K»n««l»tr»»t
Kiu
THE COLLEGE OF AERONAUTICS
CRANFIELD
SUBSONIC DRAG AND PITCHING MOMENT
CHARACTERISTICS OF SLENDER
CAMBERED BODIES
by
Sejjt ember, 1 9 5 8 .
T H E O O L L E C T B O F A E R O N A U T I C S
C R A N F I E L D
An e x p e r i m e n t a l i n v e s t i g a t i o n of t h e subsonic d r a g axid p i t c h i n g moment c h a r a c t e i d s t i c s of s l o i d e r cambered b o d i e s v / i t h p o i n t e d n o s e s and t a i l s b y -K. D. H a r r i s , B . S c . , D.C.Ae. SöIvMARY I t i s known t h a t s u p e r s o n i c a i r c r a f t a r e l i a b l e t o p o s s e s some t r i m d r a g under c r u i s e c o n d i t i o n s . F u s e l a g e camber has b e e n s u g g e s t e d a s one means of r e d u c i n g t h i s conponent of t h e d r a g , and t h e p u r p o s e of t h i s i n v e s t i g a t i o n vra.s t o o b t a i n q u a n t i t a t i v e d a t a on t h e p i t c h i n g moment
i n c r e m e n t s o b t a i n a b l e f r a n f u s e l a g e camber and i n c i d e n c e , and t h e a s s o c i a t e d i n c r e m e n t s i n f u s e l a g e d r a g .
L i f t , d r a g a n d moment m e a s u r a n e n t s have been made on a body r e p r e s e n t -a t i v e of t h e f u s e l -a g e of -a s u p e r s o n i c t r -a n s p o r t -a e r o p l -a n e . The f i n e -a i e s s r a t i o of t h e body was 1 5 : 1 , t h e c r o s s - s e c t i o n a l a r e a d i s t r i b u t i o n b e i n g
of m o d i f i e d Sears-Haack form. P a r a b o l i c nose and t a i l camber was u s e d , t h e nose ajad t a i l p o r t i o n s b e i n g made removable s o t h a t a v a r i e t y of d i f f e r e n t c o n f i g u r a t i o n s c o u l d be t e s t e d . The Reynolds number of t h e t e s t s was 14.1 x 10° b a s e d on t h e l e n g t h of t h e model, and t h e Mach number was 0 , 2 . The t e s t s were made v/ith a t r a n s i t i o n v/ire a t t a c h e d t o t h e model a t 1 C^ of t h e l e n g t h from t h e n o s e . A p r e l i m i n a r y i n v e s t i g a t i o n i n d i c a t e d t h a t t h e Rejmolds number was p r o b a b l y s u f f i c i e n t l y l a r g o t o e n s u r e t h a t t h e r e s u l t s \7culd g i v e a good g u i d e t o t h e f u l l s c a l e c h a r a c t e r i s t i c s .
The e3Cperiments sheaved t h a t nose camber p r o d u c e s a p i t c h i n g moment i n c r e m e n t i n v e r y c l o s e agreement w i t h t h e p r e d i c t i o n s of i n v i e c i d s l e n d e r body t h e o r y . The i n c r e m e n t s i n l i f t and d r a g , w h i l s t n o t z e r o a s p r e d i c t e d b y i n v i s c i d t h e o r y , a r e s m a l l . T a i l camber on t h e o t h e r hand g i v e s r i s e t o much l a r g e r l i f t and d r a g i n c r e m e n t s , and t h e increment i n p i t c h i n g moment i s q u i t e d i f f e r e n t from t h a t p r e d i c t e d b y i n v i s c i d t h e o r y . I n t h e p r e s e n t t e s t s t h e p i t c h i n g moment increment d\ie t o t a i l camber amounted t o a b o u t 1C^ of t h e t h e o r e t i c a l v a l u e .
The scope of t h e experiment Viflas i n s u f f i c i e n t t o answer t h e q u e s t i o n "What i s t h e optimum f u s e l a g e shape f o r minim'um t r i m d r a g ? " Eovjevcr, t h e i n d i c a t i o n s a r e t h a t an uncambered f u s e l a g e a t i n c i d e n c e v / i l l p r o v i d e a given p i t c h i n g moment f o r l e s s d r a g t h a n any cambered f u s e l a g e . T h i s
havrevcv n e g l e c t s t h e i n t e r f e r e n c e e f f e c t s of t h e iTing and t a i l u n i t on t h e
f u s e l a g e , and of t h e f u s e l a g e on t h e Y/ing and t a i l u n i t . F o r r e a s o n s of ( i ) t a i l c l e a r a n c e on t a k e - o f f and l a n d i n g , ( i i ) c o c k p i t l a y o u t and viev7, and ( i i i ) c a b i n l a y o u t , f u s e l a g e s w i t h camber may be r e q u i r e d , Som.e i n d i c a t i o n of t h e f u s e l a g e d r a g p e n a l t i e s l i k e l y t o be s u s t a i n e d b y t h e s e m o d i f i c a t i o n s of t h e f u s e l a g e a r e g i v e n b y t h e r e s u l t s of t h i s experimcait,
September, 1958.
T H E C O L L E G E O F A E R O N A U T I C S . C R A N F I E L D
An e x p e r i m e n t a l i n v e s t i g a t i o n of t h e subsonic d r a g and p i t c h i n g moment c h a r a c t e i a s t i c s of s l e n d e r cambered b o d i e s Tri.th p o i n t e d n o s e s and t a i l s b y -K. D, H a r r i s , B . S c , D.C.Ae. SUIMARY I t i s knOTvn t h a t s u p e r s o n i c a i r c r a f t a r e l i a b l e t o p o s s e s some t r i m d r a g under c r u i s e c o n d i t i o n s . F u s e l a g e camber h a s b e e n s u g g e s t e d a s one means of redixjing t h i s coirponent of t h e d r a g , and t h e p u r p o s e of t h i s
i n v e s t i g a t i o n was t o o b t a i n q u a n t i t a t i v e d a t a on t h e ] p i t c h i n g moment
i n c r e m e n t s o b t a i n a b l e f r a i f u s e l a g e camber a n d i n c i d e n c e , and t h e a s s o c i a t e d i n c r e m e n t s i n f u s e l a g e d r a g .
L i f t , d r a g a n d moment m e a s u r a n e n t s have been made on a body r e p r e s e n t -a t i v e of t h e f u s e l -a g e of -a s u p e r s o n i c t r -a n s p o r t -a e r o p l -a n e . The f i n e n e s s r a t i o of t h e body was 1 5 : 1 , t h e c r o s s - s e c t i o n a l a r e a d i s t r i b u t i o n b e i n g
of m o d i f i e d Sears-Haack form. P a r a b o l i c nose and t a i l camber v/as vised, t h e nose and t a i l p o r t i o n s b e i n g made removable so t h a t a v a r i e t y of d i f f e r e n t c o n f i g u r a t i o n s c o u l d be t e s t e d . The Reynolds number of t h e t e s t s ivas 14-.1 x 10° b a s e d on t h e l e n g t h of t h e model, and t h e Mach n\jmber was 0 , 2 . The t e s t s were made w i t h a t r a n s i t i o n jdre a t t a c h e d t o t h e model a t 1C^S of t h e l e n g t h f r a n t h e n o s e . A p r e l i m i n a r y i n v e s t i g a t i o n i n d i c a t e d t h a t t h e Reynolds number was p r o b a b l y s u f f i c i e n t l y l a r g e t o ensijire t h a t t h e r e s u l t s would g i v e a good g u i d e t o t h e f u l l s c a l e c h a r a c t e r i s t i c s .
The e3cperiments sho^yed t h a t nose camber produces a p i t c h i n g moment i n c r e m e n t i n v e r y c l o s e agreement w i t h t h e p r e d i c t i o n s of i n v i s c i d s l e n d e r body t h e o r y . The i n c r e m e n t s i n l i f t and. d r a g , w h i l s t n o t z e r o a s p r e d i c t e d b y i n v i s c i d t h e o r y , a r e s m a l l . T a i l camber on t h e o t h e r hand g i v e s r i s e t o much l a r g e r l i f t and d r a g i n c r e m e n t s , and t h e increment i n p i t c h i n g moment i s q u i t e d i f f e r e n t from t h a t p r e d i c t e d b y i n v i s c i d t h e o r y . I n t h e p r e s e n t t e s t s t h e p i t c h i n g moment increment due t o t a i l camber amounted t o a b o u t 105^ of t h e t h e o r e t i c a l v a l u e .
The scope of t h e experiment vra-S i n s u f f i c i e n t t o answer t h e q u e s t i o n "What i s t h e optimum f u s e l a g e shape f o r minimimi t r i m d r a g ? " However, t h e i n d i c a t i o n s a r e t h a t an uncambered f u s e l a g e a t i n c i d e n c e w i l l p r o v i d e a given p i t c h i n g moment f o r l e s s d r a g t h a n any cambered f u s e l a g e . T h i s hcavever n e g l e c t s t h e i n t e r f e r e n c e e f f e c t s of t h e iving and t a i l u n i t on t h e f u s e l a g e , and of t h e f u s e l a g e on t h e v/ing and t a i l u n i t . F o r r e a s o n s of ( i ) t a i l c l e a r a n c e on t a k e - o f f and l a n d i n g , ( i i ) c o c k p i t .layout and view, and ( i i i ) c a b i n l a y o u t , f u s e l a g e s v/ith camber may be r e q u i r e d . Some i n d i c a t i o n of t h e f u s e l a g e d r a g p e n a l t i e s l i k e l y t o be s u s t a i n e d b y t h e s e m . o d i f i c a t i o n s of t h e f u s e l a g e a r e g i v e n b y t h e r e s u l t s of t h i s e x p e r i m e n t ,
COIWEIfTS 1 . 2 .
