Document
MEMORANDUM
EXPERIMENTALLY DETERMINED EFFECTS O F VARYJNG PITCH AND CONTROL S T I F ~ E S S E S ON THE FLUTTER CHARACTERISTICS AT SUPERSONIC SPEEDS O F ALL-MOVABLE WING AND TAIL MODELS By P e r r y W. Hanson Langley Research Center Langley Field, Va.
, . . - i
NATIONAL AERONAUTICS AND
SPACE ADMINISTRATION
WASHINGTON
March 1959
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EXPERIMENTALLY DETERMINED EFFE?!TS' O F VARYING PITCH AND SUPERSONIC SPEEDS O F AIL-MOVABLE WING AND TAIL MODELS" By Perry W . Hanson The f l u t t e r c h a r a c t e r i s t i c s of geometrically,dynamically,and e l a s t i c a l l y s c a l e d v a r i a b l e - i n c i d e n c e w i n g , all-movable horizontal- tail, and v e r t i c a l - t a i l modelsofaproposed f i g h t e r a i r p l a n e were i n v e s t i g a t e d i n t h e Langley 9- by 18-inch supersonic flutter tunnel a t Mach numbers of 1.3, 1.64, 2.0, and 2.55. The e f f e c t s of varying the aileron and rudder control stiffnesses and p i t c h s t i f f n e s s were a l s o i n v e s t i g a t e d . A proposed methodof compensating foranall-movable flutter-model mountingsystemhavingan i n e r t i a g r e a t e r t h a n t h e s c a l e d value was evaluatedand was found t o be s a t i s f a c t o r y . The s p e c i f i c models with scaled design pitch stiffnesses and c o n t r o l s t i f f n e s s e s proved t o be f r e e from f l u t t e r w i t h i n t h e r e q u i r e d s c a l e d f l i g h t boundary.Except forextremely low values of p i t c hs t i f f n e s s ,t h e dynamic pressure a t f l u t t e r v a r i e d a l m o s t l i n e a r l y w i t h t h e p i t c h s t i f f n e s s of the w i n g models t e s t e d . The numericalvalueofthe dynamic pressure a t f l u t t e r w a s more s e n s i t i v e t o changes i n p i t c h s t i f f n e s s with increasing Mach number although the percent change i n f l u t t e r dynamic pressure w a s nearly constant up t o a Mach number of 2.0.
INTRODUCTION The increased usage of highly sweptall-movablesurfacesforstabi- l i z a t i o n and control of airplanes and missiles cowled with the frequent occurrence of f l u t t e r of these surfaces has l e d t o considerable interest i n a study of t h e i r f l u t t e r c h a r a c t e r i s t i c s . A t thepresenttime ana- l y t i c a l methods f o r t h e p r e d i c t i o n of t h e f l u t t e r b e h a v i o r ofsuch s
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Title, Unclassified.
c r: surfaces are useful primarily for trend studies and their use as c r i t e r i a for design i s questionable.Although some experimentaltrend studies have been made (see, f o r instance, refs. 1 t o k ) , they are f o r c the'most part limited in scope since they use scaled models ofproposed controls. The designer,therefore, i s presentlyfacedwiththe problem of having t o determine experimentally the flutter characteristics of use. Thus, a f l u t t e r eachparticularconfiguration he may wish t o investigation involving both specific and general research of geometri- c a l l y , e l a s t i c a l l y , anddynamicallyscaled modelsof the variable- incidence wing,all-movablehorizontal tail, and of t h e v e r t i c a l t a i l of a proposed f i g h t e r a i r p l a n e has been made i n t h e Langley 9- by 18-inch supersonic flutter tunnel for the Mach number range from 1 . 3 t o 2.55. The wingand v e r t i c a l t a i l were t e s t e d w i t h andwithoutcontrols.
A l l models were wall-mountedand testedseparately. The purpose of the investigation was threefold: To determinewhetherthe models were f l u t t e r - f r e e w i t h i n t h e s c a l e d r e q u i r e d f l i g h t boundary; t o i n v e s t i g a t e t h e e f f e c t s ofchangingthe wingand h o r i z o n t d - t a i l p i t c h s t i f f n e s s e s and the aileron and rudder control stiffnesses; and to evaluate a proposed method of compensating for an all-movable control model having a mount- . % assembly i n e r t i ag r e a t e rt h a nt h es c a l e dv a l u e . The investigation, accordingly, is p r e s e n t e d i n three phaseswhich p a r a l l e l t h e s e a r e a s of i n t e r e s t . L.
SYMBOLS a speedofsound, f p s e distance from control center of gravity (aileron or rudder) to h i n g el i n e ,i n .
flutterfrequency,cps f f natural vibrationfrequencyofnth mode (n = 1, 2, 3, 4, 5 ) , cps f n mass moment of i n e r t i a of controlsurfaceaboutcontrolhinge I C line,in-lb-sec2 mass moment of i n e r t i a of model mounting flange about pitch I f axis, in-lb-sec2 mass moment o f i n e r t i a of basic-model mount assemblyabout I m pitch axis, in-lb-sec 2 c . . . . . . . . . .
mass moment of inertia of modified mount assembly about pitch I O
axis (or for purposes of developing equation (A2) , t h e mount
assembly pitching inertia not representative of scaled value of airplane-wingcenter-bayinertia),in-lb-sec2 b mass moment o f i n e r t i a a b o u t p i t c h axis of model exposed panel I P (excluding mounting flange and instrumentation wire), in-lb-sec2 mass moment of i n e r t i a o f model including mounting flange and It with instrumentation wire about pitch axis, in-lb-sec2 wingand h o r i z o n t a l - t a i l p i t c h stiffness, in-lb/radian K a i l e r o n or rudder control effective hinge stiffness, K C in-lb/radian p i t c h i n g s t i f f n e s s r e q u i r e d f o r model wing with increased KO (unrepresentative) mount assembly i n e r t i a t o g i v e c o r r e c t impedance a t flutter frequency based on r e l a t i o n
KO = K + 4n 2 2 f f (IO - Im) , in-lb/radian
2 distance from model root to panel center of gravity measured perpendicular to model r o o t , i n .
M Mach nmber dynamic pressure, lb/sq f t dynamic pressure a t f l u t t e r f o r b a s i c mount-model configuration, qf lb/sq f t dynamic pressure a t f l u t t e r f o r model w i t h p i t c h s t i f f n e s s qf ,o changed t o compensate for an increased (unrepresentatiye) f t mDunt assembly i n e r t i a , l b / s q distance from p i t c h axis to panel center of gravity measured r p a r a l l e l t o r o o t c h o r d ( p o s i t i v e when center of gravity is forward of p i t c h a x i s ) , i n .
c o r r e c t impedance of model mount assembly a t f l u t t e r f r e q u e n c y , Rf in-lb/radian weightofcontrolsurface,lb WC weight of moving portion ofbasic-wing mount assemblies and Wm horizontal mount assemblies, l b L ry weight of moving portion ofmodified-wing mount assemblies, wO l b r; weightof w i n g and h o r i z o n t a l - t a i l mounting flanges, lb W f weight of model panel excluding mounting flange and i n s t r u - W P mentation w i r e , l b t o t a l weightof wing including flange and instrumentation W t wire, l b weightofinstrumentation wire, l b WW test-section density, slugs/cu f t P APPARATUS AND OPERATING PROCEDURF: f Wind Tunnel This investigation was made i n t h e Langley 9- by 18-inchsupersonic f l u t t e r t u n n e l which i s a conventional,fixed-nozzle, blowdown wind tunnelexhaustinginto a vacuum sphere from a pressurereservoir. The nozzleconfigurationsused gave Mach numbers of 1.3, 1.64, 2.0, and 2.55.
A t each Mach number the test-section density varies continuously to a controlled m a x i m u m density and thendecreases. M a x i m u m test-section conditions are depictedinthetunnelperformancecurves shown i n figure 1.
The test procedure f o r a l l Mach numbers was e s s e n t i a l l y t h e same.
The t e s t s e c t i o n andthesphereinto which the tunnel exhausts, were pumped down t o a pressure of approximately 2 pounds persquareinch test section w a s then absolute. The controlvalveupstream of the openedand the test-section density was allowed t o i n c r e a s e u n t i l f l u t t e r was observedorthe maximum densityobtainable was reached. After each run the modelswere inspected visually and the natural frequencies were just p r i o r t o t h e r u n t o d e t e r - checkedand compared with those obtained mine whetherany s t r u c t u r a l changeshadoccurred.
