Document
RM No. L7G18
·
o Z
~CA
RESEARCH MEMORANDUM
EXPERTh'IENTAL INVESTIGATION OF A PRELOADED SPRING-TAB FLUTTER MODEL By
N. H. Smith, S. A. Clevenson, and J. G. Barmby
rH'~ uocu t.NT ON LOA Langley Memorial Aeronautical Laboratory ~ATlON l A Vt~flRY CO '" f "0 tkangley Field, Va.
l ''' ... l LA~' TORY IA E'f FIEl • '" < ON. VR 'NIA
~, ~-' -
~ SHOULD BE ADDRESsm NATIONAL AUV/SORY COMMIITE£ fOft r 1512 H STRI:.ET. N. W. M WASHINGTON ~. D. 0.
NATIONAL ADVISORY COMMITTEE
FOR AERONAUTICS
WASHINGTON December 15, 1947 NACA RM No. L7G1 8 NAT IONAL ADVISORY COMMITTEE FOR AERONAUTICS RESEARCH MEMORANDUM EXPERIMENTAL INVESTIGATION OF A PRELOADED SPRING-TA B FLUTTER MODEL By N. H. Smith, S . A. Clevenson, and J. G . Barmby SlJ1-1MARY An experimental investi gaMon "Tas made of . a preloaded spring- tab flutter model · t o determine the effects on flu tter speed of aspect ratto, tab frequency, and pr eloaded Gpring constant. The rudder was mass -balanc ed, and t he 'f lu tter mode studi.ed was essentially one of three de g rees of freedom (fin bendin g cou pled with rudder and.
tab oscillations). I nasmuch as t.he sprin g was preloaded, the tab- spring sys tem was a nonlinear o ne. Frequ.ency of the tab was the most significant parameter ' in th is study, and an increase in flutter speed with increasing frequency is indlcated. . At a give n frequen cy,
the tab of high as pect ratio 1s shovm. to have a slightly lower
flutter speed than the one of low aspect ratio . Because the frequency of the prelo aded sprin g tab W a.s found to vary radical ly with am.-pH tud. e, t he flutt.er speed ' decreased with increase in initial displacement of the tab .
INTRODUCT IO N .'< ••• Fin - rudder-ta b fl utter has been found to be a significant problem in airplane design . An in ve stigatto n of tab flutter has consequently been made at the L an g ley Memorlal Aeronautical Laborat o ry of the National Advisory Committee for Aeronautics . The re sults of flutter test s of a vertical tail assembly for a medium bomber are re'Ported in reference 1. I nterest in the effects to be obta ined ,·,i th a preloaded sprin g in the rud?er-tab-c o nt r ol circuit led to the present inv estigat ion, in which te s ts were made of a fabricated tab- flutter model of rectan g ular plan form .
The idea of the prel oaded sprin g tab is many year s old . A description of this mechanism is found in reference 2 . Before an attem'Pt is made to an aly ze the preload.ed spri ng ta b, a brief statement concernin g the functions of a nonpreloaded spring -t ab type of control is considered desl ra ble. One of the features of the nonpr eload ed sprin g -t ab control, which is equipped with a ,,,ealt spr in g, NACA RM No. L7G18 is that it enables a pilot t o at tain li sh tnes8 of contr ol at high speeds without clo se a erod~la~c balance and the attendant risk of overb a lance, This type of control is similar to a free se r votab control . However, at low speeds, a stiff sprin g (irrev~rsible control) 1s desirable to retain positive acti on with appropri a te pilot "feel" as ' obtaine d in the geared-tab control. The use of a s tiff sprin g is also advantageous because it reduces the dang er of flutter to which a we ak spring~ta b control is subj ect . The preloaded spring-tab c ontro l (ver y stif f at sma ll a.mplitudes ) has been su gg ested as a means of combining the desirable fe at ures of the non- prelo aded spring tab at both low and hi gh speeds . The increase in stiffness can make the syste m suff id , ently irreversible at small runpli tudes to eliminate t.he necessity of mass balance. The re s ultant saving in weight may be ap~reciab le. Such a pre loa ded mechanism pres e nts a noill. inear problem depe ndent on the amp litude of the tab .
