Document
I
x-442
I
I
#
WMi-lNGTUN February 1961
NATIONAL AEROwlUTICS AND SPACE ADMINISTRATION TECHNICAL MEMORANDUM X-442 TRANSONIC F'LlJlTEB INVESTIGATION OF MODELS OF PROPOSED HORIZONTAL TAIIS FOR m x-15 AIR- / A flutter investigation at Mach numbers between 0.79 and 1.47 has been made in the langley transonic blowdam tunnel of dynamically and elastically scaled models of the original design and of a revised design for the all-movable horizontal tail of the X-15 airplane. A third design, which was not tested in the present investigation, was finally used in the airplane. The two designs investigated herein differed only in panel mass and stiffness distributions. Both designs had a planform which was swept back and tapered, and in each case the tail panels were independently mounted and actuated. The semispan models were mounted in a sting fuselage so that the airplane stiffnesses at the panel root were simulated, with provision for changing the stiffness in pitch. The airplane-fuselage degrees of freedom were not simulated.
I One model of the original design simulated the panel stiffness dis- l a tributions which were calculated for the airplane at standard sea-level L Other models of both the original and the temperature conditions.
revised designs simulated the calculated airplane panel stiffness dis- tributions for a reduced skin stiffness caused by transient aerodynamic heating .
The standard-temperature model of the original design had an ade- quate flutter safety margin over the Mach number range of the tests (that is, the model was flutter free at dynamic pressures up to 32 per- The high- cent higher than those for simulated sea-level conditions).
temperature models of both the original and the revised designs had adequate flutter safety margins at Mach numbers up to about 1 . 1 but had An increase in pitching inadequate safety margins at high Mach numbers.
stiffness for a high-temperature model of the original design to 118 percent of the scaled airplane value gave a configuration which had an adequate safety margin throughout the Mach number range of the investigation.
*Title, Unclassified.
.. 0.. . ... . 0 . 0 . . . . ... 0 .
C A program for determining the flutter characteristics of the compo- nents of the X-15 airplane has been undertaken by the Langley Research Center. Included in this program have been investigations at supersonic & and hypersonic speeds (refs. 1 and 2, respectively) of dynamically and elastically scaled models of the original design for the airplane all- movable horizontal tail. The present paper describes an investigation
made at Mach numbers between 0.79 and 1.47 in the Langley transonic
blowdown tunnel of dynamically and elastically scaled models of the original and of a revised design f o r the airplane horizontal tail.
The original and revised designs had the same planform and each Both designs had tail panel was independently mounted and actuated.
the same pitching stiffness at the panel root; however, the revised design had lower bending stiffness near the tip, higher bending stiff- ness at inboard stations, and was somewhat heavier than the original design. A third design, which was not tested in the present investi- gation, was finally used in the airplane.
One model of the original design simulated the panel stiffness distributions which were calculated for the airplane at standard sea- Other models of both the original and level temperature conditions.
revised designs simulated the calculated airplane stiffness distribu- b tions for a reduced skin stiffness resulting from transient aero- The transient heating effects were calcu- dynamic heating (ref. 3 ) .
lated by the aircraft manufacturer for that part of the airplane flight path which gave the greatest stiffness reduction. This condition Later occurs during descent at a very high Mach number and altitude.
in the descent, as the Mach number approaches transonic values, the stiffnesses would tend to increase so that the present models may yield conservative results.
Semispan models were used in the investigation, and the models were flexibly mounted in a sting fuselage so as to simulate the pitch, roll, and yaw freedoms at the intersection of the pitch axis and panel root.
Tests were also made with higher levels of pitching stiffness at the panel root. The airplane-fuselage degrees of freedom were not simulated.
SYMBOLS b local streamwise semichord, ft average streamwise semichord of exposed panel, ft ba average streamwise semichord of streamwise s t r i p , f t bS E1 bending s t i f f n e s s , lb-ft2 f l u t t e r frequency, cps f f a G J st i f f ness, lb -f t 2 t o r s ional s t r u c t u r a l damping coefficient of first natural vibration mode g moment of i n e r t i a of streamwise s t r i p about lateral axis through IS s t r i p center of gravity, slug-ft2 moment of i n e r t i a of panel (including spindle) i n p i t c h about panel center of gravity, slug-ft moment of i n e r t i a of panel (including spindle) i n r o l l about panel center of gravity, slug-+' moment of i n e r t i a of panel (including spindle) i n yaw about panel center of gravity, slug-& simulated p i t c h s t i f f n e s s a t intersection of p i t c h axis and panel root, ft-lb/radian simulated r o l l s t i f f n e s s a t intersection of p i t c h axis and panel root, ft-lb/radian simulated yaw s t i f f n e s s at intersection of p i t c h a x i s and panel root, ft-lb/radian Typical model length length scale factor, Corresponding airplane length M Mach number Typical model mass m mass scale factor, Corresponding airplane mass m t mass of panel (including s p i n a e ) , slugs mass of streamwise s t r i p , slugs m, dynamic pressure, lb/sq f t span of panel, f t s t a t i c temperature, OR c time scale f a c t o r , Time f o r tunnel-airstream t o move 1 model t a i l chord length Time f o r airplane t o move 1 airplane t a i l chord length velocity, f-ps reduced velocity based on a representative natural frequency,
v
-
baui V volume of frustrum of cone enclosing t h e t a i l panel, cu f t longitudinal, lateral, and v e r t i c a l axes, respectively center-of-gravity location of streamwise s t r i p , percent l o c a l streamwise chord measured from leading edge center-of-gravity location of streamwise s t r i p , percent of span measured from panel root b width of streamwise s t r i p , f t nondimensional distance along reference axis, Distance from panel root along reference axis Length of exposed panel reference axis mass r a t i o , m'/pv s t a t i c a i r density, slugs/cu f t f l u t t e r frequency, 2fiff, radians/sec n a t u r a l frequency of i t h mode? radians/sec Subscripts : A airplane M model MODELS Configurations The model components, which w e r e supplied by t h e a i r c r a f t manufac- Seven model configu- turer, consisted of f i v e t a i l panels and t h e mount.
