Drag reduction for gliders

N A S A T E C H N I C A L NEMORANDUM N A S A TM 7 5 2 9 3 DRAG R E D U C T I O N F O R G L I D E R S

'NhSA-'i'r - , 5 2 9 3 ) DRAG REDUCTION FOR G L I D E R S N78-24 7 16

!National Aeronautics a n d S ~ a c e - rlministration) 16 p HC A02/flF A 0 1 CSCL 01C O n c l a s Dr. F. X . Wortmann T r a n s l a t i o n o f " ' d i d e r s t a n i i s v e r r n i n d ~ ~ u n g b e i Segel- f l u g z e u g e n " , Aero-Revue, Vol. 40, December 1965, pp. 723-72e NAITIONAL AERONAUTICS AND SPPSE ADMINISTRATION WASHII;GTON, D. C. 20546 MAY 1 9 7 ~ 7. W r ) .

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8 , . . _ . * , , DRAG REDUCTION FOR GLIDERS D r . F. X. Wortmann* /723** 3 . W I N G PROFILE SELECTION When s e l e c t i n g t h e p r o f i l e of a g l i d e r , two aerodynamic c r i t e r i a a r e used, and t h e s e are even more i m p o r t a n t t h a n s e l e c t i n g t h e wing p i a n form: The p r o f i l e s h o u l d r e s u l t i n t h e maximum p o s s i b l e t r a v e l v e l o c i t y and t h e most f a v o r a b l e c o n d i t i o n s f o r slow f l i g h t . It i s d i f f i c u l t t o o b t a i n an overview a b o u t t h e i n f l u e n c e o f t h e p r o f i l e on t h e t r a v e l ve- l o c i t y , w j t h c o n s i d e r a t i o n o f c i r c u l a r f l i g h t . S p e c i a l i n v e s t i g a t i e n s a r e r e q u i r e d f o r t h i s [l]. Even f o r wings w i t h v e r y d i f f e r e n t p r o f i l e s , one can o b t a i n t h e same t r a v e l v e l o c i t y ; f o r example, i f we s e l e c t a p r o f i l e whose d r a g is e s p e c i a l l y low i n t h e high-speed r a n g e , i n g m e r a l this advantage i s compensated f o r by t h e l a r g e d r a g v a l u e s f o r slow f l i g h t c o n d i t i o n s , and v i c e - v e r s a . If we c o n s i d e r pre3iously-measured p r o f i l e p o l a r s , I t is found t h a t n e i t h e r one o f t h e extremes w i l l p r o v i d e t h e optimum t r a v e l v e l o c i t y . I n s t e a d , i t seems more f a v o r a b l e t o u s e pro- f i l e s w i t h extremely wide l a m i n a r d e p r e s s i o n s , which f a v o r s b o t h f a s t and slow f l i g h t c o n d i t i o n s . [ 2 ] g i v e s a n e x t e n s i v e d i s c u s s i o n o f c h i s , b u t does n o t c o n s i d e r t h e b p e c i a l m e t e o r o l o g i c a l c o n d i t i o n s .

I n a d d i t i o n t o t h e arguments p r e s e n t e d above, which a r e b a s e d on a c o n s i d e r a t i o n of a t r a v e l - x e l o c i t y , p r o f i l e s w i t h a wide l a m i n a r d e p r e s s i o n a r e f a v o r a b l e f o r o t h e r r e a s o n s : when t h e r e a r e weak upwind c o n d i t i o n s , i t i s e a s i e s t t o s t a y up w i t h them, When t h e upwind i n c r e a s e s w i t h a l t i t u d e , t h e c r i t i c a l a l t i t u d e i s lower t h a n w i t h a d i f f e r e n t kind of p r o f i l e . If t h e a i r c r a f t goes below t h i s c r i t i c a l a l t i t u d e , t h e n a O f c o u r s e , one can u s e a p r o f i l e which i s l a n d i n g must be performed.

e s p e c i a l l y f a v o r a b l e f o r f a s t f l i g h t , and i t i s a l s o advantageous f o r w e a t h e r c o n d i t i o n s w i t h very s t r o n g b u t v e r y d i s t a n t upwind f i e l d s .

*Boblingen, Reworked v e r s i o n o f a l e c t u r e a t t h e OSTIV Course i n 1964 i n Varese, I t a l y .

**Numbers i n margin i n d i c a t e p a g i n a t i o n i n f o r e i g n t e x t .

, . , - However, i t seems t h a t s u c h s i t u a t i o n s a r e rare.

It i s n o t optimum from an aerodynamic p o i n t o f view t o make a wing w i t h a s i n g l e p r o f i l e o v e r t h e e n t i r e wing. T h i s i s b e c a u s e , i n a d d i t i o n t o t h e h i g h t r a v e l v e l o c i t y , the p r o f i l e o n t h e o u t e r wing s h o u l d s a t i s f y a d d i t i o n a l r e q u i r e m e n t s .

For example, t h e a n g l e o f a t t a c k r a n g e between z e r o l i f t and maximum l i f t a l o n g t h e o u t e r wing s h o u l d b e larger t h a n f o r t h e i n n e r wing, i n o r d e r t o p r o v i d e good f l i g h t c h a r a c t e r i s t i c s f o r slow f l i g h t .

Beyond t h e maximum l i f t p o i n t , t h e d e c r e a s e s h o u l d b e slow, and g e n t l e .

F i n a l l y , t h e p r o f i l e o f t h e o u t e r wing s h o u l d n o t have any pronounced l a m i n a r d e p r e s s i o n . Otherwise, f o r f a s t f l i g h t , b e c a u s e of t h e e l a s t i c t w i s t i n g o f t h e wing, t h e o u t e r wing would f a l l o u t of t h e l a m i n a r de- p r e s s i o n a t low ca v a l u ~ s and t h i s would t h e n become a n e f f e c t i v e b r a k e .

When t i g h t c i r c l e s a r e flown, t h e o u t e r wing, which i s l o c a t e d lower i s s u b j e c t e d t o a s i m i l a r d a n g e r , b u t a t t h i s t i m e it o c c u r s a t h i g h l i f t v a l u e s . It i s e s p e c i a l l y i m p o r t a n t t h a t t h e t a i l r u d d e r e f f e c - t i v e n e s s i s n o t compromised by a n i n a p p r o p r i a t e l y - s e l e c t e d p r o f i l e .