3.
k.
5.
6.
7.
8 . S'unmary C o n t e n t s N o t a t i o n I n t r o d u c t i o n D e s c r i p t i o n of A p p a r a t u s D e t a i l s of t e s t ResiiLts D i s c u s s i o n Conclvisions Acknowle dgement s R e f e r e n c e s Appendix I - Model d a t a Appendix I I - T h e o r e t i c a l e s t i m a t e s of t h e l i f t and p i t c h i n g moment c h a r a c t e r i s t i c s Appendix I I I - Redijction of r e s u l t s Appendix IV - Accuracy of t h e r e s u l t s T a b l e I - R a d i u s and camber l i n e d i s t r i b u t i o n s P a g e 1 24
6
7
9
12 15 20 21 22 23 21^ 26 29 30 F i g u r e s 1 . Diagram of model 2. Rigging of model 3 . Turbulence g r i d and p o s i t i o n of c a l i b r a t i n g p i t o t - s t a t i c t u b e if. S t a t i c p r e s s u r e d i s t r i b u t i o n 5» E s t i m a t e d d r a g of i d g t a i l w i r e s 6. E s t i m a t e d p i t c h i n g moment of r i g t a i l vd.res 7 . V a r i a t i o n of d r a g v/ith Reynolds number 8. E f f e c t of v a r y i n g t h e boundary l a y e r 9 . E f f e c t of v a r y i n g t h e boundary l a y e r 1 0 , E f f e c t of v a r y i n g Reynolds number 1 1 , . E f f e c t of v a r y i n g Rejmolds number 1 2 , E f f e c t of v a r y i n g Reynolds nimiberContents Continued FigLJres
13. Body of r e v o l u t i o n IZf, Nose cai.nber
15. Tail camber
16. Nose and tail camber
17. Nose and negative tail camber 18. CLj^ V. '5 °
19. G^ V, C^
20. Congparison of the drag of various configurations 2 1 , 22, ^ m -C ^ v . — 0 a — 0 a
23, Body of revolution, C_ ~ 0^ tan c(. 21+, Effect of varying nose camber
NOTATION b b r e a d t h of working s e c t i o n of v/ind t u n n e l OL: d r a g c o e f f i c i e n t of f u s e l a g e b a s e d on t h e maximum c r o s s - s e c t i o n a l a r e a S C-^ d r a g c o e f f i c i e n t of f u s e l a g e b a s e d on t h e vretted a r e a S w CL d r a g c o e f f i c i e n t of t h e r i g t a i l v d r e s b a s e d on t h e r i g a r e a S C p i t c h i n g moment c o e f f i c i e n t of t h e f u s e l a g e b a s e d on t h e a r e a S a n d t h e f u s e l a g e l e n g t h 2 1 C p i t c h i n g moment c o e f f i c i e n t of t h e r i g t a i l v/ires r i g b a s e d on t h e a r e a S and leaigth 2 1 D d r a g h h e i g h t of v/crking s e c t i o n of wind t u n n e l k c a l i b r a t i o n f a c t o r of v i n d t u n n e l 1 s e m i - l e n g t h of model
1 l e n g t h of nose and t a i l p o r t i o n s of model I p l e n g t h of c e n t r a l p o r t i o n of model L l i f t L l e n g t h of model M p i t c h i n g moment r r a d i u s of model R maximum r a d i u s of model IL. Reynolds number
S me^xinum c r o s s - s e c t i o n a l a r e a of model S-, c r o s s s e c t i o n a l a r e a of model S w e t t e d ( o r s u r f a c e ) a r e a of model U wind speed U-, e f f e c t i v e f r e e s t r e a m s p e e d i n vrorking s e c t i o n v / i t h model p r e s e n t
U_ wind speed i n v/crking s e c t i o n a s d e t e r m i n e d from a c a l i b r a t i o n v i t h t h e vrorking s e c t i o n empty
V vol-umo of model
3C l o n g i t u d i n a l a x i s w i t h o r i g i n a t c e n t r e of model ( s e e F i g , l )
NOT/iTION Continued
X l o n g i t u d i n a l a x i s with o r i g i n a t t h e base of t h e
nose (or t a i l ) portion of the fuselage (see F i g . l ) ^ y a x i s perpendicular to x-axis (see F i g . l )
y camber l i n e ordinate \
a. l o c a l incidence of camber l i n e
a incidence of fuselage datum l i n e
y camber of nose p o r t i o n , p o s i t i v e vdien incidence due t o camber i s p o s i t i v e (see F i g . l )
y, caniber of t a i l p o r t i o n , p o s i t i v e v/hen incidence due t o camber i s p o s i t i v e (see F i g . l )
e s o l i d bloclcage f a c t o r
s ^ e ^ wake bloc lage factor
H c o e f f i c i e n t of v i s c o s i t y of n i r
V kinematic coefficient of v i s c o s i t y of a i r P a i r d e n s i t y
1, I n t r o d u c t i o n
I t i s v/ell knovm t h a t supersonic a i r c r a f t are l i a b l e t o possess
some trim drag ( l , 2 , 3 ) under c r u i s e conditions. I n R e f . 3 i t v/as suggested t h a t fuselage camber might be lased t o reduce t h e magnitude of t h i s trim drag. Slender body theory v/as used t o determine the amounts of fuselage camber or incidence t h a t might be required by c e r t a i n tjrpical M = 1,2 project a i r c r a f t i n order to obtain a l l the required trimming moment from the fuselage. I t Vira.s found t h a t lar@2 amounts of camber or incidence vrould probably be required, and i t was pointed out t h a t ovring t o viscous effects the t h e o r e t i c a l moments vrould not be a t t a i n e d in p r a c t i c e . Also, contrary t o i n v i s c i d theory, i t was a n t i c i p a t e d t h a t t h e r e vrould be some increase i n fuselage drag due t o camber or incidence. A programme of v/ind tunnel t e s t s v/as t h e r e f o r e proposed to i n v e s t i g a t e t h e s e f a c t o r s and t h i s report d e a l s with t h a t i n v e s t i g a t i o n .
As ejcplained i n Ref. 3 the decision t o make a s e r i e s of subsonic t e s t s ( i n a d d i t i o n t o supersonix: t e s t s t o be made a t seme othe'^ e s t a b l i s h ment) was governed by the f a c t t h a t :
-( i ) According t o slender body theory the p i t c h i n g moment coefficient of a slender body i s independent of Mach number.
( i i ) I t v^as d e s i r e d t o t e s t models v i t h pointed t a i l s . This can e a s i l y be managed v i t h subsonic models but i s not e a s i l y acoomplished vdth supersonic models,
( i i i ) The f a v i l i t i e s a v a i l a b l e a t t h e College a t t h e time of malcing these t e s t s v/ere f a r more s u i t a b l e f o r subsonic than suxDersonic t e s t i n g i n viev/ of the high Reynolds number required and the high degree of accuracy demanded i n t h e measurement of the drag and pitchin.g moment.
YiTith item ( i i i ) i n mind, i t v/as decided t h a t the t e s t s should be made i n t h e College of Aeronautics 8* x 6' tunnel using the l a r g e s t p r a c t i c a b l e model, A model length of 10 feet v/as chosen, and a fineness r a t i o of 1 5 : 1 . The length v/as l i m i t e d t o 10 feet as any g r e a t e r length v/ould have involved t h e nose of the model being dcingerously near t h e conrnencement of t h e v/orking section (see P i g . l+). Tilth t l i i s model i n t h e 8' x 6' t u n n e l , s i g n i f i c a n t tunnel i n t e r f e r e n c e e f f e c t s might be expected a t moderate t o l a r g e
incidences since the nose and t a i l v/ould touch t h e f l o o r and roof at about 30 of incidence, Hovrever, since the main i n t e r e s t i n t h e s e t e s t s v/as f o r incidences l e s s than about 5 i t v/as decided t h a t a 10 f e e t long model v/ould be acceptable. The evidence from the t e s t s seems t o be t h a t T/vith t h i s model and a v/ind speed of about 220 feet per second a s a t i s f a c t o r i l y
M This suggestion v/as f i r s t made to t h e author by Dr. Kuchemann and
large value of t h e Reynolds nuiixber (14.I x 10 ) was obtained, giving corqjarative data v/hich cf-in f a i r l y corjfidently be used t o a s s e s s t h e f u l l scale c h e x a c t e r i s t i c s of fuselage cainber and incidence.
By using a l a r g e model a s a t i s f a c t o r y l e v e l of accuracy v/as a l s o obtained fi'om t h e balance readings, although, a\"/ing to Vidriat i s thought t o be a tonperatui'e e f f e c t , i t T/O.S necessary to adopt the tedious
prócedufe of stopping the t'onnel a f t e r each vind on reading t o take the corresponding wind off reading.