r a t i o n s w e r e investigated and are designated as follows: eo-96, HO-95, HO-99, HO-105, HO-137, HO-118, and HR-101. The code f o r these designa- "C" t i o n s i s as follows: ( f o r cold) indicates that t h e panel s t i f f n e s s e s simulated t h e calculated airplane values a t standard sea-level tempera- "H" ture, ( f o r hot) indicates t h a t the panel stiff'nesses simulated t h e calculated airplane values as affected by aerodynamic heating, "0" indi- c a t e s t h e o r i g i n a l design, "R" indicates t h e revised design, and t h e number following t h e dash gives t h e root p i t c h s t i f f n e s s i n percent of Model HO-lo5 was not t e s t e d but was used t o t h e scaled airplane value.
obtain f l e x i b i l i t y influence coefficients.
Geometry The semispan models were 1/12-size versions of t h e proposed hori- zontal t a i l panels f o r t h e airplane. A sketch of t h e models giving b a s i c dimensions i s shown i n figure 1, where t h e dimensions given were t h e same f o r a l l t h e models t o within fi.07 inch.
The models had a planform incorporating 45' sweepback of t h e quarter- a panel aspect r a t i o of 1.24, and a panel taper r a t i o of 0.3.
chord l i n e , The model had a 66~005 a i r f o i l section (manufacturer's designation), modified so t h a t it had a 1 percent 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 between t h e t r a i l i n g edge and 67 percent chord N e a r t h e t i p , t h e a i r f o i l w a s f u r t h e r modified (point of tangency).
A i r f o i l by increasing t h e thickness forward of t h e 15 percent chord.
ordinates are presented i n figure 1, and some model geometric properties are listed i n t a b l e I.
Scaling I n scaling t h e airplane properties it was required t h a t t h e non- dimensional mass and s t i f f n e s s d i s t r i b u t i o n s should be t h e same f o r The m a s s and s t i f f n e s s l e v e l s f o r t h e t h e model as f o r t h e airplane.
were obtained by specifying t h e scale f a c t o r s f o r t h e fundamental model q u a n t i t i e s involved: length, mass, and time.
The s i z e of t h e models w a s limited by tunnel-wall interference considerations, and on t h e b a s i s of previous experience, t h e length scale f a c t o r was chosen t o be 2 = - I 2 The mass scale f a c t o r was obtained from t h e requirement t h a t t h e mass r a t i o p be t h e same f o r both model and airplane. This gave The density r a t i o was chosen t o be %/PA = 1.275.
The time scale f a c t o r was derived from the requirement t h a t t h e
reduced v e l o c i t y v should be the same f o r t h e model as f o r t h e air-
plane. This gives
t = (@
Since t h e Mach number i s t h e same f o r both model and airplane, -112 t=(:) 2 The s t a t i c temperature f o r t h e airplane i s a function only of TA a l t i t u d e , and f o r sea-level a l t i t u d e TA was taken t o be 5 1 9 ' R. How- ever, during a tunnel run, t h e temperature drops continually as a i r i s expended f r o m t h e reservoir. A study of f l u t t e r data obtained previously indicated t h a t 4080 R was near t h e average value of TM t h a t could be expected during t h e present tests. These values of TM and TA were used i n equation (5); hence, 0.786 was used as t h e value of TM/TA.
The pertinent model and flow parameters and t h e design s c a l e f a c t o r s which apply t o them are l i s t e d i n t a b l e 11.
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 is not. If t h e dynamic pressure and Mach number are considered t o be fixed, and a s t a t i c temper- a t u r e d i f f e r e n t f r o m t h e design value i s obtained, both t h e density and t h e velocity w i l l be d i f f e r e n t from t h e values considered i n t h e scaling.
Of mass The density and velocity changes r e s u l t , respectively, i n values L r a t i o and reduced velocity d i f f e r e n t from the design values.