It i s n o t e a s y t o s ~ t i s f y t h e s e a d d i t i o n a l and c o n t r a d i c t i n g r e q u i r e m e n t s w i t h o u t a c e r t a i n r e d u c t i o n i n t h e t r a v e l v e l o c i t y . T h i s is b e c a u s e t h e Reynolds numbers a l o n g t h e o u t e r wing, 0.5 - 1.0 x 1 0 , are a l r e a d y q u i t e small. The a u t h o r o f [ 2 ] gave a summary o f s e v e r a l p r o f i l e s h a p e s , whose measured p o l a r s do s a t i s f y t h e previously-mentioned r e q u i r e m e n t s , and t h e r e q u i r e m e n t f o r a h i g h t r a v e l v e l o c i t y .

4. DRAG RE;DUCTION BY KEEPING THE FLOW LAMINAR The p r e v i o u s discussions a b o u t t h e selection of s u i t a b l e wing p l a n forms and p r o t l l e s h a p e s do n o t a l l o w a g r e a t d e a l o f f l e x i b i l i t y t o t h e d e s i g n e r . C o n s i d e r i n g t h e p r o f i l e s e l e c t i o n , h e i s mostly de- / 7 2 4 pendent on wind-tunnel measurements. When h e s e l e c t s t h e wing p l a n form, he d o e s have c e r t a i n a d v m t a g e s compared w i t h p r e s e n t - d a y d e s i g n s , b u t o v e r a l l he cannot a c h i e v e a g r e a t d e a l o f p r o g r e s s . I n c o n t r a s t t o t h i s , i f t h e boundary l a y e r i s m a i n t a i n e d l a m i n a r , which amounts t o a r e d u c t i o n i n t h e f r i c t i o n d r a g , t h e n many more p o s s i b i l i t i e s open up.

For example, a wing i n a c o m p l e t e l y t u r b u l e n t flow can have more t h a n t w i c e t h e - s r q f i l e d r a g t h a n a wing whose boundary l a y e r remains l a m i n a r , at l e a s t p a r t i a l l y .

T h i s means t h a t t h e p r i n c i p l e of k e e p i n g t h e flow l a m i n a r r e c t a n p l a r T C X t, 0.4 -3. t s t r a p e z o i d 2 1 3 0,4 -3. 15 " 03 03 -3. 15 d o u b l e t r a p e z o i d F i g u r e 11: L i f t d i s t r i b u t i o n f o r r e c t a n g u l a r wings and d o u b l s t r a p e z o i d wings w i t h A = 1 5 and Fa = 1 . 4 .

r e p r e s e n t s t h e most e f f e c t i v e l e v e r a g e f o r r e d u c i n g t h e d r a g , which s h o u l d b e used t o a d v a n t a g e i n any a i r c r a f t d e s i g n . O f c o u r s e , t h e p o s s i b i l i t i e s c a n o n l y b e t a k e n a d v a n t a g e o f c o m p l e t e l y , i f t h i s p r i n - c i p l e i s f o l l o w e d f o r a new d e s i g n , s t a r t i n g a t t h e b e g i n n i n g . Because o f t h e great i m p o r t a n c e of t h i s p r i n c i p l e , w e w i l l b r i e f l y d i s c u s s t h e l a m i n a r - t u r b u l e n t t r a n s i t i o n phenomenon, and t h e n we w i l l d i s c u s s t h e c o n d i t i o n s f o r k e e p i n g t h e f l o w l a m i n a r .

The t h i n "laminarf1 boundary l a y e r which f l o w s i n a smooth man- n e r and which first forms on t h e s u r f a c e s o f a body i n a f l o w , n o r m a l l y c o n t i n u e s t o i n c r e a s e i t s t h i c k n e s s downst-eam i n a c o n t i n u o u s manner.

I n the b e g i n n i n g t h e s t a t e i s s t a b l e , and i s n o t s e n s i t i v e t o d i s t u r - bances, b u t t h e s t a t e r a p i d l y becomes u n s t a b l e . V h e t h e r o r n o t t h i s u n s t a b l e boundary l a y e r becomes t u r b u l e n t e a r l i e r o r l e t e r o n , depends o n t h e one hand on t h e degree o f t h e I n s t a b i l i t y and a l s o on t h e magni- t u d e o f t h e p e r t u r b a t i o n s , which comes from t h e e x t e r n a l f l o w o r from t h e wall, and are i n t r o d u c e d i n t o t h e boundary l a y e r . Except f o r d r a s - t i c changes, s u c h p e r t u r b a t i o n s which d i r e c t l y c a u s e t u r b u l e n c e are am- p l i f i e d i n a n u n s t a b l e boundary l a y e r . T h i s i s a p r o c e s s which r e q u i r e s time and a c e r t a i n p a t h l e n g t h . It i s c l e a r t h a t major i n i t i a l d i s t u r - bances w i l l produce t u r b u l e n c e e a r l i e r f o r o t h e r w i s e t h e same c o n d i t i o n s .

However, i f t h e p e r t u r b a t i o n s remain s u f f i c i . ; . n t l y s m a l l , t h e n t h e mea- s u r e o f i n s t a b i l i t y o r t h e t y p e o f t h e p e r t u r b a t i o n a m p l i f i c a t i o n p l a y s a major r o l e . I n a i r c r a f t , t h e s e p e r t u r b a t i o n s are p r a c t i c a l l y o n l y due t o t h e unevenness o f t h e s u r f a c e s , t h a t i s , t h e roughness f e a t u r e s and t h e waves i n t h e s u r f a c e . I n t h e c a s e o f r i g i d and impermeable s u r f a c e s , t h e a m p l i f i c a t i o n p r o c e s s i s de%ermined d e c i s i v e l y b y ' t h e p r e s s u r e va- r i a t i o n i n t h e f l o w d i r e c t i o n .

The l a m i n a r boundary l a y e r , f o r example, c a n be s t a b i l i z e d by a p r e s s u r e drop, s o t h a t t h e t r a n s s t i o n o n l y o c c u r s a t Reynolds numbers of R e > 15 x 1 0 . The Reynolds number is formed w i t h t h e p a t h l e n g t h , which e x t e n d s from t h e l e a d i n g edge o f t h e body t o t h e t r a n s i t i o n p o i n t * .

When t h e r e is a p r e s s u r e i n c r e a s e , on t h e o t h e r hand, t h e c o r r e s p o n d i n g

Reynolds number can be reduced t o Re = 2 x l o 4 , t h a t is, about 1/700 of

t h e v a l u e . When t h e r e ;lcne z e r o p r e s s u r e g r a d i e n t s , f o r example, i n t h e c a s e o f a f l a t p l a t e , t h e n t h e c o r r e s p o n d i n g Reynolds number o f t r a n s i - t i o n i s about 3 x 1 0 .

