8/10/2019 3849.pdf

1/33

O

Z

I ~ l l l l l ll l m ~

I l i l i l l l l

: " 'P , M [ N o 3 ' : ~ ' ' " "

] 1 : : ' I R , ,O C l l J i] lli i: ilLI I Z ,M ]11 ] ', " ] ; i " ] lli ' ~ i ii1 ', [ ] ~ ]1 1 [ ' I I "V ] liE = i , ,, M [ i] 11 [ii " , , i l' ' '~: . . . . . .. . . ' ~" "

l l l l ll i~ ~ : : 1 1 , ' . . . . . . . . . " ' : ' 1 ~ ~ . . . . . . . . . . . i . , , "

. . . . , , ,

~ I u , n , ,, : ~ , L , ,, ~l , , l l , : : : : , , a

1 ,111,, , , , : ~ , ,~ , , , ,~, . c,,,,I ~ ' , " 1 , n , , ,,, 1~ ,

I

,~,,,,, 11

111: :,',, : " ' ~ ,n ~"~ 1~ :~ . . . . .

. . . . . . . Ill . . . . . . . . . . . , , H . , d ] I~ , , ,, l,~ n " : , , o r ' ~ , , n d a

: : , " = " : , , , ; ~ ' . . . . . . . . . .

C I D , ]E : " D ~ ] IE , ,, ,,, ]II . L / N C F ,

,~ , , : : : : i ~ ~ ,~ ::: . . . . . . . . ; , , : : :: " ,~ ,~ : : i ' " , , , , ' ' " , , , , , O ]1 : ' ]11 : ::: ,, L ]I E , D '

] [ S ' ] . " ] I i i , I I I ' , : , , ] I [ I ] E ] I I I I [ J " ] . I " ] I ( ) N " ~ " , "

]E : :? ( ) ] l i ,i ll :, ,. ]E } O ]1 , ) ] 11 [;" x', ,,,,,"""', '~ ~1~,1 [ ' A , M A C ] H ]" ,,, i:g l I L ] ] I ~v I IE :ll ill',,I E ] l l , i i L , 1 ', ,, ,: ' I F ' 3

111::::~,y

[,,,,o ,,, W ,a d .

'~ ' ' " " ,IIE:~,,,,,.,,, ,,,~ ~,~

,,II [', ,liE:',,,,

I,,,,~i,,,,ll,i F o , II:",I',:IIL

~ i l l l l l O ' A I I I . . .. .

I ~ ' q i l ~ q I I ~ , I '

U , , L I L~ .. .l l . . . . . ~ ir

A iI,II::ii,,,C ll;il~, F" lilr" E S T A ii ll,i,,,,i, lliilH ~M ,lliiiiiiiN iP'ilir

. . : . . . i : ' : . ., . . . . I l l " . . . . . . . . i , , . . , J I . . . l r .

. . . . . . . , . . . . . " l l l l ' ' : : : : : i' " "

T M

, , : ' ', , : : I , I , , , , I ,]11,,,,,,~1[.

8/10/2019 3849.pdf

2/33

U D C 5 3 3 . 6 9 6 7 : 5 3 3 . 6 9 6 . 4 2 : 5 3 3 . 6 0 4 8 . 2 : 5 3 3 . 6 0 1 3 o 1 2 2 : 5 3 3 . 6 . 0 1 1 . 5

M E A S U R E M E N T S O F P R E S S U R E D I S T R I B U T I O N S A N D P R E S S U R E D R A G S A T Z E R O

I N C I D E N C E O N B O T H B L U N T A N D S H A R P A X I S Y M M E T R I C F O R E B O D I E S A T

A M A C H N U M B E R O F 3

By L C. War d

A e r o d y n a m i c s D e p a r t m e n t , R A E B e d f o r d

R E P O R T S A N D M E M O R A N D A N o o 3 8 4 9

N o v e m b e r 1 9 7 6

S U M M A R Y

A c o l l e c t i o n o f s u r f a c e p r e s s u r e d i s t r i b u t i o n s m e a s u r e d o n a n u m b e r o f

a x i s y m m e t r i c f o r e b o d i e s a t z e ro i n c i d e n c e a n d a M a c h n u m b e r o f 3 is p r e s e n t e d .