However, a combination of reduced velocity and mass r a t i o , which can be expressed i n terms of t h e dynamic pressure is independent of t h e temperature. This parameter i s simulated exactly i n the tests because t h e simulated a l t i t u d e i s interpreted i n terms of t h e dynamic pressure. Thus, the scale f a c t o r i n table I1 f o r dynamic pressure i s used t o convert t h e dynamic pressure f o r t h e airplane at any Mach number and a l t i t u d e t o t h e dynamic pressure f o r the model at t h e same Mach number and a l t i t u d e . The dynamic pressure f o r t h e air- plane i s assumed t o be that of t h e ICAO standard atmosphere (ref. 4 ) .
Note t h a t f o r 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 satisfying exactly t h e mass r a t i o and reduced velocity is believed t o be negligible i n the present investi- gation.
Experience w i t h a wide variety of f l u t t e r models has indicated 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, at l e a s t within t h e operational l i m i t s of t h e tunnel.
Panel Construction and Mounting A l l panels had aluminum box spar and r i b construction as seen i n A figure 2, which shows X-ray photographs of two of t h e t a i l panels.
photograph of a flutter-damaged panel which has had portions of the e x t e r i o r cut away t o expose the internal s t r u c t u r e is presented i n f i g - ure 3 . (Paint w a s applied at intervals along the leading edges of t h e models as shown i n f i g . 3 t o a i d i n observing the motion of t h e models The tapered spar was fabricated from two hollow during testing.)
Aluminum-alloy caps rectangular-cross-section pieces welded together.
which covered about one-fifth of t h e spar width were welded t o t h e out- s i d e of t h e spar at top and bottom and extended from the root t o about 40 percent of the panel span. A solid aluminum-alloy spindle having rectangular cross sections was welded i n s i d e t h e spar at the root and extended inboard of the root. The spindle ( f i g . 1) f o r model HR-101 w a s somewhat heavier than t h a t f o r the other models. Aluminum-alloy r o o t and t i p ribs were of rectangular cross sections and were welded t o the spar. Additional r i b s having channel cross sections were a l s o welded t o t h e spar w i t h t h e open s i d e s facing outboard. Leading and t r a i l i n g edges were made of pine, and balsa wood w a s used t o f i l l voids i n the air- f o i l shape. Small lead weights were glued i n t o t h e s t r u c t u r e at various
a
The e n t i r e outer surface points t o achieve the proper mass distribution.
of the panel was covered with lacquered silk.
The mounting system, 4, allowed f l e x i b i l i t y i n the shown i n figure pitch, roll, and yaw degrees of freedom. The t a i l panel was fastened t o two v e r t i c a l tongues extending from the steel base spring mount ( f i g . 4) by means of two screws through the spindle.
A steel stud threaded i n t o L one of t h e tongues was fastened at i t s other end t o a s t e e l cantilever beam, which was secured at i t s fixed end t o a steel mounting block. Both t h e base spring mount and t h e beam mounting block were fastened securely t o the fuselage mounting block, which was machined from s o l i d aluminum L a l l o y so t h a t it f a i r e d i n t o the 3-inch-diameter tunnel s t i n g fuselage.
The arrangement was such that the i n s t a l l a t i o n of cantilever beams having 0 different bending s t i f f n e s s e s would have a major effect on t h e root pitching s t i f f n e s s only. Provision was made f o r t h e use of a locking bar between t h e cantilever beam and t h e fuselage mounting block t o increase further t h e root pitching s t i f f n e s s .
Physical Properties Natural vibration modes.- The n a t u r a l vibration frequencies and node l i n e s were found by exciting the models with an electromagnetic shaker.
S a l t crystals sprinkled on t h e panel during resonant vibrations depicted the node l i n e s . The r e s u l t s obtained f o r t h e various configurations investigated are presented i n figure 5 . The frequencies are a l s o l i s t e d b i n table I11 where the predominant c h a r a c t e r i s t i c of each vibration mode i s indicated. I n addition t o the noted predominant c h a r a c t e r i s t i c s , pitching motion of the panel was a l s o evident i n the first, t h i r d , and fourth modes.
The average values of t h e 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 model from records of t h e decay of o s c i l l a t i o n s induced by plucking t h e model i n s t i l l air, are presented i n table 111.
Stiffnesses.- "he roll, pitch, and yaw s t i f f n e s s e s at t h e i n t e r s e c t i o n of t h e pitch axis w i t h the panel root were measured by means of an o p t i c a l system employing a cathetometer.
"he r e s u l t s are presented i n t a b l e 111.
The rolling s t i f f n e s s was measured only f o r model HR-101. The r o l l i n g stiffnesses f o r t h e other models, which were a l l of the o r i g i n a l design, were probably somewhat lower than f o r model HR-101 because of t h e i r more f l e x i b l e spindles ( f i g . 1) .
The bending and torsion s t i f f n e s s d i s t r i b u t i o n s along the span were .
a l s o measured f o r each panel by means of an o p t i c a l system which i s described i n reference 5 . The reference axis used f o r these measurements was approximately t h e 53-percent-chord l i n e .
The s t i f f n e s s d i s t r i b u t i o n s which w e r e obtained are presented i n figure 6.
F l e x i b i l i t y influence coefficients, which were measured on model HO-105, are presented i n t a b l e IV(a).