Except for t1is nonlineari ty of t he spring constan t, the fl utter para:!C.eters for a praloadeo , spring - tab system ar e the same as those for a nonpreloa r ~ed s'Pring -t ab system . SOllie of these p arameters are fin, rudder, and tab nat ural frequencies and. s tiffnesses, moments of inertia, mass and, aerodyn am ic balanCin g, tab product of in ertj,a, gear rati.o of ta b movement compared to ruddbr movement,
rU d.d.er and tab a8p,:o~ t ro , tios, and. damping . Only a few of thq se
parame ters were inve s tigated for the present study Hith th e main emp ha sis on the e1fe ct of the preloaded sprin g type of control. A theo r etical t ab - f lut ter ana lysis was not undertaken at this time .
SYMB OLS d d. istance from center of grav it y of tab to tab hin ge line, inches cg f tab exper imental frequency with rudder s tationar y for 3. 25 tab deflection, cycles per se co nd.
a'Pproxim ate expori::r'.ental tab frequency for ' 8. 25 tab deflection, c ycles p cr socond.
ta b calculated natural frequency for 8. 25 t ab deflection, cycles per second.
I rudder moment of' inertia about h in ge lIne;· inch-poun d- seco nd r It tab moment of ine rtia about hinge line, inch-pound.-second }rACA RM No . L 7C18 3
K produ~t of i nerti€)" inch-p o und - Mdond (J xy cUn, where x :Le
, ..
distanc e f r om tab-hin ge line to element ma s s dm in t a b, : tma ~ ~1S distanc e from r ud d er hin ge line to s run e elemen t k sprin g con s tant of sprin g in , preloaded s prin g mechanism, po un rls per in ch kl piano-vnre sp r in g con s tant, poun d s per inch k2 appro~im ate co m bined ', .sprin g cons ta nt for 8 .25 t ab d~ fle<:) t ion, po un ds pe r i nch n ge ar ra t io, t ap d eflection divided by Y' udo.er deflection . . ~ .
, , , fl ut t er s peed at sea level, mile s per hour
static t!npa l ance of ~ab, . · inCh-poun d.S (! s ( 1 x, w her e S i s
z
\:lnb a~ an c e of tab pe r ) uriit of tab ' s panwi se . d is tan cean d. x i s sp an i,r is e dis tanc e " : . ' half maximum amplitude of preloa ded spr in g s ys te m, inche s Fo preloa d f or ce in pr e loade d sprln g sy s t em, p ou n rIs m :m as s of prelo a de d spr i ng system, -pounds - se c on d -per in ch M Ma ch numb er AP ARA TUB ' AND T ES TS De s cr ipti on of Mo d. el A t e "t mo d el v! i th a rectan ' gu lar pl an f orm , - la S c on stru ct ed for thi s experimen t al inv e sti g ation ,. The mod . el c on si st ed. of a h orizont al an d v er tI c al t ~ il a sse mb"ly wit h the h ori7 , on t a l surf ace s e rv in e pr ime .: 1"ily a s a suppo rt f or th e vs ' rtic a l · fin ·,r ud der · ·t ab c. om b. ln a tl on ( f i g . 1) . The total we i gh t . wa s 325 pounds w it h th e r u dde r an d t ab wei f!.,hi n g a ppro x im at el y eo ' pO \:ln QS w hen m as s -b alance d . The mome nt of 2 .
in e rt ia of the r u dde r was 20 . 35 i n ch- pomd- se c on d A diagram showin g · th e t ab li nka ge i s g iv en in f i gur e 2 . Cr o ss - , e ct i on al view s T of th e te s t con f i gurat ions use 'a in t he pr esen t .1 m ss ti ga ti on are shown in fi gure 3.
