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F-15 FLIGHT FLUTTER TEST PROG Henry Katz, Francis 6, Foppe, and Daniel T. Grossrnan McDonnell A i r c r a f t Company ABSTRACT The F-15 f l i g h t f l u t t e r test program is described. S p e c i a l emphasis is given t o test philosophy, d a t a reduction techniques, and test r e s u l t s . The approach u t i l i z e d f o r t h i s program n o t only provided t h e d a t a necessary t o e s t a b l i s h a measure of s t a b i l i t y f o r all” important f l u t t e r mechanisms a t each test p o i n t , b u t a l s o allowed e x t r a p o l a t i o n of t h e data t o a c t u a l l y d e f i n e a l l c r i t i c a l f l u t t e r boundaries. Such q u a n t i t a t i v e information w a s not only use- f u l t o d e f i n i t i v e l y e s t a b l i s h t h e f l u t t e r s t a t u s of t h e a i r c r a f t as it w a s flown, but a l s o provided a s o l i d foundation f o r a s s e s s i n g t h e impact of any f u t u r e design changes.
INTRODUCTION With very few exceptions, f l i g h t f l u t t e r t e s t i n g has h i s t o r i c a l l y been conducted on a r a t h e r q u a l i t a t i v e b a s i s ; t h a t is, t h e only d a t a obtained w e r e t h e damping a v a i l a b l e a t the test p o i n t being flown, with a p o s s i b l e extrapo- There generally w a s no l a t i o n of damping trends of t h e lower damped-modes.
q u a n t i t a t i v e i n d i c a t i o n as t o t h e amount of s t a b i l i t y remaining a t any given point.
f l i g h t f l u t t e r test program w a s t o provide a The goal set f o r t h e F-15 quickly, and with a high degree of v i s i - system which would - accurately, b i l i t y - allow e x t r a p o l a t i o n of t h e d a t a t o a c t u a l l y d e f i n e critical f l u t t e r boundaries, i n a d d i t i o n t o providing a measure of s t a b i l i t y f o r - a l l t h e important mechanisms at each test point. This w a s accomplished by designing t h e a i r c r a f t e x c i t a t i o n and instrumentation systems t o provide high-quality response d a t a which could be s p e e d i l y and a c c u r a t e l y converted t o complete (i.e.$ concerning a l l modes of i n t e r e s t ) damping and frequency information which - i n turn - could be u t i l i z e d f o r r e l i a b l e f l u t t e r margin p r e d i c t i o n s The accuracy and r e l i a b i l i t y of these f l i g h t by t h e methods of Reference 1.
f l u t t e r test system d a t a not only permitted t h e p u r s u i t of a minimum f l u t t e r through
margin design concept (and with it optimum weight - see Reference 2)
i n f l i g h t v e r i f i c a t i o n of a c t u a l f l u t t e r margins of s a f e t y , b u t a l s o provided a q u a n t i t a t i v e b a s i s on which t o quickly assess t h e impact of f u t u r e design changes.
test philosophy, d a t a reduction This paper concerns i t s e l f primarily with techniques and systems, and test r e s u l t s . A i r c r a f t systems and test opera- t i o n s are covered i n Reference 3.
ABBREVIATIONS AND SYMBOLS CRT cathode ray tube s t r u c t u r a l damping c o e f f i c i e n t H p r e s s u r e a l t i t u d e , c a l i b r a t e d PC I m imaginary p a r t of t r a n s f e r f u n c t i o n a t frequency w KEAS knots e q d v a l e n t airspeed left-hand s i d e M Mach number NBFM narrow band frequency modulation PCM p u l s e code modulation dynamic p r e s s u r e Q R e real p a r t of t r a n s f e r f u n c t i o n a t frequency w right-hand s i d e temperature a t a l t i t u d e T~~ T-plot t r a n s m i s s i b i l i t y p l o t equivalent a i r s p e e d vE t r u e airspeed vT r a t i o of s t r u c t u r a l mass t o aerodynamic mass lJ d e n s i t y a t a l t i t u d e w frequency w n a t u r a l frequency n APPROACH The q u a n t i t a t i v e d e f i n i t i o n of F-15 f l u t t e r boundaries from f l i g h t test d a t a w a s accomplished by means of t h e F l u t t e r Margin technique of Reference 1.
This technique permits r e l i a b l e p r e d i c t i o n of f l u t t e r speeds on t h e b a s i s of s u b c r i t i c a l test data. Its a p p l i c a t i o n r e q u i r e s knowledge - a t every test frequency of every mode involved i n p o t e n t i a l l y c r i t i c a l
point - of damping
f l u t t e r mechanisms. This complete damping and frequency information w a s ob- tained from a unique d a t a reduction f a c i l i t y o p e r a t i n g on t h e a i r c r a f t d a t a provided by the exciter and instrumentation systems described i n d e t a i l i n Reference 3 .