10 8 30 2 x l o b

144 40 2.66 x 1 0

t

It i s easy t o f i n d o u t what t h e s e numbers mean f o r g l i d e r s , and t h e t a b l e g i v e s s e v e r a l Reynolds numbers f o r a p a t h l e n g t h o f one m e t e r , For a wing w i t h a chord o f 1 meter, f o r example, a c o n s t a n t p r e s s u r e i s s u f f i c i e n t t o m a i n t a i n t h e boundary l a y e r o v e r t h e e n t i r e chord, even f o r f a s t - f l i g h t c o n d i t i o n s ( a t 40 m / s . ) It i s only a t a l e n g t h o f about 1.1 m e t e r s t h a t t h e Reynolds number would r e a c h a v a l u e o f 3 x lo6 snd I; t h e boundary l a y e r would become t u r b u l e n t . On t h e o t h e r hand, when t h e r e is a p r e s s u r e i n c r e a s e , and t h e i n c i d e n t v e l o c i t y i s 20 m / s , a p a t h - l e n g t h o f 1 cm i s a l r e a d y enough t o completely develop t u r b u l e n c e , f o r I example, i f one wishes t o m a i n t a i n t h e flow l a m i n a r o v e r a body s u r f a c e I speed a t a l e n g t h o f more t h a n 2 m e t e r s , t h e n one needs f l y i n g a t a fast a t l e a s t a small p r e s s u r e d r o p f o r s t a b i l L z i n g t h e l a m i n a r boundary l a y e r .

Expressed d i f f e r e n t l y , i n t h e c a s e o f a a l i d e r wina, t r a n s i t i o n always o c c u r s downstream o f t h e p o i n t o f minimum p r e s s u r e , For a smooth f u s e - l a g e , t h e t r a n s i t i o n w i l l o c c u r a l r e a d y somewhat ahead o f a p r e s s u r e minimum, because o f t h e l a r g e r Reynolds numbers.

@ A t a v e l o c i t y o f u = 40 m s (145 k d h ) , - 1 5 x 10 means a p a t h

l e n g t h of 5.6 meters!

The p r e s s u r e v a r i a t i o n i s d e t e r m i n e d by t h e s h a p e and i n c i d e n c e a n g l e o f a body i n a flow. it is c l e a r t h a t t h e e x a c t knowledge o f t h e r e l a t i o n s h i p o f t h e body s h a p e a s r e l a t e d t o t h e p r e s s u r e d i s t r i b u t i o n u s i n g e x p e r i m e n t a l and t h e o r e t i c a l methods, i s i m p o r t a n t f o r main- t a i n i n g t h e flow l a m i n a r .

On t h e o t h e r hand, from t h e t r a n s i t i o n Reynolds numbers, one c a n see t h a t it is r e l a t i v e l y s i m p l e and e a s y t o m a i n t a i n t h e f l o w l a m i n a r t n t h e v e l o c i t y r a n g e o f g l i d i n g , when t h e r e i s a s u i t a b l e p r e s s u r e va- r i a t i o n , w l t h t h e c o n d i t i o n t h a t t h e a d d i t i o n a l i n f l u e n c e s , t h a t is, t h e p e r t u r b a t i o n s , of t h e l a m i n a r boundary l a y e r , can b e m a i n t a i n e d s u f f i - c i e n t l y small.

F o r t u n a t e l y , t h e free atmosphere i n g e n e r a l i s s u c h t h a t it i n - t r o d u c e s p r a c t i c a l l y no p e r t u r b a t i o n s t o t h e boundary l a y e r . Many d i d m p i l o t s b e l i e v e t h a t t h e g u s t i n e s s o f t h e thermals h a s e n unfa- v u r a b l e e f f e c t on l a m i n a r p r o f i l e s . However, g u s t s p r l m a r i i y change t h e i n c i d e n t f l o w d i r e c t i o n f o r t h e a i r c r a f t , and t h i s change is pro- bably t h e p r i m a r y n e g a t i v e f a c t o r o f g u s t i n e s s . A p e r t u r b a t i o n due t o t h e i n c i d e n t flow, t h e r e f o r e , o n l y o c c u r s i n t a i l s u r f a c e s , i f t h e y r e a c h t h e t u r b u l e n t wake o f t h e wing.

T h i s means t h a t i n a c c u r a c i e s i n t h e s u r f a c e , s u c h as roughnesses/725 and waves, are p o s s i b l e p e r t u r b a t i o n s f o r t h e most p a r t . F o r t u n a t e l y , t h e boundary l a y e r o n l y r e a c t s t o s u c h t h i n g s when t h e p e r t u r b a t i o n mag- n i t u d e h a s reached a c e r t a i n amount. The l i m i t i n g h e i g h t beyond which t r a n s i t i o n i s i n f l u e n c e d i s c a l l e d t h e c r i t i c a l roughness h e i g h t k , and i s about 1/13 of t h e boundary l a y e r t h i c k n e s s . F i g u r e 1 2 shows c r i t i c a l roughness h e i g h t f o r a f l a t p l a t e h a v i n g a chord o f 1 meter, and f o r two t y p i c a l Reynolds numbers. If one wishes t o have t h e s e v a l u e s f o r o t h e r

"' lJ"' *, one s h o u l d u s e t h e f'or-

chord v a l u e s T and Reynolds numbers . - u 0335 I x If t h e v e l o c i t y remains t h e same, t h e h e i g h t k f o r

mula - :.. , . 5 : . \I-

t t example v a r i e s a l o n g t h e s p a n a c c o r d i n g t o a. If t h e body i s p o i n t e d w i t h a F a c t o r T = 0.5, t h e n k must b e a b o u t 30% smaller a l o n g t h e o u t e r wing t h a n i n t h e i n n e r wing. The v a l u e s g i v e n f o r t h e f l a t p l a t e a r e i m p o r t a n t r e f e r e n c e s f o r v a l u e s which a r e p e r m i s s i b l e f o r t h e p r o f i l e , if we c o n s i d e r t h e f a c t t h a t t h e p r o f i l e boundary l a y e r i s i n g e n e r a l * U , = f l i g h t v e l o c i t y v = k i n e m a t i c v i s c o s i t y 29% t o 30% t h i n n e r t h a n f o r t h e f l a t p l a t e , b e c a u s e o f t h e p r e s c u r e drop. T h i s means t h a t t h e c r i t i c a l roughness hei@ts from t h e p r o f i l e n o s e t o t h e maximum p r o f i l e t h i c k n e s s p o l n t are somewhat smaller t h a n shown i n F i g u r e 12.

