Document
NASA Technical Memorandum 101427
AIAA-89-0754
Determination of Longitudinal Aerodynamic
I P
Derivatives Using Flight Data From an
s w
Icing Research Aircraft
R.J. Ranaudo
Lewis Research Center
Cleveland, Ohio
J.G. Batterson
Langley Research Center
Hampton, Virginia
A.L. Reehorst and T.H. Bond
Lewis Research Center
Cleveland, Ohio
and
T.M. O'Mara
George Washington University
Washington, D. C.
Prepared for the
27th Aerospace Sciences Meeting
sponsored by the American Institute of Aeronautics and Astronautics
Reno, Nevada, January 9-12, 1989
D E T E R M I N A T I O N OF LONGITUDINAL A E R O D Y N A M I C D E R I V A T I V E S U S I N G FLIGHT DATA FROM A N I C I N G RESEARCH A I R C R A F T R . J . Ranaudo N a t i o n a l A e r o n a u t i c s and Space A d m i n i s t r a t i o n
O I p W A L PAGE I S
Lewis Research C e n t e r
Of POOR QUALln
C l e v e l a n d , O h i o 44135 J.G. B a t t e r s o n , -.
N a t i o n a l A e r o n a u t i c s and Space A d m i n i s t r a t i o n L a n g l e y Research C e n t e r Hampton, V i r g i n i a 23665 A.L. R e e h o r s t , and T . H . Bond N a t i o n a l A e r o n a u t i c s and Space A d m i n i s t r a t i o n Lewis Research C e n t e r C l e v e l a n d . O h i o 44135 and T . M . OIMara* George Washington U n i v e r s i t y Washington, D . C . 20052 w i n g f l a p s up, t h e e s t i m a t e d d e r i v a t i v e s were A b s t r a c t degraded most a t l o w e r speeds c o r r e s p o n d i n g t o t h a t c o n f i g u r a t i o n . W i t h w i n g f l a p s e x t e n d e d t o A f l i g h t t e s t was p e r f o r m e d w i t h t h e NASA
l o " , t h e e s t i m a t e d d e r i v a t i v e s were d e g r a d e d most
Lewis Research C e n t e r ' s DH-6 i c i n g r e s e a r c h a i r - a t t h e h i g h e r c o r r e s p o n d i n g speeds.
c r a f t . The p u r p o s e was t o employ a f l i g h t t e s t N p r o c e d u r e and d a t a a n a l y s i s method, t o d e t e r m i n e In The e f f e c t s o f i c i n g on t h e changes i n l o n g i - t h e a c c u r a c y w i t h w h i c h t h e e f f e c t s o f i c e on a i r - e I t u d i n a l s t a b i l i t y and c o n t r o l d e r i v a t i v e s were w c r a f t s t a b i l i t y and c o n t r o l c o u l d be measured.
a d e q u a t e l y d e t e r m i n e d b y t h e f l i g h t t e s t p r o c e d u r e F o r s i m p l i c i t y , f l i g h t t e s t i n g was r e s t r i c t e d t o and t h e MSR a n a l y s i s method d i s c u s s e d h e r e i n .
t h e s h o r t p e r i o d l o n g i t u d i n a l mode.
L i s t o f Symbols and A b b r e v i a t i o n s Two f l i g h t s were f l o w n i n a c l e a n ( b a s e l i n e ) c o n f i g u r a t i o n , and two f l i g h t s were f l o w n w i t h w i n g span, m s i m u l a t e d h o r i z o n t a l t a i l i c e . F o r t y - f i v e r e p e a t d o u b l e t maneuvers were performed i n each o f f o u r r o l l , p i t c h , and yaw moment c o e f i - t e s t c o n f i g u r a t i o n s , a t a g i v e n trim speed, t o c i e n t s , r e s p e c t i v e l y d e t e r m i n e t h e ensemble v a r i a t i o n o f t h e e s t i m a t e d s t a b i l i t y and c o n t r o l d e r i v a t i v e s . A d d i t i o n a l l o n g i t u d i n a l , l a t e r a l , and v e r t i - maneuvers were a l s o p e r f o r m e d i n each c o n f i g u r a - c a l f o r c e c o e f f i c i e n t s , t i o n , t o d e t e r m i n e t h e v a r i a t i o n i n t h e l o n g i t u d i - r e s p e c t i v e l y n a l d e r i v a t i v e e s t i m a t e s o v e r a w i d e r a n g e o f t r i m speeds.
- C mean aerodynamic c h o r d , m S t a b i l i t y and c o n t r o l d e r i v a t i v e s were e s t i - a i r p l a n e c e n t e r o f g r a v i t y mated b y a M o d i f i e d S t e p w i s e R e g r e s s i o n ( M S R ) t e c h n i q u e . A measure of t h e c o n f i d e n c e i n t h e a c c e l e r a t i o n due t o g r a v i t y d e r i v a t i v e e s t i m a t e s was o b t a i n e d b y c o m p a r i n g t h e s t a n d a r d e r r o r f o r t h e ensemble o f r e p e a t maneu- moments o f i n e r t i a , kg-m2 v e r s , t o t h e a v e r a g e o f t h e e s t i m a t e d s t a n d a r d e r r o r s p r e d i c t e d by t h e MSR p r o g r a m . A m u l t i p l i c - p r o d u c t o f i n e r t i a , k g - d a t i v e r e l a t i o n s h i p was d e t e r m i n e d between t h e ensemble s t a n d a r d error, and t h e a v e r a g e d p r o g r a m c o s t f u n c t i o n f o r S t e p w i s e Regres- s t a n d a r d e r r o r s . I n a d d i t i o n , a 9 5 p e r c e n t c o n f i - s i o n A l g o r i t h m f o r t h e e l e - dence i n t e r v a l a n a l y s i s was p e r f o r m e d v a t o r e f f e c t i v e n e s s e s t i m a t e s , Cmbe. T h i s a n a l y s i s k n o t s i n d i c a t e d a i r s p e e d , k t s i d e n t i f i e d t h e speed r a n g e where changes i n Crn6e c o u l d be a t t r i b u t e d t o i c i n g e f f e c t s .
* a i r c r a f t mass, k g The m a g n i t u d e o f i c i n g e f f e c t s o n t h e d e r i v a - number o f p o i n t s t i v e e s t i m a t e s were s t r o n g l y dependent o n f l i g h t speed and a i r c r a f t w i n g f l a p c o n f i g u r a i t o n . W i t h r o l l , p i t c h , and yaw r a t e s , r e s p e c - t i v e l y , r a d l s e c o r d e g / s e c * J o i n t I n s t i t u t e f o r Advancement o f F l i g h t S c i e n c e , NASA L a n g l e y Research C e n t e r .
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s m a l l i c e a c c r e t i o n s and t o t h o s e l a r g e r a c c r e - S w i n g a r e a , m2 t i o n s caused b y i c e p r o t e c t i o n systems f a i l u r e s or o p e r a t o r e r r o r s .
SHP s h a f t horsepower, h p C u r r e n t l y , n o a n a l y s i s m e t h o d o l o g i e s e x i s t l o n g i t u d i n a l , l a t e r a l , and v e r t i - u,v,w t h a t p r o v i d e t h e c a p a b i l i t y t o p r e d i c t t h e e f f e c t c a l v e l o c i t y components o f i c i n g o n a i r c r a f t f l i g h t c h a r a c t e r i s t i c s .
