Transonic flutter investigation of models of the X-15 airplane horizontal tail

HNICAL M DUM

X-

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TECHNICAL M E M o R A I q D u M x-447 TRANSONIC FLuI"IIER INVESTIGATION OF MODELS OF TBE X-15 AlRPLANE HORIZONTAL WE* By Lou S. Young and Samuel R. Bland 4SWMAR.Y A f l u t t e r investigation of models of the sweptback, tapered, all- movable horizontal t a i l of t h e X-15 airplane was made i n the Langley transonic blardown tunnel a t Mach numbers between 0.72 and 1.32. The models were dynamically and e l a s t i c a l l y scaled so t h a t t h e e l a s t i c s c a l i n g includea a f l u t t e r s a f e t y margin. Therefore, Fn order f o r t h e models t o i n d i c a t e an adequate s a f e t y margin f o r the airplane, they were required t o be f l u t t e r free at dynamic pressures up t o the simulated maximum dynamic pressure f o r the airplane. The s t i f f n e s s d i s t r i b u t i o n s of t h e airplane t a i l panels t o which t h e e l a s t i c s c a l i n g was applied were those calculated f o r a reduced skin s t i f f n e s s r e s u l t i n g from t r a n s i e n t aerodynamic heating. This condition occurred a t a very high Mach number and a l t i t u d e . During descent, as the Mach number approaches transonic values, the s t i f f n e s s e s would tend t o increase; therefore, t h e r e s u l t s obtained f o r the present models may be conservative.

Full-span m o d e l s were used i n t h e investigation, and t h e panels Some were independently mounted t o simulate the a i r p l a n e t a i l panels.

semispan m o d e l s w e r e a l s o tested. The panels w e r e attached t o a mass which was f l e x i b l y mounted in a s t i n g fuselage so t h a t t h e models had solid-body freedoms i n pitch, roll, and v e r t i c a l t r a n s l a t i o n .

The r e s u l t s indicated that the airplane h o r i z o n t a l t a i l has the required f l u t t e r s a f e t y margin a t transonic speeds.

&

IBTRODETION Resemch Center has undertaken a program of f l u t t e r The Langley t e s t i n g components of the X-13 airplane over a range of speeds. In- cluded in t h i s program have been investigations of models of t h r e e

*

T i t l e , Unclassified.

The t h r e e designs different designs f o r the all-movable horizontal t a i l .

The orig- differed somewhat i n t h e d i s t r i b u t i o n s of mass and s t i f f n e s s .

i n a l design has been investigated at transonic, supersonic, and hyper- snmic rpaoda ( r n f - 1 , 3 , and 3 , - - p ~ n - + 4 - - 1 ~ ) A ~ e d s : p r l ilpqioh f o r the b t a i l was a l s o investigated at transonic speeds i n reference 1. The f i n a l design (used on the airplane) has been the subject of a hypersonic inves-

t i g a t i o n ( r e f . 4) and is t h e subject of t h e present investigation, which

was made at Mach numbers between 0.72 and 1.32 i n t h e Langley transonic blowdown tunnel. The models used i n t h e investigation were dynamically and e l a s t i c a l l y scaled from the properties of the f i n a l design f o r the L t a i l . The s t i f f n e s s d i s t r i b u t i o n s of t h e airplane t a i l panels t o which t h e e l a s t i c scaling was applied were those calculated f o r a reduced skin (See r e f . 5 . ) s t i f f n e s s r e s u l t i n g from t r a n s i e n t aerodynamic heating.

The transient heating e f f e c t s were calculated f o r t h a t p a r t of t h e f l i g h t This condition occurred path which gave t h e g r e a t e s t s t i f f n e s s reduction.

a t a very high Mach number and a l t i t u d e . During descent, as the Mach number approaches transonic values, the s t i f f n e s s e s would tend t o increase; t h e r e f o r e , - t h e r e s u l t s obtained f o r the present models may be conservative.

Full-span models were used i n t h e investigation, and the panels were independently mounted t o simulate the a i r p l a n e t a i l panels. The pitching s t i f f n e s s f o r the models was varied from approximately 104 per- cent t o 163 percent of the scaled a i r p l a n e value. The t a i l panels were attached t o a mass which was f l e x i b l y mounted i n a s t i n g fuselage so t h a t the model had solid-body freedoms i n p i t c h , r o l l , and v e r t i c a l translation. Some of the panels were tested singly after t h e i r com- panion panels had been destroyed.

SYMBOLS a speed of sound, f t / s e c ba average s t r e m i s e semichord of exposed panel, f t br root semichord of exposed panel, f t b t t i p semichord of panel, f t E1 bending s t i f f n e s s , lb-ft2 f f f l u t t e r frequency, cps

frequency of i t h n a t u r a l v i b r a t i o n mode (i = 1,2,3, . - - 16) J

fi CPS s t r u c t u r a l damping c o e f f i c i e n t of f i r s t n a t u r a l v i b r a t i o n mode g t o r s i o n a l s t i f f n e s s , l b - f t 2 I GJ moment of i n e r t i a of panel (including spindle) i n p i t c h about

I e

p i t c h a x i s , slug-ft2 simulated panel pitching s t i f f n e s s a t i n t e r s e c t i o n of panel root and p i t c h a x i s w i t h respect t o simulated fuselage mass,