The method of Reference 1 assumes t h a t d a t a is obtained a t d i f f e r e n t vel- o c i t i e s while maintaining t h e same aerodynamic c e n t e r and l i f t curve s l o p e s .
S t r i c t l y speaking, i t is t h e r e f o r e v a l i d only when Mach number is kept con- s t a n t . The emphasis i n t h i s program w a s , t h e r e f o r e , t o o b t a i n constant Mach number c r o s s s e c t i o n s which could be u t i l i z e d f o r e x t r a p o l a t i o n of t h e d a t a t o projected f l u t t e r boundaries. M = 0.80 w a s s e l e c t e d as one of t h e primary Mach number c r o s s s e c t i o n s t o o b t a i n a high subsonic e x t r a p o l a t i o n p o i n t f o r r e f e r - ence and f o r c o r r e l a t i o n with subsonic analyses and wind tunnel tests. AnotBer primary c r o s s s e c t i o n w a s taken a t M = 1 . 2 , t h e F-15 sea-level design Mach number. Additional Mach numbers a t which cross s e c t i o n s w e r e taken were selected on t h e b a s i s of analyses, wind tunnel tests, and t h e e a r l y p o r t i o n of t h e test program, which w a s dedicated t o determining critical Mach numbers by obtaining test d a t a from 0.73 t o 1.5 Mach numbers while maintaining a constant dynamic pressure (442 KEAS). The d a t a obtained a t t h i s constant dynamic pres- s u r e w e r e then reduced i n terms of t h e F l u t t e r Margin parameter t o a i d i n sel- e c t i n g c r i t i c a l Mach numbers f o r t h e various c r i t i c a l f l u t t e r mechanisms.
Figure 1 shows F l u t t e r Margin as a function of Mach number f o r one of t h e critical f l u t t e r mechanisms: antisymmetric boom t o r s i o n v e r s u s s t a b i l a t o r B a s i c a l l y , a subsonic and a supersonic l e v e l can be observed - with r o t a t i o n .
some secondary a l t i t u d e (or 11) e f f e c t s . The h i g h e s t Mach number a t which t h e lower subsonic level occurs i s j u s t s l i g h t l y above M = 0.9. Based on such data, and similar r e s u l t s f o r o t h e r modes, M = . 9 3 and M = 1.1 were s e l e c t e d as a d d i t i o n a l primary Mach numbers and 'a cross . s e c t i o n with t h r e e o r more f l i g h t test p o i n t s w a s taken a t t h e s e points.. Secondary Mach numbers of 0.98, 1.04, and 1.15 (with only two f l i g h t test p o i n t s ) w e r e s e l e c t e d t o provide intermediate checks a t a minimum c o s t i n t e r m s of f l i g h t s required.
A t y p i c a l f l u t t e r p r e d i c t i o n a t a critical Mach number is shown i n Figure 2. It should be noted t h a t t h e e x t r a p o l a t i o n is made on t h e b a s i s of a para- bola through t h e f l i g h t test p o i n t s and t h e zero airspeed p o i n t . Wind tunnel test d a t a have shown t h a t t h e a c t u a l f l u t t e r speed w i l l be o f f s e t s l i g h t l y from t h e p a r a b o l i c e x t r a p o l a t i o n toward a point obtained by a s t r a i g h t - l i n e extra- p o l a t i o n through ,the i n f l i g h t test p o i n t s alone. Thus, when t h e parabola is convex (curving toward t h e a b c i s s a ) , t h e r e s u l t s w i l l be s l i g h t l y conservative, and t h e parabola w i l l be used t o e s t a b l i s h t h e f l u t t e r boundary. I n t h e case of a concave parabola, t h e s t r a i g h t - l i n e e x t r a p o l a t i o n w i l l be more conserva- t i v e and should t h e r e f o r e receive more consideration.
Although, i n its strictest sense, the p r e d i c t i o n method is i n v a l i d f o r constant a l t i t u d e d a t a , secondary e x t r a p o l a t i o n s w e r e made a t constant a l t i - tudes of 1525 and 10 400 m (5000 and 34 000 f t ) by taking advantage of t h e f a c t t h a t , once supersonic flow i s e s t a b l i s h e d , the aerodynamic c e n t e r and l i f t curve s l o p e are a g a i n q u i t e w e l l behaved. An example of a constant a l t i t u d e e x t r a p o l a t i o n is shown i n Figure 3 .
