Document
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MODEIS OF TEIE TRANSONIC FLUTTER INVESTIGATION OF J P ALLMOVABLF: HORIZONTAL TAIL OF
A F I S r n , r n 2 L A U . ! a
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By Thomas B. S e l l e r s
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SUMMARY E 1 4 A transonic f l u t t e r investigation of models of t h e all-movable horizontal t a i l of a fighter airplane has been conducted i n t h e Lan@;ley The models were dynamically and e l a s t i c a l l y transonic blowdown tunnel.
The r e s u l t s scaled by c r i t e r i a which provide a f l u t t e r . s a f e t y margin.
showed t h a t the model had a s t i f f n e s s margin which was insufficient t o provide adequate s a f e t y from f l u t t e r at a Mach number of 1.06. An increase i n t h e model p i t c h s t i f f n e s s of approximately 4-0 percent of the anticipated design value resulted i n an adequate margin. With t h e .
model p i t c h axis moved forward from 77 percent t o 38 percent of the root chord, 83 percent of the anticipated design p i t c h s t i f f n e s s w a s necessary t o provide an adequate margin at see level.
INTRODUCTION A f l u t t e r investigation of models of the all-movable horizontal t a i l of a new fighter airplane has been made i n t h e Langley transonic blowdown tunnel. The panels of the models w e r e dynamically and elas- t i c a l l y scaled. The t a i l p i t c h and fuselage v e r t i c a l bending degrees of freedom were a l s o simulated. The primary purpose of the investi- gation w a s t o determine if the model would be flutter-free in simulated sea-level f l i g h t a t Mach numbers from 0.8 t o 1 . 3 . Additional tests were xade t o study the e f f e c t of varying the p i t c h s t i f f n e s s and pitch-axis locat ion.
s SYMBOLS J b half-chord p a r a l l e l t o plane of symmetry, f t half-chord p a r a l l e l t o plane of symmetry at i n t e r s e c t i o n bS of t a i l panel and fuselage, f t root chord at plane of symmetry, f t C f l u t t e r frequency, cps f
measured natural frequencies (I = 1, 2 , 3, . . .), cps
f i panel bending s t i f f n e s s , l b - f t E1 GJ panel t o r s i o n a l s t i f f n e s s , lb-ft2 mass moment of i n e r t i a about an axis passing through center of gravity and perpendicular t o plane of symmetry per u n i t length of exposed panel span, s l u g - f t 2 / f t Mach number M m mass of panel per u n i t length of exposed panel span, s l u g s / f t length scale factor, t y p i c a l length of model divided by corresponding length of airplane m’ mass scale factor, t y p i c a l model mass divided by corresponding airplane mass dynamic pressure, lb/sq f t time scale factor, time required f o r tunnel airstream t o move 1 model chord length divided by time required f o r airplane t o move 1 airplane chord length
s t a t i c temperature, 91
free-stream velocity, f t / s e c reduced velocity based on representative natural frequency,
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bfi
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distance i n semichords (measured p a r a l l g l t o plane of k X cg symnetry) from midchord t o center-of-gravity position n measured positive rearward from midchord nondimensional coordinate along exposed pmei 5 ~ 6 9 , fraztim of exposed panel span value of q at center of gravity of s t r i p qcg P air density, slugs/cu ft r a t i o of mss of air contained in a frustum of' a cone with P base diameter equal t o s t r e m i s e root chord and top diameter equal t o strearowise t i p chord Subscripts: M model A airplane MODEIS L Model Plan Form I 1 - The pl n form and overall dimensions of t h h o r i z o n t a l - t a i l models are shown i n figure 1. "he plan form was a modified d e l t a with slightly rounded t i p s . "he model t e s t e d was l/l3.l of t h e f u l l - s c a l e t a i l dimen- sions and had the leading and t r a i l i n g edges swept back 55' and 1 5 ' , respectively. "he t a i l had an aspect r a t i o of 3.45 and NACA 6 5 ~ 0 0 3 modified a i r f o i l sections p a r a l l e l t o t h e plane of symmetry.
Scaling In scaling the airplane properties, it w a s required t h a t the non- dimensional mass and s t i f f n e s s distributions should be t h e same f o r t h e model as f o r the airplane. The mass and s t i f f n e s s l e v e l s f o r t h e model were obtained by specifying t h e scale f a c t o r s f o r t h e fundamental quan- tities involved: length, m s s , and t i m e .