’ f t -lb/radian

Typical model length L 1 length scale f a c t o r , Corresponding airplane length I O 1 M Mach number Typical model mass m mass s c a l e f a c t o r , Corresponding airplane mass I m’ mass of panel (including spindle), slugs dynamic pressure, &V2, l b / s q ft S span of panel, f t T s t a t i c temperature, OR t time scale f a c t o r , Time f o r tunnel airstream t o move 1 model t a i l chord 1 airplane t a i l chord Time f o r airplane t o move V velocity, f t / s e c reduced velocity based on a representative n a t u r a l vibration frequency, V/ba2nf i V volume of frustum o f cone enclosing the t a i l panel,

nfi(br2 + brbt + b t 2 ) , cu f t

natural-vibration-frequency reduction f a c t o r used t o provide a margin of safety i n application of model f l u t t e r test r e s u l t s t o airplane nondimensional distance along reference axis, Distance from panel root along reference a x i s Length of exposed panel reference axis CL mass r a t i o , ml/pv s t a t i c air density, slugs/cu f t P Uf c i r c u l a r f l u t t e r frequency, radians./sec frequency of predominantly t o r s i o n a l n a t u r a l vibration mode, b U C L 2nf8 for t h e models, radians/sec Sub s cr i p t s : A airplane a a c t u a l M model t t r u l y scaled MODELS Configurations The four models used i n t h e investigation are designated by t h e numbers 1, 2, 3, o r 4. Each of t h e separate t a i l panels i s designated by the number o f the model i n which it was used, and t h e l e t t e r L or R follows each number t o indicate whether it was a l e f t or r i g h t panel, respectively. The models a r e generally t r e a t e d herein i n terms of t h e t separate panels because some of t h e panels were t e s t e d singly a f t e r t h e i r

companion panels had been destroyed. Models 3 and 4 had close t o t h e

scaled value of pitching s t i f f n e s s , while models 1 and 2 had values of pitching s t i f f n e s s which were considerably higher.

Geometry The full-span models were 1/12-size versions of t h e horizontal t a i l panels of t h e airplane.

A sketch of a t y p i c a l model giving basic dimen- sions i s shown i n f i g u r e 1.

The models had a planform incorporating about 4 5 O sweepback of t h e quarter-chord l i n e , an exposed panel aspect r a t i o of 1.258, and a n exposed panel taper r a t i o of 0.299. The streamwise a i r f o i l section derived by t h e manufacturer was a 66~005,which was modified t o have a 1-percent- chord thickness at t h e t r a i l i n g edge, with a s t r a i g h t - l i n e f a i r i n g from t h e t r a i l i n g edge t o the 67-percent-chord. point (point of tangency).

N e a r the t i p , the a i r f o i l w a s modified further by increasing the thick- A i r f o i l ordinates are presented ness ahead of the 15-percent-chord line.

i n f i g u r e 1, and some model geometric properties are l i s t e d i n table I.

A photograph of a model mounted i n t h e s t i n g and a cross-section sketch of the s t i n g are shown i n figure 2.

c Scaling Scaling the airplane properties required t h a t t h e nondimensional mass a n d ’ s t i f f n e s s d i s t r i b u t i o n s be the same f o r t h e model and t h e air- The mass and s t i f f n e s s l e v e l s f o r the model were obtained by plane.

specifying the scale f a c t o r s f o r the fundamental q u a n t i t i e s involved; that is, length, m a s s , and t h e .

The s i z e of t h e models was limited by tunnel-wall interference considerations. O n the basis of previous experience, the length scale f a c t o r was chosen t o be 2 = - The mass s c a l e f a c t o r was obtained from t h e requirement t h a t the mass r a t i o p be the same for both model and airplane and i s as follows: pM The density r a t i o was chosen t o be - = 1.275.

The time s c a l e f a c t o r w a s derived from the requirement that the

-

reduced v e l o c i t y V be the sane f o r t h e model as f o r the airplane and i s as follows: Since the Mach number i s the same f o r both model and airplane, 4 2

t = ( ? ) 1

The s t a t i c temperature f o r t h e airplane i s a function only of a l t i - TA tude, and f o r sea-level a l t i t u d e TA was taken t o be 519' R . However, during a tunnel run, t h e temperature drops contiflually as a i r i s expended c from the reservoir. A study of f l u t t e r data obtained during e a r l i e r investigations indicated t h a t 408' R was near t h e average value of TM t h a t could b e expected during t h e present tests. These values of TM and T were used i n equation ( 3 ) ; hence, 0.786 was used as t h e value L Of %?TA* The pertinent model and flow q u a n t i t i e s and t h e design s c a l e f a c t o r s which apply t o them a r e l i s t e d i n t a b l e 11. The scaling approach f o r these models d i f f e r e d from t h a t used f o r the X-15 horizontal t a i l models