NACA RM No . 17G18 In one grou p of tests, a tab with aspect ratio of 2. 78 was used with the model arr~ g ecl as follows (fig . 3 ): Configuration 1 - Gea re d - tab~ - n =- 0.5, ~There - n i s the ratio of tab deflection (relative to the rUdder) to rudder deflection Configur at ion 2 - Preloaded sprin g tab, control link in place, varyin g t ab moment of inertia Configuration 3 -- Preloaded spring tab, no rudder contro l (control link removed), var y ing p re loaded sprin g Confi g urati on 4 - Preloaded spring tab, piano-wire spring in rudder control (piano-wire s prin g system replacing control link), varyin g piano-wire sprtng constant In a s econd gr oup of tests a tab with aspect r a tio of 6.25 and - wi th the same a re a as the other tab io Tas use d wi th t he mod el arranged as follows (fi g . 3 ): Confi g uration 5 - Preloaden. spring tab, no rud cler control _ , varyin g prelo aded spring constants and t ab mo~nts of inertia.
Confi guration 6 - Preloaded s~ring tab, piano-wi r e - spring in rudder control, varying both piano-wi r e and preloaded spring constants.
In addition, t he model was provided ivi th a cable -and spring weight system which c01J~ d simulate the restrai nt in the control B,ystem of a full-scale airplane .
In strume nta tion Six midg et accelerometer pickups and one rud_ der and one tab induc tan ce position indicat or "Tere installed in the fl utt er model (fi g . 4). A pickup was in each corner of the rudder, one in the front upper fin, end one in the middle of the right side of the - horiz o ntal stabili z er . On e position indicator was at the lower front corne r of the - rudder , and the other a t the mid dle of the tab.
These posi tio n in dicator s and pickups we re used in conjunction w it h brid ge s, amplifiers J aTld a recording oscillo graph . Th e recordi ng eqUipment, which includes that used in shakin g the mo e1, is shOim in figure 5. - -------- ---~.
NACA m-1 No. L7G18 5 In s tall a tion T he model was mo~ted in the rear part of the test se0tion of the Langley 11igh- speed 7" P. Y" . lO-fo ot tun.l1.el . TYTO mount8 constructed of s te el strea.mline tu b in g w ~ re se curely bol teo. to the fl o or of the tunnel, one on either side of the model. , T he . model vTaS supported on four cantilever steel le af springs ri g idly bol te d to the m Olmts ani a.nd hin g ed. on ball-bearings t o the m od el at the emls of the horizontal s tabil izer (fi g . 6). C ab l es connected t o the t op rear of the rudder p ro v id ed a means t o s tar t and. stop flutter. T hese cab l es were brought t oget h er by a pulley system over the tmnel se c t ion. Another cab le connected to a sprin g -t r ip mechanism ",as used to gi ve the tab an initial d isplacement and SUdden release, L eads to the e lect ronic eqU ipment were brou ght out through the tU-DLel-f.loor turntable . A steel ' safety net "TaS inst a lled a pproxi. - mately three feet behind the model to minimize damage of the tunnel i n ca se the model failed .
Preliminary V ib r atio n Tests Natural frequencies and mod ' es of the tab - flutter mod.el w'ere first determi n ed in preliminary v ibration tests with the model on ri g id mounts on a bedplate in the laborato ry . For thi!:? stmly .. a movin g coil shaker was used. The results are g iven , i n table I .
Prior to t he f~rst wind-tunnel tests the frequencies were checked and confirmed. vTi th the model mounted. in . t he tunnel. (Se e fi g . 6.) The frequ81 1cy ' of . the model mOlmte.d on vertical leaf springs, which s imulated fuse l age side bend~n g , . was determined to be 600 cycles per minute . . The rudder was mass-b a lffilced for a ll tests.
After ·a ' rel'ati vely weak p i ano-wire ' spring sy st em was substituted
f or the control link, the rudder frequencY yras lov comp ar ed ,.,i th
th e tab frequency .• Curves showin decrements in amplitude f or the va rio us spring combinations were o bt a in ed by deflecting and. re l easing the tab. A typical record is sho,ID in f i g ure 7 g ivin g the shape of the decrement cu rv e and the change in f requency "Ti th amp11.tu<J.e for a preload.ed spring tab .
Because the tab osc il lated at di fferent ampli t udes in t ~ 1e va ri ous confi gura tions, it 1-I ' as convenient f or purpose s of co rre l a - tion to reduce a Ll the t ab natural-f r equency data to freque nc ies at the t1mnel tripping . displacement of 8 . 25 • This proc ed ure led .