Figure 4 shows t h e p o i n t s at which f l i g h t f l u t t e r d a t a were taken and a l s o i n d i c a t e s t h e d i r e c t i o n of t h e e x t r a p o l a t i o n s , EXCITER SYSTEM 3, f u r n i s h e s The a i r c r a f t e x c i t e r system, described ;In d e t a i l i n Reference t h e known f o r c i n g function t o which a i r c r a f t response can be measured. It has t h e c a p a b i l i t y t o o s c i l l a t e e i t h e r the s t a b i l a t o r s o r t h e a i l e r o n s . E i t h e r set of c o n t r o l s u r f a c e s can be e x c i t e d symmetrically (in-phase) o r antisymmetrically (out-of-phase). E x c i t a t i o n can be provided either i n t h e form of sweeps (slowly varying frequency through a given range) o r dwells/decays ( e x c i t a t i o n a t a given frequency f o r a c e r t a i n s h o r t t i m e , followed by an abrupt e x c i t e r shut-off).
INSTRUMENTATION SYSTEM A s described i n Reference 3, the a i r c r a f t instrumentation system c o n s i s t s primarily of s t r a i n gages, which provide n o t only t h e d e s i r e d response charac- t e r i s t i c s b u t a l s o permit r e l a t i v e l y independent measurement of t h e modes of i n t e r e s t . This is important, s i n c e it i s d e s i r e d t o s e p a r a t e t h e response i n t h e various modes, e s p e c i a l l y when these modes are c l o s e t o each o t h e r i n fre- quency. Figure 5 shows t h e sensor l o c a t i o n s on t h e a i r c r a f t and a l s o denotes t h e primary degree of freedom t o be measured by each.
DATA SYSTEM The h e a r t of the F-15 f l i g h t f l u t t e r test system is t h e d a t a handling system, It reduces the information provided by a i r c r a f t instrumentation i n response t o t h e forcing f u n c t i o n furnished by t h e a i r c r a f t e x c i t e r system t o several forms u s e f u l t o t h e f l u t t e r engineer.
The F-15 d a t a system can be divided i n t o two p a r t s : a. The on-line system, which a i d s i n t h e assessment of s t a b i l i t y a t t h e test p o i n t being flown a t t h e t i m e ; and b. The p o s t - f l i g h t system, which provides a complete e v a l u a t i o n of a l l t h e d a t a a v a i l a b l e t o a i d i n a r r i v i n g a t damping and F l u t t e r Margin t r e n d s so as t o e s t a b l i s h t h e f l u t t e r s a f e t y of t h e next p o i n t ( s ) t o be flown and a l s o t o e x t r a p o l a t e t o predicted f l u t t e r boundaries.
On-Line Data System This p o r t i o n of t h e d a t a system provides real-time information as t o t h e s t a b i l i t y of t h e a i r c r a f t a t t h e point(s) being flown. It is schematically represented i n Figure 6. A s can be seen, it involves a mixture of conventional d i s p l a y s ( s t r i p r e c o r d e r s and L i s s a j o u s f i g u r e s ) and less conventional informa- i n t h e form of d i g i t a l l y computed t r a n s m i s s i b i l i t y p l o t s , t i o n S t r i p c h a r t recorders Thirty-two channels of narrow band frequency modulated (NBFM) d a t a are displayed on four s t r i p c h a r t recorders. These channels p r e s e n t t h e output of s t r a i n gages t o d e s c r i b e a i r c r a f t response and f o r c i n g functions. The channels are arranged so t h a t components of c r i t i c a l f l u t t e r mechanisms ( f o r example, boom lateral bending and f i n bending) are side-by-side t o enable close monitor- ing f o r t h e development of any c o r r e l k t i o n between these degrees of freedom.
The d a t a displayed on t h e recorders perform t h e following functions: a.
Allow observation of any c o r r e l a t i o n between any two degrees of free- dom during a c c e l e r a t i o n i n t o an unexplored f l i g h t regime. Such corre- l a t i o n could i n d i c a t e t h e approach t o an i n s t a b i l i t y .
real-time determination of critical modal frequencies during b. Permit turbulence e x c i t a t i o n .
c . Obtain t h e damping of modes of i n t e r e s t whenever dwell/decay e x c i t a - is u t i l i z e d .
t i o n a frequency sweep.
d , I n d i c a t e t h e frequencies of maximum response during e. Monitor t h e q u a l i t y of t h e forcing f u n c t i o n during sweeps.
f . Allow observation of t h e level of turbulence, t o determine i f acqui- s i t i o n of e x c i t a t i o n response data is f e a s i b l e .
Lissajous d i s p l a y s Four Lissajous f i g u r e s each are displayed on four oscilloscopes. The p a i r s are chosen t o provide m a x i m u m information on t h e s t a b i l i t y of p o t e n t i a l f l u t t e r mechanisms. This is accomplished by "beating" t h e s i g n a l s from two gages, e.g. from boom lateral bending and f i n bending, a g a i n s t each o t h e r . The s i g n a l from any of t h e thirty-two N B F M channels can be s e l e c t e d f o r e i t h e r axis of any of the sixteen Lissajous f i g u r e s . These f i g u r e s are used t o observe t h e phase and frequency r e l a t i o n s h i p between important modal p a i r s during accelera- t i o n i n t o an unexplored f l i g h t regime, and are a l s o used t o observe t h e f r e - quency dependence of amplitude and phase during sweeps.
