A NEW SLOTTED-WALL METHOD FOR PRODUCING LOW BOUNDARY CORRECTIONS IN TWO-DIMENSIONAL AIRFOIL TESTING by CHRISTOPHER DWIGHT WILLIAMS B.A.Sc., University of British Columbia 1967 M.A.Sc., University of British Columbia 1973 THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of Mechanical E n g i n e e r i n g We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA October 1975 In presenting th i s thes is in p a r t i a l fu l f i lment of the requirements for an advanced degree at the Univers i ty of B r i t i s h Columbia, I agree that the L i b r a r y sha l l make it f ree ly ava i lab le for reference and study. I further agree that permission for extensive copying of th i s thesis for s cho lar ly purposes may be granted by the Head of my Department or by his representat ives . It is understood that copying or p u b l i c a t i o n of th is thesis for f i n a n c i a l gain sha l l not be allowed without my writ ten pe rm i ss ion . Department of The Univers i ty of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 D a t e t.]> Qdi9kf 1 9 1 6 SUPERVISOR: Dr. G.V. P a r k i n s o n i i AB3 TRACT T h i s t h e s i s deals with a new approaca to r e d u c i n g wiadtunnai w a l l c o r r e c t i o n s i n a i r f o i l t e s t i n g , by employing a t r a n s v e r s e l y - s l o t t e d w a l l o p p o s i t e the s u c t i o n s i d e of the a i r f o i l , and a s o l i d w a l l o p p o s i t e the pressure s i d e . The s o l i d elements of the s l o t t e d w a i l are symmetrical a i r f o i l s at z e r o i n c i d e n c e . T h i s geometry permits the flow to assuaa c l o s e l y the s t r e a m l i n e p a t t e r n f o r unconfined flow, without degrading the flow q u a l i t y through shear l a y e r mixing near the t e s t a i r f o i l . The theory uses the p o t e n t i a l flow s u r f a c e source-element method, with Kutta c o n d i t i o n s s a t i s f i e d on the t e s t a i r f o i l and the w a l l s l a t s . In experiments using a range of s i z e s of a i r f o i l s of t h r e e d i f f e r e n t p r o f i l e s , good agreement with the p r e d i c t i o n s of the theory has been o b t a i n e d . I t appears t h a t u n c o r r e c t e d l i f t c o e f f i c i e n t s and p r e s s u r e d i s t r i b u t i o n s , a c c u r a t e to w i t h i n one percent, can be o b t a i n e d f o r a wide range of a i r f o i l shapes, s i z e s , and l i f t c o e f f i c i e n t s , u s ing a s l o t t e d w a l l of open-area r a t i o between 60 and 70 p e r c e n t . i i i C e t t e these d _ c r i t une n o u v e l l e inethode en vue de diminuer l e s c o r r e c t i o n s da p a r o i s en s o u f f l e r i e aux e s s a i s des a i l e s . C ette methods einploie un taur a. f e n t e t r a n s v e r s a l e , en f a c e du f l a n c de d e p r e s s i o n de l ' a i l e d ' e s s a i ; et un mux s o l i d e , en f a c e du f l a n c de p r e s s i o n . Les elements s o l i d e s du' mur a, f e n t e s o n t de p r o f i l s aerodynamiques et syraetriques a 1'angle d ' i n c i d e n c e z e r o . C e t t e f i g u r e geotuetrique permet l'ecoulement d ' a i r , s u i v i e de pres par l e s l i g n e s de courant. de l'ecoulement l i b r e ; ce r e s u l t a t e s t obtenu sans diiainuer l a g u a l i t e de l'ecoulement par l e melange de l a couche de d i s c o n t i n u i t e , pres da l ' a i l e d ' e s s a i - La t h e o r i e demande d ' u t i l i s e r l'ecoulement a p o t e n t i e l des elements de l a source de s u r f a c e , s a t i s f a i s a n t l e s c o n d i t i o n s Kutta a l ' a i l e d ' e s s a i et aux a i l e s murales. Les e x p e r i e n c e s ont ete f a r t s en eaployant. des a i l e s de corde de t r b i s p r o f i l s d i f f e r e n t s . Les t h e o r i e s obtenuas r e s p e c t e n t assez bien l e s hypotheses p r a e t a b l i e s . Les c o e f f i c i e n t s p o rtances non v e r i f i e s , et l e s d i s t r i b u t i o n s de p r e s s i o n s sont e x a c t s a un pourcent pres; e t i l s peuvant e t r e obtenus pour une qrande v a r i e t e de p r o f i l s , de dimensions at de c o e f f i c i e n t s p o r t a n c e s ; en u t i l i s a n t un mur a f e n t e , de q u o t i e n t e n t r e l a p a r o i e t l a s u r f a c e t o t a l e , de s o i x a n t e a s o i x a n t e - d i x pourcent. I V ACKNOWLEDGEMENT T h i s r e s e a r c h was c a r r i e d out under the s u p e r v i s i o n of Dr. G. V. Park i n s o n , whose expert a d v i c e and guidance i s g r a t e f u l l y acknowledged. In the design and c o n s t r u c t i o n of the v i a d t u n n e l models and equipment, the work done and the advice given by the t e c h n i c i a n s of the Mechanical E n g i n e e r i n g Department was e x t r e a e l y v a l u a b l e . A l l the computing was done at the U.B.C. Computing C e n t e r . T h i s r e s e a r c h was supported by the U n i v e r s i t y of B r i t i s h Columbia and the Defence Research Board of Canada. Encouragement and support were pr o v i d e d by F.M.W. , who c o n t r i b u t e d more than her share i n our j o i n t e f f o r t . Table of Contents A b s t r a c t Resume Acknowledgement L i s t o f F i g u r e s L i s t o f P l a t e s L i s t o f T a b l e s N o t a t i o n I n t r o d u c t i o n Survey o f Windtunnel W a l l C o r r e c t i o n Methods §2.1 C o n v e n t i o n a l L i n e a r T h e o r i e s §2.2 R e s u l t s o f C o n v e n t i o n a l L i n e a r T h e o r i e s §2.3 Low C o r r e c t i o n T e s t C o n f i g u r a t i o n s A New S l o t t e d - W a l l Theory §3.1 A P h y s i c a l B a s i s f o r the New Theory §3.2 F o r m u l a t i o n o f an Ex a c t Numerical Theory §3.3 Other A i r f o i l - W a l l C o n f i g u r a t i o n s Examined Methods o f Numerical S o l u t i o n §4.1 Assembling the Equations §4.2 S o l v i n g the Equations R e s u l t s o f the New Theory Experiments t o V e r i f y the New Theory §6.1 T e s t s e c t i o n Design §6.2 A i r f o i l Models T e s t e d §6.3 T e s t Procedures v i 7. E x p e r i m e n t a l R e s u l t s 5 4 8. E x t e n s i o n s t o the New Theory 60 §8.1 P o t e n t i a l Flow C o n s i d e r a t i o n s of V i s c o u s E f f e c t s 62 §8.2 The Flow i n the Plenum: The Bounding Shear L a y e r 69 §8.3 Summary 76 9. C o n c l u s i o n s 77 Appendix 1. The I n t e g r a t i o n of a Three-Dimensional P o i n t 79 Source to a Two-Dimensional F l a t D i s t r i b u t e d Source Element Appendix 2. A Procedure f o r Block Computation o f 84 M a t r i c e s A, B, and C. Appendix 3. Two Methods o f S o l v i n g the Systems o f 91 Simultaneous L i n e a r A l g e b r a i c E q u a t i o n s Appendix 4. A S t r e a m l i n e T r a c k i n g A l g o r i t h m 96 Appendix 5. Design of the Two-Dimensional N o z z l e I n s e r t 99 Appendix 6. An A n a l y t i c R e p r e s e n t a t i o n of a L i f t i n g 10 3 V o r t e x Between a S o l i d , a T r a n s v e r s e l y -S l o t t e d and a Constant P r e s s u r e Boundary Appendix 7. Standard S o l i d Wall C o r r e c t i o n s 111 Appendix 8. A Reduced A i r f o i l C i r c u l a t i o n Determined 113 from the Measured L i f t Appendix 9. A Reduced A i r f o i l C i r c u l a t i o n Determined 116 by M o d i f y i n g the P r o f i l e Appendix 10. The Computer Program f o r the E x a c t 118 Numerical Theory Appendix 11. L i s t o f Equipment Used 152 F i g u r e s 153 Plates Tables References v i i i L i s t of F i g u r e s F i g u r e 2.1 F i g u r e 2.2 F i g u r e 2.3 F i g u r e 3.1 F i g u r e 3.2 F i g u r e 3.3 F i g u r e 3.4 F i g u r e 5.1 F i g u r e 5.2 F i g u r e 5.3 F i g u r e 6.1 P o r o s i t y parameter as a f u n c t i o n of w a l l open-area r a t i o f o r l o n g i t u d i n a l s l o t s [12] R a t i o o f a i r f o i l l i f t - c u r v e s l o p e s f o r l o n g i t u d i n a l l y s l o t t e d w a l l s : Experiment[12] V a r i a t i o n o f p r e s s u r e c o e f f i c i e n t a l o n g a s t r a i g h t boundary: Theory An a i r f o i l between t r a n s v e r s e l y - s l o t t e d upper and s o l i d lower w a l l s : Theory W a l l e f f e c t on a i r f o i l p r e s s u r e c o e f f i c i e n t : Theory Geometry and n o t a t i o n of two-dimensional source elements f o r Smith's method S u r f a c e v e l o c i t y v a r i a t i o n s f o r a two-d i m e n s i o n a l source element E f f e c t of a i r f o i l s i z e on r a t i o of l i f t c o e f f i c i e n t s : Theory Comparison o f a i r f o i l p r e s s u r e c o e f f i c i e n t s : Theory V a r i a t i o n of p r e s s u r e c o e f f i c i e n t a l o n g a s t r a i g h t boundary f o r a two-dimensional a i r f o i l w i t h zero l i f t - c o r r e c t i o n : Theory U.B.C. Mechanical E n g i n e e r i n g low-speed c l o s e d - c i r c u i t windtunnel Page 153 154 155 156 157 158 159 160 161 162 163 F i g u r e 6.2 V a r i a t i o n o f mean windspeed i n two-dimensional t e s t s e c t i o n i n s e r t on v e r t i c a l p i t o t s t a t i c t r a v e r s e 164 F i g u r e 6.3 V e l o c i t y p r o f i l e i n f l o o r boundary l a y e r i n two-dimensional t e s t s e c t i o n i n s e r t 165 F i g u r e 6.4 E f f e c t o f endp l a t e l o a d i n g s on l i f t , d rag and p i t c h i n g moment c o e f f i c i e n t s f o r two-dimensional a i r f o i l t e s t s 166 F i g u r e 6.5 C a l i b r a t i o n o f n o z z l e and t e s t s e c t i o n dynamic p r e s s u r e s 167 F i g u r e 6.6 E r r o r b a r s f o r measured a i r f o i l l i f t c o e f f i c i e n t s 168 F i g u r e 6.7 V a r i a t i o n of measured a i r f o i l l i f t c o e f f i c i e n t s on t h r e e c o n s e c u t i v e runs 169 F i g u r e 7.1 V a r i a t i o n o f a i r f o i l l i f t c o e f f i c i e n t w i t h s l o t t e d - w a l l open-area r a t i o : Experiment 170 F i g u r e 7.2 E f f e c t o f s l o t t e d - w a l l open-area r a t i o on r a t i o o f l i f t - c u r v e s l o p e s f o r C l a r k - Y a i r f o i l 171 F i g u r e 7.3 E f f e c t o f s l o t t e d - w a l l open-area r a t i o on r a t i o o f l i f t - c u r v e s l o p e s f o r NACA-0015 a i r f o i l 172 F i g u r e 7.4 E f f e c t o f a i r f o i l s i z e on l i f t - c u r v e s l o p e f o r NACA-0015 a i r f o i l : Experiment 173 F i g u r e 7.5 E f f e c t o f a i r f o i l s i z e on l i f t - c u r v e s l o p e f o r C l a r k - Y a i r f o i l : Experiment 174 X F i g u r e 7.6 F i g u r e 7.7 F i g u r e 7.8 F i g u r e 7.9 F i g u r e 8.1 F i g u r e 8.2 F i g u r e 8.3 F i g u r e 8.4 F i g u r e 8.5 F i g u r e 8.6 F i g u r e 8.7 E f f e c t o f s l o t t e d w a l l on a i r f o i l p r e s s u r e c o e f f i c i e n t : Experiment Comparison of a i r f o i l p r e s s u r e c o e f f i c i e n t s : Experiment V a r i a t i o n o f a i r f o i l midchord p i t c h i n g moment c o e f f i c i e n t w i t h s l o t t e d - w a l l open-area r a t i o : Experiment V a r i a t i o n o f a i r f o i l drag c o e f f i c i e n t w i t h s l o t t e d - w a l l open-area r a t i o : Experiment E f f e c t o f reduced c i r c u l a t i o n on a i r f o i l p r e s s u r e c o e f f i c i e n t : Theory (Appendix 8) M o d i f i c a t i o n of a i r f o i l p r o f i l e t o reduce t h e o r e t i c a l c i r c u l a t i o n t o measured v a l u e : Theory (Appendix 9) E f f e c t o f m o d i f i e d p r o f i l e on a i r f o i l p r e s s u r e c o e f f i c i e n t An a i r f o i l between a s l o t t e d upper and a s o l i d lower w a l l w i t h a plenum chamber The shear l a y e r i n the plenum chamber su r r o u n d i n g the s l o t t e d w a l l E f f e c t o f d i f f e r e n t types o f w a l l b o u n d a r i e s on r a t i o o f l i f t c o e f f i c i e n t s : Theory V a r i a t i o n o f p r e s s u r e c o e f f i c i e n t a l o n g a s t r e a m l i n e i n plenum chamber: Theory 175 176 177 178 179 180 181 182 183 184 185 x i F i g u r e 8.8 E f f e c t on a i r f o i l l i f t c o e f f i c i e n t s o f assumed p r e s s u r e c o e f f i c i e n t s on a s t r e a m l i n e r e p r e s e n t i n g the plenum shear l a y e r : Theory 186 F i g u r e A l . l Geometry f o r i n t e g r a t i o n o f a p o i n t source 187 F i g u r e A5.1 The two-dimensional n o z z l e i n s e r t 188 F i g u r e A6.1 A l i f t i n g v o r t e x between a s o l i d , a s l o t t e d , and a c o n s t a n t p r e s s u r e boundary: Theory 189 F i g u r e A6.2 The image system f o r a l i f t i n g v o r t e x between a s o l i d and a c o n s t a n t p r e s s u r e . boundary: Theory 190 F i g u r e A10.1 N o t a t i o n f o r the computer program o f Appendix 10 191 X X X LIST OF PLATES P l a t e l a . P l a t e l b . P l a t e 2. P l a t e 3. P l a t e 4. P l a t e 5. P l a t e 6. Page The U.B.C. Me c h a n i c a l E n g i n e e r i n g low-speed c l o s e d - c i r c u i t windtunnel The o c t a g o n a l t e s t s e c t i o n i n the windtunnel The a i r f o i l - s h a p e d w a l l s l a t s The w a l l s l a t s i n the s i d e w a l l frame The 616mm NACA-0015 a i r f o i l The 354mm C l a r k - Y a i r f o i l f i t t e d w i t h e n d p l a t e s 194 The 616mm NACA-0015 a i r f o i l i n the t e s t s e c t i o n 195 192 192 193 193 194 x i x i L i s t o f T a b l e s Page Tabl e 1. A i r f o i l p r o f i l e c o o r d i n a t e s 196 Table 2. Free a i r a i r f o i l c o e f f i c i e n t s : Theory 197 Table 3. A i r f o i l and w a l l c o n f i g u r a t i o n s examined 198 t h e o r e t i c a l l y T able 4. A i r f o i l and endp l a t e l o a d i n g s 203 Tabl e 5. Windtunnel balance r e s u l t s - C l a r k - Y a i r f o i l s 204 Table 6. Windtunnel balance r e s u l t s - NACA-0015 219 a i r f o i l s T a b l e 7. Windtunnel balance r e s u l t s - Joukowsky 234 a i r f o i l T a b l e 8. Q u a n t i t i e s d e r i v e d from b a l a n c e r e s u l t s 238 Ta b l e 9. P r e s s u r e c o e f f i c i e n t s f o r NACA-0015 a i r f o i l 243 Table 10. P r e s s u r e c o e f f i c i e n t s f o r Joukowsky a i r f o i l 246 Table A10 Equ a t i o n s f o r the computer program of 249 Appendix 10 x i v N o t a t i o n A.., B.., C.. m a t r i c e s o f d i s t u r b a n c e v e l o c i t i e s . D i D i D i c a i r f o i l chord c. . element of the m a t r i x C.. J i 31 C_ = D/qc drag c o e f f i c i e n t C = L/qc l i f t c o e f f i c i e n t C = Mo/qc 2 midchord p i t c h i n g moment Mo CM = Mc/qc 2 q u a r t e r c h o r d p i t c h i n g moment t ' * C n = measured p r e s s u r e c o e f f i c i e n t v q C_ average p r e s s u r e c o e f f i c i e n t on s t r e a m l i n e C = 1- (v t / u ) 2 c a l c u l a t e d p r e s s u r e c o e f f i c i e n t i d. element o f column v e c t o r o f approach f l o w 1 boundary c o n d i t i o n s ds_.,dXj,dy^. s u r f a c e element l e n g t h d i f f e r e n t i a l s H windtunnel t e s t s e c t i o n h e i g h t (or t o t a l head) K(s) p o r o s i t y parameter f o r l o n g i t u d i n a l l y s l o t t e d w a l l s m = l i f t - c u r v e s l o p e it outward s u r f a c e normal OAR t r a n s v e r s e l y - s l o t t e d w a l l open a r e a r a t i o p l o c a l s t a t i c p r e s s u r e P(s) p o r o s i t y parameter f o r porous o r p e r f o r a t e d w a l l s q = -ipU 2 dynamic p r e s s u r e r . .,r(PQ) d i s t a n c e between s u r f a c e elements Re Reynolds number X V s d i s t a n c e along the s u r f a c e As. l e n g t h o f s u r f a c e element 3 U magnitude of approach flow v e l o c i t y V.,V ,V. ,V ,V : v e l o c i t y induced by a s u r f a c e element l n . ' t . x . y . 2 * . _^ x x 1 1 approach f l o w v e l o c i t y , magnitude U x.,y. C a r t e s i a n axes f i x e d t o the j - t h surface, element 3 3 X,Y • wind axes, w i t h X - a x i s i n the flow d i r e c t i o n x aerodynamic c e n t e r d i s t a n c e ac x 0 midchord d i s t a n c e a a i r f o i l i n c i d e n c e r c i r c u l a t i o n Y ,v , ;•• s u r f a c e v o r t e x element s t r e n g t h d e n s i t y ° y V y s u r f a c e source element s t r e n g t h d e n s i t y d i s t u r b a n c e v e l o c i t y p o t e n t i a l 8 i n c l i n a t i o n o f s u r f a c e element w.r.t. X - a x i s 3 p f l u i d d e n s i t y dC T = ^-Mq midchord p i t c h i n g moment curve s l o p e \\) stream f u n c t i o n S u b s c r i p t s : F f r e e a i r v a l u e S s o l i d w a l l v a l u e L lower s u r f a c e t t a n g e n t i a l d i r e c t i o n n normal d i r e c t i o n T windtunnel v a l u e s streamwise d i r e c t i o n U upper s u r f a c e oo upstream- undisturbed- flow c o n d i t i o n — • -1 __. I n t r o d u c t i o n . I n t h e s u b s o n i c w i n d t u n n e l t a s t i n . g o i a i r f o i l s e c t i o n s , t h e e x i s t i n g t h e o r y f o r c o r r e c t i o n s t o t h e measured d a t a f o r t h e e f f e c t s o f w i n d t u n n e l w a l l c o n s t r a i n t s i s s a t i s f a c t o r y f o r w i n d t u n n e l s w i t h s o l i d w a l l s i n w h i c h t h e t e s t a i r f o i l s a r e s m a l l r e l a t i v e t o t h e t e s t s e c t i o n c r o s s s e c t i o n s , and d e v e l o p r e l a t i v e l y s m a l l l i f t c o e f f i c i e n t s . However, c u r r e n t r e s e a r c h on h i g h - l i f t a i r f o i l s e c t i o n s r e q u i r e s t e s t i n g a t v e r y h i g h l i f t c o e f f i c i e n t s , and t h e use o f r e l a t i v e l y l a r g e m o d e ls t o g i v e s u f f i c i e n t l y h i g h R e y n o l d s numbers. Under t h e s e c o n d i t i o n s , t h e w a l l c o r r e c t i o n s i n w i n d t u n n e l s w i t h s o l i d w a l l s may become u n a c c e p t a b l y l a r g e , u n l e s s w i n d t u n n e l s w i t h v e r y l a r g e t e s t c r o s s s e c t i o n s a r e a v a i l a b l e - Such w i n d t u n n e l s a r e e x p e n s i v e t o b u i l d and o p e r a t e , s o a method o f m o d i f i c a t i o n o f e x i s t i n g s m a l l e r w i n d t u n n e l s , t h a t would r e d u c e o r e l i m i n a t e t h e s e l a r g e w a l l c o r r e c t i o n s , would be most d e s i r a b l e . S i n c e t h e m a j o r c o r r e c t i o n s t o measured d a t a i n w i n d t u n n e l s w i t h s o l i d w a l l s a r e o f o p p o s i t e s i g n f r o m t h o s e f o r w i n d t u n n e l s w i t h open j e t s , an o b v i o u s p o s s i b i l i t y t o e x p l o r e i s t h e u s e o f p a r t l y s o l i d - p a r t l y open w a l l s , t o p r o d u c e c a n c e l l i n g e f f e c t s . Two s u c h f o r m s o f w i n d t u n n e l w a l l have been c o n s i d e r e d i n . r e c e n t y e a r s f o r t h i s p u r p o s e , w a l l s w i t h narrow l o n g i t u d i n a l s l o t s , and w a l l s w i t h a p a t t e r n o f s m a l l h o l e s . T h e o r i e s have b e e n p r e s e n t e d f o r p r e d i c t i o n of t h e c o r r e s p o n d i n g w a l l c o r r e c t i o n s . U n f o r t u n a t e l y , e x p e r i m e n t s h a v e shown t h a t t h e e x i s t i n g 2 t h e o r y f o r w a l l s w i t h l o n g i t u d i n a l s l o t s i s u s e l e s s f o r t h e p r e s e n t p u r p o s e s , and the t h e o r y f o r porous w a l l s i s i m p r a c t i c a l t o a p p l y . An e m p i r i c a l p o r o s i t y f a c t o r i s needed, which depends on the w a l l geometry and on the t e s t model. In t h e p r e s e n t t h e s i s , a t w o - d i m e n s i o n a l p o t e n t i a l f l o w t h e o r y i s d e v e l o p e d f o r a d i f f e r e n t p a r t l y s o l i d - p a r t l y open w a l l s ystem, and the r e s u l t s o f e x p e r i m e n t s d e s i g n e d t o t e s t t h e t h e o r y a r e p r e s e n t e d . 3 2-. Survey, of Windtunnel Wall Correc t ion Met hod s.. 2^ 1_ Conventional Linear Theor ies . In windtunnel t e s t ing of two-dimensional a i r f o i l s e c t i o n s at subsonic speeds , the windtunnel wal l cons tra in t i n f l u e n c e s the measured forces , moments, and pressure d i s t r i b u t i o n s . The current theories f or the correc t ions to be appl i ed to the measured values to account for wal l e f fec t s are s a t i s f a c t o r y only when the tes t a i r f o i l s are small r e l a t i v e to the windtunnel c ros s sec t i on , and develop smal l l i f t c o e f f i c i e n t s . Current prac t i ce for such cases i s wel l summarized in a report by Garner et a l [ 1 ]. The e s s e n t i a l feature of current wal l c o r r e c t i o n theor ie s i s the s e l ec t ion of an appropriate system of source , vortex and doublet s i n g u l a r i t i e s , together with images of the s i n g u l a r i t i e s i n the windtunnel boundaries, such that the flow c o n d i t i o n s at the boundaries are s a t i s f i e d . The l i f t - p r o d u c i n g c h a r a c t e r i s t i c s of the a i r f o i l ( incidence, camber), the a i r f o i l t h i c k n e s s , and the a i r f o i l wake, are associated with d i s t r i b u t i o n s of v o r t i c e s , doublets and sources r e s p e c t i v e l y . The c h a r a c t e r i s t i c s of the windtunnel walls are then simulated by a s s o c i a t i n g an appropriate set of images with each s i n g u l a r i t y i n .the f i e l d . For example, a s o l i d wall boundary cond i t ion requires zero disturbance v e l o c i t y normal to the boundary. This c o n d i t i o n may be simulated by an i n f i n i t e set of images i n the windtunnel wal l s ; sources, and doublets or iented i n the streamwise d i r e c t i o n , have images of the same s i g n ; v o r t i c e s have images of a l t e r n a t i n g s ign . For further d e t a i l s , see A l l e n and V i n c e n t i 4 [ 2 ] , and G o l d s t e i n [ 3 ] . When the net e f f e c t of the systems o f s i n g u l a r i t i e s and images has been c a l c u l a t e d , the v e l o c i t i e s t h e r e b y i n d u c e d a t the a i r f o i l may be d e t e r m i n e d . F o r s i m p l i c i t y both i n i n t e r p r e t a t i o n and a p p l i c a t i o n , i t i s u s e f u l i f the net e f f e c t o f a l l the systems i s the d i r e c t sum of the i n d u c e d e f f e c t s o f each of the i n d i v i d u a l sys tems . In terms of the c o r r e s p o n d i n g f i e l d e q u a t i o n s , a s u p e r p o s i t i o n i s p o s s i b l e i f the e x a c t boundary c o n d i t i o n s may be l i n e a r i z e d . The l i n e a r a p p r o x i m a t i o n s i n t u r n are v a l i d o n l y f o r s m a l l i n d u c e d v e l o c i t i e s , which i m p l i e s a s m a l l , t h i n , s l i g h t l y cambered a i r f o i l at low i n c i d e n c e . An a l t e r n a t i v e to the images t e c h n i q u e , which y i e l d s s i m i l a r r e s u l t s , i s t h e conforraa l mapping t e c h n i q u e deve loped by Woods [4 ] , The problem . o f f i n d i n g v e l o c i t y , p o t e n t i a l s i n a complex domain bounded by an a i r f o i l and w i n d t u n n e l w a l l s i s t r a n s f o r m e d , b y . c o n f o r m a l mappings , t o an e q u i v a l e n t , b u t g e o m e t r i c a l l y s i m p l e r , boundary v a l u e prob lem- The problem i s thus reduced t o the d e t e r m i n a t i o n of,, an a n a l y t i c f u n c t i o n on a t r a n s f o r m e d domain whose r e a l a n d / o r i m a g i n a r y p a r t s a r e p r e s c r i b e d on the boundary . Woods' t e c h n i q u e r e s u l t s i n i n t e g r a l e q u a t i o n s f o r the mapping f u n c t i o n s , and u s u a l l y n u m e r i c a l methods are r e q u i r e d f o r t h e i r s o l u t i o n . A l i n e a r i z e d form of h i s t h e o r y agrees wi th the r e s u l t s t o be found i n G a r n e r e t a l [ 1 ] . F o r the case of a t h i n f l a t p l a t e between p a r a l l e l b o u n d a r i e s , the s o l u t i o n s o f Havelock [ 5 ] and Tomot ika [ 6 ] a r e a v a i l a b l e u s e s t h a t Havelock uses the method of conformal t r a n s f o r m a t i o n s . o f images w h i l e The r e s u l t s are 5 Tomotika s i m i l a r . In r e c e n t p u b l i c a t i o n s , de Jager and van de Vooren [ 7 ] , and de V r i e s and S c h i p h o l t [ 8 ] , use image methods f o r t h i n a i r f o i l s with hinged f l a p s , between s o l i d windtunnel w a l l s . For porous or p e r f o r a t e d windtunnel w a l l s , Baldwin e t a l [ 9 ] propose an " e q u i v a l e n t homogeneous w a l l boundary c o n d i t i o n " . dary c o n d i t i o n i s a combination of the f o r s o l i d w a l l s and f o r an open j e t . ndary c o n d i t i o n s ar e expressed i n terms of a o c i ty p o t e n t i a l which f o r i n c o m p r e s s i b l e ace's e q u a t i o n . T he g e n e r a l l i n e a r w a l l ay be w r i t t e n : «(»>!!•+ »!.>!!• cowsS - o. F o r a s o l i d boundary where t h e r e i s z e r o d i s t u r b a n c e f l o w normal to the boundary, e q u a t i o n (2.1) has the form !*• = 0 • . (2.2) 8n . For an open j e t boundary i t i s assumed t h a t the d i s t u r b a n c e from the t e s t a i r f o i l at the j e t boundary i s s m a l l . The l i n e a r i z e d c o n d i t i o n of constant p r e s s u r e can be i n t e r p r e t e d , using B e r n o u i l l i ' s e q u a t i o n , as r e q u i r i n g zero streamwise d i s t u r b a n c e v e l o c i t y . Hence f o r an open j e t boundary, c o n d i t i o n (2.1) becomes ' 6 3* „ ' F o r p o r o u s o r p e r f o r a t e d w a l l s t h e p r e s s u r e d r o p a c r o s s t h e w a l l due t o t h e c r o s s - f l o w i s assumed t o be p r o p o r t i o n a l t o t h e n o r m a l d i s t u r b a n c e v e l o c i t y a t t h e w a l l . The r e s u l t i n g l i n e a r r e l a t i o n b e t w e e n t h e c r o s s - f l o w a n d s t r e a m w i s e d i s t u r b a n c e v e l o c i t y c o m p o n e n t s r e q u i r e s A s i m i l a r e x p r e s s i o n , b u t w i t h a d i f f e r e n t v a l u e o f P { s ) , i s u s e d f o r a w a l l w h e r e t h e p o r o s i t y c o n s i s t s o f t r a n s v e r s e s l a t s . F o r an i n f i n i t e l e n g t h t e s t s e c t i o n w a l l o f c l o s e l y s p a c e d t r a n s v e r s e s l a t s , M aeder a n d Hood [ 1 0 ] , a n d Woods [ 4 ] d e d u c e a c o n s t a n t v a l u e f o r P (s) : P = t a n g ) . (2.5) •2d I n e q u a t i o n ( 2 . 5 ) , »a' i s t h e s l o t w i d t h a n d 'd» i s t h e s l a t s p a c i n g ; a/d i s t h e o p e n a r e a r a t i o (OAB). F o r w a l l s w i t h l o n g i t u d i n a l s l o t s , a p o t e n t i a l f l o w m o d e l o f t h e c r o s s - f l o w t h r o u g h t h e s l o t s r e q u i r e s t h e d i s t u r b a n c e p o t e n t i a l t o v a n i s h and t h e p r e s s u r e t o be c o n s t a n t , i n t h e s l o t s . Hence 7 | i + K ( s ) ^ =• 0 . • •'• • (2.6). 8s 3s8n ' Maeder and Wood [ 10 ] g i v e , f o r an i n f i n i t e l e n g t h t e s t s e c t i o n w a l l o f u n i f o r m l y s p a c e d l o n g i t u d i n a l s l o t s , t h e v a l u e K = £ l o g csc(|§] , ' (2.7) where a/d i s a g a i n t h e OAS. 8 2.Z.Z. E ^ s u l t s of Convantional L i n e a r Tneories_. In the t h e o r e t i c a l determination of homogeneous boundary c o n d i t i o n s , the d e t a i l s of the s l o t or hole geometry can be, used to c o n s t r u c t an exact boundary c o n d i t i o n by, f o r example, the a p p l i c a t i o n of Kutta c o n d i t i o n s to the edges of s l o t s or h o l e s . Then by examining the flow through the w a l l from a poin t many s l o t (hole) widths away from the wa l l s the flow d e t a i l s due to the w a l l geometry are not f e l t , but only some "averaged" f l o w f i e l d i s detected. The exact boundary c o n d i t i o n i s thus re p l a c e d by a l i n e a r i z e d , averaged boundary c o n d i t i o n . In app l y i n g t h i s boundary c o n d i t i o n , the w a l l i s regarded as being g e o m e t r i c a l l y homogeneous. The advantage i s that a s i n g l e averaged boundary c o n d i t i o n can be a p p l i e d uniformly over.the plane of the w a l l so that i t i s not necessary to have separate boundary c o n d i t i o n s a p p l i e d i n s l o t s (holes) and on s o l i d s e c t i o n s . This averaging e f f e c t e x p l a i n s why the w a l l boundary c o n d i t i o n f o r porous, p e r f o r a t e d and trans v e r s e s l o t t e d w a l l s are s i m i l a r . For d e t a i l s see Maeder and Wood [ 10 ] . The same "averaging" e f f e c t , i f a p p l i e d to l o n g i t u d i n a l s l o t s , leads to erroneous p r e d i c t i o n s . In f a c t , the l o n g i t u d i n a l s l o t s render,the flow three-dimensional by imposing spanwise v a r i a t i o n s on the b a s i c two-dimensional flow c o n d i t i o n s . On the assumption t h a t , the flow i s quasi-plane, that i s the spanwise v a r i a t i o n s are only a small p e r t u r b a t i o n of the bas i c two-dimensional f l o w , an averaged.boundary c o n d i t i o n f o r the b a s i c two-dimensional flow can be deduced. For d e t a i l s see Woods [ 4 ] . In the use of such g e o m e t r i c a l l y homogeneous l i n e a r 9 boundary c o n d i t i o n s , a l l d e t a i l s of s l o t or p e r f o r a t i o n geometry, are l o s t , i n p a r t i c u l a r , t h e i r o r i e n t a t i o n ( l o n g i t u d i n a l or t r a n s v e r s e ) . Only the e f f e c t s of bulk p r o p e r t i e s such as -the p o r o s i t y or-CAE are r e t a i n e d . Wood [11] shows, f o r example t h a t the OAR f o r l o n g i t u d i n a l s l o t s would need to be l e s s than 1%, to achieve a boundary c o n d i t i o n a p p r e c i a b l y d i f f e r e n t from.-;, the open. j e t case. In p r a c t i c e , at such a s m a l l OAR, r e a l f l u i d e f f e c t s would be important, so a p o t e n t i a l flow model f o r the c r o s s - f l o w would not be v a l i d . Moreover, Wood's a n a l y s i s of t h i s boundary c o n d i t i o n i n d i c a t e s that only c r o s s - f l o w v e l o c i t i e s of l e s s than 0.5% of the mean flow would be i n keeping with the arguments f o r the l i n e a r i z a t i o n of terms i n v o l v e d i n the d e r i v a t i o n of t h i s boundary c o n d i t i o n . I n v e s t i g a t i o n s by Parkinson and Lim [ 1 2 ] , and Mokry [ 1 3 ] have found that the " p o r o s i t y parameter" P(s) i s not simply an e m p i r i c a l f u n c t i o n of w a l l OAR, but must be determined e m p i r i c a l l y f o r each a i r f o i l under t e s t . The usual procedure i s to choose a value of P(s) to match l i f t or pressure data taken at a p a r t i c u l a r i n c i d e n c e and f o r a p a r t i c u l a r s i z e of a i r f o i l and then to t r y to use t h i s same value of P(s) t o c a l c u l a t e the w a l l e f f e c t at other i n c i d e n c e s and f o r other s i z e s of a i r f o i l . G e n e r a l l y , the r e s u l t s are that P(s) depends on the w a l l OAR and the p a r t i c u l a r a i r f o i l under t e s t , an impos s i b l e s i t u a t i o n f o r the p r a c t i c a l use of such l i n e a r porous w a l l boundary c o n d i t i o n s . Figure 2.1 from [ 1 2 ] , f o r example, shows tha t f o r two d i f f e r e n t a i r f o i l p r o f i l e s t e s t e d , there are two completely d i f f e r e n t v a r i a t i o n s of " p o r o s i t y parameter" with OAR, and ne i t h e r agrees with the t h e o r e t i c a l v a r i a t i o n of r e l a t i o n (2-5). 10 Other r e s u l t s by Parkinson.and Lim [ 1 2 ] , Parker [ 1 4 ] , and Tsen [ 1 5 ] , have shown that the theory f o r the l o n g i t u d i n a l w a l l s l o t parameter K (s ) i s not useable. Figure 2.2, from [ 1 2 ] , f o r example, shows that f o r four a i r f o i l s of d i f f e r e n t s i z e , of the same p r o f i l e , the t h e o r e t i c a l w a l l i n t e r f e r e n c e curves corresponding to the values of w a l l OAR t e s t e d , are c l o s e l y grouped as though a l l of the w a l l c o n f i g u r a t i o n s were e f f e c t i v e l y open. C a t h e r a l l [16] s t a t e s t h a t "the usefulness of the method i s l i m i t e d by the doubts about t h i s ( l i n e a r homogenous w a l l boundary) c o n d i t i o n " . This i s c l e a r l y the case f o r measurements on high l i f t devices where the p r e d i c t e d w a l l c o r r e c t i o n s are of the same order as the measured values themselves. The great disadvantage of more p h y s i c a l l y a p p r o p r i a t e n o n l i n e a r w a l l boundary c o n d i t i o n s i s that the mathematical s o l u t i o n s f o r most boundary problems depend on such boundary c o n d i t i o n s being l i n e a r as, f o r example, i n complex v a r i a b l e theory. Wood [11] has developed a n o n l i n e a r boundary c o n d i t i o n fo r a two-dimensional Helmholtz j e t i s s u i n g from l o n g i t u d i n a l s l o t s , where the " p o r o s i t y " i s a f u n c t i o n of the c r o s s - f l o w v e l o c i t y . His a n a l y s i s i s f o r a n o n l i f t i n g a i r f o i l ; the extension to the case of a l i f t i n g a i r f o i l does not appear to have been made. Sears [17] comments t h a t : "Even i n those (flow) regimes where the flow p e r t u r b a t i o n s due to tunnel boundaries can be estimated, there i s a b a s i c flaw i n the idea of " c o r r e c t i n g " 11 measured aerodynamic data, because such c o r r e c t i o n r e q u i r e s t h a t the e f f e c t s of such p e r t u r b a t i o n s be known. I f the f i e l d of extraneous v e l o c i t i e s i s other than a uniform change of i n c i d e n c e , than i n some of the most important t e c h n i c a l cases these e f f e c t s are not known and cannot .be c a l c u l a t e d " . Figure 2.2, from [ 1 2 ] , a l s o shows that the theory f o r s o l i d w a l l s gives e x c e l l e n t agreement with the data. Therefore i n the absence of improvements to the theory f o r s l o t t e d - or p e r f o r a t e d - w a l l c o r r e c t i o n s , i t seems a d v i s a b l e to c a r r y out low-speed two-dimensional a i r f o i l t e s t s , even f o r l a r g e models developing high l i f t c o e f f i c i e n t s , i n c o n v e n t i o n a l windtunnels with s o l i d w a l l s . 12 2^ .3 Low C o r r e c t i o n T e s t C o n f i g u r a t i o n s . An a l t e r n a t i v e a p p r o a c h i s ' t o m o d i f y t h e w a l l s o f t h e w i n d t u n n e l t o p r o v i d e f l o w c o n d i t i o n s a s c l o s e a s p o s s i b l e t o a f r e e - a i r ( u n c o n f i n e d ) t e s t e n v i r o n m e n t . Thus t h e w a l l ' , c o r r e c t i o n s w o u l d a u t o m a t i c a l l y be s m a l l . One a p p r o a c h i s t h a t o f t h e " s e l f - c o r r e c t i n g " w i n d t u n n e l [ 1 7 ] w h e r e b y an a r r a y o f s e n s o r s ( l o c a t e d on a c o n v e n i e n t " c o n t r o l s u r f a c e " i n s i d e t h e t u n n e l b u t n o t i n t h e w a l l b o u n d a r y l a y e r s ) m e a s u r e , s a y , t h e f l o w s p e e d a n d i n c l i n a t i o n t h e r e . A c a l c u l a t i o n i s p e r f o r m e d t o d e t e r m i n e i f t h e s e m e a s u r e d v a l u e s a r e c o m p a t i b l e w i t h p r e v i o u s l y c a l c u l a t e d v a l u e s o f t h e same v a r i a b l e s f o r an i m a g i n a r y i n f i n i t e i n v i s c i d f l o w f i e l d a b o u t t h e t e s t a i r f o i l . I f n o t , a d j u s t m e n t s a r e made, i t e r a t i v e l y , u n t i l s u c h c o n d i t i o n s a r e met. T h i s c o u l d be a c h i e v e d t h r o u g h t h e u s e o f f l e x i b l e w a l l s , a n d / o r w a l l s e c t i o n s o f v a r i a b l e p o r o s i t y . O b v i o u s d i s a d v a n t a g e s a r e t h e c o s t o f " o n - l i n e " c o m p u t i n g f a c i l i t i e s p l u s t h e l a r g e number o f p r e s s u r e t r a n s d u c e r s r e q u i r e d t o e x t r a c t and p r o c e s s t h e f l o w m e a s u r e m e n t s . W h a t e v e r t y p e o f t e s t s e c t i o n i s c h o s e n , t h e " p o r o s i t y " v a r i a t i o n must p r o d u c e r e s u l t s l i k e t h o s e o f F i g u r e 2 . 3 , i n o r d e r t o s i m u l a t e c o r r e c t l y t h e f r e e - a i r f l o w f i e l d . How t h i s i s a c c o m p l i s h e d m e c h a n i c a l l y i s up t o t h e w i n d t u n n e l d e s i g n e r . 13 Is. h New S o l t t e d - S a l l T h e o r y . 3.1 A P h y s i c a l B a s i s f o r t h e New T h e o r y . One r e a s o n f o r t h e l a c k o f s u c c e s s o f t h e l o n g i t u d i n a l - s l o t and p o r o u s - w a l l t h e o r i e s i s t h e o c c u r r e n c e e x p e r i m e n t a l l y o f s e p a r a t e d f l o w s i n t h e s l o t s a nd h o l e s . S u c h f l o w s a r e n o t a c c o u n t e d f o r i n t h e t h e o r i e s , p r i m a r i l y a s t h e y a d d u n d e s i r a b l e n o n l i n e a r i t i e s t o t h e t h e o r i e s . I n a d d i t i o n , t h e s e f l o w s e p a r a t i o n s s e r i o u s l y d e g r a d e t h e m a i n f l o w i n t h e v i c i n i t y o f t h e w a l l s . The a p p r o a c h h e r e ( s e e F i g u r e 3 . 1 ) , u s e s t r a n s v e r s e w a l l s l o t s , w i t h s y m m e t r i c a l a i r f o i l - s h a p e d s o l i d s l a t s . The f l o w i n c l i n a t i o n s n e a r t h e w a l l w i l l be s m a l l e v e n f o r a n e a r l y u n c o n f i n e d f l o w f i e l d . Hence a l l t h e w a l l s l a t s w i l l o p e r a t e w i t h i n t h e i r u n s t a l l e d i n c i d e n c e r a n g e , s o t h a t f l o w s n e a r t h e w a l l w i l l be f r e e o f s e p a r a t e d wakes. M o r e o v e r , o n l y t h e w a l l o p p o s i t e t h e n e g a t i v e p r e s s u r e s i d e o f t h e t e s t a i r f o i l i s s l o t t e d . One r e a s o n f o r t h i s c h o i c e c a n be s e e n f r o m F i g u r e 3.2 w h i c h c o m p a r e s t h e o r e t i c a l p r e s s u r e d i s t r i b u t i o n s ( c a l c u l a t e d by t h e m e t h o d s o f s e c t i o n 3.2) b e t w e e n s o l i d w a l l s and i n f r e e a i r , f o r a 14% C l a r k - Y a i r f o i l . : The r a t i o o f a i r f o i l c h o r d ' c ' t o w i n d t u n n e l t e s t s e c t i o n s i z e * H , - i s l a r g e a t 0.72, a n d t h e i n c i d e n c e * a* i s e x t r e m e a t 20 d e g r e e s , t o c r e a t e a l a r g e w a l l e f f e c t . T h e s e p r e s s u r e d i s t r i b u t i o n s show t h a t a l m o s t a l l o f t h e w a l l e f f e c t i s t o i n c r e a s e t h e m a g n i t u d e o f t h e n e g a t i v e p r e s s u r e on t h e u p p e r s u r f a c e o f t h e a i r f o i l . The e f f e c t on t h e u n d e r s i d e p r e s s u r e i s s o s m a l l a s t o be n e g l i g i b l e , e v e n i n t h i s r a t h e r e x t r e m e c a s e . 