These c o e f f i c i e n t s are the results of t h e following measurements: (1) t r a n s l a t i o n deflections a t 12 s t a t i o n s on t h e panel ( f i g . 7) due t o loads applied a t these s t a t i o n s , (2) t r a n s l a t i o n a l d e f l e c t i o n s on t h e panel due t o pitching and r o l l i n g moments applied a t t h e root, and (3) pitch, r o l l , and yaw angular deflec- t i o n s a t the i n t e r s e c t i o n of t h e p i t c h axis and panel r o o t due t o loads applied t o t h e panel s t a t i o n s and due t o pitching, r o l l i n g , and yawing moments applied a t t h e root. The system employed t o measure t h e i n f l u - ence c o e f f i c i e n t s i s described i n t h e appendix.
The measured f l e x i b i l i t y influence c o e f f i c i e n t s given i n t a b l e N(a) were averaged across t h e diagonal of the matrix t o obtain t h e symmetrical matrix which i s presented i n t a b l e IV(b).
Mass properties.- The mass of each panel i s presented i n t a b l e 111.
The center-of-gravity location f o r one panel of t h e o r i g i n a l design i s shown i n figure 1; t h e center-of-gravity locations f o r t h e other panels of t h e o r i g i n a l design are believed t o be a t approximately t h e same location. The center-of-gravity location f o r t h e revised design panel is also presented i n figure 1. The moments of i n e r t i a i n r o l l , pitch, and yaw which were measured f o r some of t h e panels by means of a b i f i l a r pendulum are given i n table 111. Allmasses, moments of i n e r t i a , and center-of-gravity locations given i n t a b l e I11 and figure 1 w e r e meas- ured with t h e spindle attached t o t h e panel.
Mass d i s t r i b u t i o n data f o r a panel of t h e o r i g i n a l design and f o r a panel of t h e revised design are presented i n t a b l e s V ( a ) and V(b), respec- t i v e l y . The values f o r t h e original. design were obtained by sawing the panel of model HO-99 (which was repaired after f l u t t e r t e s t i n g ) i n t o These data have streamwise s t r i p s as shown i n t b e sketch i n t a b l e V ( a ) .
W s t of t h e data i n t a b l e V(b) been corrected f o r t h e mass l o s t i n sawing.
f o r t h e revised design w e r e supplied by t h e model manufacturer and w e r e obtained by sawing a panel similar t o t h a t of model HR-101 i n t o s t r i p s However, normal t o t h e 56.78-percent-chord l i n e as shown i n t a b l e V(b) .
t h e properties of t h e s t r i p numbered "1" and of t h e spindle w e r e m e a s - The t o t a l mass of t h i s com- ured on model HR-101 after f l u t t e r testing.
p o s i t e model given i n t a b l e V(b) is about 9 percent lower than that measured f o r model HR-101 as given i n t a b l e 111.
APPARATUS AND TESTS The f l u t t e r tests were made i n t h e Langley transonic blowdown tun- n e l which has a s l o t t e d t e s t section. The t e s t section i s octagonal i n cross section and measures 2 inches between sides. During operation % .
of the tunnel, a preselected Mach number i s set by means of a variable t e s t section, and this Mach number i s held o r i f i c e downstream of t h e approximately constant a f t e r t h e o r i f i c e i s choked w h i l e t h e stagnation pressure, and thus the density, i s increased. The static-density range L i s approximately 0.001 t o 0.012 slug per cubic foot, md Mach numbers 3 may be obtained with semispan models from subsonic values t o a m a x i m 0 value of about 1.45.
It should be noted t h a t , because of t h e expansion 9 of t h e a i r i n t h e reservoir during a run, t h e stagnation temperature con- t i n u a l l y decreases, and thus t h e test-section velocity i s not uniquely defined by the Mach number. Additional details of t h e tunnel are con- tained in reference 6. Excellent agreement between f l u t t e r data obtained i n t h e tunnel and i n f r e e air has been observed (ref. 7 ) .
I n t h e present f l u t t e r tests, t h e fuselage mounting block shown i n figure 4 was f i t t e d i n t o a s t i n g i n such a way that t h e munting block and sting formed a 3-inch-diameter fuselage which extended upstream i n t o t h e subsonic f l o w region of t h e tunnel.
This arrangement prevented t h e formation of shock waves off t h e fuselage nose wfiich might r e f l e c t from the tunnel walls onto t h e model.
The s t i n g and model weighed approxi- mately 290 pounds, and t h e system had a fundamental bending frequency of about 15 cycles per second.
Wire s t r a i n gages were mounted on t h e panel spar near t h e root as sketched i n figure 1 and were oriented so a s t o i n d i c a t e panel deflec- t i o n s about two d i f f e r e n t axes. S t r a i n gages were a l s o attached t o t h e cantilever beam ( f i g . 4 ) i n the mount t o i n d i c a t e pitching motions Of t h e model.
The strain-gage signals, t h e tunnel stagnation and s t a t i c pressures, and t h e stagnation temperature w e r e recorded by a recording oscillograph.