These are lower l i m i t i n g v a l u e s , which are c e r - t a i n l y n o t " f e l t w by t h e l a m i n a r boundary l a y e r i n t h e p l a n e c a s e . I n t h e c a s e of body s u r f a c e s , t h a t is, t h r e e - d i m e n s i o n a l f l o w s , t h e c r i - . - . ~ . -.

t i c a l r o u g h n e s s h e i g h t s are a l s o somewhat lower t h a n shown i n F i g u r e 12.

The v a l u e s f o r t h e body f r o n t p a r t must t h e n b e m u l t i p l i e d by a f a c t o r o f between 3.7 and 0.6.

The r e a s o n why t h e boundary l a y e r a l o n g t h e body f r o n t p a r t is t h i n n e r f o r a f l a t p l a t e under o t h e r w i s e t h e same c o n d i t i o n s is p r i - m a r i l y due t o t h e i n c r e a s e i n t h e body c i r c u m f e r e n c e .

The boundary l a y e r s k i n which s u r r o u n d s a body i n t h i s way i s g i v e n a t h i n n i n g - o u t i n a c e r t a i n s e n s e . T h e r e f o r e , i t grows s l o w e r i n t h e f l o w d i r e c t i o n t h a n f o r a f l a t s u r f a c e . Conversely, t h e c o n d i t i o n s a r e o p p o s i t e f o r a c o n t r a c t i o n of t h e body c r o s c - s e c t i o n : t h e boundary l a y e r m a t e r i a l flows t o g e t h e r and c a n become more t h a n t w i c e a s t h i c k a z t h e c a s e men- t i o n e d above.

T h e r e f o r e , w e s h o u l d r e a l i z e t h a t i t i s n o t a t a l l t r u e t h a t a small o i l s p o t on t h e s u r f a c e w i l l l e a d t o t u r b u l e n c e , a s one o f t t n h e a r s . I n s t e a d , n o t even a c o a r s e sandpaper w i l l l e a d t o i m p e r m i s s i b l e roughnesses. The r e q u i r e m e n t s are a l s o more s t r i n g e n t i n t h e v i c i n i t y o f t h e l e a d i n g edge o f t h e wing and t h e n o s e o f t h e body.

How d o e s one c o n t r o l t h e roughness h e i g h t ? I n s p e c i a l c a s e s , t h i s i s done by measurement, o f c o u r s e . I n p r a c t i c e , t h e t o u c h s e n s e o f t h e f i n g e r s and t h e i n n e r s i d e o f t h e hand a r e c o m p l e t e l y s u f f i c i e n t ; ( f o r example, one c a n t e s t T e s a f i l m , which i s a b o u t 8 x l o g 2 mm t h i c k ) A r o u g h n e s s which c a n n o t b e f e l t is, a s a r u l e , c o n s i d e r a b l y below t h e c r i t i c a l v a l u e . F i n a l l y , w e s h o u l d emphasize t h a t a n ideally-smooth s u r f a c e cannot p e r f o r m more towards k e e p i n g t h e f l o w l a m i n a r t h a n a rough s u r f a c e , which d o e s n c t exceed t h e c r i t i c a l amount a t any p o i n t .

F i g u r e 1 2 shows two dashed l i n e s , which have n o t h i n g t o do w i t h k e e p i n g t h e f l o w l a m i n a r .

They a r e t h e p e r m i s s i b l e r o u g h n e s s magnitude f o r boundary l a y e r s which have a l r e a d y become t u r b u l e n t . U p t o t h i s magnitude, t h e s u r f a c e i s " a e r o d y n a m i c a l l y smcoth". L a r g e r r o u g h n e s s e s i n c r e a s e t h e f r i c t i o n d r a g f o r a t u r b u l e n t boundary l a y e r , f o r example, i f t h e roughness h e i g h t i s d o u b l e d , i t i s i n c r e a s e d by a b o u t 20%. The 1 2 : C r i t i c a l Roughness h e i g h t s f o r l a m i n a r and t u r b u l e n t boun- d a r y l a y e r s f o r a f l a t p l a t e 1 m i o n g and f o r two Reynolds numbers.

v a l u e s g i v e n a r e s a f e l i m i t s , similar t o t h e l a m i n a r boundary l a y e r .

For example, i n t h e r e g i o n o f a p r e s s u r e i n c r e a s e , somewhat l a r g e r r o u g h n e s s e s a r e s t i l l p e r m i s s i b l e . F i g u r e 1 2 a l s o , a t t h e same time, shows t h e g r e a t i n f l u e n c e o f t h e Reynolds i~umbers. F o r a t u r b u l e n t boundary l a y e r , t h e s u r f a c e must b e smoother t h a n f o r a l a m i n a r boun- d a r y l a y e r , e x c e p t f o r t h e first 100 mm.

The q u e s t i o n o f which s u r f a c e waviness oan be looked upon as b e i n g p e r m i s s i b l e is n o t t o b e c s s i l y answered. Probably t h e r e i s no " p e r m i s s i b l e " waviness a t a l l . According t o t h e o r e t i c a l i n v e s t i g a t i o n s , a s u f f i c i e n t number o f waves f o l l o w i n g one a n o t h c ~ w i l l always produce a s e p a r a t i o n o f t h e l a m i n a r boundary l a y e r , even i f t h e wave a m p l i t u d e i s v e r y small. T h e r e f o r e , i t i s n o t a s t o n i s h i n g t h a t a t t h e same time t r a n s i t i o n t a k e s p l a c e c o n s i d e r a b l y e a r l i e r t h a n f o r a s u r f a c e w i t h o u t waves.

