A performance application study of a jet-flap helicopter rotor

APPENDIX A ROTOR PERFORMANCE CALCULATION I n t r o duc t i on The r o t o r p e r f o r m a n c e s u b r o u t i n e c o n s i s t s o f two p a r t s . The f i r s t p a r t i s u s e d t o compute t h e r o t o r f l a p p i n g a n g l e s and i s b a s e d on t h e e q u a t i o n s p r e s e n t e d i n R e f e r e n c e 3 . The s e c o n d p a r t u s e s t h e f l a p p i n g v a l u e s o b t a i n e d i n t h e f i r s t p a r t and computes t h e aerodynamic c h a r a c t e r i s t i c s o f t h e r o t o r b a s e d on e q u a t i o n s from R e f e r e n c e 4 .

I n t h e p r e s e n t j e t - f l a p s t u d y n i n e r a d i a l s t a t i o n s a r e assumed on t h e b l a d e p o r t i o n i n b o a r d o f t h e j e t - f l a p and f i v e s t a t i o n s on t h e j e t - f l a p . E i g h t e e n azimuth p o s i t i o n s a r e u s e d . I n t h e f o l l o w i n g d i s c u s s i o n , t h o s e terms which have b e e n added t o han- d l e t h e j e t - f l a p a r e u n d e r l i n e d .

Angle of A t t a c k and S e c t i o n C h a r a c t e r i s t i c s f o r Unflapped B l a d e A t e a c h s t a t i o n and azimuth, t h e f o l l o w i n g e q u a t i o n s a r e u s e d t o compute l o c a l a n g l e o f a t t a c k and Mach Number. A l l terms a r e w i t h r e s p e c t t o t h e r o t o r s h a f t axis.

up = A s cos 6 - B - lJs s i n f3 c o s Y

(x - ( A - 1 ) S e e c o s 6 + 1 . 1 , s i n Y

UT = + (x - K)

( A - 2 ) S The l o c a l a n g l e of a t t a c k i s a

= B o + B1 x -A1 c o s 1 - B1 s i n " + $+ OCNI (A- 5)

' P -

The l o c a l Mach Number i s U RR -

MX - -

a By u s i n g t h e s e c t i o n a n g l e o f a t t a c k and Mach Number, C R and for t h e b a s i c r o t o r b l a d e s e c t i o n e x c l u s i v e o f t h e j e t - f l a p ‘d - a r e o b t a i n e d f r o m t a b l e s of two d i m e n s i o n a l a i r f o i l d a t a .

( R e f e r e n c e 11) J e t - F l a p Momentum and L i f t and Drag C o e f f i c i e n t s A t e a c h s t a t i o n on t h e j e t - f l a p , mass f l o w and r e l a t i v e g a s e j e c - t i o n v e l o c i t y a r e computed d u r i n g t h e r o t o r power a v a i l a b l e c a l - c u l a t i o n d i s c u s s e d i n Appendix B . Momentum c o e f f i c i e n t i s t h e n computed a t each s t a t i o n u s i n g t h e f o l l o w i n g e q u a t i o n : 2m V.b

c =+

(A- 7 ) j PU (RR) UTR The f o l l o w i n g e q u a t i o n s a r e u s e d t o d e t e r m i n e d t h e C Q and c d c o n t r i b u t e d by t h e j e t - f l a p : (A- 8) = C . s i n ( a + 6 ) + S Q - C . s i n ( a + 6 ) C Q j 3 3 The m e c h a n i c a l f l a p C i s s i m p l y : d~~ - (A- 10)

- -

O - 6 C d~~ , M F The e x p r e s s i o n s f o r t o t a l C Q and C on t h e j e t - f l a p p o r t i o n d a r e : = C Q + C s i n ( a + 6 ) + S Q C . s i n ( a + 6 ) (A-11) j J j 0 - 5 6 - cos ( a + 6 ) '

- c - cos ( a + 6 )

cd = cd - s d (A- 1 2 ) j ! acd \ 0 . . 6 + - 4 \ a 6 .MF B 1 ade F 1 app i ng Char a c t e r i s t i c s The p r o c e d u r e u s e d t o o b t a i n t h e b l a d e f l a p p i n g c h a r a c t e r i s t i c s i s b a s e d on t h e f a c t t h a t n o moments may b e t r a n s m i t t e d t h r o u g h t h e b l a d e f l a p p i n g h i n g e . T h a t i s , t h e sum o f a l l moments a b o u t t h e f l a p p i n g h i n g e a t any r o t o r a z i m u t h p o s i t i o n i s z e r o .

(A- 13)

MT - MC - M I - Mw = 0

The aerodynamic moment i s g i v e n by ( A - 1 4 ) XU The c e n t r i f u g a l f o r c e moment i s (A- 15) The b l a d e i n e r t i a moment i s ..

MI = B I h E x p r e s s i n g B i n terms of Y

- -

..

B = n2$ (A- 16) The w e i g h t moment i s g i v e n by MW = M C O S 6 ( A - 17) S u b s t i t u t i n g A-14, A - 1 5 , A-16 and A - 1 7 i n t o e q u a t i o n A-13 r e s u l t s i n a d i f f e r e n t i a l e q u a t i o n i n which - -

B = f ( B , E) (A- 18)

I n i t i a l v a l u e s o f B and a r e assumed f o r t h e z e r o azimuth p o s i - t i o n and e q u a t i o n A-18 i s s o l v e d f o r 6, Using n u m e r i c a l i n t e - g r a t i o n , B and a r e p r e d i c t e d f o r t h e n e x t azimuth p o s i t i o n .

When t h e c a l c u l a t i o n h a s been completed f o r a f u l l r o t o r r e v o l u - t i o n , t h e f i n a l B i s compared w i t h t h e i n i t i a l B . I f t h e y a g r e e w i t h i n a s p e c i f i e d t o l e r a n c e , t h e c a l c u l a t i o n i s c o m p l e t e . I f n o t , t h e i t e r a t i o n i s r e p e a t e d , s t a r t i n g w i t h t h e f i n a l v a l u e of B .

R o t o r C o r i o l i s Torque A c c e l e r a t i o n o f t h e g a s up t o t h e l o c a l r o t a t i o n a l s p e e d o f t h e r o t o r d e t e r m i n e s t h e C o r i o l i s t o r q u e o f t h e r o t o r . T h i s q u a n t i t y i s i n f l u e n c e d by how f a r a l o n g t h e r o t o r a p a r t i c u l a r q u a n t i t y o f g a s t r a v e l s b e f o r e it i s e x h a u s t e d , a s w e l l as t h e amount o f t h e g a s . To d e t e r m i n e t h i s v a l u e , a n u m e r i c a l i n t e g r a t i o n i s p e r f o r m e d which assumes t h e r o t o r t o be b r o k e n up s e q u e n t i a l l y i n t o an i n b o a r d s e c t i o n , f o u r v a r i a b l e b u t e q u a l - l e n g t h j e t - f l a p s e g m e n t s , and t h e t i p n o z z l e , The p r o p o r t i o n o f t h e t o t a l f l o w e x i t i n g t h r o u g h a f l a p s e c t i o n j i s an i n n u t v a r i a b l e K The j * C o r i o l i s t o r q u e c o e f f i c i e n t i s t h e n d e t e r m i n e d as a f u n c t i o n o f g a s f l o w ( o r e n g i n e power l e v e l ) : R o t o r D r i v i n g Torque The t o r q u e d r i v i n g t h e r o t o r i s made up o f two p a r t s , t h a t due t o t h e g a s e x h a u s t i n g from t h e j e t - f l a p and t h a t due t o t h e r e s t o f t h e g a s e x h a u s t i n g from t h e t i p n o z z l e .