described i n reference 1 by the use of t h e f a c t o r 5 which appears i n

t h e scale f a c t o r s f o r some of t h e q u a n t i t i e s l i s t e d i n table 11. The f a c t o r 5 , which has t h e value of 0.85, reduces t h e n a t u r a l v i b r a t i o n frequencies t o 85 percent of those which would r e s u l t from application of t h e scale f a c t o r s as specified (eqs. (l), (2), and ( 3 ) ) . The frequency reduction was accomplished by reducing t h e s t i f f n e s s e s the appropriate amount; thus, t h e values of EI, G J , and ke i n table I1 are multiplied by t h e f a c t o r {*. The purpose of reducing t h e model frequencies w a s t o provide a margin of s a f e t y i n t h e application of t h e model f l u t t e r test r e s u l t s t o the airplane. The designed reduced v e l o c i t y f o r t h e model i s thus equal, not t o that of t h e airplane, but t o t h a t of an a i r p l a n e having s t i f f n e s s e s 72.25 percent ( c 2 = 0.852) of those calculated f o r the a c t u a l airplane f o r a reduced skin s t i f f n e s s r e s u l t i n g from t r a n s i e n t aerodynamic heating .

b The dynamic pressure and Mach number are q u a n t i t i e s which are con- t r o l l a b l e during a run; whereas, t h e temperature i s not controllable.

When the dynamic pressure and Mach number a r e considered t o be fixed and a s t a t i c temperature d i f f e r e n t from t h e design value i s obtained, both t h e density and v e l o c i t y w i l l be d i f f e r e n t from t h e values considered i n the scaling. The density and v e l o c i t y changes r e s u l t i n values of mass r a t i o and reduced velocity, respectively, d i f f e r e n t from t h e design values. However, a combination of reduced v e l o c i t y and mass r a t i o , which - 2 7 1

can be expressed i n terms of t h e dynamic pressure - ' M a qM, i s independ-

PM - - ent of t h e temperature. O n t h e b a s i s of t h i s parameter, a t r u l y scaled model would exactly simulate t h e a i r p l a n e i n t h e tests because t h e simu- l a t e d a l t i t u d e i s interpreted i n terns of t h e dynamic pressure.

Thus, t h e scale f a c t o r f o r dynamic pressure i n table I1 i s used t o convert the dynamic pressure f o r the a i r p l a n e a t any Mach n m b e r and a l t i t u d e t o t h e .)

dynamic pressure f o r t h e model at t h e Same Mach n m b e r and a l t i t u d e .

The dynamic pressure f o r t h e airplane i s assumed t o be t h a t of t h e ICAO standard atmosphere ( r e f . 6 ) . For a given a l t i t u d e , q/M2 has a constant value.

The e f f e c t of not individually s a t i s f y i n g exactly t h e mass-ratio and reduced-velocity requirements i s believed t o be negligible i n t h e present Experience with a wide v a r i e t y of f l u t t e r models has indi- investigation.

cated t h a t , at a given Mach number, f l u t t e r tends t o occur at a constant value of dynamic pressure regardless of t h e individual values of density and velocity, a t l e a s t within the operational limits of t h e tunnel.

Construction i s shown i n f i g u r e 3, which i s an X-ray photo- The panel construction Each panel had a b a l s a - f i l l e d aluminum box spar t o graph of panel 4R.

The magnesium spindle ( f i g . 1) w a s which t h e aluminum r i b s were fastened.

4L i n t e g r a l with t h e r o o t r i b , which f i t t e d i n t o t h e spar root. Panels and 4R had s l i g h t l y d i f f e r e n t construction from t h e other panels as indi- cated ir, f i g u r e 3 . The s t r u c t u r e described thus far w a s held together by means of a resinous glue reinforced with s m a l l aluminum n a i l s which can be seen i n figure 3 . The r e s t of t h e structure, consisting of pine leading and t r a i l i n g edges and b a l s a wood t o f i l l out t h e a i r f o i l shape, w a s glued t o t h e spar and ribs. Lead weights were a l s o glued i n t o t h e s t r u c t u r e at various points t o obtain t h e desired mass d i s t r i b u t i o n .

Each panel was fastened t o the fuselage mass by means of two p a i r s of flexure pivots which fixed the p i t c h a x i s ( f i g . 4 ) . The pitching- s t i f f n e s s l e v e l was controlled by a bronze spring cantilevered from t h e

spindle ( f i g . 4), which w a s connected t o t h e fuselage mass by means of

a long screw. The fuselage mass w a s made of steel and lead pieces, which were supported forward and rearward by springs cantilevered from t h e s t i n g mounting block. A schematic sketch showing t h e arrangement of t h e fuse-

m a s s i s given i n figure 4, and figure 5 shows a photograph of a model

l a g e is removed from t h e s t i n g and t h e wooden i n t h e s t i n g mounting block which f a i r i n g blocks.

Physical Properties Natural vibration modes.- The frequencies and node l i n e s of the n a t u r a l v i b r a t i o n modes were found f o r each model j u s t p r i o r t o f l u t t e r The models were excited by means of an electromagnetic shaker t e s t i n g .

f i t t e d w i t h a double-pronged s t e m so t h a t both panels could be excited simultaneously. Node l i n e s were located during t h e resonant vibrations by sprinkling sand on t h e model. The r e s u l t s of these measurements are A description of each of t h e n a t u r a l given i n f i g u r e 6 and i n table 111.

v i b r a t i o n modes i s given i n t a b l e I I I ( a ) , and t h e frequencies found on each panel are listed i n t a b l e I I I ( b ) . It may be noted i n t a b l e I I I ( b ) t h a t modes i n addition t o those found on t h e airplane were found on t h e O f the panels which were t e s t e d singly after the destruction models.