The p e r i o d i c sequence o f t h e f d e n t i c a l waves i s p r o b a b l y a n ex- c e p t i o n i n a r e a l s u r f a c e . On t h e o t h e r hand, s i n g l e i s o l a t e d waves w i l l o c c u r o f t e n . It i s l i k e l y t h a t a wave whose a m p l i t u d e i s n o t g r e a t e r t h a n t h e c r i t i c a l roughness h e i g h t i n F i g u r e 1 2 w i l l have b a r e l y any i n f l u e n c e on t h e p o s i t i o n o f t r a n s i t i o n . However, it is p o s s i b l e t h a t c e r t a i n wavelengths a r e more dangerous t h a n e t h e r s b e c a u s e o f a kind o f r e s o n a n c e . T h i s could b e t r u e f o r wavelengths o f between 80 and 150 roughness h e i g h t s . A p r e m a t u r e t r a n s i t i o n i n t h e f i r s t p l a c e meam a n i n c r e a a e d f r i c t i o n drag, but a l s o u n f a v o r a b l e c o n d i t i o n s . For example, i f t h e t a i l rudder on t h e o u t e r wing is d e f l e c t e d , t h e r e i s u s u a l l y a l s o a s e p a r a t i o n of t h e t u r b u l e n t boundary layer, which can very r a p i d l y l e a d t o l a r g e r e s i s t a n c e v a l u e s .

/726 bottom T h e m f o r e , one should not only c o n t r o l t h e q u a l i t y o f t h e s u r - f a c e s b u t a l s o t h e p o s i t i o n o f t h e t r a n s i t i o n f r o n t s i n f l i g h t t e s t s .

f o r example, t h e t r a n s i t i o n p o s i t i o n f o r d i f - I n t h e c a s e o f a wing, f e r e n t a n g l e s of a t t a c k ( o r ca - v a l u e s , o r v e l o c i t i e s v ) one should o b t a i n a v a r i a t i o n a s given i n t h e sketch. I f wind t u n n e l meaurenents a r e a v a i l a b l e f o r t h e p r o f i l e s used, t h e n by comparison one can e s t a b - l i s h whether t h e wind t u n n e l v a l u e s were a l s o achleved i n f l i g h t , and where d e v i a t i o n s o c c u r r e d . When t h e t r a n s i t i o n p o s i t i o n a g r e e s , a t t h e same time one a l s o has a v e r i f i c a t i o n t h a t t h e d r a g c o e f f i c i e n t s a r e t h e same a s i n t h e wind t u n n e l , I n a f l i g h t t e s t , t h e o b s e r v a t i o n of t r a n s i t i o n is not a s easy as i n t h e wind t u n n e l , where t h e s o f t s i n g i n g o f t h e l a m i n a r boundary l a y e r can be heard through a t u b e , and can e a s i l y be d i s t i n g u i s h e d from t h e rough n o i s e o f t u r b u l e n c e . Even when probes a r e i n s t a l l e d , a t least Microphones f o r 20 p o i n t s on each h a l f span should be o b s e r v ~ b l e .

l i s t e n i n g t o t h e boundary l a y e r a r e not s u i t a b l e , because o f t h e i r s e n s i t i v i t y t o body n o i s e . The same is f o r t o t a l p r e s s u r e probes, be- c a u s e o f t h e small s t a g n a t i o n . p r e s s u r e s . Ky colleague, D. Althaus, t h e r e f o r e developed a s i m p l e r and s a f e r method f o r o b s e r v i n g t r a n s i t i o n - . .

on g l l d e r 8 , on which h e w i l l s h o r t l y r e p o r t ,

5 . CURVED FLAPS AND BRAKES

After t h e s h o r t d i s c u s s i o n about t h e requirements and c o n t r o l of keeping t h e flow l a m i n a r , w e w i l l now make some o b s e r v a t i o n s r e - garding b r a k e s and curved f l a p s , Normally, a laminar boundary l a y e r becomes t u r b u l e n t i n t h e brake f l a p a r e a st t h e l a t e s t , e i t h e r t h e f l a p I s n o t a smooth c o n t i n u a t i o n of t h e s u r f a c e , o r it is n o t h e r m e t i c w i t h r e s p e c t t o t h e p r e s s u r e d i f f e r e n c e between t h e upper and lower s i d s o f t h e wing. Both c a u s e s can b e a v o i d a b l e , and it is not always f a v c r a b l e t o go back t o 70% o f t h e p r o f i l e chord, o r even f u r t h e r , with t h e brakes. I f curved f l a p s f o l l o w t h e b r a k e s , t h e r e g i o n be- tween 50 t o 65% of t h e chord w i l l be t h e most f a v o r a b l e , because h e r e t h e laminar boundary l a y e r i s a l r e a d y r e l a t i v e l y t h i c k , and t h e r e f o r e t h e c r i t i c a l roughness h e i g h t i s l a r g e . Also t h e p r o f i l e t h i c k n e s s s t i l l a f f o r d s s u b s t a n t i a l room f o r i r ~ s t a l l a t i o n (of p r o b e s ) . I n o r d e r t o f a c i l i t a t e t h e h e r m e t i c i t y problem, t h e topsidr. and lower s i d e f l a p s should be i n s t a l l e d i n s e p a r a t e chambers, and t h e common a x i s should be made hermetic a l o n g t h e s e p a r a t i o n w a l l of t h e chambers. Because o f t h e e l e a s t i c bending o f t h e wing, t h e f l a p s can o n l y b e made continuous ( w i t h s u r f a c e ) usiilg a c o v e r i n g s t r i p which is e l a s t i c a l l y connected w i t h t h e f l a p . The v e r t i c a l gap between t h e c o v e r i n g s t r i p and t h e wing s k i n should b e 0.5 t o 0.8 mm a t a maximum. The c o v e r i n g s t r i p should a l s o s e a l o f f t h e f l a p chamber t o a c e r t a i n d e g r e e , i f p o s s i b l e , because i n t h e flow d l r e c t i o n there w i l l be a p r e s s u r e i n c r e a s e i n gene- r a l , through which t h e flow can flow i n along t h e r e a r s t r i p gap and can flow o u t a l o n g t h e f r o n t one.

The c u r v d f l a p s and t h e t a i l r u d d e r s a r e s p e c i a l l y d i f f i c u l t , because o f t h e s m a l l Reynolds numbers. S e p a r a t e i n v e s t i g a t i o n s w i l l be r e q u i r e d t o o b t a i n t h e r e a l l y good s o l u t i o n s . It i s d e s i r a b l e t o have r o t a t i o n axes on the t o p s i d e o f t h e wing from t h e d e s i g n poin,G o f view. Aerodynamically, however, t h e f l a p s which a r e deployed downwards are e s p e c i a l l y v u l n e r a b l e t o s e p a r a t i o n , and t h e bend i n t h e upper con- t o u r w i l l i n c r e a s e c h i s danger ? o n s i d e r a b l y .