The j e t - f l a p d r i v i n g t o r q u e i s a s s o c i a t e d w i t h t h e C D term a s O i J " n e g a t i v e " d r a g i n t h e d r a g c o e f f i c i e n t e q u a t i o n A-9 g i v e n e a r - l i e r . T h i s " n e g a t i v e " d r a g c o e f f i c i e n t i s i n t r o d u c e d i n t o t h e 5 8 t o t a l d r a g c o e f f i c i e n t CD (A-12) which i s c o n v e r t e d i n t o a The t i p n o z z l e d r i v i n g t o r q u e i s d e t e r m i n e d d i r e c t l y by t h e g a s e s e x h a u s t i n g a t t h e n o z z l e , a s g i v e n i n t h e f o l l o w i n g equa- t i o n I (A- 2 0 ) Nozzle T h i s term i s c o n v e r t e d t o C ( Y ) i n t h e n e x t s e c t i o n ( E q u a t i o n QNoz A-32). F i n a l l y , b o t h C ( Y ) and C ( Y ) are combined i n t h e Q j f QNo z e q u a t i o n A-23, which b a l a n c e s a l l a c c e l e r a t i n g and d e c e l e r a t i n g t o r q u e s on t h e r o t o r .

R o t o r Performance E q u a t i o n s The r o t o r p e r f o r m a n c e p a r a m e t e r s are t h e n computed u s i n g t h e f o l - lowing e q u a t i o n s b a s e d on t h e f i n a l f l a p p i n g a n g l e s o b t a i n e d e a r l i e r . These e q u a t i o n s f o r m u l a t e r o t o r t h r u s t , t o r q u e , and h o r i z o n t a l f o r c e . They i n c l u d e t h e p r e v i o u s l y d e t e r m i n e d v a l u e s of f l a p p i n g a n g l e s , C o r i o l i s t o r q u e , and j e t - f l a p and t i p n o z z l e d r i v i n g t o r q u e .

A l l o f t h e s e e q u a t i o n s are s o l v e d s i m u l t a n e o u s l y by i t e r a t i o n , a r r i v i n g a t a n e n g i n e power l e v e l t h a t n o t o n l y p r o v i d e s t h e power r e q u i r e d t o p r o d u c e t h e r e q u i r e d t h r u s t and p r o p u l s i v e f o r c e , b u t a l s o g e n e r a t e s t h e p r o p e r j e t - f l a p e x h a u s t v e l o c i t y t o make t h e j e t - f l a p o p e r a t e a t t h e r e q u i r e d h i g h l i f t c o e f f i c i e n t s .

Blade p i t c h a t t h e t i p n o z z l e i s -

eN - eo + e l + i

- A1 c o s Y - B1 s i n Y + ecam (A- 2 1) Noz (A-22)

(A-24)

f o r each u t i m d - h , p = ~ , n

(A-26)

(A-27)

(A-29) (A-30) (A-31) (A-32)

(A-33)

( A - 3 4 )

APPENDIX B ROTOR POWER AVAILABLE (See a l s o Ref. 12) I n t r o d u c t i o n The r o t o r power a v a i l a b l e i s d e t e r m i n e d by c a l c u l a t i n g t h e changes i n p r e s s u r e and t e m p e r a t u r e o f t h e compressed gas s u p - p l i e d by t h e e n g i n e s a s it t r a v e l s from t h e e n g i n e d i s c h a r g e p l a n e t o t h e n o z z l e s l o c a t e d e i t h e r a l o n g t h e b l a d e i n t h e j e t - f l a p r e g i o n o r a t t h e b l a d e t i p . The s t a t e o f t h e g a s ( p r e s s u r e and t e m p e r a t u r e ) changes u n d e r t h e i n f l u e n c e o f d u c t w a l l f r i c - t i o n , c e n t r i f u g a l f o r c e s and h e a t l o s s e s . F i n a l l y , a t e a c h n o z z l e s e g m e n t , t h e e f f e c t i v e n o z z l e v e l o c i t y i s f o u n d , and t h e l o c a l and i n t e g r a t e d r o t o r d r i v i n g t o r q u e i s d e t e r m i n e d and con- v e r t e d i n t o r o t o r power.

Only t h e f u n d a m e n t a l s o f t h e thermodynamic p r o c e s s w i l l b e d i s - c u s s e d i n t h i s s e c t i o n ; t h e j e t - f l a p a c t i o n i n t r o d u c e s m a j o r p a r a m e t e r s t h a t a f f e c t t h e r o t o r power a v a i l a b l e s u c h a s : F l a p l e n g t h / b l a d e r a d i u s Gas s p l i t between j e t - f l a p a n d . t i p n o z z l e Mean and o s c i l l a t o r y d e f l e c t i o n o f j e t - f l a p The d e t a i l e d i n t e g r a t i o n of t h e s e j e t - f l a p p a r a m e t e r s i n t o t h e Power A v a i l a b l e d e t e r m i n a t i o n i s g i v e n i n Appendix A.

Gas C o n d i t i o n a t t h e E n g i n e E x i t W i t h i n t h e u s u a l h e l i c o p t e r f l i g h t e n v e l o p e , t h e e n g i n e a i r f l o w , f u e l f l o w , and p r e s s u r e r a t i o ( e n g i n e e x i t t o i n l e t ) form s i n g l e l i n e s when p l o t t e d on a r e f e r r e d b a s i s v e r s u s t h e e n g i n e t e m p e r - a t u r e r a t i o ( e x i t t o i n l e t ) . A t y p i c a l p l o t o f r e f e r r e d e n g i n e p a r a m e t e r s f o r a f a n e n g i n e i s shown i n F i g u r e B - 1 .

I With t h i s c h a r t , t h e r e f e r r e d a i r f l o w , ‘a ‘1 e / & , r e f e r r e d f u e l f l o w , W f / & f 8 , and p r e s s u r e r a t i o , P E / P 2 , a r e found f o r a s e l e c t - e d t e m p e r a t u r e r a t i o , T E / T 2 . Each t e m p e r a t u r e r a t i o r e p r e s e n t s an e n g i n e power s e t t i n g (T r e l a t i v e t o some e n g i n e i n l e t tem- E) p e r a t u r e ( T 2 ) . The t a k e o f f and maximum c o n t i n u o u s e x i t t e m p e r a - t u r e s a r e a l s o dependent on i n l e t t e m p e r a t u r e , a s shown t y p i c a l l y i n F i g u r e B - 2 . V a r i o u s e n g i n e a e r o d y n a m i c , m e c h a n i c a l and s t r u c - t u r a l l i m i t s a r e i n v o l v e d i n e s t a b l i s h i n g t h e l i m i t s on F i g u r e B - 2 ; t h e e x a c t d e t a i l s v a r y from m a n u f a c t u r e r t o m a n u f a c t u r e r , b u t t h e t r e n d s a r e g e n e r a l l y a s shown i n F i g u r e B - 2 .

e , W

U 3 8

x

.PI

z J I

e , .4 M

I L c

cu

6 3

-60 -40 -20 0 40 60 80 loo 120

ENGINE INLET TEMPERATURE, T2 - O F

Figure B-2. Engine Exit T e m p e r a t u r e V e r s u s Inlet T e m p e r a t u r e ~ Duct P r e s s u r e Loss from Engine t o R o t o r Hub The a r e a , t h e s h a p e , and t h e g a s p a t h d i r e c t i o n c h a n g e s a l l i n - f l u e n c e t h e p r e s s u r e l o s s from t h e e n g i n e t o t h e r o t o r hub. I f t h e a v e r a g e Mach Number i n t h e d u c t s , plenum, and c o n n e c t i n g elbows can be k e p t i n t h e .25-.35 r a n g e , it s h o u l d b e p o s s i b l e t o keep t h e n o n - b l a d e d u c t p r e s s u r e l o s s u n d e r 4 % o f t h e e n g i n e e x i t t o t a l p r e s s u r e .