T h e r e f o r e , w i t h i n t h e scope o f t h e NASA Lewis a i r - t o t a l a i r s p e e d , m/s or k n o t s as
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c r a f t i c i n g r e s e a r c h program, a h i g h p r i o r i t y has g i v e n b y ( u 2 + v 2 + w 2 ) 1 / 2 been a s s i g n e d i n m e a s u r i n g t h e e f f e c t s o f i c i n g o n a i r c r a f t p e r f o r m a n c e and s t a b i l i t y and c o n t r o l .
measured a i r c r a f t r e s p o n s e or con- E x p e r i m e n t a l d a t a a c q u i r e d from f l i g h t t e s t s p r o - t r o l s u r f a c e i n p u t v i d e t h e b a s i s f o r v a l i d a t i n g i c i n g e f f e c t s meth- f o r e s t a b l i s h i n g c o r r e l a t i o n s o d o l o g i e s , and l i n e a r a p p r o x i m a t i o n o f Cm6e c o r r e - Yo( KO) between c o m p u t a t i o n a l codes, w i n d t u n n e l t e s t s , s p o n d i n g t o some xo ( v e l o c i t y ) and f u l l s c a l e f l i g h t t e s t s . Performance t e s t - i n g , w h i c h was e x t e n s i v e l y d i s c u s s e d i n R e f s . 1 I y ( i ) computed aerodynamic c o e f f i c i e n t s and 2 , p r o v i d e d r e a s o n a b l y c o n s i s t e n t r e s u l t s and , a h i g h d e g r e e o f c o n f i d e n c e i n measurement accu- l a c o r r e c t e d ( f r e e s t r e a m ) a n g l e o f r a c y . As a r e s u l t , t h e s e d a t a a r e now b e i n g used a t t a c k , r a d or deg i n v a l i d a t i n g c u r r e n t m e t h o d o l o g i e s t h a t p r e d i c t i c e shape g r o w t h and t h e i r e f f e c t o n aerodynamic r a d or deg a n g l e o f s i d e s l i p , R p e r f o r m a n c e . However, i n i t i a l f l i g h t t e s t i n g t o e s t i m a t e e f f e c t s o f i c i n g o n a i r c r a f t s t a b i l i t y e l e v a t o r d e f l e c t i o n , r a d or deg &e and c o n t r o l d e r i v a t i v e s , showed t h a t t h e r e s u l t s c o u l d be o b s c u r e d b y t h e i n h e r e n t p r o b l e m o f n o t 0 aerodynamic s t a b i l i t y or c o n t r o l k n o w i n g t h e t r u e a c c u r a c y o f t h e d e r i v a t i v e e s t i - p a r a m e t e r s mates. S t a b i l i t y and c o n t r o l f l i g h t t e s t i n g as r e p o r t e d i n R e f s . 3 and 4 used a n e a r l y v e r s i o n c o n s t a n t o f f s e t t e r m o f a M o d i f i e d Maximum L i k e l i h o o d E s t i m a t i o n (MMLE) t e c h n i q u e t o e s t i m a t e t h e d e r i v a t i v e v a l u e s . The d e r i v a t i v e w . r . t . some r e s p o n s e or a c c u r a c i e s o f t h e s e d e r i v a t i v e e s t i m a t e s were c o n t r o l s u r f a c e i n p u t o b t a i n e d b y an a p p r o x i m a t i o n t o t h e Cramer-Rao bound g i v e n b y t h e maximum l i k e l i h o o d a l g o r i t h m .
p i t c h and r o l l a n g l e s , r e s p e c - Because i t was known t h a t t h e s e e r r o r e s t i m a t e s t i v e l y , r a d or deg i n d i c a t e d h i g h e r a c c u r a c i e s t h a n t h o s e w h i c h can be a c h i e v e d b y r e p e a t e d e x p e r i m e n t s ,5 and because a i r d e n s i t y , kg/m3 P t h e d i f f e r e n c e s between d e r i v a t i v e s from t h e base- l i n e and i c e d a i r c r a f t were found t o be s m a l l , i t was d e c i d e d t o c o n d u c t f u r t h e r f l i g h t t e s t i n g t o d e t e r m i n e a r e a l i s t i c a c c u r a c y w i t h w h i c h s t a b i l i t y v a r i a n c e e s t i m a t e o f measurement and c o n t r o l d e r i v a t i v e s c o u l d be e s t i m a t e d . The n o i s e p u r p o s e o f t h i s paper i s t o r e p o r t o n t h e r e s u l t s o f t h o s e t e s t s , and t o p r e s e n t t h e c o n c l u s i o n s drawn from t h e d a t a a n a l y s i s programs.
I n t r o d u c t i o n F o r s i m p l i c i t y , t h e f l i g h t t e s t p l a n was Modern t r a n s p o r t a i r c r a f t , c e r t i f i e d f o r s t r u c t u r e d t o examine o n l y t h e l o n g i t u d i n a l s h o r t f l i g h t i n i c i n g c o n d i t i o n s , n o r m a l l y employ i c e p r o t e c t i o n systems t o p r e v e n t i c e from a c c u m u l a t - p e r i o d c h a r a c t e r i s t i c s o f t h e r e s e a r c h a i r c r a f t .
F o u r d a t a c o l l e c t i o n f l i g h t s were d e f i n e d : two i n g o n c r i t i c a l l i f t i n g components. I f t h e s e f l i g h t s , were f l o w n c l e a n ; and two f l i g h t s were systems f a i l , or a r e i m p r o p e r l y o p e r a t e d , i c e can f l o w n w i t h a n a r t i f i c i a l i c e shape ( d e s c r i b e d l a t e r form o n t h e s e components and pose a s e r i o u s t h r e a t i n t h i s r e p o r t ) , a t t a c h e d t o t h e l e a d i n g edge o f t o s a f e f l i g h t c h a r a c t e r i s t i c s . T h i s p r o b l e m , t h e h o r i z o n t a l t a i l .
w h i c h i s a c o n t i n u a l c o n c e r n f o r c u r r e n t genera- t i o n a i r c r a f t , w i l l be o f even g r e a t e r c o n c e r n f o r F l i g h t t e s t maneuvers c o n s i s t e d o f numerous f u t u r e g e n e r a t i o n a i r c r a f t e m p l o y i n g advanced p r o - t r i m con- r e p e a t e l e v a t o r d o u b l e t s a t a s p e c i f i e d p u l s i o n systems and o p t i m i z e d aerodynamic d e s i g n s .
d i t i o n t o d e t e r m i n e t h e ensemble s t a n d a r d d e v i a - F o r example, h i g h p r o p u l s i v e e f f i c i e n c y e n g i n e s t i o n f o r t h e p a r a m e t e r e s t i m a t e s . A d d i t i o n a l such as p r o p f a n s , may n o t p r o v i d e s u f f i c i e n t b l e e d a i r f o r w i n g and t a i l a n t i - i c i n g . The use of maneuvers were a l s o f l o w n o v e r t h e e n t i r e l e v e l f l i g h t a n g l e o f a t t a c k e n v e l o p e t o o b t a i n d e r i v a - e n e r g y - e f f i c i e n t d e - i c i n g systems, w h i c h r e q u i r e t i v e e s t i m a t e s f o r d i f f e r e n t f l i g h t c o n d i t i o n s .