A s e p a r a t i o n on t h e wing s i d e not o n l y d e c r e a s e s t h e r o l l i n g moment, but i s intended t o I n c r e a s e t h e t a i l r u d d e r d e f l e c t i o n . The i n c r e a s e d d r a g a m p l i f i e s t h e u n d e s i r a b l e n e g a t i v e r o l l yaw moment.

. , S'tir.*". .--r~=l-.e.. -. .. %. . - . .; . - - . - - - . , 4 - .

; such d e t r i m e n t a i factors can be aaoeptcd. l o r a t a l l rudder because t h e I rudder 18 a n l y d e f l e c t e d over s h o r t time p e r i o d s , and u s u a l l y w i t h ;'only small nmylitudes up t o about f i v e degrees. On t h e o t h e r hand, the f l a p wing Is d e f l e c t e d by +10 o r -Is0, and r e p r e s e n t s a long pe- r i o d I n s t a l l a t i o n . It is very important t o know what t h e f l a p can do a t t h e s e l a r g e angles. The low degree of success o f e l d e r f l a p a i r - - - ~,

craft shows t h a t this I d e a dces not aut&utlaally l e a d t o a higher per-

formance, but i n s t e a d r e q u i r e s 8pecia:ly-designed p r o f i l e s [ 2 1. Un- doubtedly, the questions r e g a r d i n g f l a p p r o f i l e s o f g l i d e r s have only been touched, and advances a r e t o b e expected.

6. BODY ft i s remarkable how seldom g l i d e r d e s i g n e r s , who give s o much a t t e n t i o n t o laminar p r o f i l e s , e x p l o i t t h e p o s s i b i l l t i e s of reducing t h e d r a g over bodies. Figures 1 o r 2 , ?r a simple calcu3.ationS show that t h e body d r a g is very important f o r f a s t f l i g h t . There are two p o s s i b i l i t i e s : t h e boundary l a y e r can b e kept laminar along t t ~ e body f r o n t p a r t , and che s u r f a c e a r e a o f t h e t a i l s u r f a c e c a r r i e r can be reduced.

The f i r s t p o s s i b i l i t y can reduce t h e drag t o one-half c f t completely t u r b u l e n t bodies.

For fast f l i g h t c o n d i t i o n s , t h e Reynolds numbers a r e about /7 2 7 -6 6 x 10 up t o t h e r e g i o n of t h e wing l e a d i n g edge. A t t h e s e numbers, t h e boundary l a y e r can e a s i l y be kept laminar b y means of a s l i g h t p r e s s u r e drop. However, one must have a s u i t a b l e body shape and one must have a hermetic and smoo5h s u r f a c e of t h e f r o n t p a r t of t h e body.

This means t h e r e can be no t o t a l p r e s s u r e probes, cabin a i r condi- t i o n i n g , towing coupling, s k i d s , water r e l e a s e h o l e s , removable n a c e l l e s , o r o t h e r o v e r - c r i t i c a l roughnessee a l o n g t h e f r o n t p a r t of t h e body.

These requirements a l r e a d y r e p r e s e n t s e r i o u s d i f f i c u l t i e s , and have been r e a l i z e d i n s e v e r a l g l i d e r s . Howevw, t h e r e i s s t i l l t3e problem o f t h e p i l o t g e t t i n g i n and o u t of t h e a i r c r a f t . I n s p l t e of' a l l t h e enthusiasm f o r p e r f e c t aerodynamics, t h e p i l o t must be given a primary importance, and must have s u f f i c i e n t comfort and s a f e t y . I n many new deslgns, it has been overlooked t h a t it is necessary t o make t h e r e - moveable p a r t of t h e canopy hermetic and continuous w i t h t h e body con- t o u r . I n s t e a d , one g a i n s t h e i4mpreesion t h a t the s o l u t i o n decided

upon w a a a minimum body cross-section w 1 t . h a p i l o t l y i n g down , and

extremely l o n g canopies. A c l o s e i n s p e c t i o n shows a l l o f t h e c o n d i t i o n s for completely t u r b u l e n t s u r f a c e s t o be s a t i s f i e d . Then one can see t h a t a n e r r o r has been made t o confuse e x t e r n a l elegance w i t h aerody- namic q u a l i t y . Such bodies &re n o t m y b e t t e r i n terms of d r a g t h a n c o n v e n t i o n a l b o d j shapes, such as t h e Ka-6 a i r c r a f t .

There are v a r i o u s t y p e s where t h e canopy i s designed a c c o r d i n g t o t h e s k e t c h shown. Because of t h e s l i g h t l y concave c o r n e r , t h e l a - minar boundary l a y e r s e p a r a t e s i n t h e c e n t r a l p a r t and t h i s l e a d s t o t u r b u l e n t v o r t e x s t r i p s on b o t h s i d e s of t h e canopy. Usually, t h i s t u r b u l e n t r e g i o n t h e n r e a c h e s t h e already-endangered wing r o o t . Then, e s p e c i a l l y d u r i n g slow f l i g h t , a secondary l o s s i s produced i n t h e r e g i o n of t h e body wing t r a n s i t i o n p o i n t , which i s t h e n much l a r g e r t h a n t h e f r i c t i o n l o s s a t t h e canopy. Here a g a i n , t h e same h o l d s t r u e : one cannot expect a n o t i c e a b l e g a i n , compared w i t h conventional canopy shapes.

However, i f a c e r t a l n degree of improverncnt l a i m p o r t a n t , t h e n one should b e c o n s i s t e n t and should e v a l u a t e eriery d e t a i l w i t h t h e eyes o f a boundary l a y e r e n g i n e e r . The body c o n t o w should n o t have d l s c m - t i n u i t i e s i n t h e c r o s s - a a c t i o n , fo? keeping t h e flow l a m i n a r , and t h e Longitudinal s a c t i o n should not have any d i s c o n t i n u i t i e s e i t h e r . T h i s means a n s t r a k e r e t r a c t e d canopy shapen 13 a c o n d i t i o n here. The "canopy" t h a t is, t h e t r a n ~ p a r e n t p a r t o f t h e body, should c o n s l s t o f a f r o n t p ~ r t connected with t h e body and a removable p a r t .

- . - . . -.. * ~ .

The body contour should b e d e r i v e d from t h e shapes of t h i c k laminar p r o f i l e s , s o t h a t l o c a l o v e r v e i o c i t i e s a r e avoided, and a mono- t o n i c w i l l be maintained f o r moderate a n g l e s o f attack o r s i d e s l i p : angle.