The strain-gage t r a c e s on t h e oscillograph records w e r e used t o i d e n t i f y the start of f l u t t e r and t o obtain t h e f l u t t e r frequency. I n t h e present investigation t h e starts of f l u t t e r o s c i l l a t i o n s were very abrupt and d e f i n i t e on t h e oscillograph records. High-speed motion p i c t u r e s were The made during a l l runs and w e r e used i n observing t h e f l u t t e r mode.
models were t e s t e d a t Mach numbers from 0.79 t o 1.47 and a t simulated a l t i t u d e s from below sea l e v e l up t o about 10,000 f e e t .
RESULTS AND DISCUSSION The data obtained i n t h e 21 runs of the investigation a r e summarized i n t a b l e V I .
The data from a l l the runs are p l o t t e d i n f i g u r e s 8 t o 1 2 i n t h e form of dynamic pressure as a function of Mach number. The margin- of-safety requirement was such that a s a t i s f a c t o r y horizontal t a i l f o r t h e airplane would be f l u t t e r f r e e a t dynamic pressures up t o 32 percent higher than those f o r sea-level a l t i t u d e . Thus, i f the models a r e assumed t o represent the proposed airplane tail designs i n a l l important respects, t h e models would d e m n s t r a t e an adequate margin of safety f o r t h e a i r p l a n e i f they were f l u t t e r free a t dynamic pressures up t o 32 percent higher than those f o r simulated sea level. Curves indicating a simulated alti- tude of 5,000 f e e t , simulated sea-level a l t i t u d e , and dynamic pressures 32 percent higher than simulated sea l e v e l are shown i n figures 8 t o 12.
Model CO-96 demonstrated an adequate f l u t t e r safety margin a t Mach numbers up t o 1.44 as i s shown i n figure 8. F l u t t e r was obtained a t a Mach number of 1 . 4 4 a t a dynamic pressure above t h e f l u t t e r safety margin.
The f l u t t e r mode, observed by means of t h e motion p i c t u r e s taken during the runs, involved bending, torsion, and pitching motion of t h e panel.
" h i s was a l s o shown by oscillograph records of the output of t h e s t r a i n gages on the cantilever beam i n t h e mount. The onset of f l u t t e r was sudden and t h e o s c i l l a t i o n amplitude diverged rapidly. The model f a i l e d after a f e w cycles. Although t h e start of f l u t t e r was d e f i n i t e , motion p i c t u r e s and oscillograph records of the strain-gage signals indicated t h a t t h e model exhibited pitching and yawing motions during all runs and These o s c i l l a t i o n s may be a function of before t h e start of f l u t t e r .
the air turbulence and since t h e turbulence i n the tunnel i s d i f f e r e n t from that i n the atmosphere, it is not known w h a t significance t h e model o s c i l l a t i o n s have i n regard t o the airplane.
A s shown i n f i g u r e 9, models HO-95 and HO-99 had an adequate f l u t - A t higher Mach numbers, ter s a f e t y margin at Mach numbers up t o 1.14.
however, these models displayed an inadequate safety margin. F l u t t e r was obtained on model HO-99 a t a Mach number of 1.14 and on model HO-95 a t a Mach number of 1.42. The f l u t t e r mode and general behavior of these It should be noted that, as models were similar t o those of model CO-96.
mentioned previously, t h e chosen s t i f f n e s s reduction due t o aerodynamic i s heating which t h e high-temperature models were designed t o simulate probably more severe than would be encountered at t h e Mach numbers of t h e present investigation; thus, t h e model r e s u l t s may be conservative.
Inasmuch as t h e f l u t t e r mode observed f o r models CO-96, HO-95, and HO-99 included a s i g n i f i c a n t amount o f p i t c h deflection, i n order t o obtain a configuration f o r the high-temperature models of t h e o r i g i n a l h o r i z o n t a l t a i l design which would be f l u t t e r free over the Mach number t h e e f f e c t of increased r o o t pitching s t i f f n e s s was range of t h e tests, investigated. Models HO-137 and HO-118 had values of root pitching s t i f f - ness of 137 percent and 118 percent of t h e scaled airplane value, respec- t i v e l y , with about t h e same values of root yaw s t i f f n e s s as t h e previous models (table 111). These models demonstrated an adequate f l u t t e r s a f e t y
margin a t Mach numbers up t o 1.47 ( f i g s . 10 and ll), and no f l u t t e r was
encountered a t dynamic pressures higher than t h e safety margin. It would therefore appear t h a t a moderate increase i n t h e p i t c h s t i f f n e s s ( l e s s than 20 percent o f t h e design value) would serve t o eliminate t h e f l u t t e r encountered f o r t h e high-temperature models of t h e o r i g i n a l design a t Mach numbers near 1.4. The motion p i c t u r e s taken during t h e tests of models HO-137 and HO-118 (which did not f l u t t e r as shown i n f i g s . 10 and 11) indicated t h a t t h e pitching and yawing o s c i l l a t i o n s were of lower amplitude than those noted before f l u t t e r i n the tests of t h e pre- ( vious configurations ( f i g s . 8 and 9).