4 R was vibrated before f l u t t e r t e s t i n g

of t h e i r companion panels, only without another panel i n t h e mount. The modal c h a r a c t e r i s t i c s of the predominantly f i r s t and second symmetrical bending and first symmetrical t o r s i o n a l modes were e s s e n t i a l l y t h e same f o r 4 R alone as f o r 4 R when it .

was vibrated i n t h e complete model 4.

The averaged values of the s t r u c t u r a l damping coefficient i n t h e first natural vibration mode, as determined f o r each panel from records L of the decay of o s c i l l a t i o n s induced by plucking the panel i n s t i l l a i r , are presented i n table I I I ( b ) .

S t i f f n e s s measurements.- The pitching s t i f f n e s s a t t h e i n t e r s e c t i o n of the p i t c h a x i s w i t h the panel root ( f i g . 1) was measured f o r each panel by means of an o p t i c a l system employing a cathetometer. These values of ke a r e l i s t e d i n table I I I ( b ) .

The bending and t o r s i o n a l s t i f f n e s s d i s t r i b u t i o n s were measured f o r

panels L R and 4L by means of an o p t i c a l system which i s described i n refer-

ence 7. These panel s t i f f n e s s d i s t r i b u t i o n s are p l o t t e d i n f i g u r e 7 along with the scaled airplane s t i f f n e s s d i s t r i b u t i o n s (ref. 8). The reference a x i s used f o r t h e s t i f f n e s s d i s t r i b u t i o n measurements was t h e ??-percent- chord l i n e .

A value of approximately 20,000 f t - l b / r a d i a n was obtained f o r t h e pitching s t i f f n e s s of t h e fuselage mass a t the panel p i t c h a x i s ( f i g . 4 ) . 0 The mode shape o f t h e fuselage mass f o r t h e pitching mode was not d e t e r - mined; thus, the degree of simulation of t h e generalized fuselage m a s s h f o r t h i s mode i s not known. Measurements of t h e s t i f f n e s s e s i n r o l l and v e r t i c a l t r a n s l a t i o n were not made.

and center-of-gravity location of each a r e presented i n table I I I ( b ) . The panel mass d i s t r i b u t i o n s were not measured f o r t h e s e models; t h i s property w a s scaled from t h e airplane (ref. 8).

The moment of i n e r t i a of each panel and spindle i n p i t c h about the p i t c h axis is a l s o given i n t a b l e I I I ( b ) . data The moment-of-inertia

f o r a l l of the panels except 4L and 4 R were supplied by the model manu-

facturer; t h e values of moment of i n e r t i a f o r panels 4L and 4 R were meas-

ured by means of a b i f i l a r pendulum and were obtained by t r a n s f e r r i n g t h e moment of inertia about the center of gravity, w i t h t h e assumption t h a t the center of gravity was located i n t h e model horizontal plane.

c The spindles of several of t h e models, which were broken during f l u t t e r testing,, were cut off at t h e panel r o o t and t h e i r average mass was found t o be 0.596 x 10-3 slug w i t h a center-of-gravity location 0.073 foot from t h e panel root. The fuselage mass without the panels but including one-half the m a s s of t h e forward and rearward springs was 0.235 slug with a center-of-gravity location 0.046 f o o t forward of the panel p i t c h a x i s .

* APPARAWS AND TESTS L T h e ’ f l u t t e r tests were made i n the Langley transonic blowdown tunnel 1 The t e s t section i s octagonal i n cross which has a s l o t t e d test section.

measures 26- inches between sides. During operation of t h e section and a preselected Mach number i s s e t by means of a variable o r i f i c e tunnel, ‘6 This Mach number i s held approximately downstream of t h e test section.

constant a f t e r t h e o r i f i c e i s choked while t h e stagnation pressure and, thus, t h e density are increased. However, the runs of t h e present inves- t i g a t i o n were generally made a t dynamic pressures which were too low t o choke t h e o r i f i c e so that Mach number and density both increased during t h e runs. The s t a t i c - d e n s i t y range i s approximately 0 . 0 0 1 t o 0.012 slug may be obtained from subsonic values t o per cubic foot, and Mach nunibers It should be noted that, because of t h e expansion a maximum of about 1.4.

of t h e air i n t h e reservoir during a run, t h e stagnation temperature con- t i n u a l l y decreases; thus, t h e test-section velocity i s not uniquely defined by t h e Mach number. Additional information about t h e tunnel i s contained 9. Excellent agreement between f l u t t e r data obtained i n the i n reference tunnel and data obtained i n free a i r has been observed (ref. 10).