I f t h e f r o n t p a r t o f t h e body i s compleCely smooth and herme- t i c , t h e n one can attempt t o keep t h e body l a y e r laminar, a l s o over t h e r e m v a b l e p a r t o f t h e canopy. T h i s r 8 b e s t done by d i s p l a c i n g t h e s e p a r a t i o n gap as far back a s p o s s i b l e i n t c t h e re,ion w i t h a l a r g e r c r i t i c a l roughness h e i g h t . The smooth o u t e r contour could pro- bably be m a i ~ i t a i n e d even f o r d a i l y a i r c r a f t u s e u s i n g a groove and s p r i n g d e s i g n a t t h e f r o n t and rear s e p a r a t i o n gap. Perhapi t h e se- p a r a t i o n gap could a l s o be made hermetic a t t h e same time. There is an. underpressure o f about 10 t o 20% o f t h e s t e g n a t i o n p r e s s u r e a t t h e o u t e r e k i n i n t h e r e g i o n o f t h e l a r g e s t body c r o s s - s e c t i o n . It w i l l flow through porous p a r t s o u t o f t h e cabin. T h i s causes a laminar ; boundary l a y e l t o become t u r b u l e n t immediately. I n e a r l i e r world COT- " p e t i t i o n , sometimes canopies were s e a l e d with s e a l i n g s t r i p s . This method probabiy w i l l make it h a r d e r f o r t h e p i l o t t o g e t o u t o f t h e a i r c r a f t , and cannot b e looked upon a s a s o l u t i o n o f t h e s e a l i n g prob- lem, ( k e n if t h e roughness h e i g h t o f t h e s t r i p s i s under c r i t i c a l ) , It w i l l probably be d i f f i c u l t t o keep t h e boundary l a y e r lami- nar over t h e r e a r s e p a r a t i o n gap of t h e remov2ble canopy p a r t .

On t h e one hand, because of t h e p r e s s u r e d i s t r i b u t i o n and a l s o because of t h e l e n g t h change o f t h e p l e x i g l a s s due t o temperature changes, a c e r t a i n amount o f p l a y w i l l b e necessary. Nevertheless, t h e r e a r s e p a r a t i o n gap should n o t b e developed a s a v e n t i l a t i o n gap, c o n s i d e r i n g t h e body wing connection. I n s t e a d , t h e r e should be an e l a s t i c a l r - t i g h t s e a l .

I f one were t o f o l l o w t h e t y p i c a l concept o f a smooth and her- metic f r o n t p a r t of t h e body, and a lamlnar boundary l a y e r up t o t h e wing, t h e n of course v e n t i l a t i o n must be subordinated t o t h i s r e q u i r e - ment. The s u p p l i e d a i r could be t a k e n o f f from an i n l e t d i f f u s o r o r an a i r i n l e t cup, downstream of t h e t r a n s i t i o n p o i n t a l o n g t h e body s i d e wall; f o ~ example, under t h e wing. F l a t channels would t h e n be used t o d i r e c t t h e a i r i n t o t h e cabin, and i t would flow through s l i t s i n t o t h e canopy i n n e r s i d e s . The a i r t o be removed should b e allowed t o p a s s through t h e body, and should emerge through a s p e c i a l opening n e a r t h e s p i k e , t h a t i s , along t h e body underoide.

I - * I n t h e same way, t h e t o t a l p r e s s u r e cannot b e t a k e n from t h e f r o n t p a r t o f t h e body. The t o t a l p r e s s u r e probe c o n s i s t s of' a t u b e open i n t h e forward d i r e c t i o n , and t h e wall t h i c k n e s s shouLd b e s m a l l compared w i t h t h e i n n e r diameter. There a r e many p o s s i b i l i r . i e s f o r installing t h e probe. The t o t a l p r e s s u r e can be measured c o r r e c t l y everywhere, as long as one is o u t s i d e o f t h e boundary l a y e r and o u t s i d e o f s e p a r a t i o n r e g i o n s . However, t h e r e a r e r e s t r i c t e d numbers o f 1 7 2 8 p o i n t s f o r p r a c t i c a l r e a s o n s : It m p r e s e n t s an o b s t a c l e f o r mounting t h e wings i f mounted a l o n g t h e body s i d e w a l l s , i f mirunted a l o n g t h e body underside, t h e r e i s a danger of contamination and damage. I f t h e dimensions a t e small, t h e n it i s easy t o p e n e t r a t e i n t o t h e boundary l a y e r m a t e r i a l i f it is mounted an t h e back o f t h e body. The t i p o f t h e rudder i s a n a p p r o p r i a t e and often-used i n s t a l l a t i o n p o s i t i o n , i f t h e adjustment time of t h e a i r speed i n d i c a t o r remains s u f f i c i e n t l y small. Usually t h i s can be done u s i n g a p r e s s u r e l i n e w i t h an i n t e r n a l d i a m e t e r o f o n l y 3 mm.

The s t a t i c p r e s s u r e t a p s can a l s o be i n s t a l l e d i n t h e t o t a l p r e s s u r e probe ( P r a n d t l t u b e ) . However, t a p s on a body c r o s s - s e c t i o n a r e probably s i m p l e r and more e f f e c t i v e , and they a r e i n s t a l l e d about one c o n t r o l s u r f a c e width ahead o f t h e c o n t r o l s u r f a c e . Four o r more t a p s should make a c r o s s long t h e circumference, and t h e p o s i t i o n should be d i s p l a c e d 4 5 O w i t h r e s p e c t t o t h e v e r t i c a l . When t h e s e t a p s a r e connected, then t h e average s t a t i c p r e s s u r e i s q u i t e independent o f the o b l i q u s flow c o n d i t i o n .

If t r a n s i t i o n on t h e body s u r f a c e h a s been delayed t o t h e wing, . .

- - t h e n one can c o n s i d e r even more t h e second p o s s i b i l i t y o f r e d u c i n g d r a g : t h e body c r o s s - s e c t i o n i s c c n s t r i c t e d , and i n this way t h e s u r f a c e ex- posed t o t u r b u l e n t flow i s reduced. This a t t h e same time corresponds t o a u s e f u l boundary l a y e r p r i n c i p l e , i n which most of t h e p r e s s u r e i n c r e a s e connected w i t h t h e c o n s t r i c t i o n i s a s s i g n e d t o t h e boundary l a y e r which h a s j u s t become t u r b u l e n t . I n t h e ~ 3 ~ e o f bodies w i t h a r e t r a c t a b l e wheel, t h e c r o s s - s e c t i o n can be reduced t o t h e value r e - q u i r e d f o r s t r e n g t h , without any g r e a t concern. However, t h e r e should be a round t r a n s i t i o n i n t o t h e cone end p i e c e , It i s more d i f f i c u l t t o s p e c i f y an optimum body contour f o r a wheel a l r e a d y i n s t a l l e d , because t h e wheel d r a g i s i n c r e a s e d due t o t h e c o n s t r i c t i o n of t h e body c o n t o u r .