• to the freque nc y analysis of t he p~eloaded spring system gi ven 6 NAOA RH No. L7G18 in the a ppendix in which three approximations to the experimental condi tions were considered.. These approximations were obtained by three methods: Method A' is baseo. on the maximum displacement intercept of the sprin g system; method B, oD ! the differential equation for one-quarter cycle of the motion'; and. method C, on equal strain energy. Results of these an8~Y8es are given in 8; figure . in which frequency ratio 2~f I~ is plotted as a function . . lac of preloaded-sprin g -force ratio --.9.. .
. -' Fo Method 0, based on equal strain energy , gave frequencies t oo high . Method B ,.as the most ri g orous mathematically, but even this rrie"thdd neglects the friction which is present in the actual model. ' The approximation based on the maximum dis p lacement intercept (method A) gave tab natural frequenci es clo s est to the experimental values and this method was therefore used in all calcluations of the tab natural frequencies . Figure 9 sh o ws the comparison of the results obtained. by method A with e}.-:perimental frequency dA-ta.
In some tests the control link was replaced ,nth a piano-wire sprin g system (fi gs . 2 and 3) . By use of a f or ce- d ispl acement analysis of the complete tab-rudder link age system, the effective cons tant of the preloaded spl'ing system ka was combined 'vi th t he piano-wire sprin g constant kl to g ive the to r sional stHfness des i gna te c l a s the combined sprin g constant k . \Vi th the knmT ledge of k ' and the t ab m oment of ine ·r tia It, the tab natural frequen cy f 2 of one confi g uration fo r an :a.lllplitude of 8 .. 25 .. Tas calculated .
These calculated values of the'tao ' natur al frequency agree r~a s onaoly . well with the experimentally dete~n~d ~r e quencies, f ] -, . as give n in table II. The few ca s es of l ar ge 'Qevlatlon are probabIy ca u sed by variation s in damping .
Flut t er Tests O ' scillo g raph records were made to record the natural f r equencies of t he model at zer o airspeed for every run in the tlmnel . Other oscill ogr aph records were taken at vario us interv a ls of speed up to an d beyond the initlal flutter speeo_ . For each record the tab was tripped to develop possible flutter at low speeds . In th e nei ghbor - hood bf flutter th e tab was tripped at airspeed incre m ents of .
10 mil e s.per hour . The avera ge tr i ppin g displacement w a s 8 . 25 • AI though an attempt "l as ma e to ext ra polate to the flutter - speed point by plottin g aerodynamic damping ag ainst speed for various - NACA RM No.
L7G~8 , speeds of one configuration, no particular success ~a8 attained ' , because of scatter in the data.
The , flutter point was determined by visible means ' at the initial tripping displ~cement and is believed to be accur , ate wi thin ±~ , miles ' per h, our.
. '
A sunrrnary ' of the results , is foUnd , in :t, able II, ..
' .
..
In the tests of cohfi gurat ion 'l (geared-tab case) flutter did not occur, nor ~~s !lutter eX),Jected sinc ,e, the s1,Jring sy'Stem "Tas comparativ ely stiff. Tunnel speeds 'up to : 300 mile ,s per hou.r were attained with no tendency f.or th 'e model to flutter.
Tunnel speeds for subsequent tests were limited to les? than 200' miles per hour in order to ' save the model.
In the tests of confi gura tion 2, - the moments , of inertia of the tab were changed successively from 0 .0613, inch-pound~second2 to 0.0776, 0.1370, and 0 . 285J.~ inch-pound-second 2 by adding distributed weight a lon g th~ tra~ling edge of the tab. (For c ompa rison, the moment of inerti a of the tab stu~ , iec1.
in reference 1 was 0.1020 in.- Ib-sec .) In tn-is ' set or'tests there '-las' no, fI ,u tter.
The probable reason for the lack of flutter ,. a s again the relatively high spring stiffness of t4e system.
In or d er to obtain flutter in the desired speed range, the control link ,.as removed, and the spring stiffness of the tab system was then materially reduced ', With the ,'removal ' of this 11nk (confi gurat ion 3 ), ' fl utter occurred dt~ing the tests.
This flutter was essentially a t hree -d.e gree-of-fre edom flutter involving fin ben cUng coupled with rudder and t ab oscillations about their respec.tive hinge lines (t ab lagging by 30°)..
