved graphically 6OO / / / 3 /' 5 i f Thus it is seen that the predicted frequency f this single degree f freedm flutter is 56 cycles per secnd.

15 NACATN APPENDXB EXAMPLEOFANALYTCALMETHODOFREFERENCE 4 The fllwing example indicated hw the data f _-ng 2 is applied t the analysis f reference 4: Physical Data Mach number....7 Velcity, feet/secnd Ailern mmentf inertia abut hinge iine_ slug'ft x i-5 Ailern span, feet Wing Density chrd f at medium, mldailern slug/ft span,.feet Gemetric ailern hinge-line lcatin, percent wing chrd 8 Gemetric ailern leading-edge lcatin, percent wing chrd Natural frequency f ailern, cycles per secnd CmputedParameters (See reference 6.) b =.83 _ e -2x8 1=.6 i e =.5 i t = _ = 2.3 x 1-5 = M 2 _ = (i.2)(2_) : 64.2 radianslsecnd

16 14 NACATN 3687 Estimstin f Time Lag t = t a + t b + t c + t d ta = f _'2 Cs _ - v 1 s2 _ s - V t b = t a ds s2 - Sl a - V a where small v and is assumed equal t zer and t d is assumed t be very s chrdwise lcatin f shck wave n airfil in feet s2 chrdwise lcatin f sme pint n ailern (in feet) which can be used as an effecbive center f pressure a lcal speed f sund v lcal velcity f the medium At M = O-7 s = 35-percent chrd s2 = 83-percent chrd a - v (averaged ver the distance s 2 - Sl) : 76 fps.8_ -._ z _.526 ta = t b =.526

17 NACATN t C m = ]Q t =.113 By using equatin (19) f reference 4 : 57.3_t Then =.647m where _ is the phase angle during the scillatin by which the actual air-flw circulatin lags behind that crrespnding t ptential flw. de dt Effect f cntrl system stl_ss K _2 t e Resultant aerdynamic hinge mament cnsid-- erlng nly K a and 6D_

18 16 NACA TN 3687 Calculatin f Aerdynamic Hinge Mments The equatin f the hinge mments is as fllws (terms defined in reference 6): and is dependent n the flutter parameter v/b_. The real and imaginary cmpnents f the mment are cmputed and in nndimensinal frm are Real cmpnent - a pb4c2 maginary cmpnent - _D a Frm the gemetry f the preceding figure 3 it can be shwn that cs( - = t -K & frm which _ can be determined fr varius values f v/b_ v (l) i

19 NACA TN These values are pltted as _ against _ n the same plt as _ =.647_. The intersectin f these curves determines the resultant phase angle and frequency f scillatin as shwn in the fllwing figure 5 lo 2 3 J J \! 4 a_ = O -i J J J J By using the resultant frequency and phase angle in the fllwing equatin (als determined frm the gemetry f fig. under sectin entitled '_stlmatin f Time Lag"), the value f damping necessary t prevent the scillatin is determined. sm({ - $) : Dv',..._: sin Thus the predicted frequency f scillatin is 23.4 cycles per secnd at M =.7 and wuld take an amunt f damping equivalent t.154 pund-feet per radian per secnd per ft span f the ailern t prevent the scillatin.

20 18 NACATN 3687 REFERENCES i. Gethert, Bernhard: Cmments n Ailern Oscillatins in the Shck- Wave Range. AAF TR N. F-TR-211-ND, Materiel Cmmand, Army Air Frces, July Ericksn, Albert L., and Stephensn, Jack D.: A Suggested Methd f Analyzing fr Transnic Flutter f Cntrl Surfaces Based n Available Experimental Evidence. NACA RM ATF3, Perne, Angel, and Ericksn, Albert L.: Wind-Tunnel nvestigatin f Transnic Ailern Flutter f a Semispan Wing With an NACA 2313 Sectin. NACARM A8D27, Smilg, Benjamin: The Preventin f Ailern Oscillatins at Transnic Airspeeds. AAF TR N. 553, Materiel Cmmand, Army Air Frces, Dec. 24, Thedrsen, Thedre, and Garrick,. E.: Mechanism f Flutter - A Theretical and Experimental nvestigatin f the Flutter Prblem. NACA Rep. 685, Smilg, Benjamin, and Wasserman, Lee S.: Applicatin f Three- Dimensinal Flutter Thery t Aircraft Structures. ACTR N. 4798, Materiel Div., Army Air Crps, July 9, 1942.