I n t e g r a t e d p r e s s u r e d r a g s a r e c o m p a r e d w i t h t h e t h e o r e t i c a l d r a g s o f s h a r p c o n e s

h a v i n g t h e s a m e f o r e b o d y f i n e n e s s r a t i o s , s h o w i n g t h a t s i g n i f i c a n t d r a g

r e d u c t i o n s c a n be a c h i e v e d a t t h is M a c h n u m b e r b y t h e s u i t a b l e u s e o f n o s e

b l u n t i n g , l e a d i n g a l s o t o a n i n c r e a s e o f u s a b l e v o l u m e i n t h e f o r e b o d y o

C o m p a r i s o n s a r e al s o m a d e w i t h p u b l i s h e d d a t a f o r d e t e r m i n i n g t he p r e s s u r e d r a g

o f s p h e r i c a l l y b l u n t e d c o n e s .

R e p l a c e s R A E T e c h n i c a l R e p o r t 7 6 1 6 0 - A R C 3 7 3 5 5

8/10/2019 3849.pdf

3/33

C O N T E N T S

I N T R O D U C T I O N

W I N D T U N N E L M O D E L S A N D I N S T R U M E N T A T I O N

P R E S E N T A T I O N O F T H E R E S U L T S

C O N C L U S I O N S

T a b l e 1

S y m b o l s

R e f e r e n c e s

I l l u s t r a t i o n s

D e t a c h a b l e a b s t r a c t c a r d s

P a s e

3

3

4

6

8

9

I0

F i g u r e s I t o 21

8/10/2019 3849.pdf

4/33

I I N T R O D U C T I O N

I t h a s b e e n s h o wn , b o t h e x p e r i m e n t a l l y | a n d t h e o r e t i c a l l y 2 , t h a t a t s u p e r -

s o n i c an d h y p e r s o n i c s p e e d s a s u i t a b l e a m o u n t o f s p h e r i c a l n o s e b l u n t i n g o n a

c o n e c a n g i v e a n o v e r a l l f o r e b o d y p r e s s u r e d r a g l e s s t h a n t h a t o f a s h a r p c o n e

w i t h t h e s a m e f o r e b o d y f i n e n e s s r a t i o A s p a r t o f a s e r i e s o f w i n d - t u n n e l t e s t s

a i m e d a t q u a n t i f y i n g t h e e f f e c t s o f v a r i o u s t y p e s o f n o s e b l u n t i n g o n d i f f e r e n t

f o r e b o d y p r o f i l e s , p r e s s u r e d i s t r i b u t i o n s w e r e m e a s u r e d o v e r t he s u r f a c e s o f

s i x t e e n f o r e b o d i e s a t a f r e e s t r e a m M a c h n u m b e r o f 3 . T h e f o r e b o d y s h a p e s i n v e s t i -

g a t e d w e r e s p h e r i c a l l y - b l u n t e d s i n g l e a n d d o u b l e c o n e s, s p h e r i c a l l y - b l u n t e d t a n -

g e n t o g i v e s , t r u n c a t e d c o n e s , a n d t h r e e - q u a r t e r p o w e r - l a w p r o f i l e s A d e s c r i p t i o n

o f t h e s e t e s t s , a n d a c o l l e c t i o n o f t h e r e s u l t s o b t a i n e d a t z e r o i n c i d e n c e a r e

p r e s e n t e d i n t h is R e p o r t ~ C o m p a r i s o n s a r e s h o w n b e t w e e n t h e e x p e r i m e n t a l p r e s s u r e

d r a g s , t h e t h e o r e t i c a l d r a g o f s h a r p c o n e s , a n d d a t a t a k e n f r o m t h e E n g i n e e r i n g

S c i e n c e s D a t a U n i t i t e m n u m b e r 6 8 02 1 o n s p h e r i c a l l y - b l u n t e d c o n e s w i t h o u t

a f t e r b o d i e s ~

2 W I N D T U N N E L , M O D E L S A N D I N S T R II M E N T AT I O N

T h e m o d e l s w e r e t e s t e d i n t h e R A E ( T e d d i ng t o n ) 1 5 i n ] 0 i n b l o w d o w n w i n d

t u n n e l, t h e f r e e s t r e a m M a c h n u m b e r a t th e m o d e l l o c a t i o n b e i n g 3 . 00 . T h e

s t a g n a t i o n p r e s s u r e w a s k e p t c o n s t a n t a t 5 5 2 1 0 3 N / m 2 , g i v i n g a f r e e s t r e a m

R e y n o l d s n u m b e r p e r m m o f 4 . 1 8 1 0 4 f o r a l l t h e m o d e l s . N o b o u n d a r y l a y e r

t r a n s i t i o n f i x i n g d e v i c e s w e r e u s e d o n a ny o f th e m o d e l s .