T r a n s m i s s i b i l i t y p l o t s T r a n s m i s s i b i l i t y p l o t s are obtained by normalizing response parameters t o e.g. s t a b i l a t o r hinge a parameter which is a measure of t h e forcing function, are o s c i l l a t e d . These p l o t s are computed from moment when t h e s t a b i l a t o r s d i g i t i z e d a i r c r a f t response d a t a and present amplitude and phase information as 7 shows a t y p i c a l t r a n s m i s s i b i l i t y p l o t .
a function of frequency. Figure One real-time t r a n s m i s s i b i l i t y p t (T-plot) f o r a se ata channel t is used t o is displayed on a cathode r a y tube (C ) during a sweep.
o b t a i n response information f o r t h e critical mode of interest. The information is more a c c u r a t e than can be obtained from t h e s t r i p recorders i n a real-time environment. A s i d e b e n e f i t of t h e real-time T-plot is t h e immediate acquisi- t i o n of c o r r e c t e d f l i g h t parameters (equivalent airspeed, Mach number, a l t i t u d e , etc.) which are a l s o displayed on t h e CRT.
Hard-copy t r a n s m i s s i b i l i t y p l o t s f o r s i x s e l e c t e d d a t a channels are pro- The information from duced on a Gould p l o t t e r w i t h i n 90 seconds a f t e r a sweep.
t h e s e p l o t s , i n conjunction w i t h t h a t already obtained from the real-time T-plot, a f f o r d s t h e opportunity t o o b t a i n a check on frequency and damping values f o r most of t h e modes of i n t e r e s t . The a b i l i t y t o determine resonant frequencies almost immediately permits t h e s e l e c t i o n of accurate dwell f r e - quencies during t h e f l i g h t , thus providing good-quality decay data.
Data System Post F l i g h t This system involves a complete e v a l u a t i o n of a l l t h e d a t a a v a i l a b l e t o a t damping and F l u t t e r Margin t r e n d s s o as t o e s t a b l i s h t h e f l u t t e r a r r i v e s a f e t y of t h e next test p o i n t ( s ) , and a l s o t o e x t r a p o l a t e t o p r e d i c t e d f l u t t e r boundaries. A d i g i t a l computer is used t o extract frequency and damping in- formation by t h e methods of Reference 4 and t o provide t h e data s t o r a g e and computational c a p a b i l i t i e s required f o r t h e F l u t t e r Margin c a l c u l a t i o n s and p r e d i c t i o n s , A s can be seen, Figure 8 shows t h e data flow i n t h i s system.
t h e r e i s considerable madmachine i n t e r a c t i o n .
Extraction of frequency and damping d a t a After t h e completion of each test f l i g h t , t r a n s m i s s i b i l i t y p l o t s are gen- e r a t e d from t h e onboard tape f o r a l l parameters of i n t e r e s t , nominally 1 2 per 6 f o r each s i d e of t h e a i r c r a f t . Frequency and damping are obtained sweep, manually from t h e s e t r a n s m i s s i b i l i t y p l o t s by observing resonant peaks and c a l c u l a t i n g damping on t h e b a s i s of bandwidth and/or t h e s l o p e of t h e phase s h i f t e This information is combined with frequency and damping d a t a ob rained from t h e dwell/decays and t h e output generated by t h e automatic modal extrac- (The latter is performed i n S t , Louis because of t h e l a r g e r t i o n technique.
computer c a p a c i t y there. ) I n t h e automatic technique, based on Reference 4 , t h e resonant frequencies are considered t o occur when t h e d e r i v a t i v e s of t h e Argand arc-length reaches a maximum w i t h r e s p e c t t o frequency. These m a x i m a are e x t r a c t e d using a least- squares straight-line-slope t e s t i n g technique. P l o t s of t h e d e r i v a t i v e are provided t o t h e f l u t t e r engineer by t h e computer (see Figure 9 ) . It w a s found t h a t a Hanning smoothing technique, applied t o both t h e t r a n s f e r f u n c t i o n and t o t h e d e r i v a t i v e data, s u b s t a n t i a l l y reduces t h e e r r o r induced by experimental scatter (turbulence, etc.).
To automatically o b t a i n t h e damping values from t h e t r a n s f e r function, t h e multi-degree of freedom f u n c t i o n i s i n i t i a l l y separated i n t o s i n g l e degree of The bandwidth of these segments depends on t h e frequency freedom segments.
s e p a r a t i o n of t h e modes and is n o t t h e same f o r a l l modes, Damping values ar e x t r a c t e d f o r each of t h e segments by f i r s t f i t t i n g a l e -squares circle t o t h e t r a n s f e r f u n c t i o n d a t a i n t h e complex plane. Damping values are then cal- culated f o r each d a t a p o i n t used t o d e f i n e t h e circle, u t i l i z i n g t h e equation 2 2 0 - - w I m n .