The modelswere mounted on the mount blocks through the mount assembly. The mount blocks,inturn, were a t t a c h e d t o t h e headof a r a m t h a t w a s used t o i n j e c t o r r e t r a c t t h e models through one side of the t e s t s e c t i o n i n o r d e r t o a v o i d rough flow during the starting and stoppingoperation. The modelswereviewed through a window i n t h e ' opposite side of the test section.
The actual time for each run was approximately 3 to 4 seconds. A
multichannel oscillograph provided a continuous record of the test condi- tions and of the behavior of resistance wire strain-gage bridges attached to the model box spars. A 16-millimeter motion-picture camera, operated at approximately 1,000 frames per second, furnished a record of the model motions.
Models This investigation employed geometrically, elastically, and dynami- cally scaled surfaces of the variable-incidence wing, the all-movable horizontal tail, and the vertical tail of a fighter-type airplane. How- ever, the wing and horizontal-tail mount assemblies (that portion of the mount-model combination corresponding to the center bay of the airplane fuselage-wing combination) were not dynamically scaled. The basic wing models are designated W1 to ~ 6 , the first two of the series being without ailerons. Three of the wing models (W2, W5, and W6) were repaired and redesignated W2A, W5A, and W6A for use in the third phase of the gation. The wing mount was strengthened for the third phase of the investigation; this strengthening resulted in an increase in weight and a slight increase in inertia. When these latter three wings were tested in combination with various mount inertias, the configurations are
identified by suffixing the numbers 1 to 4 to the three redesignated
models. (These configurations are defined in table V. ) The all-movable horizontal-tail models are designated RT-1, HT-4,
and HT-5 and the vertical tail models, VT-3, VT-4, and VT-7. Vertical
tail models VT-3 and VT-4 had hinged (leaf spring) rudders.
Model Geometry The wing models were 0.0333 scale and had an exposed panel aspect
ratio of 1.71 and a taper ratio of 0.246 based ona tip chord not
including the leading-edge extension. The geometry of the wing models is shown in figure 2(a).
The horizontal-tail models were 0.0662 scale and had an exposed panel aspect ratio of 1 . 5 9 and a taper ratio of 0.196. The geometry of the horizontal-tail models is shown in figure 2 ( b ) .
Both the wing and the horizontal-tail models were effectively all-
movable surfaces. The wing pitch axis was at 69.4 percent of the root
chord and the horizontal-tail pitch axis was at 5 1 . 4 percent of the root chord.
The geometry of the vertical tail is shown in figure 2 ( c) . The
vertical-tail model was 0.065 scale and had an aspect ratio of 1.20 and a taper ratio of 0.359. Unlike the wing and horizontal tail, the vertical tail was not free to pitch. The bending moment was taken by a l/2-inch-square aluminum mount .rod located a t 69.2 percent of the root chord,the model being restrained in the pitching degree of freedomby two shearbolts a t 25 percent of therootchord. The v e r t i c a l tails normally carried a concentrated mass representing t a i l warning radar on t h e t r a i l i n g edge a t 75.7 percentspan.
Construction All the models were c o n s t r u c t e di nt h e same general manner. The details of construction of the various models a r e shown i n f i g u r e 3 .
The main load carrying member of each model was a taperedhollow aluminum box s p a r t o whichaluminum-alloy r i b s were welded.Spruce o r mahogany leading and t r a i l i n g edges were gluedtotheends of t h e r i b s t o complete theplanform. Mounting flanges werewelded t o theroots of the box spars e x c e p t f o r t h e v e r t i c a l - t a i l modelswhichhad a 1/2-inch-square aluminum mounting bar extendingintothe box s p a r .E l e c t r i c a lr e s i s t a n c e w i r e s t r a i n gageswere mounted on the box sparsneartheroot.Balsa wood w a s used t o f i l l i n t h e a r e a between t h e s t r u c t u r a l members and to give the models t h e i r a i r f o i l shapes.Piecesoflead were used t o o b t a i n d e s i r e d mass and i n e r t i a d i s t r i b u t i o n . The balsa was thencoveredwith model silk and doped. The a i l e r o n and rudder controls were similarly constructed. L The framesconsistedofspruceleading and t r a i l i n g edgesconnected i n t h e streamwise direction by aluminum-alloy ribs two of which carried hinge mounts on theupstreamends.
Model MountingSystems The mount assembliesof a l l the modelswere b u i l t i n t o aluminum mounting blocks(approximately 1.5 by 2.8 by 12 inches) whichwere attachedtothe headof the tunnel i n j e c t o r mechanism. A drawingof the
wing mount assembly i s shown i n f i g u r e 4(a) . The assemblyconsisted of
a flange mount ( t o r e c e i v e t h e model flange) welded t o t h e main mount- assembly member, the downstream end of which w a s attached to a leaf springsecuredtothe mountingblock. The upstreamend was attachedto an auxiliary spring which w a s i n t u r n a t t a c h e d t o t h e mountingblock by a a boltthatcould be moved i n t h e chordwise d i r e c t i o n . Thus, t h e p i t c h s t i f f n e s s of the wing mount assemblycould bechangedby moving t h i s b o l t t o change the effective length oftheauxiliaryspring,and/or by using springs of differentthicknesses. The mount assembly,exceptforthe area around the flange mount, was enclosed by a cover plate.
The h o r i z o n t a l - t a i l mount assembly was similar t o t h e wing mount assembly except t h a t no auxiliaryspring w a s used.Figure 4 ( b ) shows the d e t a i l s of t h i s mount. The flange mount thatreceivedthehorizontal- -1 t a i l flange was cantilevered on a leaf spring secured to the mounting *’ I block. The p i t c h i n g s t i f f n e s s w a s changedby using leaf springs of variousthicknesses.
The v e r t i c a l - t a i l mount assemblyconsistedsimply of a h o l e i n t h e mountingblock to receive the square aluminum mountingbarwith set screwsthroughtheblocktosecurethebar. Two holes were tapped i n theupstreamface of the block to receive the shear bolts on the model r o o t . (See f i g .2 ( c ) .)
Physical Properties The physical properties of the basic model configurations are given i n t a b l e I and the physical properties of the modified wing-mount con- f i g u r a t i o n sa r eg i v e ni nt a b l e 11. Table III(a) presentstypicalwefght and i n e r t i a d i s t r i b u t i o n of the model wingswithoutailerons. The geometricboundariesofthevariousstationsalongwiththecentersof g r a v i t y a r e p r e s e n t e d i n f i g u r e 5(a). Typicalweightandinertiadis- tributions of wingmodels with ailerons are shown i n t a b l e I I I ( b ) and theboundariesofthevariousstationsandthecenters of g r a v i t y are shown i n f i g u r e 5 ( b ) . Table I I I ( c ) g i v e s a typicalweightandinertia d i s t r i b u t i o n of models of thehorizontal t a i l . Figure5(c)definesthe boundaries of t h e s t a t i o n s and thecenters of g r a v i t y .
Representative mode shapes of the first three n a t u r a l modes of vibra- t i o n of a wing without aileron for two d i f f e r e n t p i t c h s t i f f n e s s e s a r e p r e s e n t e d i n table I V . The models were excited by anacousticalshaker and the mode shapesdetermined by the acceleration method d e s c r i b e d i n reference 5. Typical node linesforvariouspitchstiffnessesand con- t r o l hinge stiffnesses of some of thevarious models t e s t e d a r e p r e s e n t e d i n f i g u r e 6 . F i t c h s t i f f n e s s e s weremeasured by a n o p t i c a l l e v e r method, the estimated maximum e r r o r ofwhich varied from approximately 2 percent a t a p i t c h s t i f f n e s s of approximately 4,000 inch-pounds p e r r a d i a n t o 5 percent a t 18,000 inch-pounds perradian.Varyingthe wing p i t c h s t i f f n e s s o v e r a widerangegenerallyproduced l i t t l e change i n t h e frequencies and node l i n e s . The first andsecond n a t u r a lv i b r a t i o n modes were more s e n s i t i v e t o p i t c h s t i f f n e s s v a r i a t i o n s t h a n t h e h i g h e r modes. A s t h e p i t c h s t i f f n e s s w a s increasedover a widerange,the first-mode frequency increased slightly and the node l i n e moved somewhat c l o s e r t o t h e r o o t . The second-mode frequencyalsoincreasedslightly and the node l i n e n e a r t h e r o o t moved toward the t i p s l i g h t l y w h i l e the node l i n e n e a r the t i p d i s p l a y e d no apparentchange.