T h e m o d e l s w e r e a t t a c h e d t o t h e s t i n g b y m e a n s o f an a d a p t o r c o n t a i n i n g

v 0 r i n g s e a l s o n e a c h o f t h e s e v e n p r e s s u r e t u b e s ~ T h e g e n e r a l a r r a n g e m e n t o f

a m o d e l , a d a p t o r a n d s t i n g a s m o u n t e d i n t h e w i n d t u n n e l i s s h o w n i n F i g o l ,

t o g e t h e r w i t h a c r o s s - s e c t i o n t h r o u g h o n e m o d e l t u b e ~ t h e a d a p t o r a n d p a r t o f

t h e s t i n g . B y s l a c k e n i n g t h e a d a p t o r f i x i n g s c r e w , b o t h t h e a d a p t o r a n d t h e

m o d e l c o u l d b e r o t a t e d t h r o u g h 5 1 ~ 4 3 d e g r e e s ( o ne s e v e n t h o f a c i r c l e )~ w i t h o u t

d i s c o n n e c t i n g a n y o f t h e p l a s t i c t u b i ng .

T h e s t i n g c o u l d a c c o m m o d a t e o n l y s e v e n p r e s s u r e t u b e s, s o i n o r d e r t o

o b t a i n a n a d e q u a t e p r e s s u r e d i s t r i b u t i o n t w o s e p a r a t e m o d e l s , e a c h w i t h

d i f f e r e n t h o l e l o c a t i o ns , w e r e m a n u f a c t u r e d f o r e a c h b o d y p r o f i l e . T h e n o n -

d i m e n s i o n a l p a r a m e t e r s o f t h e b o d i e s a r e g i v e n i n T a b l e I, t h e n o t a t i o n f o r

w h i c h i s d e f i n e d i n F i g 2 f o r th e d i f f e r e n t t y p e s o f b o d y s h a p e t e s t e d . A s t h e r e

a r e t w o d e f i n i t i o n s o f t h e b l u n t n e s s r a t i o i n f r e q u e n t u s e ( i .e . 2 r / D o r d / D ) ,

b o t h r a t i o s a r e g i v e n D r a w i n g s s h o w i n g t h e a c t u a l m o d e l d i m e n s i o n s i n m m a r e

g i v e n l a t e r w i t h e a c h s e t o f r e su l t s .

8/10/2019 3849.pdf

5/33

4

The pressure measu ring holes of diameter 0. 5mm were arranged in a spiral

pattern around each model, thereby helpin g to eliminate downs tream int erferenc e

effects betwe en adjacent holes. All the tappings were carefully inspe cted prior

to the tunnel tests to ensure that there were no burrs either inside the holes,

or on the body surface around the holes.

T h e s u r f a ce p r e s s u r e s w e r e m e a s u r e d u s i n g a s t r a i n - g a u g e t r a n s d u c e r m o u n t e d

in a 48 way pressu re-s cann ing switch situa ted outside the wind tunnel. The switc h

was of the stepping variet y, pressure settling dwell times on the ports prior

to data recordin g bein g det ermine d from a numbe r of initial wind-tu nnel runs.

Each port of the scanning switc h was 0 ring sealed, with the transd ucer being

s u b j e c t ed t o a v a c u u m i n b e t w e e n p o r t s, t h us e l i m i n a t i n g t r a n s d u c e r h y s t e r e s i s

effects that woul d arise from the differ ent pressu re levels being measured.

Known reference pressures we re applied to the initial three ports of the switch,

thereby allow ing a check on the transducer calibr ation to be made for each scan

of the model pressures. The wind- tunne l stagnati on pressure was recorde d using

a tr a n s d u c e r w i t h a h i g h e r p r e s s u r e r a n g e m o u n t e d i n a m o d u l e c o m p l e t e w i t h i t s

o w n p r e s s u r e c a l i b r a t i o n s y s t em . T h e c a l i b r a t i o n p r e s s u r e s w e re m e a s u r e d w i t h

either a Texas gauge for the high values, or a vac uum gauge for the very low

pressures.

T h e d a t a r e c o r d i n g e q u i p m e n t c o n s i s t e d o f a d a t a - l o g g e r m a n u f a c t u r e d b y

Digital Measure ments Ltd. whi ch scan ned the transducer outputs at low level.

After amplification, the resulting high level analogue signals were conve rted

to digital form and finally recorded on paper tape. The wind- tunne l stagnati on

pressure was recorded for each press ure switc h reading, t hereby allowin g the

surface pressur es to be correc ted for variatio ns in the frees tream pressure.