I n the present f l u t t e r t e s t s , the models were mounted i n a s t i n g The s t i n g extended upstream i n t o t h e subsonic flow as shown i n figure 2.

region of t h e tunnel t o prevent t h e formation of shock waves off t h e f’use- the model. The s t i n g and lage nose, which might be r e f l e c t e d back onto model weighed approximately 305 pounds, and t h e system had a fundamental

bending frequency of about 15 cycles per second. The two panels were

c a r e f u l l y alined t o be a t zero angle o f a t t a c k i n the tunnel, and tunnel runs t o check t h i s t r i m were made. Wire s t r a i n gages were mounted on each panel spar, as sketched i n figure 1, and were oriented so a s t o i n d i c a t e panel deflections about predominantly bending and t o r s i o n a l axes. The strain-gage signals, the tunnel stagnation and s t a t i c pres- sures, and the stagnation temperature were recorded by a recording oscillograph. The strain-gage t r a c e s on t h e oscillograph records were used t o i d e n t i f y t h e start of f l u t t e r and t o obtain the f l u t t e r frequency.

High-speed motion p i c t u r e s were made d u r i n g some of the runs and were T w o cameras were used; one camera used i n observing the f l u t t e r mode.

t h e other camera photographed only t h e l e f t panel of each model, and * The cameras were used photographed t h e lower surfaces of both panels.

e i t h e r simultaneously o r i n sequence during the runs.

The t e s t s were made a t Mach numbers between 0.72 and 1.32 and a t simulated a l t i t u d e s down t o below sea level.

RESULTS AND DISCUSSION Interpretation of Results c A s s t a t e d i n the section e n t i t l e d IIScaling," t h e model s t i f f n e s s e s , L with the exceptions of ke f o r models 1 and 2 , were 72.25 percent of 1 , t h e values which would be obtained from scaling the airplane s t i f f n e s s e s without t h e use of t h e f a c t o r c 2 . Thus, t h e simulated a l t i t u d e s f o r t h e model are t o be interpreted as a l t i t u d e s which, if cleared by t h e model, could be reached with a 38.4-percent margin of safety i n s t i f f n e s s by t h e airplane, i f t h e model i s assumed t o closely = 1.384

(0.7225 )

simulate t h e airplane i n a l l respects. The r e s u l t s may be interpreted a l t e r n a t i v e l y by considering t h a t a f l u t t e r point obtained with t h e model represents an airplane f l u t t e r point at t h e same Mach number a t a simu- l a t e d a l t i t u d e corresponding t o a dynamic pressure 38.4 percent higher than that f o r the model.

The c r i t e r i o n f o r determining whether t h e closely scaled models (models 3 and 4) indicated t h a t t h e airplane would have an adequate f l u t t e r s a f e t y margin was t h a t the models should be f l u t t e r f r e e up t o t h e simulated maximum dynamic pressure f o r t h e airplane a t t h e various Mach numbers. A s discussed i n t h e introduction, t h e model r e s u l t s may be conservative because t h e models were scaled from airplane properties v which were calculated f o r a t r a n s i e n t aerodynamic heating condition which was probably more severe than would be encountered a t transonic Mach numbers .

h l The oscillograph records of several of t h e test runs showed a period of intermittent sinusoidal o s c i l l a t i o n s o f t h e model p r i o r t o t h e advent of t h e steady sinusoidal o s c i l l a t i o n s of increasing amplitude which indi- cated f l u t t e r . I n those cases where t h e s e i n t e r m i t t e n t o s c i l l a t i o n s tended t o obscure the a c t u a l start of f l u t t e r , t h e s e regions have been defined as low-damping regions, and data at t h e start of such o s c i l l a t i o n s are included i n t h e f i g u r e s and t a b l e s . It i s not known what significance t h e low-damping regions have f o r t h e airplane, since such o s c i l l a t i o n s may be i n part a function of tunnel turbulence, which i s d i f f e r e n t from tur- bulence i n the atmosphere.

Discussion of Results The data obtained i n t h e 15 runs of t h i s i n v e s t i g a t i o n are summarized i n table I V Y where the data p o i n t s f o r each panel are presented i n t h e L

Y

_ _ .-.

0 . 0 0 . 0 0 0 . 0 0 0 * o 0 0

0 0 0 . . 0

0 0 . . 0 0 * . 0 .

0 . 0 .

0 0 0 . 0.

sequence f o r each run. The data given i n t a b l e IV f o r t h e closely scaled models (models 3 and 4) are p l o t t e d in f i g u r e 8 i n t h e form of dynamic pressure versus Mach nuniber. Also shown i n f i g u r e 8 are l i n e s representing simulated sea-level and 10,000-foot a l t i t u d e s , and t h e maximum airplane

dynamic pressure. Since models 3 and 4 have values of pitching s t i f f n e s s

which were close t o t h e scaled value ( t a b l e I I I ( b ) ) , t h e results indicate t h a t t h e airplane would have the required f l u t t e r s a f e t y margin.

The dynamic-pressure data f o r models 1 and 2 (table IV) " e p l o t t e d a function of Mach number. The same l i n e s as i n f i g u r e 8, i n f i g u r e 9 a s representing simulated sea-level a l t i t u d e , 10,000-foot a l t i t u d e , and the maximum airplane dynamic pressure, are shown i n figure 9. As may be seen i n t a b l e I I I ( b ) , t h e pitching-stiffness values f o r these models averaged about 157 percent of t h e scaled values and, a s would be expected, greater the higher pitching s t i f f n e s s f l u t t e r s a f e t y margins a r e indicated f o r than f o r the lower pitching s t i f f n e s s . (Compare f i g s . 8 and 9.)