A typical oscillo- gra ph flutter record is shown in figure 10. This , record shows the relative positions of the various ' components of the model and the acceleration ( g ' tmits) of each of these components during the first 0.45 ' second of flutter.
, During the flutter, the tab ampli tu de '-Tas sufficiently lar ge to bend the tab connecting link.
This link, a dura lumin ' tubo, was r e pl aced with on e of steel.
The effect of changin g the preloaded spring was investigated.
Sprin gs of 8.3 pounds per inch with 2 , 25 pounds preload, of 33.3 pounds per inch with 11.3 po~ds pre l oad, and of 83 pounds per inch with 21.6 pound~ pre19ad were used.
Flutter speed vf of the model increased with an increase in preloaded spring constant (fi g . llJ.
, The ' s1.gnif~cance of this figure is quali tati ve.
S NACARM No~ L7GlS It was also ' observed that ' increasing ' the ' initial tab dispLacement caus ed the model to ' flutter at a iower speed~ ' With an S.3"~pound per-inch spring; flutter 'was encountered' at 102 miles :per hour for a large tab deflection; whereas at i50 miles per hour the slightest disturbance initiated flutter with rapidly increasing amplitude. This dependence of initial flutter speed on amplitude has many practical implications " 1:lecause the roughness of the air, the presence of gusts, and the type of maneuver have a definite effect on the initial deflections of the tab. Table II shows the change in flutter ' speed ' vi with the variation of the parameters and indicates particularly the importance of tab natural frequency.
. " .
In the tests ' of configuration '4 a piano-wire spring was installed in the control system (fi g . 2) and thereby increased the effective combined spring constant of the tab-rudder combination as compared with the spring constant for the configuration with no rudder control. Flutter similar to toot obtained in the tests " of confi~ration 3 occu rred at higher spe~ds. At these hi~er speeds this flutter was more ' difficult to control and emergency shutdowns of the tunnel 'were necessary in order t o save the mode l.
For configura ti on ' 5, , the tab was replaced with one of higher
aspect ratio and the moment of inertia of the tab was varted from
0.0246 inch-pound-second to ' O.1017, 0.0885, and , 0.0780 inch-pound- second • The ratios of products of ' inertia to tab m oments of inertia K/It were determined. How'ever, the changes in K/1t were too small to indicate the variation of , vf ' with K/It.
, " :W- ', .
, ' In conjunction with changes in It, the effect of three different , springs in the preloaAed spring mechanism was investigated.
For , the , springs With the low constant no ; variation of vf with , It was obs, erved. For the spring with the higher constant, vf increased with a ~ec:rease;in It as indicated in table II '. This result ma;r be expla ined by the following considerations. ' Lowering the ta b moment of iner tia caused the tab frequency to increase, other things ' being equal; thus, vf tended to :increase. ~O'tvever, the variation ' of vf with changes in , It ' is greater and con- saquently more easily ' observed ' at high frequencies than at low frequencies. .~ I The ' tests of configuration ' 6 were made to permit a s~udy of tab flutter , wIth thecombined , sprfng constants varied by changing both the piano-'VTire and preloaded springs. This V'ariation ' in turn changed ' the ' tab frequency and consequently vf. N~a~ the end of this set t of tests, play in the linkage system bad become , ,appreoiable and a ' 'flutter of low amplitude at 'S cycles per second , was noticed at 150 miles per hour. The amplitude was approximately which was the amplitude allowed by the play in the system.
NACA :RM No. L7G18 It was not possible in all cases to measure the tab natural frequency at the : amplitude correspondin g to the average tab tripping displacement of 8 .25 • For purposes of correlating and presenting the data the natural frequencies of the tab were calculated by ~sing a c om bined spring const a nt k2. The d, ata plotted in figure ' 12 show wide scatter, probably because of the variation in damping as well as the variation in the initial tripping amplitude.
The effect of aspect r a tio is small. Wlth ' all the flutter points on one graph, (fi g . 12) there is an indicat1.on that, for the same frequency, the tab with the ' low aspect ratio has a higher flutter speed than the one of high aspect ratio. This effect is in agreement with the results of an analysis made by W. R. G;riffin of Curtiss-Wright , Corporation, in wnich strip theory was used.