The transducer excita tion volta ges and the amplifi er gain were set so

that the overall pr essure range of each transduce r prod uced changes in the

amplified outputs of the order of 10000 counts. The observe d repeata bility

in the outputs obt ained f rom the know n reference pressures was approx imately

2 counts. Apply ing this change to both transducers, a maxi mum variatio n in

p/Eo and C of 0.006 and 0.0012 respectively, woul d be expected over the

p

complete range of the pressur e switch transducer.

3 P R E S E N T A T I O N O F T ~ R E S U L T S

The pressure di stribu tion at zero incidence for each forebody is presen ted

in terms of P/P0 and C ~ / ~ in Figs. 3 to 18; each figure al so gives d etails of the

P

8/10/2019 3849.pdf

6/33

f o r e b o d y p r o f i l e . T h e o r i g i n f o r t h e X Y c o o r d i n a t e s y s t e m wa s c h o s e n t o b e at

t h e m o d e l b a s e , w i t h t h e e x c e p t i o n s o f m o d e l s 1 6 t o 2 3 w h e r e t h e o r i g i n w a s

l o c a t e d a t t h e j u n c t i o n b e t w e e n t h e f o r e b o d y a n d th e s h o r t c y l i n d r i c a l a f t e r b o d y ,

s i n c e n o p r e s s u r e s w e r e m e a s u r e d o n th e a f t e r b o d y s e c t i on .

T h e r e s u l t s s h o w n a r e th e a v e r a g e p r e s s u r e v a l u e s o b t a i n e d f r o m s ev e n

t u n n e l r u n s , e a c h a t d i f f e r e n t m o d e l r o l l a n g l e s , t o m i n i m i s e e r r o r s d u e t o

a s y m m e t r i e s i n t h e t u n n e l f l o w o r m o d e l a t t i t u d e

F o r s o m e o f t h e b l u n t e d p r o f i l e s , n o t a b l y m o d e l s 16 t o 19 ( F i g s 9 a n d 1 0) a n d

m o d e l s 2 4 t o 2 7 ( F i g s o 1 3 a n d 1 4 ), t h e b l u n t e d a r e a w a s t o o s m a l l t o i n c l u d e e n o u g h

p r e s s u r e t a p p i n g s f o r a n a d e q u a t e d e f i n i t i o n o f t h e p r e s s u r e d i s t r i b u t i o n s t o

b e o b t a i n e d I n t h e c a s e o f b o d i e s w i t h s p h e r i c a l b l u n t i n g , r e c o u r s e w a s m a d e t o

p r e v i o u s l y p u b l i s h e d d a t a 3 s h o w i n g t h e p r e s s u r e d i s t r i b u t i o n a r o u n d a h e m i s p h e r e .

T h e e x t r a c t e d d a t a w e r e t h e n s c a l e d t o a l l o w f o r t he d i f f e r e n t n o s e r a d ii , t h e

t e s t r e s u l t s b e i n g u s e d t o p l o t t h e i n t e r m e d i a t e v a l u e s o f C Y / D s h o w n i n t h e

P

f i g u r e s . T h e s a m e p r o c e s s w a s u s e d f o r t h e t r u n c a t e d b o d i e s , t h i s t i me u s i n g

d a t a f o r a d i s c 4 a s g i v e n i n F i g . 1 9. T h i s f i g u r e a l s o p r e s e n t s d a t a f o r t w o

4

b l u n t h i g h - a n g l e d c o n es

T h e p r e s s u r e d i s t r i b u t i o n s w e r e i n t e g r a t e d t o o b t a i n t he f o r e b o d y p r e s s u r e

d r a g ( C ) , v a l u e s o f w h i c h a r e g i v e n i n T a b l e I t o g e t h e r w i t h v a l u e s ( w h e r e

P I

p o s s i b l e ) d e t e r m i n e d f r o m E S D U I t e m 6 8 0 21 F o r t h e s p h e r i c a l l y - b l u n t e d

c o n e s , t h e r e i s g o o d a g r e e m e n t b e t w e e n t h e e x p e r i m e n t a l v a l u e s o f C a n d t h e