Gas C o n d i t i o n s a l o n g t h e R o t o r B l a d e The g a s d u c t i n t h e r o t o r b l a d e d i s c u s s e d h e r e h a s a d u c t area/ b l a d e c r o s s - s e c t i o n a r e a r a t i o ( o r u t i l i z a t i o n U) o f a b o u t U = 0 . 7 3 . I n a d d i t i o n , t h e h y d r a u l i c d i a m e t e r (DH = 4 x a r e a / p e r i - meter) i s a p p r o x i m a t e l y . 1 8 times b l a d e c h o r d f o r a 1 5 % t h i c k a i r f o i l . With t h e s e g e o m e t r i c a l c o n d i t i o n s , t h e d u c t s l e n d e r - n e s s r a t i o (R/DH) i s about 5 0 t o 1. F u r t h e r , f o r s o l i d i t y u .11, a b l a d e r o o t i n l e t Mach Number o f a b o u t . 4 0 i s f o u n d t y p i c a l l y f o r a w e l l - p r o p o r t i o n e d r o t o r .

The e x a c t e q u a t i o n d e s c r i b i n g t h e change o f t h e g a s c o n d i t i o n s a l o n g a l o n g r o t a t i n g d u c t was d e v e l o p e d b y S h a p i r o ( R e f e r e n c e 13) and was expanded b y Henry ( R e f e r e n c e 1 4 ) t o i n c l u d e c e n t r i - f u g a l f o r c e s .

The b a s i c momentum e q u a t i o n i s : The e f f e c t s on d u c t Mach Number a r e shown s u c c e s s i v e l y i n equa- t i o n B - l f o r change o f s t a g n a t i o n t e m p e r a t u r e , f o r e f f e c t o f f r i c t i o n , f o r d u c t area c h a n g e s , and f o r c e n t r i f u g a l f o r c e s .

Due t o t h e i n s u l a t e d n a t u r e o f t h e p r o p o s e d honeycomb b l a d e s , and b e c a u s e o f t h e u s e o f added i n s u l a t i o n t o keep low bond l i n e ' t e m p e r a t u r e s , t h e gas t e m p e r a t u r e can b e e x p e c t e d t o b e p e r h a p s T h i s , 2 5 ' R h i g h e r a t t h e b l a d e t i p t h a n a t t h e b l a d e r o o t .

c o u p l e d w i t h t h e b l a d e geometry and e q u a t i o n B - 1 , w i l l a l l o w c a l - c u l a t i o n o f t h e o v e r a l l change of d u c t Mach Number.

The non- l i n e a r d i f f e r e n t i a l e q u a t i o n o f Mach Number v e r s u s r a d i u s ( e q u a t i o n B - 1 ) can b e s o l v e d w i t h n u m e r i c a l i n t e g r a t i o n on a com- p u t e r .

The b l a d e r o o t Mach Number can be found knowing t h e g a s f l o w , p r e s s u r e , t e m p e r a t u r e , and d u c t a r e a u s i n g t h e f o l l o w i n g equa- t i o n : (Note: S u b s c r i p t t l t t R t l r e f e r s t o b l a d e r o o t ; s u b s c r i p t "T" r e f e r s t o b l a d e t i p ) (B- 2 The i n c r e m e n t i n Mach Number i s found from e q u a t i o n B - 1 , and t h e b l a d e t i p Mach Number i s d e f i n e d by Then, knowing t h e d u c t Vach Number a t t h e b l a d e r o o t and b l a d e t i p , t h e b l a d e t i p / b l a d e r o o t p r e s s u r e r a t i o i s found from t h e f o l l o w i n g e q u a t i o n : K + 1 2(K-1)

A = - ' T i pT *DR

A 'Root 'R DT (B- 4 ) R o t o r Power A v a i l a b l e N e x t , t h e e f f e c t i v e n o z z l e v e l o c i t y i s f o u n d by d e t e r m i n i n g t h e i s e n t r o p i c a l l y expanded v e l o c i t y from t h e l o c a l * n o z z l e g a s t o t a l p r e s s u r e and t e m p e r a t u r e , and by a p p l y i n g an e f f e c t i v e n o z z l e v e l o c i t y c o e f f i c i e n t ,

Cv , which a c c o u n t s f o r t h e e n e r g y

e which i s n o t c o n v e r t i b l e i n t o t h r u s t . T h i s c o e f f i c i e n t i s a f u n c t i o n o f t h e n o z z l e geometry ( r o u n d , r e c t a n g u l a r , e t c . ) and

* " l o c a l " can be a t t h e t i p n o z z l e o r anywhere a l o n g t h e j e t -

f l a p .

6 6 A simple c o n v e r g e n t n o z z l e was u s e d i n t h e p r e s s u r e r a t i o .

d e t a i l e d a n a l y s i s and I t i s e x p e c t e d t h a t q u i t e t h i s s t u d y .

t e s t w i l l be r e q u i r e d t o o b t a i n t h e b e s t p o s s i b l e gas p a t h s f o r b l a d e t i p n o z z l e s and f o r j e t - f l a p n o z z l e s . I n t h e c a s e of t h e t i p n o z z l e , when t h e gas e x h a u s t s d i r e c t l y t o t h e a t m o s p h e r e , i t a p p e a r s (from r e c e n t t e s t s o f t u r b i n e n o z z l e v a n e s ) t h a t a n o z - I n t h e = .975 i s c o n s e r v a t i v e .

z l e v e l o c i t y c o e f f i c i e n t of (+

e g a s must p a s s o v e r t h e p h y s i c a l c a s e o f t h e j e t - f l a p , when t h e f l a p o f 0 . 1 0 - 0 . 1 2 t i m e s c h o r d , f r i c t i o n a l l o s s e s w i l l o c c u r , and a r e d u c t i o n o f C (assumed t o b e a s d i s c u s s e d i n R e f e r e n c e 1 5 b , V .96) a p p e a r s t o be a p p l i c a b l e t o t h e j e t - f l a p n o s z l e . The l o c a l j e t v e l o c i t y i s t h e n found from t h e f o l l o w i n g : . .

1 i %

1 2 K K - 1 1 'Amb (B- 5 )

VJ = c

RGTlocal 1 - -

I ' e , L

P l o c a l -

The r o t o r poGer i s t h e n d e t e r m i n e d as an i n t e g r a t e d r e s u l t o f t h e l o c a l mass flow b e i n g e j e c t e d , t h e l o c a l j e t v e l o c i t y , t h e t h e b l a d e t i p s p e e d , a t which i t i s b e i n g e j e c t e d , b l a d e r a d i u s and t h e h e l i c o p t e r f o r w a r d s p e e d . D e t a i l s of t h i s i n t e g r a t i o n p r o c e d u r e a r e g i v e n i n Appendix A. For i l l u s t r a t i v e p u r p o s e s , t h e f o l l o w i n g e q u a t i o n i s g i v e n which d e f i n e s r o t o r power f o r t h e h o v e r i n g r o t o r i n which 1 0 0 % o f t h e gas i s e x h a u s t e d a t t h e b l a d e t i p ( n o - j e t - f l a p ) f o r a h o v e r i n g h e l i c o p t e r .

W I n f o r w a r d f l i g h t , ram drag o f t h e a i r p i c k e d up a t h e l i c o p t e r s p e e d i s a l l o w e d f o r ; t h e ram p r e s s u r e r i s e a t t h e e n g i n e f a c e p a r t i a l l y compensates f o r t h i s ram d r a g .

I n f l u e n c e o f J e t - F l a p on R o t o r Power A v a i l a b l e A d e t a i l e d c a l c u l a t i o n is r e q u i r e d t o d e t e r m i n e t h e e f f e c t s on r o t o r power a v a i l a b l e of t h e f o l l o w i n g p a r a m e t e r s a s s o c i a t e d w i t h u s e o f a j e t - f l a p : Reduced n o z z l e v e l o c i t y c o e f f i c i e n t I n b o a r d l o c a t i o n of average r a d i u s o f j e t - f l a p gas F l a p d e f l e c t i o n An a p p r o x i m a t e a n a l y s i s was made o f t h e c a s e t y p i c a l o f t h e H e a v y - L i f t M i s s i o n , where 3 0 % o f t h e gas i s e j e c t e d u n i f o r m l y a l o n g a j e t - f l a p e x t e n d i n g from 7 0 p e r c e n t t o 9 7 . 5 p e r c e n t o f b l a d e r a d i u s , w i t h a h o v e r f l a p d e f l e c t i o n o f 40'.