The model used in t h e s e t e s t s c o n s i s t e d of a common c e n t r a l p o r t i o n of c i r c u l a r cross-Beet ion and constcnt d.iameter. Nose and t a i l pieces of Sears-Haack area d i s t r i b u t i o n v i t h cambers y of 0,0.075 and 0.15 radians v/ere provided. These nose and t a i l pieces v/ere manufactured so t h a t thfsy could, be r o t a t e d through 1 80 thereby x^erniitting a v/ide r.ange of c o n f i g i r a t i o n s t o be mad.e up, and p e r m i t t i n g t e s t s t o be made v/ith the models inverted so t h a t corrections could be rrade for the i n t e r f e r e n c e e f f e c t s of the supporting r i g .
The naxijjni-un camber of y = 0.15 radians v/as chosen on t h e grounds t h a t t h e fu.selage surface should nowhere be s i g n i f i c a n t l y concave. This amount of cejuoer i"- l e s s than one half the amount t h e o r e t i c a l l y req-uired (3) for some of t h e jpi'ojects (see above), but such l a r g e cambers v/ould be quite inipracticab.le from fuselage layout considerations quite apart from
aerodynamic considerations. 2. DesoT-j-pLion of apparatus 2 , 1 , Find t u m e l
A.11 the t e s t s \7erc made in the College of Aeronautics 8' x 6' General Purpose Wind Tunnel. This i s a closed v/orking section, r e t u r n flow tiinnel v/ith a c o n t r a c t i o n r a t i o of 'J:^ and a top speed of about 250 feet per
second. At a wind speed of 200 feet per second the turbulent i n t e n s i t y i s l e s s than 0 . 1 ^ . This implies t h a t the r e s u l t s vihcn corrected f o r tunnel i n t e r f e r e n c e e f f e c t s should be comparable v i t h the r e s u l t s t h a t v/ould be obtained isi free f l i g h t a.t the same value of the Reynolds number.
The vind speed i s measiurcd using a Bets nianometcr connected t o s t a t i c pressure tappings s i t u a t e d a t the upstream and dov/nstream ends of t h e contraction. Owing t o voltage flucttiations i n the power sypply t h e v/ind speed cajinot be maintained constant. At a Betz reading of 250 m.m. of water v a r i a t i o n s o.s l a r g e as ± 2 m.m. of v/ator may occur over t h e course
of a few socond.s under adverse cond.itions. Apart from these flucti:u3.tions which occur a t i r r e g u l a r i n t e r v a l s the speed remains constant to '//ithin about ± 0 . 2 m..m. of v/ater as measured on the Betz manometer.
2 , 2 . Balance
The balance i s a ïïoröen type s i x coniponent balance as nanufactxired by Test Equipment Ltd.
The s e n s i t i v i t y of t h i s balance i s such t h a t the l i f t i n d i c a t o r can e a s i l y be balanced out to v i t h i n - 0.01 of a r e v o l u t i o n , v/hilst t h e drag and p i t c h i n g moment i n d i c a t o r s can be balanced out t o v/ithin the same values i^rovided great cCiTe i s taken. One revolution of each i n d i c a t o r corresponds t o f i v e revolutions of t h e appropria.te l e a d screw and t h e s e n s i t i v i t i e s correspond approximately t o - 0.05 l b , of l i f t , i 0.004 l b . of drag and - 0.03 1^. f t . of p i t c h i n g moment.
During t h e course of t h i s experiment i t was found tliat t h e vind off zero readings of the dreg and p i t c h i n g moment balances changed s i g n i f i c a n t l y over the course of an hour of running the t u n n e l . The steps taken t o
overcome t h i s d i f f i c u l t y a.re described i n paragraph 3 . 2,3„ The m.odel
The model, see F i g . 1, v/hich v/as made of laminated mahogany, consisted of an uncambered c e n t r a l portion of length 3 f e e t with a c i r c u l a r c r o s s -section of 8 inches constant diameter. The detacha.ble nose and t a i l p o r t i o n s v/ore of Sears-Haack area d i s t r i b u t i o n , ajid the camber l i n e s v/ere parabolic in shf^e (see Appendix l ) . Three nose ejid t a i l portions were manufactured ha.virig canibers of 0,0.075 and 0.15 r a d i a n s . The r a d i u s and camber diistributicnó are given i n Table I . (The caniber i s defined t o be p o s i t i v e when t h e camber l i n e slope i s nose up r e l a t i v e t o the fuselage datum l i n e ) . Each nose and t a i l v/as manufactured so t h a t i t could be r o t a t e d through 180 , Ov/ing t o s l i g h t e r r o r s i n manufacture and uneven shrinking of the timber small steps amounting t o l e s s bhan 0,01 inches v/ere present between the nose and t a i l and c e n t r a l p o r t i o n s . These s t e p s v/ere p a r t i a l l y f a i r e d by means of s t r i p s of Sellotape v/ound roirnd the model,
The model v/as sux~>ported (Pig. 2) from a single s t r u t . The model v/§.s pivoted a.bout i t s c e n t r e , v/hich coincided v/ith the virt\xal c e n t r e of t h e balance. The s t r u t v/as shielded by a streamline f a i r i n g cut av/ay a t i t s lo\7er end t o permit the model to be r o t a t e d through an incidence range from -12 to +15 .
The incidence v/as c o n t r o l l e d by V wires v/ound on a motor operated winch attached t o the balance t u r n t a b l e . A selsyn type counter v/as used t o record the revolutions of the v/inch.
2.4. T r a n s i t i o n wire
The main s e r i e s of t e s t s v/as ma.de with a 0.014 inch diameter t r a n s i t i o n wire fixed 12 inches aft of the nose of t h e mod.el. For the S e r i e s I t e s t s
these v/ires v/ere attached by means of foijr 1 inch v/ide s t r i p s of Sellotape. For t h e S e r i e s I I t e s t s t h e v/ircs v/ere glued i n t o very f i n e grooves
scribed around, the nose. 2.5. Turbulence grid.
A few t e s t s v/ere made with a turbulence grid upstream of the model. This grid, which i s shown in P i g , 3 consisted of tv/elve 5/l 6" diameter ropes running from the floor t o the roof of the worldug section, t h e p i t c h being 2". This g r i d v/as mounted approximately 26" upstream of t h e nose of the model. The tunnel speed for thi.s t e s t v/as measured with a s i n g l e p i t o t - s t a t i c tube (see P i g . 3 ) . These calibraLtions v/ere made v i t h the model in the vrorking section, and must be considered r a t h e r approximate, 3, Deta.ils of Test
3 . 1 . T a i l v i r e c o n t r i b u t i o n t o p i t c h i n g moment
The c o n t r i b u t i o n of the V v i r e s t o the p i t c h i n g moment can be estimated (see Appendix I I I ) but t h e contribution of t h e counteiT/eight t a i l v/ire
depcnd.s on t h e moment which can be t r a n s m i t t e d through t h e attachment of t h i s v/ire to the model. Since t h i s i s not amena.blo t o calciiLation a. t e s t v/as made t o determine the magnitude of t h i s term. A drag load equal t o the estimated drag of the v i r e v/as applied at a point midv/ay betv/een the attaclxient to the model and t h e f l o o r of t h e tunnel. The p i t c h i n g moment due t o t h i s drag loaxl v/as measured on t h e balance, and from t h i s reading the e f f e c t i v e moment aim of the t a i l v i r e drag could be c a l c u l a t e d . This v/as done over the f u l l incidence range of the model,
3 . 2 . Inci.denöe calibra^tion
An incidence calibra.tion v/as nia..de for each configuration p r i o r to the coirmenccment of the wind on t e s t s . The incid,ence was measured by a s e n s i t i v e inclinometer placed on t h e r e a r end of the centre p o r t i o n of t h e model. Checks made during the course of the experiment shov/ed t h a t the incidence s e t t i n g obtained using t h i s c a l i b r a t i o n was b e t t e r than - 0 . 1 , v/ind off. Incidence measur-emoits v/ere not made v i t h t h e v/ind on but ov/ing t o the r e l a . t i v e l y small p i t c h i n g mom^ent produced by the model the e r r o r s due t o t h i s effect v/ere found t o be n e g l i g i b l e . The incid_ence, unless otherwise s t a t e d , has been taken as p o s i t i v e with the nose dov/n i n the tunnel ( i . e . t h e convention used fcr an i n v e r t e d model).
3.3. I n i t i a l t e a t s
P r i o r to embarking on the main s e r i e s of t e s t s i t was decided t o make some i n i t i a l t e s t s to determine the influence of v a r i a t i o n of Reynolds number and various forms of forced boundary layer t r a n s i t i o n . D e t a i l s of these t e s t s are t a b u l a t e d belov/ :
-( i ) Body of r e v o l u t i o n , a = 0
The drag coefficient v/a.s measured ivith :
-^.1
free t r a n s i t i o n , anda 0,014" diameter t r a n s i t i o n v.ire taped round t h e body 12" aft of t h e nose, for the follov/ing values of wind speed and Reynolds nvmiber :
-1 ^T ( f . p , s , ) 98,6 139.5 170.9 197.3 220,8 R X 10"^ 6.30 8.92 10.93 12,6 14.1 ( i i ) Cambered body ( y = - 0 . 1 5 , y+ = -0.15)
0 - , C^ and C v/ere measured over t h e incidence rainge from -12
L' D m '^^ to +12 for t h e follaving configurations :
-Model Configuration
Free t r a n s i t i o n
0,014" diameter t r a n s i t i o n wire taped around t h e body 12" aft of the nose Turbulence grid 26" upstream of t h e nose of the model f . p . s , 98.6 220,8 98.6 220,8 91.7 20.5 R X 10"^ 6.30 14.1 6,30 14.1 5.86 13.1
3*4. Main t e s t s - Series I
Prom t h e i n i t i a l t e s t s i t v/as conclijded ( s e e paragraph 5.1) t h a t the most s a t i s f a c t o r y comparative r e s i l t s v/ould be obtained using a t r a n s i t i o n v/ire and the highest p r a c t i c a b l e v/ind speed of 220,8 f , p , s,
(R^ = 14,1 X 106).