Changing t h e a i l e r o n o r r u d d e r hinge stiffness over a wide range.
producedconsiderable change i n the node l i n e s ofthehigher modes on boththe wingand v e r ' t i c a l - t a i l models.Reducing t h e p i t c h s t i f f n e s s of t h e h o r i z o n t a l - t a i l models by one-halflowered a l l t h e n a t u r a l fre- , quenciesbuthad l i t t l e e f f e c t on the node l i n e s e x c e p t f o r the f i f t h mode. The fifth-mode natural frequency was somewhat i n s e n s i t i v et o p i t c h s t i f f n e s s changes,butthe node l i n e changed considerably.
TEST PROGRAM The test program was dividedinto three phases. The purposeofthe f i r s t phase w a s t o determinewhetherthe wingand h o r i z o n t a l - t a i l models with the scaled design pitch stiffnesses and t h e v e r t i c a l - t a i l models with the scaled design bending stiffness were f r e e from f l u t t e r w i t h i n t h e p r e d i c t e d f l i g h t boundaryof the airplane (including the required safetymargin).Duringthisphaseoftesting,theaileronandrudder hinge s t i f f n e s s e s werereduced below the scaled design values to deter- mine t h e e f f e c t on the wingand h o r i z o n t a l - t a i l f l u t t e r boundary. The secondphaseof t h e t e s t program w a s t o determine the effect ofvarying the pitch stiffness of the basic wing-mount configuration a t the various Mach numbers tested./ The t h i r d phase was concernedwithanexperimental assessment of an analytical method proposed i n r e f e r e n c e 6 f o r compensating f o r u n r e a l i s t i c mount assembly i n e r t i a s . It w a s mentioned i n t h e s e c t i o n on models that the center-bay or mount assembly of the wing model was notdynamicallyscaled. It was n o t p r a c t i c a l t o b u i l d t h e mount assembly L .
with as l i t t l e mass as the scale factor indicated; as a result the mount was toomassive. The proposed method f o r compensating f o r t h i s assembly i s developed i n theappendix.
condition The modelsused i n t h e t h i r d phaseoftheinvestigation were three reworkedmodelsand the mount assembly was salvagedfromthe first phase.
The models (W2A, W5A, and W6A) and mount assembliesused i n t h i s phase a r e r e f e r r e d t o as "modified" i n t h a t t h e mass of the mount assembly was increased to various values over that of the mount assembly as o r i g i n a l l y designed. The t e s t procedure used i n t h i s phase was as follows: A model with the mount-assembly inertia approximately as originally designed and with a c e r t a i n p i t c h s t i f f n e s s w a s run in the tunnel to determine the flutterfrequency and the dynamic pressure a t f l u t t e r . The inertia of the mount assembly w a s then changedand t h e p i t c h stiffness a l t e r e d 2 2 according t o t h e r e l a t i o n developed i n the appendix: KO = K + k ~ t f f (Io - Im).
The model was again tested to determine whether the dynamic pressure a t f l u t t e r remained the same, i n o r d e r t o v e r i f y t h e e f f e c t i v e n e s s of t h e compensation. This w a s done f o rs e v e r a lp i t c hs t i f f n e s s e s K a t M = 1.30 and 1.64. I na d d i t i o n ,t h ep i t c hs t i f f n e s s K was heldconstantandthe was changed by various amounts; t h e p i t c h s t i f f n e s s mount-assembly i n e r t i a necessary to compensate for these various increased inertias was then cal- culated and the modelswere t e s t e d w i t h t h e new p i t c h s t i f f n e s s and i n e r t i a .
It should be mentioned t h a t t h e p i t c h s t i f f n e s s e s a t which the models were
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a c t u a l l y t e s t e d g e n e r a l l y were not exactly the calculated value of KO . . ...- ....... . ". . __.__. . . .
. - I 13 A -r because of t h e p r a c t i c a l f a c t o r s i n v o l v e d i n s e t t i n g t h e p i t c h stiff- nessesprecisely. The difference betweenthecalculatedvalues of KO * and the measured values are shown i nt a b l e V which also presents a sum- mary of the weight, inertia, and p i t c h - s t i f f n e s s v a r i a t i o n s f o r t h e w i n g model configurations used in the t h i r d phaseof the investigation.
RESULTS AND DISCUSSION F i r s t Phase The wing, h o r i z o n t a l - t a i l , and v e r t i c a l - t a i l e x p e r i m e n t s l results of t h e f i r s t phase of the investigation are presented in table VI(a).
Wing modelswere run a t M = 1.3, 1.64, 2.0,and2.55withthepitch s t i f f n e s s and a i l e r o n s t i f f n e s s s e t a t approximately the scaled design value without any flutter being encountered within the scaled flight boundary with the required safety margin.
The a i l e r o n s t i f f n e s s of thevarious models was progressively reduced in order to determine the effect on the wing f l u t t e r c h a r a c t e r - i s t i c s . A i l e r o n f l u t t e r a t 400 cyclespersecond was encountered a t M = 1.3 when t h e a i l e r o n s t i f f n e s s ofmodelW5 was set a t approximately one-tenththescaleddesignvalue. Motion p i c t u r e s of t h e t e s t i n d i c a t e d that t h e o s c i l l a t i o n was a pure flapping motion about the aileron hinge l i n e .
Horizontal-tail models with a pitch stiffness approximately equal tothescaleddesignvalue were t e s t e d a t M = 1.3, 1.64, 2.0, and 2.55 w i t h o u t e n c o u n t e r i n g f l u t t e r w i t h i n t h e s c a l e d f l i g h t boundary includingthesafetymargin.Inordertodefinethestiffnesssafety margin, the pitch stiffness was reduced until constant-amplitude flutter a t 300 cycles per second was encountered with model HT-5 a t a dynamic pressureof 3,225 pounds p e rs q u a r ef e e ta t M = 1.30. The p i t c h stiff- ness was approximately 60 percent of the scaled design value.
p i t c h s t i f f n e s s of model HT-5 was reduced t o approximately 50 e r c e n t of
the scaled design value, destructive flutter was encountered k : : y : t c
pressure of 2,940 pounds persquarefoot a t M = 1 . 3 . A confirmation t e s t wasmade with model HT-4 w i t h a p i t c h s t i f f n e s s of approximately 60 percent of thescaleddesignvalue. The model f l u t t e r e d a t a dynamic pressureof 2,940 pounds persquarefoot a t M = 1.3. The f l u t t e r modes for both the wingand horizontal t a i l appeared t o bea strong coupling a t t h e secondbending mode and pitching mode.
It may be noted that t h e i n e r t i a s of both the wingand horizontal- t a i l mountswere greater than the scaled design values. A s w i l l be shown rc i n t h e d i s c u s s i o n of t h e t h i r d phase of t h e . i n v e s t i g a t i o n , i n c r e a s i n g t h e .\ mount inertias caused a decrease i n t h e f l u t t e r dynamic pressure; t h e r e f o r e , t h e t e s t results of t h i s phase may be considered to be con- was t e s t e d a t M = 1 . 3 , 1.64, 2 .O, w s e r v a t i v e . V e r t i c a l - t a i l model VT-4 and2.53 a t approximatelythescaleddesignrolling stiffness and rudder stiffness without encountering flutter within the limits of the tunnel, although a region of low damping was encountered a t a dynamic pressure of 2,540 pounds persquarefoot a t M = 1.3 and2,725 pounds persquarefoot a t M = 1.64. However, the model d i dn o tf l u t t e r . A maximum dynamic pressureofapproximately 3,370pounds per square foot a t M = 1.3 and 3,760 pounds persquarefoot a t M = 1.64 and above simulatedtherequiredflight boundary. The rudder stiffness was then progressivelyreduced a t M = 1 . 3 t o approximately 40 percentofthe scaled design value without encountering flutter, although regions of low damping were encountered as before. Runs 102 and104 were made t o determine the effect of removing the mass t h a t s i m u l a t e d t h e t a i l warningradar. No e f f e c t w a s evident.
SecondPhase .