some s m a l l b u i l d - u p o f i c e b e f o r e a c t i v a t i o n , w i l l F l i g h t t e s t maneuvers were a n a l y z e d u s i n g a modi- b e t h e i r l i k e l y r e p l a c e m e n t . A i r c r a f t e q u i p p e d w i l l have t o d e m o n s t r a t e f i e d s t e p w i d e r e g r e s s i o n (MSR) a l g o r i t h m . The w i t h t h e s e systems r e s u l t s a r e d i s c u s s e d r e l a t i v e t o t h e a c c u r a c y o f a c c e p t a b l e f l y i n g q u a l i t i e s w i t h some l e a d i n g edge t h e d e r i v a t i v e e s t i m a t e s , and t o t h e d i f f e r e n c e s i c e c o n t a m i n a t i o n , e s p e c i a l l y when f l o w n i n t h e between t h e e s t i m a t e s o b t a i n e d for t h e u n i c e d t a k e - o f f or l a n d i n g c o n f i g u r a t i o n . T h i s r e q u i r e - v e r s u s i c e d h o r i z o n t a l t a i l . Some c o n c l u s i o n s ment a l s o a p p l i e s t o a i r c r a f t whose aerodynamic a r e a l s o drawn as t o t h e p h y s i c a l i n t e r p r e t a t i o n e f f i c i e n c y , enhanced b y advanced a i r f o i l d e s i g n s o f t h e d e r i v a t i v e e s t i m a t e s and t h e i r r e l e v a n c e and r e l a x e d s t a t i c s t a b i l i t y c r i t e r i o n , i s degraded when s m a l l l e a d i n g edge i c e f o r m a t i o n s o c c u r t o a i r c r a f t h a n d l i n g c h a r a c t e r i s t i c s . F o l l o w i n g t h e i n t r o d u c t i o n , t h i s p a p e r i s o r g a n i z e d i n sec- between d e - i c i n g c y c l e s . L i k e w i s e , a i r c r a f t t i o n s w h i c h d e s c r i b e t h e r e s e a r c h a i r p l a n e , e m p l o y i n g f u l l f l i g h t c o n t r o l a u g m e n t a t i o n must a l s o d i s p l a y a n a c c e p t a b l e t o l e r a n c e t o t h e s e I 2 i n s t r u m e n t a t i o n , f l i g h t t e s t maneuvers, d a t a t h e DAS. Because o f b u f f e r l i m i t a t i o n s , o n l y r e d u c t i o n and a n a l y s i s t e c h n i q u e s , a c c u r a c y o f 24 sec o f 20 SPS d a t a c o u l d be o b t a i n e d b e f o r e t h e t h e d e r i v a t i v e e s t i m a t e s , e f f e c t s o f t a i l i c e o n b u f f e r c o n t e n t s had t o be w r i t t e n o n t o a cas- h a n d l i n g c h a r a c t e r i s t i c s and c o n c l u s i o n s . s e t t e t a p e . The w r i t e - o f f p e r i o d was n o m i n a l l y 60 t o 90 sec. Hence, a l l f l i g h t t e s t maneuvers were Research A i r c r a f t p l a n n e d t o l a s t no more t h a n 24 sec. D u r i n g t h e w r i t e - o f f p e r i o d , t h e a i r c r a f t w o u l d be r e p o s i - The NASA L e w i s i c i n g r e s e a r c h a i r c r a f t shown t i o n e d and t r i m m e d f o r t h e n e x t d a t a p o i n t . The i n F i g . 1 , i s a m o d i f i e d D e H a v i l l a n d DH-6 Twin l i s t o f r e c o r d e d p a r a m e t e r s , r a n g e s , and s e n s i t i v - O t t e r . I t i s powered b y two 550 SHP P r a t t and i t i e s i s p r o v i d e d i n T a b l e 11.
W h i t n e y PT6A-20A t u r b i n e e n g i n e s d r i v i n g t h r e e b l a d e d H a r t z e l l c o n s t a n t speed p r o p e l l e r s . P h y s i - F l i g h t T e s t i n g c a l d i m e n s i o n s , mass, and i n e r t i a l s p e c i f i c a t i o n s f o r t h e a i r c r a f t a r e f o u n d i n T a b l e I. The c e n t e r o f g r a v i t y o f t h e a i r c r a f t was measured e x p e r i m e n t a l l y . These measurements The f l i g h t c o n t r o l s a r e m e c h a n i c a l l y o p e r a t e d r e p r e s e n t e d t h e z e r o - f u e l mass c h a r a c t e r i s t i c s o f t h r o u g h a system o f c a b l e s and p u l l e y s . A i l e r o n s t h e a i r c r a f t and were c o r r e c t e d i n t h e a n a l y s i s d r o o p as w i n g f l a p s e x t e n d . T h e i r degree o f move- p r o g r a m f o r a c t u a l crew and f u e l w e i g h t s r e c o r d e d ment i n c r e a s e s i n p r o p o r t i o n t o t h e amount o f w i n g d u r i n g each f l i g h t t e s t maneuver.
f l a p e x t e n s i o n . There a r e two t r i m t a b s o n t h e e l e v a t o r . The r i g h t t a b i s i n t e r c o n n e c t e d w i t h t h e L o n g i t u d i n a l s t a b i l i t y and c o n t r o l f l i g h t w i n g f l a p s y s t e m t o p r o v i d e a u t o m a t i c l o n g i t u d i n a l t e s t i n g was a c c o m p l i s h e d i n f o u r a i r p l a n e c o n f i g u - c o m p e n s a t i o n as t h e w i n g f l a p s a r e o p e r a t e d . The r a t i o n s d e f i n e d a c c o r d i n g t o w i n g f l a p s e t t i n g and t h e s i m u l a t e d i c i n g c o n d i t i o n o f t h e h o r i z o n t a l l e f t t r i m t a b i s an a d j u s t a b l e t a b , w h i c h i s o p e r - a t e d b y t h e p i l o t . t a i l p l a n e . They were: F o r f l i g h t s where an a r t i f i c i a l i c e shape was ( 1 ) C l e a n t a i l , w i n g f l a p s up ( 0 " ) ( 2 ) C l e a n t a i l , w i n g f l a p s 10" used t o s i m u l a t e a m o d e r a t e g l a z e i c i n g c o n d i t i o n o n t h e t a i l , f o r m e d aluminum caps were p l a c e d o v e r (3) A r t i f i c i a l h o r i z o n t a l t a i l i c i n g , w i n g t h e l e f t and r i g h t l e a d i n g edges o f t h e h o r i z o n t a l f l a p s up (0") t a i l , and h e l d i n p l a c e w i t h s t r a p s and clamps. ( 4 ) A r t i f i c i a l h o r i z o n t a l t a i l i c i n g , w i n g A r t i f i c i a l i c e c u t from S t y r o f o a m was t h e n s e c u r e d f l a p s 10" t o t h e t a i l caps w i t h d o u b l e s i d e d t a p e . The g e o m e t r y and p o s i t i o n i n g o f t h e a r t i f i c i a l i c e was A c o n s t a n t e n g i n e power s e t t i n g a s s o c i a t e d w i t h each w i n g f l a p c o n d i t i o n , was used w h i l e based o n an a c t u a l t a i l i c i n g c o n d i t i o n r e c o r d e d e x e c u t i n g f l i g h t t e s t maneuvers. T h i s e l i m i n a t e d o n an e a r l i e r r e s e a r c h f l i g h t i n n a t u r a l i c i n g c l o u d s . The e n t i r e a r r a n g e m e n t i s shown i n F i g . 2 . e n g i n e power as a v a r i a b l e i n t h e d e r i v a t i v e e s t i - mates. Two h u n d r e d s e v e n t y - f i v e SHPIengine was used f o r t h e 0" w i n g f l a p cases, and 219 S H P l I n s t r u m e n t a t i o n e n g i n e was used i n t h e 10" w i n g f l a p c a s e s .
The i c i n g r e s e a r c h a i r c r a f t was e q u i p p e d w i t h t h r e e l i n e a r c o n t r o l p o s i t i o n t r a n s d u c e r s ( C P T ) t o The s t a n d a r d s m a l l a m p l i t u d e i n p u t was a measure t h e p o s i t i o n o f t h e e l e v a t o r , a i l e r o n s , "2-1" e l e v a t o r d o u b l e t w h i c h was d e s i g n e d t o and r u d d e r . The e l e v a t o r CPT measured e l e v a t o r e x c i t e t h e s h o r t p e r i o d l o n g i t u d i n a l mode o f t h e p o s i t i o n a t t h e c o n t r o l h o r n t o e l i m i n a t e c o r r e c - a i r p l a n e . E l e v a t o r c o n t r o l column d e f l e c t i o n was i n p u t b y t h e p i l o t t o e f f e c t a p l a n n e d 20.3 g v e r - t i o n s f o r c a b l e s t r e t c h . F l a p p o s i t i o n , c o n s t a n t t i c a l a c c e l e r a t i o n from 1.0 g l e v e l f l i g h t , how- f o r a g i v e n maneuver, was m a n u a l l y r e c o r d e d from t h e f l a p p o s i t i o n i n d i c a t o r i n t h e c o c k p i t . e v e r , due t o an e r r o n e o u s c o c k p i t a c c e l e r o m e t e r , t h e s e maneuvers were more on t h e o r d e r o f e l . 0 g A i r s p e e d , p r e s s u r e a l t i t u d e , a n g l e o f a t t a c k v e r t i c a l a c c e l e r a t i o n . A t y p i c a l example o f one o f s i d e s l i p were measured b y means of o f t h e s e d o u b l e t maneuvers i s shown i n F i g . 4 .