0\-/ing t o the i n t e r f e r e n c e e f f e c t s of t h e s t r u t , s t r u t f a i r i n g and t a i l wires i t was decided t h a t each configturation should be t e s t e d through both the p o s i t i v e and negative incidence ranges v i t h t h e model the ' r i g h t v/ay up' and ' i n v e r t e d ' ( i . e . the nose and t a i l p o r t i o n s r o t a t e d through 180 about t h e body a x i s ) . Approximate allov/ance could then be made for t h e i n t e r f e r e n c e e f f e c t s of the r i g by taking the a r i t h m e t i c mean of the tv/o s e t s of r e s u l t s .
Per these t e s t s t h e t r a n s i t i o n v/ire v/as attached t o the model by means of four pieces of inch v/ide S e l l o t a p e , the pieces of Sellotape being placed a t 0 ° , 90 , l80 and 270° t o the v e r t i c a l plane of synmetry
through the model. The vind on readii}£^s v/ere taken through the f u l l incidence range from -12 t o +12 , follov/ed by t h e wind off zero readings, 3 , 5 . Main t e s t s - Series I I
Analysis of t h e above s e r i e s of t e s t s suggested t h a t the drag measurements v/ere not e n t i r e l y c o n s i s t e n t . Two explanations for t h i s appeared l i k e l y . F i r s t l y , i t v/as observed t h a t the method of fixing the t r a . n s i t i o n v/ires did not ensure t h a t t h e r e v/ere no gaps betv/cen the
wire and t h e model. Any v a r i a t i o n in gap betv/een one model configuration
and another v/ould lead t o v a r i a t i o n s i n drag owing t o the different
drags of the v i r e themselves. Secondly, observation of the measured d a t a showed t h a t t h e wind off zero readings of t h e drag balance •which should have been the same throughout the vihole s c r i e s of t e s t s a c t u a l l y shov/ed some v a r i a t i o n . A second s e r i e s of t e s t s v/as therefore nade to t r y t o eliminate these causes of e r r o r .
The e r r o r s caused by the v a r i a t i o n of t r a n s i t i o n v/ire drag v/ere reduced as much as p o s s i b l e by glueing t h e v/ires into very fine grooves
scribed round the bodies,
The d r i f t of t h e v/ind off zero reading v/as i n v e s t i g a t e d by taking a s e r i e s of wind on and v/ind off r e a d i n g s . This i n v e s t i g a t i o n shov/ed t h a t provided each v/ind on measurement v/as immediately followed by the
corresponding vind off measinrement the drag c o e f f i c i e n t v/as repeatable t o v/ithin - 0,0005 a t a wind speed of 220,8 f . p . s . This i s i n c l o s e agreement v i t h t h e estimated value of t 0.0004 based on the assumption t h a t the drag can be measured t o t h e nearest i O.d of a r e v o l u t i o n v/ind on and wind off (see Appendix T?).
Prom t i l l s i n v e s t i g a t i o n i t v/as concluded tha.t an acceptable l e v e l of accirracy could be obtained provided each v/ind on reading v/as imnediately
follov/ed by t h e corresponding -wind off reading. Because of t h e very considerable increase i n time involved in following tliis procedirre i t v/as decided t o r e s t r i c t the range of i n v e s t i g a t i o n t o '^ t o +4 of incidence. After about tv/o hours of running the zero readings u s u a l l y became n e a r l y
constant. YZhen t h i s occurred a zero reading v/as taken p r i o r t o the commencement of the v/ind on t e s t s , and a check reading v/as taken a f t e r t h e completion of these t e s t s . T/here any s l i g h t change of the zero reading v/as observed t h e zero readings were v a r i e d l i n e a r l y v/ith time,
I t seems probable t h a t t h e d r i f t of the zero readings i s due t o a temperature e f f e c t . Attempts t o reduce or eliminate the d r i f t by leaving h e a t e r s i n t h e b a i l e e chamber on a l l night were hewever unsuccessful, 3.6, Surface flov/ v i s i i a l i s a t i o n
An attempt v/as made t o study t h e siirfa-ce flov/ using a mixture of a l a b a s t i n e i n t e e p o l . This proved unsuccessful owing t o g r a v i t a t i o n a l e f f e c t s and the r e l a t i v e l y small value of the skin f r i c t i o n over the
r e a r of the model. Ecwevar, observation of the flow of t h e mixture -viAiilst i t was s t i l l v/et confirmed t h a t there v/as a flow s e p a r a t i o n over t h e leeward side of the t a i l . This v/as a l s o confirmed by t r a c k i n g a nylon t u f t
towards t h e surface of the body. On approaching t h e body the flow
d i r e c t i o n could be seen t o change f a i r l y abruptly i n d i c a t i n g t h e existence of a vori^ex of t h e type associated v/ith flcav separa.tion from a body.
At ell times the t u f t , \-diich v/as about one inch i n length, remained steady arid did not gyrate r a p i d l y a.s i t has been observed t o do vih.en placed i n t h e v o r t i c e s formed by sv/ept' back and d e l t a v i n g s .
2(., R e s u l t s
4.1. Corrections to observed results 4.1.1. Rig drag
The estimated drag of the tail vires has been subtracted from the observed data (see Appendix III).
The direct drag of the strut and the interference drags of the strut, the strut fairing and the tail wires have been neglected. The direct drag of the strut is certainly not negligible but it is not amenable to calculation and since the main p-urpose of the tests v/as to determine the drag increments due to incidence and camber it was decided to neglect this correction,
Prom Pig. 5 it will be seen that the drag of the tail vires is
approximately equal to the zero incidence drag of the body of revolution, Any error in estimating the drag of the wires viill therefore have aJDOut
4.1.2. Rig pitching moment
The estimated pitching moment of the V vires and the 'part estimated -part measured' pitching mom.ont of the counterweight tail v/ire have been
subtracted fran the measured pitching moment, 4.1.3. Pressure gradient correction to drag
The horizontal buoyancy due to variation of the static pressure coefficient in the v/orking section (Pig. 4) has been calculated,
-see Appendix III, To correct for this effect the observed drag coefficient results should be increased by 0,0013, or rather less than ^% cf the
minimum drag coefficient of the body of revolution, This correction has been neglected.
4.1.4. Blockage
In Appendix III it is shovm that due to solid plus wake blockage the effective free stream velocity U.^ is equal to about 1,006 times the tunnel velocity U™, To correct for this effect the observed coefficients
(including rig drag) shoiiLd be decreased by about 1^, Allowing for the drag of the rig the quoted values of body drag should be decreased by about 2^0,
This correction has been neglected. Combined with the blockage correction the quoted drag coefficients should therefore be decreased by about ^%,
4.2. Accuracy of resxilts
Ov/ing to uncertainty about the magnitude of certain corrections the absolute accuracy of the results cannot be stated. Ov/ing to neglect of the pressure gradient and blockage corrections all the quoted results are very a-pproximately ^fo high.
The scatter in the results caused by errors in measuring the balance are not kno\m vith any accuracy for the Series I tests, but fcr the Series II tests which have been used in all the quantitative res'ults presented
in this section and discussed in paragraph 5 the scatter should not exceed the follov/ing (see Appendix IV)
:-1 Coefficient 0
1 ^
AccToracjy 1U = 98.6 f.p.s. U = 220.8 f.p.s, J
t 0.026 t 0.006 1
t 0.002 t 0.0004 t 0,002 t 0.00044.3. Avera.ging of r e s u l t s
As explained in paragraph 3 t e s t s v/cre made v/ith each model
configuration the right way up and inverted. In Pigs. 13 to 17 both sets of results have been plotted so that the differences caji be seen at a glance. In Figs. 18 to 22 the points plotted are the mean of the two sets of meawSurcments. The reason for the discrepancy betv/een the two sets of raerisurements lias been assumed to be due to the interference effect of the strut and strut fairing and i t has been assumed tha.t this interference effect can be eliminated by talcing the mean of the two sets of r e s u l t s ,
YiTiilst the former assimption i s probably valid i t should be noted that the Latter assuniption may not be s t r i c t l y correct,
4.4. Comparison of experimental results vith those of slender body theory
Configuration 1 - . « C / 3 c \ m KbaJ ^ a= 0 ^n >'t Theory Exp, Theory Exp. Theory Exp. Theory Exp. 0 0 0 0 0 0,71 0 0 1.42 1.04 0,075 0 0 0,0025 0 0.78 0.0105 o . d i 1.42 1.03 0.15 0 0.005 0 0.75 0.021 0,021 1.42 1,02 0 0,15 0 0,029 0 0.82 0,021 0,002 1.42 0.98 0.15 0.15 0 0.036 0 0.82 0.042 0.022 1.42 1.00 0.15 -0,15 0 -0.024 0 0.79 0 0,019 1.42 0.99
'
ac^
\ f do\
^' J and \"a^y have been evaluated over the range
a=0 a. -0
5, Discussion
5.1 . Reynolds number ajid forcod t r a n s i t i o n effects
I n P i g , 7 the drag c o e f f i c i e n t C_ (based on v/ottcd area) i s p l o t t e d aga.inst the Reynolds number for the body of revolution a t zero incidence v/ith and v/ibhout a t r a n s i t i o n v/ire. For comparison curves of the drag
coefficient a s estitinted from t h e Royal Aeronautical Society Data Sheets (5) are also included,
ITithout the t r a n s i t i o n v/ire t h e drag coefficient increases markedly as R,^ increases from 6,3 t o 10,9 x 10°, t h e r e a f t e r decreasing very
s l i g h t l y v i t h f u r t h e r increase i n R^ up to 14«-Ix 10°, Comparison v/ith t h e estima.ted curves suggests t h a t t h e p o s i t i o n of t r a n s i t i o n moves forivajrd with increase of P^ up t o 10,9 x 1 0° and t h e r e a f t e r remains approximately, fixed i n p o s i t i o n . This deduction i s f u r t h e r s u b s t a n t i a t e d by t h e experimental r e s u l t s obtained v i t h t h e t r a j i s i t i o n v i r e a t 0,1 L
(aulthougji a t t h e lov/er- values cf R^^ the t r a n s i t i o n v/ire v/a.s a^lmost c e r t a i n l y i n s u f f i c i e n t l y l a r g e t o caiise immediate t r a n s i t i o n ) .