The secondphaseof the investigation w a s concernedwithdeter- mining t h e e f f e c t of large changes i n wing model p i t c h s t i f f n e s s e s on b f l u t t e r a t thevarious Mach numbers. The experimental results are p r e s e n t e d i n t a b l e V I 1 and i n f i g u r e 7 which shows t h e v a r i a t i o n of dynamic pressure a t f l u t t e r w i t h p i t c h s t i f f n e s s f o r s e v e r a l Mach nun- b e r s . Although therange of pitchstiffnessescovered i s r a t h e r wide, l i t t l e change w a s evident in the natural frequencies and node l i n e s , and the wingmodels appeared t o f l u t t e r i n t h e same mode regardless of pitch stiffness except for the very low p i t c h s t i f f n e s s of 460 inch- pounds perradian. The t y p i c a l f l u t t e r mode appeared t o be a strong coupling of a p i t c h mode and thesecondbending mode. The f l u t t e r mode f o r a p i t c h s t i f f n e s s of 460 inch-pounds per radian appeared t o start as a pure pitching motion that slipped into the typical flutter mode almostimmediately.Figure 8 shows framestaken from a high-speed 16 millimeter motion picture which i l l u s t r a t e t h e t y p i c a l wing f l u t t e r mode. From f i g u r e 7 it can be seenthat,exceptforvery low p i t c h s t i f f n e s s e s , t h e dynamic pressure a t f l u t t e r v a r i e d a l m o s t l i n e a r l y w i t h t h e p i t c h s t i f f n e s s . The e f f e c t of a given change i n p i t c h s t i f f n e s s on thenumericalvalueoftheflutter dynamic pressureappearsto become more pronounced with increasing Mach number, although the percent change was approximatelythe same f o r Mach numbers up t o 2.0.
Third Phase The t h i r d phase of the investigation w a s anexperimentalassessment
-
of a proposed method (presentedintheappendix)ofcompensatingfor a scaled model mountingsystemhaving a mass arid i n e r t i a g r e a t e r t h a n t h e r scaledvalue,which i s very often the case i n scalingall-movable model mounts. I n t h e p r e s e n t i n v e s t i g a t i o n , a model was f l u t t e r e d w i t h a c e r t a i n mounting system . i n e r t i a I, and p i t c hs t i f f n e s s K which were assumed to represent the correctly scaled values of a hypothetical pro- totype. The i n e r t i a of the mounting system was thenincreased.In o r d e rt o compensate f o rt h i si n c r e a s e d( " i n c o r r e c t l ys c a l e d " )i n e r t i a IO, t h ep i t c hs t i f f n e s s K was increasedto KO according t ot h er e l a t i o n KO = K + 431 2 2 ff (IO - Im) where ff i s t h e f l u t t e r f r e q u e n c y of the model with a "correctlyscaled" mount i n e r t i a . This model w a s t h e n f l u t t e r e d and t h e f l u t t e r f r e q u e n c y and dynamic pressure were compared with those of the first model configuration.This w a s done for severalvaluesofpitch s t i f f n e s s K and the corresponding flutter frequencies ff while the
amount of increase i n i n e r t i a IO - L, remained the same. If applica-
t i o n of the method compensates exactly for the increased inertia, the dynamic pressure a t f l u t t e r f o r t h e two configurations wouldbe the same.
The experimental results of this phase of the investigation are presented i n t a b l e V I I I . I n f i g u r e 9 ( a ) , t h e r a t i o of the dynamic pressure a t f l u t t e r f o r t h e model w i t h t h e p i t c h s t i f f n e s s changed t o compensate f o r anincreased(approximately 2.3 times),unrepresentative mount-assembly i n e r t i a t o t h e dynamic pressure a t f l u t t e r f o r t h e b a s i c mount-model con- i s p l o t t e da g a i n s tt h eb a s i cp i t c hs t i f f n e s s . (The numbers f i g u r a t i o p beside the data points indicate the runs fromwhich t h e r a t i o s were determined.) For t h eb a s i cp i t c hs t i f f n e s s rangeinvestigated,increasing
thepitchstiffnessaccordingtotherelation KO = K + 4rr2ff2(IO - Im)
t o compensate f o r the increased mount inertia generally held the dynamic a t flutter for the increased-mount-inertia configuration to pressure within 10 percent of the flutter dynamic pressure except for one run f o r thebasicconfiguration.
Generally,the method overcompensated s l i g h t l y s i n c e the dynamic pressure a t flutter for the increased-mount-inertia configuration w a s greaterthanthatforthebasicconfiguration. For comparison, one model w i t h increased mount i n e r t i a w a s fluttered without compensating f o r t h e i n c r e a s e d s t i f f n e s s w i t h t h e r e s u l t t h a t t h e model f l u t t e r e d a t a dynamic pressureofabout 43 percent less than that for the basic model configu- r a t i o n . O n run122,the model withincreased mount i n e r t i a f l u t t e r e d a t a dynamic pressure 25 percent greater than that for the basic configura- t i o n . Thisexcessiveovercompensation may have been due t o an e r r o r i n s e t t i n g t h e p i t c h s p r i n g . A s i m i l a r model, f l u t t e r e d under the same comparativeconditions, showed only a 5 p e r c e n t i n c r e a s e i n f l u t t e r dynamic pressure.
Since the proposed methodof compensating for too great a mount i n e r t i a a p p e a r e d t o be satisfactory over a range of pitching stiffness for an increase i n i n e r t i a a t approximately 2.3 times that of the basic 1 2 configuration, the method w a s next checked f o r a p p l i c a b i l i t y a t other mount inertia increments but for only one basic configuration pitch stiffnessofapproximately 6,000 inch-pounds perradian. The results are shown i n f i g u r e g ( b ) . The mount i n e r t i a was increased from 1.6 t o 2.9 times the basic mount i n e r t i a and was compensated f o r by increasing thepitchstiffnessaccordingtotheproposed method.Again applicatio'n The f l u t t e r dynamic ofthemthodappearedtoovercompensateslightly.
pressure for the increased-mount-inertia configurations averaged about 10 percent higher than the flutter dynamic p r e s s u r e f o r t h e b a s i c con- a maximum i n c r e a s e i n f l u t t e r dynamic pressure of figuration, with approximately 20 percent. Again, f o r comparison, the mount i n e r t i a was increased 2.9 times f o r one run withoutcompensating for the increased i n e r t i a . This configurationfluttered a t a dynamic pressureabout 50 percent less t h a n t h a t f o r t h e b a s i c mount i n e r t i a . When t h e p i t c h s t i f f n e s s was changed t o compensate f o r t h e i n c r e a s e d mount i n e r t i a , t h e f l u t t e r dynamic pressure was 7 percent greater than that for the basic mount configuration.
I n this phase of t h e i n v e s t i g a t i o n t h e f l u t t e r f r e q u e n c i e s of the increased-mount-inertiaconfigurations (when compensated f o r ) were generally within 3 percent of those of the basic configurations; thus, the results added further confirmation to the validity of the method.
CONCLUSIONS From t h e r e s u l t s of f l u t t e r t e s t s of the variable incidence wing and all-movable horizontal-tail and v e r t i c a l - t a i l models of a proposed fighterairplane,thefollowingconclusions are made: 1. The wingmodels both with and without aileron, when flown a t the scaled design pitch stiffness and c o n t r o l s t i f f n e s s , were found t o be free from f l u t t e r w i t h i n t h e s c a l e d p r e d i c t e d f l i g h t boundary (including therequiredsafetymargin)forthe Mach numbers tested. The horizontal t a i l s when flown a t scaled design stiffnesses were a l s o and v e r t i c a l found t o be f r e e from f l u t t e r w i t h i n t h e r e q u i r e d s c a l e d f l i g h t boundary.
2. The dynamic pressure required to flutter the all-movable wings a t reduced p i t c h s t i f f n e s s v a r i e d a l m o s t l i n e a r l y w i t h p i t c h s t i f f n e s s e x c e p t for extremely low values.
3. The numericalvalueofthe dynamic pressure a t f l u t t e r was more s e n s i t i v e t o changes i n p i t c h s t i f f n e s s w i t h i n c r e a s i n g Mach number although the percent change i n dynamic pressure was nearly constant up t o a Mach number of 2 .O.
f
4. A proposed method for compensating for an all-movable model
mount having an inertia greater than the scaled design value appears to have merit within the range of pitch stiffness and excess inertia investigated .
Langley Research Center, National Aeronautics and Space Administration, Langley Field, Va., August 15, 1958.