and a n g l e s e n s o r s l o c a t e d on t h e f l i g h t t e s t nose boom, F o r t y - f i v e s e t s o f i d e n t i c a l s m a l l a m p l i t u d e F i g . 3 . P i t o t - s t a t i c p r e s s u r e s were sensed b y a Rosemount 858 p r o b e , w h i c h had been c a l i b r a t e d b y d o u b l e t s were p e r f o r m e d a t a g i v e n f l i g h t c o n d i - t i o n i n each c o n f i g u r a t i o n t o d e t e r m i n e t h e accu- t h e " t r a i l i n g cone" method. The h i g h f r e q u e n c y r a c y o f t h e l o n g i t u d i n a l s t a b i l i t y and c o n t r o l r e s p o n s e a n g l e o f a t t a c k and a n g l e o f s i d e s l i p For t h e 0" f l a p c o n f i g u r a - vanes, were c o n s t r u c t e d from b a l s a wood, and b a l - d e r i v a t i v e e s t i m a t e s .
anced b y a " h e a v y - m e t a l " c o u n t e r w e i g h t . A n g l e o f t i o n s , r e p e a t d o u b l e t s were i n i t i a t e d from a a t t a c k was r e f e r e n c e d t o t h e f u s e l a g e r e f e r e n c e l e v e l , u n a c c e l e r a t e d f l i g h t c o n d i t i o n a t a t r i m speed o f 120 K I A S . For t h e 10" f l a p c o n f i g u r a - l i n e , w h i c h i s c o i n c i d e n t w i t h t h e a i r c r a f t f l o o r t i o n s , t h e s e d o u b l e t s were i n i t i a t e d from a l i n e , and a n g l e o f s i d e s l i p was r e f e r e n c e d t o t h e a i r c r a f t l o n g i t u d i n a l a x i s . l e v e l , u n a c c e l e r a t e d f l i g h t c o n d i t i o n a t a t r i m speed o f 100 K I A S .
Kohlman Systems Research, I n c . , Lawrence A d d i t i o n a l s m a l l a m p l i t u d e d o u b l e t s were Kansas u n d e r c o n t r a c t t o NASA, p r o v i d e d a s t a b i l i t y ?
t h e n p e r f o r m e d i n each c o n f i g u r a t i o n a t incremen- and c o n t r o l d a t a a c q u i s i t i o n system ( D A S ) . T h i s s y s t e m c o n s i s t e d o f an a t t i t u d e g y r o , t h r e e a x i s t a l l y h i g h e r a n g l e s o f a t t a c k ( l o w e r trim s p e e d s ) .
Power s e t t i n g s a s s o c i a t e d w i t h each f l a p c o n f i g u - o r t h o g o n a l a c c e l e r o m e t e r s , t h r e e a x i s a n g u l a r r a t e r a t i o n r e m a i n e d c o n s t a n t f o r t h e s e maneuvers, g y r o s , and a d i g i t a l d a t a r e c o r d i n g s y s t e m w h i c h r e c o r d e d 21 c h a n n e l s o f f l i g h t t e s t p a r a m e t e r s t h e r e f o r e d o u b l e t maneuvers i n i t i a t e d a t t h e l o w e r w i t h 12 b i t s p e r c h a n n e l . A l l d a t a were r e c o r d e d t r i m speeds were p e r f o r m e d i n c l i m b s t h r o u g h a median t e s t a l t i t u d e .
o n - b o a r d a t 20 Samples p e r Second ( S P S ) , and a l l c h a n n e l s were sampled w i t h i n one m i l l i s e c o n d b y D a t a R e d u c t i o n and A n a l y s i s Technique q~ a & a & R~ a 5 The r e c o r d e d c a s e t t e t a p e s from each f l i g h t were i n i t i a l l y s e n t t o KSR, I n c . , where t h e d a t a ( 2 ) 2 v 2 v 2 v were r e d u c e d t o e n g i n e e r i n g u n i t s and r e w r i t t e n on n i n e - t r a c k m a g n e t i c t a p e . These d a t a s e t s were be a6e a26e D3 t h e n t r a n s f e r r e d t o t h e NASA L a n g l e y Research Cen- t e r , A i r c r a f t Guidance and C o n t r o l B r a n c h , f o r and t h e i r c o r r e s p o n d i n g c o e f f i c i e n t s as t h e s t a b i l i t y and c o n t r o l a n a l y s i s .
s t a b i l i t y and c o n t r o l d e r i v a t i v e s : The first s t e p i n t h e a n a l y s i s p r o c e d u r e was t o c o r r e c t t h e measured d a t a f o r a l l known e r r o r s .
A l l sensor d a t a w e r e c o r r e c t e d f o r c . g . o f f s e t , a n g l e o f a t t a c k d a t a were c o r r e c t e d f o r upwash and boom b e n d i n g e f f e c t s , and s e v e r a l f l i g h t maneuvers were a n a l y z e d w i t h a maximum l i k l e h o o d a l g o r i t h m 6 t o e s t i m a t e i n s t r u m e n t b i a s e s and s c a l e f a c t o r s .
These e s t i m a t e d c o r r e c t i o n s , when a p p l i e d t o t h e ‘ m be ‘ m a6e cma26e ‘ m R 3 measured d a t a , p r o d u c e d d a t a s e t s w h i c h were r e a d y f o r model s t r u c t u r e d e t e r m i n a t i o n and p a r a m e t e r A f t e r p o s t u l a t i n g t h e aerodynamic model equa- e s t i m a t i o n .
t i o n s , t h e d e t e r m i n a t i o n o f s i g n i f i c a n t t e r m s among t h e c a n d i d a t e v a r i a b l e s and e s t i m a t i o n o f F o r t h e model s t r u c t u r e d e t e r m i n a t i o n p r o c e - t h e c o r r e s p o n d i n g p a r a m e t e r s f o l l o w s . The v a r i a - d u r e , i t was assumed t h a t , b l e chosen f o r e n t r y i n t o t h e r e g r e s s i o n e q u a t i o n i s t h e one t h a t has t h e l a r g e s t c o r r e l a t i o n w i t h ( 1 ) The g e n e r a l e q u a t i o n s o f r i g i d body y a f t e r a d j u s t i n g f o r t h e e f f e c t o n y o f t h e m o t i o n a d e q u a t e l y d e f i n e t h e a i r p l a n e m o t i o n .
v a r i a b l e s a l r e a d y s e l e c t e d . The p a r a m e t e r s a r e (See a p p e n d i x ) e s t i m a t e d b y m i n i m i z i n g t h e c o s t f u n c t i o n ( 2 ) The model f o r t h e aerodynamic f o r c e - a n d - m o m e n t - c o e f f i c i e n t s can be r e p r e s e n t e d b y m u l t i - v a r i a b l e p o l y n o m i a l s i n r e s p o n s e and c o n t r o l v a r i a b l e s . The p a r a m e t e r s i n t h e s e e q u a t i o n s a r e t h e c o e f f i c i e n t s o f t h e T a y l o r s e r i e s e x p a n s i o n a r o u n d t h e v a l u e s c o r r e s p o n d i n g t o t h e i n i t i a l where N i s t h e number o f d a t a p o i n t s and (!L + 1 ) s t e a d y - s t a t e f l i g h t .
i s t h e number o f p a r a m e t e r s i n t h e r e g r e s s i o n e q u a t i o n a t any s t e p .