High-speed motion p i c t u r e s were taken during a l l of the runs, but sequences during f l u t t e r were obtained only f o r panels lL, I R , 2L, and 4L. All of t h e motion p i c t u r e s showed random yawing and pitching o s c i l l a - t i o n s during most of each run, p r i o r t o f l u t t e r . The f l u t t e r mode w a s of t h e bending-torsion type wherein the t o r s i o n blended i n t o q u i t e large pitching deflections at the root. The f l u t t e r o s c i l l a t i o n s diverged r a p i d l y u n t i l the panel broke.

The fuselage motions were imperceptible except during t h e most v i o l e n t f l u t t e r o s c i l l a t i o n s , when some very s l i g h t motion was noted.

The motion p i c t u r e s of run 8 on model 1 show t h a t , although at the start of each burst of l o w damping t h e panel motions were i n phase, at the start of f l u t t e r t h e panels appeared t o be completely independent.

' a I n an attempt t o c o r r e l a t e t h e data obtained on t h e models with t h e two l e v e l s of pitching s t i f f n e s s ( f i g s . 8 and g ) , the following r e l a t i o n w a s assumed: The q u a n t i t i e s within t h e parentheses are nondimensional. The subscript M , t denotes t h e t r u l y scaled model, and t h e subscript M , a denotes the baq

a c t u a l model. The parameter - is r e l a t e d t o two other frequently

mt%2 a 0 m e a a earn a ma a. c b # * a 0 e a a * a a m a a a a m a 0 0 a a a a m * * a e a * a a 0 0 a a a a a a a a m 0 ..a a.

used parameters ' and bama' as follows: a bama \r; c The r e l a t i o n i n equation (4) i s only approximate and i s based on two assumptions. The f i r s t assumption i s t h a t f l u t t e r at a given Mach num- ber occurs at a given value of dynamic pressure regardless of t h e indi- vidual values of density and velocity (as discussed under "Scaling").

The second assumption i s t h a t t h e dynamic pressure f o r f l u t t e r v a r i e s d i r e c t l y with t h e model mass and d i r e c t l y with t h e square of t h e t o r s i o n frequency. Thus, the r e l a t i o n cannot take any account of a difference i n mass d i s t r i b u t i o n between t h e t r u l y scaled and the a c t u a l model.

The difference i n pitching s t i f f n e s s between t h e t r u l y scaled and t h e a c t u a l model i s accounted f o r only on t h e basis of t h e e f f e c t of pitching The dynamic pressure f o r f l u t t e r f o r s t i f f n e s s on t h e t o r s i o n frequency.

a t r u l y scaled model i s desired and may be obtained from equation (4) by

transposing; thus, where the semichords have been dropped because they are equal.

The data of figures 8 and 9, corrected on t h e basis of equation ( 5 ) t o t r u e model mass and t o r s i o n frequency values, are shown i n f i g u r e 10.

The data c o r r e l a t e over a band which l i e s at dynamic pressures higher than the scaled maximum dynamic pressures of t h e a i r p l a n e and, thus, indicate at least t h e required 38.4-percent margin of f l u t t e r s a f e t y i n s t i f f n e s s .

CONCLUSION (r A t r a n s o n i c f l u t t e r investigation was made of models of t h e a l l - movable horizontal t a i l o ane. The s t i f f n e s s e s of t h e 0 0 . 0 . 0 . 0 0 0 a 0 0 . 0 0 0 0 00.

0. 0 0 0 0 models were scaled from airplane properties which were calculated for a transient aerodynamic heating condition. "his condition occurred at a very high Mach number and altitude. The resulting model stiffnesses were reduced more severely than the airplane stiffnesses would be at transonic Mach numbers during a normal descent; therefore, the model results may be conservative. "he results indicate that the airplane horizontal tail has the required flutter safety margin at transonic speeds.

Langley Research Center, National Aeronautics and Space Administration, Langley Field, Va. , October 31, 1960.

I REFEXENCES Transonic Flutter .Investigation of Models of Proposed 1. Young, Lou S.: Horizontal Tails for the X-15 Airplane. NASA TM X-442, 1961.

2. Lauten, William T., Jr., and Hess, Robert W.: Experimental and Cal- c culated Supersonic Flutter Characteristics of Models of the x-15 Horizontal and Vertical Tails. NASA TM x-176, 1959.

3. Lauten, William T., Jr., Levey, Gilbert M., and Armstrong, William 0 . : L Investigation of an All-Movable Control Surface at a Mach Number 1 of 6.86'-for Possible Flutter. NACA RM L58B27, 1958. 0 John S.: Flutter Investigation at 6 4. Gibson, Frederick W., and Mixon, a Mach Number of 7.2 of Models of the Horizontal- and Vertical-Tail Surfaces of the X-15 Airplane. NASA MEMO 4-14-59L, 1959.

5 . Landrum, L. L . : Estimated Aeroelastic Characteristics for the X-15 Airplane (NAA Model Designation NA-240). Rep. No. NA-59-471, North American Aviation, Inc., Apr. 16, 1959.

Standard Atmosphere - Tables and Data for Altitudes to

6. Anon.: 65,800 Feet. NACA Rep. 1235, 1955. (Supersedes NACA TN 3182.)

7. Land, Norman S., and Abbott, Frank T., Jr.: Method of Controlling

NACA Stiffness Properties of a Solid-Construction Model Wing.