APPENDIX A METHOD OF COMPENSATING FOR EXCESSIVE INERTIA IN THE ROOT REGION O F FLUTIXR MODELS Generally the exposed surface of a f l u t t e r model can be f a i r l y accuratelyscaledgeometrically,elastically, and dynamically. However, i n all-movablemodels thespringsystemsused to simulate the scaled p i t c h i n g r e s t r a i n t o f t e n are not consistent with t h e s c a l e d i n e r t i a l properties of theairplaneall-movablecontrolactuatingsystem. Also, t h e s i z e of the model mount system is frequently determined by the f a c i l i t y i n which the model i s beingtested. Thus t h e i n e r t i a l p r o p e r t i e s of the root region of f l u t t e r models may not be representative of the sur- face being scaled.
A method ofcompensating for the too massive root region by a l t e r i n g the scaled design pitching stiffness has beenproposed by M r . A . L. Head.
This method may be developed in the following manner: i A t the flutter frequency, if the impedance presented to the exposed surface by the root region is the same as the -impedance which would be presented by the correctly scaled root region, it might be supposed t h a t the model would have n e a r l y t h e c o r r e c t f l u t t e r c h a r a c t e r i s t i c s . C o n s i d e r the impedance presented to the exposed surface a t f l u t t e r t o be a combina- t i o n of r e s i s t a n c e t o motion due t o the mount-assembly i n e r t i a a t the . flutterfrequency and r e s i s t a n c et o motion due t ot h ep i t c hs p r i n g . Then an undamped-mount-assembly impedance equation may be w r i t t e n as:
-Imff2(2.O2 + K = Rf = -IOff2(27t)2 + KO
or where flutterfrequency,cps f f correctly scaled pitching mass moment of inertia, in-lb-sec2 I m K c o r r e c t l y s c a l e d p i t c h i n g s t i f f n e s s , i n - l b / r a d i a n *f c o r r e c t impedance of model mount assembly at flutter frequency, in-lb/radian IO pitching mass moment of i n e r t i a of configuration that does not have a representativerootregion,in-lb-sec2 pitching stiffness required for configuration with unrepresen- KO t a t i v e r o o t r e g i o n t o give correct impedance a t f l u t t e r
frequency , in-lb/radian
i REFERENCES 1. Asher, Gifford W . , Martuccelli, John R., and Weatherill, Warren H.: F l u t t e r Model Tests of a Swept-Back, All-Moving Horizontal T a i l a t Supersonic Speeds. WADC Tech. Rep. 56-285. ASTIA Doc. No. AD-142088, U.S. A i r Force, Nov. 1957.
2. Boswinkle,Robert W . , Jr., and Morgan, Homer G.: F l u t t e r Experiments WithVariousControlConfigurations. NACA RM L57D23c, 1957.
3. Land, Norman S., andAbbott,Frank T., Jr.: TransonicFlutterInves- t i g a t i o n ofan All-Movable Horizontal Tail f o r a Fighter Airplane.
NACA RM ~ 5 6 ~ 0 6 , 1957.
4 . Morgan, Homer G . , Figge,Irving E . , and Presnell,John G., Jr.: Investigation of Flutter Characteristics of Three Low-Aspect-Ratio All-Movable Half-Span Control Surfaces a t Mach Numbers From 1.49 t o 2.87. NACA RM ~ 5 8 ~ 2 0 , 1958.
5 . Hanson, Perry W . , andTuovila, W . J. : Experimentally Determined Natural Vibration Modes of Some Cantilever-Wing F l u t t e r Models by U s i n g anAcceleration Method. NACA TN 4010, 1957.
6. Head, A . L., Jr., and Morosow, G . : F ~ U - 3 AirplaneFlutter Model Test
Results - InterimReportfor Phase I Tests. Rep. No. 10675
(Contract N O a ( s ) 57-296), Chance Vought Aircraft,Inc. (Dallas, Texas), Dec. 16, 1957.
TABLE I.- PHYSICAL CHARACTERISTICS O F BASIC-WING, HORIZONTAL-TAIL, AND V E R T I C A L T A I L MODELS Wm, W P J dodel l b lb - -
t t
.--- 157 440665 I . 1002 .1287 .0228 0 .003g 0.1269
i -
' I
----
103.6 97.4 j """ I """""
.1287 157 438662
. lo41 .0228 .0039 .1308 I -
I 1.30 137382,605 .1203 .1287 .0239 .0039 .1480 ~ 2 8 7 .29 146,395 636 .1292 .0239 .0039 .1570 .34 142 400632 r5 .lo .1128 .1287 .04 1.98 90.4 . o w .0039 ~ 3 9 6 .28 147' 410642 .1132 .1287 !5.10 .023g .0039 .1410 .O3 1.95 104.4 ---- .016: 165 519 880 1.04 .0182 .0035 .1124 .90 1.5582.9
----
. a 2 6 .016: 170 530goo .0182 .0035 .lo43 1.04
.92 1.50 88.1 ---- 168 g x ,100 .016: 1.04 .0182 .W35 .1150 .981.5292.0 *0933 ""
.40 129 380512 """_ -"
I - " " ""_ "" """""
.2793 .0542 .m45 .338a
"""_ "-
.3 128 355 5 6 .2828 .0542 . d l 5 .$15 I
---- """"" "_" """""
131 355 510 """"" .2473 I
- . f
illerona on w i n g models; rudders on vertical t a i l models.
m Controlsurfaceslocked; values supplied by the model manufacturer.
1 8 .
TABLE 11.- PHYSICAL CMRACTERISTICS O F MODIFIED WING MODELS (a) Panels -~ If' I 'PJ I It, r, i n 2 , i n .
Mode 1 in-lb-see2 in-lb-sec2 in-lb-see2 W 2 A 1 0 2 . 2 ~ 1 0 - 5 -0.19 1.82 2 9 . 5 ~ 1 0 - 5 7 2 . 6 ~ 1 0 - 5 .12 *W 5 A 108.5 2.05 83.2 25.1 2.10 %6A 25.1 104.5 79.3 -13 " . ~ * Aileron locked.
(b) Mounts I m J 1 0 9 Model wm, 1 ; wo, in-lb-see2 in-lb-see2 ." ~ """ """""" W 2 A 0.1823 95.3 x 10-5
""" " " " " " _
W 2 A l 0.2882 224.8 X 10-5
""" " " " " " _
w2A2 .2634 2 l l . 1
""" """""_
261 .o .3110 w24.3
""" " " " " " _
w2A4 .2360 167 .o """ """""" WSA .1816 93.2
""" " " " " " _
w 5 ~ 1 .2882 218.5 """ """""" W 6 A .1816 93.2
""" " " " " " _
w 6 ~ 1 .2882 218.5
""" " " " " " _
w 6 ~ 2 .2667 195 - 8
""" " " " " " _
w 6 ~ 3 269.0
- 3143
""" _ " " " " "
w 6 ~ 4 -2408 148 .2 ~ ~~~ ~ TABLE 111.- TYPICAL WEIGHT AND INERTIA DISTRIBUTION AND STRIP STATIC UNBALJ\NCE OF WING AND HORIZONTAL-TAIL MODELS (a)Typical wing withoutaileron (model W1). Stationsdefinedinfigure >(a).
Soanwise s t a t i o n - Remarks 8 6 9 4 2 1
I 5 3 I
Flange ~~~~~ ~~ ~~~~ Weight d i s t r i b u t i o n ( a f t e r compensating f o r c u t t i n g s ) , l b """""" 6 . 1 6 ~ 1 0 - 4 Chordwise s t a t i o n 1 3 . 5 9 ~ 1 0 - 4 5.29X10-4 7 . 7 8 ~ 1 0 - 4 1 5 . 7 2 ~ 1 0 - 4 1 2 . 5 5 ~ 1 0 - 4 2 1 . 3 6 ~ 1 0 - 4 62.30~10-4 2 3 . 5 0 x 1 0 - ~ Chordwise s t a t i o n 2 227.70X 10-4 17.60 21.50 12.05 29.75 38.57 69.70 90.80 112.90 200.70 6.81 """""" Chordwise s t a t i o n 3 6.55 8.52 13.04 7 2 9 17.1.7 71.60 39.40 82.50 Chordwise strip inertias, in-lb-sec2 About axis through s t r i p c e n t e r of 4 . 6 6 ~ 1 0 - 6 22.9 x 1 . 4 8 ~ 1 0 - ~ 3.01x10-6 1 6 . 2 4 ~ 1 0 - ~ 63.0 x lo-6 81.2 x 199.2 x 10-6 37.0 x 7.07x10-6 g r a v i t y p a r a l l e l t o p i t c h axis 66.0 About p i t c h a x i s 60.3 56.9 46.7 46.7 329.2 195.6 45.3 80.5 86.7 S t r i p s t a t i c unbalanceaboutpitch a x i s * , i n - l b 375.0 x 10-~1408.0 x 60.6 x 10-4 1112.2 x10-b 1-94.9 x 10-~1-88.3 X 10-41-80.5 X 10-41-84.8 X 10-41-77.6 X 10-41"p1.2 X 10-41 *Based on a c t u a l s t r i p w e i g h t s and p o s i t i v e when s t r i p c e n t e r of gravity is forvard of p i t c h axis.