14 Another reason f o r using only one s l o t t e d w a l l i s to s i m p l i f y the flow f i e l d o p p o s i t e the pressure s i d e of the t e s t a i r f o i l . A s l o t t e d lower w a l l would allow an i n f l o w of low energy a i r from w i t h i n a plenum chamber (surrounding the s l o t t e d wall) to enter the t e s t s e c t i o n upstream of the a i r f o i l . T h i s i n f l o w would c o n s i s t of a shear l a y e r and i t s a s s o c i a t e d t u r b u l e n t mixing and would degrade the q u a l i t y of the, main flow, i n the v i c i n i t y of the a i r f o i l lower s u r f a c e . There w i l l be a c o r r e s p o n d i n g outflow from the t e s t s e c t i o n back i n t o the plenum downstraam of the t e s t a i r f o i l . On the other hand, on the w a l l o p p o s i t e the n e g a t i v e pressure s i d e , upstream of the t e s t a i r f o i l , there w i l l be an outflow from the t e s t s e c t i o n i n t o the plenum. The shear l a y e r so formed and i t s a s s o c i a t e d t u r b u l e n t mixing w i l l be s h i e l d e d from the t e s t a i r f o i l by the presence of the a i r f o i l - s h a p e d w a l l s l a t s with t h e i r boundary c o n d i t i o n s impressed on the f l o w . I f t h i s shear l a y e r were i d e a l i z e d as a c o n s t a n t - p r e s s u r e f r e e s t r e a m l i n e , any i n c o r r e c t n e s s i n pressure or l o c a t i o n i n such a r e p r e s e n t a t i o n of t h i s s t r e a m l i n e should have only secondary e f f e c t s on the t e s t a i r f o i l . The plenum a i r w i l l e n t e r the t e s t s e c t i o n downstream of the t e s t a i r f o i l ; however, i t s e f f e c t on the t e s t a i r f o i l by e n t e r i n g t h e r e w i l l be much s m a l l e r than f o r any a i r e n t e r i n g the t e s t s e c t i o n upstream of the t e s t a i r f o i l . As with i r r o t a t i o n a 1 f o r low-speed most windtunnel w a l l c o r r e c t i o n t h e o r i e s , flow i s assumed, and, s i n c e the method i s designed, h i g h - l i f t t e s t i n g , an i n c o m p r e s s i b l e p o t e n t i a l 15 f l o w method can be used. The t e s t a i r f o i l (and i t s component f l a p s ) and the a i r f o i l - s h a p e d w a l l s l a t s a r e a l l t r e a t e d as l i f t i n g a i r f o i l s . Hence the f l o w s a t i s f i e s the u s u a l t a n g e n t -v e l o c i t y and t r a i l i n g - e d g e K u t t a c o n d i t i o n s . The f l o w ' p a s t t h e s o l i d w a l l s e c t i o n s s a t i s f i e s the t a n g e n t - v e l o c i t y boundary c o n d i t i o n . 16 3.2.2 F o r m u l a t i o n o f an E x a c t N u m e r i c a l Theory... The f o r m u l a t i o n h e r e i s a t w o - d i m e n s i o n a l p o t e n t i a l , f l o w t h e o r y , based, on t h e s u r f a c e s i n g u l a r i t y d i s t r i b u t i o n method o f A.H.0. S m i t h and h i s c o l l e a g u e s [ 1 8 ] . I n t h i s method, t h e s u r f a c e s o f t h e s o l i d w a l l s , t h e a i r f o i l - s h a p e d s l a t s i n t h e s l o t t e d w a l l , and t h e t e s t a i r f o i l w i t h i t s component f l a p s , a r e r e p r e s e n t e d by a d i s t r i b u t i o n o f s o u r c e and v o r t e x e l e m e n t s . A n o r m a l - v e l o c i t y b o u n d a r y c o n d i t i o n w i l l p r e s c r i b e e i t h e r z e r o n o r m a l v e l o c i t y , on s o l i d s u r f a c e s , o r n o n - z e r o n o r m a l v e l o c i t y , f o r s u c t i o n o r b l o w i n g t h e r e . S o u r c e e l e m e n t s a r e t h e r e f o r e d i s t r i b u t e d o v e r any s u r f a c e on w h i c h a n o r m a l - v e l o c i t y b o u n d a r y c o n d i t i o n i s s p e c i f i e d . V o r t e x e l e m e n t s a r e used t o s e t t h e n e t c i r c u l a t i o n a b o u t a c l o s e d l i f t i n g body. T h e r e f o r e v o r t e x e l e m e n t s a r e d i s t r i b u t e d o v e r any s u r f a c e on which a t a n g e n t - v e l o c i t y b o u n d a r y c o n d i t i o n i s s p e c i f i e d . Hence s o u r c e e l e m e n t s o n l y a r e d i s t r i b u t e d o v e r t h e s o l i d w a l l s e c t i o n s , w h i l e b o t h s o u r c e and v o r t e x e l e m e n t s a r e d i s t r i b u t e d o v e r t h e s u r f a c e s o f t h e a i r f o i l - s h a p e d w a l l s l a t s a n d t h e t e s t a i r f o i l and i t s f l a p s . The v e l o c i t i e s a t any p o i n t i n t h e f l o w f i e l d due t o a l l s u c h s o u r c e s and v o r t i c e s a r e c a l c u l a t e d d i r e c t l y . The u s u a l f l o w b o u n d a r y c o n d i t i o n of~ z e r o n o r m a l v e l o c i t y i s a p p l i e d a t a l l s o l i d s u r f a c e s . In a d d i t i o n , a f i n i t e - v e l o c i t y K u t t a c o n d i t i o n i s a p p l i e d a t t h e t r a i l i n g e d g e s o f t h e w a l l s l a t s and t e s t a i r f o i l , i n c l u d i n g f l a p s . • A g a i n i s t h e d i s t u r b a n c e v e l o c i t y p o t e n t i a l , w hich 17 .es Laplace's equation, vanishes at i n f i n i t y , and. s a t i s f i e s the above boundary c o n d i t i o n s . The p o t e n t i a l at a point P due to a s i n g l e t h r e e -dimensional, point source s i n g u l a r i t y at a point Q i s where m i s the volume flow r a t e of f l u i d emitted .by the source and r (PQ) i s the d i s t a n c e between the p o i n t s P and Q. The t o t a l p o t e n t i a l due to a l l such sources d i s t r i b u t e d over a s i n g l e surface S i s 4>(P) 0 ( Q ) d S , ( 3 .2 ) s r(PQ) where o(Q) i s the source s t r e n g t h d e n s i t y , i n c l u d i n g the f a c t o r 1/4IT , of the source element at Q. Since the disturbance v e l o c i t y i s the gradient of the v e l o c i t y p o t e n t i a l , the n o r m a l - v e l o c i t y boundary c o n d i t i o n a t a s u r f a c e can be expressed as 8© •> -> 9n = ~ V^-n + F, (3.3) where n i s the outward surface normal,, and » the undisturbed oo flow at upstream i n f i n i t y . The f u n c t i o n F denotes the value the normal v e l o c i t y must take at the a i r f o i l s u r f a c e . ? i s zero f o r a s o l i d (impermeable) s u r f a c e , but non-zero f o r s u c t i o n or blowing there. 1 8 A n a l y s i s ( H ess and S m i t h [ 1 8 ] ) shows t h a t t h e n o r m a l v e l o c i t y a t a p o i n t P on a s u r f a c e S, due t o a s o u r c e s t r e n g t h d e n s i t y d i s t r i b u t i o n a (Q) on S, c o n s i s t s o f two p a r t s . The " l o c a l " c o n t r i b u t i o n i s 2fro"(p) due t o t h e s o u r c e e l e m e n t a ( P ) a t P. The " f a r f i e l d " c o n t r i b u t i o n i s f _d_ dn 1 ) | r ( P Q ) J a ( Q ) d S (3.4) due t o t h e summation- o f t h e e f f e c t s o f a l l o t h e r s o u r c e e l e m e n t s a(Q) a t p o i n t s Q on S. The r e s u l t i n g e x p r e s s i o n o f t h i s b o u n d a r y c o n d i t i o n 2 i r a ( P ) - 9h i r ( P Q ) J a ( Q ) d S = - V - n + F oo ( 3 . 5 ) p r o d u c e s an i n t e g r a l e q u a t i o n f o r t h e unknown s o u r c e s t r e n g t h d e n s i t y d i s t r i b u t i o n f u n c t i o n c ( Q ) . T h i s e q u a t i o n i s a F r e d h o l m i n t e g r a l e q u a t i o n o f t h e s e c o n d k i n d . E x i s t e n c e a n d u n i q u e n e s s t h e o r e m s f o r s u c h e q u a t i o n s a r e w e l l known. The s u r f a c e S may be d i s j o i n t , b u t t h e o u t w a r d n o r m a l v e c t o r must be a c o n t i n u o u s f u n c t i o n o f p o s i t i o n . F o r a d i s c u s s i o n o f d i f f i c u l t i e s a s s o c i a t e d w i t h f u n c t i o n a l s i n g u l a r i t i e s i n s u c h s o u r c e d i s t r i b u t i o n s a t e d g e s o r c o r n e r s , s u c h a s a t an a i r f o i l t r a i l i n g - e d g e o r an u n f a i r e d w i n g - b o d y j u n c t i o n , s e e C r a g g s e t a l [ 1 9 ] . I n p r a c t i c e , t h e s u r f a c e s o f t h e s o l i d w a l l , t h e a i r f o i l -s h a p e d s l a t s , a n d t h e t e s t a i r f o i l and f l a p s , a r e r e p l a c e d by p o l y g o n a l e l e m e n t s . The c o n t i n u o u s d i s t r i b u t i o n o f s o u r c e s 19 thereby becomes a succession of f i n i t e d.istr ibuted-source each of these f i n i t e elements.was f l a t and of. constant uniform s t r e n g t h . S u c c e s s f u l refinements of the method have used h i g h e r -order polynomial curves f i t t e d to s e c t i o n s of the body s u r f a c e with the source s t r e n g t h d e n s i t y varying i n a l i n e a r or p a r a b o l i c way along these curved elements. For examples see Henshaw [20,21], or Hess [ 2 2 ] . The higher-order element shapes are needed f o r i n t e r n a l flow c a l c u l a t i o n s such as i n d u c t s , but f o r e x t e r n a l flow problems the f l a t elements give accurate r e s u l t s provided a l a r g e enough number of elements, i s used and t h e i r d i s p o s i t i o n on the body shape i s chosen c a r e f u l l y . Each v e l o c i t y boundary c o n d i t i o n i s a p p l i e d at a s i n g l e " c o n t r o l p o i n t " on each element. For f l a t elements a convenient choice i s the center of each element.. .Thus the exact i n t e g r a l equation f o r a continuous d i s t r i b u t i o n f u n c t i o n may be reduced to a set of N simultaneous l i n e a r a l g e b r a i c equations whose N unknowns are the s t r e n g t h s of the f i n i t e s u r f a c e elements. The above approximations become exact i n the l i m i t as N -»- °°. The method i s described as n u m e r i c a l l y exact i n the sense t h a t any degree of. accuracy may be obtained. By d e f i n i n g the l i n e a r operator elements. In the o r i g i n a l method of Smith and h i s c o l l e a g u e s . J JS. 3 _9_ dn • - as., 3^ X J J J (3.6) 20 the boundary condi t ion (3.5) appl ied at t h e . i - t h c o n t r o l point becomes N I A . . j = l a . = - V •n . +.F . . j 0 0 i 1 (3.7) This ind ica tes that A_^is the normal v e l o c i t y induced at a c o n t r o l point ' i ' by a unit strength source element . located at another point * j ' . Hence the " loca l" normal v e l o c i t y , ^ ± ± ' ^ s 2TT for a i l i= 1, 2, 3 , . . . N. . For the purposes of th i s problem, the three-dimensional point source of equation (3.1) must be integrated in to a f l a t two-dimensional d i s t r ibuted- sburce element; for the d e t a i l s see Appendix 1.. The uni t s of a (Q) are therefore: volume flow ra te per unit arc length along the contour per u n i t length i n the spanwise d i r e c t i o n . With respect to Cartes ian axes x and y f ixed to the j - t h j j element (Figure 3 .3 ) , the v e l o c i t y components induced at a point ' i ' by a source element at point ' j * are V = log K y % ) 2 + -yj) = 2 log R 2 (3.8) and V 2 j t a n -1 J 2" - tan -1 ( As, 1 y. = 2£2, (3.9) where x. and y. are the distances from the j - t h to the i - t h J J element; the j - t h element has length As . The v e l o c i t y f i e l d s j about a s i n g l e s o u r c e element a r e shown i n F i g u r e 3.'4. The d i r e c t i o n s of V v and 7„ a t ' i 1 a r e p a r a l l e l and normal t o t h e x. y. 3 3 d i r e c t i o n of the element a t ' j ' , r e s p e c t i v e l y . The i n v e r s e t a n g e n t s i n (3.9) a r e t o be e v a l u a t e d i n t h e range f - T r / 2 / +Tr/2) . The two i n v e r s e , t a n g e n t s may. be combined by means of the t a n g e n t law i n t o the a l t e r n a t i v e e x p r e s s i o n V = 2 t a n 1 Y3 Y. As. _ J i . l x j + y ? - ( ^ j ) 2 J (3.10) where t h i s s i n g l e i n v e r s e t a n g e n t i s t o be e v a l u a t e d i n t h e range (-1T, + Tr) by f a k i n g i n t o account t h e i n d i v i d u a l s i g n s o f t h e numerator and denominator of i t s argument. When c a l c u l a t i n g f l o w q u a n t i t i e s a t o f f - s u r f a c e p o i n t s which a r e c l o s e r t o t h e o r i g i n o f t h e element t h a n As/2, the f i r s t e x p r e s s i o n must be used. With r e s p e c t t o C a r t e s i a n "wind a x e s " X and Y, (X i s i n t h e wind d i r e c t i o n ) , t h e g-th s o u r c e element i s i n c l i n e d a t an a n g l e 8. t o t h e X - a x i s . Thus, A.. = V cos 9.-8. - V s i n ( 8 . - 8 . (3.11 i i y . i j x . i t v ' and B > ; L = V cos (6.-9.) + V s i n (9.-8.) .- (3.12) 3 3 1 2 Y3 1 :1 a r e the normal and t a n g e n t i a l v e l o c i t i e s r e s p e c t i v e l y i n d u c e d a t element ' i ' due to a u n i t s t r e n g t h d e n s i t y s o u r c e element a t a p o i n t ' j ' . -The " l o c a l " normal v e l o c i t y JL^ i s 2TT ; the " l o c a l " 22 t a n g e n t i a l v e l o c i t y 8 ^ i s z e r o . The d i r e c t i o n s o f a n d a t ' i» a r e n o r m a l ( p o s i t i v e o u t w a r d ) a n d p a r a l l e l ( p o s i t i v e c l o c k w i s e ) r e s p e c t i v e l y t o t h e d i r e c t i o n o f t h e e l e m e n t a t ' i ' . Hence f o r t h e e x t e r i o r f l o w a b o u t a s i n g l e c l o s e d c o n t o u r , t h e s o u r c e and v o r t e x e l e m e n t s a r e l a b e l l e d f o r c o m p u t a t i o n s i n a c l o c k w i s e o r d e r a b o u t t h e c o n t o u r . I n o r d e r t o f i x t h e c i r c u l a t i o n a b o u t a l i f t i n g b o d y , t h e u s u a l e q u a l - v e l o c i t y K u t t a c o n d i t i o n i s a p p l i e d . T h i s i s a c c o m p l i s h e d by a d d i n g f i n i t e d i s t r i b u t e d v o r t e x e l e m e n t s t o t h e body s u r f a c e , a l l o f t h e same v o r t e x s t r e n g t h d e n s i t y . The K u t t a c o n d i t i o n t h e n i m p l i e s t h a t t h e t a n g e n t i a l v e l o c i t i e s e s t a b l i s h e d a t t h e c o n t r o l p o i n t s on t h e u p p e r and l o w e r s u r f a c e s , a d j a c e n t t o t h e t r a i l i n g e d g e , must be. e q u a l i n m a g n i t u d e , and b o t h . d i r e c t e d t o w a r d t h e t r a i l i n g e d g e . S i n c e t h e v e l o c i t y due t o a v o r t e x i s s i m p l y t h a t due t o a s o u r c e , b u t r o t a t e d 90 d e g r e e s , e x p r e s s i o n s f o r t h e v e l o c i t y c o m p o n e n t s f o r d i s t r i b u t e d - v o r t e x e l e m e n t s o f c i r c u l a t i o n s t r e n g t h d e n s i t y Y(Q) c a n be w r i t t e n , c o r r e s p o n d i n g f o t h o s e o f (3. 8, 3 . 9) . F o r a d i s t r i b u t e d v o r t e x e l e m e n t o f u n i t s t r e n g t h d e n s i t y a t p o i n t ' j * t h e c o r r e s p o n d i n g n o r m a l a n d t a n g e n t i a l v e l o c i t i e s i n d u c e d a t e l e m e n t ' i ' a r e f o u n d t o be -B-. a n d A . , r e s p e c t i v e l y . The number and s i z e o f v o r t e x e l e m e n t s i s a r b i t r a r y , s i n c e t h e y a l l h a v e t h e same s t r e n g t h d e n s i t y . I t i s c o n v e n i e n t t o u s e t h e same number o f v o r t e x a s s o u r c e e l e m e n t s and t o h a v e s o u r c e and v o r t e x e l e m e n t s l o c a t e d t o c o i n c i d e e x a c t l y . The v e l o c i t i e s A . . and B.. c o m p u t e d f o r t h e s o u r c e 2 3 elements are then immediately useable f o r the vortex elements. Hence the normal and t a n g e n t i a l v e l o c i t i e s induced at the c o n t r o l point on element ' i ' due t o a system of H c o i n c i d e n t source and vortex elements immersed i n an i n f i n i t e uniform approach flow U ( p a r a l l e l to the X - d i r e c t i o n ) , are N N V n « . I Ni 3=1 J J k = l and N N V t . = J V B j i a j + JnAkiYk + U c o s V (3.14) x j = l J J k = l S i n c e a l l the vortex elements on a s i n g l e c l o s e d l i f t i n g body are of equal s t r e n g t h Y , the d e s c r i p t i o n of the flow f i e l d about an N-sided p o l y g o n a l body i s complete when the N+1 q u a n t i t i e s O i , o 2 , . . . ,o , and Y are known. For zer o F^, the normal-flow boundary c o n d i t i o n s at each of the N elements p r o v i d e s N equations V n = 0. (3.15) i while the . f i n i t e - v e l o c i t y Kutta c o n d i t i o n a t the two c o n t r o l p o i n t s adjacent to the t r a i l i n g edge p r o v i d e s the s i n g l e (N+1)st equation (3. 16) 24 For the c o n f i g u r a t i o n of a i r f o i l - s h a p e d w a l l s l a t s , s o l i d w a l l s and t e s t a i r f o i l plus f l a p s of Figure 3.1, with a t o t a l of N source elements and a l i f t i n g bodies, there are N source and M vortex strength d e n s i t i e s to be determined. The zero normal-v e l o c i t y c o n d i t i o n a p p l i e d on each element on the a i r f o i l , f l a p s , s o l i d w a l l s and w a l l s l a t s , y i e l d s the N equations N M R(k) I A d . - I y I B = Usin9., i = l , 2 , . . . N . (3.17) j = l 3 i 3 k = 1 K m = 1 nu i A Kutta c o n d i t i o n a p p l i e d to each of the M bodies ( a i r f o i l , f l a p s , w a l l s l a t s ) y i e l d s the M equations N M R(k) •V B3U + B J L >°l\lv*l (Amu + AmL > = "U (cos9 D +cos6 L ),(3.18) j-1 J r J r . k=l m=l r r r r r=l,2,...M. The s u b s c r i p t s U and L i n d i c a t e the c o n t r o l p o i n t s adjacent to the t r a i l i n g edge"on the upper and lower s u r f a c e s r e s p e c t i v e l y of the r - t h l i f t i n g body; R(k) i s the number of source (and vortex) elements on t h i s body. In summary there are: - a t o t a l of N source elements d i s t r i b u t e d over the t e s t a i r f o i l , i t s f l a p s , the a i r f o i l - s h a p e d w a l l s l a t s , and the s o l i d w a l l s e c t i o n s . - a t o t a l of M bodies r e q u i r i n g Kutta c o n d i t i o n s . M a t o t a l of J R (k) vortex elements d i s t r i b u t e d over the k=l l i f t i n g bodies; there are R (k) source elements and R (k) e q u a l -s t r e n g t h density vortex elements d i s t r i b u t e d over the k-th body. - N unknown source stre n g t h d e n s i t i e s a j 25 - M unknown vortex strength d e n s i t i e s - M+N equations i n the M+N unknowns a i , a 2,...a , y i / y 2 , YM" 2 6 3^3 Other A i r f o i l - W a l l C o n f i g u r a t i o n s Examined.- . ' Obvious s i m p l i f i c a t i o n s of the above g e n e r a l e q u a t i o n s (.3.17,3.18) are f o r a t e s t a i r f o i l (a) i n an unbounded stream (fr e e a i r ) , (b) i n the proxi m i t y of a s i n g l e s o l i d lower s u r f a c e (ground e f f e c t ) , (c) between two s o l i d w a l l s , and. (d) between a s o l i d lower boundary and an upper boundary c o n s i s t i n g of s i n g l e -s i d e d t r a n s v e r s e s l a t s with no Kutta c o n d i t i o n s a p p l i e d . In each of -the cases (a) - (d) a t o t a l of N source elements are d i s t r i b u t e d over the t e s t a i r f o i l , i t s f l a p s , the t r a n s v e r s e w a l l s l a t s , and the s o l i d w a l l s e c t i o n s . In a d d i t i o n t h e r e i s an unknown vortex s t r e n g t h d e n s i t y on the t e s t a i r f o i l and on each of i t s f l a p s . For example, f o r a s i n g l e t e s t a i r f o i l (no f l a p s ) , i n f r e e a i r , equations (3.17,3.18) reduce t o , r e s p e c t i v e l y : N N •I A..a. - y I B. . = Usin8., i = l , 2 , . . . N , (3.19) j = l 3 1 3 k=l K l 1 and J C 1 , N + I a i + C 2 , N + I a 2 + - * • + C N , N + i a N + C N + l , N + l Y l + - ' • + C N + M , N + l Y M = d N + l C1,N+M 0 1 + C2,N+M a 2 + ' '* + CN,N+M aN + CN+l,N+M Y l + * *-+CN+M,N+MYM_dN+M' where t h e m a t r i x C a n d t h e c o l u m n v e c t o r d i n t h e s y s t e m C ( 0 , Y ) - d a r e a s s e m b l e d f r o m t h e m a t r i c e s A and B by means o f e q u a t i o n s ( 3 . 1 7 , 3 - 1 3 ) , t h a t i s , C j i A j : L j = 1, 2 , . . . N; i=l,2,...N-R(k) I " I B . k=l,2,...M; j=N+k; i=l,2,'...N , m = l 32 B . j = l,2 t ' • • N;r=l,2,...M; i=N+r (4.2) c. R(k) I' (A_ +A ) k=l,2,...M;j=N+k;r=l,2,...M;i=N+r m= 1 r r and Usin6. i = l , 2 t ' ' ' N [ -ucose -ucose r=l,2 , . . . M; i=N+r (4.3) r Thus the computation of the matrix C r e q u i r e s a c c e s s t o both matrices A and B. When these m a t r i c e s a re l a r g e , C must be assembled i n b l o c k s . For d e t a i l s see the FORTRAN program i n Appendix 2. The a l t e r n a t i v e i s : c a l c u l a t e A and. B, w r i t e B i n t o p e r i p h e r a l s t o r a g e , d e - a l l o c a t e the memory as s i g n e d t o B, a l l o c a t e memory f o r C, c a l c u l a t e a l l p a r t s o f C t h a t i n v o l v e A, d e - a l l o c a t e the memory assign e d t o A, a l l o c a t e memory f o r B, read B i n t o memory from p e r i p h e r a l s t o r a g e and c a l c u l a t e a l l p a r t s of C that i n v o l v e B. T h i s a l t e r n a t i v e i s s i m p l e r t o program and appears i n Appendix 10. The l a r g e number of summations of matrix elements i n the same row i s e v i d e n t i n equations (4.2); t h i s i s the main so u r c e of i n e f f i c i e n c i e s under the present paging s y s t e o . 33 4_-_2 S o l v i n g the Eguations-_ U s u a l l y the s o l u t i o n of the complete system of N + M equations i s o b t a i n e d d i r e c t l y by G a u s s - e l i m i n a t i o n methods. For a FORTRAN G a u s s - e l i m i n a t i o n s u b r o u t i n e t h a t t a k e s account of the above mentioned paging system, see Moler [2 6 ] or Appendix 3. Another d i r e c t method, used by Hess and Smith [ 1 8 ] i s the s u c c e s s i v e row v e c t o r o r t h o g o h a l i z a t i o n process of P u r c e l l [ 2 7 ] . In t h i s method an augmented matrix i s t r e a t e d row by row such t h a t a s e r i e s of v e c t o r s o r t h o g o n a l to each row v e c t o r of the augmented matrix i s c o n s t r u c t e d . The r i g h t - h a n d s i d e v e c t o r 'd* i s used to c o n s t r u c t a s e t of N+M v e c t o r s i n (N+M +1)-dimensional space, ( G l i ' C 2 i ' C 3 i C N + M , i ' - d i } . i = l , 2 , . . . N + M . The s o l u t i o n v e c t o r (a,y) °f equations (4. 1) i s such t h a t the v e c t o r Cai, a 2 , a 3 f . . . , o^, y i , Y2,..-, y M , 1) (**-5) i s o r t h o g o n a l t o a l l the v e c t o r s of (4.4). The process of s o l v i n g e q u a t i o n s (4.1) i s e q u i v a l e n t t o d e t e r m i n i n g an (N + M+1)-d i m e n s i o n a l v e c t o r o r t h o g o n a l to the N+M v e c t o r s of (4.4) with u n i t y as i t s (N+M+1)-th component. Each row of the c o e f f i c i e n t matrix C i s used at o n l y one stage of the process, and i s not needed be f o r e or a f t e r t h a t 34 stage. Thus C i s t r a n s f e r r e d from v i r t u a l to r e a l memory a row at a time, with each row occupying the same s t o r a g e l o c a t i o n as t h a t of the p r e v i o u s row. Thus an i n s i g n i f i c a n t amount of st o r a g e i s r e q u i r e d f o r storage of a s i n g l e row. However, the components of a l l the or t h o g o n a l v e c t o r s w i l l tend to be i n r e a l memory, s i n c e they are used r e p e t i t i v e l y . The maximum t o t a l number of components occurs when the process i s about h a l f -f i n i s h e d ; the t o t a l number of memory l o c a t i o n s r e q u i r e d i s approximately (N + M) 2/4. Thus the number of equations which can be s o l v e d by t h i s process ( f o r a gi v e n c o m p u t a t i o n a l c a p a c i t y ) i s about twice t h a t f o r a G a u s s - e l i m i n a t i o n p r o c e s s . For a FORTRAN s u b r o u t i n e based on t h i s procedure, see Appendix 3. I n d i r e c t i t e r a t i v e methods such as s u c c e s s i v e - o v e r -r e l a x a t i o n (SOB) are a l s o p o s s i b l e . For a d i s c u s s i o n of such methods, see Hess and Smith [ 1 8 ] . U n s u c c e s s f u l attempts we're made t o use SOR; the method was abandoned. In g e n e r a l , the matrix C i s d i a g o n a l l y dominant, t h a t i s , the d i a g o n a l elements, 2TT, are the l a r g e s t i n the m a t r i x . However, by examining the r e l a t i o n s (4.2), i t i s seen t h a t the summations over B .. , A „ and A _ pro v i d e l a r g e elements i n t h e mi mu mL ( l a s t ) (N+M)-th column of C. In g e n e r a l , t h e , sum of a l l the d i a g o n a l e n t r i e s i s approximately equal t o the sum of a l l t h e o f f - d i a g o n a l e n t r i e s . In e s s e n t i a l l y a l l cases,, the matrix i s n o n - s i n g u l a r except f o r very t h i n bodies, such as cusped t r a i l i n g edges. Here the source and vortex elements on the two s u r f a c e s are almost c o i n c i d e n t so matrix s i n g u l a r i t i e s (rows l i n e a r l y dependent)- can creep i n . For a d i s c u s s i o n of such 35 problems, see Hess and Smith [18]. The summations N M R(k) v n. I A. . a . - I y. Y B k=l m=l m i UsinS. l (4.6) and N y B . . a j=l 1 1 M R(k) k=l m=l , i i / " • + Ucos6 D I D i . i i - , k_J:-, m i 1 (4.7) p r o v i d e the net normal and t a n g e n t i a l v e l o c i t i e s a t c o n t r o l p o i n t s »i' due to a l l source and vortex elements • j ' and ' m' r e s p e c t i v e l y , and the uniform onset flow U. The s o l u t i o n t o the s e t of eguations (4.1) i s checked by computing the v e l o c i t i e s V n , V t at each p o i n t of a p p l i c a t i o n of the z e r o n o r m a l - v e l o c i t y i i or Kutta boundary c o n d i t i o n s . At a l l c o n t r o l p o i n t s on s o l i d s u r f a c e s , V i s z e r o , and the l o c a l p r e s s u r e c o e f f i c i e n t C i s 1 c a l c u l a t e d from : = 1 -V. U (4.8) The r e s u l t i n g v a l u e s of C p are i n t e g r a t e d n u m e r i c a l l y (by t r a p e z o i d a l r u l e or the f i t t i n g of c u b i c s p l i n e s ) around the t e s t a i r f o i l and f l a p contours to determine the l i f t , drag and nose-up midchord and g u a r t e r c h o r d p i t c h i n g moment c o e f f i c i e n t s , from the e x p r e s s i o n s 1 c c|>C dx. P J 3 1 c 4>C dy. 36 C M . = 772 <|>C (x.dx.+y.dy.) , (4.9) 'MoT C where dx =ds.cos9. and dy = ds s i n 6 (4.10) 3 3 3 3 3 3 and i n t e g r a t i o n s are performed c l o c k w i s e around the p o l y g o n a l c o n t o u r s . From a c a l c u l a t i o n of the net c i r c u l a t i o n about a l i f t i n g body, re p r e s e n t e d by NA source and vortex elements. f . y ^ t N A r = Av- 1=1 l By s u b s t i t u t i o n of (4.7), i t can be shown t h a t (4.13) reduces t o C = ^JH-(perimeter of the body) , (4.14) Ii U C -where y i s the vortex s t r e n g t h d e n s i t y f o r the body under c o n s i d e r a t i o n . The C v a l u e s c a l c u l a t e d from (4.9) and (4.13) are e q u i v a l e n t only f o r an i s o l a t e d a i r f o i l . I f a second body or a 37 boundary i s present the two v a l u e s are not e q u a l . The c a l c u l a t i o n of the c i r c u l a t i o n about a p a r t i c u l a r body then depends on the s i z e of the contour of i n t e g r a t i o n . The i n t e g r a l (4.11) reduces to the c o r r e c t value only as the contour s i z e s h r i n k s to z e r o . In the f o l l o w i n g pages, a l l C v a l u e s quoted a r e c a l c u l a t e d from e x p r e s s i o n ( 4 . 9 ) . I t must be emphasized t h a t on the body s u r f a c e elements, the flow f i e l d s o l u t i o n i s v a l i d only at the c o n t r o l p o i n t s ; f o r " o f f - c e n t e r " p o i n t s any c a l c u l a t e d s u r f a c e v e l o c i t i e s are meaningless. F i g u r e 3 . 4 shows how v e l o c i t i e s vary with p o s i t i o n , on a s u r f a c e element. On a g i v e n s u r f a c e element, i f t h e normal v e l o c i t y i s p r e s c r i b e d as z e r o , i t i s i n g e n e r a l non-zero a t a l l p o i n t s of the element except the c o n t r o l p o i n t . At the edges of the s u r f a c e elements the t a n g e n t i a l v e l o c i t y approaches i n f i n i t y because of the s i n g u l a r i t y i n the e x p r e s s i o n ( 3 . 8 ) and/or the d i s c o n t i n u i t y i n s u r f a c e s l o p e . However, the flow f i e l d s o l u t i o n i s u n i f o r m l y v a l i d a t a l l o f f - s u r f a c e p o i n t s . Hence at a f i e l d p o i n t ' i ' the v e l o c i t y components . p a r a l l e l and p e r p e n d i c u l a r to the streamwise d i r e c t i o n can be computed. The l o c a l flow . d i r e c t i o n can be c a l c u l a t e d and, by s t e p p i n g from p o i n t t o p o i n t , a p a r t i c u l a r s t r e a m l i n e can be t r a c k e d . The a l g o r i t h m i s given i n Appendix 4 . A l t e r n a t i v e l y the e x p r e s s i o n f o r the stream f u n c t i o n g i v e n i n Appendix 1 can be s o l v e d i t e r a t i v e l y f o r say the y - c o o r d i n a t e , a t a g i v e n x - c o o r d i n a t e , t o l o c a t e p o i n t s on a p a r t i c u l a r s t r e a m l i n e , t h a t i s , a l o c u s of p o i n t s (x,y) can be found along 33 w h i c h t h e c o m p u t e d v a l u e o f t h e s t r e a m f u n c t i o n i s a c o n s t a n t . 39 5.. R e s u l t s of the New Theory. The use of t h i s type of two-dimensional s u r f a c e s i n g u l a r i t y d i s t r i b u t i o n method, to c a l c u l a t e p r e s s u r e d i s t r i b u t i o n s on i s o l a t e d bodies, i s well e s t a b l i s h e d . For a comparison o f pressure d i s t r i b u t i o n s o b tained from t h i s method, with p r e s s u r e d i s t r i b u t i o n s d e r i v e d from experiments and other two-dimensional p o t e n t i a l flow t h e o r i e s , see Hess and Smith [ 1 8 ] . For purposes of comparison here, the s l o p e o f the c u r v e o f l i f t c o e f f i c i e n t C L as a f u n c t i o n o f a i r f o i l i n c i d e n c e w i l l be used. As an example of the present t h e o r e t i c a l method, f r e e - a i r l o a d i n g s were c a l c u l a t e d f o r the NACA-0015 a i r f o i l , u s i n g 50 c o n t r o l p o i n t s to re p r e s e n t the p r o f i l e o f the a i r f o i l . The c o o r d i n a t e s of the 50 c o n t r o l p o i n t s used a re given i n T a b l e 1. The v a l u e s of the l i f t c o e f f i c i e n t s so o b t a i n e d a re l i s t e d i n Tabl e 3, as. a f u n c t i o n of the i n c i d e n c e a . By exact c u r v e -f i t t i n g a polynomial of order 5 through the 6 p o i n t s a t 0,2,3,5,8, and 10 degrees i n c i d e n c e , the l i f t - c u r v e s l o p e a t zero degrees was found t o be 0.1193 The co r r e s p o n d i n g v a l u e a t +3 degrees i s 0.1229. These v a l u e s would be s l i g h t l y h i g h e r i f a l a r g e r number of c o n t r o l p o i n t s was used. From t h i n a i r f o i l theory (see Pope [ 2 8 ] ) t h i s l i f t - c u r v e s l o p e m f o r symmetrical a i r f o i l s i s g i v e n by (per ra d i a n ) m = 2TT 1 + . 7 7 3 -c U + (»773|) 2 J (5.1) where t/c i s the maximum-thickness t o chord r a t i o . For the NACA-0015 a i r f o i l , the value o f is i s 6.919 per r a d i a n or 0.1208 per 40 degree. The agreement between the two t h e o r i e s i s good. S t r i c t l y the e x p r e s s i o n (5.1) g i v e s the t h e o r e t i c a l l i f t - c n r v e s l o p e o n l y at z ero degrees, s i n c e an u n d e r l y i n g assumption i s t h a t m i s independent of i n c i d e n c e . The present theory r e p r e s e n t s a uniform flow of i n f i n i t e e x t e n t , past a s e t of m u l t i p l e a i r f o i l s , and f l a t s u r f a c e s a l i g n e d with the d i r e c t i o n of the u n d i s t u r b e d f l o w . S i t h t h i s c o n f i g u r a t i o n ( Figure 3 . 1 ) , l o a d i n g s were c a l c u l a t e d f o r d i f f e r e n t t e s t a i r f o i l s d e v e l o p i n g high l i f t c o e f f i c i e n t s i n the presence of the above mentioned w a l l c o n f i g u r a t i o n . I t c o n s i s t s of a s o l i d lower w a l l i n c o n j u n c t i o n with a t r a n s v e r s e l y - s l o t t e d upper w a l l , with v a r i o u s upper w a l l OAEs. T h i s c o n f i g u r a t i o n w i l l be r e f e r r e d t o by the a b b r e v i a t i o n TSOSL., meaning t r a n s v e r s e l y - s l o t t e d upper, s o l i d lower. By comparing the l i f t c o e f f i c i e n t i n the windtunnel, C T , t o the f r e e - a i r v a l u e , C T , T F the r e s u l t s i n d i c a t e d t h a t a t r a n s v e r s e l y - s l o t t e d w a l l of about 70%OAR gave very s m a l l l i f t c o r r e c t i o n s (C -C ) f o r a l l the L T L F a i r f o i l s c o n s i d e r e d , at a l l l i f t c o e f f i c i e n t s , and up t o a i r f o i l s i z e s , c/H, as l a r g e as u n i t y . F i g u r e 5.1 shows the c a l c u l a t e d r a t i o of l i f t c o e f f i c i e n t s as a f u n c t i o n of a i r f o i l s i z e , c/H, f o r t h r e e a i r f o i l s . The f i r s t a i r f o i l i s a 14% t h i c k , 4.6% caaber Clark-Y ( r e p r e s e n t e d by 50 c o n t r o l points) a t zero and 20 degrees i n c i d e n c e (the f a c t t h a t the a c t u a l a i r f o i l would be s t a l l e d at t h i s i n c i d e n c e i s of no consequence f o r the present purpose). The second a i r f o i l i s an NACA-23012 at 8 degrees i n c i d e n c e , with a 2 5 . 6 % ( o v e r a l l chord length) s l o t t e d f l a p d e f l e c t e d 20 degrees (represented by 41 46 c o n t r o l p o i n t s o n t h e main a i r f o i l and 35 on t h e f l a p ) . The t h i r d a i r f o i l i s an NACA-0015 a t 3 d e g r e e s i n c i d e n c e -T h i s r a t i o o f l i f t c o e f f i c i e n t s i s shown - f o r two. w a l l c o n f i g u r a t i o n s . One i s w i t h two s o l i d w a l l s , a n d t h e s e c o n d i s a 70%OAH TSUSL w a l l c o n f i g u r a t i o n . I t i s s e e n t h a t w h e r e a s t h e l i f t c o r r e c t i o n f o r an a i r f o i l t e s t e d b e t w e e n s o l i d w a l l s , c o u l d be mora t h a u 5 0 % o f t h e t r u e , f r e e - a i r v a l u e , t h e p r e s e n t t h e o r y f o r one s o l i d w a l l a n d one s l o t t e d w a l l o f OAS n e a r .701 p r e d i c t s l i f t c o r r e c t i o n s o f l e s s t h a n 1%, f o r a i r f o i l s i z e c/H l e s s t h a n 1.0. I n d e e d , i t a p p e a r s t h a t a s l i g h t l y l o w e r v a l u e o f OAS w o u l d s h i f t t h e c u r v e s up s l i g h t l y , and g i v e l i f t c o r r e c t i o n s o f l e s s t h a n a b o u t , m i s c a l c u l a t e d on (-2°,8°). For the Clark-Y a i r f o i l s with a z e r o -l i f t angle of about -6.3 degrees, m i s c a l c u l a t e d on (-8°,2°). For the Joukowsky a i r f o i l with a z e r o - l i f t angle of about -3.8 degrees, m i s c a l c u l a t e d on '•(-6°,4°). From the f i t t e d s t r a i g h t l i n e the z e r o - l i f t angle can be determined as the a - i n t e r c e p t when C L i s z e r o . In a s i m i l a r manner the s l o p e o f the midchord p i t c h i n g moment cur v e , dc /da, can be determined. The p o s i t i o n Mo of the aerodynamic c e n t e r x a c / c with r e s p e c t t o the a i r f o i l l e a d i n g edge i s x a C _ Xo _ _T /7 1\ c c m where x 0 , m, c, and x are the d i s t a n c e from the l e a d i n g edge to the a x i s of measurement of the moment c o e f f i c i e n t C , the l i f t -Mo cur v e s l o p e , the chord and the midchord p i t c h i n g moment-curve s l o p e , r e s p e c t i v e l y . Table 8 c o n t a i n s v a l u e s of the l i f t - c u r v e ' s l o p e , the z e r o - l i f t angle and the p o s i t i o n of the aerodynamic 55 c e n t e r f o r the n i n e a i r f o i l s and the v a r i o u s w a l l c o n f i g u r a t i o n s t e s t e d . F i g u r e 7.1 shows a t y p i c a l v a r i a t i o n of C (a) with upper L w a l l open-area r a t i o (OAR). The s t r a i g h t l i n e p l o t t e d c orresponds t o e s t a b l i s h e d experimental f r e e - a i r l i f t - c u r v e s l o p e s (Jacobs and Sherman [ 3 1 ] , R i e g e l s [ 3 2 ] ) . The z e r o -c o r r e c t i o n OAR appears to l i e between zero and 40%; t h i s f a c t i s a l s o apparent i n F i g u r e 7.5 and w i l l d i s c u s s e d t h e r e . The r e s u l t i n g v a l u e s of the l i f t - c u r v e s l o p e s , m, f o r any of the a i r f o i l s a r e , to the degree of accuracy r e q u i r e d here, q u i t e s e n s i t i v e t o the c h o i c e of range of i n c i d e n c e over which the l e a s t - s q u a r e s s t r a i g h t l i n e curve f i t t i n g i s done. For example, f o r the 0. 