The damping values obtained on t h e b a s i s of t h e p o i n t s g = - - w w R e n f a r t h e s t from t h e n a t u r a l frequency are considered t o be t h e most accurate, s i n c e they are least sensitive t o any e r r o r i n t h e frequency t e r m . Therefore, emphasis i s placed on t h e four poirits which are f a r t h e s t from t h e resonant peak (two on each s i d e ) . The four damping values are presented, along with t h e average, i n a t a b l e included w i t h t h e d e r i v a t i v e p l o t , Figure 9.
Generally, t h e automatically e x t r a c t e d modes w i l l f a l l i n t o t h r e e cate- gories: good modes, o t h e r p h y s i c a l modes, and f i c t i t i o u s modes. I n a "good" mode t h e four damping values w i l l be very c l o s e t o each o t h e r and t h e same resonant frequency w i l l be shown i n t h e t a b u l a t i o n , t h e d e r i v a t i v e p l o t and t h e o r i g i n a l t r a n s m i s s i b i l i t y p l o t . For example, on Figure 9 t h e 18.6 Hz boom lateral bending mode and the 33.8 Hz f i n t i p r o l l mode are t h e only good modes t o be e x t r a c t e d from t h i s p a r t i c u l a r gage.
The second category of modes has t h e following c h a r a c t e r i s t i c s : a. S i m i l a r i t y i n damping of t h e two "lower" p o i n t s and t h e two "upper" p o i n t s , b u t a d i f f e r e n c e between t h e ''upper" and "lower" p o i n t s .
b. Good phase-shift a t t h e resonant frequency.
c. D i f f e r e n t resonant frequencies i n d i c a t e d by t h e t a b u l a t i o n , t h e d e r i - v a t i v e p l o t , and t h e t r a n s m i s s i b i l i t y p l o t .
i.e. real, modes of t h e a i r p l a n e , b u t Such modes are generally p h y s i c a l , t o d i s c e r n them; they are b e t t e r picked t h i s p a r t i c u l a r gage is not t h e b e s t off from some o t h e r sensor. The 9.9, 13.4, 23.5 and 26.7 Hz modes tabulated i n Figure 9 f a l l i n t o t h i s category.
The 35.4, 37.3 and 39.8 Hz modes are f i c t i t i o u s and can be recognized as such by : a. Unequal damping values w i t h i n t h e "low" and "high" p o i n t s , Low o r even negative damping i n d i c a t i o n s n o t s u b s t a n t i a t e d by deriva- b.
tive and t r a n s m i s s i b i l i t y p l o t s .
U t i l i z a t i o n of frequency and damping data Frequency and damping d a t a obtained from t h e various sources are cross- p l o t t e d versus a l t i t u d e and Mach number f o r each mode of i n t e r e s t t o make s u r e t h a t they are properly tracked. Figure 10 shows a sample p l o t of frequency and damping versus Mach number a t a constant a l t i t u d e of 1525 m (5000 f t ) . Two modes, f i n bending and boo 1 bending, are shown f o r one s i d e of t h c r a f t , t o demonstrate t h e r be A s be seeng t h e frequency and information o f r o ous However, i n some casesp e s p e c i a l l y f o r some of is generally q u i t e c o n s i s t e n t , t h e higher damped modes (see t h e fin-bending mode i n Figure l o ) , t h e r e may be some disagreement between t h e d i f f e r e n t b i t s of information. I n such cases, t h e input d a t a are reviewed regarding t h e i r relative m e r i t , e.g. t h e q u a l i t y o f t h e consistency of t h e automatically e x t r a c t e d d a t a , and t h e t h e decay d a t a , Based on a j u adequacy of t h e manually obtained d a t a , a d e t e t i o n is made on t h e q u a l i t y of t h e d i f f e r e n t p i e c e s of information, "final" frequency and damping values t o b e used f o r t h i s mode and its "reason- ableness" is evaluated by reviewing cross-plots versus a l t i t u d e and Mach number.
This "final" information f o r each s i d e of t h e a i r c r a f t is then e n t e r e d i n t o computer s t o r a g e by means of a remote "Execuport" terminal l o c a t e d a t t h e test site. These d a t a can be r e t r i e v e d e i t h e r i n t a b u l a r form o r as Gould p l o t s of frequency, damping, and F l u t t e r Margin versus a l t i t u d e and Mach number.
A t t h i s p o i n t , t h e following d a t a are t h e r e f o r e a v a i l a b l e t o t h e f l u t t e r engineer: a. P l o t s of frequency and damping versus a l t i t u d e f o r each mode of
i n t e r e s t a t each cross-section Mach number - Figure 11 is an example
of such a p l o t .
b. P l o t s of frequency and damping versus Mach number f o r each mode of i n t e r e s t a t each constant a l t i t u d e cross s e c t i o n - see Figure 10 f o r sample d a t a of t h i s kind.