P

E S D U d a t a f o r t w o o u t o f t h e f o u r p r o f i l e s ( m o d e l s 1 2 a n d 1 3, 2 0 a n d 2 1 ) . I n t h e

c a s e o f th e 7 . 5 d e g r e e c o n e w i t h d / D = 0 . 2 ( m o d e l s 1 6 a n d 1 7) t h e d i f f e r e n c e

b e t w e e n t h e t w o v a l u e s o f C i s p r o b a b l y d u e t o t h e s p a c i a l i n a d e q u a c y o f t h e

P

m e a s u r e d p r e s s u r e d i s t r i b u t i o n , a s m e n t i o n e d a b o v e, g i v i n g a n e r r o n e o u s v a l u e t o

t h e f o r e b o d y p r e s s u r e d r a g . T h i s m a y a l s o e x p l a i n t h e d i f f e r e n c e o b s e r v e d w i t h

m o d e l s 8 a n d 9 . A g r e e m e n t b e t w e e n t h e t w o v a l u e s i s n o t , h o w e v e r , v e r y g o o d f o r

t h e tw o b l u n t e d t a n g e n t o g i v e s ( m o d e l s 3 2 a n d 33 , 3 4 a n d 35 ) p r o b a b l y b e c a u s e

t h e E S D U d a t a i s b a s e d o n r e s u l t s f o r b l u n t e d c o n e s

A s t h e r e a r e n o c o n s i s t e n t g e o m e t r i c a l c o n s t a n t s o r v a r i a b l e s t h r o u g h o u t

t h e r a n g e o f b o d i e s t e s t e d , t h e p r e s s u r e d r a g s h a v e b e e n c o m p a r e d w i t h t h e

t h e o r e t i c a l p r e s s u r e d r a g c o e f f i c i e n t s o f s h a r p c o n es 5 f o r f i n e n e s s r a t i o s

b e t w e e n 0 a n d 3 . 2 ( F i g s . 2 0 a n d 2 1 ) F o r s h a r p c o n e s w i t h f i n e n e s s r a t i o s l e s s

t h a n 0 . 4 3 ( i . e . w h e n t h e b o w s h o c k - w a v e i s d e t a c h e d ) t h e d r a g c o e f f i c i e n t s a r e

8/10/2019 3849.pdf

7/33

6

a s s u m e d t o l i e o n t h e d o t t e d l i n e d r a w n f r o m t h e t h e o r e t i c a l d r a g c o e f f i c i e n t o f

a f i n e n e ss r a t i o 0 . 4 3 s h a r p c o ne , a n d t h r o u g h t h e e x p e r i m e n t a l v a l u e s o b t a i n e d

f o r t he s h a r p c o n e a n d t h e d i s c w i t h f i n e n e s s r a t i o s o f 0 . 1 8 2 a n d 0 r e s p e c t i v e l y .

F i g s . 2 0 a n d 2 ] a l s o g i v e t h e m i n i m u m d r a g o b t a i n a b l e f r o m s p h e r i c a l b l u n t i n g a s

a f u n c t i o n o f th e f i n e n e s s r a t i o a s d e t e r m i n e d f r o m t h e E S D U d a t a i t e m I, s h o w i n g

h o w t he o p t i m u m b l u n t n e s s r a t i o d e c r e a s e s w i t h i n c r e a s i n g f i n e n e ss r a t io .

F r o m F i g . 2 0 , i t c a n b e s e e n t h a t a t v a l u e s o f f i n e n e s s r a t i o l e s s t h a n

t h a t f o r s h o c k d e t a c h m e n t o n a s h a r p c on e ( f 0 . 4 3 ) , a l l b u t o ne o f t h e b o d i e s

t e s t e d h a d a l o w e r p r e s s u r e d r a g t h a n a s h a r p c o n e o f t h e sa m e f i n e n e s s r a t i o ,

s u b s t a n t i a l r e d u c t i o n s i n d r a g s t e m m i n g f r o m q u i t e l a r g e a m o u n t s o f b l u n t i n g a n d

t r u n c a t i n g . T h i s i s b o r n e o u t b y t h e E S D U d a t a w h i c h s u g g e s t s t h a t at t h e s e l o w

f i n e n e s s r a t i o s t h e b o d i e s w i t h t h e l o w e s t d r a g s w o u l d b e c i r c u l a r a r c p r o f i l e s

w i t h b l u n t n e s s r a t i o s b e t w e e n a h e m i s p h e r e ( d / D = 1. 0) a n d a d i s c ( i . e. a b l u n t

c o n e w i t h a b l u n t n e s s r a t i o o f i n f i n i t y ) .