67-N AC.A-00 15 a i r f o i l between two s o l i d w a l l s , the value of m computed on (-2°,8°) i s 0.1114, while t h e v a l u e on ( 0 - o , 1 0 O ) i s 0.1156 and the value on ( 0 0 , 1 2 ° ) i s 0.1138. T h i s i s p a r t i c u l a r l y n o t i c e a b l e f o r t h i s a i r f o i l as t h e r e i s a pronounced jog i n the Ci,(a) curve i n t h i s range o f Reynolds numbers. T h i s jog i s a t t r i b u t e d to (see T a n i [30]) the f o r m a t i o n of a laminar s e p a r a t i o n bubble by the s e p a r a t i o n of the l a m i n a r boundary l a y e r near the l e a d i n g edge and subsequent reattachment downstream. As the Re i s i n c r e a s e d , the jog becomes p r o g r e s s i v e l y l e s s pronounced. F i g u r e 7.2 shows a comparison of two s e t s o f measured va l u e s of l i f t - c u r v e s l o p e m, with the c o r r e s p o n d i n g s l o p e s from the present theory, f o r a 14% 0.53-Clark-Y a i r f o i l , as a f u n c t i o n of the upper w a l l OAR. The l a r g e w a l l s l a t s (92mm) were used f o r one s e t of measured v a l u e s , and the s m a l l s l a t s (46am) 56 f o r the other s e t . The o r d i n a t e s are normalized by the v a l u e of the l i f t - c u r v e s l o p e , m , i n the presence of two s o l i d w a l l s (zero OAB). The t e s t Re i n both s e t s of measurements was 0.5(10*), based on the t e s t a i r f o i l chord. The t h e o r e t i c a l v a l u e s of l i f t - c u r v e s l o p e m are determined from a l e a s t - s q u a r e s s t r a i g h t l i n e f i t through t h r e e v a l u e s of l i f t c o e f f i c i e n t C > computed a t -8, -3 and +2 degrees i n c i d e n c e . F i g u r e 7.3 shows s i m i l a r r e s u l t s f o r the 0.67-NACA-00 15 a i r f o i l t e s t e d at a Re of 1.0 ( 1 0 6 ) . The measured l i f t - c u r v e s l o p e s a r e shown f o r t e s t s with both t h e l a r g e and s m a l l w a l l s l a t s . The t h e o r e t i c a l v a l u e s o f l i f t - c u r v e s l o p e m a r e determined from a l e a s t - s q u a r e s s t r a i g h t l i n e f i t through t h r e e v a l u e s of l i f t c o e f f i c i e n t C , computed a t -2, +3 and +8 degrees i n c i d e n c e . F i g u r e s 7.2 and 7.3 show t h a t t h e t h e o r e t i c a l v a l u e s of m/m are h i g h e r than the e x p e r i m e n t a l v a l u e s , f o r both s a i r f o i l s , and f o r a l l OABs. T h i s d i f f e r e n c e i s about 2.8%, a t 70%OAR, and w i l l be accounted f o r by two e x t e n s i o n s to the p r e s e n t theory i n §§8.1 and 8.2. F i g u r e 7.4 shows e x p e r i m e n t a l v a l u e s o f l i f t - c u r v e s l o p e , m, (per degree) f o r f o u r s i z e s of NACA-0015 a i r f o i l i n the presence of w a l l s of d i f f e r e n t OAR, 0, 60, 70, and 80S, u s i n g the l a r g e s l a t s . A l l t e s t s f o r the t h r e e l a r g e r a i r f o i l s (c/H of 0.67, 0.51, and 0.34) were run at a Re of .0.5(10*). T h i s Re c o u l d not be reached f o r the s m a l l e s t a i r f o i l (c/H of 0.17), which was t e s t e d at a Re of 0.3(10*). The data f o r t h i s a i r f o i l were then a d j u s t e d t o correspond to the 0.5(10*) Re, u s i n g p u b l i s h e d m (Re) data f o r the NACA-0015 a i r f o i l (see Jacobs and 57 Sherman [ 3 1 ] ) . The a d j u s t e d data are the f l a g g e d p o i n t s i n f i g u r e 7.4. The r e s u l t s show a convergence toward a f r e e a i r (zero c/H) l i f t - c u r v e s l o p e value of 0.093, i n good agreement with [ 3 1 ] . The r e s u l t s i n d i c a t e zero l i f t - c o r r e c t i o n s f o r an upper w a l l OAB between 60 and 70%, i n agreement with the , p r e d i c t i o n s of the p r e s e n t theory. F i g u r e 7.5 shows the c o r r e s p o n d i n g e x p e r i m e n t a l v a l u e s of m f o r f o u r s i z e s of Clark-Y a i r f o i l i n the presence of w a l l s of d i f f e r e n t OAR, using the l a r g e s l a t s . : A l l t e s t s f o r the t h r e e l a r g e r a i r f o i l s (c/H of 0.66, 0.53, and 0.39) were run a t a Re of 0.5 (10*). T h i s He c o u l d not be reached f o r t h e s m a l l e s t (c/H of 0.25) a i r f o i l , which was t e s t e d a t a Re of 0.45(10*) - The data f o r t h i s a i r f o i l were not a d j u s t e d t o the 0.5 (10*) Re as a (Sa)- i n f o r m a t i o n f o r the 14% t h i c k C l a r k - Y s e c t i o n i s s c a r c e . : The r e s u l t s show a convergence toward a f r e e a i r (zero c / f i ) l i f t - c u r v e s l o p e v a l u e of 0.096, which agrees f a v o u r a b l y w i t h the i n f o r m a t i o n t h a t i s a v a i l a b l e ( S i l v e r s t e i n [ 3 3 ] ) . An e x t r a p o l a t i o n of the curve of m (He) of F i g u r e 11 of [ 33 ], f o r an 11.7% t h i c k C l a r k - Y s e c t i o n of aspect r a t i o 6 g i v e s a value o f ra 0.071 a t a Re of 0.5(10*). By u s i n g t h e t h e o r e t i c a l r e l a t i o n (5.1) to e s t i m a t e an e q u i v a l e n t value f o r 14% t h i c k n e s s , then c o r r e c t i n g t o i n f i n i t e a spect r a t i o , the e s t i m a t e d value of m f o r the 14% t h i c k n e s s a t a Re of 0.5(10*) i s 0.096. Here z e r o l i f t - c o r r e c t i o n s are i n d i c a t e d f o r an upper w a l l OAR l e s s than 60%. E x p e r i m e n t a l l y , from both F i g u r e 7.1 and 7.5, the z e r o -c o r r e c t i o n OAR appears to ±>e somewhat l e s s than 60%, based on a 58 f r e e a i r l i f t - c u r v e s l o p e of 0.096- I f a lower value such as 0.092 were chosen, the z e r o - c o r r e c t i o n OAR would be about 60%. The m-values f o r the s m a l l e s t a i r f o i l s h o u l d be lowered due to the d i f f e r e n c e i n the t e s t Re. P r e v i o u s t e s t s £ 3 6 ] with the s m a l l e s t a i r f o i l have been u n r e l i a b l e . I t appears t h a t t h i s a i r f o i l has a r e l a t i v e l y s m a l l e r nose r a d i u s than the l a r g e r a i r f o i l s , which might account f o r the h i g h e r m-values. F i g u r e 7.6 g i v e s a comparison of e x p e r i m e n t a l p r e s s u r e d i s t r i b u t i o n s on the Joukowsky a i r f o i l , a t +3 degrees i n c i d e n c e i n the presence of two s o l i d w a l l s , and the 70%OAR, TSOSL w a l l c o n f i g u r a t i o n , u s i n g the l a r g e w a l l s l a t s . The comparison s u p p o r t s the t h e o r e t i c a l p r e d i c t i o n t h a t t h e c h i e f e f f e c t of the s l o t t e d w a l l i s t o lower the n e g a t i v e p r e s s u r e s over the upper s u r f a c e of the a i r f o i l , without a p p r e c i a b l y modifying the p o s i t i v e p r e s s u r e s on the un d e r s u r f a c e , or g e n e r a l l y d i s t o r t i n g the d i s t r i b u t i o n . The c l o s e agreement of C va l u e s from balance measurements with those o b t a i n e d by i n t e g r a t i o n o f the p r e s s u r e c o e f f i c i e n t , C , i n d i c a t e s s a t i s f a c t o r y two-dimensional f l o w P c o n d i t i o n s . C u b i c - s p l i n e p o l y n o m i a l s a re used t o c u r v e - f i t the d i s t r i b u t i o n of C f o r i n t e g r a t i o n . P In F i g u r e 7.7,. the pre s s u r e data from F i g u r e 7.6 f o r two s o l i d w a l l s are c o r r e c t e d t o e q u i v a l e n t f r e e - a i r c o n d i t i o n s by c o n v e n t i o n a l w a l l - c o r r e c t i o n theory {Pankhurst and Holder '£34]). The a c t u a l c o r r e c t i o n formulae used are reco r d e d i n Appendix 7. These c o r r e c t e d data are compared with the 70% OAR pressure data as taken. The 70%OAR data are seen t o agree q u i t e c l o s e l y with the c o r r e c t e d s o l i d w a l l data. The c o r r e c t e d s o l i d w a l l value of 59 C i s 0.675, while the 70%OAR value of C T i s 0.651; t h i s again i n d i c a t e s t h a t zero l i f t - c o r r e c t i o n t e s t c o n d i t i o n s w i l l occur at an upper wall OAR between 60 and 70%. The hump i n the pressure d i s t r i b u t i o n s toward the r e a r upper s u r f a c e i s caused by the t h i c k e r t r a i l i n g edge of the e x p e r i m e n t a l a i r f o i l r e p l a c i n g the t h e o r e t i c a l t r a i l i n g edge cusp. Por completeness, to show how the use: of such a TSUSL w a l l c o n f i g u r a t i o n a f f e c t s other aerodynamic d a t a , some t y p i c a l c urves of p i t c h i n g moment and drag c o e f f i c i e n t s are shown, as f u n c t i o n s of a i r f o i l i n c i d e n c e -F i g u r e s 7.8 and 7.9 show the midchord p i t c h i n g moment c o e f f i c i e n t c and d r a g , c o e f f i c i e n t C_ r e s p e c t i v e l y f o r the Mo D 0.53-Clark-Y a i r f o i l , as a f u n c t i o n of a i r f o i l i n c i d e n c e , and upper w a l l OAR. The v a l u e s a t 70%OAR (near f r e e - a i r c o n d i t i o n s ) f o r C and C_ agree w e l l with c o r r e s p o n d i n g v a l u e s from D . M 0 mxn F i g u r e 68 of P i n k e r t o n and Greenberg [ 3 5 ] , and Lim [ 3 6 ] . The v a l u e s of a t a given i n c i d e n c e i n i t i a l l y i n c r e a s e and then decrease, with i n c r e a s i n g OAR. T h i s same behaviour of C D was observed f o r the ot h e r a i r f o i l s t e s t e d , both with and without e n d p l a t e s , and appears t o be a pro p e r t y of t h i s p a r t i c u l a r t e s t c o n f i g u r a t i o n . 60 Si . E x t e n s i o n s t o the New Theory., What i s a v a i l a b l e at present i s a p o t e n t i a l flow theory f o r a t r a n s v e r s e l y - s l o t t e d upper and s o l i d lower w a l l c o n f i g u r a t i o n (TSOSL), t h a t , f o r an upper w a l l OAB of between 60 and 70% p r e d i c t s low l i f t - c o r r e c t i o n s f o r a v a r i e t y of a i r f o i l s , s i z e s and i n c i d e n c e s . However, e x p e r i m e n t a l l y , the OAB at which z e r o l i f t - c o r r e c t i o n o ccurs i s l e s s than t h e OAR p r e d i c t e d t h e o r e t i c a l l y . Thus the s l o t t e d w a l l behaves e x p e r i m e n t a l l y as i f i t were o p e r a t i n g at a l a r g e r OAB. The result,, at a given OAR, i s t h a t the r a t i o s , of t h e t h e o r e t i c a l values of l i f t - c u r v e s l o p e m or l i f t c o e f f i c i e n t C L , normalized by t h e i r c o r r e s p o n d i n g t h e o r e t i c a l f r e e - a i r v a l u e s , are too high. T h i s i s because the TSOSL w a l l c o n f i g u r a t i o n theory i s a p o t e n t i a l flow r e p r e s e n t a t i o n of a v i s c o u s flow f i e l d . For example, because of v i s c o s i t y , the w a l l s l a t s a r e n o t d e v e l o p i n g t h e i r f u l l c i r c u l a t i o n s p r e d i c t e d by the p o t e n t i a l flow theory s i n c e they are o p e r a t i n g i n a Re range of 37,500 t o 180,000 (with r e s p e c t to t h e i r chord l e n g t h s ) . , Thus the net c i r c u l a t i o n on the s l o t t e d w a l l i s l e s s than the c i r c u l a t i o n p r e d i c t e d t h e o r e t i c a l l y . Hence t h a t p o r t i o n of the measured, l i f t a t a g i v e n OAR which i s due t o the c i r c u l a t i o n on the w a l l s l a t s , w i l l be much l e s s than t h a t p o r t i o n of the l i f t p r e d i c t e d t h e o r e t i c a l l y . In other words, i n order t o p r e d i c t t h e o r e t i c a l l y t h e l i f t t h a t would a c t u a l l y be measured e x p e r i m e n t a l l y on an a i r f o i l i n 61 t h i s TSUSL w a l l c o n f i g u r a t i o n , t h e r e are two v i s c o u s flow f i e l d s to be accounted f o r . The f i r s t i s the usual f r e e a i r v i s c o u s flow f i e l d about the i s o l a t e d a i r f o i l . Now a second v i s c o u s flow f i e l d has been i n t r o d u c e d , t h a t of the flow through the TSUSL w a l l c o n f i g u r a t i o n . Thus a complete s o l u t i o n would r e q u i r e the a p p l i c a t i o n of v i s c o u s theory to the t e s t a i r f o i l , the w a l l s l a t s and any shear l a y e r s which develop i n the plenum. Let C ( ;E) and C { ;T) denote l i f t c o e f f i c i e n t s o b t a i n e d from experiment and theory r e s p e c t i v e l y , and l e t C (OAR; ) and C (F; ) denote l i f t c o e f f i c i e n t s from OAR and f r e e a i r t e s t c o n f i g u r a t i o n s r e s p e c t i v e l y . For a p a r t i c u l a r OAS, i t i s r e a s o n a b l e to assume t h a t the r a t i o C (OAB;E) :C (OAB;T) w i l l be equal to the r a t i o C (F; E) : C (F;T) , p a r t i c u l a r l y i n a low-Li Li c o r r e c t i o n t e s t environment. In t h i s case the v i s c o u s e f f e c t s on each r a t i o w i l l be the same. Thus the r a t i o of C (E) t o C (T) w i l l be the same f o r f r e e - a i r t e s t s or f o r t e s t s at whatever OAR produces near f r e e - a i r t e s t c o n d i t i o n s . T h e r e f o r e i t i s s t i l l u s e f u l t o compare the r a t i o of C (OAS;E):C (F;E) , with the r a t i o of C (OAR; T) ;C (F; T) . L» Li . What i s then d e s i r e d i s a p o t e n t i a l flow c a l c u l a t i o n t h a t w i l l account f o r the v i s c o u s e f f e c t s present e x p e r i m e n t a l l y which are due o n l y t o the TSUSL w a l l c o n f i g u r a t i o n . That i s , the u s u a l v i s c o u s flow a n a l y s i s f o r the t e s t a i r f o i l w i l l s t i l l be r e q u i r e d . 62 8.1 P o t e n t i a l Flow C o n s i d e r a t i o n s of V i s c o u s E f f e c t s . There are two ways to extend the pr e s e n t theory toward such a p o t e n t i a l flow c a l c u l a t i o n . One way i s to account f o r the e f f e c t of v i s c o s i t y on the t e s t a i r f o i l and w a l l s l a t s , through the f o r m a t i o n of v i s c o u s boundary l a y e r s on these s t r e a m l i n e d shapes. The second way i s to make the geometry of the fl o w r e p r e s e n t a t i o n more l i k e t h a t which a c t u a l l y o c c u r s e x p e r i m e n t a l l y i n the t e s t s e c t i o n , w i t h the plenum s u r r o u n d i n g the s l o t t e d w a l l . The f o l l o w i n g d i s c u s s i o n a p p l i e s t o both the t e s t a i r f o i l and the a i r f o i l - s h a p e d w a l l s l a t s . F or boundary l a y e r e f f e c t s , only completely a t t a c h e d f l o w s are c o n s i d e r e d , t h a t i s , boundary l a y e r flows which s e p a r a t e from an a i r f o i l s u r f a c e are not c o n s i d e r e d . Thus, s i n c e the flow l e a v i n g the a i r f o i l t r a i l i n g edge i s a t t a c h e d , the v e l o c i t i e s and pr e s s u r e s a t the upper and lower s u r f a c e s a d j a c e n t to the t r a i l i n g edge, must be e q u a l . T h i s statement i s t r u e on a time-average, s i n c e the f o r m a t i o n o f a vortex s t r e e t i n the a i r f o i l wake r e q u i r e s the shedding o f c o n s e c u t i v e t r a i l i n g v o r t i c e s of a l t e r n a t e s i g n . For a g i v e n a i r f o i l shape and i n c i d e n c e , t h e r e i s a unique c i r c u l a t i o n t h a t w i l l s e t equal the t r a i l i n g edge v e l o c i t i e s on the upper and lower s u r f a c e s . T h i s i s the p h y s i c a l r e a s o n i n g behind t h e t h e o r e t i c a l r e l a t i o n known as the K u t t a c o n d i t i o n , t h a t i s , t h a t the v e l o c i t i e s at the upper and lower 'surfaces a d j a c e n t t o the t r a i l i n g edge (of any body which possesses a sharp t r a i l i n g edge) must be e q u a l . E x p e r i m e n t a l l y the measured value o f l i f t (which i s 63 p r o p o r t i o n a l t o the c i r c u l a t i o n ) i s always lower than the l i f t p r e d i c t e d by the u s u a l p o t e n t i a l flow t h e o r i e s ; the r a t i o of these l i f t s might be, f o r example, k. What then i s r e q u i r e d i s a procedure to reduce the usual t h e o r e t i c a l value of t h e c i r c u l a t i o n r t o a f r a c t i o n k of r . • From the uniqueness of the value of the c i r c u l a t i o n f o r a gi v e n a i r f o i l shape and i n c i d e n c e , the only p o s s i b i l i t y of red u c i n g the c i r c u l a t i o n , i f the Kutta c o n d i t i o n i s r e t a i n e d , i s to reduce the i n c i d e n c e , and/or a l t e r the shape of the p r o f i l e - . The r e d u c t i o n of i n c i d e n c e approach i s o f t e n used i n t h e comparison of the t h e o r e t i c a l and e x p e r i m e n t a l p r e s s u r e d i s t r i b u t i o n s . The t h e o r e t i c a l p r e s s u r e s are c a l c u l a t e d a t a reduced i n c i d e n c e , such t h a t the t h e o r e t i c a l l i f t (determined by i n t e g r a t i o n of the pre s s u r e d i s t r i b u t i o n s ) a t the reduced i n c i d e n c e i s the same as the measured l i f t at the measured incidence.•, T h i s procedure i s not completely s a t i s f a c t o r y as the magnitude of the n e g a t i v e p r e s s u r e . peaks i n the t h e o r e t i c a l p ressure d i s t r i b u t i o n s (near the a i r f o i l l e a d i n g edge on the upper surface) may not equal the magnitude of the peaks a c t u a l l y measured.: P h y s i c a l l y the t h i n laminar boundary l a y e r , which forms beginning a t t h e forward s t a g n a t i o n p o i n t on the u n d e r s i d e of the a i r f o i l , grows i n t h i c k n e s s as i t rounds the l e a d i n g edge and passes through the negative p r e s s u r e peaks. The ' e f f e c t of t h i s t h i n boundary l a y e r i s to i n c r e a s e the r a d i u s of c u r v a t u r e of the a i r f o i l l e a d i n g edge so t h a t the flow v e l o c i t i e s t h e r e are much lower than those p r e d i c t e d by t h e o r y . Thus the e f f e c t of the t h i n boundary l a y e r over the l e a d i n g edge i s t o reduce 64 the magnitude of the negative p r e s s u r e peaks below the magnitudes p r e d i c t e d t h e o r e t i c a l l y . Reducing the a i r f o i l i n c i d e n c e f o r purposes of the t h e o r e t i c a l c a l c u l a t i o n w i l l reduce the magnitude of these negative p r e s s u r e peaks, but not to the same degree as a c t u a l l y occurs due t o the presence of the boundary l a y e r . However, i f the c i r c u l a t i o n i s not f i x e d by t h e Kutta c o n d i t i o n , i t i s p o s s i b l e t o s p e c i f y the c i r c u l a t i o n o t h e r w i s e . The c i r c u l a t i o n may be determined f o r the t h e o r e t i c a l c a l c u l a t i o n from the measured l i f t . The t h e o r e t i c a l p r e s s u r e s are then c a l c u l a t e d at the measured i n c i d e n c e . The v e l o c i t i e s a t the t r a i l i n g edge w i l l no l o n g e r be e q u a l , but the t h e o r e t i c a l l i f t o b t a ined from the i n t e g r a t i o n of the p r e s s u r e d i s t r i b u t i o n can be made to e q u a l the e x p e r i m e n t a l l y measured l i f t . The procedure f o r t h i s c a l c u l a t i o n i s presented i n Appendix 8. F i g u r e 8.1 compares the r e s u l t i n g t h e o r e t i c a l and measured pressure d i s t r i b u t i o n s f o r the 0.67-NACA-0015 a i r f o i l a t 10 degrees i n c i d e n c e i n the presence of two s o l i d w a l l s . The t h e o r e t i c a l r e s u l t s by t h i s method are p h y s i c a l l y u n s a t i s f a c t o r y i n the v i c i n i t y of the a i r f o i l t r a i l i n g edge as such l a r g e n e g a tive p r e s s u r e s a r e i n p r a c t i c e not found t h e r e . I t i s p o s s i b l e t o lower t h e c i r c u l a t i o n developed by a l t e r i n g the shape of the a i r f o i l p r o f i l e . T h i s procedure i s j u s t i f i a b l e p h y s i c a l l y i f the a l t e r a t i o n s a r e i n keeping w i t h those which occur when the boundary l a y e r e f f e c t i v e l y m o d i f i e s the p r o f i l e shape. R e c a l l t h a t f o r an a i r f o i l , t he e f f e c t s o f v i s c o s i t y a r e 65 c o n f i n e d to the t h i n boundary l a y e r adjacent to the a i r f o i l s u r f a c e , and the flow o u t s i d e the boundary l a y e r can be c o n s i d e r e d as i r r o t a t i o n a l . Thus the boundary l a y e r m o d i f i e s the p r o f i l e shape and the p o t e n t i a l flow i s c a l c u l a t e d about t h i s modified shape, using the u s u a l e q u a l - v e l o c i t y Kutta c o n d i t i o n -The f o l l o w i n g procedure f o l l o w s and extends t h a t of P i n k e r t o n [37] whose a n a l y s i s i s f o r two-dimensional a i r f o i l s e c t i o n s t o be mapped conf o r r a a l l y onto a m o d i f i e d c i r c l e by means of the c l a s s i c a l Theodorsen method. F i g u r e 8.2 shows t h e o r i g i n a l p r o f i l e of the NACA-0015 a i r f o i l and the r e s u l t i n g m o d i f i e d p r o f i l e which r e s u l t s from the pr e s e n t procedure when t h i s a i r f o i l i s at 10 degrees i n c i d e n c e between two s o l i d w a l l s . T h i s i s the modified p r o f i l e used i n the c a l c u l a t i o n of the t h e o r e t i c a l p r e s s u r e d i s t r i b u t i o n i n F i g u r e 8.3. with r e s p e c t t o the d i r e c t i o n of the approach fl o w , the modified p r o f i l e i s e f f e c t i v e l y at a s l i g h t l y lower i n c i d e n c e and has s l i g h t l y l e s s camber than the o r i g i n a l p r o f i l e . The a c t u a l p r o f i l e ( o r i g i n a l p r o f i l e s w o l l e n by the a d d i t i o n o f the boundary l a y e r displacement t h i c k n e s s ) about which a p o t e n t i a l flow c a l c u l a t i o n might be c o n s i d e r e d , would be b l u n t at t h e t r a i l i n g edge and would have the t h i c k n e s s of the wake at t h a t p o i n t . The t h i c k n e s s of the boundary l a y e r on the upper s u r f a c e i s g r e a t e r than the t h i c k n e s s on the lower s u r f a c e , except f o r a symmetrical a i r f o i l i n f r e e a i r or between two s o l i d w a l l s , a t zero l i f t . T h e r e f o r e i f the t r a i l i n g edge was imagined to be taken ( v e r t i c a l l y ) as the midpoint of the wake, and the a f t e r p o r t i o n of the p r o f i l e were f a i r e d t o t h a t p o i n t , the r e s u l t i n g shape would be s i m i l a r to the e f f e c t i v e p r o f i l e of F i g u r e 8.2-66 The a i r f o i l i s supposed to be at i n c i d e n c e a - P o i n t s on the p r o f i l e are to be r o t a t e d about the p r o f i l e l e a d i n g edge i n p r o p o r t i o n to t h e i r d i s t a n c e from the p r o f i l e l e a d i n g edge- The d i r e c t i o n of r o t a t i o n i s such to reduce the e f f e c t i v e i n c i d e n c e , of the p r o f i l e - As not a l l p o i n t s are r o t a t e d by the same amount, t h i s i s not a r i g i d body r o t a t i o n about the p r o f i l e l e a d i n g edge. Thus the e f f e c t i v e camber of the p r o f i l e i s reduced as the t r a i l i n g e dge.is " r a i s e d " more than o t h e r p o i n t s on the p r o f i l e . The d e t a i l s of t h i s " r a i s e d " t r a i l i n g edge procedure a r e presented i n Appendix 9- F i g u r e 8.3 shows a comparison of the r e s u l t i n g t h e o r e t i c a l and measured p r e s s u r e d i s t r i b u t i o n s f o r the 0.67-NACA-0015 a i r f o i l at 10 degrees i n c i d e n c e i n t h e presence of two s o l i d w a l l s . The t h e o r e t i c a l r e s u l t s by t h i s procedure are q u i t e s a t i s f a c t o r y except f o r the n e g a t i v e pressure peak near the a i r f o i l l e a d i n g edge. The magnitude of the t h e o r e t i c a l peaks i s s t i l l l a r g e r than the magnitude a c t u a l l y measured, and w i l l always be so f o r any procedure t h a t does not i n c r e a s e the r a d i u s o f c u r v a t u r e of the a i r f o i l l e a d i n g edge to the same degree t h a t a c t u a l l y o c c u r s due t o the boundary l a y e r t h e r e . The above procedure was a p p l i e d t o the a i r f o i l - s h a p e d w a l l s l a t s to see what the e f f e c t would be of r e d u c i n g the c i r c u l a t i o n s t h e r e while m a i n t a i n i n g the f u l l K utta c i r c u l a t i o n on the t e s t a i r f o i l . For the case of the 0.66-Clark-Y a i r f o i l a t 20 degrees i n c i d e n c e i n the presence of a 70%OAH TSOSL w a l l c o n f i g u r a t i o n , t h e t e s t a i r f o i l l i f t c o e f f i c i e n t was reduced 67 from 3.010 to 2.935, t h a t i s , by about 2.5%. T h i s c a l c u l a t i o n used a value of k of 0.80 on a l l the w a l l s l a t s . Thus the e f f e c t on the t e s t a i r f o i l of the n e g l e c t of v i s c o u s e f f e c t s on the w a l l s l a t s alone i s s m a l l i n comparison with the n e g l e c t o f v i s c o u s e f f e c t s on the t e s t a i r f o i l i t s e l f . A complete a c c o u n t i n g f o r the boundary l a y e r e f f e c t s even f o r completely a t t a c h e d flows must i n v o l v e the c a l c u l a t i o n s of the l a m i n a r boundary l a y e r growth, t r a n s i t i o n t o a t u r b u l e n t boundary l a y e r , and the growth o f the wake. Seebohm [ 3 8 ] has performed such c a l c u l a t i o n s and found good agreement w i t h experiments. His procedure i s as f o l l o w s . The u s u a l p o t e n t i a l flow c a l c u l a t i o n s a r e performed f o r the a i r f o i l p r o f i l e , t h e growth of the boundary l a y e r and wake are c a l c u l a t e d . The a i r f o i l p r o f i l e i s s w o l l e n by the boundary l a y e r d i s p l a c e m e n t t h i c k n e s s and i s extended downstream t o r e p r e s e n t the wake. Seebohm develops a c o n d i t i o n to f i x the c i r c u l a t i o n (which reduces t o the e q u a l - v e l o c i t y K u t t a c o n d i t i o n f o r no boundary l a y e r and no wake) based on the p r e s s u r e d i f f e r e n c e a c r o s s the wake, c a l c u l a t e d at two p o i n t s ( v e r t i c a l l y ) above and below the a i r f o i l t r a i l i n g edge, a t the outer edges of the boundary l a y e r s . The l a s t two s t e p s are i t e r a t e d on u n t i l t h e p r e s s u r e d i f f e r e n c e a c r o s s the wake no l o n g e r changes on i t e r a t i o n . Such c a l c u l a t i o n s c o u l d be i n c l u d e d i n the present t h e o r y , on the w a l l s l a t s . A method of h a n d l i n g the s e p a r a t e d flow r e g i o n over t h e upper s u r f a c e of an a i r f o i l at high i n c i d e n c e , approaching maximum l i f t , has been developed by Jacob and S t e i n b a c h [ 2 3 ] . 68 The s e p a r a t i n g s t r e a m l i n e d e p a r t s t a n g e n t i a l l y f r o m t h e u p p e r s u r f a c e s i n c e t h e o b s e r v e d p r e s s u r e s c o r r e s p o n d t o a s m o o t h n o n -z e r o v e l o c i t y d i s t r i b u t i o n a r o u n d t h e , s e p a r a t i o n p o i n t . The s e p a r a t i n g s t r e a m l i n e h a s ah a p p r o x i m a t e l y c o n s t a n t p r e s s u r e v a r i a t i o n a l o n g i t s l e n g t h , n e a r t h e a i r f o i l , t o r e p r e s e n t t h e a p p r o x i m a t e l y c o n s t a n t p r e s s u r e i n t h e r e a l d e a d a i r r e g i o n i n t h e s e p a r a t e d wake. T h i s i s a c c o m p l i s h e d by r e q u i r i n g e q u a l p r e s s u r e s a t a p o i n t a t t h e t r a i l i n g e d g e , and a t a s e c o n d p o i n t a b o v e t h e t r a i l i n g e d g e , on t h e s e p a r a t i n g s t r e a m l i n e . The c i r c u l a t i o n i s t h u s f i x e d , a n d t h e method i s s e e n t o b e . s i m i l a r t o t h e p r o c e d u r e o f Seebohm. A g a i n t h e b o u n d a r y l a y e r c a l c u l a t i o n s must be p e r f o r m e d t o c a l c u l a t e t h e p o s i t i o n o f t h e s e p a r a t i o n p o i n t , and t h e p r e s s u r e on t h e s e p a r a t i n g s t r e a m l i n e . A g a i n s u c h a p r o c e d u r e c o u l d be i n c o r p o r a t e d i n t o t h e p r e s e n t m e t h o d , f o r t h e w a l l s l a t s , i f d e s i r e d . 69 8.2 The Flow i n the Plenum: The Bounding Shear Layer. The second e x t e n s i o n of the present theory i s t o make the geometry of the flow r e p r e s e n t a t i o n more l i k e t h a t which a c t u a l l y occurs e x p e r i m e n t a l l y i n the t e s t s e c t i o n , with t h e plenum surrounding the s l o t t e d w a l l - F i g u r e 8-4 compares the flow r e p r e s e n t a t i o n of the present theory with the p h y s i c a l f l o w which a c t u a l l y occurs i n the t e s t s e c t i o n . The p r e s e n t t h e o r y r e p r e s e n t s a uniform flow of i n f i n i t e e x t e n t , past a s e t of m u l t i p l e a i r f o i l s , and f l a t s u r f a c e s a l i g n e d with the d i r e c t i o n of the undisturbed f l o w . Hence the energy l e v e l s of the. f l o w s i n s i d e and o u t s i d e t h e t e s t s e c t i o n are the same. F i g u r e 8.5 shows a shear l a y e r formed i n s i d e the plenum chamber surrounding the upper s l o t t e d w a l l . T h i s shear l a y e r i s formed as the o u t f l o w i n g a i r from the t e s t s e c t i o n , upstream of the t e s t a i r f o i l , mixes with and e n t r a i n s the o t h e r w i s e s t a g n a n t a i r i n the plenum. T h i s shear l a y e r t h e r e f o r e d i v i d e s the two f l o w s , the high-energy flow which e x i s t s i n the t e s t s e c t i o n , and the zero-energy stagnant flow of the plenum. I n a p o t e n t i a l f l o w t h e o r y , t h i s s h e a r l a y e r c o u l d be i d e a l i z e d as a c o n s t a n t -pressure f r e e s t r e a m l i n e which leaves the t e s t s e c t i o n at the upstream end of t h e s l o t t e d w a l l , e n t e r s the plenum and r e a t t a c h e s to the s o l i d w a l l s e c t i o n at the downstream end of the s l o t t e d w a l l . The p o s i t i o n o f , and the p r e s s u r e v a r i a t i o n a long such a s t r e a m l i n e are i n i t i a l l y unknown. The i n i t i a l and t e r m i n a l p o s i t i o n s , i n c l i n a t i o n s and p r e s s u r e s c o u l d be estimated from a flow f i e l d c a l c u l a t i o n which omits r e p r e s e n t a t i o n of t h i s s t r e a m l i n e e n t i r e l y . 70 An i t e r a t i v e procedure c o u l d be developed t o c a l c u l a t e the p o s i t i o n of t h i s s t r e a m l i n e i n a segmented s t e p - b y - s t e p approach. , The p o s i t i o n of a segment would be assumed- The r e s u l t i n g flow i n c l i n a t i o n s would be c a l c u l a t e d in. the v i c i n i t y of the supposed s t r e a m l i n e and compared w i t h the d i r e c t i o n the s t r e a m l i n e i s t a x i n g t h e r e . These s t e p s c o u l d be i t e r a t e d on u n t i l a, s a t i s f a c t o r y s t r e a m l i n e p o s i t i o n was found. Such procedures are used f o r l o c a t i n g s t r e a m l i n e s i n v o r t e x wakes, but are c o m p u t a t i o n a l l y time-consuming. As the approach to a z e r o l i f t - c o r r e c t i o n w a l l c o n f i g u r a t i o n i s made, the o v e r a l l flow f i e l d w i l l approach c l o s e l y t h a t of the t e s t a i r f o i l i n a f r e e - a i r t e s t environment. An obvious p o s i t i o n t o take f o r such a s t r e a m l i n e i s t h e r e f o r e the p o s i t i o n t h a t the p a r t i c u l a r s t r e a m l i n e i n the f r e e - a i r case o c c u p i e s which passes through the two p o i n t s d e f i n e d by the ends of the s o l i d w a l l s e c t i o n s at the b e g i n n i n g and end of t h e s l o t t e d w a l l . In order to i n v e s t i g a t e the e f f e c t of i n c l u d i n g a c o n s t a n t -p r e s s u r e f r e e s t r e a m l i n e i n the present t h e o r y , an a n a l y t i c two-d i m e n s i o n a l p o t e n t i a l flow r e p r e s e n t a t i o n was developed- The t e s t a i r f o i l was r e p r e s e n t e d by a s i n g l e v o r t e x , and the w a l l s l a t s by a s e t of v o r t i c e s near the c o n s t a n t p r e s s u r e boundary-F i g u r e A6.2 shows the m u l t i p l y - i n f i n i t e s e t of v o r t e x images r e q u i r e d to s a t i s f y the boundary c o n d i t i o n s . On the s o l i d lower w a l l , the boundary c o n d i t i o n i s zero d i s t u r b a n c e v e l o c i t y normal to the w a l l . On the c o n s t a n t pressure boundary, the l i n e a r i z e d c o n d i t i o n of c o n s t a n t pressure can be expressed v i a B e r n o u i l l i ' s 71 e q u a t i o n a s r e q u i r i n g z e r o d i s t u r b a n c e v e l o c i t y i n t h e s t r e a m w i s e ' d i r e c t i o n . Thus i n s o l i d b o u n d a r i e s , t h e a p p r o p r i a t e i m a ge o f a v o r t e x i s a v o r t e x o f e q u a l but o p p o s i t e c i r c u l a t i o n ; t h e i m a g e i n a c o n s t a n t p r e s s u r e b o u n d a r y h a s i d e n t i c a l c i r c u l a t i o n . The d e t a i l s o f t h e image s y s t e m a n d t h e e g u a t i o n s i n v o l v e d a r e i n A p p e n d i x 6. The r e s u l t s shown i n F i g u r e 8.6 c o m p a r e -the p r e s e n t a n a l y t i c i m a g e r e p r e s e n t a t i o n w i t h t h e a n a l y s i s o f H a v e l o c k [ 5 ] , f o r a f l a t p l a t e (a) between two s o l i d w a l l s , (b) i n g r o u n d e f f e c t , (c) b e t w e e n a s o l i d l o w e r b o u n d a r y and a c o n s t a n t p r e s s u r e u p p e r b o u n d a r y , and (d) b e t w e e n two c o n s t a n t p r e s s u r e b o u n d a r i e s (open j e t ) . The i m a g e r e p r e s e n t a t i o n i s u n s a t i s f a c t o r y a s i t p r e d i c t s a l o w e r l i f t t h a n f o r e i t h e r t h e g r o u n d e f f e c t o r t h e open j e t c a s e ; t h e e x p e r i m e n t s i n d i c a t e l i f t s a b o v e t h e g r o u n d e f f e c t v a l u e s . T h a t t h e l i f t i s s o l o w i s a r e s u l t , o f t h e c o n s t a n t p r e s s u r e b o u n d a r y c o n d i t i o n w h i c h r e q u i r e s t h e t a n g e n t i a l d i s t u r b a n c e v e l o c i t y t o be z e r o t h e r e . The c o r r e s p o n d i n g v a l u e o f t h e p r e s s u r e c o e f f i c i e n t , C p , i s z e r o . By t r a c k i n g a s t r e a m l i n e ( i n t h e TSOSL w a l l c o n f i g u r a t i o n t h e o r y ) w h i c h l e a v e s t h e t e s t s e c t i o n t h r o u g h t h e s l o t t e d w a l l u p s t r e a m o f t h e t e s t a i r f o i l , a n d r e - e n t e r s t h e t e s t s e c t i o n d o w n s t r e a m o f t h e t e s t a i r f o i l , t h e t h e o r e t i c a l v a r i a t i o n o f p r e s s u r e a l o n g - s u c h a s t r e a m l i n e i s known. F i g u r e 8.7 shows s u c h a p r e s s u r e v a r i a t i o n , a n d , e x c l u d i n g t h e l a r g e n e g a t i v e p r e s s u r e e x c u r s i o n s a s t h e f l o w . a c c e l e r a t e s when i n the- v i c i n i t y o f t h e w a l l s l a t s , t h e a v e r a g e . v a l u e - o f . t h e p r e s s u r e c o e f f i c i e n t on t h i s s t r e a m l i n e i s 72 about -0.25. Hence any r e p r e s e n t a t i o n which uses a zero C value P i s i n c o r r e c t . \ The TSUSL wall c o n f i g u r a t i o n theory i n d i c a t e s t h a t the w a l l s l a t s c o l l e c t i v e l y have a net c o u n t e r - c l o c k w i s e c i r c u l a t i o n , s i n c e there are a l a r g e r number of s l a t s immersed i n the r e - e n t e r i n g flow than i n the e x i t i n g f l o w . However the. image r e p r e s e n t a t i o n c o r r e c t l y p r e d i c t s the e f f e c t on the a i r f o i l l i f t of i n c l u d i n g the c i r c u l a t i o n on the w a l l s l a t s v i a the s e t of v o r t i c e s adjacent to the c o n s t a n t p r e s s u r e boundary. For example, f o r a f l a t p l a t e at 26.3° i n c i d e n c e (see Appendix 6 and F i g u r e 8.6), the image r e p r e s e n t a t i o n p r e d i c t s t h a t the l i f t i s depressed 25% below the f r e e a i r value; the c o n t r i b u t i o n from the w a l l s l a t v o r t i c e s i s 2% and t h a t from the c o n s t a n t p r e s s u r e boundary i s .23%. The comparison would be b e t t e r f o r the f l a t p l a t e at 20° i n c i d e n c e , but the c a l c u l a t i o n s use w a l l s l a t c i r c u l a t i o n values from a Clark-Y a i r f o i l a t 20° i n c i d e n c e and 7 0%OAR. However, any s i n g l e p o t e n t i a l flow f r e e - s t r e a m l i n e r e p r e s e n t a t i o n cannot model the d i v i s i o n of the two flows of very d i f f e r e n t energy l e v e l , t h a t i s , t o t a l head, c o r r e c t l y . Suppose that the p o s i t i o n of the s t r e a m l i n e r e p r e s e n t i n g t h i s shear l a y e r i s known. The flow along t h i s s t r e a m l i n e s a t i s f i e s the t a n g e n t - v e l o c i t y boundary c o n d i t i o n . In a d d i t i o n , the pressure v a r i a t i o n along t h i s s t r e a m l i n e must r e f l e c t the f a c t t h a t the flow energy l e v e l on one s i d e of t h i s s t r e a m l i n e ( i n the plenum) i s z e r o . On the other s i d e (in the t e s t s e c t i o n ) the flow energy l e v e l i s t h a t of the Uniform u n d i s t u r b e d approach flow. T h i s shear l a y e r c o u l d be modelled a n a l y t i c a l l y by a vortex sheet, but t h i s • modelling was not attempted here. 7 3 P h y s i c a l l y t h e p r e s s u r e v a r i a t i o n i n t h e s h e a r l a y e r o r on a r e p r e s e n t a t i v e s t r e a m l i n e i s a r e s u l t o f t h e manner i n w h i c h t h e h i g h e n e r g y t e s t s e c t i o n f l o w l e a v e s t h e s o l i d w a l l s e c t i o n , a n d o f t h e low p r e s s u r e r e g i o n o f r e c i r c u l a t i n g f l o w s o f o r m e d i n t h e p l e n u m . To r e p r e s e n t t h e s h e a r l a y e r by t h e p r e s e n t t h e o r e t i c a l m e t h o d , c o i n c i d e n t s o u r c e a n d v o r t e x e l e m e n t s a r e d i s t r i b u t e d a l o n g a r e p r e s e n t a t i v e s t r e a m l i n e . S o u r c e e l e m e n t s a r e u s e d i n t h e u s u a l manner t o e n s u r e t h a t t h e f l o w i s t a n g e n t i a l t o t h e s u r f a c e . V o r t e x e l e m e n t s , a l l o f d i f f e r e n t s t r e n g t h d e n s i t i e s , a r e u s e d t o s e t p r e s c r i b e d v a l u e s o f t h e t a n g e n t i a l v e l o c i t y a t e a c h c o n t r o l p o i n t on t h e s u r f a c e . T h u s i f t h e s h e a r l a y e r i s r e p r e s e n t e d by, s a y , S c o n t r o l p o i n t s , t h e r e a r e a n a d d i t i o n a l unknown S s o u r c e and S v o r t e x s t r e n g t h d e n s i t i e s . T h us . t h e r e a r e S a d d i t i o n a l z e r o n o r m a l - v e l o c i t y e q u a t i o n s , and S a d d i t i o n a l p r e s c r i b a d - t a n g e n t i a l - v e l o c i t y e g u a t i o n s t o be s o l v e d . S i n c e i t i s u s u a l t o p r e s c r i b e t h e p r e s s u r e v a r i a t i o n o n t h e s u r f a c e r a t h e r t h a n t h e t a n g e n t i a l v e l o c i t y v a r i a t i o n , t h e t a n g e n t i a l v e l o c i t y b o u n d a r y c o n d i t i o n e q u a t i o n s h a v e t h e f o r m , f r o m (3. 1 4 , 3 . 1 8 ) : N M R(k) S 7 ( B . U . + A . V . ) % v r i l r i i-* r = l (8.1) = - U c o s e . ± / ( l - C ) , i = l , 2 1 p. , . . . s. Here y and v a r e t h e s o u r c e and v o r t e x s t r e n g t h d e n s i t i e s r e s p e c t i v e l y on t h e s t r e a m l i n e r e p r e s e n t i n g t h e s h e a r l a y e r . F o r 74 c a l c u l a t i o n s i n the same sense as the flow d i r e c t i o n , the squareroot term i s p o s i t i v e i f the source and vortex elements are d i s t r i b u t e d s e q u e n t i a l l y . The i n i t i a l and t e r m i n a l p o s i t i o n s o f t h i s s t r e a m l i n e a r e known, and the co r r e s p o n d i n g i n c l i n a t i o n s and p r e s s u r e s c o u l d be estimated from the flow c o n d i t i o n s on the s o l i d w a l l s e c t i o n s . I t remains o n l y t o s p e c i f y the v a r i a t i o n of p r e s s u r e (between two known end values) along the s t r e a m l i n e . Values of s p r e a d i n g c o e f f i c i e n t s f o r unbounded shear l a y e r s are to be found i n the l i t e r a t u r e , ( f o r example, [40]) and i f estim a t e s c o u l d be made of the e f f e c t of confinement which occurs here i n the plenum, such e s t i m a t e s c o u l d then be used t o s p e c i f y the p o s i t i o n of a s t r e a m l i n e r e p r e s e n t i n g the shear l a y e r . I t i s proposed that the p r e s s u r e v a r i a t i o n along the s t r e a m l i n e r e p r e s e n t i n g the shear l a y e r i s a f r e e parameter i n the a n a l y s i s here. That i s , s e v e r a l p r e s s u r e v a r i a t i o n s were assumed and s p e c i f i e d , and the computations performed. The s t r e a m l i n e t r a c k i n g procedure of Appendix 4 was used t o compute the v a r i a t i o n of pressure along the s t r e a m l i n e s of s i m i l a r p o s i t i o n and shape as are r e q u i r e d f o r s p e c i f i c a t i o n o f the p o s i t i o n of the shear l a y e r . T h i s pressure v a r i a t i o n i s shown on F i g u r e 8.7. T h i s s t r e a m l i n e l e a v e s the upstream upper s o l i d w a l l s e c t i o n and r e -e n t e r s the t e s t s e c t i o n downstream of the t e s t a i r f o i l , t h u s a p p a r a n t l y " e n t r a i n i n g " some of the e x t e r i o r flow. I t would be 75 expected, from c o n t i n u i t y , t h at t h i s s t r e a m l i n e should end on the downstream upper s o l i d w a l l s e c t i o n . Hess [ 2 2 ] e x p e r i e n c e d s i m i l a r "leakage" f l o w s i n the c a l c u l a t i o n of the i n t e r i o r flow i n a r i g h t angle bend. At f i r s t i t appeared that t h e r e were too few s o u r c e elements on the s o l i d w a l l s e c t i o n s , and t h a t the s o l i d w a l l s e c t i o n s were too s h o r t . These s e c t i o n s were lengthened from two t e s t a i r f o i l chord l e n g t h s to t e n , and the number of s o u r c e elements on a s e c t i o n was i n c r e a s e d from 20 t o 50. The "entrainment" e f f e c t was s t i l l p r e s e n t . T h i s a p p a r a n t l y i s a common problem f o r i n t e r i o r flow c a l c u l a t i o n s u sing f l a t d i s t r i b u t e d source elements with c o n s t a n t uniform s o u r c e s t r e n g t h d e n s i t i e s ; the problem i s e l i m i n a t e d by u s i n g c u r v e d source elements with l i n e a r or p a r a b o l i c v a r i a t i o n s of s o u r c e s t r e n g t h d e n s i t i e s over the elements. The "entrainment'•• f l o w r a t e here i s about 5% of the net flow r a t e ; i n Hsss's example the "leakage" flow r a t e was 12%. With the end v a l u e s of pressure s p e c i f i e d , s e v e r a l p r e s s u r e v a r i a t i o n s were t r i e d such t h a t the average p r e s s u r e along the s t r e a m l i n e r e p r e s e n t i n g the shear l a y e r was s i m i l a r t o t h e average pressure on the t r a c k e d s t r e a m l i n e s . The r e s u l t s i n F i g u r e 8.8 show how the a i r f o i l l i f t c o e f f i c i e n t v a r i e s with t h e assumed value of C . T h i s r e p r e s e n t a t i o n of the shear l a y e r i s P used i n the f o l l o w i n g s e c t i o n to compare the t h e o r e t i c a l and measured values of l i f t - c u r v e s l o p e f o r two a i r f o i l s . 