P l o t s of F l u t t e r Margin versus equivalent airspeed f o r each modal c.
combination of interest a t each cross-section Mach number (this a l s o i n c l u d e s a p r e d i c t i o n of t h e f l u t t e r speed based on a p a r a b o l i c ex- t r a p o l a t i o n ) - see Figure 12.
P l o t s of F l u t t e r Margin versus Mach number f o r each modal p a i r of d.
i n t e r e s t at each cross-section a l t i t u d e - see Figure 13.
Constant a l t i t u d e f l u t t e r v e l o c i t y p r e d i c t i o n s are then obtained by manu- a l l y s e l e c t i n g t h e Mach number from t h e constant a l t i t u d e f l u t t e r margin p l o t s a t which supersonic flow c h a r a c t e r i s t i c s appear t o be e s t a b l i s h e d (e.g. M = and u t i l i z i n g only test d a t a above t h a t Mach 1.18 on t h e p l o t i n Figure 13), number f o r t h e supersonic e x t r a p o l a t i o u at t h i s a l t i t u d e .
A cross-plot of a l l the F l u t t e r Margin p r e d i c t i o n s is then made f o r each modal p a i r of i n t e r e s t (see Figure 14 f o r a n example) and evaluated i n terms of minimum f l u t t e r margin. It should be noted t h a t , although modes as determined from left-hand and right-hand d a t a were tracked independent-ly, on t h e F-15 they w e r e c l o s e enough t o each o t h e r t h a t one f l u t t e r boundary could be used t o represent them both, RESULTS The modes t o be observed during the F-4.
selected on the b a s i s of the res and ground vibration tests, The tracked on t h i s b a s i s were: f i n f i r s t bend lateral bending, boom torsion, boom s t a b i l a t o r bending, s t a b i l a t o r p i t c h , boom v e r t i c a l bending, wing f i r s t bending, wing second bending, wing f i r s t torsion, outer wing torsion, and aileron rotation.
Data obtained f o r these various modes w e r e then evaluated i n terms of damp- ing versus airspeed a t 1525 m (5000 f t ) , damping versus a l t i t u d e a t the cross- section Mach numbers ( t o extrapolate t o the damping value t o be expected a t sea l e v e l ) , and f l u t t e r boundaries on the basis of F l u t t e r Margin of various modal p a i r s representing p o t e n t i a l f l u t t e r mechanisms.
Tables I and I1 summarize the r e s u l t s of these evaluations i n terms of minimum predicted f l u t t e r margin f o r the various mechanisms. It can be noted that there are s i x f l u t t e r mechanisms (three symmetric and three antisymmetric) with predicted f l u t t e r margins between 15 and 20 percent, substantiating the success of the minimum weight design concept pursued on the F-15.
Based on our experience t o date, we f e e l t h a t predictions can r e l i a b l y be carried only t o a velocity which is no farther from the last test point than about 1.5 t i m e s the difference between the f i r s t and last i n f l i g h t test points.
On t h i s basis, since our tests w e r e between a l t i t u d e s of 6100 and 1525 m (20 000 and 5000 f t ) , f l u t t e r velocity predictions showing greater than 25% f l u t t e r margin of s a f e t y have no s p e c i f i c quantitative values attached t o them.
Shapes of f l u t t e r boundaries Shapes of predicted f l u t t e r boundaries were generally e i t h e r i n the form of the boundary given i n Figure 14, with Mach numbers between 0.9 and 1.1 being c r i t i c a l , o r as shown i n Figure 15, with t h e maximum sea-level Mach number being c r i t i c a l .
Application t o design changes The quantitative knowledge of actual f l u t t e r margins provides a firm basis on which t o assess the impact of prospective design changes. For example, we may want t o incorporate an a i r c r a f t modification which, according to analysis (which has been substantially v e r i f i e d by correlation with quantitative f l i g h t test data) and possibly a l s o wind tunnel t e s t s , lowers the f l u t t e r speed of a c e r t a i n mechanism by 5%. I f we have f l i g h t test data i n hand t h a t show t h a t w e now have 25% margin i n t h i s mechanism, w e not only have considerable confidence t h a t w e can go ahead, but w e a l s o have no need t o go i n t o another involved f l i g h t f l u t t e r test program, W e have already had several such opportunities to apply the quantitative F-15 f l i g h t f l u t t e r test data t o the evaluation of design changes.
i g h t f l u t t e r test procedure used on t h e F-15 provides n o t only a demonstration of adequate damping throughout the a i r c r a f t f l i g h t envelope, b u t Such q u a n t i t a t i v e a l s o permits q u a n t i t a t i v e demonstration of margin of s a f e t y , information is n o t only u s e f u l t o d e f i n i t i v e l y e s t a b l i s h the f l u t t e r s t a t u s o f t h e aircraft as it w a s flown, b u t a l s o provides a s o l i d foundation on which t o assess t h e impact of any f u t u r e design changes.