TN 3423, 1955. * A Specification for the Flutter Models of the X-15 8 . Sweet, H. R.: Flutter Program. Rep. No. NA-56-738, North American Aviation, Inc., 1 Aug. 17, 1956.

9. 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 L55113a, 1956.

10. Bursnall, William J.: Initial Flutter Tests in the Langley Transonic Blowdown Tunnel and Comparison With Free-Flight Flutter Results.

NACA RM L52K14, 1953.

TABU I . - GEDMEXRIC PROPWIES OF MODELS

. . . . Modified 66~005

S t r e a w i s e a i r f o i l section . . . . . . . . . .

. . . . . . . . . 44.6

Sweepback of quarter-chord l i n e , deg . . . . .

. . . . . . . . 0.476

Panel span, f t . . . . . . . . . . . . . . . .

. . . . . . . . . 0.583

Streamwise panel root chord, ft . . . . . . .

. . . . . . . . . 0.180

Panel area, sq f t . . . . . . . . . . . . . .

Panel aspect r a t i o . . . . . . . . . . . . . . . . . . . . . . . 1.258

. . . . . . . . . 0.299

Panel t a p e r r a t i o . . . . . . . . . . . . . .

. . . . . . . . . 0.665

Planform semispan, f t . . . . . . . . . . . .

panel t o M a x i m u m streamwise chord based on extension of

fuselage center l i n e , f t . . . . . . . . . . . . . . . . . . . 0.745

Planform area sq f t . . . . . . . . . . . . . . . . . . . . . . 0.611

. . . . . . . . . 2.893

Planform aspect r a t i o . . . . . . . . . . . .

. . . . . . . . . 0.234

Planform t a p e r r a t i o . . . . . . . . . . . . .

1 6 TABLE 11.- DESIGN SCALE FACTORS O F PERTINENT MODEL AND F L O W QUANTITIES I I Quantity Numerical Symbolical

I Fundamental q u a n t i t i e s

1/12 7.378 x

9.400 x lom2

t = (?$%

T i m e . . . . . . . . . . . . . . . . .

I Derived q u a n t i t i e s

0.8865 Stream v e l o c i t y . . . . . . . . . . .

1.002 Stream dynamic pressure . . . . . . .

5.124 x

Moment o f i n e r t i a . . . . . . . . . .

4.189 x

k 8 . . . . . . . . . . . . . . . . . .

3.491 x 10-5 E1 and G J . . . . . . . . . . . . . .

9.043 Natural vibration frequency . . . . .

TABLE 111.- PHYSICAL PROPERTIES OF MODELS (a) Description of natural vibration modes Remarks 1 F i r s t Symmetrical Some Very None Strong mode on each panel.

bending when panels l i t t l e coupled (4 Weak Panel response weak.

1 1 1 Fuselage Yaw symmetrical 1 Bone

translation translation

or pitch 1 or pitch I

----------- Weak mode; coupled with 5 on severalmodels.

Strong Symmetrical hsymmetrical ------ Strong ----------- Stronger mode than J; tended t o be coupled Antisymmetrical tisymmetrical ------ with 14.

Yaw t ! I Strong Rolled down This mode w a s weak on model 2 which had a A n t i s m e t r i c a l Antisymmetricall s ~ m e on side different frequency on each panel. torsion where panel leading edge moved down

e

I Weak Same as 5, but appeared only on panel JR which Antisymnetrical t i s p m e t r i c a l &me

I 1 torsion k i

----------- coupled CSymmetrical s l i g h t Strong Apparently a coupling of 4, 8, and 14 which w a s mode strong when it appeared.

8 Symmetrical Symmetrical Large Strong Some Strong mode; panel torsion blended into pitch torsion

Symmetrical ’ Spmetrical Large

9 Strong Same as 8, but appeared only on model 4; w a s torsion panel 4L which a l s o responded i n mode 8.

i

-- ------ --- mode is probably same as 5 , but included sme yaw; t i p went f o ~ a r d as it went up.

Strong mode. I 11 I Symmetrical 1 Symmetrical

I some I Strong I ;Zt

second bending

I

Modes 1 1 and 12 sweep i n t o one another.

Antisyxmnetrical A n t i s p e t r i c a l I Slight I Strong 1 Slight

second bending I

----------- Weak mode; apparently a natural frequency of Symmetrical S p e t r i c a l ------ Strong bending panel 3L only, but the mode w a s coupled with the whole model.

14 A n t i s m t r i c a l Strong - ----- ----- Strong mode; appeared on most models, but w a s second torsion coupled with recorded only on model 4; modes 4 and 7 i n some instances.

15 Symmetrical Symmetrical ------ ------ second torsion recorded f o r 4R alone only.

16 Symnetrical Symmetrical ------ Strong ----------- N o d e l i n e s not recorded; frequencies recorded t h i r d bending for.4L and 4R alone only.