The approximate a n a l y s i s showed t h a t 9 2 % o f t h e p u r e t i p n o z z l e power would be d e v e l o p e d , b a s e d on a t h r u s t r e c o v e r y f a c t o r * o f 0 . 5 , and t h e d e t a i l e d c a l c u l a t i o n ( p e r Appendix A) showed 9 0 % o f r e f e r e n c e t i p n o z z l e power.

The f l a p l e n g t h and f l a p d e f l e c t i o n of t h e h i g h s p e e d , 2g m i s s i o n was found t y p i c a l l y t o b e s i m i l a r t o t h e H e a v y - L i f t M i s s i o n v a l u e s . However, 1 0 0 % o f t h e g a s i s e j e c t e d a l o n g t h e j e t - f l a p (none t o t h e t i p n o z z l e ) . The a p p r o x i m a t e a n a l y s i s showed r o t o r power a v a i l a b l e t o be 80% o f t h e r e f e r e n c e p u r e t i p n o z z l e power, and t h e t y p i c a l d e t a i l e d (computer) c a l c u l a t i o n showed a b o u t 7 4 % o f r e f e r e n c e n o z z l e power.

* a s d e f i n e d by t h e term s d , s u p e r c i r c u l a t i o n t h r u s t p a r a m e t e r i n R e f e r e n c e 5 , and d i s c u s s e d i n Appendix C .

APPENDIX C J E T - FLAP AERODYNAMIC CHARACTER1 S T I CS L i f t C o e f f i c i e n t v s Momentum C o e f f i c i e n t Review o f l i t e r a t u r e on t h e aerodynamic c h a r a c t e r i s t i c s o f j e t - f l a p s i n d i c a t e s t h a t t h e b a s i c d a t a was o b t a i n e d from t h e French work L. Malavard, e t . a l . , R e f e r e n c e 1 5 a . The d a t a p r e s e n t e d i n R e f e r e n c e 1 5 a was u s e d t o d e r i v e t h e l i f t c o e f f i c i e n t of a de- f l e c t e d f l a p .

The e q u a t i o n f o r t h e l i f t c o e f f i c i e n t o f an a i r f o i l w i t h a j e t - f l a p w i t h blowing on t h e upper s u r f a c e o f a m e c h a n i c a l f l a p i s e q u a l t o : - C Q = C Q + C s i n (a + 6 ) + Sk> C . s i n (a + 6 ) (C- 1) 0 j 3 The f i r s t term i s t h e l i f t c o e f f i c i e n t o f t h e b a s i c a i r f o i l sec- t i o n , t h e s e c o n d term i s t h e j e t r e a c t i o n i n c r e m e n t , and t h e l a s t term i s t h e s u p e r - c i r c u l a t i o n i n c r e m e n t . The d a t a shown i n F i g u r e 25 o f R e f e r e n c e 15a (shown h e r e i n as F i g u r e C-1) w a s u s e d t o e s t i m a t e SR' The v a l u e o f 5 . 7 f i t s t h e d a t a f o r t h e u p p e r s u r f a c e j e t and t h e f l a p l e n g t h o f 1 2 . 5 % chord. The a i r f o i l u s e d i n t h i s s t u d y f o r t h e b a s e l i n e W a r m Cycle n o - j e t - f l a p h e l i - f o r t h e b a s i c a i r f o i l i s c o p t e r was t h e NACA 0 0 1 5 s e c t i o n .

C Q o b t a i n e d from wind t u n n e l d a t a of t h e NACA 0015 a i r f o i l , R e f e r - T h i s r e f e r e n c e p r e s e n t s s e c t i o n C Q and cd a s a f u n c t i o n e n c e 11.

o f Mach Number and a n g l e o f a t t a c k .

S e c t i o n Drag C o e f f i c i e n t The s e c t i o n d r a g c o e f f i c i e n t of t h e a i r f o i l w i t h a j e t - f l a p i s e q u a l t o : c where Cd i s t h e d r a g c o e f f i c i e n t o f t h e b a s i c 15% t h i c k n e s s a i r - f o i l , s d i s t h e t h r u s t r e c o v e r y f a c t o r assumed t o b e e q u a l t o 0.5 f o r t h i s s t u d y , and C i s t h e d r a g c o e f f i c i e n t due t o t h e d e - d~~ f l e c t i o n o f t h e 1 2 . 5 % m e c h a n i c a l f l a p . The d r a g c o e f f i c i e n t of

SIN e

a =o"

2 '

Flap Length 12.5%

'I )/

I I

I I

Upper and Lower Surface Jet

( From Reference E a 1

f

L

(3

0 0 . 2 0.4 0 . 6 0 . 8 1.0

CP

Figure C-1. Lift Variation with Blowing Over Figure C-1. Lift Variation with Blowing Over 12. 5 P e r c e n t Chord Flap 7 0 7 0 t h e m e c h a n i c a l f l a p i s e q u a l t o 0 . 0 0 3 ( R e f e r e n c e 1 6 ) .

F l i g h t tests have i n d i c a t e d t h a t t h e p r o f i l e d r a g of a p r a c t i c a l 15% t h i c k a i r f o i l s e c t i o n i s a p p r o x i m a t e l y 7 % g r e a t e r t h a n shown by R e f e r e n c e 11. T h e r e f o r e , t h e p r o f i l e d r a g terms a r e i n c r e a s e d by a p r o f i l e f a c t o r of 1 . 0 7 f o r a c o n s t a n t 1 5 % t h i c k a i r f o i l .

S t a l l Angle o f A t t a c k and Drag R i s e F i g u r e 27 o f R e f e r e n c e 15a (shown h e r e i n as F i g u r e C - 2 ) shows t h a t t h e a n g l e of a t t a c k f o r b l a d e s t a l l ( d e f i n e d a s a 1 of cL m ax a j e t - f l a p a i r f o i l i s a f u n c t i o n o f j e t d e f l e c t i o n . The d a t a shown i n F i g u r e C - 2 i s f o r s y m m e t r i c a l b l o w i n g on a j e t - f l a p and C . o f 1 . 0 . F i g u r e 1 3 o f R e f e r e n c e 15a ( F i g u r e C - 3 h e r e i n ) shows t h e e f f e c t of blowing on s t a l l a n g l e o f a t t a c k f o r t r a i l i n g edge b l o w i n g , a t a j e t d e f l e c t i o n a n g l e of 55 d e g r e e s ; t h e s t a l l a n g l e of a t t a c k i s s e e n t o d e c r e a s e w i t h C f o r C = 0 . 4 - 1 . 2 . Com- j j p a r a b l e d a t a i s a v a i l a b l e f o r m o d e r a t e b l o w i n g (C = 0 . 0 - 0.158) j on t h e u p p e r s u r f a c e o f a m e c h a n i c a l f l a p i n R e f e r e n c e 15h.

T h e r e f o r e , it w i l l b e assumed t h a t s t a l l a n g l e w i l l d e c r e a s e f o r C . between 0 . 2 and 1 . 0 , when b l o w i n g o v e r a m e c h a n i c a l f l a p , and J s p e c i f i c a l l y t h e a n g l e s f o r s t a l l w i l l b e o b t a i n e d from F i g u r e C - 2 . These may b e c o n s i d e r e d s l i g h t l y c o n s e r v a t i v e due t o t h e f a c t t h a t t h e r e t r e a t i n g t i p C f o r b o t h t h e H e a v y - L i f t and h i g h - j s p e e d h e l i c o p t e r s i s less t h a n 1 . 0 .

Based on F i g u r e s C - 2 and C-3, F i g u r e C - 4 p r e s e n t s s e c t i o n s t a l l a n g l e o f a t t a c k a s a f u n c t i o n o f j e t o r i e n t a t i o n a n g l e , 6 .

C E i s c o n s i d e r e d c o n s t a n t f o r s e c t i o n a n g l e s o f a t t a c k g r e a t e r t h a n t h e s t a l l v a l u e shown i n F i g u r e C - 4 . I n a d d i t i o n , d r a g r i s e due t o s t a l l i s c o n s e r v a t i v e l y a c c o u n t e d f o r by s e t t i n g t h e t h r u s t r e c o v e r y t o z e r o when t h e s e c t i o n a n g l e o f a t t a c k i s above s t a l l .