HOI.,ever, the possibHity exists that the aspect··ratio ~ffect is due, at least in pa rt, to spanwise coupling. .
CONCLUDING :REMARKS , :Results presented of test 's of a preloaded spring -tab flutter model indicated that, with a rudd. er mass-balanced and at a low frequency compared vT1th the tab frequency, the tab frequency appears to be the most significant parameter. Because the frequency of a preloaded sprin g -tab system vTas found to vary inversely with amplitude, the flutter speed decreas ed with an increase in initial displacement of the tab. Although the effect of aspect ratio was small, it was indicated that the tab with the low aspect ratio showed a tendency to flutter at a higher speed than the tab With a higher aspect ratio hav:i.ng the , same area and frequency.
Lang ley Memorial Aeron au tical Laboratory National Advisory Committee for Aeronautics Langley Field, Va.
10 NACA RM No. L7G18 APPENDIX METHODS OF CALCULATING THE NATURAL FRE Q UENCIES OF A PRELOADED SYSTEM The ca lculations of the natural frequencies ' of ' a preloaded spring-tab system might be approached in several ways. For example, in ffgure ' 13, the forces, displacements, and other parameters involved in such calculations are repr 0 sentea , to illustrate three methods of approach. ' Method A is based on the maximum displacement lntercept , of the system; ' method B is based on the differential equa tion for ' on0-quartoIl cyc1e of the motion; and method C Is base d on the concept of ' 'eq ual strain energy.
Method A ,,- The approximation by me ' th ad A proceeds as follows: Consider f irst the force-di'splaceinent dia gram of a preloaded spring system. (Se E) :ri g . l3( a) )". In -pl aco of t he 'act"ual sys t em AB C D, choose the path A 0 D a lon g 'Thich the slop e ka is alvrays finite and constant. The use of the effective spring constant ka mathematically reduces " the ' di s continuous pro loaded spring system to a linear one in which f orce equals ka times displacement.
The ~ eometry of the fi g ure shows that or
k = k + Fo
, a ' Xci The fre quency of the s inu s oidal motiop is then given by which may be written nondimensionally as NACA EM No . L7G18 .
Metho~ B.- For the analysis according to method B, the system and symbols are given in fi g ure 13(b). Th e diffe r ential equati on of motion may be expressed as mf + kx = -Fo (x < 0) mX + 10:: ::: Fo (x > 0) The solution of the e Qu a ti o ns is ( 1) CJ, may be By proper choi c e of the ori g inal time, the ph ase angle elimin a ted.
Although the moti on 1s d iscontinuous, it is symmetrical abo,ut
x = 0 so tha t it can be compl et e ly specified by an an a ly s is of
th e motion betv Tee n the poin t x = xo , vThere it starts from rest
(t c: 0) ,and the point x = 0 it = _.L). Subs titutin g these
\ 4f b limit s into eQuation (1) g ives or and ,- -
o = - :0 + ~o + :0) coe I."~ib)
or 12 NACA RM No. L 7G18 In nondimensional form this equation may be' wri 'Gten
-- , - = -) arc cos ---
1 Jk (2\ (1 )
2rrfb m rr kx 1 +~ F o For zero preload, the nondimensional form reduces to the usual relation .' "' Metbod~.- In method C, the actual system ABC D (fig, 13(c) is repl a88d b~ the straight line path HK, constructed so that the area (N , ~ Iii) eClua lB 'are a (N ' + p). The strain energy is oq , ual to the araa under the force - disp ~acement curve; therefore, ",
Energy. = lk x2
"2 c ~
or F
kc = k + 2 O
Xo " .'
The freCluency may be written or , nondimensionally, NACA RM No. L7G18 REFERENCES 1 . Theodorsen, Theod.ore, and Smith, N. fI.: Flutter Tests of B-34 Fin-Rudder-Tab Syst e m. NACA MR, Sept . 6, 1944.
2. Brown, W. S.: Sprin g Tab Controls, R. & M. No. 1979, British A.R . C., 1941 .
NACA RM No. L7G18 TABLE I.- FREQUENCIES AND MODES OF TAB-FLUl'TER MODEL . , . .