REFERENCES 1. Zimmerman, N.H., and Weissenburger, J.T.: P r e d i c t i o n of F l u t t e r Onset Speed Based on F l i g h t F l u t t e r T e s t i n g at S u b c r i t i c a l Speeds. J o u r n a l of A i r c r a f t , Vol. 1, No. 4, 1964.
2. Shelton, J.D., and Tucker, P.B.: Minimum Weight Design of t h e F-15 Empennage f o r F l u t t e r . AIAA/ASME 16th S t r u c t u r e s Meeting, May 1975.
3. Nash, D.E., Katz, H., and Moody, W.C.: F-15 F l i g h t F l u t t e r Testing: A i r c r a f t Systems and T e s t Operations. AIAA 1975 A i r c r a f t Systems and Technology Meeting, August 1975.
C.C. and Pancu, C.D.P.: U s e of Vectors i n Vibration Measurement 4. Kennedy, and Analysis. J o u r n a l of Aeronautical Sciences, V o l . 14, 1947.
MARGIN OF SAFETY MECHANISM 15% FIN BENDING vs BOOM LATERAL BENDING 19% vs STABILATOR ROTATION STABILATOR BENDING 20% WING FIRST BENDING vs OUTER WING TORSION 25% BOOM VERTICAL BENDING vs STABILATOR ROTATION > 25% BOOM LATERAL BENDING vs BOOM TORSION > 25% STABILATOR BENDING vs BOOM TORSION > 25% STABILATOR ROTATION vs BOOM TORSION > 25% FIN BENDING vs FIN TORSION > 25% STABILATOR BENDING vs BOOM VERTICAL BENDING > 25% BOOM TORSION vs BOOM VERTICAL BENDING > 25% FIN TORSION vs FIN TIP ROLL > 25% WING FIRST BENDING vs WING FIRST TORSION > 25% WING SECOND BENDING vs WING FIRST TORSION > 25% WING SECOND BENDING vs OUTER WING TORSION GP15.07102 TABLE I 1 : MlNlMUM FLUTTER VELOCITY MARGINS FOR ANTI SYMMETRIC MECHANISMS MARGIN OF MECHANISM SAFETY vs BOOM LATERAL BENDING FIN BENDING 16% STABILATOR ROTATION vs BOOM TORSION 17% BOOM LATERAL BENDING vs BOOM TORSION 20% WING FIRST BENDING vs OUTER WING TORSION 25% STABILATOR BENDING vs BOOM TORSION > 25% BOOM VERTICAL BENDING vs STAB1LATOR ROTATION > 25% WING SECOND BENDING vs OUTER WING TORSION > 25% STABILATOR BENDING vs STABILATOR ROTATION > 25% vs FIN TORSION FIN BENDING > 25% STABILATOR BENDING vs BOOM VERTICAL BENDING > 25% BOOM TORSION vs BOOM VERTICAL BENDING > 25% FIN TORSION vs FIN T I P ROLL > 25% WING FIRST BENDING vs WING FIRST TORSION > 25% WING SECOND BENDING vs WING FIRST TORSION > 25% NORMALIZED FLUTTER MARGIN MACH NUMBER GP75 07104 Figure 1.- Flutter margin at constant dynamic pressure.
Antisymmetric boom torsion versus stabilator rotation at 442 KEAS.
PROJECTED FLUTTER VELOCITY (STRAIGHT INE EXTRAPOLATION; FLIGHT TEST POINTS ONLY) 6000 rn (20 000 FT) NORMALIZED 3000 rn (IO 000 FT) TEST POlN FLUTTER MARGIN 1500 rn (5000 FT) TEST POlN PROJECTED FLUTTER VELOCITY (PARABOLIC EXTRAPOLATION INCL.
ZERO-AIRSPEED POINT) O W b O l l O l l VELOCITY Figure 2 . - Flutter prediction at constant Mach number.
PROJECTED PROJECTED SUPERSONIC
\ \\ FLUlTER
0.6 NORMALIZED NORMALIZED FLUTTER FLUTTER MARGIN MARGIN 0.4 CRITICAL TRANSONIC CRITICAL TRANSONIC MACH NUMBER MACH NUMBER FOR THIS MECHANISM FOR THIS MECHANISM 0.2 0.2 PROJECTED SUBSONIC
\
FLUTTER VELOCITY\ 0 0 MACH NUMBER OP7*0110 7 Figure 3 . - Flutter prediction at constant altitude.
t I I I I I AIRSPEED KEAS MACH NUMBER Figure 4 . - F-15 flight flutter test points.