I t s h o u l d be n o t e d t h a t t h e r e i s an a p p a r e n t l a c k of d r a g d a t a f o r a j e t - f l a p a i r f o i l p a s t s t a l l . T h i s item c o u l d be a v e r y u s e f u l s u b j e c t o f f u t u r e wind t u n n e l t e s t i n g . F i g u r e C - 4 a l s o p r e s e n t s v a l u e s o f C v e r s u s C and 6 , u s i n g e q u a t i o n C - 1 j L m a x and s t a l l a n g l e shown on F i g u r e C - 4 . I t i s seen t h a t t h e j e t i s i n t h e range o f 40' - 50' f o r d e f l e c t i o n a n g l e f o r CL max c = .1 t o 1 . 0 .

j L i m i t Angle o f A t t a c k t e s t s a t HTC have i n d i c a t e d Roughness d a t a o b t a i n e d from f l i g h t t h a t t h e r e t r e a t i n g t i p a n g l e l i m i t f o r r o u g h n e s s ( V , ) o c c u r s a t 7 1

cL

t

(From Reference Ea)

F i g u r e C - 2 .

Lift Coefficient V e r s u s Angle of Attack and Jet Deflection 7 2

Lift

c p =

1.22

0.9

8 = 55

Lift Coefficient V e r s u s Angle of Attack and Momentum F i g u r e C - 3 .

Co efficient 7 3 STALL LIFT ANGLE

COEFF I C I ENT

OF C !

ATTACK DEG JET FLAP DEFLECT I ON ANGLE -6-DEG J e t Flap Stall Angle and C4 F i g u r e C-4. V e r s u s 6 and C j max 7 4 a p p r o x i m a t e l y 2 d e g r e e s beyond 2 - d i m e n s i o n a l s t a l l .

The Heavy- L i f t h e l i c o p t e r can c r u i s e a t V N E , which i s d e f i n e d a s 90% o f roughness s p e e d .

F o r VNE, t h e r e t r e a t i n g t i p a n g l e i s 1 . 5 d e g r e e s beyond 2 - d i m e n s i o n a l s t a l l .

The h i g h - s p e e d h e l i c o p t e r p e r f o r m s a 2 - g maneuver a t 2 0 0 k n o t s ; b e c a u s e of t h e l i m i t e d d u r a t i o n o f t h i s maneuver, t h e r e t r e a t i n g t i p a n g l e can r e a c h t h e r o u g h n e s s v a l u e o f 2 d e g r e e s beyond t h e s t a l l l i m i t . The margin shown r e f e r s t o F i g u r e C - 4 . P o s i t i v e v a l u e s u ( l . 0) ( 2 7 0 ) show r e t r e a t i n g t i p l i m i t a n g l e s less t h a n t h e l i m i t o f F i g u r e C - 4 and n e g a t i v e v a l u e s a r e f o r a n g l e s g r e a t e r t h a n F i g u r e C - 4 .

A l l a n g l e s shown a r e f o r sea l e v e l , 9S°F.

T h i c k n e s s E f f e c t s on Drag A i r f o i l s t h i c k e r t h a n 1 5 % are r e q u i r e d t o p r o v i d e enough d u c t area f o r t h e H e a v y - L i f t j e t - f l a p h e l i c o p t e r s . T h i s increased t h i c k n e s s a p p l i e s from t h e b l a d e r o o t t o t h e s t a r t o f t h e j e t - f l a p . The b l a d e t h i c k n e s s o f t h e f l a p p e d s e c t i o n i s r e d u c e d l i n e a r l y t o a c h i e v e 1 5 % a t t h e b l a d e t i p . R e d u c t i o n o f t h e a i r - f o i l t h i c k n e s s i n t h e f l a p s e c t i o n i s made p o s s i b l e by t h e f a c t t h a t t h e d u c t a r e a i s r e d u c e d a s t h e a i r is b l e d o f f f o r t h e j e t - f l a p . S i n c e t h e p e n a l t i e s o f d r a g d i v e r g e n c e and s t a l l o c c u r on t h e t i p s e c t i o n s o f t h e b l a d e , t h e y are p r o p e r l y a c c o u n t e d f o r by t h e a i r f o i l s e c t i o n c h a r a c t e r i s t i c s o f t h e 1 5 % a i r f o i l .

The t h i c k e r i n b o a r d s e c t i o n s are a t low v a l u e s o f Mach Number and t h e i n c r e a s e i n d r a g can be a c c o u n t e d f o r by m u l t i p l y i n g t h e p r o f i l e d r a g terms by a w e i g h t e d f a c t o r , d e r i v e d a s f o l l o w s : The r a t i o of p r o f i l e d r a g o f a t h i c k e r s e c t i o n t o a 1 5 % t h i c k s e c t i o n can b e o b t a i n e d from e q u a t i o n 6 , C h a p t e r 6 , R e f e r e n c e 1 7 .

The i n b o a r d s e c t i o n is assumed t o e x t e n d t o 85% o f t h e r a d i u s w h i l e t h e j e t - f l a p s e c t i o n s t a r t e d a t from 65% t o 75% f o r t h e cases i n v e s t i g a t e d . T h i s was done t o a c c o u n t f o r t h e l i n e a r t r a n s i t i o n from i n b o a r d t h i c k n e s s t o t i p t h i c k n e s s o v e r t h e f l a p l e n g t h . The w e i g h t e d f a c t o r w a s o b t a i n e d by i n t e g r a t i n g from r o o t t o t i p u s i n g t h e f o l l o w i n g e q u a t i o n :

, I x3dx

PPFweighted - - p p F r o o t t / c I 1.0

r . ?

+ P P F t i p t / c x3dx T h i s r e s u l t e d i n P P F = 1 . 1 4 f o r 2 0 % i n b o a r d t h i c k n e s s and P P F = 1 . 1 7 f o r 2 2 % i n b o a r d t h i c k n e s s w i t h 1 5 % o u t b o a r d t h i c k n e s s f o r b o t h c a s e s .

7 6

APPENDIX D EMPTY WE I GHT DETERbIINATION I n t r o d u c t i o n The empty w e i g h t s o f t h e h e l i c o p t e r s t u d i e d h e r e w e r e b a s e d on t h e s t a n d a r d u s e o f e m p i r i c a l l y - d e r i v e d s t a t i s t i c a l w e i g h t e q u a t i o n s f o r t h e s e v e r a l components i n v o l v e d . Two s e t s o f e q u a t i o n s a r e p r e s e n t e d h e r e , one f o r t h e H e a v y - L i f t m i s s i o n , and one l i s t i n g t h e r e v i s i o n s t o t h e H e a v y - L i f t e q u a t i o n s t o A common s e t o f symbols i s p r o v i d e f o r t h e h i g h s p e e d m i s s i o n .

u s e d .