75 8^2 Summary... A comparison of the curves of F i g u r e s 7.2 and 7.3 i n d i c a t e s t h a t at an upper w a l l OAS of 70%, the e x p e r i m e n t a l value of the r a t i o of the l i f t - c u r v e s l o p e s ra/m i s about 2.8% lower than the s t h e o r e t i c a l v a l u e , f o r both the Clark-Y and the NACA-0015 a i r f o i l s . Thus t h e r e i s a s m a l l r e s i d u a l d i f f e r e n c e of 2.8% to be accounted f o r by the e x t e n s i o n s to the the o r y o u t l i n e d i n §8.1 and 8.2. Assuming t h a t t h e r e are curves s i m i l a r t o the curves of F i g u r e 8.8 of the r a t i o of l i f t c o e f f i c i e n t s C /C f o r the L T L F present case, the r e s i d u a l 2.8% c o u l d be accounted f o r by an i n c r e a s e i n C of about +6%, f o r example from -0.33 to -0.31. A P value of C of -0.31 corresponds to the p r e s s u r e l e v e l P e s t a b l i s h e d by the r e c i r c u l a t i n g flow i n the plenum. F.ecall t h a t an adjustment of the same order c o u l d be accounted f o r with the procedure of §8.1, t h a t i s , by r e d u c i n g the c i r c u l a t i o n s on the w a l l s l a t s . Thus the d i f f e r e n c e between the t h e o r e t i c a l and experimental c u r v e s of F i g u r e s 7.2 and 7.3 at any OAR can be accounted f o r i n the theory by a combination o f (i) the r e d u c t i o n of the c i r c u l a t i o n s on the w a l l s l a t s by modifying t h e i r e f f e c t i v e p r o f i l e s , and ( i i ) by the r e p r e s e n t a t i o n . o f the shear l a y e r i n the plenum by a s i n g l e s t r e a m l i n e of assumed p o s i t i o n and streamwise pressure v a r i a t i o n . These e x t e n s i o n s are p r e l i m i n a r y ; f u r t h e r work i s r e q u i r e d t o e s t a b l i s h a s a t i s f a c t o r y theory. 77 9j. C o n c l u s i o n s . A two-dimensional theory which p r e d i c t s a s a t i s f a c t o r i l y c o r r e c t i o n - f r e e windtunnel t e s t c o n f i g u r a t i o n has been developed. The t h e o r y i s an e x t e n s i o n of the two-dimensional p o t e n t i a l flow theory based on the method of d i s t r i b u t e d s u r f a c e s i n g u l a r i t i e s . The extended theory takes i n t o c o n s i d e r a t i o n not only a wide range of a i r f o i l s i z e s and shapes, but a l s o the e f f e c t on the a i r f o i l l o a d i n g s of d i f f e r e n t windtunnel w a l l c o n f i g u r a t i o n s . The r e s u l t s of the t h e o r e t i c a l study i n d i c a t e t h a t f o r two-d i m e n s i o n a l a i r f o i l t e s t i n g , a windtunnel c o n s i s t i n g of a s o l i d w a l l o p p o s i t e the pressure s i d e of the a i r f o i l , and a t r a n s v e r s e l y s l o t t e d w a l l , the s o l i d p o r t i o n s of which are symmetrical a i r f o i l - s h a p e d s l a t s at zero i n c i d e n c e , with open area r a t i o between 60 and 70 p e r c e n t , o p p o s i t e the s u c t i o n s i d e of the a i r f o i l , w i l l y i e l d u n c o r r e c t e d pressure d i s t r i b u t i o n s and l i f t c o e f f i c i e n t s which are w i t h i n a few percent of t h e f r e e a i r v a l u e s . The t h e o r y p r e d i c t s t h a t t h i s l o w - c o r r e c t i o n w a l l c o n f i g u r a t i o n w i l l remain r e l a t i v e l y c o r r e c t i o n - f r e e f o r a wide range of a i r f o i l s i z e s and a n g l e s of i n c i d e n c e . Experiments c a r r i e d out on a number of a i r f o i l s f o r a Reynolds number range of 300,000 to 1 m i l l i o n (based, on. the a i r f o i l c h o r d ) , i n a two-dimensional t e s t c o n f i g u r a t i o n support the p r e d i c t i o n s of the theory. E xperimental work showed t h a t t h e c o r r e c t i o n - f r e e t e s t c o n f i g u r a t i o n c o u l d be a c hieved with a s l o t t e d w a l l c o n s i s t i n g of symmetric a i r f o i l shaped s l a t s a t zero i n c i d e n c e , when the s l o t t e d s e c t i o n was surrounded by a 78 plenum chamber. The above theory was then extended t o account f o r v i s c o u s e f f e c t s on the w a l l s l a t s , and the e f f e c t of the shear l a y e r which forms i n the plenum chamber. Measurements taken with the c o r r e c t i o n - f r e e w a l l c o n f i g u r a t i o n of the l i f t , drag and p i t c h i n g moments f o r nine d i f f e r e n t a i r f o i l s which ranged i n s i z e (chord to h e i g h t r a t i o ) from-0.17 to 0.67, showed good agreement with e s t a b l i s h e d f r e e a i r v a l u e s . Furthermore, measurements of the p r e s s u r e d i s t r i b u t i o n on two a i r f o i l s , with the c o r r e c t i o n - f r e e w a l l c o n f i g u r a t i o n , showed good agreement with pressure d i s t r i b u t i o n s measured i n s o l i d w a l l c o n f i g u r a t i o n s and c o r r e c t e d by st a n d a r d methods. The l o w - c o r r e c t i o n t e s t c o n f i g u r a t i o n theory which has been t e s t e d and v e r i f i e d i n the work r e p o r t e d i n t h i s t h e s i s can be developed t o p r o v i d e a r e l i a b l e means of t e s t i n g high l i f t a i r f o i l s i n e x i s t i n g windtunnels which can be mo d i f i e d t o ac h i e v e the l o w - c o r r e c t i o n w a l l c o n f i g u r a t i o n . Such t e s t s would otherwise r e q u i r e e l a b o r a t e t e s t f a c i l i t i e s or complex c o r r e c t i o n procedures. Appendix 1. The I n t e g r a t i o n o f a Three Dimensional P o i n t Source t o a Two Dimensional F l a t D i s t r i b u t e d Source Element The p o t e n t i a l cj> a t a p o i n t P due t o a source s t r e n g t h d e n s i t y d i s t r i b u t i o n a(Q) over a s u r f a c e S i s , from (3.2), (x,y,0) = As 2 d? _„ /(x-a2+y2+c2 (A1.2) The i n n e r i n t e g r a t i o n sums over a l l i n f i n i t e s i m a l source . elements d£d£; t o produce t h a t p a r t o f the p o t e n t i a l a t P due to a l i n e source element o f width d£. The o u t e r i n t e g r a t i o n sums over a l l such l i n e source elements t o produce the p o t e n t i a l a t P due to a f l a t d i s t r i b u t e d source element o f wid t h As, and o f c o n s t a n t u n i f o r m s t r e n g t h d e n s i t y . The v e l o c i t y components i n the x and y d i r e c t i o n s r e s p e c -t i v e l y , induced a t P by a source element o f width As, a r e : 80 V = x V 34) 3 x 3(j) 3y + + As 2 (x - C)I(x,?/y) d£, As 2 As 2 y l ( x , 5 , y ) d£ , As 2 ( A 1 . 3 ) (A1.4) where I(x,£,y) = !«»• ((x-?) 2+y 2+? 2) 3/2 (A1..5) Now _3 ( ( x - o 2 + y 2 ) / ( ( x - ? ) 2 + y 2 + c 2 ) j . ( ( x - £ ) 2 + y 2 + s 2 ) ^ (A1.6) t h e r e f o r e I ( x , £ , y ) = ( ( x - 0 2 + y 2 ) / ( ( x - £ ) 2 + y 2 + C 2 ) - ~ ( x - ? ) 2 + y 2 (A1.7) A l s o ^ ( - l o g ( ( x - ? ) 2 + y 2 ) ) = + 2 ( X " S ) , 9 5 ( x - ? ) 2 + y 2 (A1.8) ( t a n " 1 ^ 1 ) = 3 5 C-x i y J ( 5 - x ) 2 + y 2 (A1.9) Th e r e f o r e V As •log( (x - 5 ) 2+y 2) As ' 2 +log [ ( x - ^ ) 2+y 2J (Al.10) 81 V = 2tan Y 5-x t y As r , A s X + - — As ' 2 2 (tan -1 l y J - tan -1 x — As y J ) . ( A l . l l ) In a two di m e n s i o n a l i n c o m p r e s s i b l e , i r r o t a t i o n a l flow, the stream f u n c t i o n ty and the p o t e n t i a l ty are conjugate harmonic f u n c t i o n s . Thus the Cauchy-Riemann equations r e q u i r e dty _ 3 3y 3x' H i 3x 9(j) 3y (A1.12) Hence ty may be expressed as ijj(x,y) - o (|i)dy + f (x) - j ( | | ) d x + g(y) , (A1.13) where f and g are a r b i t r a r y f u n c t i o n s and ty0 i s an a r b i t r a r y c o n s t a n t . Some u s e f u l i d e n t i t i e s a r e : l o g ( y 2 + a 2 ) = - ^ ( y l o g (y 2+a 2) - 2y + 2atan 1 ) , (A1.14) tan -1 (xtan 1 — - ^-log ( x 2 + a 2 ) ) , 3x' ( A 1 . 1 5 ) tan ''"A ± tan XB = tan x ( j ^ g ) • 1 rA±B (A1.16) T h e r e f o r e , from Al.10, H = s f f " Y A + x B + c ) < ( A 1 . - 1 7 > where A = l o g ( x + % . 2 + y 2 ^ As { ( x ~ ) 2 + y 2J C = Astan B = 2tan 2xy -1 yAs [ x 2 + y 2 - ( ^ ) 2 J (A1.18) l x 2 " Y 2 - ( f ) 2 J A c c o r d i n g t o equations (Al.13) and (A1.17), the stream f u n c t i o n f o r a f l a t d i s t r i b u t e d source element o f wi d t h As and u n i t s t r e n g t h d e n s i t y i s iMx fy) = tyo + A - B + C. (A1.19) As i n e q u a t i o n ( A l . 1 3 ) , the p o t e n t i a l may be expressed as (J)(x,y) - 0 i s an a r b i t r a r y c o n s t a n t . The a p p l i c a t i o n o f the t h r e e r e l a t i o n s ( A l . 1 4 ) , (A1.15), and (A1.16) to (Al.19) r e s u l t s i n 83 ( A1.21) D = f l o g ( ( x ^ ) V ) [ ( x - ^ ) V ! ^ T h e r e f o r e t h e p o t e n t i a l f u n c t i o n f o r a f l a t d i s t r i b u t e d s o u r c e e l e m e n t o f w i d t h As a n d u n i t s t r e n g t h d e n s i t y i s (J)(x,y) = c f > o + x A + yB + D - 2As . ( A 1 . 2 2 ) The c o r r e s p o n d i n g r e s u l t s f o r a u n i t s t r e n g t h d e n s i t y f l a t v o r t e x e l e m e n t c a n be w r i t t e n i m m e d i a t e l y s i n c e i n a t w o - d i m e n s i o n a l i n c o m p r e s s i b l e i r r o t a t i o n a l f l o w 4> ( v o r t e x ) = - ^ ( s o u r c e ) , i> ( v o r t e x ) = +cj) ( s o u r c e ) . (A1.23) 84 Appendix 2._ h Procedure f o r Block Commutation of M a t r i c e s Aj_ 8 and C__ When the m a t r i c e s A., B and C are l a r g e , C might be assembled from A and B by p a r t i t i o n i n g C i n t o b l o c k s as f o l l o w s . Memory i s a l l o c a t e d f o r A, B and C a c c o r d i n g t o the s i z e "of the l a r g e s t b l o c k . * j = l , 2, . . .N* j=N+l,N+2,-. .N+M* i=l,2,..NL4 i=NSUl,NSU2 i=NKA,M r A. . D i R ( k ) r - y B . * L , m i . m = l { i i -j •; A . . ] l R ( k ) c - y B . * L -, m i m = l ' 'B . +B.T r r f 1 R ( k ) >• y (A T T +A _ L , mil mL m = l r r ::B. +B . nU jL • r r R ( k ) ' I (A +A )^ ^ , mU mL . m = l r r t e s t a i r f o i l , f l a p s and s o l i d w a l l s s l a t s r - t h s l a t r - t h a i r f o i l o r f l a p The s u b s c r i p t ' i ' r e f e r s t o the row number i n the matrix C. The meanings f o r the v a r i a b l e s NL4, NSD1, NSB2, NK1, NK2 and NKA are given i n the programs which f o l l o w . Subroutine SUB1 c a l c u l a t e s A and B i n b l o c k s as needed t o assemble the b l o c k s of C. SUB 1 i s c a l l e d twice t o s e t up the zero n o r m a l - v e l o c i t y boundary c o n d i t i o n e g u a t i o n s on a l l s o l i d s u r f a c e s . I t i s c a l l e d f i r s t f o r the t e s t a i r f o i l and f l a p s , and a l l s o l i d w a l l s e c t i o n s and a second time f o r the w a l l s l a t s . S ubroutine SUB2 uses A and B to s e t up the Kutta c o n d i t i o n 85 e q u a t i o n s on t h e w a l l s l a t s . S u b r o u t i n e SUB3 d o e s t h e . saiae f o r t h e t e s t a i r f o i l and f l a p s . The FORTRAN c o d e d v e r s i o n s o f SUB1, SUB2 a n d SUB3 f o l l o w . The s u b r o u t i n e s READER (and WRITER) r e a d ( w r i t e ) a m a t r i x f r o m ( o n t o ) a p e r i p h e r a l s t o r a g e d e v i c e , s u c h a s a m a g n e t i c d i s c . 1 C SUB1 CALCULATES A £ B IN BLOCKS 6 SETS UP -EON'S ZERO NORM VEL ON ALL SOLID 2 C SURFACES 3 SUBROUTINE S U B 1 ( A , B , C , X X , Y Y , D S , C S , S I , N , L , M f N A , N A F 2 , L 1 , L 2 , N S P S , 4 1 NSLATtNS - U l t N K l ) 5 C A,B - MATRICES OF INFLUENCE CCEFFS FOR SOURCE £ VORTEX ELEMENTS 6 c C- MATRIX FOR SYSTEM OF EQN 1S C*SIG=D 7 c SIG(M) - UNKNOWNS IN SYSTEM G*SIG=D - PART IS GAM 8 c GAM(NAFt-NSLAT) - VORTEX STRENGTHS ON KUTTA BODY. 9 c M - TOTAL U UNKNCWS= TOTAL M EQUATIONS 10 c NAF = #TE.ST A I R F O I L S I FLAPS WITH KUTTA CONDITIONS APPLIED 11 c NSU1,NSU2 - SET OF EQN'S FOR ZERO NORMAL VELOCITY ON SLATS. 12 c NK1,NK2 - SET OF EQN'S FOR KUTTA CONDITIONS ON WALL SLATS. 13 c XX,YY - CONTROL POINT COORDINATES; DS - ELEMENT LENGTH 14 c NSLAT - •# OF SLATS WITH KUTTA CONDITIONS; NSPS - U ELEM'S PER SLAT 15 c CS S I - SIN,CCS CF ELEMENT INCLINATION 16 c NA(KJ - RANGE OF CONTROL POINT #'S FOR K-TH TEST AIRFOIL OR FLAP I . E . 1,50 17 c N - TOTAL # CONTROL PTS WHERE NORM VEL IS ZERO ON ALL SOLID SURFACES 18 c L - BLOCK S I Z E 19 c L 1 , L 2 - RANGE OF CONTROL PT H'S FOR BLOCK - SET OF EQN #S ALSO 2 0 REAL A ( N , L ) , B ( N , L ) , C ( M , L ) , X X ( N ) , Y Y ( N ) , D S ( N ) , C S { N ) , S I ( N ) 21 INTEGER NA(NAF2\ 22 NSU2=NSU1+NSPS*NSLAT-1 23 NK2=NSU2=NSLAT 24 NAF=NAF2/2 25 c CALCULATE A AND B. 26 DO .1 I=L1,L2 27 K=I-L1+1 28 DO 1 J=1,N 29 I F { J . N E . I ) GO TO 2 30 A I J t K ) = 6 . 2 8 3 1 9 2 7 31 eu,K j = o . 32 GO TO 1 33 2 DXJ = XX(I }-XX{J) 34 DYJ= YY{I ) - Y Y ( J ) 35 X J = D X J * C S ( J ) + D Y J * S I ( J ) 3 6 Y J = D Y J * C S t J J - D X J * S I ( J ) 3 7 DSJ2=0S( J ) / 2 . 38 Y J S = Y J * Y J 39 S=XJ-rDSJ2 40 T=XJ-DSJ2 I Q ft CM I joo I 3 |>-4-C O >-+ •H-oo —> + •»• 00 o o _ J II X — - ) - 5 - J OO 00 —• oo ' 00 l_) Q I + CM •— — Z 00 oo < u o < — — CM >-« 00 II OO <_} >- I) II —<—>—> zz -> a CM co - J ->i- -»—* t—t 00 a oo o oo L U > cc o z a 0£ LU M cc a 00 2 - 3 C J II LU - 3 a . a LU OO on 00 < 00 a CD CC a H s: o a e> 2: r-— CC < O O - I • LL OO Of 2 LU 00 •• • - —I f-.Z II < Of 00 —I LU ^ lA o Q LU 00 CM COivf LA 43 i r\ L o l i n i n i r \ I 00 id •«• 00 .-t a . I 00 00 Z Q. + O0 Z ZD > OO z 11 11 ^ _J •XL M co 0* LO lT\ i i w i i —-II CO I » co O ^ 00 II II co a .co 00 o 00 r - i CM s0 O 00 a . < 1 u. o j OO o cc 00 —I LU > 2: ex a z a a: LU M or a a . a . < z 00 •• CO - 1-1 cfl Z l| I! O Z — LU »—4 » Q . CO - 3 3 — a 0 1 — 0 LU OO m u r-ro co i i i i < < z z II II —1 CM i i i i r - c o i i + U -»• —1 >- ai X ^ z r - Qi _ l ZZ) HI J h y— < L U >-i o CX oi 3 r— r«- r > f>- f— CO 79 80 93 94 95 96 97 98 99 100 101 102 103 104 105 106 10 7_ 108 109 110 111 112 113 114 115 116 SUB2 SETS UP KUTTA EQN'S DN WALL SLATS.' SUBROUTINE SUB2(A,B,C,NA,N,L,M tNAF2,NSLAT,NSPStNSU1,NK1) X f ~~~ REAL A ( N , L ) , B ( f l 7 T T 7 C ( K T N S n m 82 INTEGER P » Qt NA(NAF2 I 83 C A» B - MATRICES -OF INFLUENCE COEFFS FOR SOURCE £ VORTEX ELEMENTS 84 C C- MATRIX FOR SYSTEM OF EQN'S C*SIG=D 85 C M - TOTAL ti UNKN0WS= TOTAL # EQUATIONS 86 C NAF=#TEST A I R F O I L S £ FLAPS WITH KUTTA CONDITIONS APPLIED ~87 C NSU1,NSU2 - SET OF EQN'S FOR ZERO NORMAL VELOCITY ON SLATS. 88 C NK1,NK2 — SET OF EQN'S FOR KUTTA CONDITIONS ON WALL SLATS. 89 C NSLAT - # OF SLATS M Jj-_ J_UJ_T A_ CONDITIONS; NSPS - # ELEM'S PER SLAT ~9Q~~- C _ l ^ T i n — : n R A N G E ~ O F CONTROL POINT #»S FOR K—TH TEST AIRFOIL OR FLAP I . E . 1,50 91 C . N - TOTAL # CONTROL PTS WHERE NORM VEL IS ZERO ON ALL SOLID SURFACES 92 C L=NSPS*NSLAT - BLOCK S I Z E ; : : NAF=NAF2/2 NSU2=NSU1+NSPS*NSLAT-1 NK1=NSU2+1 NK2=NSU2-fNSLAT C READ IN THAT PART OF A £B WHICH CONTAINS THE INFLUENCE COEFFS FOR V E L O C I T I E S C INDUCED AT THE CONTROL POINTS ON THE WALL SLATS. CALL READER(A,N,L ) CALL READER I B , N , L ) SET UP EQNS F_Q_R KUTTA CN WALL SLA_TS_ ' "_TQ i i=i, N SLA T P=1+NSPS*(1-1) Q=P+NSPS-1 C P , Q - T.E. CONTROL PT #S FOR SLATS C 2 LOOP - TANG'L VELS DUE TO ALL SOURCE ELEM'S. ' DO 2 J=L ,N • 2 C C ( J , I ) = B ( J , P ) + B t J , Q ) 4 LOOP - TANG'L VELS DUE TO VORTEX ELEM'S ON SLATS DO 4 KS=1,NSLAT . . J=NK1+KS-1 KK=NSU1+NSPS*(KS-l) KL=KK+NSPS-i SA = 0. DO 3 K=K'K , KL SA=SA+A(K,P)+A(K,Q) 117 4 C ( J , I ) = S A 118 C 6 LOOP - TANG'L VELS DUE TO VORTEX ELEM'S ON AIRFOILS £ F L A P S . -co-co 119_ _10_ DO 6 KN- 1, NAF . 1 2 0 " K3=2*(NAF+1-KN)-1 121 K1=NAIK33 122 K2=NMK3 + 1) : ; __ 123 J-=N-NAF + KN 124 SA=0. 125 DO 5 K=K1, K2 ; - . . 126 5 SA = SA + A(K,P)+A{K,Q ) 12 7 6 C U » I ) = SA 128 1 CONTINUE __ 129 C WRITE THIS PORTION OF C INTO A F I L E . 130 CALL WRITER(C,M,NSLAT) 131 . RE TURN - ; 132 ' END 133 C SUB3 SETS UP KUTTA EQN'S ON TEST A I R F O I L S & F L A P S . 134 SUBROUTINE SUB3(A,B,C,NA,NTE,N,M,NL4,NAF,NAF2,NSPStNSLAT,NSU1,NK1 ) 135 REAL A ( N , N L 4 ) , B ( N ,NL4) ,C(M,NAF) 136 INTEGER NA{NAF2>,NTECNAF» 1.3 7 C A t B - MATRICES OF IN FLU EN CE COEF'FS FOR SOURCE & VORTEX ELEMENTS ____ 138 C C- MATRIX FOR SYSTEM OF EQN'S C*S.IG = D 139 C SIG(M) - UNKNOWNS IN SYSTEM C*SIG=D - PART IS GAM 140 C GAM ( NA F + NS LAT ) - VORTEX STRENGTHS ON KUTTA BODY. _ 141 C NL4 - M OF CONTROL POINTS ON TEST A I R F O I L , FLAPS L SOLID WALL SECTIONS 142 C M - TOTAL # UNKNOWS= TOTAL EQUATIONS 143 C NA F-ffTEST A I R F O I L S £ FLAPS WITH KUTTA CONDITIONS APPLIED 144 C NSLAT - # OF SLATS WITH KUTTA CONDITIONS; NSPS - # ELEM'S PER SLAT 145 G NA{K) - RANGE OF CONTROL POINT #'S FOR K-TH TEST AIRFOIL OR FLAP I . E . 1,50 146 C N - TOTAL H CONTROL PTS WHERE NORM VEL IS ZERO ON ALL SOLID SURFACES 147 - C NT E{K I - CONTROL PT # FOR UPPER T.E. ON K-TH TEST A I R F O I L OR FLAP 148 hSU2=NSUl+NSPS*NSLAT-l !_ 9_ M< - z nj •-CD 0 . •«-*• Z > 0 0 CO z ir-X- X CS 0 to 0 *—V z _1 z zz *—1 •«* IO —* «* 0 _ >v r-l. _ •• * —* >•*_ • _;••<-« &' il •. ""^ t i l _> If f-f ZD < 0 fe: * _ • + !-« cc _ _ _ _ w CO ^ _5 -rr CD -*r 11 1 H .<£ »—> _: i II ZD _! io. _ . 0 II t_ II _ O l» CO £_ _ z to->-+ a: • • BR _3 _•' < il II z Ml _S Z . II CDl Z . t_ H r - l H j j - T H NV ; £_ I! 2 l H II ft':. 11: 11 _ . «"» at _ o _|! -—'.: or. <: _ il w V T X .XI • .XI ^ jr—t *" to X • 'ir* •»! Z X —•_-*] «-*• O _ l -* a: o £_ o o 3 : :t_: z Ir-t .;—• CO 00 ^ M - < •"; ;: X • y-i —1 i rr —* w fc— cc zz <; O H 2: i — -t> Z5 •r -^^tal E — Q O ' 1_ Z O X QL. Ui . " •04-* 188 SUBROUTINE THETA {X,Y,THE,CP,XX,YY,DS,CS,S1,N,VNT,VTT,VM,A,B,SIG, 189 1 GAM,NA,GAMM,M) 190 REAL X X ( N ) , Y Y I N ) , D S I N J * C S ( N ) , S M N ) , A < N) , B (N) , S IG (N i , GAM { N) 19 1 INTEGER P, Q 19 2 COMMONOAO NA,NL4,NSLAT,NSPS 193 C I X , Y ) - CALCULATING FLOW PARAM * S HERE. 19 4 C XX,YY - CONTROL POINT COORDS FOR ALL SOURCE £ VORTEX ELEMS: DS IS ELEM LENGT 195 c SI,CS - SIN,COS ELEM INCLINATION 196 c N - TOTAL 3 CONTROL POINTS 197 c A,B - INFLUENCE COEFFS FOR VELOCITIES INDUCED 2 *-"> where a = - (A5.5) N o n - d i m e n s i o n a l i z i n g , l e t Z = f , R = f , B = K i> c l c l - c l _n_ ar ' (A5.6) and l e t F(k) = (1-| 2)K - E) , (A5.7) w i t h 1 0 1 ;2 = iR . ( A 5 _ 8 ) ( Z - B ) 2 + ( 1 + R ) 2 Tnen $(R,Z) = /R F ( k ) , (A5.9) where K and E are the complete e l l i p t i c i n t e g r a l s of the f i r s t and second k i n d , r e s p e c t i v e l y . To generate the uniform flow a t the e x i t of the c o n t r a c t i n g s e c t i o n , the s t r e a m l i n e s must be p a r a l l e l t h e r e . Hence an i d e n t i c a l r i n g v o r tex must be cen t e r e d at (0,0,-b). The r e s u l t i n g stream f u n c t i o n i s t h e r e f o r e u>(R,Z) = /R (F (k J ) + F ( k 2 ) ) , (AS. 1 0 ) w h e r e i 2 4R , 2 4 R , , c „ k i =• , k 2 = . ( A 5 . 1 1 ) ( Z - B ) 2 + ( 1 + R ) 2 ( Z + B ) 2 + ( 1 + R ) 2 Reference [ 2 9 ] s t a t e s t h a t when b i s 0.46936a the v e l o c i t y d i s t r i b u t i o n over a flow core area of r a d i u s 0.42241a i n the median plane between the vortex r i n g s w i l l be uniform to w i t h i n 1 p a r t i n 500. The e l l i p t i c i n t e g r a l s can be e v a l u a t e d simply from polynomial approximations 17.3.34 and 17.3.36 of [ 4 1 ] . A program was w r i t t e n to search f o r the value of R which, f o r a gi v e n 1 0 2 value of Z gives the same value of ty as through a s t a r t i n g point ( E 0 , Z o ) - In t h i s way the coordinates (R,Z) of the stream surface were generated, using a value of ty of 0.10510. R 0 i s chosen to be 0.30 (see Figure 6 of [40]) to o b t a i n a thr o a t f l o w u n i f o r m i t y w i t h i n 0.23. Thus ro i s 0.30a. The req u i r e d t e s t s e c t i o n entrance area i s 0. 34 8m2. Hence ur2} i s 0.348m2. Therefore r 0 i s 333mm and 'a' i s 1110mm. The nozz l e l e n g t h i s chosen t o be 1.52m, due to p h y s i c a l r e s t r i c t i o n s i n the e x i s t i n g converging s e c t i o n , hence the nozzle entrance area Tix^ i s f i x e d at 1.068m2. Hence r , i s 583mm, or 1.751r 0 or 0.525a. Therefore S i i s 0.525, z i i s 4.53ro or 1.37a. Hence Z i i s 1.37. The t a b l e of nozzle coordinates f o l l o w s . Z , z, R, r are as above, and w and h are the e x i s t i n g width of the c o n t r a c t i n g s e c t i o n and height of the new nozzle i n s e r t r e s p e c t i v e l y . A~7T r 2 z . z R r = w h w h 0.0 0 mm .3 00 333mm 0.34 84m2 9 1 4mm 381mm 0. 1 111 .300 3 33 .3484 915 381 0.2 222 .300 333 . 3484 916 381 0. 3 333 .301 334 . 3507 917 383 0.4 444 .304 337 . 3575 920 389 0.5 555 .309 343 .3706 927 400 0.6 666 .318 353 . 3924 934 421 0.7 777 .331 367 . 4248 942 452 0. 8 888 .343 386 ' . 4700 952 • 496 0.9 999 .370 411 .5298 962 554 1.0 1100 .395 440 .6065 979 626 1.1 1221 .4 26 473 .7023 1002 7 10 1.2 1332 .460 511 .8199 103 6 803 1.3 1443 .498 55 3 .9617 1082 902 1.37 1524 .525 583 1.068 1 123 951 103 AH An.aly_t.ic R e p r e s e n t a t i o n of a L i f t i n g Vortex between a S o l i d a XEiLHSversexy-Slgtted and a Constant P r e s s u r e Boundary.. The f o l l o w i n g d e s c r i b e s an a n a l y t i c two-dimensional p o t e n t i a l flow "method of images" model f o r a l i f t i n g a i r f o i l between a s o l i d lower boundary and a t r a n s v e r s e l y - s l o t t e d upper boundary c o n s i s t i n g of a i r f o i l - s h a p e d s l a t s . A c o n s t a n t p r e s s u r e boundary o u t s i d e the s l o t t e d w a l l r e p r e s e n t s a f r e e s t r e a m l i n e t h a t " d i v i d e s the t e s t s e c t i o n flow from the plenum flow. The a i r f o i l ana the w a l l s l a t s are r e p r e s e n t e d by p o i n t v o r t i c e s which are "imaged" a p p r o p r i a t e l y . The image of a vortex, i n a s o l i d boundary i s a vortex of equal but o p p o s i t e c i r c u l a t i o n ; the image i n a constant pressure boundary i s a v o r t e x of i d e n t i c a l c i r c u l a t i o n . From [ 4 1 ] , the complex p o t e n t i a l f o r an i n f i n i t e v e r t i c a l row of p o i n t v o r t i c e s of the same s i g n , spaced a d i s t a n c e 'd' a p a r t , i s where the " c e n t r a l " vortex i s at zo, and the s t r e n g t h K i s r e l a t e d to the c i r c u l a t i o n r ( p o s i t i v e c l o c k w i s e ) by with r e f e r e n c e to F i g u r e s A6.1, A6.2, the image system f o r F(z) = Klog s i n h - r ( z - z 0 ) ( A 6 . 1) ( A 6 . 2 ) a s i n g l e vortex between the s o l i d and c o n s t a n t p r e s s u r e 104 b o u n d a r i e s i s t h e sura o f f o u r s e t s o f i m a g e s . U s i n g t h e n o t a t i o n o f F i g u r e A6.2, two s e t s a r e o f p o s i t i v e c i r c u l a t i o n , " c e n t e r e d " w i t h z 0 v a l u e s o f a i and ( a + 2 b ) i . The o t h e r two s e t s a r e o f n e g a t i v e c i r c u l a t i o n , " c e n t e r e d " a t - a i and - (a + 2b) i . A l l f o u r s e t s have t h e same s p a c i n g , 4 (a + b) . The c o m p l e t e s y s t e m of images f o r t h e s i n g l e v o r t e x immersed i n a u n i f o r m flow U (from l e f t t o r i g h t ) h as t h e complex p o t e n t i a l F(z) = Uz + K l o g s i n h A ( z - a i ) + K l o g sinhA(z-(a+2b)i) ( A 6 . 3 ) - K l o g sinhA(z+ai) — K l o g sinhA(z+ (a+2b) i ) ., where A = irS+bT • ( A 6* 4 ) The complex v e l o c i t y w(z) i s the d e r i v a t i v e o f F(z) with r e s p e c t t o z. Hence f o r the s i n g l e v o r t e x , w(z) = U + KA(cothA(z-ia) + cothA(z-i(a+2b)) (A6. 5) - cothA(z+ia) - cot h A ( z + i (a+2b) )) ». To c a l c u l a t e t h e f o r c e on the v o r t e x r e p r e s e n t i n g the a i r f o i l , due t o t h e e f f e c t o f t h e two b o u n d a r i e s , the B l a s i u s r e l a t i o n {[41]) i s u s e d , 105 D - i L = w2 (z) dz, (A6.6) where D and L a r e the f o r c e s i n t h e X and Y d i r e c t i o n s . , r e s p e c t i v e l y . I n t e g r a t i o n i s performed about a c o n t o u r e n c l o s i n g o n l y the a i r f o i l v o r t e x . To e v a l u a t e t h i s i n t e g r a l u s i n g r e s i d u e s , w i t h the. a i r f o i l v o r t e x a t i h , t h e c o e f f i c i e n t i n the L a u r e n t s e r i e s e x p a n s i o n o f w 2 ( z ) of the term i n 1 / ( z - i h ) i s r e q u i r e d . The L a u r e n t s e r i e s e x p a n s i o n f o r the c o t h f u n c t i o n about i h i s _„ / -„\ 1 . ( z - i h ) z - i h , ,,r n s coth(z-xh) - r—- + - . — - - - — j - = — - + ... (A6.7) z-xh 3 45 The r e q u i r e d c o e f f i c i e n t i s 2UK + 2 K 2 A ( c o t h A ( z - i ( a + 2 b ) ) - c o t h A ( z + i a ) - c o t h A ( z + i ( a + 2 b ) ) ) . . (A6.8) The r e s i d u e a t i h i s 2UK + 2 K 2 A i ( + c o t ( 2 A b ) + c o t ( 2 A a ) + c o t ( 2 A ( a + b ) ) ) , (A6.9) s i n c e c o t h ( i z ) = - i c o t (z) . (A6. 10) T h e r e f o r e \ • D - i l . = ( ^ ) 2 i r i (Residue (ih) ) . (Ab.11) S u b s t i t u t i n g f o r K i n terms of. r , D i s z e r o , and 106 L - L 0 ( l - j j ^ c s c ( k a ) c s c ( k b ) ) , (A6.12) w here k - 2TaTbT ' ( 4 6 - 1 3 ) ana L 0 = pur (A5. 14) i s the t u n n e l l i f t . T h i s i s the e x p r e s s i o n f o r the r e d u c t i o n i n l i f t e x perienced by a s i n g l e p o i n t vortex between a s o l i d lower boundary and a c o n s t a n t pressure upper boundary. I f t h e v o r t e x i s midway between the two boundaries, Lo = 1 ~ 4UH ' < A 6* 1 5> Using (A6.14) and C T = T — — , (A6.16) ° | P U 2 c where •c' i s the a i r f o i l chord, Now c o n s i d e r the v o r t i c e s Y r e p r e s e n t i n g the a i r f o i l -n 1 0 7 s h a p e d w a l l s l a t s . From e q u a t i o n s ( A 8 . 4 ) , (A6.5) u s i n g . t h e n o t a t i o n o f F i g u r e A 6 . 1 , CO w ( z ) = J k B ( c o t h B ( z - 2 i h - n r ) + c o t h B (z-2i(h+£ ) - n r ) ^ n n ^ n n n n = - o o (A6.-18) - c o t h B ( z + 2 i h - n r ) - c o t h B ( z + 2 i ( h + e ) - n r ) 1 n n n. J i s t h e a d d i t i o n a l c o m p l e x v e l o c i t y due t o t h e f o u r s e t s o f i m a g e s c o r r e s p o n d i n g t o 'n* i n f i n i t e v e r t i c a l r o w s o f p o i n t v o r t i c e s y s p a c e d a h o r i z o n t a l d i s t a n c e ' r ' a p a r t . H e r e k = , B = TTOT-I r . (A6.19) n 2TT n 4 (2h+e ) n and * r ' i s r e l a t e d t o t h e s l o t t e d w a l l o p e n - a r e a r a t i o . H ence t h e c o m p l e t e c o m p l e x v e l o c i t y f i e l d f o r t h e v o r t e x r r e p r e s e n t i n g t h e t e s t a i r f o i l , t h e v o r t i c e s y r e p r e s e n t i n g t h e w a l l s l a t s , a n d t h e u n i f o r m f l o w U, n i s . w ( z ) - U + K A ( c o t h A ( z - i h ) + c o t h A ( z - i ( 3 h + 2 6 ) ) - cothA(z+ih) - cothA(z+i(3h+26))) ( A 6 . 2 0 ) CO + Y ' k B (cothB (z-2ih-nr) + cothB (z-2i(h + e )-nr) L n n v n n n n=-°° - c o t h B ( z + 2 i h - n r ) - c o t h B (z + 2 i (h+e .) - n r ) ) n n n } where 6 and e a r e t h e d i s t a n c e o f r a n d y r e s p e c t i v e l y f r o m 108 the constant pressure boundary. ' F o l l o w i n g the p r e v i o u s procedure to c a l c u l a t e the c o e f f i c i e n t of. 1 / ( z - i h ) i n the Laurent s e r i e s expansion f o r w2 ( z ) , the r e q u i r e d c o e f f i c i e n t i s , using (A6.9), 2UK + 2K 2Ai(cot(2A(h+6)) + cot(2Ah) + cot(2A(2h+6))) + 2K T k B (cothB -xh-nr) + cothB -x(h+2e )-nr) L n n A n n n n = - c o (A6.21) - cothB (+3ih-nr) - cothB (+i(3h+2e ) - n r ) K n n n . wnere A = T(2h+6T* ( A 6 * 2 2 > Mow using coth(x+iy) = c o t h ( x ) c s c 2 ( y ) - i c s c h 2 ( x ) c o t ( y ) ( A 6 . 2 3 ) c o t h 2 ( x ) + c o t 2 ( y ) t o c a l c u l a t e the r e s i d u e of w2 (z) at i h , and u s i n g (A6.12) and (A6.10) , " " L = pur - £|^-(cot (Bh) + cot(8(h+S))) - •— y y B c s c h 2 ( B n r ) F ( B ,h,e , n , r ) , (A6.24) 2TT L 1 n n n n n n=-°° and 109 D pr Y y B coth(B nr)E(B ,h,_ , n , r ) , (A6.25) " rt y~\ Y\ n n 2TT ^ 'n n n=-°° nwhere TT 2(2h+S)' B n 4(2h+£ ) ' n ( A 6 . 2 6 ) E(B ,h,e ,n,r) .= G(B h) + G(B (h+2e )) n n n n n + G(3B_h) + G(B y.(3h+2e_)) , n n n F(B ,h,e ,n,r) = H(B h) + H (B (h+2 e )) n n n n n H(3B h) - H(B (3h+2 e )) n n n In the above e x p r e s s i o n s (A6.27) (A6.28) G(u) = esc (u) c o t h 2 ( B n r ) + c o t 2 ( u ) n (A6.29) and H(u) = c o t (u) c o t h 2 ( B n r ) + c o t 2 ( u ) n (A6.30) When a l l o f the y are of i d e n t i c a l s t r e n g t h , and a l l o f the e ( d i s t a n c e o f Y from the con s t a n t p r e s s u r e boundary) a r e n n 110 e q u a l , t h e .drag f o r c e D i s z e r o , s i n c e c o t h (B_nr) i s an o d d f u n c t i o n of n . N u m e r i c a l l y ' i t i s s a t i s f a c t o r y t o t a k e n g r e a t e r t h a n 10, t h a t i s , 21 or more v o r t i c e s y . F o r t h e c a s e o f a f l a t p l a t e a t 26.3° i n c i d e n c e , and average v a l u e s o f y £ t a k e n f r o m s t r e a m l i n e , c a l c u l a t i o n s f o r a 0 . 6 6 - C l a r k - i a i r f o i l a t . 20° i n c i d e n c e i n t h e p r e s e n c e o f a 70%OAR.TSOSL w a l l c o n f i g u r a t i o n , the v a l u e s of the e x p r e s s i o n s a r e . 0 6 2 5 , 1 = 0 . 1 , £ = 0.67, | = 0.67. (16.31) H ence ~ - 1 " ( 0 . 1 6 8 ) ( I ) - ( - 0 . 3 1 7 ) ) c u c s = 1 - 0. 235 - 0. 020 = 0. 745 , (A6.32) an d t h e d r a g f o r c e D i s z e r o . Hence t h e e f f e c t o f t h e w a l l s l a t c i r c u l a t i o n y on t h e t e s t a i r f o i l i s s m a l l c o m p a r e d t o t h e e f f e c t o f t h e c o n s t a n t p r e s s u r e b o u n d a r y on t h e t e s t . a i r f o i l . A n o t h e r p o s s i b l e a n a l y t i c r e p r e s e n t a t i o n o f t h e b o u n d i n g s h e a r l a y e r , i s a v o r t e x s h e e t , a c r o s s which t h e r e i s a jump i n t a n g e n t i a l v e l o c i t y and t o t a l head. T h i s was n o t a t t e m p t e d h e r e . r U, = 1.40, I l l A p p e n d i x 7. S t a n d a r d S o l i d W a l l C o r r e c t i o n s The f o l l o w i n g s e v e n e x p r e s s i o n s a r e r e p r o d u c e d f r o m p a g e 382 o f [ 3 4 ] , a n d a r e t h e e x p r e s s i o n s u s e d f o r t h e c a l c u l a t i o n s h e r e i n . T h e y a r e w r i t t e n f o r t h e i n c i d e n c e c o r r e c t i o n a p p l i e d a s a n e q u i v a l e n t c h a n g e i n l i f t . The c o r r e c t i o n s a r e t o b e a p p l i e d a t t h e m e a s u r e d i n c i d e n c e . The s u b s c r i p t s T a n d F i m p l y m e a s u r e d a n d e q u i v a l e n t f r e e - a i r v a l u e s r e s p e c t i v e l y . The f i r s t f i v e e x p r e s s i o n s a r e , r e s p e c t i v e l y , t h e c o r r e c -t i o n s t o be a d d e d ( r e g a r d l e s s o f s i g n ) t o t h e m e a s u r e d v a l u e s o f w i n d s p e e d , i n c i d e n c e a n d l i f t , q u a r t e r c h o r d p i t c h i n g moment, a n d d r a g c o e f f i c i e n t s . AU = U F - U T = e U T (A7.1) Aa = a_ - a_ = 0. (A7.2) A C L " = - 2 E V K V 2 ¥ ( V 4 C M C T > £ ? " <"- 3> A C H C = C M = "Sic = - 2 e C M c + ! V ^ ( W ' ^ f ' ( A 7 - 4 ) 4 4 F 4 T 4 T 4 T A C D = C D - CD T = - 2 £ C D T + 27(CL + 4 C M c > ( C L ~ If D> ' " - T T I n t h e a b o v e e q u a t i o n s , e i s c o m p o s e d o f t h e c o r r e c t i o n s 112 f o r wake and s o l i d blockage, and i s g i v e n by 1 rc^ e = f f e ) C D _ + A K ' (A7.6) where K = ^ ( | ) \ (A7.7) and c/H i s the model s i z e . The q u a n t i t y A i s o b t a i n e d from F i g . 6 . 8 of [ 3 9 ] . In p r a c t i c e , the a - d e r i v a t i v e v a l u e s are determined g r a p h i c a l l y . Otherwise the f o l l o w i n g v a l u e s may be used: = 27T, = 0 , _ M ^ = 0 , ^ = . 2 . ( A 7 . 8 ) The f o l l o w i n g c o r r e c t i o n i s a p p l i e d t o the measured p r e s s u r e d i s t r i b u t i o n s (at the measured i n c i d e n c e ct^) : 113 _E___S__ __ _ _______ _______ _ _ _ _ _ i _ _ _ 2 _ __________ ____ ___ ________ L i f t . In t h i s method, the usual Kutta c o n d i t i o n , of equal v e l o c i t i e s on the upper and lower surfaces of a l i f t i n g body, adjacent to the t r a i l i n g edge i s abandoned. The c i r c u l a t i o n i s to be determined from the measured l i f t . To s i m p l i f y the equations, consider a s i n g l e t e s t a i r f o i l between s o l i d w a l l s . The a i r f o i l i s represented by N c o n t r o l p o i n t s , and the two plane s o l i d walls by M-N a d d i t i o n a l c o n t r o l p o i n t s . Thus the t o t a l number of c o n t r o l p o i n t s i s li. There are t h e r e f o r e Pi. unknown source s t r e n g t h d e n s i t i e s o and a s i n g l e unknown vortex stre n g t h d e n s i t y y on the a i r f o i l . Thus H+1 equations are r e q u i r e d to determine the M+1 unknowns. There are M c o n t r o l points at which the norma 1 - v e l o c i t y boundary c o n d i t i o n must be s a t i s f i e d ; these y i e l d M equations. In the n o t a t i o n of §3.2, the t a n g e n t i a l v e l o c i t y a t a p o i n t • i ' i s The (M+1)st equation u s u a l l y c o n t a i n s the Kutta c o n d i t i o n at the . a i r f o i l t r a i l i n g edge. The usual Kutta c o n d i t i o n i s expressed as M N ( A 8 . 1) = - V (A8. 2) x i + 1 114 w h i c h r e s u l t s i n t h e e q u a t i o n M N | 1 ( B j i + B j i + l ^ 0 j . + . Y k I 1 ( A k i + A k i + l ) = - U ( c o s 0 i + c o s 9 i + 1 ) ( A 8 . 3 ) f o r t h e c o n t r o l p o i n t s ' i ' and ' i + 1 ' a d j a c e n t t o t h e t r a i l i n g e d g e . The r e s u l t i n g f u l l K u t t a c i r c u l a t i o n ?o a b o u t t h e a i r f o i l c a n be c a l c u l a t e d f r o m t h e d e f i n i t i o n N = 4 V-d£ = I V As. J C i = l \ 1 (A8.h) To d e t e r m i n e t h e c i r c u l a t i o n r f r o m t h e m e a s u r e d l i f t , t h e K u t t a - J o u k o w s k y l a w e x p r e s s e s t h e m e a s u r e d l i f t f o r c e , L, o n t h e a i r f o i l a s L = PUP . (A8.5) The m e a s u r e d l i f t c o e f f i c i e n t C L i s d e f i n e d a s C T = T - V " ' U 8 - 6 ) p U 2 c 2 where ' c 1 i s t h e a i r f o i l c h o r d . T h e r e f o r e T = f U c C L - (A8.7) The l e f t . s i d e o f e q u a t i o n (A8-7) i s t h e r e f o r e w r i t t e n N N M N I V As. = I I B a + Y I A + UcosG I As. , i = l t i 1 i = l A j = l 3 1 3 k = l K l ^ 1 (A8.3) and (A3. 7) become; M C N r N r N ^ y B . . A S . • i 3 1 x a . + 3 I l i = l 2 A k i As . l J (A3.9) = -U N J c o s 6 . A s . i = l 1 1 + ^ C C L The l a s t row o f t h e m a t r i x C i n t h e s y s t e m o f e q u a t i o n s C ( o, y)-d, w i l l now be N 'j ,M+1 = I B ± A s i , j = l , 2 , . . . M , (A8.10) i = l N r N = y y A 'M+1, M+1 . L , L -. k i ' i = l <-k=l As. = c o n s t a n t , l ( A8. 1 1) and t h e l a s t c o m p o n e n t o f t h e r i g h t h a n d s i d e v e c t o r w i l l be M+1 -U N J c o s O . A s . i i i 1 x + | U C C L (A8. 12) The e x p r e s s i o n s ( A 8 . 1 0 ) , (A8. 11) and (A8.12) r e p l a c e t h e c o r r e s p o n d i n g e x p r e s s i o n s i n (4.2) and ( 4 . 3 ) . 116 ________ __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ i_______2_ __________ k i _ 2 _ _ _ _ i _ _ _ _ _ P r o f i l e F o r a t w o - d i m e n s i o n a l a i r f o i l p r o f i l e w h i c h c a n b e mapped c o n f o r m a l l y • o n t o a. c i r c l e o f r a d i u s R, t h e f u l l K u r t a c i r c u l a t i o n T 0 i s [ 3 7 ] (A9 1) F o = 4TTRU s i n ( a - c t o ) , where U, a and a 0 a r e t h e f l o w s p e e d , i n c i d e n c e , a n d z e r o - l i f t a n g l e r e s p e c t i v e l y . I f t h e c i r c u l a t i o n i s r e d u c e d t o a v a l u e k r 0 , t h e n T = k f 0 = 4 T r R U k s i n ( a - a 0 ) •= 4 T r R U s i n ( a - a 0 - A a ) . (A9.2) Hence Aa = ( a - a 0 ) - a r c s i n ( k s i n ( a - a 0 ) ) (A.9.3). i s t h e e f f e c t i v e r e d u c t i o n i n i n c i d e n c e r e q u i r e d t o r e d u c e t h e c i r c u l a t i o n (and h e n c e t h e l i f t ) t o t h e f r a c t i o n »k» o f t h e f u l l K u t t a v a l u e . I n ' o r d e r t o a c h i e v e a' r e d u c t i o n i n t h e " e f f e c t i v e c a m b e r , t h e p r o f i l e s h a p e i s m o d i f i e d b y " r a i s i n g " t h e t r a i l i n g - e d g e . P o i n t s on t h e p r o f i l e a r e r o t a t e d a b o u t t h e p r o f i l e l e a d i n g e d g e .through an a n g l e w h i c h i s p r o p o r t i o n a l t o t h e d i s t a n c e f r o m t h e l e a d i n g e d g e . T h e d i r e c t i o n o f r o t a t i o n i s s u c h t o r e d u c e t h e 117 e f f e c t i v e i n c i d e n c e o f t h e p r o f i l e . F o r an o r i g i n o f p r o f i l e c o o r d i n a t e s ( x,y) a t raid-chord, and f l o w f r o m l e f t t o r i g h t , t h e e x p r e s s i o n 0(x) = ^ - ( 1 + ~ ) , ( A 9 . 4 ) where * c ' i s t h e a i r f o i l c h o r d , w i l l a s s i g n a z e r o r o t a t i o n t o t h e p o i n t a t t h e l e a d i n g edge and t h e f u l l r o t a t i o n Act t o t h e p o i n t a t t h e t r a i l i n g e d g e . The m o d i f i e d p r o f i l e c o o r d i n a t e s a r e t h u s x' = xcos0(x) - y s i n 6 ( x ) (A9.5) yy = ycos9(x) + x s i n 9 ( x ) . The e f f e c t i v e r e d u c t i o n i n camber i s r o u g h l y p r o p o r t i o n a l t o . t h e amount o f l i f t ( o r c i r c u l a t i o n ) b e i n g d e v e l o p e d . The z e r o - l i f t a n g l e a 0 f o r t h e p r o f i l e w i l l n o t c h a n g e , s i n c e when a e q u a l s a 0 , A a w i l l be z e r o . 