OF GAGE TYPE FIN TORSION RUDDER ROTATION - _ 0 BENDING A TORSION STRAIN GAGES STABlLATOR 0 HINGEMOMEN 0 ACCELEROMETER (BOTH SIDES GAGED) OUTER WING BENDING BENDING (WITH STORES) NDAMENTAL WING FUNDAMENTAL WING BENDING (CLEAN) TORSION (CLEAN) OP,B071010 Figure 5.- Location of instrumentation.
32 CHANNELS NARROW BAND FM; 1 "REAL-TIME" TRANSFER FUNCTION TR DISPLAYED DURING FU SWEEP ON CATHODE 90 RAY TUBE AFTER SWEEP 32 NARROW BAND 16 LISSAJOUS COMPLETION FM PARAMETERS FIGURES DISPLAYED DISPLAYED CONTINUOUSLY ON CONTINUOUSLY ON 4 STRIP RECORDERS 4 OSCILLOSCOPES OP75071012 Figure 6.- On-line data reduction of telemetered signals.
PHASE R/H Boom Lateral Bending Normalized to R/H Stabilator Rotation -90 -180 .....................
1 .oo DATE ....................... 01/24n4 Hpc 1512 m (4959 FT) ..................
0.75 M ............................. 1.105 CONDITION OF SWEEP EMPEN. SYMMETRIC ............................
VE 663.4 KTS 0.50 VT ........................... 718.7 KTS (1 ................... 72.35 kPa (1511 PSF) TAF 4% (392'F) ........................
0.25 PA ....... 1.06 k g / J (0.002057 SLUGS/FT3) Figure 7 . - St. Louis transmissibility plot.
DATA STORAGE AND MANAGEMENT MANUAL EXTRACTION EXCITATION AND DAMPING VALUES Figure 8 . - Post-flight data system schematic.
FIRST DERIVATIVE R/H Boom Lateral Bending to R/H Stabilator Rotation Normalized HERTZ F'-15 FLIGHT FLUTTER ANALYSIS SYSTEM FREQUENCYAND DAMPING DATA AVG FLIGHT RO. .................. .341 NUM FREQ DAMP DAMP DAMP DAMP DAMP DATE ................... 01/24/74 1 9.90 0.123 0.114 0.169 0.164 0.142 RUN NUMBER .................. .02 2 13.40 0.038 0.031 0.024 0.024 0.029 Hpc ............... 1512m (4959 FT) 18.60 0.019 0.018 0.020 0.021 0.019 M ........................ 1.105 4 23.50 0.118 0.100 0.272 0.240 0.183 CONDITION OF SWEEP EMPEN.SYMMETRIC 5 26.69 0.005 0.001 0.034 8.033 0.018 VE .................... 663.4KT-S 6 33.80 0.025 0.026 0.023 0.028 0.026 VT .................... 718.7KTS 7 35.48 -0.002 4.002 0.001 0.001 0.001 Q .............. 72.35kPa (1511 PSF) a 37.31 0.033 0.027 0.007 0.008 0.019 TAF ................. .4OC (392'F) 9 39.80 0.005 -0.008 -0.009 -0.014 0.005 PA ..... .1.06 kg/m3 (0.002057 SLUGS/FT3) - Figure 9 . - S t . Louis Argand derivative plot and automatic frequency and damping extraction results.
STRUCTURAL DAMPING g (XI y Manual Techniques y Automatic Techniques FREQUENCY HZ 0.7 0.8 0.9 1 .o 1 .l 1.2 GP7i07lC14 MACH NUMBER Figure 10.- Frequency and damping versus Mach number for symmetric f i n bending and boom lateral bending modes.
L/H data at 1525 m (5000 f t ) altitude.
STRUCTURAL DAMPING -7 0 g (%) -20 FREQUENCY '9 HZ 18 0- SEA AIRSPEED
LEVEL ALTITUDE - krn
(iP75-0710 14 Figure 11.- Frequency and damping versus a l t i t u d e f o r symmetric boom lateral bending a t constant Mach number of 1.10.
1.50 1 .oo NORMALIZED FLUTTER MARGIN 0.50 I I 1 150 300 450 600 750 900 G P X 0,105 EQUIVALENT AIRSPEED - KTS Figure 12.- F l u t t e r margin versus equivalent airspeed.
Symmetric boom lateral bending v e r s u s f i n bending f o r constant Mach number of 1.10.
MACH NUMBER OP76.071DIS Figure 13.- F l u t t e r margin versus Mach number.
Synrmetric boom lateral bending versus f i n bending a t constant a l t i t u d e of 1525 m (5000 f t ) .
AIRSPEED KEAS MACH NUMBER DP75-07,016 Figure 14.- F l u t t e r boundary f o r f i n bending v e r s u s boom lateral bending mechanism - symmetric.
MACH NUMBER G P I S 07,017 Figure 15.- F l u t t e r boundary f o r wing f i r s t bending versus o u t e r panel. t o r s i o n mechanism - symmetric.