Model HR-101 had an adequate f l u t t e r safety margin a t Mach numbers up t o 1.12 but had an inadequate safety margin a t higher Mach numbers ( f i g . 1 2 ) . F l u t t e r was encountered f o r t h i s model a t a Mach number of 1.42, and t h e f l u t t e r mode and model behavior w e r e t h e same as those described previously f o r model CO-96. The s i m i l a r i t y of f l u t t e r behavior of this model t o t h a t of t h e models of t h e o r i g i n a l design suggests t h a t an increase i n the root pitching s t i f f n e s s might a l s o be b e n e f i c i a l f o r the revised design.
c ONCLUS I O N s
A transonic f l u t t e r investigation has been made of dynamically and c e l a s t i c a l l y scaled models of the o r i g i n a l design and of a revised design The results f o r t h e all-movable horizontal t a i l of t h e X-15 airplane.
of t h e investigation supplied t h e following conclusions: 1. "he standard-temperature model of t h e o r i g i n a l design had an adequate f l u t t e r safety margin (i.e., t h e model was f l u t t e r f r e e a t dynamic pressures up t o 32 percent higher than those f o r simulated sea- l e v e l conditions) at Mach numbers up t o 1.44.
2. Models which simulated t h e calculated e f f e c t s of aerodynamic heating f o r both designs had adequate f l u t t e r s a f e t y margins a t Mach 1.1 but had inadequate safety margins a t higher numbers up t o about Mach numbers. However, t h e simulated design heating condition was probably more severe than would be encountered a t t h e Mach numbers of the present investigation so that t h e model results may have been conservative.
0 0 . 0 .
. m 0 . 0 0 0 0 0 0 .
3 . A n increase i n t h e pitching s t i f f h e s s at the panel r o o t f o r a high-temperature model of the o r i g i n a l design t o 118 percent of t h e scaled airplane design value produced a configuration which had an adequate f l u t t e r safety margin at Mach nunibers up t o about 1.G.
Langley Research Center, National Aeronautics and Space Administration, Langley Field, Va., October 20, 1960.
APPENDIX M E A - OF FLMIBILITY I " C E COEFFICIENTS L A photograph of the system employed t o measure t h e t r a n s l a t i o n a l deflections of the panel i s shown i n figure 13. Twelve d i f f e r e n t i a l transformers were mounted above t h e model so t h a t probes attached t o t h e i r internal, s l i d i n g slugs r e s t e d on t h e influence c o e f f i c i e n t sta- tions. The readout device contains a d i f f e r e n t i a l transformer which L can be connected t o any one of t h e transformers above t h e model and which d e f l e c t s an o p t i c a l s c a l e as it responds t o changes i n t h e mag- 0 n e t i c flux i n the transformer on t h e model induced by deflection of the model.
The output from a d i f f e r e n t i a l transformer i s affected by t h e proximity of ferromagnetic material, so t h a t it was necessary t o c a l i - b r a t e each transformer while it was i n the same environment as during t h e measurement.
The transformers were therefore arranged i n t h e loca- t i o n s they would have on the model (positions shown i n f i g . 7), and each transformer was deflected incrementally by means of a micrometer t o obtain a f a c t o r t o convert scale readings f o r t h a t transformer i n t o inches of deflection. Variations i n the scale deflection readings f o r a range of known deflections of t h e micrometer were used t o estimate t h e accuracy, l i n e a r i t y , and r e p e a t a b i l i t y of t h e instrument readings.
After calibration, the model was i n s e r t e d and t h e undeflected scale was recorded. A reading f o r each of t h e transformers above t h e model load was applied t o t h e model- and the deflected scale readings of t h e transformers were recorded.
An o p t i c a l system employing t w o theodolites was used t o measure t h e angular deflections a t t h e i n t e r s e c t i o n of t h e p i t c h a x i s with t h e panel root. Two small mirrors were mounted a t t h e i n t e r s e c t i o n oriented normal t o each other as i n figure 7 so t h a t pitching, yawing, and r o l l i n g angular deflections could be measured.
Loads were applied t o t h e panel by means of a l e v e r arm and s t r i n g s and pulleys.
The c h a r a c t e r i s t i c s of t h e system were such t h a t t r a n s l a - t i o n a l deflections f o r the yaw loading could not be read.
The t r a n s l a t i o n a l and r o t a t i o n a l deflection readings were converted i n t o deflection ( i n feet o r r a d i a n s ) per u n i t load t o obtain the values i n table I V ( a ) . Note t h a t t h e angular deflections measured f o r each c unit load on the panel have t h e dimension radians per pound and t h a t t h e t r a n s l a t i o n a l deflections measured f o r t h e u n i t pitching and r o l l i n g moments have t h e dimension foot p e r foot-pound; these measurements are
labeled "semiangular influence coefficients ."
The matrix of angular influence c o e f f i c i e n t s has the dimensions radians per foot-pound. The p i t c h deflection f o r an applied pitching moment i n table IV gives a value of pitching s t i f f n e s s which agrees t o within 0.4 percent with the value given i n t a b l e III measured f o r t h e same model (HO-105) by means of t h e cathetometer system.