(3) L i n e a r t e r m s i n t h e T a y l o r s e r i e s expan- s i o n make g e n e r a l l y l a r g e r c o n t r i b u t i o n t o a e r o d y - A t e v e r y s t e p o f t h e r e g r e s s i o n , t h e v a r i a - namic f u n c t i o n s , f o l l o w e d b y h i g h e r - o r d e r t e r m s .
b l e s i n c o r p o r a t e d i n t o t h e model i n p r e v i o u s s t a g e s and a new v a r i a b l e e n t e r i n g t h e model a r e r e e x - The t h i r d a s s u m p t i o n , r e s u l t i n g i n a con- amined. Any v a r i a b l e t h a t p r o v i d e s a n o n s i g n i f i - s t r a i n t on t h e s e l e c t i o n o f s i g n i f i c a n t t e r m s i n c a n t c o n t r i b u t i o n (due t o c o r r e l a t i o n w i t h more t h e r e g r e s s i o n e q u a t i o n , i s what g i v e s r i s e t o t h e r e c e n t l y added t e r m s ) i s removed f r o m t h e model.
M o d i f i e d S t e p w i s e R e g r e s s i o n ( M S R ) t e c h n i q u e .
The p r o c e s s o f s e l e c t i n g and c h e c k i n g v a r i a b l e s c o n t i n u e s u n t i l no more v a r i a b l e s a r e a d m i t t e d t o MSR i s a m o d i f i e d v e r s i o n of l i n e a r r e g r e s - t h e e q u a t i o n and n o more a r e r e j e c t e d . E x p e r i e n c e s i o n , w h i c h can d e t e r m i n e t h e s t r u c t u r e o f t h e shows, however, t h a t t h e model based o n l y o n t h e aerodynamic model e q u a t i o n s , and e s t i m a t e t h e s i g n i f i c a n c e o f i n d i v i d u a l p a r a m e t e r s i n t h e model model p a r a m e t e r s . The d e t e r m i n a t i o n o f an ade- i n Eq. ( 1 ) can s t i l l i n c l u d e too many t e r m s and, q u a t e model f o r t h e aerodynamic c o e f f i c i e n t s t h e r e f o r e , may have p o o r p r e d i c t i o n c a p a b i l i t i e s .
i n c l u d e s t h r e e s t e p s : t h e p o s t u l a t i o n o f t e r m s S e v e r a l c r i t e r i a f o r t h e s e l e c t i o n o f an adequate t h a t m i g h t e n t e r t h e model, s e l e c t i o n o f an ade- model a r e i n t r o d u c e d i n R e f . 7 , and t h e d e t a i l s o f q u a t e m o d e l , and t h e v e r i f i c a t i o n o f t h e model t h e e n t i r e p r o c e d u r e a r e e x p l a i n e d i n t h a t s e l e c t e d . The g e n e r a l f o r m o f aerodynamic model r e f e r e n c e .
e q u a t i o n s can be w r i t t e n as A p p l y i n g t h e s e c r i t e r i a , an a d e q u a t e model
= 80 + 0 1 x l ( t ) + . . . + 0 n x n ( t ) ( 1 )
y ( t ) e q u a t i o n f o r t h e a i r p l a n e p i t c h i n g moment c o e f f i - c i e n t was d e f i n e d b y a T a y l o r S e r i e s e x p a n s i o n , where y ( t ) r e p r e s e n t s t h e r e s u l t a n t c o e f f i c i e n t o f aerodynamic f o r c e or moment. I n t h e p o l y n o m i -
c = c + C , a + C , ( 5 )
n a l r e p r e s e n t a t i o n o f t h e a e r o d y a m i c c o e f f i c i e n t ,
6e + Cmq E
mo a 6e 01 t o 0 n a r e t h e s t a b i l i t y and c o n t r o l d e r i v a - t i v e s , 8 , i s t h e v a l u e o f any p a r t i c u l a r c o e f f i - t h e s o l u t i o n o f w h i c h p r o v i d e d an adequate f i t t o c i e n t c o r r e s p o n d i n g t o t h e i n i t i a l s t e a d y - f l i g h t t h e measured f l i g h t d a t a . I n a s i m i l a r manner, c o n d i t i o n s , and x i t o Xn a r e t h e r e g r e s s o r s t h i s p r o c e d u r e was used t o e s t i m a t e t h e o t h e r l o n - f o r m e d b v t h e a i m l a n e o u t D u t and c o n t r o a r i a- g i t u d i n a l s t a b i l i t y and c o n t r o l d e r i v a t i v e s b l e s or i h e i r c o m b i n a t i o n s ’ .
d e s c r i b e d i n t h i s r e p o r t . The a n a l y s e s f o r t h e C , and Cm d e r i v a t i v e e s t i m a t e s , and t h e r e l a - F o r example, i f we l e t y = Cm, t h e a r p l ane t i v e e f f e c t s o f t a i l i c i n g o n t h e s e e s t i m a t e s i s p i t c h i n g moment c o e f f i c i e n t , we may choo e t h e g i v e n i n F i g s . 5 t o 8 . A p h y s i c a l i n t e r p r e t a t i o n
c a n d i d a t e v a r i a b l e s , X i , X2,. . . Xn, as
o f t h e s e r e s u l t s w i l l be d i s c u s s e d i n a l a t e r s e c t i o n o f t h i s r e p o r t .
A c c u r a c y o f t h e D e r i v a t i v e E s t i m a t e s The 45 r e p e a t d o u b l e t maneuvers, i d e n t i c a l l y s t a n d a r d e r r o r f o r v a l u e s o f e x e c u t e d i n each o f t h e f o u r c o n f i g u r a t i o n s , p r o - ' m v i d e d a s t a t i s t i c a l l y s i g n i f i c a n t d a t a base f o r 6e p a r a m e t e r and e r r o r e s t i m a t e a c c u r a c y s t u d i e s .
The s t a n d a r d e r r o r c a l c u l a t e d f o r each ensemble s ( y ) = s p A ( y ) * R a t i o o f ensemble t o program o f p a r a m e t e r e s t i m a t e s v e r i f i e d t h e e f f e c t i v e n e s s R a v e r a g e o b t a i n e d from r) o f maneuver s e l e c t i o n t h r o u g h d e m o n s t r a t e d r e p e a t - T a b l e 111.
a b i l i t y o f t h e p r e d i c t e d p a r a m e t e r s . I n a d d i t i o n , a c o m p a r i s o n o f t h e a v e r a g e o f t h e s t a n d a r d e r r o r v a l u e s e s t i m a t e d b y t h e computer p r o g r a m t o t h e s t a n d a r d e r r o r f o r t h e ensemble, p r o v i d e d an e v a l - u a t i o n o f how r e a l i s t i c t h e p r o g r a m e s t i m a t e d s t a n d a r d e r r o r v a l u e s were. The r e s u l t i n g i n t e r v a l i s one w i t h i n w h i c h we can e x p e c t 95 p e r c e n t o f a l l p r e d i c t e d e l e v a t o r Repeat maneuvers were a n a l y z e d u s i n g t h e Mod- e f f e c t i v e n e s s v a l u e s t o f a l l . F i g u r e 9 p r e s e n t s i f i e d S t e p w i s e R e g r e s s i o n and t h e r e s u l t i n g mean t h e s e p r e d i c t i o n i n t e r v a l s and g i v e s an i l l u s t r a - v a l u e s o f c o e f f i c i e n t s were c o m p i l e d i n T a b l e 111. t i o n o f b o t h t h e a r e a s i n w h i c h i c i n g e f f e c t s a r e Accompanying each p a r a m e t e r e s t i m a t e i s t h e a v e r - d i s c e r n a b l e as w e l l as t h e speed r a n g e i n w h i c h w e age s t a n d a r d e r r o r a s s o c i a t e d w i t h i t as g i v e n by c a n n o t a t t r i b u t e any change i n Cm6. t o t h e a r t i - t h e e s t i m a t i o n a l g o r i t h m , t h e s t a n d a r d e r r o r f o r f i c i a l i c e shape. A s i m i l a r a n a l y s i s can be done t h e ensemble o f v a l u e s f r o m t h e 4 5 r e p e a t maneu- on o t h e r p a r a m e t e r s b y f i t t i n g them i n a p i e c e w i s e v e r s , and t h e r a t i o o f t h e two. The r a t i o g i v e n l i n e a r f a s h i o n .