118 A p p e n d i x 10. The C o m p u t e r P r o g r a m f o r t h e E x a c t N u m e r i c a l T h e o r y The p r o g r a m c o n t a i n s a s u b r o u t i n e MAIN1, w h i c h c a l l s a l l o f t h e f o l l o w i n g s u b r o u t i n e s : CALCAB, ASSEMA, ASSEMB, ASSEMD, CPS, FORCES, a n d MODPRO. I n a d d i t i o n , s u b r o u t i n e s RE, WR, a n d WRD a r e r e q u i r e d f o r r e a d i n g a n d w r i t i n g m a t r i c i e s f r o m / i n t o p e r i p h e r a l s t o r a g e . The s y s t e m o f e q u a t i o n s i s s o l v e d b y t h e s u b r o u t i n e ATXB, d e s c r i b e d i n A p p e n d i x 3. The U.B.C. ( s y s t e m d e p e n d e n t ) s u b r o u t i n e s GSPACE a n d FSPACE a l l o c a t e a n d d e a l l o -c a t e , r e s p e c t i v e l y , b l o c k s o f r e a l memory r e q u i r e d f o r t h e m a t r i c i e s A, B, a n d C. The U.B.C. s u b r o u t i n e CALLER i s u s e d t o c a l l s u b r o u t i n e s w h i c h u s e m a t r i c e s t h a t h a v e memory . a l l o c a t e d b y GSPACE. A s u b r o u t i n e WALLCO i s u s e d t o c r e a t e t h e c o n t r o l . p o i n t c o o r d i n a t e s f o r a l l t e s t a i r f o i l s , f l a p s , s o l i d w a l l s e c t i o n s a n d w a l l s l a t s . The c o n t r o l p o i n t c o o r d i n a t e s XX and, YY, a l o n g w i t h DX, DY, DS, CS, a n d S I , a r e w r i t t e n i n t o p e r i p h e r a l s t o r a g e s o t h a t a l l c o o r d i n a t e s may be c h e c k e d b e f o r e f u r t h e r c a l c u l a t i o n . The d e f i n i t i o n s o f t h e v a r i a b l e s u s e d a r e d e s c r i b e d b y comment s t a t e m e n t s w i t h i n t h e s u b r o u t i n e s . The c o n t r o l p o i n t s (XSOLSL,YSOLSL) f o r a n a r b i t r a r y s o l i d s u r f a c e s u c h a s t h e p l e n u m b o u n d a r y a r e r e a d i n a t e x e c u t i o n 119 time by the program which c a l l s WALLCO. The c o n t r o l p o i n t c o o r d i n a t e s (XM,YM), and the v e l o c i t y VTI, on the s t r e a m l i n e r e p r e s e n t i n g the shear l a y e r a r e r e a d i n by the program which c a l l s MAIN1. T h i s program a l s o reads i n the c o o r d i n a t e s of the s l a t l e a d i n g edges (XLE), c e n t e r s ((XCENT,YCENT))., and t r a i l i n g edges (XTE), the flow angle t h a t each s l a t sees (ALF), and the f r a c t i o n o f the f u l l c i r c u l a t i o n (Kl) r e q u i r e d . As shown, t h i s program handles o n l y a s i n g l e t e s t a i r f o i l ; a s i m i l a r program i s used f o r a f l a p p e d a i r f o i l . The n o t a t i o n f o r the enumeration of the c o n t r o l p o i n t s i s shown i n F i g u r e A10.1. The l a y o u t o f the system of e q u a t i o n s to be s o l v e d i s shown i n Tab l e A10.1; the numbers i n p a r e n - . theses i n d i c a t e the p a r t i c u l a r DC—loop i n the program which assembles the c o r r e s p o n d i n g c o e f f i c i e n t s f o r the unknowns i n the e q u a t i o n s . The e q u a t i o n numbers (rows i n the m a t r i x C) a r e i n d i c a t e d by 'E*. Ac r o s s the bottom of T a b l e A10.1, the range of the index o f summation ( j , k, p o r q) f o r each column o f the m a t r i x C i s s p e c i f i e d . A complete sample run w i t h the r e q u i r e d c a l l i n g programs f o l l o w s . The sample i s shown f o r the C l a r k - Y a i r f o i l a t 20° 120 i n c i d e n c e , i n a 70% OAR TSUSL w a l l c o n f i g u r a t i o n . The shear l a y e r i s modelled by a s t r e a m l i n e which i s r e p r e s e n t e d by 20 c o n t r o l p o i n t s , t h a t i s 20 source and 20 v o r t e x elements. The a i r f o i l i s r e p r e s e n t e d by 50, the upper s o l i d e n d - w a l l s e c t i o n s each by 20, and the s o l i d lower w a l l by 80 c o n t r o l p o i n t s . There are 8 a i r f o i l - s h a p e d s l a t s , each r e p r e s e n t e d by 9 c o n t r o l p o i n t s . Thus t h e r e a re 262 c o n t r o l p o i n t s where the zero n o r m a l - v e l o c i t y boundary c o n d i t i o n i s s p e c i f i e d , and 20 c o n t r o l p o i n t s where the t a n g e n t i a l v e l o c i t i e s a r e p r e s c r i b e d . T h i s l e a d s t o 262 unknown source s t r e n g t h d e n s i t i e s and 29 unknown v o r t e x s t r e n g t h d e n s i t i e s . The r e s u l t i s 291 e q u a t i o n s i n 291 unknowns. The v e l o c i t y d i s t r i b u t i o n on t h i s s t r e a m l i n e r e p r e s e n t i n g the shear l a y e r i s s p e c i f i e d , and corresponds t o a p r e s s u r e c o e f f i c i e n t w i t h the average v a l u e o f -0.35, and i s s i m i l a r t o the mean v a r i a t i o n o f p r e s s u r e shown i n F i g u r e 8.7. The p r o f i l e s o f the w a l l s l a t s a re m o d i f i e d t o reduce t h e i r c i r c u l a t i o n t o 0.8 times t h e i r f u l l c i r c u l a t i o n . The output from the program.includes the p r e s s u r e . d i s t r i b u t i o n s on the w a l l s , the w a l l s l a t s , and the a i r f o i l . A l s o p r i n t e d are the l i f t , drag, and p i t c h i n g moment c o e f f i c i e n t s f o r the a i r f o i l and the w a l l s l a t s . MICHIGAN TERMINAL SYSTEM FORTRAN G(41336) MAIN 10-22-75 12159113 PAGE P001 0001 000? 0003 OO01 0005 0006 0007 0008 0009 0010 00 11 0012 0013 0011 0015 0016 0017 0018 PC19 0030 0021 0022 0023 0021 0025 0026 0027 0028 0029 0030 0031 0032 0033 0031 0035 0036 0037 REAL XX(262),YY(262),DX(262),DY(262),DS(262),CSC262),SI(262) REAL SlG(291),VTT(262),CP(262),GAM(9),MU(20),GNU<20) REAL VTI(20),XM(21),YM(21) REAL AXX(2a2),AYY(242),ADXC2«2),A0Y(24?),AD3C242),ACS(242) REAL ASK2H2) C XM.YM •. PROFILE COORDS FOR STREAMLINE REPRESENTING SHEAR LAYER C XX,YY - CONTROL POINT COORD3> DX.OY.OS - ELEMENT LENGTHS C SIG - SOURCE STRENGTH OENSITlES (ALSO USED AS SOLUTION VECTOR IN C SYSTEM ) C (GAM,MU,GNU APE PART OF SIG) C VTT.CP - TANG VEL, PRESSURE COEFF'. REAL XQ(10),YQ<10),XH(10),YR(10) C XQ,YG,XR,YR - MODIFIED SLAT PROFILE COORDS REAL XCENT(fl),XLE(8),XTE(8),ALF(8 ) ,KH6) REAL YCcNT(ft),DTHICK(8) C AXX,AYY ETC - CONTROL PTS TO BE READ IN FROM FILE (PUT THERE BY C WALLCO) EQUIVALENCE (AXX,XX),(AYY,YY),(ADX,DX),CADY,DY),(ADS,OS) EQUIVALENCE (AC3.CS),(ASI.SI) INTEGER CALAH,CALCD,WRAR,WRCD,SDLV,GAUSS,ITER,CALCP,C»LCL,HSIG C O M M O N / e i / NW5,NSLAT,N3U1,NKA,NM2,MS V,NA,NSPS.NTEU,NTEL C O M M 0 M / A 2 / U,CH C0HM0M/B3/NUl,NWuT,NU3,NWU2,NLl,NKLl,NL3,NWL2iNS0Ll,NS0LSL,NP1, 1 NFLAT,N3PF,Ni1 C0MM0H/H4/CALAB,CALCD,WRAB,wRCD,S0l.V,GAU3S,ITER,CALCP>CALCL,HSIG C0Mn0H/n5> NPi,MP2,NL« REAL TITLE(20) REAI)C5,303) TITLE 303 FORMAT C20A/I) WRITEr6,304) 301 FORMAT(IH1) WRITE(h,305) TITLE 305 FOR MAT(iX,20A4) RE AD(5,25) CALAB,CALCD,WRAB,WRCO,SOLV,GAUSS,ITER,CALCP, CALCL » HSI G 25 Fn.7.MAT(20I«) WRITE(6,1) CALAB,CALCD,WRAB,WRCD,SOLV,GAUSS,ITCR,CALCP,CALCL,H3IG 1 FORMAT ( 'CALABr I ,I2,2X, ICALCO" 1 , 12, 2X, 'WRABa M 2 . 2 X , 'WRCO=M2,2X, { 'SOLVr',12,2x,'GAUSS=',I2.2X,'ITERai,I2,2X,'CALCP',I2,2X, 2 "CALCL"',12.2X,'HSIG=',12) RE A.i (5.30) NA,NWUl,NHU2,NwLi,NWL2,NS0LSL,NFLAT,NSPF,NSLAT,NSPS, t MSV 30 FORMAT(20I4) WRITE(6,31) NA,NWUl,NWU2,NKLl,NWL2iNS0LSL.NFLAT,NSPF,NSLAT,NSPS» 1 MSV 31 FORMAT<'NAs<,13,2X,•NWU1a•,13,2X,1NwU2a',13,2X,'NWL1a 1,13,2X, 1 INWL2=',IS,2X,'NSOLSLs',I3,2X,•NFLATt>,IS,2X,INSPFs',13,2X, 2 INSLAT=',I3,2X,iNSPSai,I3,2X,iMSVat,13) READ(5,32) NfEU,NTEL,CH,U 32 F0RKAT(2I1,2Ffl'.3) WRITE(6,400) NTEU,NTEL,CH,U 400 FORMAT ('NTEU= I ,I3,2X, 'NTELa' ,I3,2X, • CH= ', F8'. 3, 2X, 'U= ' ,F6,1) C READ COCROS FOR AIRFOIL, WALL & WALL SLATS FROM WALLCO FILE (WALLS & C SLATS HAVE YY = 0'.) READ(2) AXX,AYY,ADX,AOY,AOS,ACS,ASI YWal'8'. . 1.000 2.000 3.000 4.000 5,000 6.000 7.000 8,000 8.000 9.000 10.000 11.000 12.000 13.000 14.000 15.000 15.000 16.000 17.000 18,000 19.000 20.000 21.0o0 22.000 23.000 24.000 25.000 26.000 27.000 28.000 29.000 30.000 31.000 32.000 33.000 34.000 35.000 36.000 37.000 38.000 39.000 40.000 41.000 12.000 43,000 44,000 45.000 46.000 47,000 48,000 49,000 50.000 51.000 52.000 • 53.000 MICHIGAN TERMINAL SYSTEM FORTRAN G(H336) MAIN I0-22-73 003B 0039 0010 OOH' COM2 0013 0011 eo-'i5 0016 0017 oo ie 0019 0050 0051 0052 0053 0051 0055 0056 0057 0058 0059 ooto 0061 0062 0063 0061 0065 0066 0067 0068 0 06? 0070 0071 0072 0073 0071 0075 101 33 31 35 C NUleNA+J NU3 = NuUNWUl MU'lsNu3 + NWU2-I WLUNU3 + NWU2 NL3=NLl+NWLl NL'l = NL3 + NwL2-i MS0LlrNL1+l IFCNSOLSL'.EO'.O) NSOLl=NLfl NF1=N|.1+N30LSL*1 I F C N F L A T ' . E O ' . O ; . N F I * N L4+N S O L S L NF1 « 1ST CON P T ON 1ST F L A T S L A T NSUi=NL1+NS0LSL*NFLAT*NSPF*i I F CN3LAT.E0'.0) NSU1=NLU+N30LSL*NFLAT*NSPF NSIin = NSUl + NSLAT*NSPS»l IF(NSLAT.EO'.O) NSU2=NSU1 NSU2 - L*ST CON PT ON L A S T S L A T Nil - 1ST CONTROL PT ON STREAMLINE FOR SHEAR LAYER Mil=NSU2+l I F CMSV.LQ'.O) NilsNSU2 WRITER,101) NU1,N';3,NL1,NL3»NS0L1.NF1,NSUI,NSU2,NI1 FORMATC'NU1««,I3,2X,INU3»',13,2X,"NL1"',I3,2X,• NLS»',13,2X, 1 iNSOLi"'#i3,2X,INF 1 = 1,I3,2X.'NSU1s',13,2X,'NSU2=1,13,2X,I Nils•, 2 13) NWALL - TOTAL * OF CON PTS ON ALL FLAT SOLID WALL SECTIONS NWALL=NWU1+NWU2+NWL1+NWL2 NW3 - TOTAL * CONTROL POINTS ON AIRFOIL SOLID WALL' SECTIONS & SLATS MWS=NA+NWALL+NSPS*NSLAT+NSOLSL+NSPF*NFLAT NKA « » OF EON FOR KUTTA ON TEST AIRFOIL NKA=NSU2+NSLAT*1 NSVT - TOTAL » SOURCE & VORTEX ELEMS NSVf=NWS+MSV NM2 «• » OF LAST EON FOR ZERO NORM VEL ON INNER EDGE OF S,L« NM2sNKA*M3V NUN - TOTAL « UNKNOWNS NUN=NtaS+2*MSV»NSLAT*l NFL - TOTAL « CON PTS ON FLAT SLATS ( N O K U T T A ) NFLsNSPF*NFLAT NSL - TOTAL * CON PTS ON A L L AIRFblLSHAPED S L A T S NSL=NSPS*N3LAT . WRITE (b.33) NA,NWALL,NSOLSL,NFL,NSL,NWS FORMAT('NA=',13,2X,'NWALL"',13,2X,INSOLSLo',13,2X,INFL"',13,2X, I iNSLs ' .njZX^NwSst.IS) WRITE(6,31) MSV,N3VT FORMAT('»3V=',l3,2X,'N3VT»",IS) WRITE(6,35) NKA,NM2,NUN FORMAT('NKA=',13,2X,'NM2s•,13,2X#'NUN«I,13) NA « a CON P T S ON SINGLE TEST AIRFOIL NlaNA+1 N2=NA+NWU1+NWU2 SET TESTSECTION WALL HEIGHT DO 2 I=Nl,N2 YW - Y-C00RO FOR UPPER AND LOWER W A L L S YY(i)=YW . N3=N2tl N«3N2*NwH + NKiL2 12159113 PAGE P002 51.000 55,000 56,000 57,000 58,000 59,000 60,000 61.000 62.000 63.000 61,000 65.000 66,000 67,000 68.000 69.000 70.000 71.000 72.000 73.000 71.000 75.000 76.000 77.000 78.000 79.000 80,000 81.000 82,000 83.000 81,000 85.000 86,000 87.000 88,000 89.000 90.000 91.000 92.000 93.000 91.000 95.000 96.000 97.000 98,000 99.000 100.000 101.000 102.000 103,000 101,000 105,000 106.000 107.000 108.000 MICHIGAN TERMINAL SY3TCM FORTRAN G(fll336) MAIN 0076 OO 3 i=N3,Nfl 0077 3 YY(I)=-YW 0078 IF(NSLAT.EO'.O) GO TO 500 0079 DO 1 I=NSU1,N3U2 0 0 8 0 fl YY(i)=YY(I)+YW 0081 5 0 0 CONTINUE 0032 IF(NSLAT'.EO'.O) GO TO 15 C XCENT.YCENT - CENTER OF SLATS 0083 REA0C5,16) (XCENT(K), Kai,NSLAT) OOSfl WRITEC6.308) 0085 308 FORMAT('XCENT') 0086 WRUE(6,1B) (XCENT(K), Kai,NSLAT) 0087 REA0C5,'i6) CYCfNT(K), K»l,NSLAT) 0 0 3 8 WRITEC6.309) C089 309 FORMAT('YCENT') 0090 KRITE(6,18) (YCENT(K), K«l,NSLAT) C MODIFY SLAT PROFILES FOR REDUCED CIRCULATION 009{ REAn(S,50) MOD 0092 50 FORMAT(12) 0093 wnifecft.si) MOD Oo9f | 51 FORMAT<'M0DPR0a',J2) C MOOiFY PROFILES.IF IMOD' NOT ZERO 0 0 9 5 IF(MOD,CO'.0> GO TO 15 C XLE.XTE - X-COOROS OF SLAT LEADING & TRAILING EDGES 0096 READ(5,16) (XLECK), K=l,NSLAT) 0097 16 F0RMAT(i3F6'.l) 0098 WRITE(6,306) 0099 306 FORMAT(* XLE1) 0100 WRITE(6,18) CXLE(K), Kn1.NSLAT) 0101 18 F0RMATUX,13F6'.l) 0 1 0 2 REA0(5,16) (XTE(K), Kai,NSLAT) 0103 WRITE(6,307) 0101 307 FORMAT( 'XTE *) 0105 WRlfEt6,1B) CXTECK), K=l,NSLAT) C ALF « FLOW ANGLE AT EACH SLAT 0!06 READ(5»16) (ALFCK3), KS=1,NSLAT) 0107 WRlfEC6,310) ClOB 310 FORMAT('ALFI) 0109 WRITEC6.18) CALF(K), Kai,NSLAT) C Ki « FRACTION OF CIRCULATION 011 0 REAO(5.17) (Ki'(K). Kai,NSLAT) 0111 «7 F0RMAT(16F5'.3) 0112 WRITE.6.311) CMS 311 FORMAT (' K 1 ') 0111 WRITE(6,19) (KICK), K»l,NSLAT) 0115 19 F0RMAT(1X,16F5.3) C DTHiCK . SYMMETRIC DISPLACEMENT THICKNESS 0116 READ(5.17) (DTHICK (K), Ka1,NSLAT) 0117 WRlfE(6,3l2) 0118 312 FORMAJCDTHICKI ) 0119 WRITE{6,19) CDTHICK(K), KoJ,NSLAT) 0120 NPS=((NSP3-l)/2)-i 0121 NSP=NSPS»1 0122 MPsNSPS+1 0123 DO 11 KS=1,NSLAT 12)59113 109.000 110,000 111,060 112.000 113.000 111.000 115.000 116.000 117.000 118.000 119.000 120.000 121.000 122.000 123.000 121.000 125.000 126.000 127,000 12e,000 129.000 130.000 131.000 132.000 133.000 131.000 135.000 136,000 137,000 138.000 139.000 110.000 111.000 112.000 113.000 111,0Q0 115.000 116.000 117.000 118,000 119.000 150,000 151,000 152.000 153.000 151.Opo 155.000 156,000 157.000 158,000 159.000 160,000 161.000 162.000 163.000 PAGE P003 h 00 M.CHIOAN Tt£RM_NAl. SY3TEM FORTRAN 6(11336) MAIN 10-22-75 12I59US PAGE P001 0121 0J25 0126 0127 oi'2B 0129 01*9 0131 0132 0133 0131 0133 0 136 0137 0138 0139 oi iq 0111 0112 0]13 0111 0115 0116 0117 0118 0119 ©ISO 0151 0152 0153 0.51 0155 0156 0157 0158 0159 0160 0161 0162 0163 0|61 0165 0166 0167 0168 0169 0170 11 15 16 17 18 15 C 22 23 36 NT»NSllUNSP3»(KS-l) 161.000 MTsNT+NSP 165,000 MlnMT.NPS 166.000 NLaNT+NPS 167,000 ALZ - ZfRO LIFT ANGLE FOR SLATS (0015) 168.000 ALZaO. t 169,000 CALL MODPRO(XX,Vy,DX,OY,03,CS,SI,NSVT,XR,YR,MP,NT,MT,ALF(KS),ALZ, 170.000 1 Kl(KS),0THICK(K3),XCENT(KS),YCENT(KS),ML,MT,NL,NT,XO,YQ,XLE(KS), 171.000 2. XfECKS)) 172. 000 CONTINUE 173.000 CONTINUE 171.000 MVS=MSV+1 175.000 iF(MSV.EQ'.O) GO TO 36 176.000 READ COORDS FOR STREAMLINE FOR SHEAR LAYER 177,000 READ(5»16) XM 178.000 REAOC5.16) YM 179.000 F0RMAT(l'2F6'.l) 180 . 000 WRITEC6.17) XM 181.000 WRITE'C6,18) YM 182,000 •F0RMAT('XMi,10F7",2:-' 183.000 FORMAT<'YMi,10F7.2) 181.000 DO 13 K=1,M3V 185.000 I=NwD+K 186,000 J= K+1 . . , 187.000 XX(I)a(XM(K)+XM(J))/2, 188.000 YYCJ)=(YMCK)+YM(J))/2. 189,000 DXCI)=XM(J).XM(K) 190.000 OY(i)=YH(J)«YM.K) 191.000 D3{n=S0RTlDX(I)*0X(I)*0Y'(I)*DY(I)) 192.000 CS(I)=BX(I>/nS(I) 193.00* Si(I)=DY(I)/DS(I) 191,000 M1,M2 * RANGE OF CONTROL PTS * I S ON SHEAR LAYER 195.000 MlaNW9+i 196.000 M2=NWS+MSV . 197,000 KRITE(6,7) 198,000 FORMAT('STREAMLINE FOR SHEAR LAYER•) 199,000 WRITE(6,6) 200.000 FORMAJ(7X,'XX',6X.'YY',6X,«0X',6X, . • , . . . . O.BOOOjBOOO.8000.8000.8000.8000.8000,SOC D T H I C * o'.o o'.o o'.o o'.o o DEl.CPST = -u'.00943(RAD) 0Fi.EPST = -O^0l678C«AO) O E L C P S T = - 0 . 0 3 0 8 9 ( R A D ) N F L " 0 N S L " 7 2 N W S . 2 D 2 ITER" 0 CALCP 1 CALCl" 1 HSIGa 0 0 NFLATa 0 NSPF" 0 NSLATa 8 NSPSa 9 MSV" 2 0 NF1«IT0 NSUl«17i NSU2e2(|2 Nll"24S 12.0 15'. 2 -3'. 6 0.0 '15".0 -15.6 • 12*.0 27.6 21'.0 • S 7 . 8 IB'.O • 39*.6 -36*. 0 5.5 11.0 10. T D - o ' . o 5 3 2 4 n )O n . C P S T = o ' 0 1 9 2 4 ( R A O ) 0EL C P S T = 0 0 3 B 7 K R A O ) DELEPSTa O . 0 3 7 6 7 C R A O ) XM x« YM Y M Y " 00 00 -A.e'oo 22 60 18 . 0 0 STREAMLINE XX ' 49' 5 0 0 a'l 5 0 0 39 5 0 0 5 " ; 5 0 0 2 9 5 0 0 2 1 , 5 0 0 19 5 0 0 I'I,500 9 5 0 0 '1,500 - 0 , 5 0 0 . 5 , 5 0 0 .'JO,500 . 1 5 , 5 0 0 - 2 0 , 5 0 0 - 2 5 , 5 0 0 -30,500 -35,500 - 4 0 , 5 0 0 - 4 5 . 5 0 0 4 7 , 0 0 • 3 . 0 0 18 20 22.90 42,00 -8.00 0 0 0.0 -0 5 4 ( R E G > - 0 , 9 6 ( R E G ) - 1 , 7 7 ( D E G ) - 3 , 0 9 ( D E G ) - 3 , 0 5 ( D E G > 1 1 0 C 0 E G ) 2,22 ^ ' , - ' v f - ^ C l ! ' ' t ^ O ^ N ^ N - . . C i n K l — ' - O c J A j m c j CO =3' • ^ 0 ' J 5 N f V l t C N . ' O a 3 r - 3 N n i o n j r v j - " 4 ( C ? r • - ~ K I o j — o i n * - o . - * t O - * « m - « o - r o o o o o o o o o o o o O O O O O O I o o o o o o o o o o o cr c PJ o • t r i t t ' 111 Ul UJ uJ Li UJ l w i n a - K i o e o o a , crjXJL - O ' C O i o c i O ' r - o c o i r t . © - O e G - O C r K l c j r — O — K l f Aj o» A J r - co e>. o in C - o —• « A J A I K I A J O J — C J O - cr r - »-* * o o o o o o o o o o o o o o o o o o • » t » t UJ Ui UJ Ul uJ r j I D oo 3^ 3 o =r o o «-• a -C i n ffi ^ » - ru —« CT - O — • • =3 in i to n j i K I A J tu UJ UJ UJ in O -O CO <" Mfueorj ( O ^ N C N - ^ f U - O C J • s t i t r r i U l U UJ UJ UJ (\j ry f CO CC : K I r~- L i-- o • -c - 4 -O- =r CT P U to oj • t I UJ Ul UJ C 7 C o r j co —• o j (U C 5 ^ r » o o- C -« -4 ^) *H » t • r • Ul UJ UJ UJ Ui c M O O h f f -< in r~ i i L T c c o o - a i o o - o m K i — . s - c w o - • AI c r - r*- =r cr o o o o o o o o o o o I I r i — —• rj — —. — O O O O O O O r • • r » ii » u i u i tu u i U J u i u i r T V J K l l / l O ^ I l i T C f f l C M T - • f j co c K> a i KI o r j -o m a B O ^ O - ^ M K K M / l i n i -" <; in o- — • - c s f M y o o o o o o o o o o o o o o o o o o o o o o o o o o o rvi —. I t I—< —< • » o o A l O Kl O o j C J OJ AJ 0 o 1 I W UJ .£> K l OJ IP O in oo K I in I P r j O K l OJ K l K l OJ OJ OJ CT - 4 CVI O J — ' - * O J O o o o o o • • • I I I Ul U l Ul U J Ul U J Kl C~ Kl r— Ul o =3 —« O Kl cr o o »— c O J — * r*-ry c o -o -o —• LJ-l O —• —« s£) o o < • I U! U l OJ OJ in o j K l O — c0> OJ —» o o U1U1 U) UJ bJ LU UJ UJ UJ U i ^ • - « c G K i < c r i j r v j > o o c c c c s ; u i i r K l » - < o a - M - * - » 0 ' < O W < C K » U l 0 3 f U I T ( M J 1 0 ' f t J O O M ^ O O -—••OOJLOCT- CT U~> ~ * CO — • 1/1 >£ U"> <0 , o O O O O O O O O O O O O O O O O O O O O O O O O O O tn o ST O OJ a- in O PJ OJ <-* eo K l * o -o c t » . —• OJ U l CU eO O O o c f- CO CC K l Oj —• OJ cc o- o o co cc o~ cr sr AJ Aj - * cr • • » • » * Ul U) Ul Ul Ul Ul 1 — co L O eo O J • z3 K I cx r J =r ro h- * - O ( M - O M 5 r j t> u i i n in -o a- —• c* • t o aC O CO AJ —» UJ UJ LU Ul U l Ui U l Ul U l UJ J J N N J - C ^ n j ^ O * ' ' Kl N OJ.OJ ^ O K I C T C O - O J C O I P O - O - O J O C T -w f- — • 0 s —• IP • C" - i O -3 Kl 7 O O O O O O O O O O O O O O O o o o o o o o O O O O O O • • • I t U I U I U I U I U U I U J U U I U K \ s i o 9 3 W o > c 3 r j f - r j u i ' O i n . « -MOJKIOJTO—if\J-^LT>'~OC-O O O O O O O O O O O O O O O i i i • i i • r LJ LJ UJ U l U l UJ UI U l ^ • f l c c o u i t c c ' ^ i / i - ' i n o p ' o i \ i - * K i c i r ( \ i o ( \ j - o ^ 3 ( H P > o O J C T O — ' L T O d O t C O j O O r - ^ T ,«»•»«.•.•»•.•%•.«.•.••«•.•-• O O O O O O O O O O O O O O in m o oj •c in oj i n O OJ o in rj in O A i t i l I I L J L J U I U I L J U J U J u J U I t U l / M 0 O C 0 - < 0 , O O C I ' < M ^ C O O O K I co r- tc o — ' r - L n o j — > r - c - o o h C - O c O f J M 3 S D O N ( T cr r— O- K l r j K I r j r j ^ )^ x in to o j O O O O O O O O O O O O O O O I f U J U J Ul Ul U l U l UJ t L T - C D O C O C O r - O O J — O I T . C Q L P J lf\ * 4 v CO ~ PJ O O C 0 < X c C P ^ * - < — « -O ^ N a ; J3 ^ L l -rj r* o i n r J n ~ o M c ( ^ r. , i rj o •< •r,j—«r-<-«r O O O O O O O O I o o o o < I • » I o o ( 1 1 1 I U l Ul Ul U l U l UJ U l Ul Ul Ul ~+ C 7 f J N O." 3 CO CC K1C? = 3 C ~ P J C T O O K I C C M C " — . K i — c o o a t m r - = r K i c c r j c o r j r * o r - c o - ^ M o t-T U* M 0 " N N K1 O r-l K l U"l K l ' - ^ r j n r J r j - H ^ n o i n « - 4 - " -< r j i i - „ K W V V «. Ul Ul Ul U l Ul liJ I n c - 4 o; o - 4 i n co i n o o o c~ r o j ^ o M c cc i n « r - » c c o j i r o j ; L l (v cC N r - M (?• O K l CC' o- r— o j t i-i i o in r~ 1*1 u i o c& c - T < —c cc 3 n K l - - ' - r j > 0 - 0 - « -o o o o o o o o o o o o o o o o o o o o o o o o o o o o " O AJ O O O I I O O O O O Ul U J U I U 1 U I U J U 1 L J U I U I U I n i n a D K l v D h O f i l p O - ^ O O - M C O 1"*'*-* o < r c o i n o j O L i c c o ' - * o o ' o- K i n w i o o r-r- o j =r O J o j —* O J f -W ' N -7 r j -3 o ' « r j i i O K i o o - * •v M f i n r j n - - ^ N ir- s - « - n Ul Ul UJ Ui U l U l Ul Ul Ul . I -j o N ^ a n r - < o r » - o L " i o j c - c w A J O O O !T'K1 C ' N C M UJ1-o j c o t r o e o o IP a j O ' N - 1 " o- : t'i ^ i « O T C M ' > r j : - < i \ ; K i > - * » . • N C' C —« f-1 •— O IT. —• 0 128 »-._—«.—..—.— O O O O O O O O O O O O O O O O O O O O O O O O C t O O O — » o o o C O o o o o o o o o o o I » • I I * i i • * f a AJ A i A i A I A i t_ —» o o o o »-. © © o o o o o o o o o in c o r- c D. i n -o -*J • • _ rj ( • * CT* 3" CO O rvj _ un ~D CO _ LA » r t t i a t t t t t t t i t » i i o o © o o » * O CO - r - co - _ « • • . =7 sr t i • r O A J I I O m I O I O IO- U~> U"> IT* IT* : : t O K i r j r j ^ o o i i t i i t t t t t t t o o o o o >- o o o o o > - • - • - _ • CO CO CC CO CO CO. • . • , • > . • . • - * . • • - * . . . • - « - • . . . • » • , • - • - • _ • . «^ «- * • _ « . • _ • _ • _ • . • . • . • . • _ • . • . « * . * . • . • I C " « O O g l T . rtO:jr-«AiNC(C 3 C ? Off _ —« Il O « L' O IC _ O O" O O CT J^ . fUN£C(OUlh- !TM O K O M O _• K I r - to sr i n _V 3 KI 4 O t t I O AJ t/1 - * CT-i >o w a ; i " » * _ W eo N IT,. «. «^ «- «w • < KI W W W W K I CO CO C O W - * ; 3 , - a i * ' 5 ~ 0 ' - < 0 0 , M W O K ( 0 0 ' - " 0 " - < M C > t r e K > O N K I M O S - * N M J ' 0 < D > 0 ' < - < ' 0 - O C , r t • 83 C ^ ' - ' I T I T K I r- K 1 i * « . * * M O C ! - " K I O O C T CT o r - O f \ l ~ *7 O I T « h « S O O - O N f f l P J LO O _'—-< IT N O 1/1 C ST K—'-ooraoQ-cir 3 »o r j « a O C ^ O I ^ S I K I I O W O C r— r*- r*- < o > o i n u > > n ? s o t o M r j f j - * _ © —» K I u*i co A I c- o-ro-_ * * . * . • , • • »_ • . • . • . «- ». », •_ « « . ».. » . • . • « . • . •>. «. • • . * > or t o KI r o K i r i i f \ j P j f u f ' j A j ( \ j - < ^ ' « - ' - - i « - ' » - - < ^ ' ' H - o o o o o o o o o o o o o o o o o o o o o o o > - « - < i \ J K l t l t t l l t l t t 1 •: I » I • o o - o o _ - © © © _ • _ » I t » I I • ' I O O D V I D O O O ' ^ r t * * _ i c ^ " o =y o _ r - - — D O ^ r r » - K i i — " h - o o o o o © © © o o o o f f i O M J i h N C M N N O - CT-O 0 _ ! * ^ C C C ^ O " C > O C * » O x G ~ 0 " 0 " 0 - 0 ^ 0 " « c O •-. «. «. * . « . * . • _ • . •_•_«. ». • . • . • . « . • . - . « . • . * . • . « . • . • •- •- •. •- • •- *. •- «. •- •- ». •- •» • > © © © © o © —* o o o o o c > o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o r t r t r t f - t i r t r c t i i t i a a k a © o o © o i_ o o o o o O o o o o o o i u i s n i n o o ' N O ' j ' f u o a ) ? w N i \ i M 5 i n 5 ! / i . - 0 ! r o c o c o K i W > o ! n ^ N c > « ) c o o s r o c o r j o ^ r ' - ' o e c K i - H IM 4 (M O CO X>_"»U"1—' O r - - r - - r - - c O _ ' C > O O O O O O o r u > O r i J X ' K I » - « _ * e 0 , > N ' 0 ' f l ^ l r - N O C C O « - i M ' j M \ J i D N K i a ) « O O O C T C > C > C > C ^ C ' C ' 0 " 0 " 0 " 0 - 0 V 0 0 0 tr> o r*- co - t - « -4 > o o o o o > *4 *4 . ' O O O O O O O O o o o o - • O O O O O O O O O O O O O O O O O O O O O O O O v ^ > o o o o o « a a r * _ o t ^ » M i n ^ - > o w _ < o , j i a - « - M C f f i i ^ O ' ^ K i * 5 ( O N i > « m- K K « c - r-t—* r** o >0' -o L*^ fi o- -o K I " — * r . r/i tr r j t > ; - « P J K I 3 e ro f \ i i — O O O « _ O O O O O O O O O O O O O O O . * - « C I O O O O O O O O O O O O C > O » _ > O O C ! O I —*-.T-t:»-i n j r j t t t l i l t t i l AJ O CT SO CO ' » - ! P L"> ? ^ C to o o o o o > o o o o o t I I I t O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O C l O O O O O O O O O O O O O O O O O o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o • - O O O O O O O O O O O O O O O O O — " O O O O O O O O O O O O O O O O O O O C O O O O O O O O O O O O 2 . V «. • , « - • - «. «. « - • . • . • . * _ • . -. •- •- «- •- *w •- •. «. •- • > o o o c > o o o o o o o o o o o o o o o o o o o o o o o o o o o o c - o o o o o o o o o o o o o o o o o • t r i i i . 1 I I I. I o o o o o o o o o o o o o o o 2. * . i . • 1> o o o © © • e K o • ^ « ^ ^ l n o ^ M o M ^ f t J M ^ ^ ^ c 3 ^ o ^ u o r t o D ^ w f t l l ^ J W W f J l ^ J f u w nj n i n i M N o MO^ONITO KIKICT-• HC O ' S i n o o - f u s o o r j o: n j i / i t t ' ^ c r cc o , K i m s o j o - < - 7 ^ . 7 3 i r - T - T i 5 3 ! 7 ^ q ' a m s o 1 w 7 « i n IM - c h-O N O ~ K l O J O O O - < « - i A J ( \ J K i r / l K i T ~ cr — L"» m m _1 -O C M M M M M M K I r t M l O M M t f l r O r t M M - C C ^ O N O ' C f ' _ J O O O O O O _ » © o o o o © c > o o © © o o o o o © © o © o o o o o © o o o © o © © — ' O o o o o o o o o o o © © © _ > © * r _ ' O C > c r ' 0 © • 1. t t 1 1 a I I I - I I I I I t I I I I I I J t I I I • I • i — j f V j f V A j ^r a A I —* c1 ec>r—'f^ * r— m K I r y — 0 K I U ^ 0* U K ^ CC CT cr; • r- fu KI> r — A J C C LO C J O K * - O C T - A I m c o ' - ^ t o o* K I - , T - ' - > - * K > C T K ^ 1 —«—- —« > O ^ ^ « « « « ^ ^ O O O 0 O O 0 O 0 0 O O - * A J M 0 f ^ C ' K * A j « _j > o O —> o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o • * r • 1 l l l l l t t l l > o o o © o CC K m " 3 f O ~ O f ^ O C T « O A J O C Q _ ^ I ^ O O C O O : 3 - i n ^ C T C T ^ O J K (C C .»-ik_'-«cC L^Kl -_ LO —> O O 1.1 CT- O O O L."Vr- O't-- _1 Ki — AJ C3K\OJ AJ1—i'P---< <"M L"*'!*- O t-n'r-'—• ••r-KV—i OJ O Al OT »-•-«'—<•——•>-« < ( r ) ' ( N C K I f t l O O « « H l \ i n j l \ l K I C ' 5 ' C C 1 ! T C - C C C K I M O C - * ©—<—« AJAJAIKlK1Klir!T=rmin^O—tr>COO* ©«-«K»nj t o o © © © © 3 - •> O O C > 0 © 0 — * O C > O O O C i > © C O O O © 0 0 © _ > 0 © 0 0 © © © © © © © © © © © © © © © C > O 0 - * - « - « « L J > © © © © © » 1 t a * » • I I * a 1 a 1 1 -0,020 -0.022 0.022 -0,028 -0,032 -0,038 •0,013 -C,056 -0.072 -C',100 -0,153 -0,289 -0,591 0.138 UPPC LEFT VNST C'l97 • 0,117 • 0,091 0,005 0,078 0,072 0,066 0,062 0,038 0,055 0,052 0.0'|9 0,017 0,013 0,011 0,039 0.037 LO"CR LEFT VMST -CJ035 -0,036 -0,037 -0,038 -0,039 -0,010 - 0 , 0 1 1 -0,013 -0,011 -0,015 / -c,016 -0,017 -0,018 -0,019 -0,050 -0,051 • 0,052 -0,053 -0,053 -0,031 -0.035 0,023 0 % 2 6 0,028 0,032 0.072 9^ .100 0.153 0-.2fl9 0J.591 -0.138 SOLID VNVT •0,117 •0,1?2 -0.106 •0^ 091 •0.035 •0J07« -0,072 • 0 . 0 3 8 -0'.055 • 0 ) 0 5 2 - 0 . 0 U 9 -0'.017 •o'.Oul -0'.0U3 •o'f 0£| 1 -0.039 •0'.037 SOLID V!JVT 0'.035 o".036 0.037 0^038 0,039 0,0 u > - * - * — • • - ' r t j A J A J A j A i A J A i A j A i A , » - " - 4 - H I — — ——.00000000000 C G O O O O C C O O O G G O O O C C O i - ^ O O O O e O O O O C O O O O O O O O O O C G C O C O O e O O O O O O C O O C O © O O O O O G O G O O O O O O O O O O 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 * « • * « « • s » » k i i t r i s o w i n » - * ' 3 i ( v o « i r o t i f - o A J M A J -—1—«—*Cu ru r j m K \ CTiniT>in>c__^_ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 5 J i o ^ a f - N O r - c O i < i - « K i ( 7 ' i ^ r j a ^ r h - c o r — i n r u c o ^ x A j j i n o K i a i r - o ^ o o . ^ u ^ t n i n ^ C T r ^ r o r u r u ^ « w o o o o o o o o o o o ^ « - 4 « ^ . — . — > • » • • . • . . • • . • > • • • • • > > • . > - • • • • • • . • • • - • - . > . - • • . • 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 . 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ' (\j O 1 TO to to m, ! « * 1 1 AJ Aj • Jt AJ O CC LP nj A J — — t i l t Kl O fO -O I ) t e c a: tc * 4 • * 1 A J l f*i A J CD « • O ^ I T - O O . 1 5 « » n r j < f s EC CC CC CO t • * r • AJ f - —< =T 1 CO KI , 7 i f f i M T K i cc cC co cc e t 1 •• I r- L-> -o ( 0 r - K I o- h c c c O o c c C o Q c _ c O c o c O c O c _ < c a 2 m c c a 3 C ^ * • » t t C f r t l t l f t t l t l 1 • t t ft I I t l I I" I I I t i l l • K i o - » » o N O t , T L " i c , a c n j c o n c > 3 A J A J I P —«cr o =1 — « C J A ; O < 7 } A J — » A I C C I P C C K I O i c f - o c e M n M w - • m ^ ' j i ^ r y w o o r j u i t t ' ^ ^ i D i c t o o K i s n o c ' - in r j M ^* io r j o w r - M c w i f t s a 3 0 , o - ^ p j r t - r i / ' ' O S e o o n j K i t " ! N o r i j 7 r - o r j j ) 0 ' ro r- rvj s u i -o t i t t e r * . a o o - i ^ W f V J K l K l K l K l K l c r c C C C ^ C » K l - - 9 - 9 . D . t n s K i r j - i i n O K I h - 3 O K l O r - l ^ O ' / l l T a > O K > = j e O cn CO © CO A J O C L P ^ I P — < A J C 0 < _ _ D A J - — « r - c C K > r O _ o K i s i a M O , K i o u , , r j _ c c o j w o c N r j r j X ^ K o o o ^ i O i n r j T — 5 ^ c r 0 7 t O w ( C L ^ o _ ' < o r v j c o - - < o D ^ a f u r j A j r j K i , i i r - - f f ' o t > « D N _ 5 K i - * o f - ? — - H ^ N O K U J C O ^ o • ' 7 ' l c ^ ^ o o ^ J - ^ c t ^ ( ^ - ^ K l c l ^ J D ^ ^ l O ( f O • o o » ^ ^ r J K l m ^ ^ / l o ^ o ^ I J ' 0 ' ' ( ' J ^ / l l I l > t 1 o O o o o o « • A J A I A J A J A J A j A I A J A J A J A J A J A J K l K I K l K I sTKIWOC: OCMO- CKi.OMTKi«0 ©•—* . • - * . — . « _ « . * . * . — . « . • ) . • . — . • . • . • . • • • * O O O C X O O O O C O O O O O O O O O O Q- KI CO CO - < C - 0 _ K i r » O v S C ( D - < - < ^ a J ) K i C O K l N O K i i r ' S C * - < f t J K I c r i / " , f c - c O O A J s O WC C a n j C O ' W I f i C O O M J O r - O ' O. —\—• u " . l / l i n O O O O O O O N N N •^ oooi^ r*--r--cococoo"0-c-ovO'Ov' 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 > o o o o o o o o o o o o o o 00• 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 H-000=> O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O k—. •« «. «. a. .a. a. a. a. a. a. «. a. a*.«. a. a. a. a. a. a. a. a. a_ a. a» a. a. a. a o o o o o o o o o o o — — • - < — — _> 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 _37tf>^ftl_PJOKl--0!r f - N N -C C PJ O S i n KI O • — • r j A l A j P J A J A J > _ < ^ , _ < _ , _ . _ < o o o o o o o o o o o o o > 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 r j r j — < — ^ — < — < o o 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 O f - « AJ KI l_""l C C O r j 3 45 B O . -• f J K I K I f v j : -• 00 o o o o o —!—«—«—4 —« r j A J A J P J P J P J A I O O O a O O C > O G O O O O O O O O O O O I I I I I I I , | ~ . - C C > O t n 3 K l K i r \ | : « O C f ' _ N - 0 3 M A l l -4 O © I —« A j r j K I K l S T = r ^ T L H T ' L n u M n i r i _ o - o « f l l r -t n — — - « — t w — . , * 0 0 0 0 © 0 0 0 0 © 0 0 © 0 © 0 0 0 0 0 0 0 0 0 © 0 0 0 0 l O O O O O O O O O O O O O O O ' I ) I I, I r i i i i i i i t a i t r ' O O O O O O O O O O O O O O O O O O O © O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O _ «w *. a_ a. *. a. a. a. a. •„ a. a. a. a^ *, *. •_ a. a O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O »— O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O > o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o O © O O O o o o o * I t • 1 t l i i i i i . » r i i v t i t . k » ' i i i t i t ( t s » ( ' t i t L f— _ > o o o o o _ > _ » _ » o o o o o o o o o o _ j o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o « t _ » o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o J « t 4 * 4 a * a l t l l l l l l l l _ : a i l l l l l l l l t t l l l t l l t t l l t l l l l l l l l l l l l l l l l a ( O O O f - C O O O — * — i O C 3 N C r - r j O N H O LP C" — O' O l P C r - < O N l O r j ^ O « r j l P C > 5 0 N ^ r j ^ O C > c C S N 3 i r i 0 ^ 5 M r j n ^ U*. Ifi IT- IT iT- b" O O O C O U l U"l 3 K C l\J J I - b l ' N C A J KI IT li"i IT- K*. AJ —« O CT CC • I"** O IT S ST t r K l K J K I K l K I A J A j A J A I A J A J A J A J A J A J A J A J A I O O O O O O O C O O O O O O O O O O O O > 0 0 0 — * O O O C O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O > o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o I I K I I I I I I I * ! t i i t i i i t i i r i t i i t i i i i i i i t i r i i r r X LZ fflOat-C0C?OO-^O«3MDM,J0SH O lA O CT O ^ 7 N O N I P ' \ l * < O « r j L ' l t > 7 O N ! 7 N « - O 0 ' C N N 0 I P ! / l = I :j K I A J P.J — Lip in t innocooo i i l i r j - o A J ar i— i / v r - O - A J K I L"» •_,"> L i c K i f u ' « o o co • r- o I A £ « • H K I 0 0 0 - 4 - 4 O O K 1 f u s t f u c c r v i t p o - c r o -»-«-c—»oc--« — o o - o ^ « 4) o j i o i n •-.IT. M O O — —« O c o o i n i O M 0 3 i \ i c c C J . • O W n M N O W h O I I I . . I l l L T l A j - C e C c c r - - ' - — « m C L - 4 — r - o - y - K i A i n j — o ^ i n J J - O f i i n e j ' f f • H l s O ' K i r ' K M M O - H Q . O W I M M S - O f ' l i n O A J C T O * C T O C O = T O ' * A I 3, -4 CT ff —i -C CO f l CO - • sO —• o o o cr o ' in cc M a AJ ru CV 7^ CD —• CT- 3 f U O — O f f ( O t O C O f f O - * >• ( M O N CO O M IU • • ff • s r - N r - o c c o c N I S N I M N C O C a D I C N S K N K e o c o c O c o i s N S t - S c O c O i O C O ' S "f— K N CC CO CO —« AJ o —* m o KI cr AI D U l O - O - U l f l X c r K l K I CO- ». •. v. «s- « . • t • i t m c o f f o a r - K i A j o X - © c j c T - 4 f f . o - « c r * o CO I"- K l -O ff — < I M O U 1 f t J K l - « A l A j AJ c o K i o o o i n o a ' c o e O C K t N P J K I i n K i c O h O S O S c C C C ^ c C O O f f f f C O U * . K l c r A l O A l l T A J O C T f f O O A l O f f l T f f e C c r > O f f O 1— A I . - 4 ff1 — i n A T — ( - O ^ i n N K I O - T J O A J K l - 0 0 0 0 - - 0 » « M ffffnj^3in-^=Tr—ff K O « S r j - * K I * ' K t O r- ff o to ao —• • o r - o o o r - AJ • - A J K i r - f f A j c o - c r O — ' f f U l K t A J O f f O h - O f f f f f f O f f f f C O O O O f f f f c O O c O f f f f O ,»-. «. •- •- •- •• • > - * 0 0 0 0 0 0 0 — • > r * i O A J f f - O K l — ffCCff j - O f f f f f f O f f f f C O f f C O f f f f O O O C O f f f f f f O K I O C O K I O O O f f l 1— O ff ff ff O f f f f C O f f O O f f f f C C O c E f f f f f f c o m e r — K » r - f f K i J 3 cr ff• o* o o CD ff-cc ff O f f f f f f f f O t O f f f f f f co in ff —• K I P^- ff f — f f f f f f O O C O f f O f f f f f f f f O C O f f I— ftjcrocrsiAiNrjcr > O A J — » c r o r - c r A J c r > . » H O O O — 4 0 0 0 0 M D K I N t M O O O c O H O d f t l O I / I C C O w K l > c r c f c r K i * 4 K l K i f J ( \ J l ~ . •.*-•-•«-•-•-*-•-• > 0 0 0 0 0 0 0 0 0 I I t I O c O f f N ^ O c O f f O f - K i a - D a K i i n ~ c o r s »—. «. •-*-•-• : > o o o o o o o o o . B ft t • ft k - e X f f K l A J C O ^ J K I C O C T > f f c o f f o x A j i n i n i n h-» « . • . * . • „ • _ • . * » * . • > o o o — « o o o o o • I ft ft I ff AJ nJ AJ O —• AJ o cc — — t o c f f i n > r * * i - . c o i n M ^ T „ «w • > o o o o o o o • • • I I i n e o n j o o c j c o o r -h-; —., —• r j AT l- ec • r- i - 4 KI ( o « o c c - o c c r - ^ - o i n K - c c u o o c o f f o ; — * C O C J K l O r j C O C T - 4 - . K l O K l f l Cf C Aj4-«r-.CC • t— A I I —• i n i n eo K I ff cr t i t n r - > O N - ^ o r - M A J c r • O C C C I C O N C O N W • »— i n o- o K i e c K t e o f f i n COCO O n j K l c r c O K I - 4 C T . * i - o cc co m o o co in M o AI NO AI o o o o o o o o o o o o o o o o o o o • - o o o o o o o o o z . •. •- • > o o o o o o o o o o o o o o o o o o o o o o o o o o o * - 0 0 0 0 0 0 0 0 0 2 . « . « . • . • . • - • . • . • - • > 0 0 0 0 0 0 0 0 0 I I I o o o o o o o o o o o o o o o o o o I — o o o o o o o o o o o o o o o o o o o o o o o o o o o f - 0 0 0 0 0 0 0 0 0 o o o o o o o o o o o o o o f - o o o o o o o C C r - « 0 0 - » S f f O I - O K l -T - T O U l -T 1 K l o o - ^ o c r o — o — i o > © o o o — * o o o o • I I I ! N C C r - C O K l N ^ O •U— O PJ CT -1 O Iji . 7 in Cf 0 0 - 4 0 — o — o — o > o o o o — 4 0 0 0 0 • I. I ft I I r - r - r — — • o r - r - m o • H - r j ^ c f c r o u i - T O - o o o — « o c r o c r o — « o > o o o o — < o o o o r r i i i ff . T N t n o f l j r - K t n j U V f f C T K l O O ST ff? ff o o o o c r o — o — » o > 0 0 0 0 - 4 0 0 0 0 • I ft ft ft • co o ?— i n o AI r -H i n O J T K I O ^ c f o o — o c r o c r o z . •* s. v • > 0 0 0 0 - 4 0 0 I r t i • t c e c c c i n i n N c r K i ? r t- AJ K l CC ff m m c o r— o ff>CTffOO-4L-lOOCT • r- z . • .—* O O O O O O O O I » n o I ft I I I ffff-4=T-4r-ffr-£> I- | j ' KV N CC ff d =T K I T -CO > K > A J A J K 1 K 1 0 A J K 1 K > CO 2 . «• • „ • » * . • . »- • — > o o o o o o o o o C I ft * ft f J O 5 fO O -O N O PJ . | _ 2 3 C J i M N 3 O W a- z . • ..«.*.. . — : > o o o o o o o o o • ft I I I I i n i*- o f J " n ff m o I ^ C T C T C T C C K l K t O K l A J 0 > O K I K I O h N C - - 0 O 2 . • . « . * . •« A J 3 > 0 0 0 0 0 0 0 0 0 cr -< 3 N co in N t - s J U l f f U" -3 O IP L T - > P J C K l - L " i O C f • A J > 0 0 0 0 0 0 0 I I I »~ AJ O K I T t l O K l AI K l t c n C C O N - ' ' " « - 0 * M " f— > o e > o - 4 « - « o o — « o < t i l l CO O — « f f C - 4 - t O ( V i * 4 0 o —• -4 4\j cr o O ff'-* « ( n M « K i t o M - i \ i c e r > OOOti— o o o o < 1 I ft " _ J CO co c o K t r u c r o n j c r P j P i 5»^b_ AJ K l Ul O h - Kl O K l CO t— > O O O O — t O O O O < t I I - J CO ff cr O K t K V C X cr O CO AJ cr ff L I K I ff tn cr r— O W O C l M K l h - 4 S T O O f_ > O O O O W M O O O ft I ft ft O -< C * 0 0 0 — - 4 0 < ft; ft t CO 0',0?7 -0,279 0.156 -0.247 SLAT »216 VNST -o',44t -0,463 -0,136 0-'130 1,251 0,703 0,268 0 101 0.397 221 VNVT 0',397 0,3o7 0.183 o',024 -0,251 -0,259 -0.221 -0'.228 -0'.386 0,183 0.091 VNOT 0* Oil 0,156 -0,0t7 -0 454 -1,000 -0,444 -0,047 0,126 .0.010 0,000 0.000 VNT • 0'. 000 • O'.OOO - o ' . o o o - o ' . o o o - o ' . o o o o ' . o o o o ' . o o o 0.000 o ' . o o o •0.078 .0.333 VTST 0.001 -0.315 -0.175 0.369 1 .I'll 0.825 0.331 -0.136 -0'.265 0,560 0.511 VTVT •01203 .0,150 -0.170 •ol190 -0.010 0',265 0,375 0,162 0.466 0.996 i',207 22.870 VTOT .0'.999 -0.988 .0'.999 .0'.891 0'.002 0.896 0' 999 0.992 I'.OOO VTT -1.201 -1.452 -f.343 -0.712 T.433 1.986 1.704 1.318 1.201 . ASUM 3,358 8,175 24.983 23^ 049 20,332 20,432 21.680 -t ' 173 18,10 -1,26 •1.146 0^084 10.022 17.92 -0,18 •0,456 0,562 BSUM YY XX CP SIG -8' 002 18.03 -12.18 •0,442 0.599 1,149 17,88 -13,26 -1.108 0.099 7.307 17,76 -14,69 -0.804 0.110 i2'.89« 17.88 -15,40 0.493 0,172 8. 348 18.00 -15.58 -1.054 0.134 -5.410 18.12 -15,40 -2.945 .0.039 • fe', 44 1 18,23 -14,69 -1.905 .0,100 -3'.587 18.14 -13,27 -0.737 -0,134 7'. 7 01 18,03 -12,18 .0.442 .0,602 S L A T »225 VIJST -o',414 -0,3l'9 -0,004 0,468 0,969 0,424 0,1Q4 0,036 0.379 S L A T «234 V N S T -O'163 0,141 0,529 0,863 0,245. •0,057 0.134 STRCAMLINC VNST 0',089 0,830 0,476 0,397 0,342 0,328 0,156 0,074 -0,096 -0,274 -0,375 -0,460 .0,487 -0 421 -0,407 -0,331 -0.262 233 VNVT 0^ 343 0.148 0,015 •0,057 -0.147 •0'.342 24 2 VNVT 0'.094 VNOT O'071 0,171 -0,047 -0,459 - 1 , 0 0 0 -0,439 -0,047 0,111 -0.038 V NOT O' 069 0,171 -0.047 ".0*, '158 -1,000 -0,439 -0,047 0,112 -0.036 •0,071 0,137 0.194 OJ105 0.014 • 0'.098 FOR SHCAR LAYF.R VNVT -0'.049 -0'.790 -0J416 -0.317 • 0',262 -0,209 -0.037 0,235 0,373 0.435 O',460 VNOT -0^ ,040 -0,040 -0,060 -0,080 -0,080 -0,119 -0 119 -0 139 -0,139 1 0 0 0,019 0.087 0.322 0'.268 0J192 0,066 0,031 -0,158 »0'. 186 -0,060 -0,0 0,060 0,100 0,139 0 139 0 196 0,100 0,139 0.100 VNT VTST - o ' . o o o .0.255 - o ' . o o o -0.540 -0.000 -0.252 -0^ 000 0.452 -0.000 1.910 o ' . o o o i. o ' . o o o 0 .484 0' 000 -0.099 0.000 -0.203 VNT VTST . o ' . o o o -0.326 . o ' . o o o -0.558 - o ' . o o o •0.454 -0,000 -0.113 -0.000 0.793 o ' . o o o 0.777 o ' . o o o 0.597 o ' . o o o 0.224 - o ' . o o o 0.035 I VNT VTST - o ' . o o o •0.849 o ' . o o o 0.298 • o ' . o o o 0.281 - o ' . o o o 0.204 - o ' . o o o 0.392 -0,000 0.457 - o . o o o 0.580 - o ' . o o o 0 .588 -0,000 0.582 0.000 0.5f'3 o ' . o o o 0.349 o ' . o o o 0.215 0' 000 0.059 o . o o o -0.071 o ' . o o o •0.115 0'000 •0.202 0 000 -0.273 -0.000 -0.269 - o ' . o o o -0.256 - o ' . o o o -0.171 VTVT 8* 188 0,209 0,199 0 J209 0,277 0,192 0,201 0.256 0'.268 VTVT 0,267 0,255 0,266 0,313 0,320 0.067 • o'000 0,006 0.022 VTVT •0,319 •0,309 -0.261 • 0'.479 -0^ 573 -0,732 -0,781 -0.600 iO'470 -0.316 - o ' . i e s -0'. 136 -0'.033 0' 054 0,098 0,111 0.072 VTOT .0' 997 .0.985 .0".999 .0'889 0.002 0'.899 0.999 0".9?q 0.999 VTOT »0'.998 -0'.985 • 0'.999 .0.889 0' 002 0.898 0'.999 0'.994 0'.999 VTOT -0'.999 • 0'.999 • 0'.998 • 0'.997 • 0'.997 -0'.993 -0'.993 0'.808 -0.990 0'.759 -0'.995 • 0'.998 • I'.OOO -0.998 • 0'.995 »0'.990 • 0'.990 -0'.9B1 -0'.995 -0'.990 -0'.995 VTT •1.065 •1^ 317 -1.052 -0'.228 2.190 2.219 1,684 1,151 1.065 VTT -f.057 -1.289 -1.187 -0.688 1.116 1.742 1.595 1.224 l'.057 VTT •1,015 •1.020 •1.026 -1.054 -1.084 • l ' . 109 -1.145 -1.183 -1.217 -l'.24I -T.249 -1.255 -1.255 -1.251 • l'.241 -l'.225 -T.200 - l ' . 166 -1.136 -1.095 ASUM 5^ 666 4,791 5,430 10,191 25.486 21^ 553 18,379 18 335 19.559 ASUM 6^ 772 5,808 6,381 11,032 25.567 20),770 17,431 17,290 18.449 ASUM -1 f,696 •12,560 -6,478 -15.433 -7' 946 -ll,5(/j -11,110 -11,112 -13.140 -ll'.917 - 1 3 ; i i o •12.416 -12', 223 -12,'123 -10.616 -12', 381 -9 316 -10,026 -9 276 -5.801 BSUM .7^ 097 2,175 7,784 12,464 6.486 -6,815 -7.185 .4'. 044 6'.869 BSUM -6^ 934 2.417 7,799 12.113 5'.579 -7'.291 -7'.315 • 4'.009 6'.742 YY XX CP SIG 18,06 -24,18 -0.133 l'.068 17.89 -25, • 26 •0.734 0,172 17.76 -26, ,69 .0.107 0.164 17.87 -27 ,40 0.948 0.218 18.00 -27 ,58 -3.794 0,124 18.12 -27 ,40 -3.925 -0.099 18.23 -26 ,69 -1.835 •0.157 18,16 -25 • 27 -0.325 -0,204 18,06 -24 .18 -0.133 -1,070 YY 18,06 17.89 17.76 17.87 18.00 18.12 18.23 18.16 18,06 XX •36,18 •37,26 •38,69 •39,40 •39,58 •39,40 •38.69 '37,27 •36,18 CP •0.117 -0.661 •0.409 0.526 .0,245 -2.033 -1.545 •0.499 -0.117 SIG 0.666 0,095 0.086 0.138 0,121 -0.019 -0,076 -0.128 -0.689 BSUM YY XX CP SIG -4',866 16.10 49,50 -0,030 0.024 8,277 18,30 44,50 -0.040 .0,(106 -3.238 18.55 39,50 -0.053 -0.010 -3.127 18.90 34,50 •0.111 •0.016 •1.312 19,30 29,50 -0.175 -0.009 -4'.578 19.80 24.50 -0.230 0.010 0^ 351 20,40 19,50 •0.311 0.018 -1,842 21.05 14,50 -0.399 0,011 0.351 21.75 9,50 •0.461 0.061 0,326 22.35 4,50 •0.540 0,020 0.467 22.75 -0.50 •0.560 0.197 t',591 22.90 -5,50 -0.575 0,080 0.869 22.75 -10.50 -0.575 0,0*>6 2.284 22.35 -15,50 •0.565 0.059 1.748 21.75 -20.50 -0.540 0.050 1^ 846 21.05 -25,50 .0.501 0,028 3,213 20.20 -30.50 -0.440 0.005 -0.417 19.45 -35.50 -0.360 •0.019 7^ 470 16,85 -40,50 -0.291 •0.052 2.238 18.25 -45,50 -0.199 -0.0>>8 CAM" 0'.23810E-Ol -0'.O26ilC -02-0'.1015hE-Ol -0'.16088E -0l.0', ,9:»665E-62 0 ' . 