Frequency Mode Nodes (cpe) 1 Bottom of fin 7.5 36.0 Bottom of fin and diagonal from bottom front rudder to top of tab 64.0 Bottom of fin and through rudder and fin at 75 percent Bpan measured from baee 86.5 Bottom of fin and diagonals from top and bottom of rudder to top and bottom rear of tab, respectively, and from bottom front to top rear of fin NATIONAL ADVISORY COMMI'ITEE FOR AERONAUTICS NACA RM No. L7G18 TABLE II.- TESTS OF A PRELOADED SPRING-TAB FLtJrl'ER MODEL Wi th Rudder Control Link Aepect It d f Con1'1gu- %dx It ~ cS K/It 2) (in.-1b-sec (cps) ration ratio (~) (lb/in.) (lb/in.) (in.) ( in.-1b) 0.0613 110.0 1 2.78 -------- -------- 1.81 6.32 5.18 >300 1.81 6.32 .0613 5.18 >200 2 2.78 39·1 33·3 1.81 .0613 5.18 20.0 >200 2 2.78 8.3 6.32 Very .0776 4.78 16.5 >200 2 2.78 8.3 1.98 7.26 high 11.04 .1370 4.23 14.2 >200 2 2.78 8.3 2.50 3.28 19.08 .2854 3.70 >200 2 2.78 8.3 9·0 - Without Rudder Control Link Con1'1gu- Aspect It d 1t1 1t2 Z It f1 f2 vf cS 2 KIIt (in.) ( in.-1b) (in , -lb-ssc (cpe) (cps) (mph) ration rat10 1b/1n.) (lb/in.) (lb/in.)
1.10 11.04 0.1370 4.23 2.03 104 2.78 8.3 -------- 23.4 2·502 11.04 4.23 4.37 108 2.78 -------- 109·0 2·502 .1370 3·20 3 33·3 11.04 4.23 5.60 6.44 1 30 2.78 83.0 -------- 2.502 .1370 3 233·0 4.20 4 2.78 3.6 171.0 2.502 11.04 .1370 4.23 5.5 133 33.3 6.17 4 2.78 6.5 19 8.0 2.502 11.04 .1370 4.23 170 33.3 5·9 4 2, 78 10.8 216.0 2.502 11.04 .1370 4.23 7.50 6.16 ~a> 33·3 6.10 4 2.78 8.5 169.0 2.502 11.04 .1370 4.23 5.45 ~90 33·3 6.25 8.3 -------- 28.2 1.28 3.38 .0245 7.33 5.40 5.38 1>150 6.25 8.3 -------- 28.2 14.52 .1017 6.42 2.20 2.61 78 5 2·593 -------- 28.2 2.437 10.a> .0885 2.40 2.78 6.25 8.3 6.55 85 28.2 8.a> .07a> 6.69 6.25 8.3 -------- 2·375 2·50 3·02 85 .1017 6.42 4.90 4.74 6.25 -------- 92.5 2.593 14.52 85 5 33·3 6.25 -------- 2.437 10.a> .0885 6.55 5.40 5.09 5 33·3 92·5 85 6.25 -------- 8.a> .07a> 6.69 5.70 5.46 5 33·3 92·5 2·315 85 -------- 6.25 83.0 204.0 2.593 14.52 .1017 6.42 7.17 5 5·15 90 83.0 -------- 204.0 2.437 10.a> .0885 6.55 6.38 7.63 100 6·25 204.0 6.77 8.10 6.25 83.0 -------- 2.315 8.a> .07a> 6.69 120 .1017 6.42 4.36 6.25 8.3 3.6 63.0 2.593 14.52 70 5 3·90 6.25 8.3 3.6 63.0 2.437 10.a> .0885 6.55 4.79 4.19 70 6.25 8.3 3.6 63.0 2.315 8.a> .0780 6.69 4.05 4.45 70 6 8.3 274.0 8.80 .0780 6.69 8.54 9.40 149 6·25 25·3 2·375 6 8.3 8.5 108.6 8.a> .07a> 6.69 6.48 5.94 114 6·25 2·315 6 8.3 16.2 181.0 8.a> .07a> 6.69 7.45 7.75 6.25 2·315 139 0.40 6 6.25 8.3 36.0 332.0 2·315 8.a> .07a> 6.69 9.26 149 8.10 6 8.3 18.4 202.0 8.a> .0780 6.69 >150 6·25 2·315 9·36 8.a> .0780 5.81 6 8.3 548.0 2.375 6.69 3.30 >150 6·25 55 ·0 114 .4 8.a> 6.09 128 6 6·25 3.6 2·375 .07a> 6.69 7.83 33·3 140.8 8.a> .07a> 6.76 6 6.5 2·375 6.69 6.51 149 6·25 33·3 6 6.25 10.8 182.0 8. a> .07a> 6.69 7.42 7·70 >150 33·3 2·315 6 8.5 160.9 8.a> .07a> 6.69 8.45 7·22 138 6·25 33.3 2·315 , 07a> 8 . 