The, fact t h a t t h e experimentally deterrrined drag v/as h i j g e r than t h a t p r e d i c t e d by Ref, 5 i s only t o be expected since no allor/ance has been made f o r t h e drag of t h e s t r u t and t h e interference dra.gs of t h e s t r u t , the s t r u t f a i r i n g and t h e t a i l v/ires. Also, no c o r r e c t i o n s v/cre made for blockage or tunnel s t a t i c pressure g r a d i e n t . The blockn.ge c o r r e c t i o n vrould decrease the drags by r.bcut 2% (allc/zing for the -wire drag of t h e r i g ) w.hilst the s t a t i c pressure gradient v/ould increase t h e drags by a.bout
^%; an o v e r a l l decrease of about ^fo,
y
F i g s . 8 and 9, which are fcr the case of y = V = 0.15, show t h e effect of a r t i f i c i a l l y varying the nature of the boundary la57er by the use cf a t r a n s i t i o n v/ire and a. turbulence generating grid. At the lov;erReynolds
H 6
number of 6.3 x 10 ( P i g . 9) the l i f t , drag and p i t c h i n g moment c h a r a c t e r i s t i c s are a l l a f f e c t e d by the clria.nges in t h e boundary layer condition. At the
higher Reynolds number of 14,1 x 1 0° (Fig. 8) only the drag r e s u l t s are appreciably affected by these changes i n boundary layer conditions.
X I n the f i g u r e s 8 - 1 2 i n c l u s i v e the incidence i s ta.kcn as p o s i t i v e
vd.th nose up in t h e -tunnel. The reason for the cha_nge in sign convention i s t h a t for -this s e r i e s of t e s t s , on the effect of Reynolds number,
t h e bodies t e s t e d had n e g a t i v e nose and t a i l cambers, but fcr comparison v i t h the remaining t e s t s i t i s p r e f e r a b l e t o r e f e r to t h e s e as p o s i t i v e nose and t a i l camber v i t h the consequent changes i n sign convention, ÏS The Reynolds numbers a r e s l i g h t l y lower for the t e s t s v/ith the
A peculit^rity cf t h e drag r e s u l t s i s a kink i n t h e curves betv/een « = 0 and « = 3 for the t r a n s i t i o n free t e s t s . This f e a t u r e i s not present i n t h e r e s u l t s obtained with t h e t r t m s i t i o n v/ire or the turbulence g r i d . This s'uggests t h a t the kinlc i s due t o free movement of the
t r a n s i t i o n front "ivith change of incidence. At f u l l scale values of the Reynolds number t r a n s i t i o n v/ould be nearer the nose than i n these t e s t s , and t h e p o s i t i o n of the front v/ould vary l i t t l e v i t h incidence (for t h e small incidences ijri wliich we ai-^ i n t e r e s t e d ) . I t t h e r e f o r e secins reasonable t o conclude that b e t t e r comparative data -VTill be obtained by making the t e s t s on the d i f f e r e n t body configurations v/ith a t r a n s i t i o n wire. (The turbulence g r i d might be used, i n place of the t r a n s i t i o n v i r e but i t s effect v/ould probably be too severe, and in any case a proper
c a l i b r a t i o n cf the v/orking section v/ith the turbulence g r i d i n p o s i t i o n i s not a v a i l a b l e ) ,
F i g s , 10, 11 and 12 show t h e effect of change of Reynolds number, '7ith free t r a n s i t i o n (Pig, 10) the l i f t and drag c h a r a c t e r i s t i c s ere
appreciably ai'fected by cliange of R^, whilst the pitcliing moment c h a r a c t e r i s t i c s are only s l i g h t l y affected. 'Tith t h e t r a n s i t i o n v i r e (Pig. 11) the l i f t
and dra.g a.s well as the p i t c h i n g moment chp.ra.cteristics are l i t t l e affected by change of R^, P i g , 12 shews t h a t t h e turbulence g r i d has a similar e f f e c t t o t h a t of tl'ie t r a n s i t i o n v/ire i n ncJcing the c h a r a c t e r i s t i c s almost independent of change of Reynolds number. There i s hov/evor one respect in*v/hich the r e s u l t s sean t o bo more influenced by change of R^ vri.th t h e v/ire or grid than with free t r a n s i t i o n and t h a t i s i n the l i f t c h a r a c t e r i s t i c s near zero incidence. Hcnrover i t i s shov/n i n Appendix IV t h a t t h e p o s s i b l e s c a t t e r i n the l i f t c o e f f i c i e n t r e s u l t s may cunount t o - 0.026 a.t t h e lower t e a t Reynolds number. Bearing i n mind t h a t these t e s t s v/ere also made using the technique of measuring t h e balance v/ind off zero readings a f t e r m.easuring the v/ind on readings through the f u l l incidence range i t i s quite concei-vable t h a t t h i s apparent Reynolds number effect i s spuric?us.
The general concl\.ision drav/n from these r e s u l t s i s t h a t a t e s t Reynolds number cf 14.1 x 10 i s s u f f i c i e n t l y l a r g e t o give r e l i a b l e
comparative d a t a . I n f a c t , in so fnr as the l i f t c h a r a c t e r i s t i c s cxe concerned, comparison of B'igs. 8 and 9 v/ill show t h a t except for the case of free t r a n s i t i o n v/ith low Reynolds number almost i d e n t i c a l r e s u l t s are obtained o.t the h i ^ and lev/ Reynolds numbers for a l l three conditions of t h e boundary l a y e r . The samü i s t r u e t o a somev/hat l e s s e r extent v/ith t h e pitcliing moment ohara^ct o r i s t i c s .
Prom these t e s t s i t wa.s therefore decided t o maJce t h e main s e r i e s of t e s t s a.t a Reynolds number of 14.1 x 1 0° and t o \:ise a t r a n s i t i o n v/ire t o eliminate the kinks i n t h e drag curves.
5 . 2 . Incidence and camber e f f e c t s
The r e s u l t s of the Scries I t e s t s are given i n P i g s . 13 t o 17. Yifhilst the dra.g r e s u l t s of tliis s e r i e s of t e s t s a.re somev/hat inaccurate for the reasons cutlincd in paragraph 3*5 the r e s u l t s of t h i s s e r i e s serve t o show t h e general nature of t h e lif-b, drag and p i t c h i n g moment c h a r a c t e r i s t i c s over a v/ider range of incidence than do the S e r i e s I I t e s t s .
The f i r s t point worthy of note i s the good agreement of t h e l i f t and p i t c h i n g moment r e s u l t s v/ith t h e model the r i g h t v/ay up and i n v e r t e d . This i s p . a r t i c u l a r l y t r u e of t h e p i t c h i n g moment r e s u l t s , and i t suggests tha.t talcing the c'-irithmetic meaJi of t h e tv/c s e t s cf r e s u l t s should y i e l d an accurate c o r r e c t i o n t o t h e l i f t and pitching moment r e s u l t s for the i n t e r f e r e n c e e f f e c t s of the s t r u t and i t s f a i r i n g . The agreonent betv/een the two s e t s of drag resiJlts i s f a r poorer. Inspection of the graphs shov/s t h a t the drag i s i n v a r i a b l y higlier yAien the model i s t a i l down. This secans reasonable since the s t r u t and f a i r i n g are then on t h e lecv/ard
side of the model and might be escpectcd t o cause a greater i n t e r f e r e n c e drag than v/hen on the v/ind-v7;.ird side of the model. I n t h i s connection P i g . 23 shov/ing G-. p l o t t e d a.gainst C_ tan ^ i s of i n t e r e s t . The nose dov/n
( t a i l up) r e s u l t s give, very n e a r l y , Gp^ = 0.178 + C-. t a n a. Now. i f the skin f r i c t i o n drri-g remains constant \ i t h change of incidence we v/ould e-xpect the drag c o e f f i c i e n t t o vary approximately as C_ t a n a. This r e s u l t suggests t h a t t h e i n t e r f e r e n c e drag due t o the s t r u t and i t s f a i r i n g may be almost consta.nt v/hcn t h e nose i s dov/n i n the tunnel and. tha.t
a more accurate measure of t h e drag v/ould be obtained by p l o t t i n g the curves to pass through the ]points measured v/ith the nose dov/n. Hov/ever, since t h e r e i s i n s u f f i c i e n t evidence t o support t h i s hypothesis the drag curves have i n a.ll cases been taken as t h e mean of the nose up a.nd nose dov/n t e s t s .