A t t h e h i g h e r f i n e n e s s r a t i o s b e t w e e n 2 . 0 a n d 3 . 2, a l l th e b l u n t e d a n d

t r u n c a t e d s i n g l e c o n e s t h a t w e r e t e s t e d g a v e p r e s s u r e d r a g s h i g h e r t h a n s h a r p

c o n e s o f t h e s a m e f i n e n e s s r a t i o , w i t h t h e e x c e p t i o n o f m o d e l s 1 6 a n d 1 7 ,

t h o u g h i n t h i s ca s e t h e e x p e r i m e n t a l d a t a is s u s p e c t ( s ee a b o v e ) . T h i s f i n d i n g

i s n o t s u r p r i s i n g a s t h e m i n i m u m b l u n t n e s s r a t i o t e s t e d w a s 0 .2 , a n d t h e E S D U

d a t a s h o w s t h a t f o r m i n i m u m d r a g t he b l u n t n e s s r a t i o w o u l d h a v e t o b e l e s s t h a n

0 . 2 . B o t h of t h e b l u n t e d t a n g e n t o g i v e s l i k e w i s e g i v e h i g h e r d r a g s t h a n f o r t h e

e q u i v a l e n t s h a r p c o n e of f i n e n e s s r a t i o 2 , t h o u g h it s h o u l d b e n o t e d t h a t t h e

d i f f e r e n c e i s s m a l l f o r t h e t a n g e n t o g i v e o f b l u n t n e s s r a t i o 0 .3 . T h u s i t w o u l d

a p p e a r t h a t a s i g n i f i c a n t a m o u n t o f b l u n t i n g o n a t a n g e n t o g i v e i s p o s s i b l e

w i t h o u t m u c h o f a d r a g p e n a l t y r e l a t i v e t o a s h a r p c o n e o f t h e s a me f i n e n e s s

r a t i o .

I t i s i n t e r e s t i n g t o n o t e t h a t t h e b l u n t e d d o u b l e c o n e s ( m o d e l s 2 4 a n d 2 5,

2 6 a n d 2 7) h a v e a l m o s t i d e n t i c a l p r e s s u r e d r a g s t o t h e t h r e e - q u a r t e r p o w e r l a w

b o d i e s o f t h e s a m e f i n e n e s s r a t i o ( m o d e l s 2 8 a n d 2 9 , 3 0 a n d 31 ) w h i c h a r e

g e n e r a l l y a c c e p t e d a s b e i n g a m o n g t h e b e t t e r l o w - d r a g n o s e s h a p e s .

4 C O N C L U S I O N S

S u r f a c e p r e s s u r e d i s t r i b u t i o n s h a v e b e e n p r e s e n t e d f o r a r a n ge o f d i f f e r e n t

a x i s y m m e t r i c f o r e b o d y p r o f i l e s a t z e r o i n c i d e n c e a n d a t a M a c h n u m b e r o f 3 . T h e

i n t e g r a t e d p r e s s u r e d r a gs h a v e b e e n c o m p a r e d w i t h t h e t h e o r e t i c a l p r e s s u r e d r a gs

o f s h a r p c o n e s a n d w i t h d a t a e x t r a c t e d f r o m E S D U d a t a I t e m 6 8 0 2 1 o n b l u n t e d c o n e s.

8/10/2019 3849.pdf

8/33

T h e m a i n c o n c l u s i o n s f r o m t hi s w o r k a r e : -

a ) f o r f o r e b o d y f i n e n e s s r a t i o s l e s s t h a n 0 6 , t he p r e s s u r e d r a g o f a

s p h e r i c a l l y - b l u n t e d o r t r u n c a t e d c o ne is s u b s t a n t i a l l y l o w e r t h a n t h a t o f a

s h a r p c o n e of th e s a m e f i n e n e s s r a t i o ~

b) a s t h e f o r e b o d y f i n e n e s s r a t i o i n c r e a s e s , t h e a m o u n t o f b l u n t i n g r e q u i r e d

f o r m i n i m u m p r e s s u r e d r a g d e c re a s e s ;

c ) o n l y a s m a l l a m o u n t d / D = 0 . 2 ) o f s p h e r i c a l b l u n t i n g o r t r u n c a t i o n ca n

b e u s e d o n c o n e s o r t a n g e n t o g i v e s w i t h f i n e n e s s r a t i o s b e t w e e n 2 a n d 3 2 i f

p r e s s u r e d r a g s c o m p a r a b l e w i t h t h o s e o f sh a r p c o n e s w i t h t h e s a me f i n e n e s s r a t i o