f o r each p a r a m e t e r i s t h e f a c t o r b y w h i c h t h e p r o - gram e s t i m a t e d s t a n d a r d e r r o r f o r t h a t p a r a m e t e r E f f e c t s o f T a i l I c e o n H a n d l i n g C h a r a c t e r i s t i c s s h o u l d be m u l t i p l i e d t o p r o d u c e a r e a l i s t i c e x p e c t e d s t a n d a r d e r r o r . For example, t h e s t a n d - The e f f e c t s o f i c i n g o n t h e h o r i z o n t a l t a i l MSR for Cza s h o u l d be a r d e r r o r e s t i m a t e d b y p l a n e were o b t a i n e d b y a n a l y z i n g a l l o f t h e dou- m u l t i p l i e d by 2 . 9 t o a c h i e v e a r e a l i s t i c a p p r o x i - b l e t maneuvers e x e c u t e d t h r o u g h o u t t h e a t t a i n a b l e m a t i o n t o an a c t u a l ensemble s t a n d a r d e r r o r . r a n g e s o f speed and a n g l e o f a t t a c k . The MSR ana- l y z e d r e s u l t s o f t h e s e maneuvers, i n t h e form o f A f u n d a m e n t a l i s s u e t h r o u g h o u t t h i s r e s e a r c h t h e e s t i m a t e d s t a b i l i t y and c o n t r o l d e r i v a t i v e s , i s t h a t o f d i s t i n g u i s h i n g between t h e e f f e c t s o f a r e p r e s e n t e d i n F i g s . 5 t o 8 . Each p a r a m e t e r i c e and t h e i n h e r e n t v a r i a b i l i t y o f p r e d i c t e d v a l u e i s p l o t t e d w i t h +2u e r r o r b a r s based o n t h e p a r a m e t e r s . I n a d d i t i o n t o t h e e r r o r a n a l y s i s s t a n d a r d e r r o r as g i v e n b y t h e computer program.
p e r f o r m e d o n t h e v a l u e s o b t a i n e d f r o m t h e 4 5 The MSR a n a l y s i s i n d i c a t e d t h a t n o n o n l i n e a r terms r e p e a t maneuvers, t h e Cmro e s t i m a t e s f o r t h e 0" were r e q u i r e d f o r an a d e q u a t e aerodynamic model.
T h i s f l a p c o n d i t i o n were c o n s i z e r e d ( F i g . 6 t c ) ) .
F i g u r e s 5 and 6 show an a n a l y s i s f o r t h e 0" s e t o f p o i n t s was chosen f o r t h i s p o r t i o n o f t h e a n a l y s i s because each of t h e t w o g r o u p s o f v a l u e s c a s e s . The c z d e r i v a t i v e s i n d i c a t e an a p p a r e n t l o s s of e l e v a t o r e f f e c t i v e n e s s , e s p e c i a l l y ( i c e d and u n i c e d ) l e n d t h e m s e l v e s t o l i n e a r low a i r s p e e d s t h a t c o r r e s p o n d w i t h h i g h e r a t a p p r o x i m a t i o n s . Also, d e t e r m i n i n g a p r e d i c t i o n a n g l e s of a t t a c k . The p i t c h i n g moment d e r i v a t i v e s , i n t e r v a l i n t h i s p a r t i c u l a r case Serves t o quan- Cma. Cmq. and Cmbe. w h i c h have an i m p o r t a n t t i t a t i v e l y e n f o r c e what i s q u a l i t a t i v e l y a v e r y n o t i c e a b l e d i f f e r e n c e i n p a r a m e t e r s for t h e i c e d l e f f e c t on a i r p l a n e s h o r t p e r i o d s t a b i l i t y and con- u n i c e d c a s e s . A f t e r a p p r o x i m a t i n g t h e two groups t r o l c h a r a c t e r i s t i c s , a r e . a l s o more s t r o n g l y o f p o i n t s b y s t r a i g h t l i n e s , p r e d i c t i o n i n t e r v a l s a f f e c t e d b y t h e i c e c o n t a m i n a t e d h o r i z o n t a l t a i l a t low speeds. A t h i g h e r speeds, t h e e f f e c t s o f a b o u t t h e s e l i n e s were c a l c u l a t e d as f o l l o w s : t a i l i c e become n e g l i g a b l e . T h i s a n a l y s i s was s u p p o r t e d b y p i l o t comments r e p o r t i n g t h a t a t low speeds, t h e " i c e d " a i r p l a n e was l e s s r e s p o n s i v e t o e l e v a t o r c o n t r o l i n p u t s , and more w e a k l y damped i n p i t c h . These comments, however, were n o t based ( 6 ) i n d e f i n - o n s p e c i f i c p i l o t i n g t a s k s n o r m a l l y used where i n g p i l o t r a t i n g s , b u t o n t h e p e r c e i v e d r e l a t i v e d i f f e r e n c e s ( c l e a n v e r s u s i c e d ) i n l o n g i t u d i n a l l i n e a r a p p r o x i m a t i o n o f c o n t r o l f o r c e , r e s p o n s e , and p i t c h i n g moment cha- Yo( xo) C m c o r r e s p o n d i n g t o r a c t e r i s t i c s w h i l e p e r f o r m i n g p a r a m e t e r i d e n t i f i - some ( v e l o c i t y ) v a l u e c a t i o n maneuvers. F u r t h e r , t h e m a g n i t u d e o f t h e s e e f f e c t s were n o t j u d g e d t o be g r e a t enough t o a* 0 . 0 5 t o a c h i e v e a 95 p e r c e n t change p i l o t r a t i n g s i f such a n e v a l u a t i o n were p r e d i c t i o n i n t e r v a l t o have been c a r r i e d o u t .
n number of p o i n t s I n t h e t e n d e g r e e f l a p c a s e s , F i g s . 7 and 8, t h e e f f e c t s o f h o r i z o n t a l t a i l i c i n g show an oppo- t a * / ~ , n-2 s t u d e n t t - d i s t r i b u t i o n s i t e t r e n d when compared w i t h t h e 0" c a s e s .
A n a l y s i s o f t h e s t a b i l i t y and c o n t r o l d e r i v a t i v e s S s t a n d a r d e r r o r ( c a n he one show s l i g h t l y d e g r a d e d p i t c h i n g moment c o e f f i c i - I o f t h r e e l i s t e d b e l o w ) e n t s up t o speeds o f a p p r o x i m a t e l y 90 k n . Above t h e s e speeds, t h e r e i s a more p r o n o u n c e d degrada- S P A ( Y ) = a v e r a g e o f s t a n d a r d e r r o r s o b t a i n e d t i o n i n t h e s e d e r i v a t i v e s , and t h i s a n a l y s i s was from t h e computer p r o g r a m a g a i n v e r i f i e d b y p i l o t comments. D o u b l e t maneu- i = p q [ - ] + I X Z ( p ' - q r ) + v e r s p e r f o r m e d a t 100 k n w i t h a r t i f i c i a l t a i l i c e were accompanied by e l e v a t o r f o r c e l i g h t e n i n g and a s t r o n g " b u r b l e " f e e d b a c k i n t h e c o n t r o l s a t h i g h (A6) T h i s c h a r a c t e r i s t i c was n e g a t i v e p i t c h r a t e s .
a l o n g w i t h t h e k i n e m a t i c r e l a t i o n s assumed due t o t h e h i g h t a i l downwash a n g l e i n d u c e d i n t h e p i t c h o v e r p o r t i o n o f t h e d o u b l e t maneuver, 6 = q cos 4 - r s i n 4 c a u s i n g a s i g n i f i c a n t amount o f s e p a r a t e d f l o w t o (A7) o c c u r on t h e h o r i z o n t a l t a i l p l a n e . T h i s o c c u r r e d 41 = p + ( q s i n 41 + r cos 4 ) t a n 8 (A8) a t a l o w peak l o a d f a c t o r o f a p p r o x i m a t e l y 0 g, w h i c h as m e n t i o n e d e a r l i e r i n t h i s r e p o r t , was where u , v , and w a r e t h e v e l o c i t y components; e r r o n e o u s l y i n p u t because t h e c o c k p i t g m e t e r r e a d 6 and 8 a r e t h e r o l l and p i t c h a n g l e s ; g i s i n c o r r e c t l y .