The s i z e of the model w a s limited by the tunnel-wall interference e f f e c t s , and on the b a s i s of past experience t h e length scale f a c t o r w a s chosen t o be The mass scale fagtor-wasobtained from a requirement t h a t the mass r a t i o p should be t h e same f o r the model as f o r t h e airplane, which r e s u l t s i n I n order t o locate simulated sea-level a l t i t u d e i n the t e s t s near the middle of the tunnel density range available at a Mach number of 1, the density r a t i o was chosen t o be p d p A = 2.00. This location of simulated sea-level a l t i t u d e allows a l t i t u d e s below sea l e v e l t o be obtained and d e s it possible t o indicate f l u t t e r margins f o r cases wherein f l u t t e r does not occur above sea level.
from a requirement t h a t the The time scale f a c t o r was obtained f o r the model as f o r the air- reduced velocity should be the sane plane, which r e s u l t s i n -1
t =rf)
Since the Mach number i s the same f o r the model as f o r t h e airplane, the time scale f a c t o r may be written i s a function only of The s t a t i c temperature f o r t h e airplane TA a l t i t u d e and f o r sea-level a l t i t u d e was taken t o be 5 1 9 ' R . However, i n t h e tunnel, the temperature continually drops as air i s expended from the reservoir s o t h a t the temperatures obtained at the various f l u t t e r points during an investigation are d i f f e r e n t . A study of 408O R w a s near the average value previous f l u t t e r d a t a indicated t h a t of the s t a t i c temperature t h a t would be expected during the present runs, and t h i s value w a s used t o obtain the temperature r a t i o used i n T d T A = 0.786.
t h e scaling: A l i s t of pertinent wing and flow quantities and the design scale A f a c t o r of 0.76, which i s used i n f a c t o r s used a r e given i n table I.
some of the scaled quantities i n table I, occurs because the s t i f f n e s s e s of t h e model were made 76 percent of those which would r e s u l t from The application o f t h e s c a l e f a c t o r s as specified. (eqs. (1) t o ( 3 ) ) .
9.9 0 .
I purpcse o f reducing the model stiffnesses was t o provide a margin of s a f e t y i n the application of the model f l u t t e r - t e s t r e s u l t s t o the air- plane. It may be noted t h a t the s t i f f n e s s reduction r e s u l t s i n a design reduced velocity f o r t h e m d e l b e i n g equal, not t o t h a t of the airplane, but t o t h a t of an airplane having s t i f f n e s s e s 76 percent of those of the a c t u a l airplane.
Eecause t h e temperature during a run i s not-a controllable quantity, V the exact value of the design reduced velocity (through eq. ( 3 ) ) i s not obtained. The two quantities which a r e controllable during a t e s t a r e d y n d c pressure and Mach number. If the dynamic pressure and Mach number a r e considered t o be held constant, a change i n temperature r e s u l t s i n a change in density and velocity. Thus, the consequence of a temperature during a run d i f f e r e n t from t h e design temperature is t h a t neither the reduced velocity nor the mass r a t i o i s simulated exactly.
However, a combination of reduced velocity and mass r a t i o , which can be expressed i n terms of the dynamic pressure - 2 vM
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i s independent of t h e temperature, and t h i s combination is exactly simulated i n t h e tests by t h e expedient of interpreting the simulated a l t i t u d e i n terms of dynamic pressure. Thus, the scale f a c t o r i n t a b l e I f o r dynamic pressure is used t o convert the dynamic pressure f o r the airplane a t any a l t i t u d e and Mach number t o the dynamic pressure f o r t h e nodel a t the same a l t i t u d e and Mach number. The dynamic pres- sure for the airplane is assumed t o be that obtained from the ICAO standard atmosphere ( r e f . 1 ) . It may be noted t h a t , f o r a given a l t i t u d e , q , ! ~ ~ is a constant quantity.
The e f f e c t of not individually satisfying exactly t h e mass r a t i o and reduced velocity i s believed t o be negligible i n t h e present investi- gation. Experience with a wide variety of f l u t t e r models has indicated t h a t , at least within t h e operational limits of t h e tunnel, flutter at a given Mach number tends t o occur at a constant value of dy-namic pres- sure regardless of the individual values of density and velocity.