a r e t o b e o b t a i n e d ~

d) t h e p u b l i s h e d d a t a | o n t he p r e s s u r e d r a g o f s p h e r i c a l l y b l u n t e d c o n e s

w i t h o u t a f t e r b o d i e s s h o w t he s a m e t r e n d s a s t h e t e s t r e s u l t s f o r b l u n t e d c o n e s

w i t h a f t e r b o d i e s 9 t h o u g h t h e a b s o l u t e l e v e l s a r e n o t a l w a y s t h e s a m e ~

e ) t h e p u b l i s h e d d a t a I d i s a g r e e w i t h t h e p r e s s u r e d r a g s m e a s u r e d o n b l u n t e d

t a n g e n t o g i v e s ~

f ) a p p r o p r i a t e l y - p r o p o r t i o n e d b l u n t e d d o u b l e - c o n e s c a n h a v e t h e s a m e p r e s s u r e

d r a g s a s t h r e e - q u a r t e r p o w e r l a w b o d i e s o f t h e s a m e f i n e n e s s r a t i o .

T h e i n t e l l i g e n t u s e o f s o m e f o r m o f n o s e b l u n t i n g h a s a n u m b e r o f

a d v a n t a g e s o v e r a s h a r p n o s e , n o t o n l y in r e d u c e d p r e s s u r e d r ag T h e s e

a d v a n t a g e s i n c l u d e a h i g h e r i n t e r n a l v o l u m e , a n d a l o w e r p e a k h e a t t r a n s f e r r a t e

t o t h e b o d y n o s e T h u s t h e o r e t i c a l m e t h o d s a r e r e q u i r e d a t a n y r e l e v a n t M a c h

n u m b e r f o r d e t e r m i n i n g t h e o p t i m u m t y pe a n d a m o u n t o f b l u n t n e s s f o r p r a c t i c a l

b o d y s h a pe s o f g i v e n f in e n e s s r a t i o T h i s c o l l e c t i o n o f p r e s s u r e m e a s u r e m e n t s

s h o u l d p r o v i d e a g o o d b a s i s f o r c h e c k i n g m e t h o d s d e v e l o p e d f o r u s e at s u p e r -

s o n i c M a c h n u m b e r s

8/10/2019 3849.pdf

9/33

T a b l e l

S U M M A R Y O F R E L E V A N T B O DY G E O M E T R I E S I N T E G R A T E D

P R E S S U R E D R A G S A N D F O R E B O D Y D R A G S F R O M R E F . 1

oo

Model

No.

2riD

d D

6 a n d 7 0 . 1 6 3 0 . 1 3 3 0 . 3 9 0

8 a n d 9 0 . 4 4 1 0 . 1 9 8 0 . 2 8 0

1 2 a n d 1 3 0 . 3 8 2 0 . 3 9 6 0 . 5 6 0

1 6 a n d 1 7

3 125

0 . 1 9 8 0 . 2 0 0

2 0 a n d 2 1 2 . 4 6 6 0 . 3 9 7 0 . 4 0 0

3 6 0 . 1 7 4 0 . 0 8 6 0 . 2 5 0

3 7 0 . 0 8 6 0 . 0 4 3 0 . 2 5 0

4 a n d 5 0 . 1 8 2 0 0

l 0 a n d l l 0 . 4 0 0 0 . 2 0 0

o R / D

02

C

P

1 4 a n d 1 5 0 . 3 0 0

1 8 a n d 1 9 3 . 0 3 8

2 2 a n d 2 3 2 . 2 7 9

3 8 0

2 4 a n d 2 5 3

26 and 27

2 8 a n d 2 9 3

3 0 a n d 3 1 2

3 2 a n d 3 3 2

j

0.400

0.200

0.400

01

5

s

o o

0 . 0 9 8 0 . 1 0 0 1 0 . 3 5 6 . 9 4 /

0 .1 2 ] 0 .1 2 5 1 4. 3 6 ] l . 0 l / . . / ~

Expt.

] 4760

1 . 1 5 2 0

Ref. 1

] lO0

Forebody shape

Spherically blunted cone

I I t

1.0920 ]. ] 2

0.0600 0.090

0. ]600 O. 162

1. 4500 ~ . . . . . . ( Ref. )

] 5320 / (Re f. ) ..