1 0 TABLE 111.- TYPICAL WEIGHT AND INERTIA DISTRIBLPPION AND STRIP STATIC UNBALRNCE OF W I N G AND HORIZONTAL-TAIL MODELS - Continued (b)Typical wing withaileron (model W4). Stationsdefinedinfigure5(b).
Spanvisestation - Remarks 9 8 6 4 7 5 2 1 Flange 3 Weight d i s t r i b u t i o n ( a f t e r compensating f o r c u t t i n g s ) , l b - - - - -- - - -- -- Chordwise s t a t i o n 1 3.72X10-4 8 . 0 2 ~ 1 0 - 4 8 . 9 8 ~ 1 0 - ~ 9 . 3 6 ~ 1 0 - 4 2 0 . 7 3 ~ 1 0 - 4 1 2 . 1 8 ~ 1 0 - 4 21.05xlo-4 25.88xlo-4 54.30x10-4 Chordwise s t a t i o n 2 10.47 18.15 24.33 42.00 2Y3.50X10-4 31.93 57 .go 93.80 125.50 198.50 """""" Chordwise s t a t i o n 3 5.87 12.98 14.00 18.04 ~ 6 1 . 8 0 121.00 7 .oo *75-55 73.30 Chordwise s t r i pi n e r t i a s ,i n - l b - s e c 2 About axis through strip center of 1 . 6 1 ~ 1 0 - 6 ~ 1 9 . 0 x 10-6 4 . j O x 1 0 - ~ 7 . 7 5 ~ 1 0 - 6 7 . 2 8 ~ 1 0 - 6 f74.4 x 10-6 185.5 x 10-6 4 1 . 1 5 ~ 1 0 - 6 18.85~10-6 50.4 x 10-6 g r a v i t y p a r a l l e l t o pitch axis
*76.6 I 76.6 I *71.6 I 53.9 145.7 I 79.1 I 87.6 159.7 pitch axis
1200.3 1449.3
I S t r i p s t a t i c unbalance about o i t c h axis*. in-Lb
*Hingesand screwsattached.
+*Based on actual strip weights and positive when s t r i p c e n t e r of gravity is forward of pitch axis.
Aileron mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73.1 Aileronmment of inertia about axis through its center of gravity and paralleltohinge line . . . 2.23 Aileron moment of inertia about hinge l i n e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.40 I' I E TABLE 111.- TYPICAL WEIGHT AND DERTLA DISTRIBUTION AND STRIP STATIC UNBALANCE OF WING AND HORIZONTAL-TAIL M O D E L S - Concluded (c) Ty-pical h o r i z o n t a lt a i l (model HT5). Stationsdefinedinfigure 5(c).
Spanwise s t a t i o n s - Remarks 6 4 2 5 1 Flange 3 Weight d i s t r i b u t i o n ( a f t e r compensating f o r c u t t i n g s ) , l b -------------- I 64.25 x L O m 4 ) 38.33 x 10-41 51.95 x I 16.95 x I 11.90 x 10-41 11.45 x I Chordwise s t a t i o n 1
182.40 X 1 168.20 85.20 1 58.20 Chordwise s t a t i o n 2
I 9.9
16.07 Chordwise s t a t i o n 3
I 17.35
~~~ ~~ Chordwise s t r i p i n e r t i a s , i n - l b - s e c 2 About axis through strip center of 2.88 x 14.22 x 8.81 x 10-6 36.2 x 10-6 49.7 x 10-6143.3 x 10-6 7.44 x g r a v i t y p a r a l l e l t o p i t c h a x i s 226.8 181.6 9.09 About p i t c h a x i s 196.0 111.3 68.4 146.1 S t r i p s t a t i c unbalanceaboutpitchaxis*,in-lb -143.5 x 10-4 1-58.3 x 10-4 1-116.0 x 10-4 1-225.0 x 10-4 1-275.3 x 10-4 1-267.2 x 10-4 1-196.0 x 10-4 I *&sed on a c t u a l s t r i p weights and positive when s t r i p c e n t e r of gravity i s forwardof p i t c h a x i s .
TABLE I V . - FiEEpRESENTATIvE M O D E SHAPES OF WIIiG MODELS [Deflections normalized on m a x i m u m deflection] (a) K = 4,075 in-lb/radian Chord, Span, percent percent 0 40 10 (* 1 100 60 30 90 70 50 fl = 138 cps " 0 -0.010 0.156 0.245 0.528 0.750 25 .030 .210 50 .075 .266 .j62 .125 .326 75 -435 -755 .920 .175 .395 .512 .835 1.000 ___ 0 -0 .Ojg -0.300 - .010 - .070 25 - .286 - .117 50 - .269 75 - -197 - .248 - .224 - -317 ~- f 3 = 648 CPS -0.183 -0.137 0.061 0.351 0.718 0.810 0.802 0.802 0.802 - . o x -.015 -.038 -.046 "305 -.069 -.168 -.611 -.651 -.641 -.596 -.588 -.702 -.840 -.244 -.763 "939 -.940 -.962 -.970 -.984 -1.000 -1.000 li 1 -.084 I -.038 1 .122 1 -351 I ::63: 1 : ; : : 1 :i'f;
: ; ; : 1 . 5 8 j - .~ " _ _ _ _ _ _ _ . "
"Chordwlse stations based on chordlengthsnotincludingleading-edgeextension.
(b) K = 9,770 in-lb/radian ___ ~- ~ .- "" Span, percent 3ercent fl = 142 cps 0.121 0.860 .892 0.637 -692 0.312 .376 0.204 .255 .448 -. 006 .015 .083 .147 .925 .747 .325 .223 .015 .047 .136 .206 .806 .404 .962 .525 .296 100 .038 .072 .1gg .280 1 .ooo A63 .605 .479 .376 v F ; [ 7 : - : 6 6 -0.025 -0.019 0.016 0.057 f 2 = 399 CPS -0.229 0.429 0.143 -0.254 .286 -.226 .572 -.25O -.212 -.267 -.017 -.I43 .714 .4rg -.172 -.263 .031 -.076 -.243 -.JOO -.309 75 -.OW .858 .572 -.074 -.267 -.157 -.371 -.bo0 -.340 "069 1.000 .714 .074 -.257
0:;;; (Ioj: I - ! : : ; : I-::;?; ; i I O : : z $
" f 3 = 654 cps __- ~ 1.000 0.886 0.507 0.750 0.993 0.964 0.157 -0.429 -0.500 -.186 .814 .157 "272 25 .872 .714 .857 50 -.057 -.079 -.257 -.279 ,572 "772 -507 -657 -.722 -.729 75 - .886 -.TOO "343 "143 .457 r 0 . 7 0 0 -.757 -.743 "729 -.943 -.857 "643 -.986 -.986 -.979 "971
"950 I -.964
*Chordwise stations based on chordlengthsnotincludingleadlng-edgeextension.
T A B U V.- SUIMARY OF MASS, I N E R ! l T A , AND PITCH STIFFNESS VARIATTONS FOR VARIOUS CONFIGURATIONS OF W I N G M O D E L S ~ ~~ .~ ~ Original(reworked) model Modified model configuration ~~ . configuration .
Calculated K g , Measured KO, Wm, l b &, in-lb-sec2
'0, lb 1'0, in-1b-sec21 in-lb/radian in-lblradian
I
w a - 1 - 3;840 6,000
6 , 100
11 , 720
7,600 7,710 w2A-2 6,000 6,000 6,000 . .