H e a v y - L i f t m i s s i o n . - The f o l l o w i n g e q u a t i o n s a r e u s e d f o r c a l - c u l a t i o n o f h e l i c o p t e r component w e i g h t s : Main R o t o r Group . 8 7 g w . 2 3 1

wr - - K j f K m r r 1 . 0 4 2 7 b (RC)

g (D- 1 )

.938,+, .246\, . 706+200

- 3 b1.067 + 2.413 x 1 0 (RC) g t where K = 1.1 ( w i t h j e t - f l a p ) j f = 1 . 0 ( n o - j e t - f l a p ) Kmr = .92 (Cold Cycle) = 1 . 0 0 (Warm Cycle) = 1 . 1 0 (Hot Cycle) T a i l S u r f a c e s = 2 . 5 5 KtsSts Wts where K t s = . 7 0 W 2/ 3 = 2 2 1 (+) Sts gb T a i l R o t o r 1.213 = 3 . 7 0 K t r (RCbItr (D- 3) 'tr 7 7 w h e r e : K = . g o tr W

(RCb)tr = 1 7 . 9 8 (e)

gb Body Group ( f u s e l a g e )

. 611s. 551

WB = .0819 K W (D- 4) B g where: K, = . 7 5 J5 W 2 / 3 S = 1549 (+) gb A l i g h t i n g Gear 1.169 W = 8.344 x K l g wg 1g F l i g h t C o n t r o l s .460w . 2 4 2 + 180 - 4 . 8 4 (RCb)

w f c - K f c

g where: Kfc = .90 N a c e l l e s 2 4 + 4 3 . 3 1 K n a c W L n g N e = .OS W (D- 7 ) 'nac eng where: K n a c = .80 Engine I n s t a l l a t i o n W = 1 . 1 0 W r e N e P a i r eng A i r I n d u c t i o n and F i l t e r s = .00906 N N 'ai eng e 7 8 Exhaust System (D-10) N = . 2 2 3 W ' eng e 'es (D-11) L u b r i c a t i o n System ( i n c l u d e d i n APU w e i g h t ) F u e l System ( f u e l b a s e d on 4 - t r i p e n d u r a n c e m i s s i o n = W f ) (D- 1 2 ) = 2 9 5 + 7 0 . 6 N t + . 0 6 1 4 Wf wf s Engine C o n t r o l s and S t a r t e r ( f i x e d p r o p u l s i o n s y s t e m s ) (D- 13) = 60 + 60 N e W f P J e t - D r i v e System (D-14) 2 . 3 2 N + 5.136 DeNe + 2 2 . 6 4 DeNe * " W j d = .0888KdivDe e where: S u b s c r i p t "g" d e n o t e s c o n d i t i o n s a t e x i t o f

d i v e r t e r v a l v e (Kdiv - - .95 1

W = Gas f l o w / e n g i n e g N e = number of e n g i n e s De = d i v e r t e r v a l v e e x i t d i a m e t e r ( i n . ) 1 / 2 = 2 ; g e

-

De

m r

d e s

-

W i s a f u n c t i o n of t h e d u c t Mach The f l o w f u n c t i o n I ' = ( g T e ) ADP e The r e l a t i o n s h i p between t h e Number and s p e c i f i c h e a t r a t i o .

i n t e r n a l f l o w l o s s and t h e d i v e r t e r v a l v e w e i g h t i s d e t e r m i n e d A f l o w f u n c t i o n o f by t h e c h o i c e f o r the flow Yach Number.

.178 (Mach Number = . 2 ) h a s b e e n f o u n d t o p r o d u c e a good com- p r o m i s e between w e i g h t and p r e s s u r e l o s s e s .

) d e s d e n o t e s t a k e o f f r a t i n g a t h o v e r d e s i g n c o n d i - ( t i o n s .

Yaw Fan/Rotor D r i v e System + Accessory Gearbox = 25.19 K W (D-15) y f d (Rcb);r Yfd = .894 where: K Y f d R o t o r Brake Wrb = 2 0 0 l b s ( c o n s t a n t ) (D-16) A u x i l i a r y P r o p u l s i o n Group W = 506 l b s ( c o n s t a n t ) ( D - 1 7 ) aPu I n s t r u m e n t s W i = 400 l b s ( c o n s t a n t ) (D-18) H y d r a u l i c s a n d Pneumatics Group (D-19) where: K h = .90 E l e c t r i c a l Group W e l = 3 . 8 6 K W ' (D-23) e l g where : K e l = .90 A v i o n i c s W = 1280 l b s ( c o n s t a n t ) (D-21) av IR Countermeasures Device W i r = 5 0 0 l b s ( c o n s t a n t ) ( D - 2 2 ) Armor = 560 l b s ( c o n s t a n t ) W (D-23) arm Crew/Passenge r F u r n i s h i n g s and Equipment 2 4) = 1000 l b s ( c o n s t a n t ) (D- 'fe A i r c o n d i t i o n i n g Group (D- 2 5) = 350 l b s ( c o n s t a n t ) 'ac A n t i - I c i n g Group (D-26) W = 1 0 0 l b s ( c o n s t a n t ) an A u x i l i a r y Gear (Cargo H a n d l i n g D e v i c e s ) W = .03418 W l l where: W l l = l o a d l i f t e d (D- 2 7) ag (1bs) Weight Empty W = e q u a t i o n s D - 1 t h r o u g h 0 - 2 7 e U s e f u l Load (Wul) a. C r e w @ 240 lbs/man x 5 = 1 2 0 0 l b s (D- 2 8) O i l @ 1 7 . 5 l b s / e n g i n e x Ne b . (D-29) c. Unusable F u e l @ . 0 1 W f u e l ( p r i m a r y m i s s i o n ) (D-30) d . M i s c e l l a n e o u s Equipment = 1 0 0 0 l b s ( c o n s t a n t ) e. F u e l ( u s a b l e ) p r i m a r y m i s s i o n ( a s r e q u i r e d ) = W f u e l f . P a y l o a d 6 0 , 0 0 0 l b s Gross Weight (Wg)

l v = w e + w - + Warmup F u e l

g u l - mm

R e v i s i o n t o H e a v y - L i f t w e i g h t e q u a t i o n s f o r h i g h s p e e d -- m i s s i o n .

Body Group . 6 1 1 s . 5 5 1 WB = . 1 2 6 K W B g 8 1 where: S = 9 2 0 f t .

. 6 1 1 W B = 5 . 4 1 K W B g F 1 i gh t C o n t r o l s .460w . 2 4 2 = 4.84 K f c (RCb) w f c g N a c e l l e s Engine C o n t r o l s ( F i x e d p r o p u l s i o n )

I

= 20 + 1 0 Ne wfP R o t o r Brake Wrb = 3 0 l b s . ( c o n s t a n t ) Aux i 1 i a r y P r o p u l s i o n W = 1 0 0 l b s . ( c o n s t a n t ) aPu I n s t r u m e n t s Wi = 1 5 0 l b s . ( c o n s t a n t ) A v i o n i c s W a v = 400 l b s . ( c o n s t a n t ) I . R . Countermeasures Device W i r = 300 l b s . ( c o n s t a n t ) Armor W = 5 0 0 l b . ( c o n s t a n t ) arm

Crew/Passenger F u r n i s h i n g s G Equipment

A i r C o n d i t i o n i n g Group 1 0 0 l b . ( c o n s t a n t ) A n t i - I c i n g Group 30 l b . ( c o n s t a n t ) A u x i l i a r y Gear 0 l b s .

F u e l System = 2500 Wf = - 1 7 4 W f u e l

wfs r 4 4 0 0

Unusable F u e l WUf = . 0 0 5 W f u e l M i s c e l l a n e o u s Equipment 0 l b s .

C r e w 2 men a t 2 4 0 = 480 l b . ( c o n s t a n t ) O i l 35 l b . ( c o n s t a n t ) P a y l o a d 6000 l b s .

APPENDIX E OPTIMIZATION PAMMETERS I t i s n o t e d on p a g e s 1 2 and 2 2 t h a t t h e b l o c k s p e e d i n t h e s u b - j e c t s t u d y i s c o n s t a n t , T h e r e f o r e , t h e P r o d u c t i v i t y p a r a m e t e r i s t h e same a s PayloadlEmpty Weight. Lengthy c o s t s t u d i e s o f t e n - y e a r l i f e - c y c l e costs o f heavy l i f t h e l i c o p t e r s have b e e n made b a s e d on s o u r c e d a t a s u c h a s R e f e r e n c e 1 8 . I t was found t h a t ( n e g l e c t i n g s u c h r e l a t i v e l y c o n s t a n t i t e m s a s i n i t i a l d e v e l o p m e n t , f l i g h t crew p a y , and t r a v e l ) , f u e l c o s t s r e p r e s e n t less t h a n s i x p e r c e n t o f t h e t e n - y e a r c o s t s . The o t h e r n i n e t y - f o u r p e r c e n t of c o s t s a r e p r o p o r t i o n a l t o empty w e i g h t a t a Thus i t i s e a s y t o f i x e d p a y l o a d , o r t o p a y l o a d / e m p t y w e i g h t .

show t h a t t h e c h o i c e of P r o d u c t i v i t y ( a s d e f i n e d on page 2 1 ) a s t h e c r i t e r i o n f o r comparison i s t h e c o r r e c t p a r a m e t e r .