O f c c ~ ~ * n e , t h e s e c o n s i d e ? a t i o n s can only b e considered i n an e n t i r e l y new d e s i g n . I n an a l r e a d y - b u i l t a i r c r a f t , one h a s t o r e a c h a compromise. I n a Ka-6 a i r c r a f t , f o r ~ x a m p l e , it i s very worthwhile t o make t h e body nose hermetic and smooth, b u t it would n o t make s e n s e t o change t h e v e n t i l a t i o n , because t h e r e is a t u r b u l e n t v o r t e x a t t h e d i s - c o n t i n u i t y between t h e canopy and t h e body. It i s a l s o worthwhile t o u s e round s u r f a c e s i n f r o n t o f and t o t h e s i d e s o f a f i x e d wheel. Ac- c o r d i n g t o wind-tunnel measurements, t h e d r a g c o e f f i c i e n t o f a h a l f - r e t r a c t e d wheel f o r an a i r c r a f t with t h e dimensions o f a Ka-6 i s cw = 5.0 x without a cover. It is reduced t o 3.8 x l o m 4 i f s m a l l round s u r f a c e s a r e used, and t o 2 x by means o f a p r i m i t i v e outgoing flow cover, f o r which t h e i n i t i a l c r o s s - s e c t i o n i s t h e c r o s s - s e c t i o n o f t h e wheel.

F i n a l l y , we would l i k e t o 3 i s c u s s antenna i n s t a l l a t i o n . Some- t i m e s one f i n d s antennas which a r e perpenflicular t o t h e body s u r f a c e .

T h e i r d r a g i s about as g r e a t a s t h e d r a g o f one-half o f a c o n t r o l s u r - f a c e .

7. CONTROL SURFACES For a c o n t r o l s u r f a c e c o n s i s t i n g o f e l e v a t o r s and r u d d e r s , t h e p r o f i l e shape should be s e l e c t e d a c c o r d i n g t o t h e p o s i t on of t h e rud- d e r a x i s , s o t h a t t r a n s i t i o n o c c u r s w i t h c e r t a i n t y j u s t ahead of t h e rudder. The rudder gaps must be c a r e f u l l y s e a l e d , j u s t ss f o r t h e a i l e r o n . One u s u a l l y uses h o r i z o n t a l t a i l ' assemblies w i t h q u i t e - t h i n p r o f i l e s , with a r e l a t i v e t h i c k n e s s between 6 and 9%. A t t h e s e s m a l l p r o f i l e t h i c k n e s s e s , t h e p r o f i l e shape h a s a n e g l i g i b l e i n f l u e n c e on t h e drag. However, t h e r e is an e x c e p t i o n i n t h e c a s e o f t h e pendulum rudder: h e r e t h e r e can b e t r a n s i t i o n s which a r e d i s p l a c e d f a r towards t h e back w ~ t h c e r t a i n p r o f i l e s , f o r example, t h e s e r i e s 66 N A C A p r o f i l e s .

However, t h e s e shapes have t o be somewhat modified so t h a t t h e sudden t r a n s i t i o n t c p r e s s u r e i n c r e a s e a t about 6 0 % chord does not l e a d t o s e p a r a t i o n o f t h e laminar boundary l a y e r . T h i s d e s i g n problem must not be overlooked. It i s 2 e s i r a b l e t o have a c e n t e r of g r a v i t y p o s i - t i o n n e a r t h e r o t a t i o n a x i s , t h a t is a t 22-25% chord, The s u r f a c e q u a l i t y r e q u i r e d t o keep t h e flow laminar behind t h e a x i s o f r o t a t i o n r e q u i r e s an extremely l i g h t d e s i g n . It does n o t make sense t o sweep back t h e c o n t r o l s u r f a c e s , because sweepback has an unfavorable i n f l u e n c e on k e e p i n g t h e flow l a m i n a r . The c o n t r o l s u r f a c e s s h o u l d n o t s t a r t w i t h t h e wedge-shaped e x t e n s i o n s i n t h e body, b u t s h o u l d o n l y have s h o r t round s u r f a c e s . The wedge-shaped f i n d i s p l a c e s t h e t u r b u l e n c e of t h e body boundary l a y e r o u t w a r d s , b e c a u s e o f i t s e x t r e m e sweepback, and t h e f r a c t i o n of t h e s u r f a c e o f t h e c o n t r o l s u r f a c e i n a t u r b u l e n t f l o w i s u n n e c e s s a r i l y i n c r e a s e d .

The above d i s c u s s i o n a b o u t s e v e r a l p o s s i b i l i t i e s o f r e d u c i n g d r a g , i s n e i t h e r c o m p l e t e o r new. I n many p l a c e s w e had t o g i v e ge- n e r a l recommendations i n s t e a d o f p r e c i s e d a t a . N e v e r t h e l e s s , a con- s e q u e n t a p p l i c a t l o n of t h e s e p r i n c i p l e s , which a r e r e l a t i v e l y s i m p l e , and can b e b r o u g h t a b o u t w i t h o u t g r e a t t e c h n i c a l c o m p l e x i t i e s , w i l l b r i n g a b o u t a m e a s u r a b l e p e r f o r m a n c e i n c r e a s e .

F i n a l l y , we w i l l a g a i n emphasize t h i s p o s s i b i l i t y , which n o t onl:? t h e d e s i g n e r h a s , b u t any g l i d e r p i l o t , who i s c o n c e r n e d w i t h h i s a i r c r a f t .

REFERENCES 1. Wortmann, F. X . , S c h w o e r e r , K . : I n f l u e n c e of P r o f i l e P o l a r s F l i g h t Performance of G l i d e r s . S c h w e i t z e r , Aero-Revuew, b e r , 1963, and OSTIV-Publication V I I .

2. Wortmann, F. X . : S e v e r a l Laminar P r o f i l e s f o r G l i d e r s . S c h w e i z e r Aero-Revue, November, 1 9 6 3 , and OSTIV P u b l i c a t i o n , V I I .