t h e a c c e l e r a t i o n d u e t o g r a v i t y ; p i s t h e a i r den-
s i t y ; in i s t h e a i r p l a n e mass; I x . I y , I z and
Conc 1 us i ons I x z and t h e moments and p r o d u c t o f i n e r t i a ; S , b,
and c a r e t h e w i n g a r e a , span and mean a e r o d y -
Based on t h e a n a l y s i s and r e s u l t s h e r e i n , t w o namic c h o r d ; and a d o t o v e r a symbol r e p r e s e n t s f u n d a m e n t a l c o n c l u s i o n s were drawn r e g a r d i n g t h e t h e d e r i v a t i v e w i t h r e s p e c t t o t i m e . The t o t a l use o f a M o d i f i e d S t e p w i s e R e g r e s s i o n a l g o r i t h m a i r s p e e d V i s g i v e n b y i n e s t i m a t i n g t h e e f f e c t s o f i c i n g on a i r c r a f t s t a b i l i t y and c o n t r o l c h a r a c t e r i s t i c s : ( 1 ) The o f t h e a r t i f i c i a l i c e shape a t t a c h e d t o e f f e c t s t h e t a i l were m e a s u r a b l e as changes i n t h e l o n g i - Here, Eqs. ( A l ) , ( A 3 ) . ( A 5 ) , and (A7) t u d i n a l s t a b i l i t y and c o n t r o l d e r i v a t i v e s f o r a l l d e s c r i b e t h e l o n g i t u d i n a l m o t i o n w h i l e Eqs. ( A 2 ) , f l i g h t c o n d i t i o n s t e s t e d , and ( 2 ) t h a t a m u l t i - p l i c a t i v e r e l a t i o n s h i p was i d e n t i f i e d between t h e ( A 4 ) . ( A 6 ) , and (A8) d e s c r i b e t h e l a t e r a l m o t i o n o f t h e a i r p l a n e . The a n g l e s o f a t t a c k and s i d e - ensemble s t a n d a r d e r r o r and t h e e s t i m a t e d s t a n d a r d s l i p a r e g i v e n b y e r r o r from t h e M o d i f i e d S t e p w i s e R e g r e s s i o n r o u - t i n e . The n u m e r i c a l v a l u e r e p r e s e n t i n g t h e r a t i o a = t a n - l ( w / u ) and p = s i n - l ( v / V ) o f t h e ensemble s t a n d a r d e r r o r , t o t h e e s t i m a t e d s t a n d a r d e r r o r f r o m t h e p r o g r a m when a s s i g n e d t o The aerodynamic f o r c e s and moments a r e r e p r e - each c o n t r o l or s t a b i l i t y d e r i v a t i v e , a r e i n d i c a - o f t h e l e v e l of c o n f i d e n c e one s h o u l d have s e n t e d b y t h e c o e f f i c i e n t s Ca(a = X , Y , Z , 1 , m, t i v e or n ) . I t i s p o s t u l a t e d t h a t t h e s e c o e f f i c i e n t s i n t h e e s t i m a t e d v a l u e o f t h a t p a r a m e t e r .
can be w r i t t e n as a T a y l o r ' s s e r i e s p o l y n o m i a l e x p a n s i o n a b o u t an e q u i l i b r i u m t r i m c o n d i t i o n as The r e s u l t s o f t h i s f l i g h t t e s t p r o g r a m i n d i - c a t e t h a t MSR i s a v i a b l e t e c h n i q u e f o r d e t e r m i n - i i n g t h e e f f e c t s o f i c i n g o n t h e l o n g i t u d i n a l s t a b i l i t y and c o n t r o l c h a r a c t e r i s t i c s o f an a i r - a a , o (A9) c r a f t . A p p l i c a t i o n o f t h i s f l i g h t t e s t and a n a l y - i =1 s i s t e c h n i q u e s h o u l d p r o v e v e r y u s e f u l f o r v a l i d a t i n g s t a b i l i t y and c o n t r o l p r e d i c t i o n s from where 0 and a r e t h e unknown param- w i n d t u n n e l s or c o m p u t a t i o n a l methods. a ,o e t e r . F o r a = X , Z , o r m, t h e i n d e p e n d e n t v a r i a b l e s x a r e Appendix j P o s t u l a t e d Models
a, $, and be
The s i x - d e g r e e - o f - f r e e d o m e q u a t i o n s o f m o t i o n f o r t h e a i r p l a n e a r e : and f o r a = Y , 1 , or n , t h e y a r e L
P. $ , r b
ir = -qw + r v - g s i n e + e cX ( A 1 )
F u r t h e r m o r e .
v2s
(A2)
v = - r u + pw + g cos e s i n 4 + + cy
AXj = x j ( t ) - X ( t = 0) j R e f e r e n c e s
w = - P V + qu + g cos e cos 4 +
cz
1 . Ranaudo, R . J . , M i k k e l s e n , K . L . , M c K n i g h t , I X Z 2 R.C., and P e r k i n s , P . J . , J r . , " P e r f o r m a n c e
( p q + i ) + LQ c
D e g r a d a t i o n o f a T y p i c a l T w i n E n g i n e Commuter
21X = q r [ - I +
Type A i r c r a f t i n Measured N a t u r a l I c i n g C o n d i - t i o n s , " A I A A Paper 84-0179, J a n . 1984. (NASA (A4) TM-83564).
2 . M i k k e l s e n , K . L . , M c K n i g h t , R.C., Ranaudo, R . J . , and P e r k i n s , P . J . , J r . , " I c i n g F l i g h t Research: Aerodynamic E f f e c t s of I c e and I c e (A5) Shape D o c u m e n t a t i o n w i t h S t e r e o P h o t o g r a p h y , " A I A A Paper 85-0468, J a n . 1985. (NASA TM-86906).
6 . K l e i n , V . and Morgan, D . R . , " E s t i m a t i o n o f 3. Ranaudo, R.J., e t a l . , "The Measurement of B i a s E r r o r s i n Measured A i r p l a n e Responses A i r c r a f t P e r f o r m a n c e and S t a b i l i t y and C o n t r o l U s i n g Maximum L i k e l i h o o d Method," NASA A f t e r F l i g h t Through N a t u r a l I c i n g Condi- TM-89059, 1987.
t i o n s " . A I A A Paper 86-9758, A p r . 1986.
(NASA TM-87265).
7. K l e i n , V . , B a t t e r s o n , J.G., and Murphy, P . C . , " D e t e r m i n a t i o n o f A i r p l a n e Model S t r u c t u r e 4. J o r d a n , J.L., P l a t z , S . J . , and S c h i n s t o c k , from F l i g h t D a t a By U s i n g M o d i f i e d S t e p w i s e W.C., " F l i g h t T e s t R e p o r t o f t h e NASA I c i n g R e g r e s s i o n , " NASA TP-1916, 1981.
Research A i r p l a n e , " KSR 86-01, Kohlman Systems Research, I n c . , Lawrence, KS, 1986, NASA CR-179515.
5 . Maine, R . E . and I l i f f , K.W., " A p p l i c a t i o n o f Parameter E s t i m a t i o n t o A i r c r a f t S t a b i l i t y and C o n t r o l : The O u t p u t - E r r o r Approach," NASA RP-1168, 1986.