A s c o n f i r m a t i o n o f t h e v a l i d i t y o f s e l e c t i n g a p r o d u c t i v i t y c r i - t e r i o n r a t h e r than a f u e l / p a y l o a d c r i t e r i o n a s t h e o p t i m i z a t i o n p a r a m e t e r , T a b l e s E - 1 and E - 2 below (which a r e b a s e d on T a b l e s 4 and 5 on pages 2 7 and 3 0 ) g i v e t h e t r a d e - o f f o f P r o d u c t i v i t y , F u e l / P a y l o a d , and R e l a t i v e T o t a l V a r i a b l e L i f e Cycle C o s t s a s a f u n c t i o n o f d u c t Mach Number and d i s k l o a d i n g , r e s p e c t i v e l y . , TABLE E - 1 EFFECT. OF DUCT MACH NUMBER Duct Mach Number 0 . 3 1 0.43* R e l a t i v e Re 1 a t i v e Cost F a c t o r C o s t F a c t o r P r o d u c t i v i t y (127.4) . 9 6 6 (130.4) . 9 4 4 F u e l / P a y l o a d (.2081) .OS3 (.2198) .056 T o t a l V a r i a b l e L i f e 1 . 0 1 9 1 . 0 0 0 Cycle C o s t s

* Mach No. f o r h i g h e s t p r o d u c t i v i t y

TABLE E - 2 EFFECT OF DISK LOADING D i s k L o a d i n g - l b / f t 2 7 9** R e l a t i v e Re l a t i v e Cost F a c t o r C o s t F a c t o r P r o d u c t i v i t y (129.7) .949 (130.4) . 9 4 4 Fue 1 /Pay l o ad (. 2046) . 0 5 2 (. 2198) .056 T o t a l V a r i b a b l e L i f e 1 . 0 0 1 1 . 0 0 0 Cycle C o s t s

**

Disk Loading f o r h i g h e s t p r o d u c t i v i t y To p r e p a r e T a b l e s E - 1 and E - 2 , t h e v a l u e s o f P r o d u c t i v i t y and F u e l / P a y l o a d were n o t e d from T a b l e s 4 and 5 r e s p e c t i v e l y , a t t h e d u c t Mach No.

( 9 l b / f t 2 ) which showed t h e ( . 4 3 ) and d i s k l o a d i n g h i g h e s t p r o d u c t i v i t y i n t h e n o t e d t a b l e s .

Based on s t u d i e s p r e - p a r e d from R e f e r e n c e 1 8 , a r e l a t i v e c o s t o f .944 was a s s i g n e d t o P r o d u c t i v i t y and a r e l a t i v e c o s t o f . 0 5 6 was a s s i g n e d t o F u e l / P a y l o a d ( t o t a l = 1 . 0 0 0 ) . Then t h e P r o d u c t i v i t y and F u e l / P a y l o a d were n o t e d from T a b l e s 4 and 5 f o r t h e d u c t Mach No. and d i s k l o a d i n g which gave t h e l o w e s t F u e l / P a y l o a d i n t h e r e f e r e n c e d costs a s s o c i a t e d w i t h changed p r o d u c t i v i t y T a b l e s . The r e l a t i v e and F u e l / P a y l o a d were d e t e r m i n e d by m u l t i p l y i n g t h e o r i g i n a l r e l a t i v e c o s t s by the r a t i o s o f P r o d u c t i v i t y and F u e l / P a y l o a d , r e s p e c t i v e l y , as f o l l o w s f o r d u c t Macn No. = 0.31.

P r o d u c t i v i t y : Revised c o s t = . 9 4 4 x 127.4 1 3 0 * 4 = - 9 6 6 Fue 1/Pay l o a d :

Revised c o s t = .056 x ,m = . 0 5 3

For t h e d u c t Mach Number r e d u c t i o n i n T a b l e E - 1 t h e r e i s a 5.3% r e d u c t i o n o f f u e l / p a y l o a d v e r s u s a 2.3% r e d u c t i o n i n P r o d u c t i v i t y .

For t h e d i s k l o a d i n g r e d u c t i o n i n T a b l e E - 2 t h e r e i s a 7 % r e d u c - t i o n i n f u e l / p a y l o a d v e r s u s a 0 . 5 % r e d u c t i o n i n p r o d u c t i v i t y .

However, b e c a u s e o f t h e g r e a t e r i n f l u e n c e of P r o d u c t i v i t y , it is s e e n t h a t t h e v a r i a b l e l i f e c y c l e c o s t s would have b e e n h i g h e r i n b o t h t h e c a s e o f o p t i m i z i n g d i s k l o a d i n g o r o f o p t i m i z i n g d u c t Mach Number by t h e u s e of l o w e s t f u e l / p a y l o a d i n s t e a d o f h i g h e s t p r o d u c t i v i t y .

APPENDIX F SELECTION OF NUMBER OF BLADES FOR BASELINE V E H I C L E A b r i e f s t u d y was made o f t h e p o s s i b i l i t y o f u s i n g a t h r e e - b l a d e d r o t o r f o r t h e r e f e r e n c e Warm Cycle h e l i c o p t e r w i t h o u t a j e t - f l a p .

I t was found t h a t a h i g h e r P r o d u c t i v i t y (115.5) c o u l d be o b t a i n e d , e s s e n t i a l l y b e c a u s e t h e t h r e e - b l a d e d r o t o r i s n o t a s c o n s t r a i n e d by d u c t a r e a r e q u i r e m e n t s a s t h e f o u r - b l a d e d r o t o r , which had a P r o d u c t i v i t y o f 1 0 8 . 8 ( F i g u r e 5 ) . However, t h e i n d i v i d u a l b l a d e s of t h e t h r e e - b l a d e r o t o r a r e w i d e r a n d , t h e r e f o r e , d e e p e r t h a n t h o s e f o r a f o u r - b l a d e d r o t o r . The r a t i o o f b l a d e r a d i u s / s p a r is t h e b a s i c p a r a m e t e r i n f l u e n c i n g b l a d e d e p t h ( R / t ) , which b e n d i n g f r e q u e n c y , is 80 f o r t h e t h r e e - b l a d e r o t o r and 9 0 f o r t h e f o u r - b l a d e r o t o r . A lower ( R / t ) r a t i o s i g n i f i e s a s t i f f e r b l a d e . As a r e s u l t , f o r e q u a l d i s k l o a d i n g a n d / o r g r o s s w e i g h t , t h e t h r e e - b l a d e r o t o r f i r s t mode f l a p w i s e b e n d i n g f r e q u e n c y i s h i g h e r t h a n t h a t o f t h e f o u r - b l a d e r o t o r , and w i l l a p p r o a c h 3 p e r r e v , t h u s i n c r e a s i n g t h e p o s s i b i l i t y o f h i g h 3 / r e v b l a d e b e n d i n g s t r e s s e s . C o n s e q u e n t l y , t h e f o u r - b l a d e r o t o r d e s i g n was u s e d f o r a n o - j e t - f l a p r e f e r e n c e b e c a u s e o f t h e lower b l a d e bend- i n g f r e q u e n c y .

I t s h o u l d a l s o be n o t e d t h a t t h e b l a d e r a d i u s / s p a r d e p t h r a t i o ( R / t ) f o r t h e t h r e e - b l a d e Hot Cycle j e t - f l a p r o t o r ( w i t h i t s s u b s t a n t i a l l y n a r r o w e r c h o r d ) i s 9 7 , l e a d i n g t o an a c c e p t a b l e b l a d e b e n d i n g f r e q u e n c y .

RE FE RENCE S Anon: J e t - F l a p Rotor P r e l i m i n a r y A p p l i c a t i o n S t u d y .

1.

Vought A e r o n a u t i c s D i v i s i o n , LTV Aerospace C o r p o r a t i o n .