The t h e o r e t i c a l C ~ a r e l a t i o n s h i p as piredicted by slender body theory has been evaluated (see Appendix I I ) and has been p l o t t e d in each fifjjre. Prom P i g . 14 and the t a b l e in ppjragraph 4 . 4 i t w i l l be seen tha± a t a = 0 the cambered nose plus uncambered t a i l configuration produces almost exactly t h e t h e o r e t i c a l p i t c h i n g mcmait c o e f f i c i e n t .
Moreover t h e l i f t coefficient i s at t h e same time very close t o the t h e o r e t i c a l value cjf zero. This shows t h a t the flow over t h e nose of such a cambered
body approxima.tes very c l o s e l y t o t h e t h e o r e t i c a l in-viscid flov/ except for the presence of a t h i n boundajry l a y e r . From P i g , 15 aj^d the ta.ble in paragraph 4 . 4 i t v/ill be seen t h a t the same i s not t r u e of t h e body with
cainbered t a . i l ajid uncambered nose. I n t h i s case the p i t c h i n g mrment c o e f f i c i e n t pi'oduced by the t a i l a t a = 0 i s only about 10^ of t h e H C..^ v/ould only vary as C,. t a n a. i f t h e p o s i t i v e increment in pressure
±) L
on t h e lov/er holf of the body •was accompanied by an equal negative increment on the upper half. Since t h e l i f t i s p r i m a r i l y ca.used by separation of t h e flow and the formation of body v o r t i c e s i t follows t h a t 0-, v/ill only vary approximately as C_ tan a ,
18
-theoretica.1 •value and the l i f t coefficient i s not zero. I t i s evident as confirmed by the t u f t t e s t s (paragraph 3.6) tha.t flov/ separation i s occurring on the leeward side giving r i s e t o the v/ell known type of vortex flov/ associated vvith bodies a t incidence.
I n Pig. 13, 'Vihich i s for the body of r e v o l u t i o n , the t h e o r e t i c a l C ~ «£ r e l a t i o n s h i p i s p l o t t e d for the nose alone and f o r t h e nose plus t a i l . The t h e o r e t i c a l 0^.^ a r e l a t i o n s h i p for the nose alone i s a l s o p l o t t e d .
L
Since the r e s u l t s referred, t o above i n d i c a t e t h a t t h e c.'ïmbered nose must have flow c Harare t oris t i c s v e r y similar t o the c h a r a c t e r i s t i c s predicted by i n v i s c i d theory i t seems l i k e l y t h a t t h e nose of t h e body of revolution would also have c l i a r a c t e r i s t i c s very similar to those p r e d i c t e d by theory
over a small incidence range - say - 2 . I f t h i s i s Oicccpted. i t becomes apparent t h a t the uncambered t a i l i s only providing about i+C^o of the t h e o r e t i c a l p o s i t i v e p i t c h i n g moment and about 6C^ of t h e t h e o r e t i c a l
negative l i f t which i t should produce a t incidence (over the rajige of i 2 ) . The r e s u l t s of the Scries I I t e s t s are shov/n i n P i g s . 18 to 22 where only t h e meaji r e s u l t s irro p l o t t e d . The l i f t and manent r e s u l t s are i n close a^p^cement with those of the Series I t e s t s , but except for the
'banana f u s e l a g e ' (y = 0 . 1 5 , y+ = -0.15) t h e drag c o e f f i c i e n t s are s l i g h t l y lower for the Series I I t e s t s . Lower drags v/oxild be expected i n the Series I I t e s t s ov/ing t o t h e fact t h a t jji t h e Series I t e s t s the t r a n s i t i o n v i r e s stood s l i g h t l y proud of t h e surface a t some p o i n t s aroimd t h e periphery.
The r e s u l t s gi-ven in the ta,blo in pa.ragra.ph 4 . 4 , v/hich have already been r e f e r r e d to above, have been based on the S e r i e s I I t e s t s .
5 . 3 . Comparison of t h e various configurations
The primary object of t h i s experiment was t o obtain quantitattive data on the d.rag and p i t c h i n g moments due t o incidence and camber. To f a c i l i t a t e comparison of t h e r e s u l t s the mean drag c o e f f i c i e n t s from t h e Series I I t e s t s tiave been p l o t t e d a.gainst incidence i n P i g . I 8 and against the mean p i t c h i n g moment c o e f f i c i e n t in P i g . 19. P i g . 20 i s a l s o a plot of G.. ~ C , but t o a s s i s t i n coni[:)aring t h e drags the drag scale has been considerably enlarged and t h e r e s u l t s have been presented i n such a v/ay t h a t the r e s u l t s fran a l l the p o s s i b l e camber configurations can r e a d i l y be compa.red. The possible range of s c a t t e r of the drag p o i n t s i s shov/n
on t h i s f i g u r e . The s c a t t e r i s s u f f i c i e n t l y small t o permit confidence t o be placed i n t h e comparison of the r e s u l t s .
Referring f i r s t t o P i g . 18 i t vsill be seen t h a t a t zero incidence t h e drag i s l e a s t for the body of revolution. Replacing the uncambered nose by t h e y = 0.15 nose r e s u l t s i n a small increase i n dra.g. The increase in drag caused by replacing t h e t a i l of t h e body of revolution by the
v/ith the cambered t a i l i s a.lmost independent of the nose camber,
With change of incidence from zero the drag increment due t o camber v a r i e s in the expect eel manner; t h a t i s t o say the drag increment increases when the combineei incidence due t o datum l i n e incidence plus fuselage camber" l i n e incidence increases numerically and decreases v/hen t h e combined iriciience decreases numerically,
The objof-t of using fuselage incidence cr comber i s t o produce a p o s i t i v e coni;ribation t o t h e p i t c h i n g moment c o e f f i c i e n t to a s s i s t i n trimming the a.ii'Ci:'aft under c r u i s e conditions. From Fig. 20 i t appears t h a t for t h e part.icular ran^';c of configiirations chosen for these t e s t s the minimum dra.g v/ill be obtained by using a body of revolution a t incidence for any value of 0 up t o about 0.07. For higher values of C a lower drag i s given by an •uncambered nose ajid a. sv/ept up t a i l (negative y ) , but since the dat'um l i n e incidence v/C'uld then exceed 4 and t h e fuselage
dra.g increment r e l a t i v e t o t h e minimum fuselage dra.g v/ould exceed l^ó i t seems unlilcely t h a t a C in excess of 0.07 w-ould. be used in pra.ctice. Hov/ever, the upsv/cpt t a i l configuration might s t i l l be required i n
preference to a completely uncambered fuselage owing t o the g r e a t e r t a i l clearance t h a t v/ould be a.vailable for t a i e - o f f and la.nding.
Prom t h e dra.g point cf view the fuselage v/ith p o s t i v e l y cambered nose and zero t a i l camber i s n e a r l y as good as the uncambered fuselage, and i t has t h e axivantage of producing a given p i t c h i n g moment for a. smaller datum l i n e incidence.
The other configurations v/hich might p o s s i b l y be of seme use are the nega.tivoly cajribered nose a-nd t a . i l fuiselagc aarid t h e 'banana' fuselage v/ith p o s i t i v e nose camber and negative t a i l camber. The fermer hov/ever r e q u i r e s a l a r g e r datxim l i n e camlser than any of the other configura,ti.ons t o produce a given C , Both configurations v/ill lead t o a t l e a s t a 3% t o 1^0 increase in fuselage drag as compared v/ith t h e body of r e v o l u t i o n a.t zero incidence,
F i g s . 21 ajid 22 c^re p l o t s of C ~ « an.d C ~a t o large sca.les.
F i g . 21 sliOws t h e very small C increment contributed by t h e cambered t a i l , F i g . 22 shews the much l a r g e r C^. increment t h a t i s produced by t a . i l camber
L
as a g a i n s t nose camber ajnd a.lso shows t h a t t h e effects of nose caniber and t a i l caimber measured, s e p a r a t e l y can be combined t o determine the e f f e c t s of combined nose and ta.il comber.
The t e s t s r e f e r r e d t o so f a r i n t h i s discussion have been confined t o vairicus configurations -with nose ajid t a i l cambers of 0,15. The Series I I t e s t s included one t e s t v/rlth a. nose camber of 0.075 ^-nd zero t a i l camljer. The mean r e s u l t s from t l i i s t e s t crc- shovai i n F i g . 24 v/here t h e r e s u l t s f o r y = 0 and. 0,15 ore also shown. I t w i l l be seen t h a t v/hcreas t h e C r e s u l t s
•vary linearly wi^th nose camber, as v/ould be escpected fran the close agreement of experiment with theory, the CL results do not vary linearly vdth camber. The drag results are not easy to explain since it •would appear that at zero incidence the drag increment due to 0,075 nose camber is as great as the increment due to twice this amount of camber. Possibly this is a case in wliich •the possible range of scatter of the results
combined vdth small errors in manufacture of the models have combined to produce a misleading result.