Model Construction Two models were used i n t h i s investigation and are designated as models 1 and 3 . A t y p i c a l model, which i s shown p a r t i a l l y and completely assercbled i n figures 2 and 3 , respectively, consisted of dynamically and e l a s t i c a l l y scaled t a i l panels joined together by an e l a s t i c a l l y scaled crossover yoke, an e l a s t i c a l l y scaled f l e x i b i l i t y fixture, and 4 a mounting block with cover.
The d e t a i l s of t h e t a i l - p a n e l construction are shown i n the photograph of figure 4. The panels were made with a tapered hollow aluminum-alloy box spar, t h e center l i n e of which w a s located along the 0.57 l o c a l chord l i n e and extended from t h e panel root t o t h e t i p s . Several aluminum-alloy r i b s , which were channel shaped i n cross section, were welded t o t h e spar. Mahogany s t r i p s formed the leading and t r a i l i n g edges and completed t h e panel framework.
The frmework was f i l l e d with balsa and t h e e n t i r e s t r u c t u r e w a s covered with s i l k .
The U-shaped crossover yoke was rectangular i n cross section and was made of aluminum alloy. A 0.088-pound lead weight ( f i g .
2 ) w a s attached t o the upstream v e r t i c a l face of t h e crossover yoke i n order t o locate the center of gravity of the t a i l s t r u c t u r e a t t h e correct position. This weight w a s interchangeable and w a s mounted on each model p r i o r t o t e s t i n g .
The f l e x i b i l i t y f i x t u r e i s shown i n f i g u r e 5 as assembled f o r t h e r e a r pitch-axis location. The model w a s attached t o the two t a i l mounting pads (one on each s i d e ) with two screws i n each pad.
Flexure hinges at t h e rear of each pad fixed the location df t h e p i t c h axis. The pitch- spring links indicated i n figure 5 were s m a l l b o l t s . These b o l t s con- nected the f r o n t end of t h e mounting pads with the p i t c h springs. The p i t c h springs and the fixed p a r t of t h e flexure pivots were attached t o the main p a r t of t h e f l e x i b i l i t y f i x t u r e by two screws passing through each of the two rearward mounting lugs ( f i g . 5 ) . The fuselage v e r t i c a l bending was simulated by t h e fuselage v e r t i c a l spring shown a t the f r o n t o f the f i x t u r e .
The location of the p i t c h axis w a s changed from the rearward loca- t i o n s ( f i g s . l and 5 ) t o the forward location by removing as a u n i t t h e flexure pivot assembly, t a i l mounting pad, pitch-spring link, and p i t c h
spring, then r o t a t i n g t h i s u n i t lao, and attaching the fixed portion of
the flexure pivot and the fixed end of t h e p i t c h spring t o the forward mounting lug ( f i g . 5 ) . The forward and rearward p i t c h axes were located a t t h e 0 . 5 8 ~and 0 . 7 7 ~ stations, respectively.
The p i t c h s t i f f n e s s was varied by inserting p i t c h springs of varying thicknesses.
Physical Properties of Models The values of torsional, bending, and p i t c h s t i f f n e s s of a t y p i c a l model were determined by the method described i n reference 2.
Briefly, t h e system w a s an o p t i c a l one through which the deflections of the t a i l J panels were magnified and measured when a known moment w a s applied t o I n order t o determine the panel mass and center-of-gravity t h e panel.
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location, a panel w a s cut i n t o several chordwise segments ( p a r a l l e l t o t t h e plane of symmetry) approximately 1/2 inch wide. Each segment w a s weighed and its center of gravity located. The moment of i n e r t i a of each segment about an axis passing through the center of gravity of t h e semeEt m d perpendicular t o the plane of symmetry w a s found by swinging each segment on a t o r s i o n a l pendulum.
The center-of-gravity location, mam moment of i n e r t i a , mass per u n i t length, and l o c a l chord r a t i o for several spanwise s t a t i o n s are ~ - a - - b ~ u l ~ t e d i n tdjvle 11. The vzhes of EI G , G ~ Guf f ~ r the t-;o ~ d e h are p l o t t e d i n figure 6. The mass-property differences between the t a i l panels were assumed t o be small, and only one s e t of mass properties are given.