1.4880 / Sharp cone

].0520 f Truncat ed cone

] 0 7 4 0 f

0.0940 f

0.2780 ~

1.5660 ~ Disc (Ref.4)

0.0614 / Spherically blunted double cone

0.1232 J

0.0612 ~ ~ power law

0.1226 ~

0. 1625 0. ]87 Spherically blunte d tangent ogive

0. 2920 0. 355

34 and 35 2

8/10/2019 3849.pdf

10/33

C

P

C

P

C

p v a c

D

d

f

L

P

P0

P

q

R

r

X

Y

e I a nd e

S Y M B O L S

f o r e b o d y p r e s s u r e d r a g c o e f f i c i e n t

p r e s s u r e c o e f f i c i e n t P - P o ~ / q

p r e s s u r e c o e f f i c i e n t w h e n p = 0

m a x i m u m b o d y d i a m e t er

d i a m e t e r o f n o s e b l u n t i n g s ee F i g 2 )

f o r e b o d y f i n e n e s s r a t i o L / D

o v e r a l l f o r e b o d y l e n g t h

s u r f a c e p r e s s u r e

f r e e s t r e a m s t a g n a t i o n p r e s s u r e

05

i e . v a c u u m c o n d i t i o n s

f r e e s t r e a m s t a t i c p r e s s u r e

k i n e t i c p r e s s u r e

radius of tangent ogive prof ile see Figo2)

r a d i u s o f b o d y a t j u n c t i o n b e t w e e n s p h e r i c a l n o s e b l u n t i n g a n d

foreb ody profi le see Fig2)

a x i a l d i s t a n c e a l o n g b o d y c e n t r e l i n e p o s i t i v e u p s t r e a m )

r a d i a l d i s t a n c e f r o m X a xi s

a n g l e s b e t w e e n c o n i c a l s e c t i o n s a n d t h e X a x i s s ee F i g . ~

8/10/2019 3849.pdf

11/33

]0

No

Author

P.G. Pugh

L.C. Ward

P.G. Pugh

J.Wo Peto

L.C. Ward

J F C a m p b e l l

D.H. Tudor

A m e s R e s e a r c h S t a f f

R E F E R E N C E S

Title, etc.

F o r e d r a g o f s p h e r i c a l l y b l u n t e d c o ne s i n s u p e r -

sonic flow.

Engi nee rin g Sciences Data ~nit Item 68021 1968)

A p a r a m e t r i c s t u d y o f t he u s e o f n o s e b l u n t i n g

t o reduce the supersoni c wave drag of forebodies.

ARC Current Paper 127 1 1974)

E x p e r i m e n t a l v e r i f i c a t i o n o f p r e d i c t e d s t a t i c

hole size effects on a model with large stream-

w i s e p r e s s u r e g r a d i e n t s .

NPL Aer o Rep ort 1313 ARC 31900) 1970)

Pre ssu re dis trib uti ons on 140 , ]60 and 180

cones at Mach numbers from 2.30 to 4.63 and

angles of at tack fro m 0 to 20 .

NAS A TN D-5204 1969)

Equations , tables, and charts for compre ssible

flow.

NA CA Repo rt 1135 1953)

8/10/2019 3849.pdf

12/33

S c a l e

{3 50 t 0O mm

P . . . , ~ I i

M o d e t A d a p t o r S t i n g

; - = - . . . . . . = : i , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . _ ~

G e n e r a l a r r a n g e m e n t

S c a l e

Mod el ~ / - - - - C a mps - -- -~ ._~ '0 ' r ing_ 0 10 20m m

k~.Ty,g o n :. ~p l as ti c L o c a t i n g p e g \ ~ A d a p t o r , i i n ; s c r e w ' h o l e

( u i n g r o m m o a e l I 1 I I f ~ } ~ t

A d a p t o r a n d ' O ' r i n g s e a l i n g d e t a i l s

P r o p ri et a ry t r a d e n a m e - f o r m u l a t i o n R 3 6 03

Fig I

G enera l a r rangement o f m ode l mou nt ing on t he w ind - t unne l s t ing ,

and de ta il s o f ' 0 ' r i ng adap to r

i3

8/10/2019 3849.pdf

13/33

Fig 2

Spher i ca l l y b lun ted

s i n g l e c o n e

f = L / D

L

Spher ica lly b l un t ed ~ ~ .

d o u b l e c o n e

f L/D

__1

=ale I

T r u n c a t e d c o n e

Sp he r i ca l ly b l un t ed I

t a n g e n t o g i v e

c ~ f L I D

_ L

L

f L/D

Fig 2 G eom et r ica lnom enclature used or the forebodies. C yl indr ica l

af terbodies are not show n

8/10/2019 3849.pdf

14/33

Fig 3

_

114 58

Y

X