5.4. Limitations of the experiment
It raust be emphasised in concluding this discussion that this experiment has a number cf limitations in so far as applying it to estimate the drag of a conrplete supersonic aircraft is concerned. The main limitations would seem to be
:-(i) the relatively low value of the Reynolds number, (ii) the low Mach number ( M = 0.2),
(iii) the absence of interference effects on the fuselage due to a lifting vdng and, to a lesser extent, the tail unit,
(iv) the influence of the flow perturbations due to fuselage incidence and camber en the performance of the -wing and tail unit,
There is some evidence from these tests that the effect of item (i) may be small. The effect of the low Mach number of these tests may well be impcrtajit, but this effect can only be determined by a coniparable series of tests at higher Mach numbers at other establishments. The interference effects listed under items (iii) and (iv) might also be expected to be important. The body vortices due to incidence or camber might have a considerable effect on the performance of the tailplane; particularly the spanvdse distribution of lift,
6, Conclusions
This experiment has shown that nose camber gives a pitching moment increment very close to that predicted by inviscid slender body theory. The drag penalty, v/hich is zero on inviscid theory, is quite small, and so is the increment in fviselage lift. On the other hand tail camber does not give results agreeing m t h inviscid theory. The drag and lift increments are several times larger than those due to nose camber, and the pitching moment increment is quite unrelated to the theoretical increment, For the model tested in this experiment the pitching moment increment due
to tail camber, measured about the mid point of the model, was about 10^ of the theoretical moment Increment.
The optimum fuselage configuration for minimum trim drag of a
f a c t t h a t i n t e r f e r e n c e effects from t h e fusela,ge on t h e flov/ over t h e wings epid t a i l u n i t , and from t h e vdngs and t a i l u n i t on the fuselage, have not been studied; nor v/a.s t h e t e s t made a.t supersonic speed. Hov/ever, the evidence scans t o be t h a t for a given increment in pitcliing moment the minimijm fuselago drag i s given by nn uncambered body at incidence. P r a c t i c a l considerations of obtaining adequa.te ground clearance of t h e t a i l for ta.ke-off and landing may danand the use of negative t a i l camber. The experiment shov/s t h a t such camber can be used vdth l i t t l e , if any, adverse effect on t h e p i t c h i n g moment of the fusela.ge for a given da.tum l i n e incid.encc. The drag penalty of such nega.tive t a i l camber may be considerable a t zero incidence, but as fioselage incidence increases the drag p e n a l t y decreases u n t i l above a c e r t a i n value of incidence or p i t c h i n g moment t h e drag i s a c t u a l l y decreased by nega.tive t a d l cam.ber. I n the present experiment with y, = -3,15 ra.dians t h i s occurred at a.bout 4 (0,07 radians) of incidence,
The other configurations which might p o s s i b l y be of seme use, both of them having nega.ti-ve t a i l camber, are the configurations vdth e i t h e r p o s i t i v e cr negative nose co.mber. The former gives a reduction in fuselage
incidence for a given p i t c h i n g moment -v/hilst t h e l a t t e r r e q u i r e s a l a r g e r incidence than the other configurations t o develop a given p i t c h i n g moment but i t feives a more fa.vovirable nose shape f o r the layout and viev/'from the
cockpit. Both configurations lead to s i g n i f i c a n t increa.ses of fuselage drag - about 3% t o l^o for the models tested..
7, Acknowle dg ement s
The author i s indebted to Mr. G,G.Appleby a.nd l&r. R. Malet de C a r t e r e t for t h e i r help in cond.ucting t h e experiment ajid.reducing t h e r e s u l t s .
Also Mr, G.D.Bruce and Mr. L. Wilsher v/ho painstalcingly made the models and Mr. S, L i l l e y v/ho helped vdth a n'umber of small yet important
8. References 1. Richardson, J.R. 2. Harris, K,D. 3. Harris, E.D.
4.
5.
P a n k h u r s t , R.C. H o l d e r , D.;7, Notes on d r a g - d u e - t o - l i f t and t r i m dra.g, ( U n p u b l i s h e d ) . 1957. Comments on 'Trim D r a g ' . ( U n p u b l i s h e d ) , 1957.The u s e of f u s e l a g e camber and i n c i d e n c e a s a mea.ns of r e d u c i n g t h e t r i m dra^g of s u p e r s o n i c a i r c r a f t , (Unpublished) 1957. Yfind-tunnel t e c h n i q u e . P i t m a n . The Royal A e r o n a u t i c a l S o c i e t y Da.ta S h e e t s , Vclume I , B o d i e s 02.04.01 and . 0 2 .
iiPPEI^IX I Model Data 1, Area and camber d i s t r i b u t i o n s
The c e n t r a l p o r t i o n , common to a l l t h e models, i s uncambered, 3 f e e t in length v i t h a c i r c u l a r c r o s s - s e c t i o n 8 inches in diameter.
The nose and t a i l portions are of c i r c u l a r c r o s s - s e c t i o n vdth a SeajTSHaack area d i s t r i b u t i o n , namely :
-,3 1 L -^1 2 2 - ^1
V2
where R = 4" \ = 42"The camber Linos a r e parabolic in form, i . e .
dx.
y
T.
o r y„ y 2
Three s e t s of nose a.nd t a i l x:)orticns v/ore made v i t h cambers y = 0, 0,075 o-nd 0,15 r a d i a n s ,
The a c t u a l r a d i u s and camber d i s t r i b u t i o n s are given i n Table I , 2, Reference a.rea.s
Maximum c r o s s - s e c t i o n a l area S S = 0.349 s q , f t . Surface (or v/etted a.rea.) S
]; ^ v/
For t h e purpose of comparing t h e drag r e s u l t s -vdth estimated data the drag c o e f f i c i e n t G^^ v/as based on the v/etted area. S.
v/
S = l 6 . 8 l s q . f t , w
3 . Volume V
AFPENDLX I I T h e o r e t i c a l estiraa.tcs of t h e l i f t a.nél p i t c h i n g moment c h a r a . c t e r i s t i c s 1 . S l e n d e r body t h e o r y According t o s l e n d e r body t h e o r y t h e l i f t i n t e n s i t y p e r u n i t l e n g t h on a body of c i r c u l a r c r o s s s e c t i o n i s : -( 1 ) ( 2 ) (3) (4) 2, T h e o r e t i c a l estiraa.tes 2 . 1 , O v e r a l l l i f t
From ( 2 ) , s i n c e a l l t h e models a r e p o i n t e d a t t h e t a i l (and n o s e ) , t h e o v e r a l l l i f t i s z e r o indLcpendent of camber or i n c i d e n c e ,
2 . 2 , P i t c h i n g moment due t o camber
Prom R e f , 3 t h e p i t c l i i n g moment due t o p o s i t i v e nose and t a i l cai.iber a t z e r o i n c i d e n c e ( a = O) i s 2 2 2 M = pu y ïT R ' ' -f 1 __ 5 1 i e ^ r 2 _ ^ i 1 ;
f = P U ^ / (S^a)
dx dx ^ f ^ 2 r 1^ L = PU'' S„ a L 1 J_-L The p i t c h i n g moment i s I n t e g r a t i n g b y p a r t s M = ~ pU^ Gc S^^ ^ ^ - 1 X dx „ 1 - / S„ a dxii ^
APTENDIX I I Continued
2 . 3 . P i t c h i n g moment due t o incid.ence
Consider t h e •uncambered body a t incidence o , The nose p o r t i o n w i l l c a r r y a l i f t L , t h e c e n t r a l p o r t i o n v d l l carry no l i f t , and t h e t a i l p o r t i o n v d l l ca.rry a l i f t L, v;hich w i l l be equal in magnitude but opposite i n sign t o t h a t of the nose l i f t L . The p i t c h i n g moment due t o incidence may therefore be obtained by estimating L (and L.) and the c e n t r e of
n b
pressure p o s i t i o n of t h e nose (ajid t a . i l ) . Prom (2)
L = PU^ S a n
Prom (4) the moment M about t h e r e a r of t h e nose p o r t i o n i s
' O .2
\ =
^' [^
Sf
«^1
I r e = PU^ a / S dx - 1 ^1The la.tter i n t e g r a l i s t h e volume of the nose,
• ' - 1 , ^-^i '^
n
Hence M„ = ;XS a jr IT S 1
Thus t h e c e n t r e of pressure cf the nose i s a t X _ M ,
The t o t a l pitcliing moment on t h e body a.t incidence i s t h e r e f o r e
2 - r "^ ?
M = 2 p U S a [ ^ 7 r l ^ + - | P 2a r 3 -, •'"2l^m
= 1
LT^
"^
\^_TJ
i . e . C = 1.424 a m r^ ClC or m d a = 1.424i^JTE^DK I I I
Reduction cf Results 1, Dynamic pressiire and v e l o c i t y
Prom the tunnel c a l i b r a t i o n da.ted 19.8.55 k = 1,13
v/here _ k
Now (p^ - ipj^ = 1 ^ h lb,/sq.ft.
vdiere h i s the Betz r-oading i n m.m. of water. Hence ^ pU^ = 1,13 x-1^32^ x h w 25,4 i . e , i puf, = 0.2315 h I b . / s q . f t . ajid U = 13.95 ^h f . p . s . v/ 2, B.alance ca.libra.tion
The balance c a l i b r a t i o n s given by preliminary t e s t s (which d i d not include the e f f e c t s of i n t e r f e r e n c e ) are :
-5,155 (R^ - R ^ ) ( l b . ) D = 0,423 (R, - R, ) ( l b . ) z M = -3.068 (R^ - R ) ( I b . f t . ) *'a a z 3, Evalioation cf coefficientB(\mcorrected) "L <^ w m — = = •§• PU^S D •1 „ . 2 « •g- PU s D
i
Al\
M PU^Sl = 63.8 ^1 - ^ 1 ^ h = 5.23 \ " \ h = 0,1087 \ " \ z -3.795 \ " \ zAPPENDIX I I I Continued
4. Tunnel i n t e r f e r e n c e c o r r e c t i o n s 4 . 1 , S t a t i c pressure graidient
\ Because of t h e length of t h e model t h e s t a t i c pressijre gradient
cannot be t r e a t e d as a constant, and. so the standard methods of estimating the c o r r e c t i o n t o the drag coefficient are inapplicable. To obtain an approximate guide to t h e magnitude of t h i s correction we may c a l c u l a t e t h e h o r i z o n t a l buoyancy.