The moment of i n e r t i a about the forward and rearward p i t c h axes of t h e t a i l panel assemblies which included t h e t a i l panels and crossover yoke with lead w e i g h t w a s determined by swinging t h e tail panel assembly as a physical pendulum. The values of moments of i n e r t i a obtained i n t h i s manner were 0.002195 and 0.001947 slug-ft2 f o r t h e forward and rearward hinge-line locations, respectively. The mass of t h e t a i l s t r u c t u r e w a s 0.0157 slug and the center of gravity was located at the 0 . 6 5 ~ s t a t i o n and 0.21 inch below t h e t a i l - p a n e l chord plane.
The frequencies that correspond t o t h e natural modes of vibration were determined by exciting t h e t a i l panels over a range of frequencies with an electromagnetic vibrator. Node l i n e s were defined by sprinkling salt onto t h e wing while the panel was excited at a natural frequency, and the stationary grains of salt formed along the panel node l i n e . The modes of vibration f o r t h e model with Arselage f l e x i b i l i t y included yawing nodes which tended t o destroy the node l i n e s indicated by the grains of salt and which made t h e selection of the natural frequencies, node l i n e s , and modes quite d i f f i c u l t . In order t o obtain a b e t t e r indication of the natural frequencies, the output of t h e s t r a i n gage t h a t responded t o t h e p a r t i c u l a r mode of i n t e r e s t together with the input t o t h e vibrator were fed i n t o the v e r t i c a l and horizontal axes of an o s c i l l o - scope. When a natural frequency was reached, t h e t r a c e on the o s c i l l o - scope would form an e l l i p t i c a l pattern which w a s symmetrical about t h e horizontal and v e r t i c a l axes. Also, t h e model was viewed under a strobo- scopic l i g h t which helped t o identify t h e mode of vibrations. The cantilevered modes were obtained with t h e t a i l panels clamped j u s t inboard of the fuselage l i n e . The n a t u r a l frequencies and corresponding node l i n e s f o r the models cantilevered and with fuselage freedoms are presented i n figures 8 and 9, respectively.
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APPARATUS AND TESTS Tunnel and Model Support System The f l u t t e r t e s t s were conducted i n t h e Langley transonic blowdown tunnel which is a 26-inch octagonal s l o t t e d tunnel. The tunnel operates over a range of Mach numbers from approximately 0.6 t o 1.4.
The operating characteristics (tunnel dynamic pressure may be increased at a constant Mach nmber) a r e p a r t i c u l a r l y s u i t a b l e f o r f l u t t e r t e s t i n g and these characteristics a r e discussed i n d e t a i l i n reference 2. Because of t h e expansion of air i n the reservoir during a run, the stagnation temperature continually decreases; thus, t h e t e s t - s e c t i o n velocity i s not uniquely defined by the Mach number.
A schenatic drawing of the model support system i s shown i n f i g - ure 7. The Eounting block w a s r i g i d l y mounted i n a 3-inch-diameter cylindrical s t i n g fuselage. The s t i n g fuselage extended upstream i n t o the subsonic flow region of the tunnel entrance cone, and the downstream end w a s supported by a s t r u t which spanned the tunnel. The extension of the sting i n t o the subsonic region of the.tunne1 prevents the formation of a bow wave and i t s possible r e f l e c t i o n on t h e model. A discussion of the e f f e c t s on f l u t t e r t e s t s of t h e degree of root f i x i t y afforded by the support system and the sting boundary layer i s presented i n reference 3.
Instrumentation Tunnel stagnation pressure, s t a t i c pressure, and stagnation temper- a t u r e were t r a n s n i t t e d by suitable pickups t o amplifying equipment and recorded on a multichannel automatic recording oscillograph simultaneously with the strain-gage outputs from t h e model. Each t a i l panel was equipped with t w o sets of s t r a i n gages which responded t o panel bending and t o r - s i o n a l deflections. P i t c h deflections were detected by a set of s t r a i n gages xounted on weak auxiliary springs (removed f o r c l a r i t y i n f i g s . 2 t o 5 ) which were connected between t h e free end of the p i t c h spring and the forward o r rearward mounting lugs on t h e fuselage f l e x i b i l i t y f i x - t u r e . Two auxiliary springs were used, one f o r each p i t c h spring. The fuselage v e r t i c a l deflections were detected by a set of s t r a i n gages which were nounted on the fuselage v e r t i c a l spring.
A f l u t t e r - i n d i c a t i n g system w a s used during the investigation t o detect the onset of f l u t t e r . The system consisted of two oscilloscopes, one f o r each t a i l panel. The outputs from t h e bending and torsion gages f c r e a c h panel were fed i n t o t h e horizontal and v e r t i c a l axes, respec- Before t h e wing f l u t t e r e d , the trace on t i v e l y , of an oscilloscope.
