C.P. No. 277 C.P. No. 277(18.617)

40 A.R.C. Technical Report

4, 1

(18.617)A.R.C. Technical Report

MINISTRY OF SUPPLYI

A E R O N A U T I C A L R E S E A R C H C O U N C I L

CURRENT PAPERS

Flutter Calculations on a Rudderwith Trailing-Edge Spoiler

LI. T. Niblett, B.Sc.Tech.

E

LONDON: HER MAJESTY’S STATIONERY OFFICE

1956

PRICE Is. 6d. NET

,

. . .

C.P. No.277i

Report No. Stmcturcs 202

May, 19%

ROYAL AIRCRAFT ESTAELIS~

Flutter Calculations on a Rudder with Trailing-Edge Spoiler

by

Ll. T. Niblett, B.Sc.Tech.

Flutter calculations made on a rudder with trarrlzng-edge spoilers

are described. The results obtained agree with the flight experience

which has been acquired so far (except for the frequency of the flutter)

in spite of the simplicity of the aerodynamic assumptions. It has been

found that, as mth tab flutter, a form of flutter involving the main

surface (fin) occurs with an overmassbalanccd spoiler.

LIST OF CON1'cNTS

1 Introduction

2 Details of ca1culat10m

2.1 Binary Flutter Calculations2.2 Quaternary and Ternary Flutter Ca1clilat10ns

3 Chparison of Results of Calculations and Flqht E.rpcnence

4 conclusions

LUJG of Symbols

References

m

3

3

45

6

7

7

7

LIST OF ILLUSTRATIONS

Traling-l?;dge Spader (A) B'itted to Mctcor ~-58Type Rudder

Vanatxon of Flutter Speed vnth Massbalance(Ruditcr-Spodcr Binary)

Effect of Spader Damping on Rudder-Spader Flutter Speed

Effect of Spoiler Massbalance on Flutter Sped

1

1 Introduction---

Flzght tests have been carried od recently on a Meteor e.ircrafY toccmpare the effectiveness of a traiUng-edge spoiler wxth that of thestandard rudacr tab. The oalculat~ons described below were made toinvestigate the flutter stablllty of the spoilers.

Two spaders have been fittcdto the rudder at different times.One rcplacedtho tab and used the tab's control circuit, whiJxt the otherwas separate iYcm the tab and enabled a &roct ccPnparrscn of :he cffective-nesses cfthespoder and tab to be made. Flg.1 1s a sketch ol' the arrange-ment of the first of these spoilers, xferred. to in tnc prwent paper asspoiler A.

Flutter calculations were made on each system. Those on the firstsystem took account of only two degrees of free&m, rudder rotation andspoiler rctatlon, and showed that the spader should flutter at a speedprcportxonal to the spoiler frequeccy; the flutter could be elzmwatedbyspoiler nagsbalance. The azrcraft flew with an umnassbalanced spoilerwthout expenencxng any vibration. Vhen the second spollcr was fitteaa high-frequency vxbration commencca at a low axspeed. A ternary fluttercalculation involving rudder rotation, rudder torsion and spoiler rotationwas made, zla It was again shown that massbalance was an effective meansof eldunating the flutter. A quaternary calculatzon, In whxh a finflexural moat was s&id to the above ternary, was made to check whether anover-massbalanced spoiler would give rise to flutter sznn1a.r to the 'ternarybranch' type of tab flutter. Such a branch has been found.

An accocnt of the calculations 1s @ven in section 2. Tho resultsare compared Tnvlth the flight cxperlence In section 3, the agrzzlent beingfound to be reasonably good.

2 Detads of Calculations

The arcraft to u!h.x.ch the spoilers were fitted was a Meteor 7 vdth aMeteor 6 type rudder. The first spodcr, spoiler A, which replaces thetab, 1s connected to the tab clrcut so that it 1s used for trmng,prod&n&r aerodynamic balance through a gearing, and is also connected. toan R.A.E. Type F autostablllser. The second spoiler, spcdcr PI, vdxlch ison the top part of the rurl?ler, 1s on a circuit of Its ovm and is not usedather for trinrming or for balancing. In the flutter calcclatlons bothspoilers arc considered to be &reczll attnchedto the rudder by springsand Lash-pots and no account is taken of the trdng and balancing dutlcsof spoiler A.

The rudder is e.lso fitted with trailing-edge strip, whose contri-bution to the aerodynamic tinge mcment is not known accurately. In thebinary and ternary calculations this contnbutlon 1s vamped, whdst inthe quaternary the value that results In the lowest flutter speeds forthe binary and ternary 1s used. Factors to represent the change in the&rect rudder &ping coefhcient due to the trxdxng-edge strip areobtained from ReP.l.