21 NACA TN TABLE WNG AND ALERON PARAMETERS i 2 2 r_ a x_ r_ C i_std 694 B 55O lo x i x i i x OO _rwing gh g_ g fhl i fa f 1 Mcr Mch A g i.4._.81 2._i ' lO lo lo

22 2 NACA TN 3687 TABLE E_PER_ DATA ft smplltud_mini5 Ailern deg finit eps C5_ deg P3 slugs/cu ft Ailern amplitude, deg Minit finit' cps Figure 5 Figure 8 Wing 1A w_ x l z _.78_ 69.78_ 68 79_ 69 75_ 7.7_ x loo lz5 Wlng lb i.359 x l h3 l l z.78 Wlng 3.261x i i Figure 6 Wing 2.84 x _11, _ _ % _ 78.76( 7Q.75( 8.8_ 77( 1 6/_ 81t.7_ !48 7, _ _ i.8271._ i41.152R 95-Z OO x Figure 9 wing A kip i ft-lb/radian slugs/eu ft slug-ft 2 O.O285.O O x per ft span Figures i and ]i 1.3 x _ z.685 i Minit finit' cps O O

23 NACA TN TABLE ll COMPARSON OF REF]_ENCE ANALYSES WTH EXPERMENTAL DATA Reference 4 Reference 2 Wing P_ s]ugs/c_ ft Damping t Buzz Buzz Mech prevent buzz frequency number range Aerdynamic frequency Buzz frequency Fren Air Fren Air Fren Air Fren Air Fren Air B ]1 B O ll O.8h Experimental data Wing P_ slugs/cu ft Damping inherent in ailern Ailern natural frequency Ailern frequency Fren buzz range Air Ailern Mach number fr Fren range buzz Air B i i B i.5 65-]_ i i

24 ,,OT = 4.1 M OJ m. _D ',4) 1_.

25 NACA TN Figure 2.-Mdel C munted in the Langley 4_2-ft flutter research tunnel.

26 2b_ NACA TN ,--4 1 Q 4 lo _4 J J

27 NACA TN Wing.4 blue steel springs Dural munting blck Spanwi se laminatins Figure 4.- Diagramatic view shwing ailern munted t wing n steel hinges_

28 26 NACA TN S m =.7 >,-4 O D J Wing A Wing B Wing 3 /111 r/ 'lllj /.9._5 e_h ' [.8O --_.75 E/MOt 7. <> -"- -_>'- - _- [] i- i --O- Wing A m 9 <> Wing B <> Wing 3 : ' r_ :,,-.t 8 [] D <> 7 O DO O 6 _- 5 m D O i 4i _ Density, slugs ft-3 Figure _.- Ailern frequency, Mach number, and amplitude against density at nset f buzz. Wings 1A, 3_B, and 3; e =.

29 NACATN S 5.34 _ i. 7_ -O -- Wing 2 /.9.85 #ch B.8 c O DO D i : [!, llo 8 a i ' _f' 9! ' 6 m q 5 _ Denmlty, slues ft-3 Figure 6.-- Ailern frequency, _ch number, and amplitude against density at nset f buzz. Wing 2; _ =.

30 28 NACATN 3687 f_ c 1 71 _ C _ - JJ q _,lacu _- _.r--t,r-t,r-t

31 NACA TN / h, Wing 3 t 111 Buzz range 12 O f y_ O _ Mach number Figure 8.-Ailern frequency and amplitude against Mach number. Wing 3; P =.521; c_ =.

32 3 NACATN 3687 Wing 1A J///,// lo.9 ).6 "_9-6 = Angle f attack, degrees E_---O 2.67 degrees ailern amplitude, slnusldal mtin f ailern O----O.$9 degrees ailern amplitude, nn-peridic scillazry mtin f ailern Figure 9.- Buzz Mach number against angle f attack. Wing 1A; D =.261.

33 NACA TN i _ O O_ Spring cnetant, k Figure 1.-- Ailern buzz frequency against ailern spring cnstant. Wing 1C; M =.76; p =.586 (average); _ = 1.31 x l -5. r 6O O O h 4O l 2 3 4xz-5 Figure ii.-- Ailern buzz frequency against ailern mment f inertia. M =.76; p =.586 (average); k =.525.

34 _2 i_aca TN 3687 r_ C) O (2. U'A O CO e c) ) O O O ;4 ko.r4 O O ill D r--t Q r4 NACA - Langley Field, Va.