E NACA R&I 9 1 the osc lloscope w a s random but, when the bending and t o r s i o n frequencies a simple Lissajous figure.
were t h e sanie ( f l u t t e r ) , the t r a c e formed The f l u t t e r tests were &e with t h e model mounted along t h e tunnel center l i n e . Several low-speed run6 were made and t h e model angle of a t t a c k w a s adjusted u n t i l there was no appreciable deflection of t h e panel t i p s . Tiis angle w a s assumed t o be the aagie of zero iiit.
At t h e beginning of a t y p i c a l f h t t e r test, the oscillograph w a s started and the tunnel stagnation pressure was increased u n t i l the model obtained on e i t h e r one w a s seen t o f l u t t e r or the Lissajous figure w a s o r both of the oscilloscopes. When f l u t t e r w a s apparent or the scaled airplane f l i g h t boundary w a s reached, t h e tunnel speed w a s reduced After each run, t h e model w a s checked visually f o r dimage.
ixmediately.
Also, the t i p of the panel was deflected and released and t h e r e s u l t i n g decay of free-bending o s c i l l a t i o n s was recorded on the oscillograph.
This was done i n an e f f o r t t o detect any s t r u c t u r a l damage suffered by the panel i n t h e previous run. Tests w e c e made with several values of p i t c h s t i f f n e s s with the p i t c h axis a t t h e forward and rearward locations.
The i n f i n i t e p i t c h s t i f f n e s s tests were made with t h e fuselage flexi- b i l i t y f i x t u r e and p i t c h freedom locked by s u i t a b l e shimming.
DISCUSSION OF RESULTS General Comments The r e s u l t s of the f l u t t e r t e s t s are given i n t a b l e I11 and p l o t t e d i n figure 10 as dynamic pressure q against Mach nuniber with curves of s l r u l a t e d a l t i t u d e a l s o indicated. Several data points i n figure 10 a r e denoted as points of intermittent f l u t t e r . The term intermittent f l u t t e r describes a condition wherein, f o r short periods of time, t h e frequency of the motions f o r the various degrees of freedom approach a comon value.
As s t a t e d i n the "Scaling" section of t h i s report, the model stiff- nesses were 76 percent of t h e scaled airplane s t i f f n e s s e s . Since t o a first-degree approximtion for most configurations, t h e dynamic pressure required f o r f l u t t e r varies d i r e c t l y with the model s t i f f n e s s level, a f l u t t e r point obtained with the model at a given Mach number and dynamic pressure suggests t h a t the airplane w i l l f l u t t e r a t the same Mach number a dynamic pressure 32 percent a t a simulated a l t i t u d e corresponding t o 0 . ... . 0.. .
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NACA RM L57Kl3 10 . ....
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- 1.32 than'thai obfained with the model. This statement higher - -
(0 ?76
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assumes, of course, t h a t the model exactly simulates the airplane.
Simulated Airplane Tests Model 3 simulated the airplane design configuration (rearward pitch- axis location and p i t c h s t i f f n e s s of 788 ft-lb/radian) and w a s t e s t e d 10 show i n t e r - The data i n figure a t Mach numbers of 0.85 and 1.06.
and q = 1,880 lb/sq f t , which i s a value mittent f l u t t e r at M = 0.85 of q s l i g h t l y above the simulated sea-level f l i g h t boundary. However, * at M = 1.06 and q = 2,330 lb/sq f t destructive f l u t t e r occurred.
This point w a s within t h e simulated flight boundary of the airplane, which indicates t h a t t h e model had an insufficient s t i f f n e s s margin.
Effects o f Pitch S t i f f n e s s With Rearward P i t c h Axis model 1 w a s I n order t o indicate the e f f e c t of pitching s t i f f n e s s , For these t e s t s , t h e t e s t e d w i t h the pitching degree of freedom locked.
A s shown fuselage v e r t i c a l bending degree of freedom w a s a l s o locked.
i n figure 10, f l u t t e r w a s not encountered within t h e f l i g h t boundary' When t h e p i t c h s t i f f n e s s w a s decreased t o w i t h t h e model cantilevered.