The calculated maximum e r r o r of the instrument used t o measure t h e t r a n s l a t i o n a l influence coefficients, obtained * o m the c a l i b r a t i o n d a t a and checking of t h e weights used, varies according t o the s i z e of t h e d e f l e c t i o n between f0.12 X 10-5 f t / l b and f3.2 x 10-5 f t / l b . The calcu- l a t e d maximum e r r o r of t h e semiangular influence c o e f f i c i e n t s measured this instrument v a r i e s according t o the s i z e of the deflection with
between fall X 10-5 per pound and f3.2 X 10-5 per pound. The best
indication of t h e o v e r a l l accuracy of t h e measurements i s obtained from t h e symmetrization of t h e matrix of table IV(a) i n t o t h e matrix of t a b l e IV(b). The symmetrical matrix in table Iv(b) was obtained by averaging t h e corresponding off-diagonal elements of t h e o r i g i n a l matrix.
semi- O f t h e off-diagonal elements measured, not including t h e angular or 83 percent a r e within +3 percent of t h e angular influence coefficients, averaged values, 95 percent are within k 5 peircent of the averaged values, and t h e remaining 5 percent are w i t h i n f10 percent of t h e averaged values.
The off-diagonal elements of t h e angular and semiangular influence coef- f i c i e n t s are i n somewhat poorer agreement.
REFERENCES 1. Lauten, W i l l i a m T., Jr., and Hess, Robert W. : Ekperimental and Calculated Supersonic F l u t t e r Characteristics of Models of the X - 1 5 Horizontal and Vertical T a i l s .
NASA T M x-176, 1959.
2. Lauten, W i l l i a m T., Jr., Levey, Gilbert M . , and Armstrong, W i l l i a m 0 . : Investigation of an All-Movable Control Surface a t a Mach Number of 6.86 f o r Possible F l u t t e r . NACA RM L58B27, 1958.
L 3 . Landrum, L. L.: Estimated Aeroelastic Characteristics f o r t h e X - 1 5 Airplane (NAA Model Designation NA-240).
Rep. No. NA-59-471, 0 North American Aviation, Inc., Apr. 16, 1959.
4. Anon.: Standard Atmosphere - Tables and Data f o r Altitudes t o
65,800 Feet. NACA Rep. 1235, 1955. (Supersedes NACA TN 3182.)
5. Land, Norman S., and Abbott, Frank T., Jr.: Method of Controlling Stiffness Properties of a Solid-Construction Model Wing. NACA TN 3423, 1955- 6 . Unangst, John R., and Jones, George W., Jr.: Some Effects of Sweep and Aspect Ratio on t h e Transonic Flutter Characteristics of a Series of Thin Cantilever Wings Having a Taper Ratio of 0.6. NACA
RM L55113a, 1956. *
7. Bursnall, W i l l i a m J.: I n i t i a l F l u t t e r Tests i n the Langley Transonic Blowdown Tunnel and Comparison With Free-Flight F l u t t e r Results.
NACA RM L52KL4, 1953.
F
....... ...............
. . . . . . . . . . . . . . . .
.
TABLE I . - GEOMETRIC PROPERTIES OF MODELS
Streamwise airfoil section . . . . . . . . . . . . . . . Modified 6 6 ~ 0 0 5
Sweepback of quarter-chord line. deg . . . . . . . . . . . . . . . 45
Panel span. ft . . . . . . . . . . . . . . . . . . . . . . . . . . 0 . 4 7 3
Streamwise panel root chord. ft . . . . . . . . . . . . . . . . . 0.588
Panel area. sq ft . . . . . . . . . . . . . . . . . . . . . . . . 0 . 1 8 1
Panel aspect ratio . . . . . . . . . . . . . . . . . . . . . . . . 1.24
Panel taper ratio . . . . . . . . . . . . . . . . . . . . . . . . 0.30
Fuselage diameter. ft . . . . . . . . . . . . . . . . . . . . . . 0.250
Gap between panel root and fuselage. ft . . . . . . . . . . . . . 0 . 0 0 7
Pianform semispan. ft . . . . . . . . . . . . . . . . . . . . . . 0 . 6 0 5
Maximum streamwise chord based on extension of panel
to fuselage center line. ft . . . . . . . . . . . . . . . . . . 0 . 7 0 3
Planf'orm area based on extension of panel to fuselage
center line. sq ft . . . . . . . . . . . . . . . . . . . . . . . 0.532
Phnform aspect ratio based on extension of panel to
fuselage center line . . . . . . . . . . . . . . . . . . . . . . 2.752
Planform taper ratio based on extension of panel to
f'uselage center line . . . . . . . . . . . . . . . . . . . . . . 0.25
e a a a e a + a a a a * a a a a a a a a a e a a a a a a a e a a * M: a a a a a a e a a a a a a a e a a a a a a e a a a TABLE 11.- DESIGN SCALE FACTORS OF P E R T I " MODEL AND FLOW QUANTITIES c- Design scale factor Quantity Symbolical Numerical Fundamental quantities .1
Length . . . . . . . . . . . . . . 2 1/12
Mass . . . . . . . . . . . . . . . m = ( $ ) Z 3 7.378 x
Time . . . . . . . . . . . . . . . t = (%)-1'2z 9.400 x
TA
-
Derived quantities
+ 0.887
Stream velocity . . . . . . . . . .