No aerodynsmic fllutter derivatlvos are available for spoilers, andthe only steady-motion derlvntivcs avaxlablc arc those for the rate of changeof ld't ?nth spoiler deflectlon ana the rata of change of control-swfacetinge moment lath spader deflection. The cthcr spoiler demvatlves aretaken to be negligible. This is so for the spoiler hinge-moment stiff-ness derivatives if they arc of the same or&z as the spader static

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derivatives. All the derlvatlves arc evaluated according to thereccmmendatmns of hhrhnnxk for surfaces of low aspect-ratio2, viz:-

(1) estimated steady-motion values are assumed for the stiffness&arivatlves,

(2) the damping derivatives arc assumed to be the same as thecorresponhng stiffness derivatives \rherc poszblc (e.g.e. ?A assumed to be Ca ),

(3) the reasining dsmping derlvatlvcs are obtained from acomparison of the three-dimensional steady-motion &mvatlveSand the tumng-polnt values of the two-dimensronal d.sm~ngand stiffness denvatlves.

All the derivatrves are assumed to be xx%zpendent of frequencyparameter. The steady-motion derivatlvcs used arc low-speed estimates.

2.1 B1nar.y Fldter Calculations

If we consider blnarv flutter involving rotations of the rudder andspoiler we s.rT?ve at the &tical deterrmnantal equation

- a,, u2 + bjl iv + c,, t c,, y, - aq2 v2 + q2

- 91 "2 - “22 !J2 t y

(9, = 9,)

=o (1)

where the symbols have their usual meaning and the fwst generaliscdcoordinate 1s rudder rotation and the second is spodcr rotation.Structural damping has for the mcment been neglected. It vdl be notedthat all aerodynamxc coeffiolents for the spoiler are zero except thecross stiffness cj2, rudder hinge moment dw to spollcr rotation.

The con&tions for stabdity3 are then:-

all y * a22 Cc,, + c,l Y) - 812 cl2 > 0 (2)

ajz2 y - a12 "22 =I2 ' o

Both these con&tions are fulfilled at all speeds if a,2 ana cl2have opposite signs, that 1s If the spollcr 1s dynmnically ovcrmsssbalanced.The more critical of the conditions is (3) slnoe fran it, vhhen a,2 1s zero1.e. when the spoiler 1s dynarmcally massbalanced, s.n osclllatlon of thespoiler willbcmaint~ned due to the el%nation of the couphng franrudder to spoiler. The cntzcal speed, aj2 * 0, 1s @ven by

.

a12 y = 92 Cl2 (44

i.e.

o r

v2 = a12 . -=222a22 Cl2 P sc

(4b)

v‘q2 1-5=-

‘\ )(4c)

Cl2 O2c, for Y.22 = p SC4 cd2' a22

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The flutter speed of the spoiler decreases, therefore, as the mass-balance 1s increased until the spoiler is dynamically overbalanced, inwh-Lch condition it 1s stable at all speeds. The flutter speed alsod~qem3.s &rectly on the frequency of the spoiler. The flatter Prequency1s given by the rmaginary part of equation (1)

i.e. w = w;1 (5b)

At a critical flutter condition thcrc is no rudder rotation in thefiutter mods, and the spoiler oscxllatcs at its own natural frequency.The effect of a typical massbalanclng arrangonent on the flutter speed ofspollor A is shown zn Fig.2.

When the natural frequency of the spoiler was measurcdit was foundthat the spoiler was quite highly dsmpcd anfi the effect of strWtu?Yii. *dzmplng on Its flutter speed has been calculated. The mar:<& effect ofa small smount of structural damping on the s!lape of the fldtcr speedversus massbalance curve 1s shown in I"lg.2. F1g.j shows hori the fldterspeed of an !xmassbalanced spoiler vanes lvlth the &mount of wing inthe spodec urclut. It will be seen that over the normal part of theJamping range the flutter speed varies llttlc xtth the rudder lunge momentdue to trading-edge strip. If the spo~lcr~s natu.ral frequency 1s aisothat of the rudder the flutter speed for 1~ values of the &m~lng ISabo& half that rnth the rudder free. The flutter frequvncy decreasesat first mth lncreaslng dsmplng when the rud&r 11s free, the decrementsbclng greatest for the rudder vnth least aerodynamic balance. Rhcn thoflutter sr~eed becomes higher, however, the frequency starts to Increase,presumably due to the lncrcased aerodynsnnc stiffness of the rudder.VLth stiffness in the rudder cxclut, the frequency Increases very slightlym'ch Increase of dnmplng. The crltlcal frcquenoy parameter for theunaampea spoiler, based on the hn mea‘] chord, is 2.9.