1,093 ft-lb/radian, intermittent f l u t t e r w a s present a t t h e f l i g h t boundary. With t h i s intermediate p i t c h s t i f f n e s s , one f l u t t e r point w a s T h i s f l u t t e r point w a s considerably obtained at a Mach number of 0.8.
it should be noted t h a t probably a more above the f l i g h t boundary, but c r i t i c a l Mach number would be near M = 1.0. In summary, with t h e rear- ward pitch axis location, increasing t h e p i t c h s t i f f n e s s 40 percent of the design value allowed the model t o reach the simulated f l i g h t boundary without f l u t t e r i n g .
Effect of Pitch-Axis Location less On the assumption that, with t h e p i t c h axis moved forward, p i t c h s t i f f n e s s would be required t o free the model from f l u t t e r within the f l i g h t boundary, a s e r i e s of tests were conducted with the p i t c h P i t c h axis moved forward from the 0 . 7 7 ~s t a t i o n t o the 0 . 5 8 ~s t a t i o n .
s t i f f n e s s e s of 497, 631, and 865 ft-lb/radian were t e s t e d i n t h i s phase of the investigation and t h e r e s u l t s are plotted i n figure 10.
A p i t c h s t i f f n e s s of 865 ft-lb/radian w a s sufficient t o prevent A decrease i n pitch s t i f f n e s s t o f l u t t e r within the f l i g h t boundary.
631 ft-lb/radian was marginal as indicated by the intermittent f l u t t e r Further reduction i n t h e which was obtained at the f l i g h t boundary.
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pitch stiffness t o 497 ft-1blradia.n resulted i n intermittent f l u t t e r at M = 0.86, q = 13.2 lb/sq f t , and f l u t t e r at M = 1.09, q = 18.7 lb/sq Ft, which is well within the f l i g h t boundary. Overall, the data show that with the pitch axis located a t 0 . 5 8 ~ ,the pitch stiffness required t o pre-”-eat f h t t e r of the mdel witfih the flight boundazy was approxi- mately 631 ft-lb/radia,n or 80 percent of the design pitch stiffness of 788 ft-lb/radian.
An analysis of transonic f l u t t e r tests of a model of the all- movable horizontal t a i l of a new fighter airplane i n the 26-inch Iangley transonic blowdm tunnel produced the following conclusions.
1. The model with the anticipated design pitch stiffness had a stiffness margin which was insufficient t o provide adequate safety from f l u t t e r a t a ~ a c h number of 1.06.
2. An increase i n model pitch stiffness of approximately 4 0 percent of the anticipated design value resulted-in an adequate maxgin.
3. With the model pitch axis moved forward from 77 percent t o 58 percent of the root chord, 80 percent of the anticipated design pitch I ! - stiffness was sufficient t o provide an adequate margin.
Langley Aeronautical Iaboratory, National Advisory Committee f o r Aeronautics, Langley Field, V a . , October 21, 1957.
REFERENCES
1. Anon.: Standard Atmosphere - Tables and D a t a f o r Altitudes t o
65,800 Feet. NACA Rep. 1235, 1923. (Supersedes NACA TN 3182.)
2. Unangst, John R . , and Jones, George W., Jr.: Some Effects of Sweep and Aspect Ratio on the Transonic Flutter Characteristics of a Series of Thin Cantilever Wings Having a Taper Ratio of 0.6.
NACA RM LZI13a, 1956.
3. Sellers, Thomas B., and Laad, Norman S.: Flutter Characteristics at Transonic Speeds of a 45' Sweptback Wing With and Without Inboard Modifications a t the Leading and Trailing Edges. NACA RM ~56128, 1957 * ....... ...............
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........
0 . 0 . 0 NACA RM L57KL3 0 . 0 . 0 .
. e . . 13
0. 0.0 . ........
TABLE I . - DESIGN SCALE FACTORS
r T
[a= 2.00; = O . ? %
TA Fundamental quantities: . . . . . . . . . . . . . . . . . . . . . . .
k n g t h , 2 0.076 m s , m 1 = -1 5 4 3 ....................
0 . 8 ~ x loo3
PA =me, t = 1 . . . . . . . . . . . . . . . . . .
0.0857 Derived quantities: . . . . . . . . . . . . . . . . .
Stream velocity, tt-1 0.887 Stream aynamic pressure, z-1mlt-2 . . . . . . . . . . .