9 9 9 ( I 1 E " 0 2 0'.17789E"01 o ' . 1 1 4 3 0 E -GAM"» 0 ' . 6 1 i a 5 E - 0 1 Mu< ' ' MU: GNU = V 0.-71097 VKL = - 0 ' . 7 l 0 S 0 FORCES ON BODY # i , 5 0 CENTER AT C O'.O , o'.O ) CU 3 3',013I'1 COT= 0 ' . 0 6 5 9 9 CMOs 0 ' . 5 7 0 3 B CM« = CIRC« 37'.0638f CLCs 3 ' . o 9 6 4 0 PERIMs 49,298 FORCER ON BODY # 1 7 1 . 1 7 9 CENTER AT ( 4 6 ' . 2 0 , le'.OO) ilT- 2'.07780 C O r = O ' . 4 o 0 9 6 CMOs - 0 ' . 3 S 3 4 7 CM4 = Cl«C= l'.R8B9i CLCs l'.0'l911 PERIMs 7 ' . 3 7 7 5 FORCES ON HODY # i f lo,l8A CENTER AT ( 3 l ' . 2 0 , IB'.OO) CLT = -o',24827 COT= -0* . 0 o 7 5 0 CMOs - 0 : . 1 0 2 7 0 CM4* ClRCs - 0 ' . 4 4 0 1 3 CLCs - o ' . 2 4 4 5 2 PCRIMs 7'.3776 FORCES ON BO')Y #189, 197 CENTER AT ( 2 2 ' . 2 0 , 18 ' .00) CLT3 . o ' . f l a s f l o CDT = - o ' . 0 5 4 2 5 CMOs -0.20537 CM4 = ClRCs -0'.7112B CLCs -0'.111B2 PERIMs 7 ' . 3 7 7 6 FORCES ON IIPOY #198,206 CENTER AT ( 10 ' .20, l f l ' , 0 0 ) CLT= -0',7569l CRTs -o'.14861 CMOs -0'.36254 CM4 = ClRCs - 1 . 17703 CLCs -o'.65391 P E R I Ma 7'.3778 FORCES ON BUOY #207,215 CENTER AT ( -f.80, IB'.OO) CLT= -O',5066S CDT= - o ' . 0 2 9 4 4 CMOs -o'.23201 CM4s ClRCs - 0 . 6 * 2 1 3 CLC= -o'.37S96 PERIMs 7'.3778 ON tfnDY #210,224 CENTER AT C -13'.80, IB'.OO) 0 ' , 4 7 6 7 7 COT= - 0 " . 0 4 0 6 6 CMOs 0 ' . 2 4 9 3 3 CM4 = 0.72990 CICs 0.10550 PERIMs 7 ' . 3 7 7 6 ON BODY # 2 2 5 , 2 3 3 CENTER AT < -25'.80, IB'.OO) 0',7C."66 CDl's -O'. 15769 C MOs 0 ' . 3 5 7 3 5 CMIs 1'.28502 CLCs 0.71390 PERIMs 7 ' . 3 7 7 7 ON tinOY # 2 3 4 , 2 4 2 CENTER AT C -37'.80, l f l ' , 0 0 ) 0',50513 CPTs - o ' . 0 { 7 2 2 CMOs o'.20048 CM4» 0 ' . 7 8 5 l j CLCs 0 ' . 4 3 6 3 4 PERIMs 7 ' . 3 7 7 7 0 1 FORCES C L T = ClRCs FORCES f L T = ClRCs FORCES C L T = C I R C S - 0 ' . 18295 -1.02292 » 0 . 0 4 0 6 4 P0'.09392 - 0 ' . 1 7 3 3 2 • 0 ' . 1 0 S 3 7 0 . 1 3 0 1 4 0 ' . 1 6 1 4 4 0 ' . 0 7 4 1 9 I' EXECUTION TERMINATED isiG S LO xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx^ M I C H I G A N TERMINAL S Y 3 T E M FORTRAN 0 ( 4 1 3 3 6 ) MAIN1 10*22-75 10119136 PAGE POOl 0001 0002 0003 9001 0005 0006 0007 OOOB 0009 0010 0011 0012 0013 0014 0015 0016 SUBROUTINE MAiNlCXX.YY,DX,0Y,D3,CS,S!.N»S!G,M,VTT.CP,GAM,NG.MU, 1.000 i GNU,NM,VTI,XC,YC,NLS) 2.000 REAL XX'(N),YYiN),DX(N),DY'(N),DS(N),CS(M),SI(N) 3.000 XX,YY > CONTROL POINT COORDSf DX,DY,D3 » ELEMENT LENGTHS 4.000 CS,SI - COS,SIN OF ELEMENT INCLINATION 5.000 REAL XC(NLS),YC(NLS) 6.000 XC,YC - CENTERS OF WALL SLATS 7.000 N i TnTLA * CONTROL POINTS 8.000 REAL Slr,(M),VTT(N),CP(N),r.AM(NC),MU(NM),GNU(NM) • •• 9.000 SIG - SOURCE STRENGTH DENSITIES (ALSO USEO AS SOLUTION VECTOR I N 10.000 SYSTEM ) 10.000 (GAM,MU,GNU,' ARE PART OF SIG) 11.000 M- TOTAL * UNKNOWNS IN SYSTEM C*SIG=D 12.000 VTT,CP - TANG VEL, PRESSURE COEFF'. 13.000 GAM - VORTEX STRENGTH DENSITIES ON TEST AIRFOIL t S L A T S 14.000 MIJ.GNU - SOURCE 8 VORTEX STRENGTH DEN'S ON STREAMLINE REPRESENTING 15.000 S'.L'. 15.000 REAL V T I ( N M ) 16.000 VTI - PRESCRIBED TANG'L VEL ON SHEAR LAYER STREAMLINE 17.000 CALAB,CALCD,CALCP,CALCL - IF NONZERO CALCULATE A,B,C,D,CP,CL 18.000 K- R A B, w R C D - IF MONZr-IP WRITE A,B,C,D INTO FILES 19.000 SOLV - IF NONZERO SOLVE SYSTEM OF EONS C*SIG=0 . 20.000 GAUSS - IF NONZERO USE GAUSS-ELIMINATION 21.000 ITER - IF NONZERO USE ITERATIVE METHOD 22.000 HSIC - IF NONZERO ALREADY HAVE SIG IN FILE FROM PREVIOUS R U N 23.000 INTEGFR CALAB,CALCD,WRAB,WRCD,SOLV,GAUSS,ITER,CALCP,CALCL,H3IG 24.0 0 0 COMMON/81/ N»S,NSLAT,NSU1,NKA,N«<2,MSV,NA,NSPS,NTEU,NTEL 25.000 N*3 - TOTAL # CONTROL POINTS ON AIRFOIL SOLID WALL SECTIONS & S L A T S 26.000 NSLAT'.NSPS - aSLATS,((CONTROL PTS /SLAT 27. 000 flSU 1 - 1ST CONTROL ON 1ST SLAT 28.000 NKA - EON M FOR KUTTA CONO'N ON TEST AIRFOIL 29,000 MSV - » CONTROL PTS ON STREAMLINE FOR SHEAR LAYER ( M U , G N U ) 30.000 NA - ((CONTROL PTS ON SINGLE TEST AIRFOIL 31.000 NTEU, M T F L - CONTROL PT * » TEST AIRFOIL TU'. ( U ' . L ) 32.0Q0 NM2-- « OF LAST EON FOR Z E R O NORM VEL ON INNER EDGE OF S.L'. 33.000 C0MH0N/B2/ U,CH 34.000 U - UNIFORM ONSET STREAM SPEED 35.000 CH - SINGLE TEST AIRFOIL CHORO 36.000 COHMON/P.3/NU1,NWIII (NU3,MWU2,NL1.NWL1,NL3,NWL2»NSOL1,NSOLSL,NF1, 37.000 1 NFLAT,N3PF,NI1 38,000 NU1,NU3.NL1,NL3 - 1ST CON PT ON EACH FLAT SOLID WALL SECTION 39.000 NWIJ1,NWU2,NWL1 ,NWL2 - « CON PTS ON EACH F L A T 30LIO WALL SECTION 40 . 000 N30LSL - * CON PTS ON ARBITRARY SHAPED SOLID SURFACE E'.G', PLENUM 41.000 BOUNDARY 41,000 NSOL1 - 1ST CON PT ON ARBITRARY SOLID SURFACE 42.000 NFLAT,NSPF - « FLAT SLATS, « CON PTS OFLAT SLAT - NO K U T T A APPLIED .43.000 NF1 - 1ST CON PT ON 1ST FLAT SLAT 44.000 Nil - 1ST CON PT ON SHEAR LAYER 45.000 COMMON/B4/CALAB,CALCD,WRAB,KRCD,SOLV,GAUSS,ITER,CALCP.CALCL.HSIG 46.00 0 EXTERNAL CALCAB,ASSEMA,AS3EMB,ASSEM0,RE,WR,WRD,ATXB,CPS,FORCES 47.000 N3VT=N " 4 8.000 NUNsM 49.000 NDA=4*N3VT*NSVT 50.000 NDBsNDA 51.000 NDCs4*NUN*NUN 52.000 I—' 4s> MICHIGAN TERMINAL SY3TEM FORTRAN G(41336) ..AINl 10-22-73 tOt19136 PAGE P002 0017 CALL GSPACE(A,NDA.0,&30n 53.0Q0 o o i a CALL GSPACE(B,NDH,0,&302) 54.000 0019 iF(CALAB.Nc'.O) GO TO 200 5 5 . 0 0 0 0 0 2 0 LA = 3 56.000 0 021 MsNSVf 5 7 . 0 0 0 0 0 2 2 HaNSVT 58.000 0 0 2 3 CALL CALLER(RE,AfiPTR(N),IPTR(M),IPTR(LA)) 59.000 0021 LB = 4 60.000 0 0 2 3 N=NSVf - 61.000 0026 M=NSVT 62.000 0027 CALL CALLER(RE,B,iPTR(N),IPTR(M),IPTR(LB)J 63.000 o o 2 e GO TO 2ol 64,000 0029 200 N=NSVf 65.000 0030 MrNSVT 66.000 0031 CALL CALLER{CALCAB,A,B,IPTR'(N),IPTR(M),IPTR(XX),IPTR(YY5,IPTR(0X), 67.000 1 IPTR(0Y),IPTR(05), IPTR(CS),IPTR(SI» IF'(HSIG),NC,0) GO TO 201 68.0 00 0032 69,000 O033 IF(WRAB.NE'.O) GO TO 202 70.000 0034 IFCCALCD'.EO'.O) GO TO 2 0 3 71.000 0 0 3 5 GO T0 204 72,000 0036 202 MsNSVT. 73.000 0 0 37 M=NSVT 74.000 0 0 3 6 LA = 3 75.000 0039 CALL CALLER(WR,A,IPTR(N),IPTR(M),IPTR(LA)) 76.000 C 0 1 « N=NSVT 77.000 o o i i M=NSVT 78.000 0042 LB = 4 79.000 0 0 1 3 CALL CALLER(WR,B,iPTR(N),IPTR(M)»IPTR(LB)) 80.000 O O H IF(cALCO'.eo'.O) GO TO 205 81.000 0045 204 IFC^RAH'.NE.O) GO TO 206 82,000 0016 N=NSvf 83.000 0017 MsNSVT 84,000 0 0 1 6 LB = 4 85.000 0 0 1 9 CALL CALLER(WR, B, JPTR (N) , IPTR (M) , IPTR(LB)) 86.000 0050 206 CALL FSPACE(B,»303) 87.000 C051 CALL r,SPACE(C,NDC,0,&304) 88.000 0052 M=NSVT 89.000 0053 MBNIJN 90.000 0 0 5 1 CALL CAi LERitASSEMA,A,C,IPTR(N),iPTR(M)) 91.000 0055 IFCWRAR'.NE.O) GO TO 207 92.000 0056 LA-:: 93.000 0057 MsNSVT 94.000 0058 MzNSVT 95.000 O059 CALL CALLER(WR,A,iPTR(N),IPTR(M)fIPTR(LA)) 96.000 0060 CALL FSPACE(A,*305) 97.000 0061 N0B=4*"SVT*NSVT 98.000 0062 CALL GSPACEitB,NOB,0,8306) 99.000 0063 LB = 4 100.000 0061 N=NSVT 101.000 0065 MsNRVT 102.000 0066 CALL CALLER(RE,B,iPTR(N),IPTR(M),IPTR(LB)> 103,000 0067 207 N=N3VT 104.000 0 0 6 e M = NIJN 103,000 0069 CALL CALLER(A3SEMB,B,C,IPTR(N),IPTR(M)) 106.000 0070 ND0=4*NUN 107.000 Ul MICHIGAN TERMINAL SYStEM FORTRAN G(«13S6) MAIN1 10-22-73 10119136 0071 CALL r,SPACE(D,N0D.0,i307) 108.000 0072 NsNSVT 109.000 0073 M=NUN 110.000 0071 N i = M 51V 111.000 0075 IFtMSV.CO'.O) Nfal 112.000 0076 N2=NXE - 113.000 0077 IF(MXE.EQ'.O) N2 = l 111.000 0078 CALL CALLER(A.1SEMr),0,IPTR(M),IPTR(CS),IPTR(SI),IPTR(N),IPTR(VTn, 115.000 l" 1BTR(N1).IPTR(VT0),IPTR(N2)) 116.000 0079 iF(SOLV'.LQ.O) GO TO 208 1 17 .000 0080 IF(r,All33'.NE'.0) GO TO 209 l ie .000 0031 IF(ITER.NE.O) GO TO 210 119.000 0082 208 IF(WPCO.I:0',0) GO TO 21 1 120.000 0033 210 LC=7 121.000 0081 NsHi.iN -• 122.000 0085 MsNUN 123.000 0086 CALL CALLER(WR,C,iPTR(N),iPTR(M),IPTR(LO) 124.000 0087 LD=8 125.000 00?8 MrNUN 126.000 0089 CALL CALLERC<.Rn,D,IPTRCN),IPTRE.O) CO TO 215 112.000 0105 NOAs'l*NSVT*NSVT 143.000 0106 CALL r,SPACE(A,NDA,0,*309) 144.000 0107 LA=3 . 145.000 0108 NsNSVT . . . 146.000 0109 MsNSVf 147,000 0110 CALL CALLER(RE,A,iPTR(N),iPTR(M),IPTR(LA)) 118.000 C ! l { 215 NrNSVf 119.000 0112 MrNUN 150.000 ' 0113 KsNJLAT 151.000 C114 IF (NSLAT.EO'.O) KSJ - 152.0Q0 0115 LsMsV 153.000 0 1 1 6 iF(MSV.EO'.O) Lsl , 154 .000 0117 CALL CALLER(CPS,IPTR(CP),IPTR(VTT)nPTR{XX),IPTR(YY),IPTR(C3)» 155.000 1 IPTR(SI),JPTR(N),IPTRCSIG),IPTR(M),IPTR(GAM),IPYR(K),IPTR(MU)r 156.000 2 iPTR(GNU),jPTR(L),A,B) 157.000 Olie 213 IFCCALCL'.EO.O) GO TO 216 158.000 0J19. CALL FfiPACE(A,&310) 159.000 0120 CALL FSPACE(B,&311) 160,000 0121 . NsNSVT 161.000 0122 Nl=i 162.000 •liCHIGAN TERMINAL SYSTCM FORTRAN G<41336) MAIN! 10-22-75 10119136 PAGE P004 0123 0124 0125 0126 0127 0126 0129 0130 C 13 i 0132 0133 0131 N2SNA XA--0'. YA = o'. CALL CALLER(FORCES,IPTR(CP),IPTR(XX),IPTR(YY),IPTR(DX).IPTR(DY), 1 IPTP(OS),IPTR(VTT),IPTR(N),IPTR(U),IPTR(CM),IPTR(NI),IPTR(NJ), 2 IPTR(XA),1PTR(YA)) IF(NaLAT'.Ed'.O) GO TO 2 00 { K = 1,NSL AT Nl = MSlll + NSPS*(K-l) N2=M1+NSFS-1 CHrj'.h xs=xc'rK) YS=i«'. CALL CALLER(FORCES,IPTR(CP),IPTR(XX),IPTR(YY),IPTR(OX).IPTR(DY), 1 IPTR (IIS), IPTR (VTT), IPTR (N), IPTR (U), IPTR (CH), IPTR (NI), IPTR ( N 2 ) , 2 IPTR(XS),IPTR(YS)) 0135 2 CONTINUE 0136 IF(HRIG'.NE.O) GO TO 217 0137 216 CONTINUE 0138 GO TO I 99 0139 203 STOP 203 o i i o 205 3T0P 205 c i i i 211 STOP 211 0142 212 STOP 212 0113 217 STOP 217 0111 301 STOP 30 i 0145 302 3T0P 302 0146 303 STOP 303 0147 304 STOP 301 0148 305 STOP 305 0149 306 STOP 306 0150 307 STOP 307 0151 308 STOP 308 0152 309 STOP 309 0153 . 310 STOP 310 .0154 311 STOP 311 0155 99 RETURN 0156 END •OPTIONS •OPTIONS • STATISTICS •STATISTICS* IN IN EFFECT • IO,EnCDIC,SOURCII,N0LI3T,NODECK,LOAO,NOMAP EFFECT^ NAME = MAINl , LINECNT a . 37 3J . J , :LE STATEMENTS = 156,PROGRAM SIZE s NO DIAGNOSTICS GENERATED 69S2 163.000 164.000 165.000 166.000 167.000 168.000 169.000 170.000 171.000 .172.000 173.000 174.000 175.000 176.000 177.000 n e . o o o 179.000 180.000 181.000 182.000 183,000 184.000 185,000 186.000 187.000 188.000 189.000 190.000 191.000 192.000 193.000 194.000 195.000 196.000 197.000 198, 000 199.000 200,000 NO ERRORS IN MAINl LO MICHIGAN TERMINAL SYSTEM FORTRAN G(41536> CALCAB 10-22-73 0001 SUBROUTINE CALCAB(A,B,N,M,XX#YY,DX,DY,DS,C3,SI) C CALCAB CALCULATES MATRICES A, B OF INFLUENCE COEFFICIENTS 0002 REAL XXCN),YYCN),DX(N),DY(N),OS(N),CS(N),SI(N) 0005 REAL A(N,M),B(N,M) 0 0 01 COHMOM/Bl/ NWS,NSLAT,NSU1,NKA,NM2,MSV,NA,NSPS.NTEU,NTEL 0005 DO ? I = i,M 0006 DO 2 J*1,N 0007 IFCl '.EQ'.J) GO TO J 0008 OXJ=XX(I)-XX(J) 0009 DYJiYYd)-YY(J) C X . I . Y J - DIST. riCE OF 'II TO ' J ' IN 'J< COORD'. SYSTEM 0010 XJ = DX . !*CS (J)+DYJ*SI ( J ) 0011 YJ=DYJ*C5(J)-DXJ*3I(J> 0012 l)SJ2 = r>r>CJ)/2'. 00 1 S D3J4 = DS.I2*D5J2 0011 XJS = X.I*XJ 0015 YJS = Y.r*YJ 0016 XP = X.J + DSJ2 0017 XM=XJ-DSJ2 0016 XP3=XP*XP 0019 XMS=XM*XM C XJ IS ZERO IF ELEMENTS VERTICALLY ABOVE EACH OTHER 0020 IFCXJ'.EQ.O.) GO TO 140 C PHIX IS VELOCITY IN *IND DIRECTION 0021 PHIX=ALOG((XPS+YJS)/(XMS*YJS)) 0022 GO TO 141 0021 140 PHiXrO'. C Y J IS ZERO IF ELEMENTS ARE ON SAME FLAT HALL SECTION 0024 141 IFfYJ'.EO'.O'.) GO TO 142 C PHIY IS VELOCITY PERP*. TO WIND RIRN 0 025 PHIY=2.*ATAN2((0S(J)*YJ),(XJS+YJS-DSJ4)) 0026 GO TO 143 <027 142 PHlYao. 0028 143 IFCSI '(.D'.EO'.O'.) GO TO 144 0 029 31•J = Sl(i)«CS(J)-CSCI)*SI(J) 0030 coj=cs(i)*cs(j)tsi(i)*si(J) C A is NORMAL VEL IN 'I' COORD SYSTEM c 8 is TANG ' L VEL IN W COORD SYSTEM 0031 A(J,I)=PHIY«COJ-PHIX*SIJ 0032 B(J,I)=PHIX*COJ+PHIY*SIJ 0033 GO TO 2 0034 3 A(TJ,I) = 6'.283l05 0035 B(J,I) = o ' . 0036 GO TO 2 0037 144 3ij=SI(I)*CS(J) 0038 COJ=CSCI)*CS(J) 0039 A(J,I)=PHIY*C0.1-PHIX*SIJ 0040 B(J,I)=PHIX*COJ*PHIY*SIJ 0041 2 CONTINUE 0.042 RETURN 0013 END ': • OPTIONS I N EFFECT* ID,EBCDIC,SOURCE, NOLIST, NODECK»LOAD, NOM AP • OPTIONS I N EFFECTii NAME = CALCAB , LINECNT » 57 •STATISTICS* SOURCE STATEMENTS s 43,PROGRAM S I Z E B . 1700 •STATISTICS* NO DiAGNOSTTCS GENERATED NQ ERRORS IN CALCAB 10119137 PAGE P001 2 0 1 . 0 0 0 2 0 2 . 0 0 0 203.000 204.000 205.000 206.000 207.000 208.000 209.000 210.000 211.000 212.000 213.000 214.000 215.000 216.000 217,000 2 i e . o 6 o 219,000 220.000 221.000 222.000 223.000 224.000 225.000 226.000 227.000 22e,000 229,000 230.000 231.000 232.000 233.000 231,000 235.000 236.000 237.000 23e.000 239,000 240.000 241.000 242.000 243.000 244.000 245.000 246.000 247.000 248,000 249.000 250.000 251.000 U) CO MICHIGAN TERMINAL SY3TEM FORTRAN G(11336) \SSEMA 1 0 - 2 2 - T 5 1 0 1 1 9 | 3 7 PAGE P 0 0 I 0 0 0 1 0002 0003 0001 0005 0 0 06 0007 0008 0009 0010 0011 0012 0013 0011 0015 0016 (.017 0018 0019 0020 0021 0022 0023 0021 0025 0 026 0027 0028 0029 003Q C031 0032 0 0 3 3 0 0 3 1 0 0 3 5 C 0 3 6 0 0 3 7 0 0 3 8 0 0 3 9 ooio 0 0 1 1 0 0 1 2 SUBROUTINE AS3EMA(A,C,N,M) c c is MATRTX FOR SYSTEM C * S I G » D C ASSC.MA ASSEMBLES THOSE PARTS OF C THAT DEPEND ON A'. REAL A(N#N).C(M,M) INTEGER i:,P.O C0MMON/B1/ NWS,NSLAT,NSUt,NKA,NM2,MSV,NA,NSPS,NTEU,NTEL • COMMON/B2/ U,CH NSPsNSPS-1 NN2=NM2+MSV NWSV=MWS+M8V C»**«« LOOP 1 - ASSEMBLE NORMAL VEL EQNS FOR ALL NWS CONTROL PTS ***** DO 19 1=1,NWS C E iS EOUATION « E = I C L00P2 - NORM VELS AT A L L NWS C, P'. DUE TO ALL NWS SOURCE ELEMS DO 2 .1=1, NWS 2 C(J,E)=A(J,i) iF(MSV.EB'.O) GO TO 19 C LOOP 8 - NORM vELS AT A L L NWS CON PTS DUE TO SOURCE ELEMS (MU) ON C S'.L DO 8 K=i,HSV J = N K A + K M=NWS+K 8 C(J,E)=ACM,i5 19 CONTINUE IFCNSL AT'.EO'.O) GO TO 12 C****«LOOP '[O - ASSEMBLE KUTTA EONS FOR AIRFOIL-SHAPED SLATS ***** DO 52 KS=1,NSLAT KL = NSUl+N3PS*(K3-'l) • KU=KL+NSP E = N*'S + KS C LOOP 13 - TANG VELS AT T.E*, 00 13 Ks'l, NSLAT J=NwS+K P = NSU'f*NSPS*+ACH,NTEL) 3 1 2 . O p O C(J,NKA)=SA 3 1 3 , 0 0 0 3A = o'. 3 1 1 . 0 0 0 LOOP 2 3 - TANG VELS AT TE3T A I R F O I L T'.E*. O'.T'. VORTEX ELEMS ON TEST 3 1 5 . O o O AIRFOIL 3 1 5 . 0 0 0 DO 2 3 Kil.NA 3 1 6 , 0 0 0 3A = SA + A'CK,NTEU)+A(K,NTEL) 3 1 7 . 0 0 0 C(NKA,HKA)=SA 3 1 8 , 0 0 0 iFCMSV'.EQ'.O) GO TO 2 1 3 1 9 . 0 Q 0 LOOP 26 - TANG VELS AT TEST A I R F O I L T.E*. o'.T*. VORTEX ELEMS (GNU) ON 3 2 0 . 0 0 0 DO 26 K = 1,MSV 3 2 1 . O O O J = M<2 + K 3 2 2 . 0 0 0 M=NwS+K 3 2 3 . 0 0 0 C(J,NKA)=A(M,NTEU)*A(M,NTEL) 3 2 1 . 0 0 0 I F ( M S V . E O ' . O ) GO TO 61 3 2 5 . 0 0 0 C«****ASSEMf)LE NORMAL VELOCITY EONS FOR MSV CON PTS ON S,L'. 3 2 6 . 0 0 0 DO 27 KM=1,MSV 3 2 7 . 0 0 0 IsMwS+KM 3 2 8 . 0 0 0 E=NKA+KM 3 2 9 . 0 0 0 C LOOP 28 - NORM V E L S AT MSV CON P T S O'.T'. A L L NWS SOURCE E L E M S 3 3 0 , 0 0 0 0 0 28 Jal,NWS 3 3 1 . 0 0 0 C ( J . E ) = A ( J , I ) 3 3 2 . 0 0 0 LOOP 33 - NORM VELS AT MSV CON PTS O'.T'. A L L MSV SOURCE ELEMS (MU) 3 3 3 . 0 0 0 ON INNER 3 3 3 . 0 0 0 DO 3 3 Kel.MSV . 3 3 1 . O g o J = Nk'AtK 3 3 5 . 0 0 0 MBNHS+K 3 3 6 . 0 0 0 C(J,E)=A(M , i ) 3 3 7 . 0 0 0 CONTINUE 3 3 e . « o o ***»*ASSCMBLC TANG'L V E L EONS FOR MSV CONTROL P O I N T S ON INNER EDGE OF 3 3 9 . 0 0 0 S IL*.***** 3 3 9 , 0 0 0 DO 35 KM=1,MSV 3 1 0 , 0 0 0 I=NWS+KM 3 1 1 , 0 0 0 E=NM2+KH 3 1 2 , 0 0 0 IFCMSLAT'.En'.O) GO TO 37 3 1 3 , 0 0 0 LOOP 38 - TANG VELS AT MSV CON PfS D'.T'.ALL VORTEX EiEMS ON S L A T S 3 1 1 . 0 0 0 DO 38 Kc1/NSLAT 3 1 5 , 0 0 0 PsMSUl+NSP3*CK-l) 3 1 6 . 0 0 0 OsPtNRP 3 1 7 . 0 0 0 J=NwS+K 3 1 8 . 0 0 0 3A = o'. 3 1 9 . 0 0 0 DO 39 M=P,0 3 5 0 . 0 0 0 3A = SA + A(M,I) • • - • 351 . 0 0 0 C(J,E )=3A 3 5 2 . 0 0 0 SA = o'. 3 5 3 . 0 0 0 LOOP 10 » TANG V E L S AT MSV CON PTS D.T'.ALL VORTEX CLEMS ON TEST 3 5 1 . 0 0 0 3 5 1 . 0 0 0 28 3 3 27 C C 39 38 37 C C AIRFOIL O MfCHICAN TERMINAL SY3TCM FORTRAN C ( H 3 3 6 ) A9SEMA t0-22"75 l o t 10137 PA6E POOS 0081 0035 0036 DO 40 K « 1 , N A 10 3AaSA + A ' ( K , n C(NKA,E)a3A LOOP 42 • TANO V E L S AT MSV CON PTS D'.T.ALL VORTEX E L E H S (GNU) ON C . C s L" 0097 * * 0 0 4 2 Kil.MSV 0 0 8 8 JeNM2+K 0 0 3 9 MsNwS+K OO'Q 1 2 C(J.E)=A(M,i) t'O'l 3 5 CONTINUE 0 0 9 2 61 CO'iTlNUE 0 0 9 3 RETURN 0094 END •0PTJOM3 I N EFFECT* ID , EHCDIC , SOURCE,NOLI3T,NODECK#t.OAD#NOMAP •OPTIONS IN EFFECT* NAME = ASSEMA , LINECNT • . 5 7 •STATISTICS* SOURCE STATEMENTS s 94,PROGRAM SIZE a •STATISTICS* NO DIAGNOSTICS GENERATED NO CRRORS I" ASSEMA 353 . 0 0 0 356 , 0 0 0 3 5 7 . 0 0 0 3 5 e . 0 0 O 3 5 8 . 0 0 0 3 5 9 . 0 0 0 3 6 0 , 000 3 6 1 . 0 0 0 3 6 2 . 0 0 0 3 6 2 . 5 0 0 3 6 3 . 0 0 0 3 6 4 . 0 0 0 3 6 5 . 0 0 0 2980 MICHIGAN TENMjNAL SYSTEM FORTRAN 0(11336) 'SSEMB 10»22»75 10U9I38 PAGE P001 0001 0002 0003 0001 0005 0006 0007 0008 0009 o o i o e c u 0012 0013 con O0I5 O0I6 0017 t i o i e 0019 0020 0021 0022 0023 0021 0025 C026 0027 0028 0029 0030 0031 0032 0C33 C031 0035 0036 0037 0038 0039 ooio 001 i 0012 0013 SUBROUTINE ASSEMBCB,C,N,M) 3 6 6 . 0 0 0 C A3SEMB ASSEMBLES THOSE PARTS OF C THAT DEPEND ON B*. 3 6 7 . 0 0 0 REAL BCS(NTEL)) 187.000 I F ( M S V . C O ' . O ) G O TO 16 188.000 L O O P 17 - NORMAL ONSET FLOW VEL • ALL MSV CON PTS 6.N SHEAR l ' . 189.000 D O 17 K=1,M3V 190.000 JsNWS+K 191.000 I=NKA+K 192.000 D(I)=H*SrCJ) 193.000 L O O P 18 - TANG'L ONSET FLOW VEL • ALL MSV CON PTS ON SHEAR L' . 19a.000 * PRESCRIBED TAN ' L VEL THERE*. 195.000 DO 18 K=1,MSV . • • • 196.000 JshwS+K 197.000 I=NM2+K . 19e .00O D ( I ) = - U * C 3 ( J ) + V T I ( K ) 199.000 CONTINUE 500.000 RETURN 501.000 END 502.000 IN E F F E C T * ID,EBCDIC,SOURCE,NOLI ST,NODECK,LOADiNOMAP IN E F F E C T * NAME = ASSEMD , LINECNT » 5T SOURCE STATEMENTS = 29,PROGRAM SIZE n 1191 - • NO DIAGNOSTICS GENERATED 13 15 C 11 17 C 4 8 16 u NO CRRORS IN ASSEMD 4 ^ MICHIGAN TERMINAL SYSTEM rORTRAN G(41336) CPS 10-22-.73 10119t 36 PAGE P001 o o o f SUBROUTINE CP3o2o 00 3 K=1,M8V 526.000 0 021 IsNKA+K 527.000 0022 J=NM2+K 528.000 c • MU - S'.L'. SOURCE STRENGTH DENSITIES 529.000 0023 MUCK)=SiG(I) 530.000 c GNU - VORTEX STRENGTH DENSITIES FOR SHEAR LAYER 531.000 0021 3 GNUCK)=SIG(J) 532.000 C025 4 LL»0 533.000 0026 DO } 2 lel.NVN 534.000 0327 li=I+N3P " 535.000 002B LK="SultLL*NSPS 536.000 0029 IFCI . C f " . ' , 1) WRITE(6,52) 537.000 0030 ' 52 FOIiMATClHl) . , • •• • • 538.000 C VNSf.vTST - TOTAL NORMAL & TANG'L VELS DUE TO SOURCE ELEMS 539,000 C'031 VN3f=0, 540.000 C032 VT3T=0. 541,000 0033 ASM=ol 542,000 0031 B3MiO. 543.000 0035 DO 5 .i=i#Nws • - 544.000 0036 VNSf=VNRT+A(J»I)*SIG(J) 545.000 0037 VT3T=VTST+BCJ,I)*SIG(J) 546.000 003B ASM=A3M+A(J,I) 547.000 0039 5 BSM=BSM+B£J,I) 548.000 0040 A3 = 0. 549.000 004 1 B3 = o'. 550.000 0012 IF CNSLAT.EO'.O) GO TO 8 551.000 •t 043 DO 6 K=ltNSLAT ' • . 552.000 eon • P=N3Ui'tNSPS*(K-l) 553.000 0015 QsP+NSP 554.000 C P,Q - {ST & LA3T CON PTS OS A SLAT 555.000 c AP.BP - NORM * TANG VELS DUE TO VORTEX ELEMS ON SLATS 556,000 0046 AP = o'. 557.000 MICHIGAN TERMINAL SYSTEM FORTRAN G(11336) "PS 10-22-75 10H9I38 PAGE P002 0017 0018 0019 OcSO 0 051 0052 0053 0051 5 055 0056 0057 0058 C059 0060 0 061 0062 0063 0061 Oo65 0066 0067 0068 0069 0070 0071 0072 0073 0071 0075 0076 0077 0 078 C079 0030 0031 0032 0083 OoSI 0085 9086 0C87 0088 0039 0C90 0091 0092 0093 BP = 0 . 00 7 M=P,Q AP=AP+A(M,I) 8PaflP + r>(M,I) AP.= AP*GAM(K) nP=BP*GAH(K) A3=AS+AP PS=ns+BP AT.BT - NORM AT = 0 . BT*o'. no •> . ! = ! i NA AT=AT+A(J,I) BT=BT+R(J,I) AT=AT*GAMM RTsHTftGAHM AM,B« - NORM & TANG VELS DUE TO VORTEX ELEMS ON TEST AIRFOIL t. TANG VELS DUE TO MSV SOURCE ELEMS ON INNER EDGE OF NORM & TANG VEL3 DUE TO MSV VORTEX ELEMS GNU ON INNER C •C S'-L'. AM = U'. BM = u'. C . AG,BO C EDGE OF S ' L ' . AG = O'. BG = o'. IFCMSV.EO'.O) GO TO 11 n o i o K=I,MSV J=NWS+K AG=ACH A'CJ,I)*GNUCK) flG=HGtB(J,I)*GNUtK) AM = AM+A(.J,I)*MU(K). 10 RM=RM+RCJ,I)*MU(K) 11 VNST=VNST+AM VTST=vTST+BM C VNVT.VTVT - TOTAL NORM t TANG VEL DUE TO ALL VORTEX ELEMS VNVTs-HS-BT-HG VTVT=AStAT+AG C VNOT,VTOT - NORM & TANG-VEL DUE TO UNIFORM STREAM U VNOf=-U*3ICI) VTOT=U*CSCI) VNT=VMnT+VNVT+VNOT VTT'ci) = VTST + VTVT + VTOT C VKL V K U - T E S T AIRFOIL T'.E*. KUTTA VELS IF(l'.r"'.NTEU) vKUrVTTCI) IF(l'.EQ'.NTEL) VKL = VTT'(I) CPCI) = 1'.-VTTCI)*VTT(I) iFti'.r's'.n GO TO ni IFUl'.EC.NUl)' AND*. CNWUl'NE',0)) GO TO 12 IFC'CI Ea'.NU3),ANDr(HWU2.NE',0)) GO TO 13 IF(CI.EO'.NLI) AND ( N W H . N E . O ) ) GO TO 11 tFCJl,EO.NL3)lAND.CNWL2.NE'.0)> G 0 TO 15 IFCCI EO'.N8OLI).AND'.) GO TO 46 IFC(I.L:(!.NF1)'.ANO'.(NFLAT'.NE.O)) GO TO IT IF((NSLAT,.EO'.0).OR".(l'.GE',NSU2)) GO TO 70 iFCCl'.Eo'.LKj'.ANn'.CLL'.LE'.NSLAT)) GO TO 18 70 CONTINUE 558.000 559.000 560.000 561 .000 562.000 563.000 561.000 565.000 566.000 567.000 56e,000 569.000 570.000 571.000 572.000 573.000 571.000 571.000 575.000 576.000 577.000 577.000 57e.000 579.000 580.000 581.000 582.000 583.000 581.0(10 585.000 586.000 587.000 588.000 589.000 590.000 591.000 592.000 593.000 591.000 595.000 596,000 597.000 598.000 59").000 600.000 601.000 602.000 603.000 601.000 605.000 606.000 607.000 608,000 609.000 610.000 M I C H I G A N T E R M I N A L S Y 3 T E M F O R T R A N G ( H 3 3 6 ) C P 9 10-22"T5 lOt t<9t3R P A G E P 0 0 3 009q 0095 CO'6 0097 00<"8 C099 0100 '0131 01 32 C 1 03 0 101 0105 0106 0107 010B 0109 0110 0 1 11 Ci 12 0 113 0114 01 15 0116 o i 17 0118 0119 0!20 0121 Cl'22 0123 9'24 0123 0126 0127 0123 0129 0130 0131 0132 0133 0134 C135 0136 0137 0138 0139 c i i o 0111 0142 0113 0144 •OPTIONS iF((I.EO.Nii).AND.(MSV'.HE.O)) GO TO 49 GO TO 12 00 F0RMAT.C4X, 'VNST' ,4X, l VNVT ', 4X, I VNOT t, 4Xi 'VNT ' »5X» 'vfST',4X,'VTVT•, 1 IX,'VTOT'»4X,'VTT',5X,'ASUM',4X,'BSUM',5X.'YY',5X,'XX',5X,'CP'i 2 6X,'SiG') 41 WnifE't6,30) 30 FORMATC'MAIN AIRFOIL') GO TO 51 42 WRlfE(6,31) 31 *^ n.i.\,-('o.nv-.' Ri«.c-: cwilw M A L L ' ) GO f o 51 43 wRITEi'6,32) 32 FORMAT('UPPER LEFT SOLID MALL') GO fo 51 44 WRITE'c6,33) 33 FORMAT('LOWER LEFT SOLID WALL') GO TO 51 45 WRITE(6.34) -34 FOfiMATCLOUER RIGHT SOLID WALL 1 ) no fo s i 46 WRITE(6,35) 35 FORMAT('G0LIO STREAMLINE WALL') GO TO 51 47 WRlfE(6,36) .. - . 36 FORMAT('FLAT SLATS/NO KUTTA') GO TO 51 48 IFd'.ME'.NSUl) GO TO 67 wRlfE(6,37) 37 FORMATPUPPER SLATS') 67 LL=LLtl 69 IF(LL',GT'.NSLAT) GO TO 12 MRITE(6f68) I,II 68 FORMAT(/,'SLAT *',I3.2X,I3) GO TO 51 49 WRlfc'(6,38) 38 FORMAJ£'STREAMLINE FOR SHEAR LAYER") 51 WRITEC6.40) 12 WRI TEC'', 13) VNST, VNVT, VMOT, VNT, VTST, VTVT, VTOT. VTT'(I), ASM, BSM, YY(I),XXci),CP(i),SIG(I) 13 FORMATdX, 10F8.3,2F7.2,2F8,3) IF(wSLAT.CO'.O) GO TO 20 WRlTi : (6iH) GAM WRlfEC6,18) GAMM FORMAH'GAMMs • ,G12-.5) IF(MSV.EQ'.O) GO TO 19 WRlfE(6,15) «U KRITEfh,16) GNU FORMAT ('GAMs ', i0G12*.5) FORMAT('MU=',10G12.5) FORMAT('GNU=' , iOG12'.5) WRlfE(fc,17) VKU,VKL FORMAT (' VKU=' ,G12'.5,2X, ' V K L » ' , Gl2'.5) RETURN END I N EFFECT* 10,EBCDIC,SOURCE,N0LI3T,NODECK,LOAO,N0MAP 20 18 14 15 16 19 17 6 1 1 . 0 0 0 6 1 2 . 0 0 0 6 1 3 . 0 0 0 6 1 4 , 0 0 0 6 1 5 . 0 0 0 6 1 6 . 0 0 0 6 1 7 . 0 0 0 6 1 8 . 0 0 0 6 1 9 , o r o 620 . 000 621 . 0 0 0 6 2 2 . 0 0 0 6 2 3 , 0 0 0 6 2 4 . 0 0 0 6 2 5 . 0 0 0 6 2 6 . 0 0 0 6 2 7 . 0 0 0 6 2 8 . 0 0 0 6 2 9 . 0 0 0 6 3 0 . 0 0 0 631 . 0 0 0 6 3 2 , 0 0 0 6 3 3 . 0 0 0 6 3 4 . 0 0 0 6 3 5 . 0 0 0 6 3 6 . 0 0 0 6 3 7 . 0 0 0 6 3 8 , 0 0 0 6 3 9 . 0 0 0 6 4 0 , 0 0 0 641 . 0 0 0 6 4 2 . 0 Q 0 6 4 3 . 0 0 0 6 4 4 , 0 0 0 6 4 5 . 0 0 0 6 4 6 . 0 0 0 6 4 7 . 0 0 0 6 4 8 . 0 0 0 6 4 9 . 0 0 0 6 5 0 . 0 0 0 651 . 0 0 0 6 5 2 . 0 0 0 6 5 3 . 0 0 0 6 5 4 . 0 0 0 6 5 5 . 0 0 0 6 5 6 . 0 0 0 6 5 7 . 0 0 0 6 5 8 , 0 0 0 6 5 9 . 0 0 0 6 6 0 . 0 0 0 6 6 1 . 0 0 0 6 6 2 . 0 0 0 6 6 3 . 0 0 0 6 6 4 . 0 0 0 MICHIGAN TERMINAL SYSTEM FORTRAN G(11336) i-ORCES 10-22-75 0001 SUBROUTINE FORCES(CP,XX,YY,DX,DY,OS,VTT,N.U.CH,Nl,N2,XC.YC) 0002 REAL C P C''0«X X ( N ) , Y Y(:N),D X C N ) , D Y C N),D S < N > , V T T C N ) C XCYC - CENTER OF BODY 0003 WRITEC6.5) N1.N2.XCYC • 0001 5 FORMAT (' FORCES ON BODY * • , IS,1,',13,3X,1 CENTER AT (',F7*,2, t >.>.F-:s,n'i 0005 C L T B O 0006 COTBO*, 0007 CM0=0. 000B CiRCeO. 0009 PER=0*. 0010 DO 1 I=N1,N2 0011 CLT=CLT-CP(i)*OX(i) 0012 CDTBCDT+CP(t)*DY(I) 0013 C1RC=CI«C+VTT(I)«0S(I) C P E R - ROOY PERIMETER CC11 PCRiPCfND3(i) 0015 1 C M O = C M O + C P C I ) * ( ( X X ( I ) - X C ) » D X C I ) * ( Y V { I ) . Y C ) * D Y ( I ) ) C CLT - TUNNEL LIFT COEFF'. 0016 CLT=CLT/CH C COT - TUNNEL DRAG COEFF*. (THEOR »Y ZERO) 0017 CDT=CDT/CH C C*0 - TUNNEL MIDCHORD PITCHING MOM, COEFF*. 0018 C M O i C M O / C H / C H C CM'I - TUNNEL OUARTERCHORD PITCHING MOM'. COEFF*. 0019 CMflsCMO-CLT/'1'. C ciRC - CIRCULATION ABOUT BODY C CLC- LIFT COEFF'. FROM CIRCULATION 0020 CLC=2,*CtRC/CH/U 0021 wRITEC6,2) CLT,CDT,CM0,CM1 0022 2 FORMATCCLTi'.Flo'.S^X.'CDTa'.Flo'.-S^X.'CMOs'.Fio'.-S^Xj'CMfl 1 F10'5). 0023 HRiTEf6,3) CIRC,CLC,PER 0021 3 FORMATCCIRCa'.FlO'.S^X.'CLCo'.FlO.SjZX.'PERIMBljGia'.S) 0025 RETURN 0026 , END •OPTJONS IN EFFECT* 10iEBCDIC,SOURCE,NOL1ST,NODECK.LOAD,NOMAP •OPTIONS IN EFFECT* NAME = FORCES , LINECNT " 57 •STATISTICS* SOURCE STATEMENTS s 26,PROGRAM SIZE B 1276 •STATISTICS* NO DIAGNOSTICS GENERATED NO ERRORS IN FORCCS 10H9I39 PAGE P001 665.000 666.000 667.000 666.000 669.000 670.000 671.000 672.000 673.000 671.000 675.000 676.000 677.000 67e.000 679.000 680.000 681.000 682.000 683.000 681,000 685.000 686.000 687.000 688.000 689.000 690.000 691.000 692.000 693.000 691.000 695.000 696.000 697.000 698.000 699.000 700.000 14 o o o o o o o o o o o o o o o o o o o o o o o o o o o o c - o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o O O O O O O O O O O O O o o o o o o o o o o o o o o o o o o o o o o o o - o . o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o . o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o J r " n a uioVJ tr*o- r j i n en* OVOJ c o - o to . • ^ b ^ o ^ « ( ^ o w f J l o c . ^ o ^ « ( ^ o * < ' , J ' M ^ r t n c ^ « « ^ o » ^ ^ J W ! ^ ^ n o o o o o o o o o - - « w - - -H r j r j r j r j r j r j r j r j r j r j i o ro M M M KI KI KI KI n c =r =r ~ — — — — - LO LfVLn LH LO i n ru <, ~ co _» •> ULJ« »JZ CO z •»-» o »to n c >- Lu » a. C i » - « ~ X » z z X •» w 2 O 3 >- >-* U D » >- —I » — >- z *-« e_ * Z X X X Z X X ^ u c x 0 U J - -or >- ^ 01 » Z a. C h- X. O Z >- " a L J >- >-u » * L_J X '-x ^ Z » Z CL - r-4 a c - w I H U X ^ — . • — X X U- *J s < z O *-» CJ Lu » -(D D < < 3 LJ LJ cr cr cc z. « L r - o c LO •—*- • • CT 1— C" If fl u u r- cr < L i t ^ IU II U_ cr ti. •--*-« 1 N O I I CT • -K X -O LO LO C U I ru ru r j r j »-N U J _ 4 - J ' -J C O a a . u o u 1; II n • 1- o cr u LJ G i <: t~ a o * W . I- C. G C LJ < _J 11 n » - £ c:. h- O C l -LJ UJ c: c •j-> I— v- I x : Z Z IU •» U U ' H • J '_> X < ;< 1 II 11 It o o —<; X C ( . • o r\! e: tu x . »-i _J * Z i-t (_) c: u_ H U C X >- + -« CO *-e 1-c ru a . w w CO z z LJ LU o o z z < < H H U U » I I ru ru cr.n +. x >- x >• I Q _ « — X >- II II j ro >-«!-«>-: o x » X X ru 1 o 11 '-> a. a. » x >- x >-CL w o Z LU J H ' XOO+.-C ^ ^ » » Z Z . x >• - • —• Lu '—I "_' ^ U . . • -. - . I I X . il- X < < 'J X J U II ^ * < * wv^t-i-k c C 1 H M H i ^ j H h i n i 1 r j . v « ~ ^ L". _ . C U O H h H H H . MX>. «^ a o JO: c c.^*'-' a 11 n w 11 11 n - w 11 ^ • COUU.li. I ' J O Z 11 o u. u. C X >• X • - • < U « M > - H M ^ o « " »-» • X X O X X o X >• L> •H s: x >- C3 r u f\ * r i n o e» o o o o o 0 0 0 o O O O O co o o - — • ro ^n *r i n o* r * - 0 0 o 0 0 — • — « — • —• ^ O G> O O O CT C> C> O O O O O C ' C ' ^ ' O O C ' C * O O O O o " —« a i KI c IP o r - c o* o • —< <\r KI cr tn o > r - co cr- • ru"»n er r u r u o j r u f t J P J f u r v j r u r u M KIKIKIMMMMK\ m c r c j c c cr 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 T> & cr> o cz> c> C C> C- t> i » O o c» -> o o o c - o c » o o O O ' O O O O M I C H I G A N TERMINAL SYSTEM FORTRAN G ( 4 1 3 3 6 ) HOOPRO 10-22-75 0045 M=MP-I C XX.YY - NOW M O D I F I E D CONTROL P O I N T COORDS. 0046 DO 5 I=L1,L2 0047 J=l-Lt+1 0048 K = .W1 0049 XXCl) = (XH(J) + XM(K))/2'f 0050 YY(I)=(YMCJ)+YM(K))/2. 0051 OX(I)=XM(K)-XM(J) 0 0 5 2 DYCI)=YM(K)-YM(J) 0 0 5 3 D3CI)=S0RTCDX(I)*0Xa)+DYCI)*DY'(I)) 0054 CS(i)sDXCI)/DS'(n 0C55 5 3i(i)=DY(I)/D3'CI) 0C56 RETURN 0057 END • O P T I O N S I N E F F E C T * 10,CMCDIC,SOURCE,NOLIST,N O O E C K.LOAD.NOMAP •OPTIONS IN E F F E C T * NAME = MOOPRO , L I N E C N T * S7 • S T A T I S T I C S * SOURCE STATEMENTS = 57.PROGRAM S I Z E s • S T A T I S T I C S * NO D I A G N O S T I C S GENERATED NO ERRORS I N MOOPRO 2700 10119t40 P A G E P002 756.000 757.000 758.000 759.000 760.000 761.000 762.000 763.000 764.000 765.000 766.000 767.000 768.000 769.000 MICHIGAN TERMINAL SY3TEM FORTRAN G(11336) RE 10-22-75 0001* SUBROUTINE RE(A,N,M,LA) 0002 REAL A(N,M) OC03 READ(LA) A 0001 RETURN 0005 E N O •OPTlGNS IN EFFFCT* 10.EBCOIC,SOURCE,N0LIST,NOOECK,L0AO,NOMAP •OPTIONS IN EFFECT* NA«C = RE , LINECNT • 57 •STATISTICS* SOURCE STATEMENTS * 5.PROGRAM SIZE s 410 •STATISTICS* NO DIAGNOSTICS GENERATED NO ERRORS IN RE MICHIGAN TERMINAL SY3TEM FORTRAN G(11336) WR 10-22-75 C00 1 SUBROUTINE WR(A,N,M,LA) 0002 REAL A(N,M) 0003 WRITE(LA) A 0001 RETURN 0005 END • OPTIONS IN EFFECT* In, EBCDIC, SOURCE , NOLIST, NODECK, LOAD, NOMAP •OPTIONS IN EFFECT* NAME = WR , LINECNT * 57 •STATISTICS* SOURCE STATEMENTS = 5,PROGRAM SIZE o *STAT13T1C3» NO DIAGNOSTICS GENERATED NO CRRORS IN WR 440 MICHIGAN TERMINAL SY3TLM FORTRAN G(11336) WRO 10-22-T5 0001 0002 0003 OC01 0005 SUBROUTINE WPD(D,M,LD) REAL D(M) wRITE(LO) D RETURN END • OPTIONS IN EFFECT* ID,EBCDIC,SOURCE,NOLI ST,NODECK,LOAD,NOMAP •OPTioNS IM EFFECT* NAME a wRD , LINECNT « 57 •STATISTICS* SOURCE STATEMENTS = 5,PROGRAM SIZE o •STATISTICS* NO DIAGNOSTICS GENERATED NO ERRORS IN WRD 38B NO STATEMENTS FLAGGED IN THE ABOVE COMPILATIONS', EXECUTION TERMINATED 13IG lOllRJll PAGE P001 770.000 771.000 772.000 773.000 771.000 lOllRHl PAGE P001 775.000 776.000 777.000 778.000 779.000 10ll9t11 PAGE P001 780.000 781.000 782.000 783.000 781.000 152 A p p e n d i x 1 1 . L i s t o f E q u i p m e n t U s e d I n s t r u m e n t B a r o c e l P r e s s u r e S e n s o r T y p e 511 (10mm Hg = 10 V o l t s ) B a r o c e l E l e c t r o n i c M a n o m e t e r T y p e 1018B B a r o c e l S i g n a l C o n d i t i o n e r T y p e 1015 D i s a D i g i t a l V o l t m e t e r T y p e 55D31 D i g i t e c D i g i t a l V o l t m e t e r M o d e l 2780 L e e d s & N o r t h r u p M i c r o v o l t I n d i c a t i n g A m p l i f i e r M o d e l 9835-B D r u c k p r e s s u r e t r a n s d u c e r M o d e l PDCR-22 D e s c r i p t i o n p r e s s u r e t r a n s d u c e r f o r p i t o t s t a t i c t u b e m e a s u r e m e n t s 4-1/2 d i g i t v o l t m e t e r f o r w i n d s p e e d f r o m p i t o t s t a t i c t u b e . a m p l i f i e r f o r B a r o c e l ' p r e s s u r e t r a n s d u c e r s . 3- 1/2 d i g i t v o l t m e t e r f o r w i n d t u n n e l b a l a n c e m e a s u r e -m e n t s . 4- 1/2 d i g i t v o l t m e t e r f o r w i n d t u n n e l b a l a n c e m e a s u r e -m e n t s a n d S c a n i v a l v e p r e s s u r e m e a s u r e m e n t s , s t r a i n g a u g e a m p l i f i e r f o r A e r o l a b w i n d t u n n e l b a l a n c e . f o r S c a n i v a l v e a i r f o i l s u r f a c e p r e s s u r e m e a s u r e m e n t s 154 157 160 161 -4- i ' 1 •14-4 1 1 i i_ ! I 1 i 1 1 l 1 ! i 1 I 1 1 ! i 1 1 j 1 1 i a F i g u r e 5 2 Comparison o f a i r f o i l p r e s s u r e ! 1 i 1 1 —l—:— i 1 1 ! ! ! 1 ! 1 i i 1 1 ] i ! : c o e f f lnifitir.s: Theory 1 1 i 1 i i i 1 1 ! 1 ! I i 1 1 > i i 1 i 1 1 > I 1 .1 _L 1 1 l : ! ! I 1 j TTT 1 > i 1 i i 1 1 i i 1 •< l l 1 1 1 1 ! i ! ! 1 1 I 1 I ! i i 1 l L . . L M i j 1 1 ! 1 1 1 i j i 1 i 1 ! 1 1 j j i - j - i i i r i 1 1 I ! ! 1 I ! 1 > 1 i ( i ! 1 1 I i i 1 i 1 i i i I I ! ; j I 1 i I t ! 1 [ t * i I 1 i 1 '< 1 l i 1 i 4 - 1 1 1 1 I 1 •H+ j j ! ! 1 1 j ' 1 - T r 1 ! i i 1 1 1 1 1 ! ! i i i i i ...1 1 1. I i 1 i ! 1 1 1 1 i i i < i I 1 1 1 i 1 1 M l 1 ! i 1 ! ! i -}- 1 1 i i i I 1 1 i ! ! 1 1 ! i 1 ! 1 1 1 1 ! 1 I ' ! 1 ! 1 i 1 i 1 I i t i i • 1 1 1 i ! 1 • ! ! '• 1 -H 1 - ! 1 _ . i H | i P 4-- 1 1 4 I j 1 i |! 4- 1 < X f f 4-4-- / • 4 i -\ i — I 4 - / c ¥- \ Hi 1 » 1 1 1 _ C L 1 1 1 1 1 i { 1 !' i \ HS -WW-—\-{& "-I- 4-f 1 • j - 1 C11 \ / -M M i. ..v J . 1 i i M M i i i i f>°A a t \- 1 I i 1 'v- -f j i 1 i i Qt/v K A . i i ! V P c r 1 1 1 -i.. i - H i 4 1 I ttl (TTT ~1 R" r- i 1 ill i 31! 1 I - 4 4 - 1 r> y a [ hfl Ii- n 6 \ t ! i i. >t _ ii.- M i l B | M i J> *T a i \ j i , i 1 1 ret r — - i M l . ! 1 1 1 -trb r-- •ff H-T U t i 1 i i i 1 i i i 1 j i'L 1 j 1 \\ 1 i i M i i i i l l 1 1 1 I ) ! H i l j i 1 i 1 1 ! 1 I ! ! 1 1 I I i i ~]—j— i ,'„. i ~ 4 " L V "1 i - j -i 1 . _ i i 1 I . i r T I i 1 I i i i i ( • i i — T ~ 1 1 1 l I 1 1 >^ I 1 ! i i t! i } i 1 ! " i 1 i i V j 11 I | i 1 ! S N I— - f - ! 1 - p s i - f - - I i i r ! !, r" ! i I I i i i I ! >*. i - I -J 1 i i ! I i 1 1 i i ! i 1 i 1 i i i 1 1 1 i 1 ! ! i 1 —i—\— —j— 1 i 1 : i 1 i i • j I L 1 f - i 4 — | --—j -1 i i 1 i i i i — 1 ~ i • i i — r - 1 i 1 i i i i i i - 4 - r 1 I- i • I i • | -44- l I I 1 i 1 i I 1 1 \ 1 i I i i 1 t I i 1 - 4 " i T" i | " i i — r — 1 i 1 | i ! 1 i i i i 4- i I i TT"..._I u- - i i 1 I I M 1 1 M M M M i i i 1 1 | ; 1 i I i i i i 1 i -j- i i i _ 1 1 i i " T i I l - 1 4 - 4 , ._! - ' - L i . 1 ~~t~ 1 I i i i 1 ^ ; j ' -4+ 1 ! 1 _ 1 i i ~ F ~ T T i _ 4 i i T T s i i r 1 1 1 M '" , 1 • i i 1 i i i l i i i 1 I ' M i i 1 1 i i 1 1 M i i 1 1 1 l ! i l i i i i i I ! 1 ! I 1 i i l i - j — 1 | 1 —r~ -44 —r \ ! i i 1 ! 1 '. : -1 1 'i 1 1 1 1 . M M ! I .1. I i i i I i i i : i i 1 1 ! 1 ! 1 '• 1 ' | — T T ...1 1 % I -r _ i _ 1 • i i i i t | i r r 1 . . . . . I- - ! - ! -j * \ 4- ._!_ . ! _ !__ 1 j 1 1 i i i :< 1 [ -j \ N 1 .1 I j -|- i - U I i (1 f : R! ~ A / f I 4 •1 1 1 i X >: i i h [ ( } ii rj"l'.L t .„L. § ft 1 ! i 1 >' 3 i . 1 ( "T ~rr _L. 1 ; I t 1 >' * i ft j t i 1 ! i i \ h _ _-|_ ! 1 - !. f [ Id i / \ A _ - j . . I • • ^ r~ . - ( • r ! . ' i , l / i) \ i 1 t \ L , O H i r' "\ • t-1 -1-I.. [ "] 1 _ 11 •" - 4- • -1 " « 1 1 L 1 ! 1 y i / r ty j 1 | J "J Q O i 1 { i L'TJrL I 1 j •1_ I 1 I ; "T ] \ j .... j / & I j ~\~ " 4 \ ~\'~ ._.}. !... 1 r i u • i V _1_ t ) J t f Li ) } I l 1 f 1 N ""] ~| C f i I i j / 4 ] f « *• \ t' << i L V • j < u La e. m i. *. .-- - - * : i_ a . »• • - - - - - - - c B - - - - - -c - - - _ - * « ? - t- C t , ^ m ] I * > 1 <* « s T ! i < t r i i » i •! i i - t / c i: ( ft >v ( "I I J -1 i. oc U i 1 1 ,.;.L fh » j I ! i > 1 I 'ttt «* "~r I • I , i _ r ! 1 j i ! r . . . c V 1 I £ A -|_!_ : ! - - il * e B - - J L': U . . . _ - - - --- - L i . ... t sua c «< u 12S3S1 _l_ • -I.J.-r i ; i r t i _i_ ~ j _ el "/ "1" L I ) " " ! ' ' ! i • i ! _ V a r i a t i o n of along for - -- -tigure • J pressure c o e i i i c i e n t a s t i d i y n t correction uuunucix y - - -±t a two -•axmensxonax a x r i o i j . wx t n zero f rneoxy - _ - -16.3m F i g u r e 6.1 U.B.C. Mechanical E n g i n e e r i n g low-speed c l o s e d - c i r c u i t windtunnel F i g u r e 6.2 V a r i a t i o n of mean windspeed i n two-dimensional t e s t s e c t i o n i n s e r t on v e r t i c a l p i t o t s t a t i c t r a v e r s e CTi 166 F i g u r e 6.4 E f f e c t of e n d p l a t e l o a d i n g s f o r two-dimensional a i r f o i l t e s t s 167 168 Figure 6.6 Error bars for the measured a i r f o i l rHi1 I i l i f t c o e f f i c i e n t s 169 - _ L L L - L i -F i g u r e 6.7 V a r i a t i o n of measured a i r f o i l l i f t c o e f f i c i e n t s on t h r e e c o n s e c u t i v e runs I'M ; 1 I M i J - .» > U 1 1 1 - i 1—1 • ' ! ! I_L < > ! ! ! ! M l fHT-H i F-H Lr i i j - t i J4 ^ 4 t : T T £ i i M i n i ' i i l i ' i l p T i . l : 4 H - T H + H - 4 T - 4 - - - h r + h - 4 + f - r - ^ - H - ^ = f T + "! h 4 H T t + h r H T S S I 1 T f c r T j S H 4 - _ u ^ -f—r-r-M4 444^-44—- r - - !4- - L - u L . _L I 4 i I ' M 1 i I M i ' i 4 ^ 1 : 4 4 ^ 1 ^ 4 - ! f f - p T Z M T i r x t i z z z ^ ^ ^ 4 4 - - g & 4 ^ g ^ ^ p f e 4 ^ -1 ' 1 . | | 1 .'-V4- - r 1 I 1 1 1 1 1 / " ~ f -Ui-U-Ui- 1 1 1 r4--U... 1 ' M /I " I T T 44-I r f - 4 - r 1 + 1 4-TT-4-4 4 / - = MI 1 i 1 1 f-n 1 i/|Ar— 1—h T 4 r i ^ - 4 M X ^ 4 - r - - - T : T - - - T ^ :?=5z : = : : 170 i ! .' M i l ! 1 ; 1 1 ; III " 1 J M J M i M'T l i i - T 1 ' 11 1 i r. - -----MI T - t L 1" 1 d i / - A 4 C % - ^ -i /—' T T h r - T T T T — T M H -- t t / 1 " - L - T r h - j u 1 d ± l~ E S':--i4Zx^: V 8 ( ^ % [ :AR:: _, . / . . LJ-,... " 11 1 T " M L __4|_i_ MMJ L-4-L44 ^~ T i [ 1 H-1 M i _ i I ' ' " T - , S3:—| 1 - ' ; 1 1 -4- M ' h . 1 i ' - T i _ 1 L 1 _I_| X J x : ± 4 M - - E x T - I ^ - - r r - - - N T _ -1 i 1 ___i - - , 1 1 , , 1 M i_ _ i _ i ^ - ^ - ^ 1 : 1 , 1 j 1 i z b f a : i _ J L," T 1 i -J 1 pOJ j L . 1 - T 1 ! 1 11 1 — 1 1 i 1 i 11 1 1 1 r - n 1 | 1 — J — - ; | • 1 -L-i 1—„ M—/ I 1 1 1 U | | 1 u l - z + p z ^ z z P z z ^ z z x z ^ z T - ^ - H — 4 - r r L - f f - J 1 1 —i- ~i — : 1 ! : '"• ' — r - - , ^ " i - T - ^ r ^ M I d G T T - T : 4 ^ 4 4 ^ I , I _ M I M ' • • -J i / M I M I"1" - M i 4_ X X • 7 M i i 1 - I - l i F ! M . _ l _ ' - -4H _ Z _ j _ i "TT" j _ ~ U i . _ i i A / Ii • - • -Hr , _ j_ u T T 4 -^X—^-^-L-^-^-M-n- r X : ^ C T # L X - ^ : _ t t : _ i M M -4- !• • 1 i i i / i i i M M --H H — r — r ± H - t R T drxx d+q- £ z ± zzrzr ± 4 4 - 1 : 1 - 4 ^ T f e x E 1 ? 1 ^ i H j f f - i U - 4 f 4 ^ ^ ; 1111 i ! 1 111 11 -144 U —j U _ L M _ . L . ..I...I '/ 1 M l 1 M -: 1 _]_ _ M / L • 1 i i i M~ . L. 4. 1 1 / 1 1 1 i 1 1 - M l MM i i i ' imi / i 1 •• i M 1 T T r r r —rrr 11 MI 11 i t / M 1 1 MI -I----h —'Mr M 1 _j 1 1/ M 1 1 i r - M.I - J - U r — i - 1 — M — L i i _,_ 1 ' g i i M . 1 1 _ i • - -1 MI 1 -r' I T " L - i—4-- 4- Mm< MI- _ M 1 x T T T T 1 1 - ' -xr x " M 1 0 0 1 1 ' ' ' ' 1 1 1 > ' 1 M r , s - -i-L, ~rrH— T ± T 4 - x i + i m A o M H T t T ^ —H^e4Hff U ! TUl— 1 - 1. |T' 1 1,' U4-. Mil .... M - I 11 I-l 1 -H- h " f - 4 - r T - T T f 4 ^ L r - 4 4 4 L - 4 ^ _ 4 p T T T - --j-j-H-- F i g u r e 7.1 V a r i a t i o n o f a i r f o i l l i f t cc ' - ~ r x !_J 1 , L J L t- —L ' 1 1 I - L i - . 4 -X ± E V X : X X : 4 ± I 4 ± - L - - T X ! T T 1 1 - j - •• 1 11 - - T i X 1 T T T - ^ - n U r t^~vf 1 1 i f f f , - T - E 1 1 M " : x : x 4 t T F i T ± : : : _ _ _ T T 4-1 1 X ~ T T 1 j • - ~M 1 i 1 4 — J J ^ - A ^ j X X X T ^ T T - T — H r — i L +J L p - l f - L - ^ J 4 - X - T 1 1 , 1 ' T T T ± r ~ - ^ r f f - ^ r r - r L -. 1 T ! T f i T " "f^f M . . | I M l 1 I|J?S M l M' 1 - H — r r 4 4 - 4 - -H+4- 44--^ -TTT-- 4 ± + r i r44dio!4"| H 1 H p - 4 - 1 - T j - r C ^ r - M . , 1 . L T . H H 4 r r n — r T Izzzzzz. > e f f i c i e n t w i t h r s l o t t e d - w a l l o p e n - a r e a r a t i o : E x p e r i m e n t 171 172 o n r a t i o o f l i f t - c u r v e s l o p e s f o r d l X ' NACA-0015 a i r f o i l j± — H~h~r 173 F i g u r e 7.4 E f f e c t o f a i r f o i l s i z e o n l i f t - c u r v e s l o p e f o r NACA-0015 a i r f o i l : E x p e r i m e n t 174 1 I .U ! ! M i i . i M M ! - U _ ! .L M M 1 ! i 1 ! I t j i 1 i | i 1 ! | . i , . , .... r-7- 1 —r~ ! i i i i i _} 1 l _) j i 1 1 M M j [ i 1 i' I • i ! \ | 1 i i i • ; > ! 1 i I i 1 1 M i i i i ; i 1 ! 1 i l i ! 1 1 1 1 i ! I i M I ! 1 ! 1 i - _ | _ L i _ L. 1 ! | 1 1 1 1 ' 1 1 1 \ i I i i 1 I I 1 1 1 1 M M ! j 1 i 1 i I I t i ; . M M - | i ! j 1 L l L i i i i > 1 M M ' 1 1 i M M M I i 1 1 1 l l 1 i j • i 1 ', M i l i l l ! M l . i 1 i I i 1 1 1 ! j ! i : i 1 i j i 1 1 i 1 1 1 i l l ! 1 ! ' ! - - 4 " t-j 1 U - l l i i i 1 • 1 i "] 1 ! | 1 1 - I i i ! I ' 1 i 1 l L i 1 i 1 r n r 1 i ! 1 i I i i 1 I I j i 1 M i l M M i r i 1 i l i l i 1 : 1 1 i i i j 1 i i j | 1 ! " i T 1 1 ! I .1 i M l ! i i i M M \ - i 1 1 i M M 1 i 1 1 1 i i 1 1 1 l i j i i J i 1 1 1 i 4 . L' J j ._ _ L i Li L l 1 1 i 1 1 1 | j 1 1 1 1 - 1 i 1 T - P-\t ti~ — '*! 1 O ! i 1 1 1 f 1 ! i 1 > * = t O j 1 . 1 1 1 I e a. •* 1 X n I -r. 1 j I ! ' 1 i 1 1 l 1 1 - C. 1 . i . l . U ( j | 1 1 l 1 I i ! —(— 1 1 1 | 1 | r .).. 1 l 1 ! i 1 i 1 I 1 I i i 1 j 1 i 1 1 1 1 | 1 v r - i I 1 / 1 c y i i >— \ l 1 1 I | j— i 1 i 1 i i i 1 i j | 1 1 1 1 1 1 1 i 1 l 4 1 i i 1 1 ; j ' 1 Y I ) ! u ! n 1 1 i u 1 L, i 1 1 1 | i " i i • 1 t ! i 1 i i 1 i i j 1 1 1 1 I i I 1 1 1 1 i 1 1 1 i 1 i 1 i 1 1 1 i 1 i i 1 i 1 | 1 I 1 1 [ . 1 1 3 1 1 1 i JUJU I 1 1 i i . 5 s, 1 ! 1 1 1 1 i i i ! i . 1 1 1 | 1 1 r i 1 ! 1 i s >. I 1 1 1 i i 1 1 1 | i ' i 1 1 1 j 1 1 i i I 1 I 1 1 1 I 1 •N - 1 1 i I 1 1 I 1 i i i 1 M "> 1 A I ! 1 1 ; 1 • 1 I i " I -1 1 t • 1 I | , — * _ l_ 1 O l f 1 | 1 1 1 i 1 1 «»» _ - I M 1 "** /a 1 t 1 i 1 1 sL 1 1 J l_L.i M i i I I 1 _ 1 t~ I I 1 3 - -j— .7!** 1 ! i • r % , i . --. "V . I t 1 — r f \ r. 1 1 •< i I 1 ; . i , - i i l l i i M i l 1 1 1 j i I 1 1 1 1 - ' J _ I 1 i I 1 1 1 1 i ' >v - tJVL/ AXI \ 1 1 j 1 i 1 1 1 1 i I | 1 1 1 1 1 I 1 1 i i J— i 1 1 ! i i [ i 1 I i ; I i I ; i i i 1 1 1 t i i 1 1 1 , i 1 ! I 1 1 i i I ! 