The drag coefficient due t o the h o r i z o n t a l buoyancy i s
1
^ ^
^ = i? i-i'p^
^"^ ^
where
0 = static pressure coefficient along centre •^s line of empty working section,
D„ has been evaluated by graphical integrations giving
'°D. = - 0 , 0013
This amounts to slightly londer 1^ of the minimum drag coefficient of the body of revolution.
4.2. Blockage worrections
Up
- \ ('*% *
g
v/here e = solid blockage factor
s ^ and e = wake blockage factor
w ^
The solid blockage factor ^„ is approximately given (Ref. 4, p.3^4) by
e = 0.65
s
s
V h ^
"where V = volume of body plus fairing h = height of working section b ~ breadth of v/orking section
AEEENDIX I I I Continued
The v/alce blockage f a c t o r i s given (Ref. 4 , p.348) by _ 1 _§„ r
w - 4 bh D
v/here S i s t h e area on wMch G-^ i s based, and C^^ i s t h e o v e r a l l drag coefficiont including t h e f a i r i n g . S u b s t i t u t i n g i n these tv/o formulae v/e have e = 0.0056 s e = 0.00031 w Hence, U = I.OO58 U
Thus the e f f e c t i v e f r e e stream v e l o c i t y U„ i s a l i t t l e more than - ^ g r e a t e r than the tunnel v e l o c i t y U_,
4 , 3 . Rig correction
Rig drag coefficient CL r i g
The drag of the t a i l vdres has been c a l c u l a t e d assuming a drag coefficient of u n i t y based on f r o n t a l a r e a . The r i g drag c o e f f i c i e n t C_
rig based on the model reference area S of the model is plotted in
Fig, 5.
I t v/ill be seen t h a t the v/ire drag i s approximately equal t o the zero incidence drag of the body of r e v o l u t i o n .
Rig p i t c h i n g moment coefficient C r i g
To determine the c o n t r i b u t i o n of t h e countenveight t a i l v/ire t o the p i t c h i n g moment a drag load v/as applied t o the wire midv/ay betv/een i t s attachment to the fuselage and t h e f l o o r . The p i t c h i n g moment v/as read on the balance and hence t h e e f f e c t i v e moment arm of t h e drag load Vfas foxind. This effecti^ve moment arm i s p l o t t e d i n F i g . 6 ( a ) .
Using the estimated t a i l v/ire drags r e f e r r e d t o above the p i t c h i n g moment due t o the t a i l v/ires v/as then calculated. The wire p i t c h i n g moment
c o e f f i c i e n t C based on the model reference area S and reference length m .
r i g
Accuracy of t h e r e s u l t s The s e n s i t i v i t y of t h e b a l a n c e i s such t h a t t h e r e v o l u t i o n c o u n t e r s can be b a l a n c e d out t o v / i t h i n t h e f o l l o w i n g l i m i t s : -L i f t b a l a n c e t 0,01 Drag b a l a n c e - 0,01 P i •behing moment b a l a n c e - 0.01
These l i m i t s a p p l y v i t h wind on and v/ind off and l e a d t o t h e folio-wing l i m i t s i n t h e d e t e r m i n a t i o n of t h e c o e f f i c i e n t . Coefficient
°D
0 1 m Accuracy U = 98.6 f . p . s , t 0,026 + 0.002 t 0,002 " - — I--— .. . . . 1 U = 220.8 f , p . s , j t 0,006 + 0,0004 t 0,0004 iThe B e t z manometer could be r e a d t o t h e n e a r e s t 0,1 m,m. of w a t e r b u t ov/ing t o t h e u n s t e a d i n e s s of t h e t u n n e l v e l o c i t y i t would p r o b a b l y be more r e a l i s t i c t o assume t h a t t h e a c c u r a c y of measurement v/as t o w i t h i n i 0 , 2 m,m, of v/ater. T h i s c o r r e s p o n d s t o an accuracjr of - 0.2% i n t h e measurement of t h e s p e e d a t 9 8 . 6 f . p . s . and - 0.04% a t 2 2 0 , 8 f , p , s ,
TABIE I
Radius and camber l i n e d i s t r i b u t ions ^1 ( i n s . ) 0 8.4 16.8 21.0 25.2 29.4 33.(> 31.Q 39.9 42.0 y ^ ( i n s . ) = 0.075 0 0.063 0,252 0.394 0.567 0 . / / 2 1,008 1.276 1.575 = 0.15 0 0.126 0.504 0,788 1.134 1.5Vf 2.016 2.552 3.150 ( i n s . ) 4.000 3.879 3.510 3.224 2.862 2.414 1.859 1,107 0.698 0
NOSE PORTION
T
CENTRAL PORTION. TAIL PORTION.
R = 4 >3S
I
t o - 3
FOR RADIUS r- a CHAMBER LINE DISTRIBUTIONS. SEE TABLE I.
y ^ ft Yi ARE POSITIVE AS SHOWN.
S C A L E : - '/|2 F U L L SCALE.
D
FIG. 2. RIGGV4G OF MODEL
FIG. 4. STATIC PRESSURE DISTRIBUTION ALONG CENTRE LINE OF WORKING SECTIOK
FIG. 6 a
y^
\ 1 ^^ r FIG. 6biESTIMATED PITCHING MOMENT OP RIG TAIL WIRES
\
X
N
^ POSITIVE WITH «osE DOWN!] i>F I G S ESTIMATED DRAG OF RIG TAIL WIRES
- » - FREE THAWrriOK H ' | - O - O-OU M a TRANnnON > EXPERIMENT
W1>E « • 0 1 L „ J R t a S . OAT* SHEET ESTMXTES.'
4 6 e K) la M M
FIG 7 <S,.K>* •
MWIATION OF DRAG COEFFICIENT WITH REYNOLDS NUMBER BODY OF REVOLUTION. , Z - " 0 °
- . / " F R E E TRANSIT ® S R „ - W IK I C °"* r -TRANSITION WIRE / 0 0 ( 4 " TRANSITION W«E S R N - t 4 l K O ' , / T U R B U L E N C E GRID * S R „ - 13-1 X 10^
FIG 8. EFFECT OF VARYING THE BOUNDARY LAYER. FI& 9. EFFECT OF VARYING THE BOUNDARY LAfER
INCIDENCE POSITIVE WITH
NOSE UP ISn^O-IS s.,_ INCIDENCE POSITIVE WITH NOSE UP « t - O 15
FIG. lO. EFFECT OF VARYING REYNOLDS NUMBER.
FREE TRANSITION. FIG. IL EFFECT OF VARYING REYNOLDS NUMBER. 0 - 0 1 4 " TRANSITION WRES.
INCIDENCE POSITIVE WITH NOaE UP
FIG 12 EFFECT OF VARYING REYNOLDS NUMBER.
TURBULENCE SRICL
FIG la BODY OF REVOLUTION.
R N > I 4 ' I I lO* 0'OI4* TRANSITION «IRE
„ INCIDENCE POSITIVE
0-4 " WITH NOSE DOWN. O INCIDENCE POSITIVE
0-4 " WITH NOSE DOWH INCIDENCE POSITIVE WITH NOSE UP
FIG. 14. NOSE CAMBER.
5-o S2 u. 3 i
1 1
'm
i Iv
til
'1'
0 ó ó <! d" J U -. ^ 1 > (mm\ / i
r\°\°nW°\ i .1 il-^kUl^
li
s * A V-.1
il
-a B- -o—•«?-O OIS OIS -O-IS - e a ^ ""^^^... =:.;-4u« ""^ "--^^ «jjajsr-j-Co <:i O I B — = ... <k --3!= > ^ " J(-.X j ^ - 0 0 8 - 0 0 6 - 0 0 4 -O-02 0'02 0'04 0'06 O'OB Cm • FIG. 19.
R „ - 14-1 X lO* O 0 1 4 ' TRANSITION WIRE GLUED TO NOSE.
0 1 8 5 O I 7 S 0 - I 7 0 O'165 -OIS O I S -OIS -OIS CAMBER
U N E NUMBERS ATTACHED TO THE PO»nrs ARE THE lh4CIDENCE OF THE FUSELAGE DATUM LINE. —] 1
t POSSIBLE RANGE OF ., SCATTER OF POINTS^
.^40
0 1 0
FIG. 20. COMPARISON OF THE DRAG OF VARIOUS CONFIGURATIONS. R M « 1 4 I > 10* O O I 4 TRANSITION WIRE GLUED TO NOSE.
C T R ~ < <