1.572
b e n t of i n e r t i a , 2%' . . . . . . . . . . . . . . . . 0.0051 x 10-3
EI and GJ, 0.7623m~t-~ . . . . . . . . . . . . . . . . 0.399 x lo-'
. . . . . . . .
Natural vibration frequencies, J o 6 t - l 10.17 TABU 11.- PHYSICAL PROPERTIES OF TYPICAL TAIL PANEL m, b
- X 2
cl3 slug-ft /ft slug/ft bS 0.000~0 0.0268 0 093 0.038 0 953 .0200 000399
. o l l
.878 .113 .000148 .0106 .086 .803 .188 .000122 .Ol27
- .188
.264 9 725 .000197 .0152
- .091
.000095 .ox20
- -276
.414 583 .000027 .0044 .005 .510 .490 .000041 .0084 .051 .434 .000008 .0030 .044 .640 .000008 .0046 .067 .288 .716 .000002 .0017 .130 .210 ,000001
. o o l l
- .030
.a66 0. ... 0 0 . 0 0 0 0 0 0 0 . 0 0 0 . 0 .
0 . 0 0 0 . 0 . 0 0 0 0 0 . 0 0
.... 0 0 0 0 . 0 0 0 0 ... 0 0
0 0 0 0 0 . 0 0 0 0. 0 . 0 0.0 0.
NACA F@I L57Kl3 .+
k E
k 4J P) 4J c, 4J 4J c,
'-
3--+ k d B N ID
w R
c.84 (u 0 N N a ,
=<
-9 k E !
W W H + 4 l4 m c a t- .tJ m m t - 8 m \ o w CU (u C U N R NACA RM L57Kl3 J E 0 . 0.. . 0.0 . 0 . 0 . . . . 0.0 0 .
. 0 . . 0 . . 0 . . 0 . .
0 . .
. . 0 . . 0 . . . . 0 . . . ....
0 . . . 0 . . .
0 . 0.. . 0 . 0 . .
NACA RM L57IU3 NACA RM L57Kl3 I Ir R e . e.. e.
e. e.. e .e. e e. e. e e . e .
e . e . . e . . e e * * * e . e e e . . . * * * e . e .
- - - 0 . - - -
e : e - -
NACA RM L57Kl3 rl 'TJ r?
0.
i .rf c !
F.
", I .
.:: i: 0. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 * .
e o 0 0 0 . 0 0 0 0 0 . 0 0 . 0
0 . 0 . 0 0 0 0 . 0 e . . 0 . 0 0 0
* e o 0 0.0 0 0 . 0 0 0 0 0 NACA I 3 4 L37Kl-3 Y m 0) m m pt S I k c, m 0 0 0 0 I-i y\ 3 m N r( cd b a CI 0 d m k +> I I I I I I I 1 I I 0 0 0 0 I 4 u - 0, N f H W NACA RM L57Kl3
I
m Q . c C d \o ru
--t
I U k
I $
m NACA RM L57K3.3 t93 697 705 695 680 f4 *5 875 867 878 8% ! - .
I Figure 8.- Cantilever panel node l i n e s and frequencies.
............... . . 0.. 0 .
. . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . .
...........
NACA RM L 5 W 3 k
w
m a , rl V I I
L E
NACA RM L57Kl3 I k m n P W P- NACA RM L57Kl3 I 0. 0.0 . . . 0 . 0. . 0.0 . 0.0 0.
0 . . 0 . 0 0 . 0 . 0 . 0 . 0 .
..................
. . . . . . . . . . . . . . . .
- - - ...........
NACA fiM L57Kl-3 .
m NACA RM L57Kl.3 I M E
e . . . e . . 0 0. 0. e 0.. 0 . . e 0 0
e . . . . e e.. . e. . e 0 .
e . 0. 0 . 0 . . 8 e . . . e . 0 .
0 . . . 0 0 . . . . e . e . e
,E
0. 0. . . 8 . e . . e
NACA RM L57Kl.3
Flut tor I Pitch I r - - - r - l
Y (a) Rearvard pitch axis.
Figure 10.- Flutter data.
NACA RM L’37Kl3 I F l u t t e r P i t c h s t i f f n e s s ,
None I I n t e r m i t t e n t I Steady f t - l b / r a d i a n
I t
I /
7-
Simulated s e a - l e v e l - f l i g h t boundary I ,\ ft M (b) Forward pitch axis.
Figure 10. - Concluded.
NACA - Langley Field, Va