~ 9 9 4 9 T 4 0 rl

a 4 4

4 4 X X X X x x C O W m a , W N 0 " 2 s [ : [ : [: '9 r ' 9 rl rl rl rl P a " c - m CO n f

w s

n i n n rl I 0 0 ? I I 1 0 0 0 0

M f W & I ? / 9

N t- m t- t - t -

5 s

9 9 9 0 0 9 o o 0 0 0 0 N r 7 7 7 7 0 rl 4 4

4 a a

x x X X x x \o N

% a

$ ' a '9 '4 0 0 L" ' " 9 0 0 0 ~ n In a0 g . 9 0 0 n N n x : f f _ _ N n 4) rl t - rl rl N N 9 9 9 1 9 0 0 0 0

.,'

I I I I I I I I I I I I I I I I I I I I I I j; I I r l r l I I I n n I n n I n a r l 0 n n 8 n I I n n 2 2 3 3 n W C O t - 0 n 3

5 %

- I w 1 I N I I 8 n X f I n I

+

k ? \ D D P - - c o v 3 c o f c u I n l n l n l n c u U l t - c u c u N 3 n m A - o C U O f r o r n c u c u c u r n f f f cucurn r n r n f f f N r o M r O f A - -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Q W 0 8 0 0 o o o q q o 8 0 0 o o q o o . . . . . . . . 0 0 0 0 0 0

. . . . . . . . . . . . .

hD ? O rl m !

I rl

i

I n cu f 0.00 .35 .54

r

P 1.20 P 1.35 1.46 cn 10.00 1.50 15.00 1.77 1.77 20.00 2.00 2.00 25.00 2.18 2.18 30.00 2.52 2.32 2.42 2.42 35.00 40.W 2.48 2.48 2.50 2.50 45.W 2.49 2.44 2.35 2.18 2.08 6 5 .50 Sactlon 8-8 L I I I Modlilsd 668005 I t -- p - N O t e t i e l r l n g w n l ~ t e d 3/32 to clear penal Figure 1.- Sketch of panel. Dimensions are in inches.

a c cd t'i m a , ri G d _- .a

\

* I c u

\

a l .

L-60- 6907 Figure 3 . - X-ray photograph of panel 4R.

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 0 0 0 0 0.0 0.

I

I

I

I

I

\

I

rl c' -c-_

m h 0 . m

_I

m l c I I 0) 4 m I I $ I-------- % T 5 - E

P A A 1 n

h .e- I In 0 0 0.0 0 0 0 0 0 .

.

0.0 0 0 25 Right panel \o rl

-----

4 f ; ’ WlO

I No node l i n e f15 523 \ I \ position (a) Model 1.

Figure 6.- Measured natural vibration frequencies and node lines.

............... .......

. . . . . . . . . . . . . . . .

. . . . . .

. . . . . . . . .

...... ........

Right panel Left panel Mode Mode Frequency (CPS) fl

- _ - -- --- --

l h 6 f 2 No node l i n e f 3 232 - 26h f5 - - 3hO f a

- - -

fll

-----

lr2 9

z1

Shaker position L (b) Model 2.

Figure 6.- Continued.

c 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 O 0 0 -

0 . O 0 = O 0 0 0 = = ' o o O 0

0 0 Right panel Left panel Mode Frequency Mode F'requency ( C P 1 (CPS 1 lC6 1h0 182 102 h30 h30

/

-Null area- fll = 383

i ? Shaker

position ( c ) Model 3.

Figure 6. - Continued.

Right panel Left panel t Mode Frequency Mode (CP8 1 fl

_ _ _ --. _ _ - - - f 2

Ill9 N o node l i n e f 3 17 9 N o node l i n e f h 23iL-2h0

-

f S

--

2 3h f 7

300 ---- f a

26h

----- f 9

383 1 fll --I---- f 1 2 No node l i n e f l h No node l i n e f l h b80 N o node l i n e fl$ $20 No node l i n e f l q 8hO No node l i n e f16

1 . 2 /--

---

(a) Model 4.

Figure 6.- Continued.

.. . . a

. . a e . . . a :.i'..---.. .

. a . . . . a a .

.. a .

-- .e. .. a .

a 0. a*

- - = = - . a - -

. . . a a .

Mode Frequency

(CPS 1

l C 6 376' 505.

N o node line fl6 \D rl

A

p s i tion (e). Model 4, right panel alone.

Figure 6.- Continued.

Mode Frequency (cps ) f 1 115 No node line f2 14 3

----

f8 305 - - - fll 408

----

fl$ e;s9 ( f ) Airplane scaled values.

Figure 6.- Concluded.

Figure 7 . - Measured panel torsional and bending stiffness distributions

canpared w i t h scaled airplane stiffness distributions.

T

U i Figure 8.- T e s t dynamic pressure versus Mach number for model6 3 and 4.

is close t o scaled value.

k~ I

3F

Figure 9 . - Test dynamic pressure versus Mach number for models 1 and 2 .

averages 157 percent of scaled value.

ke 3 2 0 0 Jpen s p ~ b o l s i r , d i c a t e rnaxIritlr. q , no f l u t t e r 3oLir: s y r r h o l s i n d i c a t e s t a r t o f flu1 t e r

I I I I I I

2 900

Y

P a+L' 0 P c n 2CGC %, t lb/sq ft 1 6 G O Eol; 4c, 0 I Figure 10.- Dynamic pressure versus Mach number.

NASA - Langley Field, Va L-1016