1 1 L i i I 1 1 1 ! i 1 1 I i 1 1 1 1 i i 1 1 1 i 1 1 1 1 1 I i 1 1 . t— 1 . 1 i ! i 1 1 i 1 1 1 1 1 i 1 1 1 1 1 1 i ! ! i 1 1 1 i 1 ! 1 1 1 1 1 1 i I i 1 -4 p. 1 1 1 1 i I 1 1 1 ! 1 1 I 1 \ 2 \ > I 1 1 1 1 1 1 ' i I I I | 1 . 4 1 1 1 i 1 i ; 1 1 ! 1 ! | 1 1 t i i 1 1 | . 1 1 i i I 1 1 1 1 ! i 1 i i . i 1 1 1 i i 1 1 1 : ! 1 i ; i i 1 ; j 1 1 1 1 1 i 1 I 1 1 i 1 ! i 1 i | 1 i 1 i ...... 1 | j 1 1 i i 1 1 1 | i 1 ! 1 i i 1 ! 1 i 1 i 1 i 1 i ; 1 ! i i |. I i i 1 | i 1 1 1 I 1 ! 1 I 1 | 1 1 i ( 1 i 1 1 i r I ! 1 1 I i I i 1 i I ! ! 1 j i i i I I l i l t i i i I >< F 1 1 I 1 ! : l I 1 1 1 1 i | 1 1 1 1 ! . l i i i / L | 4 | I i | i i i 1 j_ i 1 i 1 ! i 1 ! 1 l H 1 1 j 1 ~r 1 i 1 i i 1 i | • • 1 1 i ! 1 ! i i IT I 1 i j ! 1 1 ! t i i i 1 ! 1 1 I • '• i i i i ' ' M i I ' l l i . i i 1 i I i 1 i « L M M II i ! i i ! t i i • i i 1 i i M M i 1 i C 1 1 i i 1 (A AS l ! ! r M I A ft 1 1 | i-U-TL f ! I 1 i J 1 i 1 I Zi 1 IV. o 1 j i irXJ- 1 + 1 I i I I . 1 i 1 I M i l l I I 1 i 1 I 1 " M - r r i I i i i i • 1 M M 1 ! 1 1 i 1 ! M U M 1 ! i i i 1 1 I M i l 1 j 1 i l | 1 1 1 1 1 : 1 i 1 1 ; 1 ! i 1 1 ' I 1 i i , 1 i i i 1 | 1 n 1 1 I I i ! I i i • i I 1 1 1 i p | | 1 i 1 1 i i _J I ! 1 1 i 1 i 1 1 I 1 i i ! i i ! 1 I [ I 1 1 i i 1 1 ; ; i 1 I 1 L _ 1 1 1 1 1 ! I 1 I 1 i 1 i i ! — t j- 1 i I i i 1 ! "i " 1 i ; i : ! 1 i ! 1 1 . 1 T M M 4 i T T i 1 i 1 i 1 - 4 - 1 44- i i i 4 4 - 4 4 j M 1 1 I ! -1444- i i i M M 1 | i i 1 - 4 - U 1 M M . 1 i. i 4 4 4 - I F i g u r e 7.5 E f f e c t o f a i r f o i l s i z e o n l i f t - c u r v e s l o p e f o r C l a r k - Y a i r f o i l : E x p e r i m e n t 175 177 179 i l l _ i i j lH-hi- ...LA I. ; | { i zhLtT _ — _ - i ! 1 {—•—-f — T - i _ L I _ i _ M M 1 1 -J4f 1 i 1 1 ! 1 1 1 i '!" 1 M M i j_ i t i M . f r i -i— i h f _ i | " i~ 1 M M | 1 M M 1 1 : T ~4 — — 1 r T 1 1 ! 1 T 1 1 1 ' 1 i I 1, 1 1 M M _! 1 "i 1 i ! ^ I 1 1 i i i ; 1 j ! ' 1 1 M M .L ] j 1 1 1 i 1 1 ! 1 I i 1 1 ! i ; ! ! 1 1 1 1 i i i i ! ! 1 111 _J_I - 1 1 ! 1 1 1 1 i 1 i i I 1 1 1 1 1 1 1 1 I l1 t 1 1 1 • 1 1 1 — 4 ! 1 1 : 1 1 1 ; M M _ U ' i T : r r I ! | 1 ' 1 -L 1 i r ! 1 1 1 1 | 1 i i - - j -i_i I 1 I 1 1 I 4 1 i 1 4 1 1 T i 1 i i I 1 i i _Lj 1 1; ... 4- M-- I ! ! 1 ] 1 I i 1 1 i 1 i | 1 i 1 1 I"! 1 ! [ ! 1 ! I 1 . t I — 1 1 i I I i i 1 1 1 1 1 1 1 ! 1 M M 1 r r 1 1 : 1 ' i i V X 1 t i i .1 1 i 1 \ i 1 1 i 1 i 1 1 1 M_ 1 i I 1 i 1 1 1 1 1 1 : ; ! i id: i 1 1 | i i i I ! 1 -}-1 j i — r 1 1 i I I ! 1 1 | - M 1 1 ' 1 1 | | | T 1 1 ~i—p" 1 ! ! i I I 1 1 1 I ; i ! i ! 1 i \ 1 i 1 ! 1 1 1 1 1 4+44 L 4 1 1 1 1 ! n 1 1 F i ~I 1 1 1 T i 1 i-S w < i . 1 M 1 I J 1.1 1 1 L i 1 I 1 1 i ! 1 1 v t\ _ A. C h 1 /\ iv J 1 ! 1 1 1 i 1 —:—I—I— r 1 \ /• V SCT: I \J M i rr u 1 1 1 i 1 i 1 1 1 I i ! _ l-H-i • h r 1 111 4TT 1 1 i I 1 — : — r i 1 M 1 T—1— — ! i t f ! | P h—4 •~W •Jfo.t - 1 1 1 1 1 i 1 1 1 I r -4-44 1 I] I - t - 1 1 V i 1 444- 1 ~ T 1 1 r _ t 1 h H - 1 1 c T U r f 1 1 1 i 1 1 i 1 1 I 1 _l_ 1 1 1 - 4-r • 1 i T • 1 1 ~i—1—r- 1 I 1 t • \ 1 1 p i I i t i 1 iitrr — ,.l | t 1 ! 1 1 I ! 1 t 1 1 r y u \ U TT: s 1 "1— 1 1 1 I 4—j— j 4 r i i -4 I 1 1 1 1 1 1 ' I ''• j 1 — 5 - 1V 1 1 r I 1 1 ! —1- f i 1 i L - U 1 \ i \* t ! 1 ! -~J~ t 1 - i 1 1 44 I 1 \ T* I i I i I 1 7- i l _ il 1 1 1 1 1 1 -p-L i i 4 4 - 1 1 • f i V •• 1 • n0r i n * 4 -r I T 1— l i i T 1 J C M \ 1 M M 1X2 LI - a LV r J -V J O 1 1 I M 1 1 1 I \ \ i l 1 1 M l . 1 1 1 1 1 1 M M 1 - i - i - 11 - t i -t =41 rr-11 1 ! n 4 4 n 4r-i ey f-t Y~ m r+~ 1 1 . . ., — t " J ii 1 1 I 1 1 r r LI ' 1 J J L ti - + 1 1 1 i 1 \ - ii^-1 1 1 t 1 III 1 1 1 ; 1 \ y 1 1 1 1 \ 1 ! ! i ~ j T t - - V 1 1 1 1 j 1 i 1 44—4- 1 i 1 J -V4-— 1 1 I 1 1 i • — — 1 1 1 1 1 i \ 1 ! 1 4 1 1 1 4 1 i 1 1 I i 1 1 1 1 i i t 1 1 1 \ l 1 1 ... 1 | 1 1 1 .1 1 I i ' 1 1 | 1 1 1 1 1 4 ! 1 i | t - V 1 1 1 . . 1 1 1 1 i !" v \ — L 1 1 I -)-| 1 rv \ ! i j -t— 1 1 1 i i > ( 1 1 1 1 | i i 1 1 1 1 | l 1 1 1 1 1 i 1 > * - - L . 1 | 1 i 1 1 -4 — r — 4 I 1 1 j s -> i 1 j 1 1 l 1 1 1 1 1 t 1 1 1 I >wS4_ ! 1 1 1 1 J _ ! 1 1 ^ I »-4 1 1 ! 1 1 1 1 4 " 1 -- 1 i I 1 | 1 1 « 1 1 - j - 1 1 1 I -- 1 1 i i 1 i 1 1 i ! 1 1 1 " I T 1 i I 1 1 i ! j | J i 1 i 1 T \ 1 T T T i 1 1 1 ! 1 1 i 1 1 1 j j 1 1 i 1 | 1 1 11 1 • K I 1 1 1 1 1 i 1 1 | 1 1 1 1 1 1 1 1 1 • 1 1 - ! 1 1 1 1 " ! 1. i 1 1 1 1 ^ T 4 - 1 1 S > T ~ P 1 44 1 1 1" 1 —I— 4 1 —4 1 41- 1 1 1 1 i : 1 I 1 1 11 1 1 1 N 1 i 1 4 T i i i j i - f .!.. ..!., ; 1 1 1 1 1 i 1 |. - 4 . i 1 -i—ra 1 i > i 1 1 ! | t 1 1 t 1 4 - 4 4 1 j 1 1 1 1 V « S I I*" 4 4 4 - - 1 - r V 1 1 1 1 1 i ...| ; 1 1 1 1 1 1 J + t > ^& 1 i 1 n 1 i i i -1" r 1 I 1 1 1 t -4 1 i 1 1 1 1 -4 | 1 ! " ; J__ "S \m — — .{. | I u 44 i i 1 - r f t n "7*- i - ~ -1= 1 11 1 1 1 , v „,„,... I I J i_ 1 1 I i 4 i 1 1 i i J 4"^ T i 1 11 11 4 - 1 1 1 1 1 1 1 1 1 1 1 1 1 1 > 1 T i i 1 1 i ' ! i -14— i i. *> »• 1 I 1 : 1 __. 1 1 1 M M n i n •|" I i ! 1 1 I i 1 1 j | | 1 1 1 i i 1 M 1 v ! 1 ! *> i i 1 ; 1 1 ; 1 i ! 1' ! i i i r 1 1 ! i i 1 j •1 • 1 1 1 j ] I M " 1 1 1 1 ! ! i \ ! i 1 1 i 1 : 1 ; 1 1 1 1 i I I 11 M i 1 ! 1 - & i -j .... ; ' ! ' M M 1 1 i 1 1 1 • 1 1 I I I ! 4 4 - 4 4 i 1 1 1 1 w i 1 i 11 i 1 I 1 1 1 -7- 1 ! ! I 1 1 T + 1 I 1 1 1 i 1 1 l 1 j ! ! 1 11 i 1 ! 1 ; I j 11 1 1 | 1 I I 1 T I 1 ' i ! 1 lii i ' i 1 i 1 ! 1 "1 1 1 I T i I 1 1 ; 1 i 1 I i I -| i 1 1 I 1 1 I I ! i 1 1 1 ; i : 1 ! 1 i 1 1 [_ 1 I 1 I 1 1 i J_l 1 : 1 1 'i I i i f i , i ! i 1 1 1 1 1 \ ! i 1 1 i j ! 1 1 1 I 1 1 I 1 1 1 -J—J— 4 1 ! 4 f i i i T J i J +H- 4- 1 1 1 1 1 1 1 i 1 1 i 1 1 1 I ! i 1 1 1 1 4 1 1 — i — 1 1 • T~| 1 -. L . i j !.. i l l .1. i_ 1 F i g u r e 8.1 E f f e c t o f r e d u c e d c i r c u l a t i o n on a i r f o i l p r e s s u r e c o e f f i c i e n t : T h e o r y ( A p p e n d i x 8) F i g u r e 8.2 M o d i f i c a t i o n of a i r f o i l p r o f i l e to reduce t h e o r e t i c a l c i r c u l a t i o n to measured v a l u e : Theory (Appendix 9) 03 O 181 (a) Theory Figure 8.4 F i g u r e 8.5 The shear layer, i n the. plenum chamber surrounding the s l o t t e d w a l l CO 184 F i g u r e 8.6 E f f e c t o f d i f f e r e n t t y p e s o f w a l l b o u n d a r i e s o n r a t i o o f l i f t c o e f f i c i e n t s : T h e o r y 00 VJ1 186 4 1 T ~ T " - ! : : I I I ! M 1 i TTTT"' rr i r -> M i L ;~T -- ...... I ' M :4J ! 1 . j r-i 11 !' I ! 1 I I 1 1 1 1 I_I. ' 1 • 'i M M 4 , r ! 1 i i i i l l ! 1 M 1 r : T L K ! I i 1 1 1 1 1 11 1 1 i i -fl ! •• i ; _ ! M i l 'Ml 1 1 i i 1 1 TT i i i r i i T T 4 ! 1 1 ! i : i i I I 1 ! 1 i i ! ; 1 I I I ! M M , M i l . M M +t-h-i i i 1 I 1 1 1 1 ' 1 I I i 1 f t -i i i ! 1 i 1 i i i ! 1 i I 1 1 i I 1 i ! j 1 1 r 4 l 1 1 1 1 1 1 I i -TTT 1 !'" i / i f-j—1 1 i i i 1 ! -H ! 1 1 I i 1 4 i i ! 1 < 1 1 1 ! 1 1 1 1 -r-1 1 1 ! ! te Ml r r 1 1 1 ! 1 ! ! : i ! 44 1 1 ! 1 1 1 1 1 i i ! i ; 1 : i 1 1 ' 1 1 1 J-4 1 \ 1 1 1 1 ! 4 M ! I 1 i i i i i i ' i i i i i i -rC ' 1 I i 1 ! i I Jk 1 1 WT i i t 1 1 1 | 1 ! 1 1 i I 1 +41 i i 1 1 1 M l ! 1 I 1 ! 1 44 L.....1 i i A i i i i i : I i I i i i < tit i i i i i i i I 1 i 1 ! 1 1 1 j 1 I 1 ^ i L L i I i 4 r , 1 ! 1 1 1 1 1 1 r4 1 1 1 1 i i ! 1J i S( 1 1 )°/ 1 i i i i i i i TA i R i i i i i i 44 i i i t X _ 1 ' 1 1 1 1 -4 i i 1 i i i i ' i M 1 1 i i i i _r i i i 4 1 r i i 4-i r fXf -hi k 11 i 1 1 i 1 t ; ' i i 1 1 1 1 1 t f 1 1 1 r f 1 - j— J f 1 i -4 i i I i 1 'I i • i • i-i i •• .... 4 i ! . -i i 1 1 i i 4 4-l ! I i 1 1 1 1 1 i j 44 } I ~r i 1 i I 1 ...!_ I 1 1 1 i —r 1 1 1 4 i • i i 1 Xt € T i . i i i 1 4 -i ! 1 1 f [4f n i . i i T - --+ i i i i i i i i i i i i i 1 1 1 - 4 -i i 1 I i i i ! 1 1 i l -4-1-4 T i i i i ! ! 1 -444 1 i i i ! 1 1 1 1 I 1 1 j ir i i i — "A // 1 1 1 1 1 1 1 1 1 — L 1 1 ' f i 1 1 r - 1 i v 4+ 1 A // i i 4-r^ E > ^ i i --a V- 1 ftp a m 4^ 1 -I I 1 i 1 1 1 1 I i 1 m i I 1 1 4S —I—j Js« m _—_ I 1 I I I 1 44- 1 1 i i i i I 1 =u ::| 1 i i I i — . — L . ( 4— i— -, | | I 1 1 i i ti- i t 1 [— i — i ! i i 1 — | n Q-8€ )-* f f -i , . i 1 [ i i 1 i fr --)-1 I 1 1 i 1 1 i t • i r/—-f r r \ -4 t l "f l i . . j . . . ! 1 I I i i 1 1 i j — i i f L 4 —r — 1 — i i i 1 1 i i i — 1 \ 1 ! | i I 1 | i f ! | I | i i • ! 1 i i i I 11 _ | — i i i i 1 1 ! T 1 1 I 1 i 4 -i i I I i I ! I 1 T44- 1 1 i i X . 1. I 1 1 1 T T T - -4- i i *w i i i • i M l ' i i : T" —lT\ _ X J i ._ i i u _ 1 1 i i i 1 I i i 1111 i ! 1 1 | i H T - 1 - 1 I i 1 ! M i I i . J ! : i ! 1 1 i I r - JU 1 i \f\ I l l " 1 1 i TTTT- M l ! f\ | 1 - M M i i i • -r\ t 5 4 r - T 1 1 jr\ rrr. r 4rh r r r- - r "1 T T T i 1 1 10 1 I 1 I i 1 M i l W T - I 1 1 1 i y i . 1 1 1 1 1 ! i 1 m ; ' 1 4~ I - • i i I i ! 1 1 i —!—1—1 1 ! 1 1 I 1 M M M M 1 I ! !'•• ' i l l 1 1 1 t 1 i : 1 I i i t i l l !—j i — t - 1 1 i i 1 i i i 1 1 1 — ! i I M ' I • i 1 1 1 1 1 1 1 1 ' i 1 . M l M M M M i l l ! M M 1 i i 1 1 i J i i 1 -— ! 1 ! ) 1 1 : i ' i l l I ' M I M ! 1 ' —pr 1 I i i i i i 1 i i i ! 1 i i i 1 i L.| 1 1 1 1 M M M M M 1 | ' M l i F i g u r e 8.8 E f f e c t on a i r f o i l l i f t c o e f f i c i e n t s o f assumed p r e s s u r e c o e f f i c i e n t s on a s t r e a m l i n e r e p r e s e n t i n g the plenum shear l a y e r : Theory F i g u r e A l . l Geometry f o r i n t e g r a t i o n of a p o i n t source 188 Pfr.O.z) Axi-symmetric (b) *~ z Figure A5.1 The two-dimensional nozzle i n s e r t E-2 t h + S Constant-pressure boundary H il I 1 1 ) 1 1 I I I Figure A6.1 A l i f t i n g vortex between a s o l i d , a slotted, and a constant pressure boundary: Theory u> OJ Q Q + + ro cr cr I a~ ro cr I Q Q - a - - o - C T * -II Q ro cr ( D I OJ o + cr OJ Q + cr W 1 <±) a + cr Q + cr Fiaure A6.2 The image system for a l i f t i n g vortex between a s o l i d and a constant pressure boundary: Theory NSLAT * NSPS NSOLI NU2 NUI U NTEL ^ NWLI NLI JH f i < r i i i > i ' i ' f » > > 11 1 r NWL2-NL2 NL3 NL4 i i i i r'lMiVi * ' '*' > i > > • i i i ) i r } i i Ji / i i it f > i' / i / t / i i i / >Hi Figure A10.1 Notation for the computer program of Appendix 10 192 Plate l b . The octagonal testsection i n the windtunnel 193 P l a t e 3. The w a l l s l a t s i n the s i d e w a l l frame 195 P l a t e 6. The 616mm NACA-0015 a i r f o i l i n the t e s t s e c t i o n . 196 T a b l e 1. A i r f o i l p r o f i l e c o o r d i n a t e s . 14% C l a r k - Y NACA-0015 J o u k o w s k y 1 1 % X Y U Y L . X + Y X : y U X Y L 0. 00 4. 19 4. 19 0. 00 0. 00 0. 00 3. 92 0. 05 3. 53 0. 32 5. 15 3. 15 0. 40 1. 37 0. 02 4. 16 0. 40 2. 90 0. 96 6. 15 2. 49 1. 00 2. 13 0. 35 4. 89 1. 09 2. 31 1. 92 7. 24 1. 98 1. 90 2. 88 0. 97 5. 41 2. 11 1. 77 . 3. 20 8. 35 1. 54 3. 20 3. 65 1. 91 6. 28 3. 45 1. 29 4. 80 9. 35 1. 15 4. 80 4. 37 3. 15 6. 96 5. 14 0. 88 6. 72 10. 26 0. 84 6. 70 5. 02 4. 74 7. 62 7. 10 0. 55 8. 96 1 1 . 14 0. 60 9. 00 5. 63 6. 63 8. 26 9. 41 0. 29 1 1 . 52 1 1 . 94 0. 38 1 1 . 50 6. 15 8. 77 8. 85 1 1 . 99 0. 12 14. 40 12. 65 0. 21 14. 40 6. 60 1 1 . 17 9. 38 14. 87 0. 02 17. 60 13. 25 0. 09 17. 60 6. 97 13. 86 9. 85 18. 05 0. 00 2 1 . 12 1 3 . 70 0. 02 2 1 . 10 7. 25 16. 76 10. 25 2 1 . 45 0. 07 24. 96 1 3 . 94 0. 00 25. 00 7. 43 19. 89 10. 58 2 5 . 10 0. 20 29. 12 14. 00 0. 00 29. 10 7. 50 23. 24 10. 83 2 8 . 95 0. 40 33. 60 1 3 . 95 0. 00 33. 60 7. 47 26. 74 10. 99 33. 02 0. 65 38. 40 1 3 . 74 0. 00 38. 40 7. 32 30. 44 1 1 . 07 37. 25 0. 96 43. 52 1 3 . 34 0. 00 43. 50 7. 07 34. 27 1 1 . 06 4 1 . 59 1. 29 48. 96 12. 73 0. 00 49. 00 6. 69 38. 22 10. 98 46. 06 1. 66 54. 72 1 1 . 85 0. 00 54. 70 6. 22 4 2 . 26 10. 80 5 0 . 58 2. 04 60. 80 10. 80 0. 00 60. 80 5. 62 46. 39 10. 55 5 5 . 12 2. 41 67. 20 9. 44 0. 00 67. 20 4. 91 5 1 . 15 10. 19 59. 69 2. 77 73. 92 7. 83 0. 00 73. 90 4. 09 54. 75 9. 86 64. 19 3. 10 80. 96 5. 92 0. 00 8 1 . 00 3. 14 58. 93 9. 43 68. 59 3. 40 88. 32 3. 86 0. 00 88. 30 2. 07 63. 05 8. 95 72. 86 3. 66 96. 00 1. 45 0. 00 96. 00 0. 84 67. 12 8. 44 76. 96 3. 86 100. 44 0. 00 0; 00 100. 59 0. 00 7 1 . 09 7. 92 80. 83 4. 01 74. 94 7. 38 84. 43 4. 11 78. 62 6. 85 87. 73 4. 16 82. 12 6. 34 90. 71 4. 17 85. 37 5. 85 93. 29 4. 14 88. 40 5. 40 9 5 . 50 4. 08 90. 71 5. 07 97. 27 4. 01 93. 29 4. 70 98. 61 3. 94 95. 50 4. 39 99. 50 3. 88 97. 27 4. 16 100. 0 3. 84 98. 61 4. 00 99. 50 3. 90 100. 0 3. 84 Table 1 c o n t 1 d . Main A i r f o i l 0.00 1.00 " 0.00 1.00 2.40 -1.10 2.50 3.61 -1.71 4.00 4.45 -2.10 7.00 5.65 -2.55 10.00 6.43 -2.92 15.00 7.19 -3.50 20.00 7.50 -3.97 25.00 7.60 -4.28 30.00 7.55 -4.46 35.00 7.43 -4.53 40.00 7.14 -4.43 45.00 6.80 -4.35 50.00 6.41 -4.17 55.00 6.00 -3.92 60.00 5.47 -3.65 65.00 4.95 -3.35 67.00 - -3.18 69.00 - -2.83 70.00 4.36 -2.51 71.00 - -1.98 72.32 - -1.02 74.57 - +0.67 75.00 3.78 77.82 - 2.30 80.00 3.08 2.67 82.70 2.64 2.64 196A NACA-23012 F l a p X y u X Y L 0.00 0.04 0.00 0.04 0.45 0.99 0.36 -0. 72 1.08 1.59 0.95 -1.00 2.11 2.27 1.74 -1.15 3.65 2.93 2.44 -1.21 5.17 3.33 3.44 -1.21 6.68 3.55 4.95 -1.15 7.69 3.57 6.45 -1.07 8.69 3.52 7.45 -1, 03 10.18 3. 32 8. 46 -0.99 12.66 2. 86 9.96 -0. 94 15.13 2.36 12.47 -0. 82 17.61 1. 85 14.98 -0.71 20.09 1. 35 17.49 -0.61 22.07 0.93 20.00 -0.46 24. 05 0.52 22.01 -0.33 25.54 0.21 24.02 -0.19 26.53 0.00 25.52 -0.08 26.53 0.00 O r i g i n o f f l a p c o o r d i n a t e s i s (78.87,-0.81) f o r 6=20°. T a b l e 2. F r e e a i r a i r f o i l c o e f f i c i e n t s : T h e o r y . NACA-0015 a 0 C L C M 0 / . d a 0 0.000 0.000 0.0000 0.1193 3 .365 .086 - .0050 .1229 5 .607 .143 - .0086 .1300 10 1.210 .282 - .0204 • 14% C l a r k - Y a 0 C L C M 0 C M c d C L d a - 6 . 3 0.000 -0.087 •4 -0.087 0.1206 -3 .401 .012 - .0883 .1208 0 .763 .101 - .0901 .1203 5 1.362 .244 - .0965 198 Ta b l e 3. A i r f o i l and w a l l c o n f i g u r a t i o n s examined t h e o r e t i c a l l y . A l l s o l i d w a l l s are 4.88m lo n g , w i t h MWUl = MWU2 = 20, and NWL1 = NWL2 = 4 0 . The s l o t t e d w a l l i s 2.44m l o n g , composed o f l a r g e (92mm) NACA-0015 s l a t s w i t h NSPS = 9. A i r f o i l i s i n the c e n t e r of the t e s t s e c t i o n ; NA = 50 f o r C l a r k - Y and NACA-0015; NA = 81 (46 main and 35 f l a p ) f o r NACA-23012. F u r t h e r notes are found a t the end o f t h i s t a b l e . a CM 0 CMc 4 1. C l a r k - Y a i r f o i l a) Fre e a i r -8 -0.203 -0.137 -0.086 2 1.003 + .159 - .092 20 3.088 .603 - .169 b ) S o l i d w a l l s -8 -0.250 -0.150 -0.087 c/H = 0.53 -3 .444 + .014 - .097 2 1.140 .178 - .108 20 3.632 .711 - .197 c) 40% TSUSL -8 -0.270 -0.153 -0.086 NSLAT = 16 -3 + .376 -000 - .094 c/H = 0.53 + 2 1.012 .149 - .104 20 3.179 .610 -. .185 d) 60% TSUSL -8 -0.260 -0.151 -0.086 NSLAT = 1 0 -3 + .377 + .003 - .092 c/H =0.53 + 2 .992 .148 - .100 20 2.986 .572 - .175 199 T a b l e 3 ( c o n t ' d ) . a C M 0 C M c 4 c/H C l a r k - Y ( c o n t ' d ) ( 6 0 % ) 20 3.061 .579 - .186 0.66 70% TSUSL 20 2.929 0.570 -0 .162 0.25 NSLAT = 8 20 2.907 . 562 - .164 .39 20 2.923 .560 - .170 .53 20 2.970 .563 - .180 .66 20 3.084 .573 - .198 .86 20 3.200 .587 - .213 1.0 -8 - .256 - .149 - .085 .53 -3 + .381 + .005 - .091 .53 + 2 .989 .149 - .098 .53 80% TSUSL -8 -0.250 -0.14.8 -0 .086 0.53 NSLAT = 5 -3 + .388 + .007 - .090 .53 + 2 .994 .152 - .097 .53 20 2.888 .554 - .168 .53 NACA-0015 a i r f o i l F r e e a i r -2 -0.243 -0.058 + 0 .003 + 8 + .970 + .227 - .015 15 1.803 .412 - .038 20 2.382 .530 - .065 S o l i d w a l l s -2 -0.305 -0.068 + 0 .008 0.67 + 8 +1.223 + .272 - .034 .67 10 1.510 .333 - .045 .67 20 3.074 .675 .093 .67 + 3 .371 .087 - .006 .17 3 .388 .090 _ . 007 . 34 200 Tabl e 3 ( c o n t ' d ) - — a CM 0 4 c/H 2. NACA-0015 (cont'd) b) S o l i d w a l l s (cont'd) 3 .416 .094 - .010 .51 3 .453 .100 - .013 .67 3 . 546 .116 - .021 1.0 c) 40% TSUSL -2 -0.327 -0.072 +0.010 0. 67 NSLAT = 1 6 + 3 + .364 + .081 - .010 . 67 8 1.039 . 227 - .033 .67 20 2.592 . 550 - .098 .67 d) 60% TSUSL- -2 -0.320 -0.070 +0.010 0. 67 NSLAT = 10 + 3 + .359 + .081 - .009 .67 8 1.006 .222 - .230 .67 20 2. 421 .514 - .092 .67 e) 70% TSUSL +3 0. 355 0. 084 -0.005 0.17 NSLAT = 8 3 . 356 .083 - .006 .34 3 .358 .083 - .007 .51 3 . 361 .082 - .008 .67 3 .365 .082 - .009 1.0 f) 80% TSUSL -2 -0.311 -0.068 +0.010 0.67 NSLAT = 5 + 3 + .367 + .084 - .007 .67 8 1.000 .224 - .026: .67 20 2.335 . 500 - .086 .67 3. NACA-23012 a i r f o i l a) F r e e a i r + 8 2.442 0. 320 -0.291 201 Table 3 (cont'd) a V CMc 4 c/H NACA-23012 (cont'd) 70% TSUSL +8 2.415 0. 308 -0.295 0.2 NSLAT = 8 8 2. 305 .290 - .286 ' .4. . . . . . . 8 2.318 .283 - .296 .6 8 2.296 . 280 - . 312 -8 8 2.442 .280 - .331 1.0 C l a r k - Y a i r f o i l Compare C (C ) w i t h C T ( T ) , J-i p Li w i t h NA = 110 • and a = 20 o L p CM 0 4 c L ( D i ) F r e e a i r 3.117 0.548 -0.231 3.114 i i ) S o l i d w a l l s , c/H=.66 4.165 .744 - .298 3.742 C i r c u l a t i o n on w a l l s l a t s reduced by m o d i f y i n g s l a t p r o f i l e s , NSPS = 1 5 , a = 20°, c/H = 0.66. k C L CMc 4 70% TSUSL 1.0 3.010 0.569 -0.184 NSLAT = 8 .8 2.935 .556 - .178 • 7 2.610 .502 - .150 Shear l a y e r r e p r e s e n t a t i o n . MSV = 2 0, a = 20°, c/H = 0.66, V. = / ( l - C ). t p ' C P C L CM 0 CMc 4 i ) 60% TSUSL 0.0 2.420 0. 451 -0.155 NSLAT = 1 0 -.12 2.686 .502 - .170 T.28 3. 305 . 572 - .187 202 Tabl e 3 (cont'd) 4c) C l a r k - Y - Shear l a y e r r e p r e s e n t a t i o n ( c o n t ' d ) . C P CMc 4 i ) 60% TSUSL ( c o n f d)-.35 3.188 .600 - .197 NSLAT = 10 -.44 3.390 .640 - .207 i i ) 7 0 % TSUSL 0. 2. 321 .433 - .147 NSLAT = 8 -.12 2.591 .486 - .162 -.28 2.951 .558 - .180 -.35 3.101 .586 - .190 -.44 3. 308 .626 - .200 5. NACA-0015 a i r f o i l w i t h reduced c i r c u l a t i o n , a = 10°, s o l i d w a l l s ; a reduced a i r f o i l c i r c u l a t i o n determined. C T C M C M L Mo Mc _4 i ) from measured l i f t (k = 0.741) 1.120 .335 +0.0549 i i ) by m o d i f y i n g the p r o f i l e (k=0.724) 1.120 .280 - .0003 Notes: The p o s i t i o n s o f the w a l l s l a t s c o r r e s p o n d e x a c t l y t o those i n the e x p e r i m e n t a l setup. The s l a t s are spaced u n i f o r m l y , b e g i n n i n g w i t h a s l o t opening a t the upstream end on the s i d e w a l l . The number of l a r g e s l a t s r e q u i r e d f o r 40, 50, 60, 70 and 80% OAR i s 16, 13, 10, 8, and 5 r e s p e c t i v e l y . The e f f e c t o f i n c r e a s i n g the number of c o n t r o l p o i n t s on the t e s t a i r f o i l i s seen i n 1(a) and 4 ( a ) ( i ) ; o f i n c r e a s i n g the number of c o n t r o l p o i n t s on the w a l l s l a t s i n 1(e) and 4(b) (k=l). 203 T a b l e 4. A i r f o i l a n d e n d p l a t e l o a d i n g s . J o u k o w s k y R e = . 5 ( 1 0 ) 6 S o l i d W a l l s Ct C L C* Mc 4 Mc 4 c* C D -7 -.350 -.345 -.0719 - . 0 7 2 3 .0330 . 0194 -6 -.245 - . 2 4 1 -.0727 -.0728 .0317 . 0180 -5 -.137 -.134 -.0728 -.0727 .0309 .0171 -4 -.025 -.024 -.0727 -.0723 .0308 . 0168 -3 .086 .086 -.0724 -.0717 .0314 .0172 -2 . 194 .192 -.0716 -.0706 .0323 ' .0179 -1 .299 .296 -.0712 -.0699 .0340 .0193 0 .408 .403 -.0705 -.0689 .0361 .0212 1 .512 .506 -.0693 - . 0 6 7 3 .0384 . 0233 2 .617 .610 -.0669 - . 0 6 4 5 .0410 . 0259 3 . .721 .713 -.0652 - . 0 6 2 5 .0441 . 0289 4 . 820 .811 -.0639 -.0607 .0482 . 0326 5 .917 .907 -.0628 - . 0 5 9 1 .0530 .0370 6 1. 009 .998 -.0617 -.0574 .0592 .0425 7 1.103 1. 091 -.0600 - . 0 5 5 1 . 0652 .0478 8 1.192 1.179 - . 0 5 8 1 -.0524 .0719 .0534 9 1.277 1.265 -.0557 - . 0 4 9 1 .0790 .0594 10 1. 340 1. 326 -.0536 -.0466 .0869 . 0672 11 1.382 1.368 -.0540 - . 0 4 6 5 .0972 .0773 12 1.408 1. 394 -.0620 -.0546 .1161 .0959 13 1.199 1.186 - . 1 6 1 1 -.1538 .2551 .2345 C L ' C 5 c ' C D l o a d i n g o n a i r f o i l p l u s two e n d p l a t e s C M c ' C D l o a d i n g o n a i r f o i l o n l y 4 Table 5. Windtunnel balance r e s u l t s -0.25-Clark-Y Pt = ' . «5(lO )6 SOLID WALLS ALF CL CD CM0 CMC/'I -10 ' . -0'.3'l5 0'.0260 -0.0916 -.«»'. -0 .251 0'.0?35 -o'. w.o -0 .0907 -o'. 151 0'.0221 -0.133 r-0 . 0906 -T. -0 ' . 057 0'.0215 -0.107 -0.0910 -6 ' . O'.O'II 0'. 0 2 0 1 —0.080 -0.0908 -5". 0'. I l l C '. 0 2 0 7 -0'.053 -0 .0911 - 1 ' . o'.2'U 0'. 0205 -0 .026 -0 .0908 0'.313 0'.02() '1 0-002 -0 .0908 " 2 r (>'.13S 0'.02?1 o'.032 -0.0871 o'.553 0'.0237 0.060 -0.0905 0'. (i'.665 0 -.0256 0'.037 -0.0942 i ' . 0 .753 o'.0278 0'. 1 11 -0.0920 2'. 0-815 0'.0302 0. 110 -0.0905 i'. 0'.938 0'.0330 0'. 168 -0 .0889 l ' . T.030 0'. 0373 0.193 -0.0880 5'. '1'. 1 oa O'.03(i7 0'.2 18 - 0 . o i a s 6'. l ' . 185 0'.0133 0.211 -0 .0820 l'.256 o'.oi87 0.260 -0,0782 B'. l'.321 0'.0532 0 -,286 -0.0736 r .3^6 0'.05R8 0.305 - 0 . 0 7 U 16'. r . ' i27 0-0650 0.321 -0,0655 i r . r . ' i35 0'.0716 0'.331 -0.0572 12'. 0'. 0788 0.333 -0.0513 13'. r . ' i26 0'. 1 03'l 0.322 -0.0638 11'. f. 388 0 -. 1218 0'.308 -0 .0682 -Y a i r f o i l s CL ARKnY Rti = *.'15(10)6. 'I0ZSS+P TSU AI.F CL CO CMO CMC/1 10'. -o',330 0'. 0237 -0 ' . 187 ^•0.0963 -9' -0,237 0'. 0218 -0 .160 -0'. 0916 -0 ' . I'll 0'.0195 -0-131 -0 .0915 -7' -o'. 016 0 ' . 0 1 « 9 -0'.107 -0 .0938 -6' 0'. 0 •'! 8 0'.0177 -0 .0 82 -0 .0912 •*5' 0. I ' l l 0'. 0 17 6 -0-055 -0,0911 0'.2'I0 0 0 1 7 '1 -0 .027 -0 .0921 — > 0'. 5'40 0'.0176 0.000 -0.0933 - 2 ' ()'.'I3 0 O". 01R5 0'.0 29 -0 ,0896 - i ' 0 .533 0'. 020 1 0'.055 -0 ,09 16 o' 0'.6'I3 0'.0231 0,081 -0 .0968 r . ()'.729 o'.0262 0.105 -0 .0958 z'r 0^8 15 0'. 0 285 0.130 -0 .0915 0',90l" o'.0315 0.155 -0 ,0933 0'.986 0-0316 0*. 181 -0.0911 5 » f.062 0'.0389 0.200 -0 .0885 6 1.133 0'. 0'I26 0 .227 -0 ,0852 7 1.201 0'.0'I62 0.2'19 -0 ,0826 8. l'.?68 0'. 0119 0-269 -0 ,0795 ?'. l'.323 0'.0550 0.288 -0,0761 10 * l ' . 359 0', 0 6 0 6 0.30a - 0 . 06.85 11. l'.377 O'. 0675 0.316 -0 .0609 12 m r .562 0'. 0765 0.319 ^0,0589 13 • l ' . 366 0'.09;i 3 0.309 -0 . 0636 11 • 1-333 0'. 1 162 0 ' . 2 9 « -0 ,0701 15. f .293 0'.1378 0'.280 -0 ,0718 CLARK-Y RC=.15(l"0)6 10%L5+P TSUSL ALK -10'. -< -8'. -7'. - 6 ; -5'. -1*. -z: -?-'. - 1 . 0". 1'. 2\ 3 1 5 6 7 e 9 10 *h 12. 13'. 15. Cl, -(>'. 310 • 0'. 2 'i 5 •O'. 117 -()'. 052 O', 012 O'. 133 0'.237 0'.335 O-. 126 0*.52H o'.6'll 0'.725 0'.812 0'.89 7 0'. 9 31 l ' . 053 132 ,203 ,267 .361 I'. 377 1-379 l'.365 1/.329 I'.293 cn 0 0 219 O', 0222 0'.02()0 O'. 0 196 0'.0181 0'.0182 0'.0185 0'.0192 0'.0196 ,0213 ,0212 ,0265 ,0201 0'.0319 0'.0319 03^5 0128 . 016 6 ,0502 ,0550 ,06o'l ,0666 ,0761 ,09i|8 .1165 0.1379 CHO -0 ' . 185 - 0 . 159 -0.132 -0.107 -0.081 -0.055 -0.028 -0.000 0'.023 0.051 O',073 0.103 0'. 128 0. 151 O'. 178 0'.201 0.221 0'.216 0.266 0.23 6 0'.302 0.312 0'.315 0'.307 0.290 0'.277 CMC/4 -0,0928 r-0.0921 -0.0917 -0.0921 -0,0921 -0.0919 -0.0923 ~0 . 0909 -0,0875 -0,0391 -0.0951 -0.0937 ^0.0927. -0 , 0899 -0.0888 -0.0353 -0.0827 -0.0796 .-0,0758 *0 ,0715 0^ ,0618 -0.0586 -0.0551 rO .0591 -0.0676 -0,0715 205 Table 5 - 0.25-Clark-Y Ri: = '.45Cf0)6 50XL.S + P TSUSL CLARK-Y Rl! = '. '15 (10) 6 70ZL3+P TSUSL ALF CL CO CMO CMC/4 ALF CL CD CMO CMC/4 10'. -o'.333 0'.0239 -O'. 181 -0.0929 -IO'. -0'.324 0'.0273 -0'.133 -0.0925 -9'. -0.24U 0'.0210 -.0.158 -0.0915 -9'. -0'.228 0'.023'l - 0 ' . 157 -0,0929 -8. -0.113 O'.02o5 -o'.131 -0,0916 -8'. -O'. 132 0'.0222 -0.130 -0.0924 -7'. -0'. 019 O'. 0131 -.0.106 -0.0915 -7'. -O'. 038 0'.0212 -0 .103 -0.0922 -6'. O'. 015 0'. 0185 -0.080 -0.0915 0'.057 O'. 0 196 -0'.077 -0.0920 -5'. 0'. 110 0'.'173 -0.051 -0.09)6 ~sf. 0.153 0-.0191 -0.051 -0.0926 "If 0'.236 0'.0175 -0'.027 -0,0910 -4'. o'.246 O'.O 199 -0.021 -0,0919 *" • 0'.335 0'. 0 1 3 I 0.001 -0.0906 -3". 0'.34 2 0'.0198 o'.ooi -0,0914 0'.'I22 o'.oiaa 0'.029 -0.0870 0'.4 27 0'.0202 0'.032 -0,0372 0'.525 O'.02o7 • o'.osi -0.0898 o'.533 0'.0219 0'.058 -0,0910 0'. o'.63'l 0'.0230 0.080 -0.0912 0'.639 0'.0 239 0.083 -0.0952 t. 0'.720 0'.0251 0'. 105 -0.0932 f'. 0.722 0'.0263 0.108 -0,0939 2'. 0'.801 0'.0277 0.129 -0.0917 2'. 0'.807 0'.0284 0'.133 -0.0926 3'. 0'.S91 0'. 0 295 0.155 -0.0903 3'. 0'.892 0'.0293 0.158 -0,0913 4'. 0'.978 0'.0320 O-. 180 -0.0386 '4'. ()'.974 0'.0320 0.132 -0.0895 5'. T.051 0'.0373 0'.203 -0.0861 5'. V.05 0 0'.0354 o'.205 -0,0877 6'. .1.127 0'.0102 0.226 -0.0835 6'. 1'. 1 17 0-.0379 0.226 -0.0349 7'. l' . 195 0'.0137 0.217 -0,0301 7'. l' . 185 0'.0117 0'.24 7 -0.0326 8'. T.257 0'.0474 0'.268 -0.0762 8'. l'.243 0'.0462 0'.268 -0.0778 l ' . 1'. 311 0'.0521 0.236 -0,0724 1. i'.297 0'. 0 5 1 0 0'.236 -0,0741 10'. 1.35 0 0'.0577 0'.301 -0,0671 IO'. T.330 0'.0563 0.300 -0.0637 11'. f.372 0'.0613 0.311 -0.0623 .11. 1.339 0'.0628 0'.309 -0.0613 12'. T.370 0'. 0739 0.315 -0.0575 12'. l'.34 0 0'.0732 0.310 -0,0603 13'. l'.354 0'.09;>5 0.301 -0,0639 13'. T.323 0'.0928 0'.293 -0,0679 11'. 1'. 311 0'. 1156 0.286 -0,0718 14'. T.285 O'. 1 150 0'.233 -0.0734 15'. 1.282 0'. 1352 0.275 -0,0749 15'. i',246 0'.1337 0.268 -0,0773 CLARK-Y RE = '.'I5(T0}6 60%L3+P TSUSL . C\ ARKrY Rlt = *. 45 C {0) 6 80XL3+P TSUSL ALF CL CD CMO CMC/4 ALF -10'. CL CD CMO CMC/4 -10'. -0'.328 0'.0236 -0 .183 -0.0931 -0',313 0'.0258 -O'.l 74 -0.0881 -9'. -o'.23'l O'. 0210 -0 .158 -0.0933 -9 . -0.214 0'.023'l -0.118 -0 ,0886 O * -0.137 0'.0191 -0 .131 -0.0929 -8'. -0 ' . 123 o'.02?6 -0.122 -0,0874 -7 ' . -0'.013 O'.O 175 -0 .105 -0.0930 - 7 . -0.030 O'.02l0 -0'.095 -0.0863 -6'. 0'.051 0'.0161 -0 .079 -0,0921 -6'. 0'.063 O'.O 19 1 -0.073 -0.0900 -5'. 0'. 146 O'.O 151 -0 .053 -0.0925 -5'. O'. 155 O'.O 191 -0,048 -0,0396 -4'^ 0'.2'll O'.O 158 -0 .0 26 -0.0915 - l ' . 0.251 O'.O 138 -0'.021 -0.0893 -3:. 0'.336 0'.0161 0 .001 -0.091 1 - 3 ' . 0'.343 O'.O 191 0.006 -0,0880 -2'. 0'.425 o'.0166 0 .029 -0.0878 -?-'. 0'.131 o'.oiao 0 .034 -0.0843 - i ' . 0'.530 o'.oiao 0 '.055 -0,0907 "1". 0'.53S 0'.0202 0'.060 -0,0080 o:. 0.637 0'.02()7 0 .080 -0.0955 O'. o'.oio 0'.0219 0.035 -0,0910 1'. 0'.722 0'.0229 0 .a 0 4 -0.0946 i'. 0'.725 0'.0234 o'.l 10 -0.0898 2' 0'.307 0'.0254 0 .130 -0,0927 2: 0',806 0'.0215 0.135 -0,0873 z'. 0'.893 0'.0277 0 .155 -0.0909 3'. ()'.890 0'.0270 0.160 -0,0850 1'. 0'.978 0'.0302 0 .180 -0,0895 4'. 0'.967 0'.0296 O'. 135 -0.0313 5'. 1.055 0'.0352 0 .203 -0.0873 5'. l'.042 0'.0336 0.206 -0,0300 6. 1.127 0'.0381 0 .226 -0,0810 6'. r.107 0'.0366 0-,228 -0,0761 7'. I'. 193 0'.0116 0 .247 -0.0807 7'. l' . 167 0'.0H3 o'.218 -0.0716 8'. l'.258 0'.0461 0 .267 -0.0780 8. l'.230 O'.O'ISI 0.268 -0,0692 9'. 1.310 O'. 0509 0 .286 -0,0727 •— i C o o o o o o o c o o * ' ' 'ft -'ft -ft " ' • - • • • 'ft. -ft ' •ft. ' ' • 'ft 'ft • • ' * • '» " •« • • - n I ru ru L-l l - i 14 14 r ru -o ^i + - J J l cr- -4 —1 CC CO CO Co •CO -c Co CD CO CO o CP 2z -0 w 43 ru J l ca X i o 0> CO ft— I i O Co ft— ru CO J l o -a o •o CO o o o - j 1/1 ru X i c- -u. ro •c U J CO .0 03 CO X i ro ft— c o w LTI o C3 ro —i CO c »-» t— l-» I I 1 1 1 i I 1 1 V— > Ul i i L-l ru o •o CO - j J i t i L-l ru i—- o * - * ru L-I X i J l 0- - 4 CO O •r- O • " ' • ' • ' • • • • ' • ' '• -» -ft ' • ' ' • ' • - T ! r~ 1 1 1 1 33 1— 1— •*-• ir-* i-* • o • o c o O o o o O O o O 3^ • ' ' • ' ' • ' •» -' » » - • -' • • • -•» -• * - • ' « ™* - * * ' * ' 'ft • >• -' • ' • * « -'ft -ft •ft - ft -'ft " I ru ro ro L-l L-l L-l ro r j *- o -0 >C- CD c- 'Jl X i L-l L-l r j o r j L-J r-. - C ru L I i-* o e'- o L-J 0- ro Ci —J -0 -S -0 r— ro L-J i i X? _ i L-l r j >—-• o ro C Co Ul er- -o -o w J l — Co ~ j •Jl J l ru L-J ru L-I - J *~ • J l J l o c o o o o o o o o c c o o O o c o o O O © n • • - B * « - » * « • • • - « -• • - » * '1 » " » - ft - ft ' • - » -ft •-ft • ft - ft ' ft - £ -n II o o o o o o o o o o o o o o o o o o c o o o o o o • * ru *-* o - o c> U l J l J l X i X i L-' L< r j ru ru ru ru ro ru ru ro ru ru ro ro X i o L-l X i CO i i J l ru O L-J >— CD c - X i ru o r- • o c :"U ru X i - i LTi ru J l — O c- a- - 4 Co L-J a- c- I-* ~J - 4 3~ L-l CD ~4 o J l CO ru — IV L-l v . I I 1 I I I i i O c o c o o o o o o o o o C O o O O o o o o o c o o w « • • • » • t • « - » • • - • - • * • -'t • 't ' i ' • v - t ' ft ' ft - ft - ft ' ft ' • - » - t - ft " 3-ro ro ro ro ro ro ro r j ro ro ** *-» r— o o o o o o o o i— »—• t—- ^-* C3 CO -C -o •CO a i u i » — c- X i ru - c - J . X i ru o r-o J l -4 o ru J l CO ° * -0 o CD J3 L-J L-J ro CD L T *~ L-l •o — ru - 4 L-l CO L-l Co - o CO 1 I 1 t 1 I 1 l I i 1 I I j t t 1 I ( 1 I I I 1 I 1 O o o o o o O o O o O o C3 o o O o o o O o o O o o o C3 o o o o o o o o o o o o O o o o o o o o o o o o o o O + —4 -J J l c> Cr- - J —1 -Co CD CO CD CD CD 43 CD CD CD CD CO CD CD CD CD -0 •v T3 X i » — X i Co ru co X i -o >-* ru L-l - 4 CD -0 O t i ~4 CD 00 -0 CD CD o • t i J ) I—• •Jl t i IM J J -0 o >— U4 c - J l ~ J U4 CD X i => ~4 ro Co X i 1—' -( CO co — • - • * — >-*- T l i t t I I ul x i L-J M • — , o o Co - 4 - c - j i t i L-I ru ft-»-o ft-ru u i : J i c - - 4 C 3 0 o r _ I K * K * : - * it-* - K * | H - it— i o • IV L-J L-J L-I L-J L- l L-J r j 1— O CO CD ^4 C- J l 3- c Xi c- o- t i o J I co r j Xi - j -co c ro L-J ro ro L-I L-J i i x= X: L-; L-J ro •o c - a i r i M i * i O c s j s j ) x - o i - i ( M \ j f - i ) x - i 5 » w - j i I i I o o o o o o o o o o o o o » -• -• -* -• "• -» •• -c •j - c c i * r j L-I r O O O O O O ' o o o o o c o o o c o c o o o . -. -. •• -. -. -. -. - . -, -, - . •. •, •. •. • -. -. -. •» - n ft— .v-- o o o o o o o o o o o o o o o o o o o o o o o o o L-i *-* o -4 c - c- J l J I Xi t i L-J L-J L-J L-! ro ru ru ru ru *— v • I\J ru ru ru ru J l ~4 J I 0- C- Ci J l C C- ru -0 J l C-4 O --4 'LH L-J •-* c -0 43 O O L-J Xi 0 1 * - i : U l - 0 X i ^ l j 1 t - f c T o i \ j o w - J 3 - M C - C - 0 C M \ J W ^ J O U l I o o o o o o o o o o o o o o c c o c o o o o c. o • 2 ro r j L-I u i L-J r j ro ro ro ro ro K * i— o o o o o o o ft— i— o CD o ft— O 42 ro 'Ji ft— .ro co -o i i i i i i o o o o o o x i r u o c o u ' i r u o c D L n r u o r u J i ~ 4 o L - j ' j i c o C - LT X i L-J O L i 43 X i O J l -0 1 I O O ' I I I I I I o o o o o o 1 I o o cr ro 9> I c - i—• LT O I 1 !-t o o o 3: CO CO o o r-> + \ • — X i 0 - ru TS o o -4 -4 O O O O O O J l C- C- - 4 o o o o CO 03 CO CD CD O O O O -0 CD CC X i O ' J l - 4 r u - 4 L-l ' J l O ru X i - 0 >— L- l L-J -O C- O O O O -o -o a O fU t t -O - X i o - 0 * — 4 i J l t i f t - f t — M 03 J i C - — Co I •- ft- >- ft- ft- ft- • I « I ft I I I I » ft— > . •JI t i L-I ru — o -o co ~4 cr- J I x ; L-4 ru — o • * ru L-4 X : J ; O- --I CO •& o r~ . - . . - . - . - . - . - . - . - . - . - . - . - , - . - . - . - . - , - . . . . -p — ' « - > * ; H - i i - * I K * ,v* ^ K * o I I I i o c o o o r u r-j L-J L-I L-J L-I ro r j >- o o -o a -o c- J I t i L-J L-J r j >- o o — v L-I r— LH -3 L-J i i i i . V JO TO LH CD ft- L-J Xi -4 O CO 43 O ft- r j L-I v l L T — L-J ru ' J i r u J I x i -o ^ ru x: L-I ft- ro co u i -o L-J O L-J CO J I X= L-J C - O i i CO O C O O O O O O C O O O O O O O O O O O O O O O O O • • '• '• "• • •• •• '• '• '• "» •• •• •• •• •» •• -r> ft— ft— O O O O O O O O O O O O O O O O O O O O O O O O Q w • - co -4 o- j ! j l X i X i X i L-I L- i L-I L-I f j r u ro ro r u >— * - r u r u r u r u a o -o . o r u -4 v co t i o co t i v o -4 ' j i r u o 43 co 43 o •— :L-I L I O r u^4 - J 3 ' C o r o-4JlL4CotiO - L f t J f t — X i r u L - i r O f t — -4 -3J W PJ ft* Xi I I I I I I I I O O O C O O C O O O O O O O O O O O O O t » ft t • . t • , - , , - , - , - , - , - . - , - , - , , - , t , • xro ro ro L-J L-I ro r j ro ro ro ft— r - -— >— o 0 o o o o 0 0 K- ft— ft— ft— 0 -4 CO 43 O O O —1 'Jl L-l •— 42 C- X i ft- -0 i i ru o L-J J i co o L- l ff- co o w >o a s :AJ ? c» i u - i •> a £ 41 u i -4. rj in ft* s w o w - s> 1 1 t 0 0 0 t J 0 0 0 0 1 1 1 1 1 i 0 0 0 0 0 0 o o I I I I I I 0 0 0 0 0 0 r 1 o o I o o . 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 - - J - - 4 ^ ^ ^ - 4 ' - - J ' C D C D C D L 1 D - D - 0 - O - O 4 3 a 4 ^ r u L n o 4 i r L ' 3 3 o L 4 ^ - c o f t - r u L - i L 4 a 3 c > o o . - f t - r u o u 4 r u x i r u--CDLnLn - - j L 4 0 3 ~ 4 r u r u o L 4 f t — L-I u i c -4 4> c - o- o 33 o cs -3 X I 33 II CO CO O OS 207 T a b l e 5- 0.39-Clark-Y CLARK-Y RE = '.5(10)6 SOLID WALLS CLARK-Y RE = '.5(10)6 10XS3+P TSUSL ALF CL -10'. -0.376 -9'. -o'.278 -8 . -0.176 -7 . -0.075 -6 . 0.0 25 -5 '. ()'. 128 -4 '. 0'.233 "* i . 0.3^2 -2 . 0.441 -1 . 0.546 0 '. o'.659 1. 0.753 2 . 0,8/11 3 '. 0'.933 4 '. 1.024 5 . 1.107 6 . T. 187 7 . f.265 S . i ' .34i 9 . 1'. 4 1 2 10. . T.475 11 . T.522 12 . ' 1". 5 6 1 13 . T.585 n . i',598 15. T.535 16 . 1.541 CLARK'-Y ALF CL -10 . -0.360 -9 . -0.273 -8 . -()'. 176 -7 . -0.001 -6 . 0'. 0 11 -5 . o'. 11 o -1 . (,'.206 -3 . •(')'. 305 -2 . O'.IOl -1 o'.489 0 . 0'.597 i . 0'.687 2 . 0'.771 3 . 0'.852 4' . 0'.933 5' . 1'. 0 1 1 6' . 1 '.079 7' . 1.151 8' . 1 '.219 9' . T.2P8 10' . T.348 11' . T.396 1?' . 1-031 13' . i'.460 14' T.481 15' i',4 85 16'. T.442 CD 0'.02l3 0'.0216 0'. 0 19 7 0'.0183 O'.O 176 O'.O 179 0'. 0 1ft6 0'. 0196 0'.0206 0'.0218 0'. 024 0 0'.0263 0'.0290 0'.0327 0'.0368 0'.0423 0'. 0 4 7 0 O'.05J6 0'.0570 0'.0635 0'.07()5 0'.0785 0'.0837 0'.1021 O'. 12/11 0'.1952 0'.2181 CMO -()'. 192 -0. 166 - 0'. 11 0 -0.111 -o'.087 -0'.060 -0'.033 -0.001 0'.025 0'.052 0'.079 O'.l 06 0'.133 O'. 160 0'.187 0'.212 0'.236 0'.260 0'.233 0.304 0'.324 0.339 0.351 o'.359 0'.354 0.301 0'.301 CMC/4 -0.0917 -0.0923 -0.0929 -0.0933 -0 .0935 -0.0936 -0.0911 0919 0933 0936 0966 0950 0912 -0 . 0886 -0.0863 -0.0829 -0.030 1 -0.0772 -0.0735 -0.0704 -0.0672 -0.0635 -0.0615 -0.0600 -0.0675 -0.1081 -0.1102 RE=.5(10)6 10%L5+P TSUSL CD 0'.0254 0'. 0221 O'.02o2 O'.O 188 0'.0179 O'.O 170 O'.O 175 0'.0183 O'.O 197 0'. 0208 0'.0233 0'.0261 0'.0291 0'.0326 0'.0366 0'.0424 0'.0473 O'.O 5.2 6 0'.0580 0'. 0 61 'I 0'.0708 0'.0778 0'.OS60 0'.0917 O'.l 0 75 0'.1376 0'.1932 CMO -0. 188 -o'. 161 -0.139 -O'.l 13 -0'.088 -0.0 62 -0 .036 -0.009 0'.019 0'.015 0'.070 0'.095 0.120 O'.l 15 0'.170 0'.193 o'.211 0'.236 0.257 0'.276 o'.295 0'.309 0'.323 0.330 0'.336 ()'.330 0'.282 CMC/4 -0.0897 -0.0893 -0,0903 -0.0905 -0.0911 -0,0912 -0.0916 -0,0920 -0.0903 -0.0889 -0.0928 -0,0922 -0.0906 0876 0851 0332 0800 -0.0779 -0.0753 -0.0742 -0.0704 -0.0688 -0.0642 -0.0641 -0.0642 -0.071 1 -0.1106 ALF -10' -9 -8 -7 -6 -5 - 1 -3 -2 -1 0 1 2 ii 4 5 6 7 e < io'. n'. 12'. 13'. H . 15'. 16'. CL -0'.358 -d'.266 •0.170 •0'.077 0'. 0 1 5 ()'. I l l 0 .205 0.303 0'.402 0 . 4 H R ()',598 0'.689 0'.771 d'.855 0'.942 1'. 0 15 i'.0S9 l' . 159 1.226 i',298 T.353 i'.398 l'.4 33 l'.4 62 l'.480 i'.4 88 r.4 21 CD ' 0239 0205 0188 0178 0175 0175 0183 O ' . O I O S 0'.0202 O'f0220 0.0247 0'.0279 0'.0310 0'.0315 0'.0386 0'.0126 0'.0469 0'.0519 0'. 057 4 0'.0634 0' 07(15 0.0768 0'.0859 0'.0962 0'.1070 O'. 1332 0'.1887 CMO -o'.188 -0.163 -0'.138 -o'.l 12 -0.087 -0'.062 -0'.036 - 0', 0 0 9 0.019 0'. 015 0'.071 0'.096 0.122 0'. 147 0.173 0.195 0'.217 0.239 0.260 o'.279 0'.298 0.312 0'.322 o'.331 0.336 0'.329 0.279 CMC/4 0.0903 ' 0902 0907 0906 0907 0919 0911 0921 0908 0089 0931 0929 0901 -0.0878 -0.0862 -0.0838 -0.0313 -0.0792 -0.0759 -0.0763 -0.0 711 -0.0685 -0.0683 -0.0660 -0.0657 -0.0751 -0.1116 -0 -0 -0 -0 -0 -0 -0 -0 -0 -0 -0 -0 I ft ft — ft ft ft — I I I 1 I I I I 1 — > o - J I i i i - i M i - o o o o - i i c u r u - : o f ro i - i £ U i c - - J n -o o r ~ • - • • . - . - . •• - . - . - , - . - . - , ••• - • . • . - . -« - . •• - . ••• - n i i i i »— i f t ft Ift ;ft ,ft ft 'ft i f t Ift ' f t ' o o o o c o o o o o o o o o o o • - . * . - 4 -ft •• "ft "ft -. "ft "ft •. -. "• "• '• -O i'i i 2 i L - I L - I r j r j — c -o -o co -o c - LTI - i x i L - I ro •— ies o i— ro L-J r~ C- « T J O - I i : -0 L-l 3- O 14 -1 O l-l i l - J 43 CO O O ft ""0 L-l C LT i i L - l ^ J i - 4 c - o - c w - 4 ' a c ' 3 i - 4 4 i » > - . u c a ; w 4 ) j i r j o o r u j i u i O O O O O O O O O O O O O O O O O O O O O O O O O O O ft "ft "ft -• *» "• "• "• "ft *• -• -» .-« •» *• -« -• -• *• *o ftftftOOOOOOOOOOOOOOOOOOOOOOOOC? -4 W O 'Jo - 4 - 4 C - ' j l l/l - - L - H - l i y f u i\) l\l - * ft- ^ - ft1 r j fo CD 43 ft ; CO O P J J l 43 14 CD L4 43 PO 43 0 - L4 O C O — 4 ' C r - J l J l C * - - - I ' i 3 r u C " -c - W f t - W ' j i r j ^ j ^ i y ^ i - i f t - o r o o f t - ^ f t * »— r u c - c - r u x i - ^ J i o O O O C O O G O O O O O O O C O O O O I I o o I o I o o r j f j w w w r j r j f j f j r j r j - * ft ft* o c o o o o o o - * - * r - o C - 0 f t f t O C C a C - x r y O 0 ) C - - f t 4 ; - 4 - r u o l ' J 0 1 ! 3 O l ; l - T - 4 — L 4 c o i / i - 4 c > f t 4 i L n a - - 4 c o c > L ^ - O L n f t C T - r o L ^ f t < ^ o o o o o o o t r o o I I I I o o o o I I 1 o o o I I 1 o o o I I o o o • • JC I ft- ft ft ft ft ft- ft I t I I I I 1 I I ft- > o i n i - i-i r\> — o 4 3 C o ~ j c - L n i i i - i r \ j ft-o ft.ru 14 c j i a - -4 n -o o r - . O . -ft - . -I -< - . - . 'ft -ft "ft 'ft ft -ft -ft "ft -ft -ft -ft 'ft -ft ft -ft -• "• --T1 r-1 I I I 33 ft i — ft- ,ft |ft- ft ft- ft ft ft ft ; o o o o o o c o o o o o o o o o •Xi . ". -. - . -. -. . -. -• -• -« -« -. - . •. -. ". - . -. -. - o I i-i i-.J s a s w w r j r j f e 4 ) 41 co - J t - u i i i-i u ru ft o o •— ro l-i r~ - < - 4 43 LH L-l O - 4 ro C- O L-l 0 - 43 ft C i J l CD - 0 CD 4/ O O ft TO - 0 C- C- Ul C- L-4 4 i L-4 L-l r O ( M C I \ J > * W - O O C I S ft.C- C O L 4 - 4 r u O E - 4 W C X I O O O O O O O O O O O O O O O O O O O O O O O O O O O m « *» - • • •• - . - • •« -t " • "• •• -» •• -» • -< •• •• •• - o II ft— ft ftOOOOOOOOOOOOOOOOOOOOOOOOCo" . - 43 c - o o co ~4 c> J i J l i i 4^ i J l-i ru ro ru ft ft ft « ft ft •-* ru r o ' J l O ' J l L-l fti-J X i CD ft;J! O J l ft'ii ft - 4 J i ft.'43 CD 4 C O- C> - j C O c i i y O 2 4 ) £ o i o r j i i i j - o o o 4 ) o o c - a i w f t 0 - o i 4 i , i r j - 4 4 ) i \ / *~> O O O O O O O O O O O O O O O O O t i l l O O o o I I ) I o o ft "i t "* -t "t "• • • "t " • "• "» "ft "ft '» "* "t "t *» -t * i '» ' • 'ft ' ru ru 14 14 14 14 ro ru ro ro ro ft ft ft o o o o o o o o ft ft *-* ft o L " - c o r u r u f t - o r o - 4 j - i j i f t 4 3 C - — - - c s i - i r u o w j i a j o i i j - c a c - o c- ru i i - 14 43 • - ro r j - o - 4 u 4 ) n o n - - J W 31 a o i - o t 1 1 o o l i f t 0 0 0 0 I I o o l i l t 0 0 0 0 I I I I I I 1 I 0 0 0 0 0 0 0 0 I I o o 10 c -cr J l : 1 -S *-*> 1 1 JU . -o o-ft 0 O O O O O O O O O 0 O 0 O O 0 O O O O O O O O 0 0 O + ft O O O O O 0 O 0 O 0 O 0 0 0 O O O O 0 0 0 O 0 O 0 O 0 1— : o C- 0 O c - - 4 -4 -4 — 4 1-4 'CD CD CD CD O 43 CD •CD CD CO CO CD CO CD 'CD CD O 43 0- c - O G- - 4 •-4 —1 —4 CD CD CO CO 43 43 CO CD CO CO •CO CO CO CD CD CO "0 0 14 O - 4 ~4 43 ft i i U l - 4 CD >— 14 J l - 4 O >— ICO CD 4j 43 43 00 CD CO 0 -4 X i - 4 O i i L4 L4 L> 43 ru 14 U l -4 O ru j i 0- O O - -J - 4 43 CD CD •CO - 4 -J CO CO i i c a O CD 14 •C O CD U l ft i i ru O Co ft J l ru L-J ft— - 4 43 CD 14 03 u J ru -4 14 —\ -4 -4 O C- O c- O X i X i 14 ru 14 0 4) J= -4 O cr- ru Co 14 -4 43 43 14 ru - 4 CO cr 10 in i i L - I ru 1 ft I I I I I I I I I ft 3.-o 4) co -4 cr- i n x i 1-1 r u ft-o •— r u 14 x ; j i c - -o, co 43 o r -ft "ft "ft •• -. -ft -ft -ft -ft -• - . - . -. - . - . -• - . - . - . - T l I I I t ft .ft- .ft- ,ft- (ft- |ft Ift ft ; o o O O O O O O O O O O C 0 0 0 • - . -. . -. •• -. -. - . - . -» - . - . - . - . -. -. -. -. - . - . - . -. -. - o r j r-j L - I 1-1 14 r j r j ft ft 1 0 o 43 co co --j c - n i i Xi i-< ru ft o o ft ru 1-1 r~ ro i n ro 14 o co 14 co ft 0- o i i co ft 14 o- CD 43 o ft ro L4 i i x i L4 r j ft 43 j l cc o Xi ft.L-J ro ro o J I J I J l - — . J I c - a IU J I -4^O C 0 L-I i : J I C-0 0 0 0 0 0 0 0 0 0 0 0 o o o c o o o o c 0 0 0 0 0 ft.ft 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 o o o c> x i o -4 c> u"i u l i i i i X i L4 L - I r o r o r u ft ft ft ft ft ft ft ft -— r o r u r u — L - I r j x - - j 14 ' a x c J l - :-4 ' i i -4 • j l u i i i i i X i j l Co icn ^ i i 14 u i i 4 u l --4 x~ o 14 c a co r o o J l J I L 4 co r j '43 3- x i o o r u - * •— 1 1 1 t 1 { 1 O O O C O O O O O O O O = . O C C . O O O O O O O O O c o o • • • •• -ft • • • • •» 'ft •» •« -ft -ft -« "ft -ft -ft -ft -ft 'ft -ft -ft -ft • • •« -ft -ft -ft - 3 r u ro ro 14 ro ro ro r j ro ro ro ft ft ft ft o o o o o o o o o ft ft ft o 14 j l co o 43 'a - 4 J l u i rv o co C- X i ro c 4 J I M o M J l - J 4 ; . V i - J -4 L - I 43 ft J I 0 - ru c- 43 ft i i J I - 4 • i i ro C D u i ft -4 o n o x= co ro - 4 — 1 [ t o o I I I I I I 0 0 0 0 0 0 1 1 1 1 : i ! 