1.002 1
Stream dynamic pressure . . . . . .
5.124 x Moment of i n e r t i a . . . . . . . . .
5.799 x 10-4 22mt-2 k e , k $ , k q . . . . . . . . . . . .
0.483 x
E 1 and GJ . . . . . . . . . . . . . 23mt-2
Flexibility influence coefficients: 11.98 Translational . . . . . . . . . .
143 9 7 Semiangular . . . . . . . . . . .
1,725 Angular . . . . . . . . . . . . .
Natural vibration frequency . . . . t-1 10.64
N I I I I I I R \ I I I I I I I
I I I I I t g I
I I : i I I I I I I I I 1 4 P a' f 4 m
21 B
Sa
* v *
f!L
21 P
rl N nzt n w t-Q m o 4 3 2 Ln n a P d '?
4 N nf n w t-m m o rl N 4 4 4 w w w w n n I P-t-t-t-aJcc I 9 9 9 9 9 9 ; 0 I .
a d
4 cu 03 m w a
x R
t - -
0 I I I 0 I rl X r l N z ' c \ t - I f?????
I I \D a d & .
I ~- ~~~ . . . . . . . . . . . . . . . . . . . . .
t
u C U t , k z c .
! 3 P; m M CO d M
s" 3 8 f
I -P vi .
0 . 0.. . . . 0.. . 0.0 0 .
0 . 0 . 0 .
. 0 . . 0 . . .
0 . 0 . 0 .
. . . 0.. 0 .
c n I K\
A
Figure 1.- Sketch of panel. A l l dimensions are i n inches.
h c d
Y
x I X t: w \D I - a n "1I C E a a,
+
rn a, +J rn d d d: I c n k rt\ I k I4 m m 0 P a a c d m Y d cd 4 0 I O o m rn e m a, a I a 0
A '1
A0 VI m .i Y m F .
f: u) m I In .
0 .8 . 9 1.0 .1 .2 . 3 .4 .5 .6 . 7 11 a l o n g reference u l a
.-
( a ) Model CO-96.
,ions 'e 6.- Measured panel bending and t o r s i o n s t i f f n e s s d i s t r i b u t compared w i t h scaled airplane s t i f f n e s s d i s t r i b u t i o n s .
t , . - .. ... . .
... ...
.... . .
... . . .. ..
.
.. ... . 0 ......
1 along reference axis (b) Models of o r i g i n a l design which simulated e f f e c t s of aerodynamic heating.
Figure 6.- Continued.
e e.. e.
e. e.. . e.. e. e. .
e e . . 0 . . e . .
e . * . e .
. . . e e . . e . . . e . e .
. . e .
. e e . e . .
e. e.. e.
32 e. e.. . .
0 J, lb-ft'
t ; '
4 0 w \o E L lb-f t2 . 1 .2 . 3 .4 .5 .6 .7 .d .9 1 . 0 q alonr rere-nctt a x i s (c) Model HR-101.
Figure 6.- Concluded.
3 F
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 - 0
0 0 0 0 0 0 0 0
\
'\
c
\
I 4-99 t n K i r r or I d !
\
\
'i
I - 2 . 2 6 5 - 3 - 1 7 5 Figure 7.- Sketch of panel showing streamwise strips and influence A l l dimensions are in inches. Circled coefficient stations.
numbers indicate stations at which influence coefficients were measured.
0 Start of f l u t t e r 0 M a x i m u m q, no f l u t t e r .8 .9 1.0 1.1 1.2 M Figure 8.- Flutter characteristics of model C O - 9 6 .
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 35 4,800 4 . 4 0 0 4,000 3,600 3 . 2 0 0 2,800 98 ldsq ft 2.400 2,000 1,600 1,200 8W 40C C Figure 9.- Flutter characteristics of models HO-95 and HO-99.
YJlllllrrr
. . . . . . . . . . . . . . . . ............... .......
0 . 0 0 . 0 . 0 i - o ..... ...
0 . 0 . ....... ......
4,800 ?- a 2,800 2,000 1,600 1,200 L O O ,8 . 9 1 . 0 1 . 1 1 . 2 1 . 3 1, M Figure 10.- Flutter characteristics of model HO-137.
c
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 O 0 O 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 . ..
e o ::. : - 0 . 37
0 0 0 0 0.
. 8 -9 1 . 0 1 . 1 1 . 2 1 . 5 Y Figure 11.- F l u t t e r c h a r a c t e r i s t i c s of model HO-118.
L,,dOO 4,000 5,600 t;' w \o 2,300 ./sq ft 2,400 2,000 1,600 1,200 -7 .8 .v 1 . 0 1 . 1 1 . 2 1.3 1 . 4 1 . 5 M Figure 12.- Flutter characteristics of model HR-101.
"
ii (D
P w I M rt m P Ep