Volume I - Summary R e p o r t , N69 - 25567; Volume I1 - A n a l y s i s R e p o r t N69 - 25568, 7 F e b r u a r y 1969.

2 . H . G . , and S u l l i v a n , R . J . : R o t o r Blade Design f o r a S m i t h , F a n - J e t - P o w e r e d H e a v y - L i f t H e l i c o p t e r . P a p e r p r e s e n t e d a t N a t i o n a l A e r o n a u t i c and Space E n g i n e e r i n g and Manu- S o c i e t y o f Automotive E n g i n e e r s f a c t u r i n g Meeting.

(Los Angezes, C a l i f o r n i a ) , 6-10 O c t o b e r 1969.

3 . Gessow, A , and C r i m , A . : A Method f o r S t u d y i n g t h e T r a n s i e n t B l a d e - F l a p p i n g B e h a v i o r o f L i f t i n g R o t o r s a t Extreme O p e r a t i n g C o n d i t i o n s . NACA TN-3366, 1955.

A. : E q u a t i o n s and P r o c e d u r e s f o r N u m e r i c a l l y C a l c u - 4. Ges sow.

t h e Aerodyn l a t i n g amic C h a r a c t e r i s t i c s o f L i f t i n g R o t o r s .

NACA TN '-3747, 1956 5. Evans, W.T., and McCloud, J . L . ,111: A n a l y t i c a l I n v e s t i g a t i o n o f a H e l i c o p t e r R o t o r D r i v e n and C o n t r o l l e d by a J e t - F l a p . NASA TN-D-3028, 1965.

6. F r a d e n b u r g h , E . A . : Aerodynamic E f f i c i e n c y P o t e n t i a l s o f R o t a r y Wing A i r c r a f t . P r o c e e d i n g s o f t h e 1 7 t h Annual N a t i o n a l Forum, The American H e l i c o p t e r S o c i e t y .

(Washington, D.C.) , 1 7 Play 1960.

7. Krebs, R.W., and M i l l e r , W.S.: A n a l y s i s o f a P r e s s u r e J e t Power P l a n t f o r a H e l i c o p t e r . NACA RM E54L23, 1955.

McCloud, J . L . ,111, and Evans, W.T. : Performance C h a r a c t e r - 8.

i s t i c s o f a J e t - F l a p R o t o r . P r o c e e d i n g s o f t h e C o n f e r - e n c e on V/STOL and STOL A i r c r a f t . NACA SP-116, 1966, pp 29-40.

9. T a n n e r , W.H. : C h a r t s f o r E s t i m a t i n g R o t o r Performance i n Hover and a t High Forward S p e e d s . NACA C R - 1 1 4 , 1964.

1 0 . F i n n e s t e a d , R . , Conner, W . , and Bass, W. : E n g i n e e r i n g F l i g h t Test AH-1G H e l i c o p t e r (HUEY COBRA) P h a s e D , P a r t 2 Performance. Addendum. F i n a l R e p o r t USAASTA R e p o r t on USATECOM P r o j e c t No. 4-6-0500-01, March 1971.

S h i v e r s , J . P . , and C a r p e n t e r , P . : E f f e c t s o f C o m p r e s s i b i l i t y 11.

on Rotor Hovering Performance and S y n t h e s i z e d B l a d e - S e c t i o n C h a r a c t e r i s t i c s D e r i v e d from Measured R o t o r P e r - formance of B l a d e s Having NACA 0015 A i r f o i l T i p S e c t i o n s .

NACA TN 4356, 1958.

Bachmann, B . : Power A v a i l a b l e C a l c u l a t i o n P r o c e d u r e and 1 2 .

O p e r a t i o n a l A s p e c t s o f a T i p j e t - P r o p e l l e d R o t o r S y s - tem. P a p e r p r e s e n t e d a t 2 6 t h Annual N a t i o n a l Forum American H e l i c o p t e r S o c i e t y (Washington, D.C.) , J u n e , 1970.

1 3 . S h a p i r o , A.H. : The Dynamics and Thermodynamics o f Compress- i b l e F l u i d Flow. The Ronald Press Company, 1953.

1 4 . Henry, J . R . : One-Dimensional, C o m p r e s s i b l e , V i s c o u s Flow R e l a t i o n s A p p l i c a b l e t o Flow i n a Ducted H e l i c o p t e r B l a d e . NACA TN-3089, 1953.

1 5 a . Malavard, L . , J o u s s e r a n d o t , P . , and P o i s s o n - Q u i n t o n , P . : J e t - I n d u c e d C i r c u l a t i o n C o n t r o l . Aero D i g e s t , Vol. 7 3 , Nos. 3 - 5 , S e p t e m b e r , O c t o b e r , November, 1956.

i s b a * K o r b a c h e r , G . K . , and S r i d h a r , K . : A Review o f t h e J e t - F l a p U n i v e r s i t y o f T o r o n t o I n s t i t u t e o f A e r o p h y s i c s R e p o r t U T I A Review No. 1 4 , May, 1960.

S p e n c e , D . A . : The L i f t C o e f f i c i e n t of a T h i n , J e t - F l a p p e d 1 5 ~ .

Wing. P r o c e e d i n g s o f t h e Royal S o c i e t y , Vol. 238, 1956 pp 46-68.

15d. D i k e , D . T . , Dunn, H.S. Hazen, D . C . , and L e h n e r t , R . F . : A S t u d y o f t h e Low Speed Aerodynamic C h a r a c t e r i s t i c s of H i g h - L i f t Flow C o n t r o l l e d P r o f i l e s a n d Wings. Aero- n a u t i c a l E n g i n e e r i n g R e p o r t 349, P r i n c e t o n U n i v e r s i t y , 1958.

1 5 e . S p e n c e , D . A . : The L i f t on a T h i n A i r f o i l w i t h a J e t - A u g - mented F l a p . The A e r o n a u t i c a l Q u a r t e r l y , A u g u s t , 1958.

pp 287-299.

*NOTE: R e f e r e n c e s t h r o u g h 15h c o n t a i n t h e o r e t i c a l and t e s t i n f o r m a t i o n on j e t - f l a p a i r f o i l s e c t i o n c h a r a c t e r i s t i c s c o v e r i n g from 1956 t h r o u g h 1970. T h e s e r e f e r e n c e s con- f i r m t h e c h o i c e o f R e f e r e n c e 15a f o r t h e s c o p e o f i t s d a t a .

1 5 f . Thomas, F. : I n v e s t i g a t i o n s I n t o I n c r e a s i n g t h e L i f t o f Wings by Boundary L a y e r C o n t r o l Through Blowing.

Z . F l u g w i s s . 1 0 , No.2, pp 46-65, 1962 (Royal A i r c r a f t E s t a b l i s h m e n t L i b r a r y T r a n s l a t i o n No. 1267) 15g. Williams, J . , B u t l e r , S . F . J . , and Wood, M . N . : The Aerody- namics of J e t - F l a p s . A e r o n a u t i c a l R e s e a r c h C o u n c i l R.GM. 3 3 0 4 , 1963.

1 5 . h S c h e r r e r , R. : S y n t h e s i s o f F u t u r e High L i f t Systems. P a p e r a t N a t i o n a l A e r o n a u t i c and Space E n g i n e e r i n g p r e s e n t e d and Manufacturing Meeting.

S o c i e t y o f Automotive E n g i - n e e r s (Los Angeles, C a l i f o r n i a ) , 5 - 9 O c t o b e r 1970.

1 6 . A b b o t t , I . , and VonDoenhoff, A . E . : Theory o f Wing S e c t i o n s .

Dover P u b l i c a t i o n s , 1 9 5 9 .

17. H o e r n e r , S.F. : Aerodynamic Drag. P u b l i s h e d by a u t h o r , 1958.

18. Leone, M . : H e a v y - L i f t H e l i c o p t e r System C o s t Model. Hughes T o o l Company - Aircraft D i v i s i o n R e p o r t 397-P-0001.

A p r i l 1970 ( C o n f i d e n t i a l )