TABLE VI.- MpERIbENTAL RESUL'IS OF FIRST PHASE OF INVESTIGATION (a) Wing models - - ' 4 , KC , D, a, M Remarks i u n lugs/cu f t 't/sec n-lblradian :ps - - - -
"-
1 . 3 0 0.00409 h i m u m conditions; 1 6 998 28.75 j 5 5 no f l u t t e r
"_
1.64 .00298 VIaXimum conditions; 6 930 28 -75 j 5 9 no f l u t t e r
"-
.oo236 862 llaximwm conditions; j 6 0 2.00 10 28 -75 no f l u t t e r
"_
llaximum conditions; 12 .00152 790 J 5 9 2-55 28 -75 no f l u t t e r "- 1.30 .00408 llaximuum conditions; 20 22.2 993 no f l u t t e r
"-
1.64 .00308 %ximum conditions; 2 6 20.3 928 5 5 0 no f l u t t e r
"-
1.30 .00384 Maximum conditions; 28.0 995 3 5 5 5 5 no f l u t t e r
-"
Maximum. conditions; 1.30 .00384 6.0 995 3 6 675 no f l u t t e r .00220 400 Aileron fluttered; 1.30 984 45 2 . 7 675 limited arnplitude
"-
.00350 Maximum conditions; 42 1.64 9 30 5 . 7 no f l u t t e r
"_
Maximum conditions; 2.00 .00250 880 2 8 . 0 38 675 no f l u t t e r
"_
880 Lost aileron in 2 .oo .00250 6.0 3 9 695 openingshock
"-
1.30 .00414 1,000 Maximum conditions; 19.62 30 552 no f l u t t e r
"_
Maximum conditlons; 1.30 .OO414 32 17.7 555 no f l u t t e r
"_
Maximum conditions; 1.30 14.4 -00375 995 33 534 no f l u t t e r
"-
Maximum conditions; 1.30 .00380 6 .o 620 995 3 4 no f l u t t e r "- Maximum conditions; 1.64 .00302 28 19.62 928 no f l u t t e r ""_ .00323 --- Maximum conditions; w2 . 5 1.64 938 I no f l u t t e r 1.30 .00390 1,000 310 ! ~ a x i m ~ m conditions; w4 I 93 28.75 534 no f l u t t e r
- 1
L - I 1
TAPLE VI.- EXPERlMENTAL RESULTS OF FIRST PHASE OF INVESTIGATION - Continued
(b) Horizontal-tail models a, ff , Model RUll
I
Remarks f t / s e c cps , - -
c
-r
I HT-1 14 394 610 1.30 0.00414 1,000 M a x i m m conditions; no f l u t t e r RT-1 2 406 625 1.64 .00317 Maximum conditions;
! no f l u t t e r
H T - 1 8 408 I 625 2 .oo .00229 862 Maximum conditions; no f l u t t e r HT-1 1 1 400 1 621 1,000 Maximum conditions; .00152 2.55 780 no f l u t t e r H T - 1 18 .00413 1 , 0 0 0 Maximum conditions; 1.30
I no f l u t t e r
!
HT-1 21 1,000 1.30 .00432 1,000 Maximum conditions ; 374 I no f l u t t e r I
"_"
HT-1 1.64 .00324 M a x i m u m conditions; 25 373 936 no f l u t t e r HT-5 43 1,060 1.30 .00358 Low damping; 415 995 325 CPS HT-5 41 1,060 1.64 Maximum conditions; .00350 936 no f l u t t e r HT-5 40 408 1,080 2.00 .00250 Maximum conditions; no f l u t t e r HT-5 44 1,012 1.30 .00345 1,000 375 Low aamping; 300 CPS HT-5 44 1,012 .00378 Constant amplitude 375 1.30 1,003 f l u t t e r
HT-5 46 1,012 .00348 1;ooo D e s t r u c t i v e f l u t t e r
365 1.30
""_
HT-4 22 Divergent flutter * 00339 990 377 1.30 - -
- 1
W L E V I . - EXPERDENTAL RESULTS O F FIRST PMSE OF INVESTIGATION - Concluded
(c) Vertical-tail models - - - KC , 9, P, a, Model R W f2 J Remarks M Lb/sq ft slugs/cu ft ft/sec in-lblradian CPS - - - -
""_
1.30 2,610 0.00316 Low damping; 370 cps VT-7 990 91 355 oscillations
"_"
VT-7 1.30 .00406 Maximum tunnel 91 355 3,395 VT-4 1.30 .00306 Low damping; 360 cps 2,540 994 94 136.5 356 oscillations 1,000 MaxFmum tunnel VT-4 1.30 .00415 94 136.5 3,500 .00235 LOW damping; 360 CPS VT-4 1.64 930 95 136.5 354 2,725 oscillations VT-4 1.64 .00326 Maximum tunnel 95 136.5 3,810 932 VT-4 2 .oo .oo238 Maximum tunnel; 136.5 3,800 894 97 358 no flutter VT-4 .00151 Maximum tunnel; 98 136.5 358 2.55 3,055 790 no flutter VT-4 65.6 1.30 .00368 Low damping; 360 cps 99 348 3,072 995 oscillations VT-4 65.6 .00414 Maximum tunnel 1.30' 99 348 3,470 997 VT-4 100 2,180 .00262 Low damping; 360 cps 1.30 990 52.3 355 oscillations VT-4 100 1.30 ,00407 1,000 Maximum tunnel 52.3 355 3,470 101 1.30 .00302 Low damping; 360 cpe VT-3 99.2 348 991 2,505 oscillations Maximum tunnel VT- 3 101 1.30 .00414 99.2 348 996 3,470 ~ VT- 3 102 .00425 Low damping; 360 CPE 99.2 350 700 1.30 3,530 990 oscillations
1 VT-3* 104 .00422 Low damping; 350 cps !
99.2 600' 1.30 990 356 3,500 oscillations i - *Radar mass removed.
I I * A I 1 TABLE V I 1 . - EXPERIMENTAL RESULTS O F SECOND PHASE O F INVESTIGATION " I 1 I -
llodell Run 1 KJ 1 flJ
Remarks I
1 in-lb/radian cps w1
I 140 0.00461 i 1,000 1 3 4 0 390 654 804 1,000 1.30 3,485 I Constant amplitude
I I f l u t t e r w1 1,000 . 1.30 ~ 2,990 i Divergent f l u t t e r 825 .00359 ' 993 ~ 323 47 3 9 8 : 675 147 68 w1 142 804 1,000 , 1.30 ~ 2;5lO Divergent f l u t t e r 394654 -00334 ' 995 w1 402 ~ 660 144 Divergent f l u t t e r .00251 993 54 817 1.30 1,000 2,090 w1 404 ~ 650 820 Divergent f l u t t e r .00166 ! 986 ~ 52 143 1,000 1.30 1,365 808 , 1.30 , 70 Divergent f l u t t e r 3 9 5 ' 643 138 .00120 1,000 967
Divergent f l u t t e r 3 6 8 ' 632 124 750 ~ 940 1.30 698 .00095
390 640 128 .00064 72 Divergent f l u t t e r 795 990 1.30 463 Low damping 140 .00301 1.64 . 3,540 j 805 I 1,000 66 Divergent f l u t t e r .00292 816 ' 998 1.64 , 3,440 Divergent f l u t t e r .00293 1.64 I 810 990 3 , 4 5 8 Divergent f l u t t e r .00267 1.64 I 3,130 ' 805 1,000 Divergent f l u t t e r .00234 1,000 1.64 390 2,690 .00201 400 1,000 1.64 Divergent f l u t t e r 2,282 w1 ' 5 9 Divergent f l u t t e r .00149 1 . 6 4 w1 3 8 3 7 5 980 1,693 w1 Divergent f l u t t e r .00072 1.64 808 3 8 6 74 w1 Divergent f l u t t e r .00050 1.64 390 990 73 w1
Low damping .00243 2 .oo
3 8 4 960 78 3,725 w1 Divergent f l u t t e r .00218 2.00 3 8 5 960 79 3 J 300 w1 81
Divergent f l u t t e r .00176 2 .oo 2,600
382 960 w1 82 Divergent f l u t t e r ; .00094 2.00 3 7 7 975 J 3 7 O model broke Barely fluttered .00243 2.00 w2 85.