TABLE I . - P H Y S I C A L C H A R A C T E R I S T I C S
OF THE D E H A V I L L A N D DH-6 T W I N OTTER
I C h a r a c t e r i s t i c I Low I H i g h 1
Geome tri c : Wing a r e a , in2 39.02 19.81 Wing s p a n , m A s p e c t r a t i o MAC, m 1.981
I M a s s , kg 1 4150 I 4600 I
I n e r t i a s , kg m 2 : 21 279 21 787 I x x 30 000 31 027 I Y Y 44 986 48 639 1432 1498 1 x 2
TABLE 11. - C H A R A C T E R I S T I C S OF FLIGHT TEST I N S T R U M E N T A T I O N
[21 channel d i g i t a l r e c o r d i n g c a p a b i 1 i t y o f t h e f o l l o w i n g p a r a m e t e r s such t h a t f o l l o w i n g u n i t s , r a n g e s and
r e s o l u t i o n s a r e p r o v i d e d . I
Parameter Range Resol -
u t i o n L o n g i t u d i n a l a c c e l e r a t i o n , g u n i t s tl 0.002 ? 1 L a t e r i a l a c c e l e r a t i o n , g u n i t s .002 Normal a c c e l e r a t i o n , g u n i t s +3,-1 . 0 0 4 P i t c h r a t e , d e g / s e c r l 5 .029 Roll r a t e , d e g l s e c 250 ,098 Yaw r a t e , d e g l s e c 230 . o s 9 P i t c h a n g l e , deg 245 .088 Roll a n g l e , deg 290 .176 A l p h a , deg +15,-10 .024 +19,-16 L e f t a i l e r o n p o s i t i o n , deg .034 R i g h t a i l e r o n p o s i t i o n , deg +19,-16 . 0 3 4 E l e v a t o r p o s i t i o n , deg 220 . 0 3 9 Rudder p o s i t i o n , deg t 1 8 .035 B e t a , deg 21 5 .029 B a t t e r y A v o l t a g e , V
A i r s p e e d , m/sec o t o a 5 .oa3
A i r t e m p e r a t u r e , " C -18 t o 38 .os5 V o l t a g e s y s t e m r e f e r e n c e A l t i t u d e , rn - 1 50 t o 3000 3.08 R e f e r e n c e v o l t a g e 1 R e f e r e n c e v o l t a g e 2
TABLE 111. - MEAN VALUES OF STABILITY AND CONTROL
DERIVATIVES CALCULATED FROM 45 REPEAT MANEUVERS USING MODIFIED S T E P W I S E REGRESSION.
[ F l a p s , 0"; 120 KIAS; b a s e l i n e ( n o i c e ) . ] Parameter Mean v a l u e , S t a n d a r d e r r o r s a R a t i o ,
e s E ( e ) / s ( e )
S E ( 8 ) S(8) -5.66 0 . 0 4 9 3 0.0169 2 . 9 czci -19.97 1.047 .386 2 . 7 c z q
- .608 .028 1 .0122 2.3
Czde -1.31 .0147 .0191 . 8 Cma .4314 1.5 -34.2 .6444 Cmq -1.74 .0248 .0131 1 . 9 Cmde J
4 3.81 I-
(12.5)
____/
15.77(51.75>
P
FIGURE 1. - NASA LEWIS RESEARCH CENTER ICING RESEARCH A I R - CRAFT, ALL DIMENSIONS ARE I N M (FT).
1-85-47631 ( a ) ARTIFICIAL TAIL ICE ATTACHMENT.
c
W (b) FULL SPAN VIEW OF THE ARTIFICIAL ICE SHAPE.
FIGURE 2. - ARTIFICIAL MODERATE GLAZE ICE ATTACHED TO THE TAIL OF THE ICING RESEARCH
A I RCRAFT ,
CRIGINAL PAGE I S
OF POOR QUALITY
FIGURE 3. - FLIGHT TEST NOSE BOOM SHOWING 0 AND VANE INSTALLATION.
1 1 I
l2 r
W W fl CL k J W
I J
l 2 r
7 - W W a 14 r W W fl 4 - -6 V W v)
's
W P U
-4.8 r 0 UNICED
ICED
-lo r
-40 I I I I
-0.6 * * T I
al uo N V -1 .o A -1.2
- 1 . 3 -
& E -1.4 V
0 UNICED -1.5 -
ICED -1.6
- $ f
I I I I
-1.7
-
I I
-50 -1.5 r
I N IT IAL VELOCITY, kn
FIGURE 6. - PITCHING MOMENT COEFFICIENT DERIVATIVE
ESTIMATES FOR 0' FLAP SHOWING THE EFFECTS OF TAIL ICING USING THE MSR TECHNIQUE. 20 ERROR BARS ARE FROM THE MSR PROGRAM.
1 4 -4.8 0 UNICED -5.0 ICED -5.2 CJ -5.4 N V -5.6 -5.8 -6.0 -6.2 -30
-0.4 r
-
-0.5
-
-0.6
Y -
-0.7 I L o N V
I I I I
60 70 80 90 100
I N I T I AL VELOCITY, k n
FIGURE 7. - VERTICAL FORCE COEFFICIENT DERIVATIVE ESTI-
NATES FOR 10' FLAP SHOWING THE EFFECTS OF TAIL ICING USING THE MSR TECHNIQUE. 20 ERROR BARS ARE FROM THE MSR PROGRAM.
-
-0.6
0 UNICED
- ICED
-0.8
-1 .o
E
-1.2 -1 .I\ -1.6 -28 -30 -32
I 5
V -34 - 36
t l
J . .
I I I I
-38 INITIAL VELOCITY, kn
FIGURE 8. - PITCHING MOMENT COEFFICIENT DERIVATIVE
ESTIMATES FOR IOo FLAP SHOWING THE EFFECTS OF TAIL ICING USING THE MSR TECHNIQUE. 20 ERROR BARS ARE FROM THE MSR PROGRAM.
1 6 -1.6 ~ -1.8 t o E V -2.0 ICED -2.2
o UNICED
I I I I 1
-2.4 I I
70 80 90 100 110 120 130
IN IT I A L VELOCITY
FIGURE 9. - 95 PERCENT PREDICTION INTERVALS ON ELEVATOR EFFECTIVENESS VALUES FOR THE ARTIFICIALLY ICED VERSUS UNICED AIRCRAFT TAIL. WING FLAPS AT 0'.
1 7
Report Documentation Page
National Aeronautics and
-
Space Administration 2. Government Accession No. 1. Report No. 3. Recipient's Catalog No.
NASA TM-101427 AIAA-89-0754 4. Title and Subtitle 5. Report Date Determination of Longitudinal Aerodynamic Derivatives Using Flight Data From an Icing Research Aircraft 6. Performing Organization Code 7. Author@) 8. Performing Organization Report No.
R.J. Ranaudo, J.G. Batterson, A.L. Reehorst, E-4528 T.H. Bond, and T.M. O'Mara 10. Work Unit No.
505-68- 11 9. Performing Organization Name and Address 11. Contract or Grant No.
National Aeronautics and Space Administration Lewis Research Center Cleveland, Ohio 44135-3191 13. Type o f Report and Period Covered Technical Memorandum 12. Sponsoring Agency Name and Address National Aeronautics and Space Administration 14. Sponsoring Agency Code Washington, D.C. 20546-0001 15. Supplementary Notes Prepared for the 27th Aerospace Sciences Meeting sponsored by the American Institute of Aeronautics and Astronautics, Reno, Nevada, January 9-12, 1989. R.J. Ranaudo, A.L. Reehorst, and T.H. Bond, NASA Lewis Research Center; J.G. Batterson, NASA Langley Research Center, Hampton, Virginia 23665-5225; T.M. O'Mara, George Washington University, Washington, D.C. 20052 and Joint Institute for Advancement of Flight Science, NASA Langley Research Center.
17. Key Words (Suggested by Author@) 18. Distribution Statement
Unclassified - Unlimited
Aircraft stability and control Flight test measurements Subject Category 08 Icing effects 19. Security Classif. (of this report) 20. Security Classif. (of this page) 21. No of pages 22. Price' Unclassified Unclassified 18 A03 National Aeronautics and SECOND CLASS MAIL Space Administration
111111
Lewis Research Center ADDRESS CORRECTION REQUESTED Cleveland. Ohio 44135 P o a t a g e u d F ~ P a i d N.tknd Aeronautics and Space Administration NASA461