2.2 @aternary and Ternary Flutter Calculations

The quaternary flutter calculatlcn i‘ias made on spoiler B. Thedegrees of fro&an added to those of the binary calcdatlon are fin linearbcn&.ng and rudder torsion. Rudder torsion 1s inclcdd as the naturalfrequency of spoiler B is higher than that of spodcr A and near to thenatural frequency of the rudder torsion moat In vduch the tap and bottompsrts of the rudder move against each other as r@ja bodies, all the tinstbmng in therrr interconnactxon. The fin flcxllre mode is included tocheck whether flutter sx.milar to the 'ternary I autter of tabs IS possible;in the clrcumstanccs the shape of the mode was not thought to be jmportantand a linear mode was assumed for simplicl%y.

The curves of flutter speod versus spoiler massbalance for a wideran&e of fin frequencies are shown ~1 Flg.I+. The Tluttcr cquatlons weresolvea on the R.A.E. flutter simulator and 1 per cent of cri.tlcs.1 strco-tural damping was included in all the modes. The rudLlcr-spader ternarycurves are generally sxmilar to the rudder-spader binary curve of Flg.2vnth spader dsmplng xncluhd, In marked contrast to the binary curves(of Fig.2) without spollcr dsmping. The curves of Fig.4 for zero f‘lnstxffncss are based on extrapolated results, and whdst the flxtter speedsare probably faxcly accurate, since they are cxtrapolatcd from smoothcurves, there may be large errors III the flutter frequencies. Thequaternary flutter curve follows the ternary-rddcr rotatxon, rudder torsion,spoiler rotation-flutter curve closely w%en the spoiler massbalance is less

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than static for all fin frequencies except the frequency pertinent toFig.& when the quaternary curve is modified by a near coincidence of thefin and spoiler frequencies producing a low binary fin-spoiler flutterspeed. Fran a ternary-fin bending, rudder rotation, spoiler rotation-flutter oalculation which has been made and g~vos a higher fltiter speedthan the quaternary, it would seem that of the rudder frwdassthc torsion ,is the more important in ths quaternary flutter.

For the low fin frequencies the quaternary flutter speed rcs~~nspractically coincident mth the ternary-rudder rotation, rudder torsion,spoiler rotation-speed until at 1857: static spoiler massbalance, wherethe ternary flutter has almost disal~peared, a second branch of thequaternary flutter appears. (The spoiler is aynarmcally massbalancedfor rudder rotation at twice the value for static balance). In thissecond branch the critical speed decreases 8s the massbalance is Increased,and the important rudder motion is rotation. AS the fin frequency isincreased the transition to the second branch Lrst occurs with less mass-balance and then the overbalance branch disappears cgnpletely, theatition of the fin ben&.ng mode leadang only to minor modifications ofthe ternary rudder-spoiler curve.

3 Ccnroarison of Results of Calculations and Flip%t Experience

No evidence of vibration was obtained in flight when the aircraftflew with the urrmassbdlancea spoiler A. Tho effectiveness tests weremade at speeds up to 250 knots and the aircraft was fitted with vibrationmea.%XTng equpment .

The frequency of the spoiler was measured on the ground and nasfound to be 25 c.p.s. when the spoiler was oscillating with small w&i-tude. The oscillations were observed to be qlute heavily dsnrped, thedaqnng beirg estimated to be at least 10% of critical. Referring toFig.2, it is seen that, for this value of wing, the calculated binaryflutter speed when the undamped frequency of the spoiler is 25 c.p.8. andthe rudder is free is at least 325 knots. Thas theoretical speed isconsistent 81th there being no evidence of vibration in flight.

When spoiler B was fitted and flolm \nthout massbalance a persistenthigh-frequency vibration started at loo arspccds. The vibration was notsevere but increased in severity on one occasion \!hen the spo~~lcr upera-ting rod broke due to fatigue. The frequency of the vibration hasmeasured as 52 osp.S. 50% static massbsl,ulca made llttlo a-Lffercnce tothe vibration but when the massbalance was increased to 100s the vibrationduappewed and has not occurred since.

This behavzour 1s explsanedto some extent by the left-hsndbranchcsof the quaternary flutter o'urves. The thcordical flutter speed? agreereasonably vrell with fkght evldencc but the theoretical flutter frequencydoes not. The theoretical flutter frequency of the unaassbalanced spoileris 41.7 C.F.S., which is the natural frequency of the spoiler, whole thefrequency measured in flight is 52 0.p.S. Arbitrary changes in the directspoiler structural damping and aerodynsrmc stiffness that have beeninvestigated in an attgnot to irrprovc the agreement between the theoreticaland practical frequencies give.no better results. The spoiler secmedtohave little &mping when its frequency was measured, and reasonable amountsof structural wing were included v,bon the flutter equations wore solvedon the R.A.E. flutter simulator.