3 7 5 975 3,780 w2
Divergent f l u t t e r .00146 2 .oo 84
975 2,157 w2 8 6 Divergent f l u t t e r .00222 2.00 370 965 3,417 w2 Divergent f l u t t e r .OOlOl 2.00 3 9 3 990 83 1,475 w2 Divergent f l u t t e r .00125 352 960 2.55 87 2J470 Divergent . f l u t t e r ; w2 .00152 89 3 6 7 950 2.55 model broke TABU V I I 1 . - EXPERIMENTAL RFSULTS OF THIRD PHASE OF INVESTIGATION - K, P, Model f4 7 f f , M Remarks .n-lblradian ;lugs/cu f t CPS CPS - - - - W 2 A 1.30 0.00094 210 Divergent f l u t t e r 3,840 695 w2A-1 680 1.30 .00102 206 Divergent f l u t t e r 6,150 W 2 A 6,000 1.30 .00186 260 Divergent f l u t t e r w2A-1 800 1.30 .00187 246 Slowly divergent 9,580 f l u t t e r W 2 A 1.30
9 , 820 .00349 Slowly divergent
f l u t t e r W 2 A 1.30 .00266 288 Slowly divergent 7,710 805 f l u t t e r w2A-1 12,050 800 1.30 .00286 Slowly divergent f l u t t e r w2A-4 8,000 1.30 .00222 266 Slowly divergent f l u t t e r w2A-2 800 9,080 1.30 .00213 260 Divergent f l u t t e r w2A-3 10,850 1.30 .00212 264 Slowly divergent f l u t t e r W 2 A 6,100 Divergent f l u t t e r 1.64 .00155 260 w2A-1 800 1.64 .00167 260 Slowly divergent 9,750 f l u t t e r W 2 A
1.64 . o o u 3 284 Slowly divergent
7,600 790 f l u t t e r w2A-1 11,900 1.64 .00265 Slowly divergent 780 294 f l u t t e r W 5 A 1.64 .0010g Divergent f l u t t e r 3,870 196 w5~-1 614 1.64 .00108 200 Divergent f l u t t e r 5,880 6,060 626 1.64 W 5 A .00185 Divergent f l u t t e r
I
w5~-1 8,900 1.64 .00185 Divergent f l u t t e r W 5 A 1.64 .00232 Divergent f l u t t e r 7,580 w5~-1 , 132 10,860 600 1.64 .00242 Divergent f l u t t e r W 6 A 6,000 624 1.64 132 .00172 Divergent f l u t t e r W6A-4 120 600 7,200 1.64 .00187 Divergent f l u t t e r w6~-2 8,200 120 600 1.64 .00194 Divergent f l u t t e r w6~-1 120 600 1.64 .00180 Divergent f l u t t e r 8,500 I w6~-3 120 1.64 9,800 590 .00186 Divergent f l u t t e r w6~-3 6,000
11.3 1.64 . ooogo Divergent f l u t t e r
W 6 A 1.64 .00055 Divergent f l u t t e r 2,500 584 W 6 A 460 118 1.64 Divergent f l u t t e r 590 .00039
I!
" " - i 1 4 - . ....
Mach number Figure 1.- PerformancecurvesoftheLangley 9- by 18-inch supersonic f l u t t e r t u n n e l showing maximum test-section conditions obtainable.
Airfoil section: NACA 6 5 A 0 0 5 at root NACA 6 5 A 0 0 4a tt i p ,0333 scale model chord-extension 4.69 6.76 m (a) Wing geometry.
Airfoil section: NACA 6 5 A 0 0 4 scale model ,0662 (b) Horizontal-tail geometry.
Figure 2.- Geometry of w i n g , horizontal-tail, and vertical-tail models. A l l dimensions are in inches.
c Airfoil section: NACA 66A005(mod.) at root NACA 66A004(mod.) attip .065 scale model (c) Vertical-tail geometry.
Figure 2.- Concluded.
Spruce leading and trailing edges glued Bays between ribs to ribs filled with balsa wood
- Aluminum ribs welded
to box spar Aluminum box spar Lead ballast Electrical resistance wire strain gages Flange welded to box spar (a) Wing without aileron.
Spruce leading and filled with balsa wood Aluminum ribs welded Aileron hinge mounts Electrical resistan wire strain gages ( b ) Wing with aileron.
Figure 3 . - Details of t y p i c a l model construction.
F
Spruce leading and / - * L \luminum cap
trailing edges glued
to ribs -<
j \ Aluminum box spar
- Aluminum ribs welded
to box spar Lead ballast Bays between ribs filled with balsa woad "
- Flange welded to box spar
-. ..
(c) Horizontal tail.
Mahogony leading and trailing edges glued Boys between ribs filled with balsa wood Aluminum box s Aluminum ribs welded Lead to box spar
Blocks t o ---"4 receive - Mounting bar welded
to box spar shear mount (a) Vertical tail.
Figure 3 . - Concluded.
w t Upstream spring Side view Side view
Flanqe mount -- Tunnel wall line -
Downstreamspring ~~ ~ ~~ I I Mounting block Mounting block _I TOP view Top view (a) Wing-mount assembly. (b) Horizontal-tail-mount assembly.
Figure 4.- Mount assemblies for wings and horizontal tails.
I t Centers of gravity 0 Panel without flange X Panel with flange t Strip Block I J 2.0 Inches (a) Typical wing without aileron (wing model Wl).
Figure 5.- Streamwise strip, block, and panel centers of gravity of typical wing and
horizontal-tail models.
w c n Centers of g r a v i t y 0 Panel without flange X Panel with flonge + Strip without hinges @ Strip with hinges
- Block w i t h o u t h i n g e s
0 Block with hinges I i 2.0 Inches ( b ) Typical wing with aileron (model W4).
Figure 5.- Continued.
I I Centers of gravity 0 Panel without flange x Panel with flange t Strip Block 2.0 Inches
Pitchaxis - 1
(c) Typical horizontal tail (model HT5).
Figure 5. - Concluded.
* Node Frequency, c PS I 4 0 "
"_
6 5 0
-" -
- ""
I O 0 0 Node Frequency, CPS I 2 8 "
"- \ /
"- -
- "_ -
Y
9 90 I
i- Pitch axis
(b) Wing without aileron; K = 2,535 in-lb/radian, run 73.
and
Figure 6.- Typical model node lines for s o = representative pitch
control stiffnesses.
Node Frequency, C PS I 2 8 "-"
-"-
"_
5 55
"-
7 30 c 1 - Pitch axis Node Frequency, C P S I t 8 "_" 3 90 "- 526 -- - 675 (d) Wing with aileron; K = 17,300 in-lb/radian; Kc = 2 . 7 in-lb/radian; run 45.
Figure 6. - Continued.
I Node Frequency, C P S I 3 3 "
"-
62 I
"- -
----- 1080
I-- Pitch axis (e) Horizontal tail; K = 2,260 in-lb/radian; run 40.
Node Frequency, C P S I 1 7 " " L
"- -
""-
1 - Pitch axis (f) Horizontal tail; K = 1,174 in-lb/radian; run 46.
Figure 6 . - Continued.
Node Frequency, C P S
"-
- - - 438
, "" " - - - 6 5 0
Mount -
I Mount I - shear rod bolt .
-
(g) Vertical tail; Kc = 136.5 in-lb/radian; run 98.
Node Frequency, CPS
"_
\
i / /
/
I
r Mount Mount
shear (h) Vertical tail; Kc = 52.3 in-lb/radian; run 100.
Figure 6. - Concluded.
Model M 0 w - l I .30 I .64 I J w - l 2.00 A W - I 2.00 0 w - 2 2.55 0 W - 2 1.30 t J W - 2 A 1.64 V W - 5 A X W - 6 A 1.64 Run number beside each data point
E 1 0 1 2
. X 10+3 K , in- Ib/rod Figure 7.- Variation of dynamic pressure a t f l u t t e r w i t h p i t c h stiffness.
c M 1.30 W 2 A - W 2 A I Run numbers beside 0 1.64 W 2 A - W 2 A I each data point n 1.64 W 5 A - W 5 A I
+
Mount assembly inertia increased from that of configuration W 2 A tothat of W 2 A I , but without being compensated for by increasing pitch stiffness K (a) (IO - Im) held constant while varying K with corresponding ff .
Figure 9.- Effect on flutter dynamic pressure of changing mount assembly moment of inertia and compensating for the change by changing the pitch stiffness according to the rela- tion K~ = K + 4 r r 2 f f 2 ( ~ 0 - I~).
10-16-58~
, i .
" I 1 ~l
&" M Configurations K
Basic Modified 1 0 1.30 W2A W2AI, W2A2, W2A3,W2A4 6000 260 1 . 6 " 0 1.64 W5A W5AI 6060 244
A 1.64 W6A W6AI W6A2, W6.43, W6A4 6000 232 ' 1 1 1 1
x 1.64 W6A W6A3 (inertia increased but not compensated -
I
for with increased pitch stiffness) 1.41 Run numbers beside each dota point (b) K and corresponding f f heldconstantwhilevarying (Io - Im) by varying Io.
Figure 9.- Concluded,