10 6 6 . 25 16.2 233.4 8.80 6.69 9·13 176 33 · 3 2·315 6.10 6 18.4 263.0 2.3~ 8. 80 .07a> 6.69 >190 6·25 9·25 33·3 6 6.25 83.0 3 .6 238.0 8.a> .07a> 6.69 7.86 8.81 143 2·315 6 83.0 6.5 264.0 8.a> .07a> 6.69 8.64 6·25 2·315 9·26 157 10.8 8.80 0.46 6 6.25 83.0 306.0 2·375 .07a> 6.69 9.98 183 6 6.25 83.0 8.5 284.0 2.315 8.a> .07a> 6.69 9.68 167 9·76 6 6.25 83.0 16.2 2.315 8.a> .07a> 6.69 9. 188 357.0 0·77 8.a> >200 6 6.25 83 .0 36.0 543.0 2.375 .07a> 6 . 69 2·92 3·30 NATIONAL ADVISORY Cct!KI.'l"l'EE FOR AERONAtJ1'ICS NACA RM No. L7G1 8 . ....
•
NACA LMAL 47330 Figure 1. - Preloaded spring -tab flutter model.
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NACA RM No. L7G18
Configuration 4
Configuration 1 Co nfi g uration 2 Configuration S NATIONAL ADVISORY COMMITTEE FOA AERONAUTICS Co nfi g uration 3 Configuration 6 Fi gure 3. - Test configurations.
NACA RM No.
L7G18 21 _ o Accelerome te r c Posi t10n )0-1 in d icator 4.75 0 T I...
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Figure J NACA RM No. L7G 18 Figure 6. - Prel o aded spring-tab flutter model mounted in the Langley high - speed 7 - by 10 -foot tunnel.
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o o 1.0 2.0 Tab T. E. displacement, in.
Figure 9. - Frequency as a function of tab displacement. Tab aspect ratio, 2.78; It; = 0.1370; 33.3 and 83 pounds per inch spring constants.
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time timing tripping position lower lower upper upper seconds position cycle hour; indicator indicator front displacement rear rear Initial Rudder 0.01 Increasing -front Rudder Rudder Stabilizer Fin Tab &:J Reference Rudder Rudder , ,.
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~ NATIONAL ADVISORY
-
COMMITTEE FOQ AERONAUTICS
I
1 1 1
2 4 6 10 --Jk, ~lb/ in.
Figure 11. - Flutter speed as a function of the square root of pre- loaded spring constant. No rudder control; aspect ratio, 2.78; It = 0.137 inch-pound-seconds .
I • 32 NACA RM No. L7G 18 '!- 'J...
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Aspect rat10, 0 2.7g - X Aspect rat10, 6.25 NATIONAL ADVISORY
COrITTEE, FOR ArONAurj"S
2 4 10 6 12 Calculated natural frequency, f2' cps Figure 12. - Flutter speed as a function of calcul-ated natural frequency for a tab deflection of 8.25 . Aspect ratio, 2.78 and 6.25.
NACA RM No. L7G 18 A Force, F Slope, k Slope, k a Displacement, x D (a) M ethod A.
Force, F Slope, k - --1-----1 Displacement, x (b) Method B.
k o Foroe, r Slope, k D1splacement, x NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS K (c) Method C.
Figure 13. - Methods of calculating the approximate natural frequency of a pre l oaded spring system.