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h Conclusions

Calculations have ,gvcn reasonable explanations of the flutterbehadour of two spoilers bkt have not sccurntol;r prc&ctcdthc flutterfrequency in the case where flutter was cxpcr~enced in flqht.

Flutter in vrhch both the mzu.n surrace and ms;~n control-scrfacc playnecessary parts is possible when the spo’ollur 1s overmassbn3.al~ce:oa.

LIST OF SYMIXZS

b2

c

Cl 1

s

Y

EITV

z

!J

w

9

w2

rcspectxvely the non-&.mcnsxxkl total inertia, aerodynannc

dmpmg and otlffncss coeffxwnts m tho flutter cquatzons

the rate or change of t& static rud&x iunge moment vnthrudder angle

fin reference chord

ratlo of stiffness In rudder rotation mode to that Inspoiler rotation mode (3,,&2)

fin reference lcngkh

direct structural stiffness x.17 rth mode

crltlcal flutter speea

negatlvc b2 due to rud?ter tradrng-&;e st7xp

orltlcal frequency parameter

cr3.tlcal flutter frequency

uncouplea still-a3r freqwncy of fin

mcouplod still-ax fraquency of spollcr

Author(s)

I X. C. LsmbourneA. Chinneck andD. 3. Bdts

Tltlc, etc.

Measurcmcnts of i~crodynam5.c Dcrivatlvcsfor a Horn %lanccElZlevator.H&M 2653 Janlxary, 191+9

.

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No. Author(s1

2 I. T. M~nhmnick

3 H. Templeton

Title, ctc

Aerodynamic Denvat~ves - Paper No.4of k Symposium of tnc Fll;ttcr Problemin Aircraft Dcslgn (E&ted byH. TempIoton and G. R. Brooke;.R.A.C. Report No. Structures 147.A.R.C. :6,0E1 &lay, 1953

The Techlvque of Flutter Calm.l.atiom.Cum-ent Paper X0.172 Ap~5.1, 1953

-a-CT.207R.CP.Z?T.K3 - Prmted sn Great 3vrtarn

S E C T I O N A - A .

. STRIP 0 -80” WIDE STRIP 0.80” WIDE

.

SPOILER SECTION (FULL SIZE.)

FIG. I. TRAILING-EDGE SPOILER(A) FITTEDTO METEORlvlK.8 TYPE RUDDER.

uwz( 3

WITSCYCLE

r I I

-..- CONSTANT SPOILE.? STIFFNESS CONSTANTSPOILER DAW’IN~ (I.4 7& CF+TltPs FoqUNMASSBALANCED SPOILER)

STABLE

PEqCENTAtX DYNAMIC MASSBALANCL

FlG.2. VARIATION OF FLUTTER SPEED WITHMASSBALANCE (RUDDER -SPOILER BINARY)

- - RUDDER AND SPOILEF FF(EQUENCIES

= - b2 DUE TO TqAILINQ-EDGE STPIP.

CUqVESA!jE THE VALUES OF “1%

.

PERCENTAGE CRITICAL DAMPING.

E

FIG.3. EFFECT OF SPOILER DAMPING ON

RUDDER- SPOILER FLUTTER SPEED.

(a)

6 0 0129 3

2 0 0 0, =18.6CPS, 7

44 3? 3p 2s O~~CPS)&O” 1 0 0 z o o 300 400

PERCENTA@ STATIC MASSBALANCE

200 qs26.2 CPS.-

4036 sp 95 02(CPS.)0 loo coo 300 4.00

(Cl

FlG.4(a-c) EFFECT OF SPOILER MASSBALANCE ON FLUTTER SPEED.. . .I * . r

,r .

0, f 34.7 C?S _

qo J.5 ql 25 02 (c PS)0 loo 200 300 400

2QO

LL40 35 300 100 2

cd) (e)PEqCENTA[;E STAftC MASSBALANCE

2 2 3

S

T-0,s 43-7 CPS.-

q5 02 (CPS3 300 4

- FIN-fiUOD~-SMILE8 FLUTTER(QUATERNARY )

- - - @JDOEq-SPOt LEe FLUTTEq(TERNARY)

-f-s FIN -SPOlLEq FLUTTER(BINARY)

W, FIN FLEXURAL FWQUENCY.Op SPOILER FqEQUENCy

THE FlGU&S BY THE POINTS ON THE

CUqVES ARE IWE FtjEQUENCrES IN Ct’S.

IO

FIG,9(drelEFFECT O F S P O I L E R M A S S B A L A N C E O N F L U T T E R S P E E D .

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C.P. No. 277(18.617)

A.R.C. Technical Report

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