1 i i 1 1 1 1 i 1 1 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ft . ft ft ft . ft • ft ft ft ft ft ft ft ft » . . -ft ft . . -ft ft • ft -3: ftOOOOOOOOOOOOOOOOOOOOOOOOOOO C O - 4 ' B - «• L> 0- - 4 ' ? - 4 S S - 4 ' » 3 1 3 3 0 J O i a C s a 0 3 f J 1 3 f f l \ . X i J T ^ X = X i - 4 4 3 f t 4 3 l 4 J ] - - 4 4 ) f t l 4 - - 4 C D ^ C ? - - 4 - - 4 ^ ^ U l X ^ u i f t 0 3 i = r u - N i r j f t 4 > r u c B - 4 0 o - - 4 4 - - ' J l c o i 4 w I ftftftftftftft 1 I I I I I I 1 I ft > C - J l i 14 ro -O O O "4 C- LT X l-l M ft-'O - M L-l i J l C- -4 "3> o o r • - . - • - . - • • • • • * • • ' • - • - • • • - • < ~n t i l l ft Ift Ift ' f t ' f t ft i f t ft i f t ' f t ( f t ' O O O O O O O O O O O o o o o o . - . ' . - . - . " . "• -ft -ft - • « "• ' • • ft -ft -ft "• '. •• -ft •• -• "ft - o l-l 14 14 L-J 14 L4 PJ rJ ft O O 43 CO CD C- LH X i X i L4 PJ ft O O ft TO 14 ! . ft i i 43 -^1 X i O 0 - O i_- CD r o 0 - 43 P0 i i C- '33 CC O ft ft r u 14 LH i i 14 14 ft:43ftorL'-4l4iiLnroL4ru'JlXi'J14)-44)l4ruOC>.ii-4-~lCOfti 33 O O O O O O O O O O O O O O O O O O O O O O O O O O O m ft - t -ft -« -• •• ** '« "• "• '• - "« *• *» "• *» ' t '» *• *• -• •• *o || ftftOOOOOOOOOOOOOOOOOOOOOOOOOC? ft - -4 x i c CD -o c> c- JI j l X i i i L4 14 r u r u ru ft ft ft ft ft ft ft *— ft r u r u Ul fti—iJ! 14 C - 43 14 - 4 ' — .0 - ft - 4 O ~ 4 i i ft - 0 ~J'C> 'Jl J l J l J l - 4 • 43 V J l *~. u i cr - 4 cn 14 PO J l i n co i^ J l o ^ l-i i l - o x i ro ft i i o ft cc ru ru 43 3s I 03 co a. co 01 -4 >— O O ru -4 J i x; ru c - o ru co ft u i o 43 ft J J C O .1 -4 : T J 4 ! - 4 X . U O " J J l - 4 O r j J | - 4 0 0 - r o C O X l L 4 C D X i 4 ) X i C O X i I I I I t o o o o o I I I I I I I o o o o o o o I I I I ! o o o o o o o t i l l O O O O O O O o o r-i : J l I I I I I I * I o O O O O O O O C C C C O C O O O O O O O O O O O O C O O ' - ' • 't •% •• - . - • • - • - ' • ' • ' • » ' • 'ft ' • ' • 'ft » • . ft • 'ft t - • - . ' i o -r j r o U 11 w o r j ro r j f J r j ft ft ft ft o o o o o o o o ft ft ft o ft O 0 O C L 4 0 0 0 0 O 0 O 0 0 0 O O O 0 O O O O 0 0 O 0 O 43 O 0 - 0 - 14 ~4 '-4 '-4 —4 -4 ' - 4 'CD av CD CO 43 CD 03 CD CD CD CD CD iS O 01 \ ' c r i n c c - - 4 ^ 4 2 f t i 4 i n u i - - 4 - O f t i i C r - -00-4*4 a c o c o c o - 4 - 4 - 4 C - j i & \j\ ~ w & ^ G- & w ~ \j\ >j\ t\t ss \ * w ss co + 13 CO r o I i i i i i i t i i >- > c- J I c u I\J >- o o c» - j o - i r i £ « « i - , r o w c ^ o - J m a o r . •• • ~ft -ft -ft - ft - - - T ] I I I I *~ i _ >- — '*— •*— "© © © o © o o o © o o © © c o © . •« -. -. •• -• • •• •• •• -• -• •• -• -rt u ; i t H u w C J o o ui 2 u n rj - o o - rj u i r -r r j ^ « - C 1 r j . o - j i n 3) o c - - n ^ L-J - 4 >-.c- a >—• = a N in i> -o c t> o ~i j) - J I o J I —>i cr* ft ui c* - 4 -i -< o o o o o c o o o © o o c o o O © © © o © o o o C O Ci m 1—" o o © o c o o o o o o o o o o o © o o o o o o o o C3 l l - 4 w 43 c- Ul U l ft ft L-l L4 Ul ru ru ro ft— *— t— t—• t— *— »-* »-* ro ro • * CD ft 43 - 4 •3D »—. ift 3D ru - 4 'L4 43 U! CO U l ro 43 Co - 4 •c- c- C"- - 4 '43 •:n U l 00 O -o OD o LM - J 0- »-» ru ro L-4 ft-» - J CO ft ru - 4 Ul - 4 - 4 o — rj i—i I 1 1 1 | 1 1 l o © o o c o c o O c c c o o © c o o o c o c © O o o c o r> w t ' ft ' 1 • 'ft • • • t " • ' t ' 'i " » - • " • • ft " • " ft ' t • • ' • • • ' • " 1 ' t " • " * • • • i " a-r j u i U J L~J L4 L-J r j ro ro ro r j •— *-» >— t — o o o o o o o o *-* »-* »-* o c o ru t— o CO c- ft ro o CO :-•* ft 1— 43 - 4 ft ru o L4 'Ul CO o ro Ul - 4 c- ft o --( o o cr* o 43 o CO c- ro Co Ul o Ul » • cr- ro c> =• Ul CO L4 Cr- o o 1 1 1 1 1 1 I 1 I 1 i 1 i I I 1 I 1 i 1 i 1 1 I I 1 I o o o o o o o o o o o o o o o o o o o o o o o o o O o O CO OJ , o o © o o o o o o © © o o o o o o o o © o o o o o o D -t-c - J Ul 0*- 3 - o* o- - 1 —J •CO CO ca CO CO CO CO CO CD 00 00 CO CD CO 33 X o UI 00 o L4 cr* ~c >— ft 0 - CO o ft Ul Co 43 Ul 0- CO - 4 - 4 Ct* - J CT" a- Ul ft Ul o Ul o 43 U J ft Ul Ul CO o 43 >—- rj •43 U4 U4 L-J •Jl UJ CO ro CO 43 Ul —< t n I — I I I 1 I I I I 1 — > C > U l f t L 4 r u — 0 4 3 C D - > I C > U l f t L 4 r U H ^ O i — r U L M f t U 1 t ? - - - 4 C 0 4 3 o r -. -. -. - -• • -. -• -• -» -• •• • I I I I . -. •• -• • •• •• 'ZI ru ro L4 L4 L-; L-I ro rj •— • — ' = -o -0 co -4 - c .<) W U Jl o O o o o o o O o o O O o c o o o o o O O o o o C c n _ o o o o o o o O O o o o o o o o o O o o © o o o a c- 43 -4 Ul OT ft ft L4 L4 ro ru ro ro >-* I-* »-» »-* —*• ro ru ru C L4 CO ft o 0* L4 CO c** L4 o -4 0- Ll Ul U! Ul Cr CO ft L4 L4 -4 o ru ft L4 L4 Ul O -4 — CO U! Ul L-I ft cr -4 c ^4 co -4 CO — 1 1 1 1 1 1 1 { C c C o c O o C C o C c o o C o O o c C J o C o o c o « - » • , -• ' • -* " • ' » *t ' « - '• * t " * " • ' t ' 1 • * • t ' t ' • ' » • 1 ' » ' t • ro 04 UJ L4 ro ro ro ro ro r 0 ^* o O o o o o o *-* *-* *— •—"• o O o o 43 CC -4 Ul Ul 43 -4 ft ro o -4 Si ro o ro Ul -4 | o L4 Ul '00 -4 o -4 43 Ul c- ft ft - L-4 «-* CO - o Ul ° 'Ul L-I CD - 43 L4 O Ul o I I I I 1 i i I 1 1 1 1 1 1 i 1 1 I i 1 I 1 1 1 I I I o o o O o o o O o o o O o o o o O o o o o o O O o o o 1— o o o o o o o o o o o o o c o o o o o o O o o o o o c -4 <> o -4 -4 — J ~4 — J •00 CO CO CO 43 •CO Co 43 43 43 CO CO 00 •CO CD 43 o o o- o O ft U l -4 43 L4 cr- CO o ru co 43 o O 43 >Co 43 00 00 ft -4 ru ft O C- ft 43 o ft CD L4 U! CO L4 c- o O -4 U4 - J ~4Ln - 4 L 4 LT. -4 -4 o -> I -< 33 m I I CO co + TJ I — — — • - — • - > - I I I I I t l l l - - 3 > c r - u i f t L 4 r o - - o 43 co -4 o L T ft L -4 ru c ,ru L 4 e . U I C ~ - 4 C O 41 o r . -. -. -. -. •, -. -. -. ^, -. -« -. -. -. -. •. -. -. •. -n 1 1 1 1 IN- i^ * it— ^ 1 0 Q O O O 0 0 0 0 o c: o c* o o • - . •• - . - . * . -« - . - . •• . - , - . - o L 4 ft ft ft ft L4 1 4 ro ro •— o c 43 co tc-- ui ft L - I L 4 ro >— c o ro L - I r~. -4 LT '.n L4 *— -J L4 -4 »— L4 4^ O TJ ft C- CO 43 CO 43 C O C- Cr L'l c o 4 3 c - - u i r o - 4 r o c r - c ; C N f t r o -4—4 ui UJ L 4 30 -4 ro -4 t—.co ft -4 •—•ft c c o o o c o o o o o o c o o o o o o o o c o c o o o • - t - . - . •« - • - . - , - . - . •» . • • - » - . -rt »— •—;»-* G O O O O O O O O O O O O O O O C O O O O O O O C 3 ooroo430=- -4 0 - c > L > T u i f t f t u i L 4 r o r u r u r u - — • — - — - » * • • — r u r o L4 43 ft L4 ft C- 43 L4 C> >— ,0> !\1 O C ft O O CO -4 —4 —4 -4 '43 C L4 c r - — - - . i o L i f t r u o o f t c 3 , - c o c > c o u i - - 4 o c o f t - - * c ^ r o f t c v r u - - 4 c o I I I i i i • I c o o o c c t o o o o o c o o c c o c o o o c c c c o o o • *• "t " t " • "t -| "i ' • ' * "t "» *t * t "t -« *• '• '« "t * zz. r j w w w w w r j r j r j r j r j - - i - t - K o o o o o o o o - - H H w o - 4 r u r u r j - o - o - 4 J l u i - > c - 4 i r j o - 4 - - - o w c - 3 i o w c - c a L l O C O f t C r C ^ r o f t u , l f t L - 4 r O O U ) O U I C > ' U 1 4 3 C O f t O U I 4 3 f t - - f t I I I I I I I I I 1 ! I I I I I I I I I I I I I I I I o o o o o o o o o o o o o o o o o o o o o o o o o o o n • •>.••.•-..........-....... 3: o o o o o o o o o o o o o o o o o o o o o o o o o o o o J 3 M 9- c o r> j - - 4 - j - 4 - j s a o o j - f i o o K s s f l a i s i B o a a N . ' C0roL4»— L4LT. -4-— r u f t C O O r u U l - 4 0 C > C O C 0 4 3 0 4 3 0 C O C 0 4 3 C o f t a c - t - o - o o o o j - o - j p c w w c - r o o w o ' - w o c o c - r j (D m » C3 . - ( _ l 'Ul (« in CO + T J CO CO 1 1 1 1 1 1 1 1 I ft— > Ul L-4 ro »— 43 CO - 4 a- Ul ft L4 r j *— • o - »-» • ru UJ ft Ul - J Co 43 o •I— • - • '. • • - a - • * •• - • " • • ft -'ft -ft -' • -'ft •' ft -ft * • 'ft - • • • n o I -•T . it— 1*-* • ^ o C o o a o = o o 1 © 1 c 1 © I 3> ^3 » - • ^« - • * ' •• ~ « - • - • - • '- • -ft -« -• -ft • ft -« * « -ft ft -• * ft ^ •ft - ft - ft •• o L4 L4 L-I L4 L4 L4 ro -0 43 CO -4 •c-- Ul ft ft L4 ro o © »— • ro L-J r- i ro 43 cr- ft O Ul 40 ro L l •Co i— L4 L l -1 o 43 o ro L4 ft ft L4 -< CO CO c -4 43 O 43 o O c~ LH 43 ro CO 0 s Co U i ro 14 »-* i cn ro — . © 43 — © o o o O o O O o o o o O o o o o o O c o © © © © © 33 o m o O c c O o o o o O o o o o o o c o o o O © © © o CJ l l w 43 Co - 4 a- Ul Ul ft ft U ' U ' UJ ro ro ru h— —* •— »-» >— 1—-ro ro ro • ' -^ 4 '43 - 4 • f t CO ro 3- :o- N— Co ru - 4 • ft ro CO -4 c*- c- ^4 •CO © L4 -4 Ul CO Ul - 4 Co - 4 ro o o cr o 00 o — CO Co ~4 o ro UI Ul — — L-J ro r—\ I 1 1 t 1 1 I I o c o c o C o o o o o o o o C o O c o c c © © © © o t-3 \ ' t • » ' •» • ' t ' • ' ' t •» " a • '» ' • ' 'ft ' 'ft " f ' 'ft ' t ' ' ft " ft ' • ' 'ft ' 'ft ' ' I ' ' c ' •ft ' ft ' ft ' ' • • Ci 0-ro ro UJ L4 L-J L-J ro ro ro ro ro ft-* r-» o o o o o o o O •— *— I-— *— © —N Co O 43 -41 'Ul U J 43 c- ft ro 43 -4 ft ro o L l Ul c= o ro \T, -j L-4 ft CO - 4 O — => ro L4 L4 »- 43 Ul r-o -1 ro -4 U J - ° c- LT 43 Ul CO - 4 © 1 , I 1 e 1 1 i I 1 I 1 1 1 i I I I t 1 1 i 1 I 1 I I O o o O o o o o o o o o o o o o o O o o o o o o o o o Ci CO ^ — o o o o o o o o o o o o o o o o o o o o o o o o o o n c o ! M - 3 : - S ' - 4 ' - 4 - 4 - 4 ' a 3 o a 4 ) O a a c B 3 3 » 3 a » a \ ' r - © U l L 4 U 4 C - C O O f t O * C O ' — r O U l O O r — C 0 C 0 O 4 3 C 0 C D C o - 4 - 4 - 4 f t l ^ r O O O - — G > U l - 4 © - — -4-rOftU143-— '— ^ - © U 1 U | U 1 * - 4 U 4 4 3 U J U 4 CO + T J CO cr CO r O O KO I ftftftftftftftftft t I I I I I I I I ft > c a - J C - L n c w w t - o ^ c o - ^ c ^ i n - i i w r y f t O f t r u w i i L r . c>-4co 43 o r~ • -, - i -• "» -t -• -• -• -t -, '• ~. - T ) I I I I ft : f t ft ft i , — : — ft 1 f t - f t It— I f t ft I f t -ft- i o o o c o o c o o o o o o o o . -. •. •« -. -. -. -. -. -. -. -. -. •. -. » -. -. -. '. •. -. -. -. o i n j l J l L n L n _ i i i . i i l 4 l 4 r j f t : f t C 4 3 C 3 - l ' l - L n i i - - - l 4 r j f t O O f t r u l 4 r _ ft I— — ft ft o -s i u i CD r J cr- co ft L J i s o - - J • co 43 43 o •-• >— .-* r o s> c o> i i ft.c,ar>siairjoLnorvj4irjft,3iWic»woc?s]icc,aii,i o o o o o o o o o o o o o o o o o o o o o o o o o o o o o • - i •• •» -. -. -. •• - i •« -. •• -• • -. •. •» -• -r> r j f t f t f t f t f t f t o o o o o o o o o o o o o o o o o o o o o o o ft sO CT" i s 14 ft C O CO - 4 L I J l i i t,"l L*I r u IV PU ft ft ft* ft ft ft ft ft i \ J J l . V CD v ft IL I r u o o ft i s ca r u c> ft ' 3 - o 3 - L-I o co - I ' O 3 - 3 - 0 -4 • 43 r u i / i i - s j o M r j o i / i r u ^ ' i r j o i s i - i - o - o f u r u f L i ^ r j o o o o o O o c c c o o c O o c o o o o o • ' '% •» ' " * '« ' f ' 't ' ' • ' » ' 't ' '• ' ' t ' '» ' ' • ' ( - - f ' • • -r o L-: L - l J l L - l J J L - l J l r o r j r o r j r o ft ft ft ft o o o o o o ft r o r o r o — o - 0 -s i J I L-4 ft - c 3 - i i r o -c -s i j - ,-o sO CO J l ft* • L> L - l C - - J - 3 - - 4 • J l — r o -0 J l o J l o J l I 1 1 I I I 1 I I i 1 1 I I 1 1 l 1 1 I 1 o o o o O o o o o o O o o o o o o o o o o ft ft o o o o o o o o o o o o o o o o o o o c c o CD CD - J —4 ~ J - 4 •CO CO •CD CD CD CD CD CD o CD sO cc o L-J i n ft o sO CD 43 r u 41- 3 - - 4 - 4 CO - 0 o ft sD o C - o CO 43 U l -s i o o o l - l U l i s c - CO J l U l J l U l • t i r o i n I I t i l l . o o o c c n o o o O J l 'Jl I o Co O L-l C- Co i i 4 ) L i -.C-I I o o O O O O 43 43 43 CD ft O O 43 o so ru c-o r> • cr o n co ^ . 4 j e I -c 33 n II Co •ft T3 W C Co ro o 43 CO -si c- i n .£* 14 r u ft* o •43 CO - 4 0 -ft ft ft ft I f t ft I f t i f t ft I f t i f t i f t I f t i f t • „ i c- c- c- c- c- c - c- c- i n i n J l ^- L4 r j »— l-J i i i i L4 14 L4 r o 43 c- r o •CO o r o i i CO 14 O O - 4 43 — C- CO co c- r u 14 c- 4 i o o c o o O o o c o o o O o O ro r j r o r o ft ft i t - H- ft o o o O o o 4) o t i •— 43 - J i s r u o 43 - 4 c- J l J l — i n J I o o L4 o c— t i 3- ru 4) CD 43 L4 - 4 43 — 14 Ul r o r o 14 - 4 —4 o r u 43 - 4 r u u i o o O o o o o o o o o O O o O l - i 14 L4 l - l 14. u i Ul 14 14' 14 14 14 r o r o r o o r o "U 14 14 t i t i i i i i JJ r u ft 43 c-43 o - o- J l O J l J l 43 J l CD co J l r o 43 — — r o 1 4 I - 4 C - - J C P n i i i = C - C > - 4 - 4 r - o c J i r j c c o r - r m u o o o o o o o o o o c o c o o o o o o o o o o o o o o o o o i l 4 r u r u r u f t f t f t f t f t f t f t f t r u r u L 4 C O 4 i f t i O - 4 - C - C - J I C > - 4 - 4 3 r u 0 -U i O - O - i i f t - C - J l O C D L n C D i i o r U I I I I I I I I o o c o c o o o o o o c o o ftK-ftOOOOOO O J J ft CO J l r u LT- —4 O 14 C- -0 ' I t t o o o f I t 1 't CO 43 CD O O O O ' 43 43 43 ft L 4 CT- • ft IC- O I o > 33 3 T I •< 33 . II L J ft r\ O ?? in CD ft L-J o 43 CO CD 'Jl :u 43 c- ru OL 1 t t I t t o o o O o o o a o o o O o o n zti 4) 43 43 43 43 43 v. i> •3- ' J l J— C: 1 4 ru i - t ~ ru t i C- O ru Co LS ftftftftftftftft— I I I I I 4 I I I ft >-c o - s i c - L n i i i - i r u f t . o 4 3 C D - 4 a - L r , X i i - i r u f t O f t . r j i 4 i i L n c - - o c o 4 3 o r -I -. -» -. -. -. »• -. '• -. •• •. -. -. "• ~. -• -t -« -. - T l I I I I t — V- I f t ft i_ !— ft l u * jft i f t ft V- i f t ft o o o c o o o o o o o o o o o • - . - . - . - . •• -4 -. -. -. - . -. -« - . -. -. -. -. -. -. -. -. -. -. -. - n O IT L H J l J l i i i i i i 14 L 4 r j ft ft o 0 CD - 4 C- J l . t i i i 1 4 r o — O O ft r o L-l r~ O o ft ft ft o C - r j - 4 ft i n - 4 o r o i . - j l - 4 co 43 43 o ft ft ro r o c- c- LT i n i n i i j l 43 r u ft r u 14 t : - J o 43 r o r o 14 - o ft r o i . - cc 4) r j i n o i n cc i - co o o o o o o o o o o o o o o o o o o o o o o o o o o o o o • - » - . •» - i •> •• - i -» - t -. •• •• -. -. -. -t •• •• -» -• -. -• •• -• -r> ( \ j f t f t f t f t . f t ft o o o o o o o o o o o o o o o o o o o o o o o 0 co t i r o ft o ca -4 c^ c- J I t i i i 14 14 i - i r u ru r u ft ft ft ft ft ft ft ft r u 4) 43 43 CD .0 PO O -4 —4 - 4 O i i 4) 14 CD t i C CT- ro O 43 - 1 CP J l LP C- - 4 43 i i U l 0 i i r J C " i i O L 4 C D C 0 C D u l O - 4 4 > O O L n 4 7 J l i i - i r 0 J l - 4 C - 4 ) O O I I 1 I I I I I c o o o o o c o o o o o o o o c o o c o o o o c o o o c o n r o L-I L4 i - i L-i 14 J J i - J r o r o r o ro r o ft ft ft ft o o o o o o o o ft ft ft ft o 4 ! O ft r o TO " J ft O 45 - 4 J l L-l ft 43 C- i l ft 43 0 - i i ru O U l J l CO O 1 4 ' J ! CO 14 O i i O 14 ft i i 4-" ft L I i i 14 ?J O - 4 14 CD i i 43 J l O CD 14 CO L-J CO r u CO r u 1 I I 1 I 1 I ! I I 1 I I I I I I I I I I I I I I I I f I o o o o o o o o o o o o o o o o o o o o o o o o o o o o o n ftOOOOOOOOOOOOOOOOCOOOOOOOOOOOO C 4 3 4 3 C C - 4 — J - 4 — 4 - 4 - 4 ' C O 3 ) C Q C O C C 3 ) 3 : C D O i l 5 O - 0 O C 3 3 ) C 3 3 3 C a ' 3 ) \ . c ? ? O i - " 3 - C " C > C » » f t W i i J ? - J C o 4 ) c . 0 O - O O 4 ) C 0 C C 3 l 3 : i 4 * f t i n c D - s i u l i \ i r u ^ o o ' j i r j f t 4 i i L - j . 4 3 C P 4 i r o f t r u - c 33 CO CO 03 L_ Co 211 T a b l e 5 - 0.53-Clark-Y CLARK-Y Ru='.5(10)6 5 0 XLS +P TSUSL CLARK-Y RC = . 5 ( 1 0 ) 6 70XLS+P TSUSL ALF -10'. -9'. -fi'. -7'. -6'. -5'. -4. -2'. -r. o'. r. 2'. 3. 4'. 5'. 6'. 7'. e ' . 9'. 10. i r. 12'. 13'. 14'. 15. 16'. 17'. lfi'. 19'. 20'. CL - 0 . 3 1 4 - 0 ' . ? 5 2 - 0 ' . 1 5 7 - o ' . 0 6 3 0 . 0 3 0 0 . 1 2 4 0 ' . 2 2 1 0 . 3 1 9 0 ' . 4 0 9 O'. 4 9 9 0 ' . 5 9 5 O'. 6 8 6 ()'. 7 6 9 0 ' . 8 5 5 g ' . 9 1 2 T . 0 2 4 1 ' . 1 0 1 T. 1 7 6 l ' . 2 5 f 1 '. 3 1 9 T.373 1 ' . 4 0 5 1 ' , 4 1 2 l ' . 4 6 9 l ' . 4 « 8 1 ' . 4 9 0 l ' . 4 R 8 " l ' . 4 8 3 l ' . 4 6 3 l'.O 4 1 1 . 4 0 8 CD 0'.0225 O' .O 190 0'.0162 0'. 0 11 0 O'. 0130 O' .O 123 '0122 0137 0152 0164 0191 0230 0'.0263 0'.0315 0'.0375 0'.04?7 0'.0480 0'. 0511 0'.0605 " 0688 0763 0856 0967 1 1 0 1 1279 O'. 1466 O'. 1681 0'. 1885 0'.2093 0'.2283 0'.2500 CMO CMC/1 ALF CL -0.179 -0 .0874' -10'. -0'.331 -0.151 -0 . 08'69 -9'. -0'.240 -0.129 -0.0872 -8. -0'. 143 -0.105 -0.0801 -7'. -0.053 -o'.os 1 -0.0381 -6'. 0'. 037 -0.056 -0.0086 -5'. 0'. 130 -0.031 -0.089-5 -4'. 0'.224 -0'.005 -0.0904 -3'. 0'. 3 1 6 0'.021 -0 .088 t 0.109 0.016 -0.0076 • -V. 0'. 19 <| 0.070 -0.089 1 o. 0'.587 0.095 -0.O890 r. 0.672 0.118 -0.0076 1'. 0'. 756 0.113 -0.0861 - 3. 0'.836 0.166 -0.0858 4'. 0'.924 o'. 189 -0.0851 5'. ()'.992 0.211 -0.0035 6'. {'. 068 0'.232 -0.0817 7'. l ' . 137 0'.252 -0.0813 8'. l ' . 198 0.272 -0.0791 • 9'. T.256 0 .289 -0.0770 10'. l'.302 0'.302 -0.0720 ['.342 0'.310 -0.0729 12. l'.37i 0.318 -0.0713 13'. i'.393 0.319 -0.0758 14'. 1'. 4 0 1 0.313 -0.0824 15'. 1'. 4 01 0'.309 -0.0364 16. '['.383 0'.300 -0.0911 17'. l'.361 0.292 -0.0976 0.279 -0.1061 CLARK-Y 1 0.265' -0.1121 CLARK -Y Rir = '.5 " c i0)6 60XLS + P TSUSL ALF CL -10'. -0'.336 -9. -0'.215 -8'. -0.151 -7'. -0'. 057 -6'. O'. 0 34 -5'. 0.127 -4'. 0'.221 -3. 0.315 -2 0'. 10 9 O ' . l 93 o'. O'. 589 i ' . 0'.678 2'. 0'. 762 0'.813 4. 0'.932 5. l'.O05 6'. i ' . 08 7 7'. !'. 151 8'. 1.223 9'. ~l'.282 10'. ['.333 ll'r 1 '.379 i'.'113 13'. '['.4 37 14'. 1 .151 15'. ['.4 53 16'. l ' . l 16 17'. 1 '.131 18'. 1 '. 4 0 7 19'. 1.375 CD 0'.0216 0'.0212 0 ' . 0 l - i 5 O'.O 177 0'.0171 O'.O 168 O'. 0169 0'.0175 O'.O 188 o'.02ol 0'.0228 0'.0266 0'.0310 0'.0352 0'.0402 0'.0 4S3 0'.0503 0'.055 3 o'.06()5 0 ' . 0677 0'.0718 o'.osn 0'.0960 0". 1078 " 1228 14 00 1583 1768 1 9 i | 9 ' 2145 CMO -0.179 -0'. 155 -0. 129 -o'. 104 -0.030 -0.055 -0.031 ••0'.005 0.022 0'.016 o'.071 0.095 0.118 0'. 1 4 2 O'. 165 0.188 0.209 0'.230 0.250 0'.268 o'.281 0.296 0.305 0'. 3 1 1 0'.312 0'.307 0'.300 0.289 0.281 0'.268 C M C / 1 - 0 . 0 8 7 8 - 0 . 0 0 0 3 - 0 . 0 8 7 0 - 0 . 0 8 8 1 - 0 . 0 3 8 6 - 0 . 0 8 9 3 - 0 . 0 9 0 1 - 0 . 0 9 0 5 - 0 . 0 3 9 1 - 0 ' . 0 H 7 5 - 0 . 0 8 8 9 - 0 . 0 0 9 7 - 0 . 0 3 9 0 - 0 . 0 8 7 0 - 0 . 0 8 7 7 - 0 . 0 8 5 1 - 0 . 0 8 6 1 - 0 . 0 0 3 2 - 0 . 0 0 1 3 - 0 . 0 7 8 9 - 0 . 0 7 6 1 - 0 . O 7 5 6 - 0 . 0 7 5 5 - 0 . 0 7 5 8 - 0 . 0 7 8 3 - 0 . 0 8 3 8 - 0 . 0 8 9 8 - 0 . 0 9 7 5 - 0 . 0 9 8 7 - 0 . 1 0 4 1 C D C M O C M C / 4 0 ' . 0 2 3 7 - 0 . 1 7 6 - 0 . 0 8 6 1 0 ' . 0 2 0 1 - o . 1 5 1 - 0 . 0 3 6 0 O' .O 1 7 3 - o ' . 1 2 5 - 0 . 0 8 5 2 O' .O 1 6 1 - 0 . 1 0 1 - 0 . 0 8 6 0 0 ' . 0 1 1 0 -o'. 0 7 6 - 0 . 0 8 5 8 0 ' . 0 1 2 8 -o'. 0 5 2 ' - 0 . 0 8 6 6 0 ' . 0 1 2 9 -o'. 0 2 7 - 0 . 0 8 7 3 0 . 0 1 3 2 -o. 0 0 3 - 0 . 0 3 8 0 O' .O 1 3 6 0 . 0 2 4 - 0 . 0 0 6 5 0 ' . 0 1 1 2 o'. 0 1 8 - 0 . 0 8 5 3 O' .O 1 6 4 0 . 0 7 1 - 0 . 0 8 7 2 O' .O 1 9 2 o ' . 0 9 5 - 0 . 0 8 6 5 0 ' . 0 2 2 4 ()'. 1 1 8 - 0 . 0 O 5 0 0 ' . 0 2 6 2 o ' . 1 4 2 - 0 . C O 3 9 0 ' . 0 2 9 9 o'. 1 6 5 - 0 . 0 R 4 7 0 ' . 0 3 4 3 o'. 1 8 6 - 0 . 0 8 1 9 0 ' . 0 3 9 2 o ' . 2 0 7 - 0 . 0 8 1 t O'. 0 1 5 9 o'. 2 2 6 - 0 . 0 7 9 9 0 ' . 0 5 1 4 0 . 2 1 5 - 0 . 0 7 7 2 0 ' . 0 5 7 l o ' . 2 6 3 - 0 . 0 7 4 1 O' .O 6 3 9 o ' . 2 7 8 - 0 . 0 7 1 3 0 ' . 0 7 1 2 o ' . 2 8 9 - 0 . 0 7 0 8 o ' . o o i i o'. 2 9 7 - 0 . 0 7 0 1 o ' . 0 9 5 2 0 . 3 0 2 - 0 . 0 7 0 3 O ' . l 1 i l 0 . 2 9 3 - 0 . 0 7 6 1 0 ' . 1 2 6 0 •o. 2 9 1 - 0 . 0 0 . 0 5 0 ' . 1 4 3 9 o'. 2 8 6 - 0 . 0 8 3 5 0 ' . 1 6 2 t o'. 2 7 4 - 0 , 0 9 0 0 80%LS+P TSUSL ALF •10'. - 9 ' . -6. -5'. -4'. -3'. -2'. o'. 1 . 2'. 3'. 4'. 5'. 6'. 7'. fi'. 9'. i0'r 11. 12'. 13'. 14'. 15'. 16'. CL •^0.315 -0'.224 -0'. 132 -(>'. O i l 0.047 0'. 137 0'.227 ()'. 320 0'. 4 1 1 0'. 493 0'.588 0'.671 0'.751 0'.830 0'.908 (t'.982 ['.052 1'. 11 2 l ' . 168 l'. 2 1 6 f.24 3 "['.282 T.296 1 .304 T.29 0 r.265 '['.238 CD ' 0 213 0179 0157 0115 0132 0125 0 133 O' .O 137 O' .O 111 "0155 0165 0191 0214 o'.022 I o I O O O O I I I I o o I: I O O O O I I I ! 0 O O O o o 1 I I I. I I o o o H ft ft ft o o o o o o o o H H ft H r j r j r j rj r; M i'i M f l M |>1 0 o 1 I o o I o o o o o o o c o o o o o o o o o o o r - i n o cr- ru o ft r\j r j K I OO r— oo c: o r- c- ro -o u i C J i n Li rvi r j - o m M -o ft o cc c* o rv - i c L i ' - tc 3 o i i i 1 in u i c c- M'N 3 ru cc M IM IM rv ru —< —• ru r j A J ru K I M a — i n -o -o r— oo c - O f t i - i c r - o o o o r u O O O O O O O O O O O O O O O O O O O O O O f t f t f t f t f t . f t T j r M U . «- «. •- «- •- •- •- •- •- «. «- •- «. • •- •• •- •- •. •• •- • O O O O O O O O O O O O O O O O O O O O O O O O O O O O O N I u-'ft c- K I i n ru cc si rj ru c - r - r j r— o cc.'ft K i -o i n c- M t-i r- o r— ao s C r - o o x o c o- a:- o; N c L-I c M ft o -a ? r j rj- c ft o o ^ -c o r - - o _j i-i ru — o o o- ft ru M cr i n O' r— co o- o o- ft ru ru M cr — i n i n m o in in to. •. •. •- •- «.. •. • - •- ». •- •.. •- •- •• •- • O O O O O O O O O O O O O O O: ft: ft. ft. ft ft!—1 ft-ft: ft. ft ftl ftl ft t i l l U.. •- •- •.. •. •- •-. »s •.. •. • .. : •.. •.. • I o c tc N -O Li i-l I M : — O f t ru m cr in -JO r- co 0- o ft rj I-I c r u o MO < —• 1 I I I I I I I I ftft — ft — ftftftft I o CO I => .ii ft ^.•^ VJO U J MO Cc OJ-J K C J r - a m c o t - o ' j i - M c o o o f r o - r i i r o f j M M cr cr.. oo o- o o —i r\i n ru — ru —< cc er M o- r— m t— M er IT. C- —• JO • ^ ^ ^ ^ o o o o o o o o o c r c - c - o c o o o o o o o o c c c ^ c c c p o ^ a O O O O f t f t f t f t f t f t f t f t f t O O O O O O O O O O O C O O 3E . • • . • • • « . . • • ... • . • • « «. •. • • . - . . « • • . • • U O O C O O O O O O O O O O O O O O O O C O O O O O O 1 I I I I 1 1 1 I I I I I 1 1 I 1 1 1 1 I 1 I I I I M i n cc ft M m i— r - ru — oo i n a- ru o i n o cr c c i — er r - a- —• o o-o ^ I " O C ^ O l 1 o l ^ J U - ^ O l 1 0 C f t o - O c c f t M 3 ; ^ r a l l / l o r j ft ft ft o o o o o o O f t f t f t f t P j n j r j r j K i K i M K i r O K i K i 3C . *. *. •. *. •. ». *. *. •. ». ». ». ». », a. t . «. * . • . » . • . » 4 4 O O O O O O O O O O O O O O O O O O O O O O O O O O O 1 I 1 I I I I t N i " ^ f o f ? 3 r u M i n o M O f t e i \ i i c a r j C f t ^ r t M 5 i " r f i r i O 7 » r c , ~ t - r j - o o o c - c - o o o f « s i n i n i r c o f r u i ! 5 w r o ' ' V e s e o c c i o f f f i r t i t ^ f f f f i c e e e i c i t ' C f . ' C - N e s c - o o i - i O O O O O O O O O O O O O O O O O O O C O O O O O O O f t f t f t a • + co _1 o <_) o 1' o o o I I I O O O O O I I I I i o o O O O O O t I I I I O O O O O O O O 1 I I I I I I I 0 o 1 1 o i f l o » o i r . o 3 f t O o i o r j - i r c r o . ' s r . f - f t f j - o c i - i i / i ? a o f t r j c r o = 3 f t a o ~ f t f t ^ - C o o o r n i n o C ' c r j o - - - « O f t r u i \ ; r j f t f t o o ft ft -< ft o o o o o o o o ft ft ft ft r j rj r j r j ru t-1 t-i ro K I M M M K I 31 . • . « . • . • . » . • . » . t . * . » . ». « . ». » . » . » . » . » . • « c j o o o o o o o o o o o o o o o o o c o o o o o o o o o o o I 1 I I 1 1 I I -o 111 CO c- =0 0- f j o Li 00 M — o ft O -o r- o r- o- oo ro M r~ in — ft r- 00 CO CO ro Kl IC- Kl O 0- bl r-. JO -rr — in CC- 0 ru r - Li r- ft 0- 0 0 «o =T o- m r-T (%•- ru l-l ^7 a I-l cc' M CC M Cf in' r- ru =7 -T 1-1 rv 1 ft -JO KI' ft 0 0 O. ft ~ ' 0- t- 0C f ti- IT-ft cc -c- r - p- O' r— >c ir 0- t-1 c-M nj Ts' ro rj ru ro ru ro ru ru M KI o LO in o r - OT-4c-unxsi4ruftOOCD-inj^ • - . • • • • - 4 - . - . - 4 - . - . - . -• - . - , - . - . -. •• -, -4 -4 - . -4 -4 *-n r i r~ i i i i ft ft ft ft — ft | _ K* i f t . f t I f t I — : O O O O O O O O O C O G O O O O ' *3 • -4 -4 4 -4 -4 4 -4 -4 "4 4 "4 "4 ~ 4 '4 "4 "4 "4 '4 "4 " 4 "4 4 4 "4 CV X i ~ 2 i 2 a u " j r j I - c -o o 3i i - i i-i ro ro o o I - ?j u r i o w s a a rj j ? rj r s w JI co e r j i - i i i j -4 a JI o e " - - J f - f in -< 0 c- i c- ^ i oo io m co j i ft.'ji c ft i-i - i — . j l - o - i c co l-i Jl i) w a 30 o c o o o o o o o o o o o o c o o o o o o e o c o o o o o m • -4 "4 -4 -4 - , -4 - . -4 - . - , - . "4 " % " 4 '4 " O l| r j f t f t f t f t f t f t f t o o o o o o o o o o o o o o o o o o o o c o t -»- -o -J J l i i ro >-* o oo co -o 3- c- Jl J i it- is l-i I-' ro ro ro ro ru ru ro ro ru i-i in -a -ji ui ui co j i ru o . — ' i - i n -j*—'cr- o ui o ui >-* -o 3- is ft.ft.ft.-u is 0- fti <-.-O f t i i i o w f t o a w - j - i w o o o o s u i f t i - i o w f t f t f t o c o w *— C • I I I I I I I I C O O O O O O O G O C O O O G O O O O O G O G O G G G C G O o-4 - . -4 t . • - . '4 - . . » - • "4 - . 4 - » - ». - 4 •« « - 3 C rj r j ro ru ui i-i ro ro ro ro ru ro •— ft — •— ft o o o o o o o o o c-^ C Q o - o o o - o c C 3 C - i : r j ' 0 - o i r u i ' - 3 c - w - - f t W C > c o f t i ' i c > c c o J I o o - i rj o - j »-*-o ro ro ft J O JO — i J I ft cr- i-i co is ro —i ro CD ru —-i ro - - i i-e r~ 1 I i I I i i I • I i i i I i i I i t I f I > I I i i r i o o o o o o o o o o o o a o o o o o o o o o o o o o o o o o o *-4 4 4 4 4 . . . 4 . . . . 4 4 4 4 • 4 4 4 4 4 4 4 4 4 4 4 3 - X ft— ft O O O O O O O O O O O O O O O O O O O O O O O O O O O ftlftlo O i l 3) 3; Co C3 C B C 5 CO ' C O S i l O i O - O O i i - C O O O O i l 43 03 CC -s.' —J 1 - J f t f t O - f t O O l - l f t — £.33 03 4 3 4 3 0 1 — ftftOft.-Ul4ftft O O O 43 4) 42 J) i - i r u J 3 f t O o c v ' J i J 3 C v o r o - j * s r u f t f t J 3 c > c ^ i - w u i c co I ftftftftftftftftft I I I I t 1 I I I — > C D — j i > u i i 2 L ' i i V f t O O c o - - i c > i n i s i - i r u f t • - "• •« *• '• *• "• .-• -• -• •• -• -11 1 1 1 1 ft'ft ft I f t I f t ft I f t 1ft '.ft ' f t I f t ' f t ' f t ' f t i C o o o o o o o o o o o o o o Jl j l ui ui j l j i is _s L-I l-i P J ft c o 43 CD - j c- Jl is i-i ro ro ft o o — rj i-i r* o - i-i w r j c; s i u o r j £ D co o ro £ n r- - 4 s 3 c o o « co - i - i 0 J I o ft o o c c o c a c - i c c i i i i n i c - -—.cc c c - c a c ro x roro o o o o o o o o o o o o o o o o o o o o o o o o o o o o o 4 "4 - . "4 •» ' I -4 "4 " 4 - 4 "4 "4 "4 >4 "4 • "4 "4 "4 "4 "4 "4 "4 "4 "4 "4 "O ro ro ft*—ft ftftftooooooooooooc-oooooooo co i - i f t J 3 c - u i i J f t O JO c o - o ^ u i j i i s i s i - i u i r u r u r u r u f t f t f t r u r u r u i - i in l-i ft.-o o ft.in ru ru ru i-i cr- 43 i-i -4>—:o- t — i c - j i ru o u co 3) c w -j.ry c > i n , J l - i s ; f t j i i r i r u o i ' i j i f t r o o j l i T f t f t O a o j i i n r ^ 1 I I I I I I I o o o o o o o o o o o o o o o o o o o o o c o o o o o o o o 4 -4 "I - . 4 -4 "4 4 - • -4 4 "4 "4 "4 4 "4 "4 4 4 4 "4 4 4 - 4 - 4 2 ro ro w l-i l-i w i-i ro ro ro ro ro ro ft ft ft ft o o o o o o o o ft ft ft ft o O J O O f t f t f t O O C o c - s r o o - j ' j i w o c o C ' j i f t f t i ' j c ' c o f t W C - ' C o 14 in r j o 4a ro OD 4) in L ! is 1 4 ft 43 - 4 L-I 43 C P ru - 4 1 4 rj - 4 ft c- o in o L ! 1 1 1 t I I I [ 1 I I 1 I I I I 1 I 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4 4 4 4 « ' 4 ' 4 4 4 4 4 > ' 4 4 4 4 4 4 4 . . . . . . . . » ^ ftftOOOOOOOOOOOOOOOOOOOOOOOOOOOO ftio430 0orj3-4-4--lor'ioccCD0333LOCDa>'Ooca L - l ft O O L 4 0 C C P ' C P 4 3 r U L 4 r O ' J l C > - 4 4 3 4 3 0 C D C 0 . 0 4 3 0 C O C D C D ' r a C D 4 3 4 i w 4 ) o - j s t w 4 i c - i v r j 4 ) o r y i n — ft'aiwww^rjfuoJi'Ufjc-ft3 CJ o c r r- M-> fl> x in -< . 11 ON ON I J l 0 (a ft ri O 7? v. I 1 3 + 13 CO. CO | I 1 I 1 1 1 < 1 ft > 1 1 I 1 1 1 1 1 1 ft > c- 'Jl 4a 14 ru ft . 0 43 Co --4 0 - n i s 14 ro ft O ft •ru 14 i s Jl CP - 4 Co 43 0 c- Jl i s 14 rj 0 43 CO - 4 in 42 14 ro ft O »— rj 14 i s Jl c- - 1 Co 43 0 r* • 4 CL -4 --rt O 1 1 1 1 3> 1 1 1 1 O ft I — i f t I — ft '— I *— 1— i n — i f t I f t 0 0 0 c 0 O O •0 O 0 O 0 0 O c 0 CO ft ft O O 0 O O 0 0 C 0 c 0 O O O 0 X3 A 0 X •r. X O ft P i ro rj r u ro •— i f t ' 0 O 40 30 CD - 4 3 - Jl i s i - i ru ru ft- 0 0 ft ru L4 r~ 1 14 14 14 l-l 14 L-l P J rj ft . f t 0 43 CO 33 - 4 O in i s 1-1 P J ft ft • 0 0 ft PO 14 r - i —J CD 14 14 14 ro 0 c- ro 0- O i s -1 O ro i a 3- -4 0= 43 0 ft rj c- L T i s ro -< i s CP O CP i s rj Co 14 -4 O 14 0- CO O r j i s -n 3- CD CO 43 0 ft -! 3- 3- cn -c Ul CD O - 4 J l CP 0 0 ft* :--4 ru 43 14 Ul L H ro -CO — -J l -L4 - U i CD — -4 43 in 3- L4 CP c- U i CP C U l 43 43 03 — >- . 3 - = 43 - 4 - ft* . CP CC - 0 0 O O 0 0 c c 0 0 c O 0 O O 0 ^5 O c 0 0 O 0 0 0 0 ,2 0 O O 0 0 0 O 0 O O O c O O O c O O = - 0 O 0 rn 4 0 II 0 ii ft — O 0 0 0 0 0 0 0 O 0 O O 0 0 0 O 0 0 0 O 0 O 0 0 0 CO • * ft .ft ft 1— 0 0 0 0 O O O 0 O O O 0 0 O O O O 0 0 O O O 0 CO • * ru O 43 CO - 4 CP in j a i s 1-: 14 L-! P J ru ru r j >— ft t—- »— »— ft 1— ft ro ro ru J l J l U ! ft 0 43 CO - 4 3- CP U l 42 i s i s 14 U ' ru PU ru ru ru ft ft ft *— PU ru 1-! J i 43 3 - -* 1 0 11 ft L4 0- ft .'-4 • i s ft .43 - 4 i s ft .'43 03 -4 Ln i s cn 3 - 03 O L-l -4 ft-v - 0 ru 3- 0 0 • V J l c 12 43 Ul 1— IC- r u 03 3- 14 ft 0 CD —1 03 43 ft • j i O 1-— 0 ru - i 14 J l J-1 Jl CO o- 0- 43 14 ru CP 43 o- Jl O 0- - 4 U4 — i ru 43 43 U l CO - - 4 — 43 Ul O •0 0- -0 43 CO 0- -J »-— 43 43 ru CP -14 ru U4 i s - 4 U l ft 1 I 1 1 1 1 1 1 0 - • 1 1 1 1 1 I 1 I - < c 0 0 c O 0 0 0 0 0 0 O O 0 O O O 0 O 0 0 <=•• O 0 0 0 0- 0 0 O O 0 0 O c 0 0 O 0 0 O 0 0 O 0 0 c O 0 O 0 •=> =- O 0 ' 3 -ro ro ro ro ro rj ro ro ro ro ft — ft . f t O 0 O O 0 O 0 0 ft ft • - r - 0 Co ru ro ro >j ro ro ro ro ro ro ft ft ft ft ft 0 O 0 0 0 O 0 O — ft ft ft X 0 - 4 »— - S C7* c- 0- O 0 j i J l ro 0 CO O i s ft 43 - 4 i s ru 0 U l j i - 4 0 ro J l - 4 0 C" •Co Co •CO Co CO - 4 J i L-l — 43 - 4 J l J l ft CO C- i s ft ft- U l c- 0= O l-J •JI CO O 0 14 J i j l 0= O — " Co ro 14 14 - 4 — " CP ru J I — 43 14 Co 14 - 4 M - 4 => 43 CO 3- ft* =• 14 3- 0 - 4 - 4 Ul 14 0 c- — 0 CP ft* Jl 0 — 43 ru - 0 ru .-: 1 1 I 1 1 1 1 ! 1 I 1 1 1 I i 1 I 1 1 1 1 1 1 1 1 1 f CO t •i I I 1 1 1 I t I 1 1 t I 1 I < I 1 1 1 1 I 1 1 1 1 C3 0 O 0 0 0 0 0 0 O 0 0 O O 0 O O O O 0 0 O 0 0 O 0 O O 0 + ' O 0 O O 0 0 0 O 0 0 0 O 0 O 0 0 0 0 0 0 O 0 p 0 0 0 0 0 —• C2 X 3C 13 0 O 0 0 0 0 0 0 O 0 0 O O 0 O O O O 0 0 O 0 0 O 0 O O O O 0 O O 0 0 0 O 0 0 O O 0 O 0 0 0 0 0 0 O 0 0 0 0 0 0 O 33 CD - 4 ' -4 - I - i - 4 - 4 - 4 - 4 - 4 - 4 CD CO Oc CD 00 CD 03 CO CD 03 CD 03 Co Co 03 -v -t 43 Co - 4 - 4 :-4 - 4 - 4 CO CD CD CO CO Co CD '03 CD CO 03 CO CO CD CO 33 03 CD 03 CJ - 1 ' 00 J l cr- 0- L4 L-4 i s 14 Jl 00 43 ru 14 U l O G- 3- 0- 0- - 4 OP J l 4a J l 42 Jl 42 co 42 03 O 43 O 0- - 4 O ft 14 ru Jl 3- 3 - 03 03 in 3 - CO 03 CD 3- - — — •- •— I I I I I I I I I >- 3> *-4C>UtftL-4:U--— © O W - - 4 C * L J l f t L 4 I V ' - - " - 1 © * — . -. -. -. -, -. -. - . - -. -. - . -. -. -. - . -. - . - . -. -» -. --n I I I I 1— !-—•-— t— .-* ;o o o •© o © o o o o © o © o © © i i 2 •-: i U L-I U TJ >-' - O 4) JJ 3> - J ' C - £ U TJ - - C C >"."J L-I T c L-I - ^ r j fi c r j D 5 r j »n - j CJ w v i n -4 co CD o c o co - J c* n a L-I -o r j ft • c- L-4 o L-J L-I i — • o ro — j © co c w » w o - I P J £ I o O O O O O O o o o o o o o o o o o o o o o o o c o o o o • • • • • • • • • • • • •• - • • • - • •» -» - . • • -t - . -» -• •• -• •• -rs •->---.*— - - - • • - - - - - • o o o o o o o o o o o o o o o o o c i ' O o o o c c ; •Co C- ft L-4 O 43 CO - J C- C Ul Ul ft L-4 L-I ru rj rj t-* t— i — ru ,v M W O D I f i O C L - I V C C ' - l r-.Jl O t f i L - l f i C i . V f i f i 4D 43 © L-I —4 i\> - C r - - - 4 C o o a ' 3 W r o f i L - l u l a - C c C 0 0 3 - - 4 W O - S - f c * r j a r W O I I | I I I I < I 1 > —J C3- Ul ftL4 ru »—'© 43 CO -4 C7-L1 ft 04 ru ;© »— l\J L4 ftUl C- -4 Co o o r o . . . - . -. -. -. - . -. - . -. - . -. -. . -n r-> I I I I -3 *— '"—• »-* I*— -—-:•—•<•--• I-— '© o c © o o o o o o o o o o o o X . - . . - . - . - . - . - . •. - . - . . -. - . - . - . - . - . - . - . - . -(-I •I ft ft Ll ft ft ft L-4 L-4 rU rj O -43 43 CO -J C- Ul ft L-4 L-4 TJ •—• •© O >— IU L-4 V < LH 43 •— -0 -4 rj 43 LT 43 rj ft -4 O rj ft LT -4 —4 Co 43 O O <— • - -J -4 C- LH C- CJ C Ll -4 C- -0 TJ *--•.© CO -—43 L-4 I—-.U4 C CO Ll LD *-*•. C- O Ul C" O Ul -4 • XI n O O O O O O O O O O O O Q O O O O O O O O O O O O O O O ii • -. -. -. -. -. -. -. -. -. -. • ; -. -o • * -—•*—»— *— - — - - f c O O O O O O O O O O O O O v . - O O O O O O O O O ui 43 Co ui ft ru o 43 co - 4 -4 c- U; ui ft L 4 L 4 L 4 ru ru ro ru ru ru ru ru L-I - J ' - * 43 •—• ;'J1 Co CO 43 43 L 4 J1 © ft 43 ft O 0- ft "*0 ~* • 43 43 O IV Ul -4 "U »-* C - - - - - f t - - - * O U T L 4 r u - - - 4 L 4 - - - 4 0 O 0 - ' f t r u U i r u o r j O C 0 L 4 L 4 O O C 0 U l Ul ON / - . - ON I 1 I 1 1 • 1 I 1 I 1 1 I I 1 I o o O O O O O o © o O o O o o o o o O O o e o O o o o O (-> cr- o o o O o C O O O O O O o o O O o c. C o c o O C o c © O o ro r j ru L4 Ul r j ru rj ru r j ru -—*• 1—- I— t—» O o o o o o o o i-» r—• t~* o o ru L-4 L-4 L-4 L-4 L-4 ru ro ru ro ro ru _ i—• o o o o o o o O ^ t— 3T O Ul -4 4J 43 o O 43 43 -4 Ui Ll -— '43 -4 Ul U4 o CO c* U4 04 c- CO i — L4 CO o CO o O 43 CO ft ro o CO 0- L-4 43 c- ft *-* U4 c- 00 *— c- 43 o Ul ru 43 L4 — Co o cr -4 43 43 43 43 cr U4 43 Ul — CO ru - CO L4 Co ru C"* ru ft i4 C/I L4 o - c- .Ll -1 ro - — Ul Ll L4 -- 43 ft O Ul o Ul ro -4 L-4 •CO — o c-.—- J-t I I I 1 1 1 1 • 1 1 I 1 I l 1 1 1 1 1 I 1 I I I i 1 1 1 C.3 i I I I 1 | 1 i i i i 1 1 I I 1 1 t 1 1 i 1 I 1 1 I i 1 Co co O O o O O O O o O o o o O o o o o o o o o o o o o o o o o + -g o o O O O O O O O o o O o o o O O o o o o O O o o o o O n -t-— O a o o o o o o o o o o o o o o o o o o o O o O O O o o 1— O O O O o o O o O o o o o o o o o o o o o o o O o O o TJ o 43 CO CD -4 -4 •-4 -4 CO CO CD oo 'CO Cc 30 CO 43 Co CO 43 43 43 C0 'CO Co Co 33 00 \ -(• •— "O 43 •43 43 CO CO CD CO CO CD CO 43 43 43 43 43 43 *2 43 43 43 43 43 o —1 ru — CO ru 43 ft U! 43 o •— ru L4 ft -4 CO 43 o CO 43 O O O 43 43 43 CD 43 CD ft CO ft o cr- O O ru -i -4 43 43 43 CO o ,— ,— ru ft L4 ru L4 ft L4 L4 i — ru ru L-4 L4 ft CO -4 o L4 ft 43 CO O Co CD CD 43 CD o C- CD •— 3D O -4 -4 O o ru Ul ro -4 Ul -43 -4 43 CO 43 43 L-4 04 O V— L4 c- CO 43 43 c O Ul -4 ft •— ,TJ t— 43 c- CD ft —*• CO r-ri 1 1 1 1 1 i 1 1 1 -— > 1 1 1 1 1 1 1 1 1 :> Ul ft L 4 ru O 43 CO -4 cr- Ul ft L4 ru i—» o •—• •ru 0-1 ft Ul 0- -4 CO 43 O V ---» Ul ft L 4 ru o 43 Co -4 •o Ul ft L 4 ro o ru L 4 ft Ul a- -4 CO -0 o r -•• -TI CL Tl CL 1 1 1 1 -> 1 1 1 1 !--* '>-» .*-* :»--. It—• 1-* '© o O © © © c o © © © o o © © •© 33 >— v<* '»-» w— >-• --* It-* ;•-*• :*--• '—* •c © © © © © © © © o o © © © o © S3 IK « -"0 no ro r J ro ro *-* © © 43 CO -4 -4 o LH ft L4 ro >—» o o »-» •U L4 1- 1 L 4 L-4 L4 L-I L 4 L-4 ru ru ' C c •43 CO CO -4 re- Ul ft L-4 ru t— • _ © © ru L-J r— 1 43 ft 43 '3> -4 ft o ft Co t—» ft -4 43 t— L4 ft -4 Co 43 o >— -4 •C-- LT ft -< ro 3- -4 et- ft ro Co L 4 cr 43 L 4 L'l 43 »—» L 4 ft L1 -1 Co 43 43 o >--• -4 c- LH ft -< — 43 ru -4 04 Ul 04 i—. . f t — L 4 C C- 43 — .CO :> ro Ul ro ru CQ -4 c-* 43 ru - ui 43 L-4 — o — CC "~ , 43 ru © ru CD -4 C L4 .'CO ru L 4 Ul CO L 4 © © © o o C © O o o © O O o o O © o © © © o © © O o n c o O o © O © © © O O O o o © © © o O o © © © O o o © r-l n II il © o o o o O o o © O O o © o o © © o o © o o © o a . - t— t—k i© © © o o © o o o o o o O o o © o o © O © o O O • * © CO -4 C- c- Ul .Ul ft ft L 4 L 4 O! ru ru ro ru ro *— >-* ru ru ru ru ru Ul 01 L-4 © 43 -4 - 4 c* Ul Ui ft ft L 4 L 4 ru ru ru ru 1— t— ru ru L 4 u, C- L 4 43 43 43 »--• -4 •ru --4 L 4 43 0- ro 43 c- L 4 •o o CD CO © ;T-U .n 43 .—V ' c ru cn ru © 43 ru Ul CO >— iUl © Cr* •v CO UI ru o CO - 4 - 4 •cr- CO O . V C- i — • .—V * 00 -4 ru 04 O 43 ru 04 CO 04 -4 -4 © CO CO o Ll 43 0- © o ru o 43 CD 43 LT O o ru ru L-4 L-4 CO oi o- — -4 o- 43 O 'CO Ul 43 on o o L— i 1 1 i I l 1 1 I 1 1 I i 1 I ' c © © C © © o o c o O O o c O O o o o © o o © o o o o 0~ © o c © © O o o o o o © © © o c © © o © © © o O c c O r> • t • t • * » • t a • 1 2 t • • " * ' # • » - f ' * • t ' » ' t • » • 't * 1*1 ' t ' 1 * t • t " • - • ' t • • • t ' . • » ' tt ' 3 : ro ru ro ro ro ro ru ro ru ro >-* t-» *—» o o o o o o o o ^* o CO . ro ru ru ru ro ro ru ru ru ro © o o O o © © r - t-* o -4 ft c- -4 CC -4 -4 Ul Ul ru © co L 4 -— 43 (3-* ft 1— o 01 Ul CD © 04 U1 C0 o c —4 CO Co CD co c- Ul 04 43 -4 01 04 *— CO C- ft •— •—* L 4 c- Co O Ul Ll -4 O ro -4 CO O CO Ul -4 o — o © C? L-4 o -4 L-i Co 43 L-4 Co ru c- © 'Ul —. Ml L4 43 00 43 c- — .43 04 Ul Ul -4 -4 -4 - © -4 L 4 © 01 —' c- o Ul CO ro c* 43 • 1 1 1 I 1 I 1 l t t 1 1 1 I I 1 I 1 , 1 i 1 1 I 1 co 1 1 1 J I I t I I i 1 1 t 1 I 1 1 1 1 1 I 1 I I I 1 1 CO o O O o o O o o o o © o o O o O o © © O o o O O o o r> 4- • o O o O o o O O o o O O o © o o © o o o O o o O o o O n + X -a X o © O o o © o o o o o o © o o o o o © o o © o o o o n © © © o o o o O © © o O © O o o O o © o O o o © o © © r i CO -4 — J •-4-4 -4 -4 —4 -4 -4 CO CO CO CO -30 CO CD LS CO 30 CD CO CO 32 CD CD V.' — ; t •0 CD CO -4 -4 ~4 -4 -4 -~4 co CO CO Co co •CO Co CU Co Co 03 CO CO CO CD Co CO CO •v. • —1 ft L-4 U". >—» *— o C- -4 -4 CD o L4 ft Ul ft ft U". -4 Ul Ul ft Ul L 4 L 4 Ul ft cn 04 Ul © Ul ft O CO 43 ft U! CO CC -4 -4 CO 43 CO Co -4 -4 G- cr Ul ft CO 04 CO 1—» ru ui ft © CO O Ul 04 CO O -4 Ul CD Ul O 43 ru ru o cr- Ul ft cr- c- -4 •— U! Ul *— 43 43 -"•*• © on c- 04 o 04 -4 04 04 CO c* 04 -4 C7C CO CO t-o. Table 5 - 0.66-Clnrk-Y CLARK-Y WE=(to)6 SOLID WALLS CLARK-Y RE = '(10)lS 4 0XLS+P TSUSL ALF CL CD CMO CMC/4 - lo ' . - 0'. '13 7 0 .0304 -0'.196 -0 .0843 -0'.319 0 .0270 -0'.174 -0.0927 -s'. -()'. 198 0 .0211 - O ' . l 47 -0.0959 -7'. -0 .085 0 .0226 -O'. 120 -0.0977 -6'. O'. 0 28 0 .0213 -O'. 0 9? -0.0986 -5'. (>'. 145 0 .0209 -d'.063 -0.0999 -4'. 0'.262 0 .0209 -o'.035 -0 .10 11 -3'. 0'.379 0 .0216 -0'.005 -0.1016 — 2' o'. 196 Kl .0227 0.025 -0 .10 11 - r " 0'.599 0 .0215 0.053 -0.0999 0'. 0'.697 0 .0266 o'.oao -0.0980 r . 0'.807 0 .0301 O ' . l OH -0.0983 2'. 0'.931 0 .0351 0'. l i t -0.0974 3'. T.031 0 .0106 0 . 169 -0.0910 4'. 1 .134 0 .0169 O'. 196 -0.0932 5'. T.233 0 .0534 0.224 -0.0905 6'. 1.339 0 .0602 o'.250 -0.0918 7'. T.4 26 0 .0692 0.276 -0,0879 fi'. 1'.529 0 .0791 0.298 -0.0911 9'. T.603 0 .0900 0.320 -0.0380 10'. T.657 0 .1026 0'.335 -0.0861 11'. "r.692 0 .1201 0.3-12 -0.0879 12'. T.730 0 .1391 0.319 -0.0907 13'. T.77 0 0 .15^5 0.352 -0.0974 11'. l'.78 6 0 .1806 0.355 -0.0932 15'. l'.826 0 .2010 0.357 -0.1070 16'. l'.837 0 .2267 0.359 - 0 . 1084 17'. 1 '.810 0 .2554 0.355 -0,1132 IB'. it'.846 0 .2893 0.316 -0.1251 19'. T.837 0 .3294 0.335 -0.1361 20'. l',S56 0 .3729 0.325 -0.1531 ALF CL CO CMO CMC/4 -10'. -0.417 0'.0289 -0.195 -0,0070 -9', -0'.313 0'.0252 -0.170 -0 ,0386 -s'. -0.209 0'.0?26 -0.144 -0,0089 -7'. -0'.107 O'.02o7 -0.113 -0',0399 -6'. -0'.006 O'.O 196 -0'.093 -0.0909 -5'. O'. 095 O'. 0 199 -0.067 -0.0913 - 4 ' 0. 199 0'.0?.08 -0.040 -0.0916 - 3 ' 0'. 30 i 0'.0218 - o ' . o n -0.0923 -2' . 0'.399 0'.0234 0'.0 12 -0.0918 - l ' . 0'.491 0'.0259 0'.036 -0,0912 O' . 0'.581 0'.0289 0.061 -0.0902 i ' . 0'.677 0'.0331 0.006 -0.0904 2' . 0'.789 0'.0386 0.115 -0.0904 3' . 0'.885 0'. 0 4 5 0 0'. 110 -0 . 0904 4' . 0'.981 O'. 0508 0.165 -0.0902 5' . l'.075 0'.0575 0.190 -0.0901 • 6 . l ' . 166 . T.258 0'. 0 61 3 o'.211 •-0,0900 7 0'. 0 7 1 8 0'.237 -0.0905 8 . it'.346 O'. 0316 0.259 -0.0909 9 . T.126 0'.0912 0'.280 -0.0901 10 l' , 489 O'. 1 025 0.297 -0.0396 1 1 . r.537 0'. 1 110 0.312 -0.0866 12 . l'. 86 0'. 1269 0'.324 -0,0869 13 . T.626 O'. 1436 0'.33t -0.0900 i4 . 1.663 O ' . l 6 12 0.336 -0.0945 15 T.690 O'. 1783 0.339 -0.0978 16 . T.698 0'. 1933 0'.337 -0.1017 17 i',693 0'.2203 0.332 -0.1063 18 . T.676 0'.2471 0'.318 -0.1163 CLARK-Y RE='(10)6 40%3S+P TSUSL ALF CL CD CMO CMC/4 -10'. -o'.ni 0'.0287 -0 .195 -0.0863 -9'. -0.307 O'. 0252 -0 .170 -0.0894 • -8'. -0'.203 0'.02?5 -0 .144 -0,0901 -7'. -0.101 0'. 0207 -0 .119 -0 .0915 -6'. -0.002 0'.0198 -0 .093 -0.0922 -5 ' . 0'. 1 0 0 0'.0199 -0 .067 -0.0928 -4'. 0'.202 O'. 0207 -0 .040 -0 .0929 -3'. 0 .303 0'.0219 -0 .011 -0.0933 -2'. O'.l 03 0'.0230 0 .013 -0,0929 - i ' . 0.493 0'.0255 0 '.037 -0 .0926 0'. 0'.531 0'.0285 0 '. 0 6 2 -0.0909 1'. 0'.676 0'.0322 0 .087 -0.0917 2'. 0'.7S8 0'.0378 0 .115 -0 .0923 3'. o',878 0'.04 31 0 '.111 -0.0907 4'. 0'.963 0'.0489 0 .161 -0.0912 5'. i'.059 0'.0553 0 .188 -0 .0909 6'. l ' . 150 0'.06?'l 0 .212 -0.0908 7'. i'.239 0'.07t0 0 .231 -0.0920 8'. T.324 0'. 0 3 0 2 0 '.256 -0 .0919 < 1.393 O'. 0902 0 .276 -0,0397 10'. T.427 0'.0932 0 .238 -0.0861 l l ' . l' .483 0'.1097 0 .30? -0 .0865 12'. l ' .535 0'.1237 0 .313 -0.0892 13'. l'.58l) O'.l'IOl 0 .320 -0.0934 14'. 1.620 O'. 1533 0 .325 -0.0988 15'. 1 '.619 0'. 1779 0 .329 -0 .1026 16'. 1 '.661 0'. 1976 0 .328 -0 .1066 17'. T.665 0'.22o'l 0 .322 -0.1139 18'. T.656 0'.2489 0 '.295 -0.1390 I 1 1 1 1 I 1 I i t ft— >CO - J c- Ul ft L-I ru O 43 Co - J O Ul ft L 4 ru •— ru L 4 •— Ul C- - 4 •Co 43 © ••n - _ :~ !*—* •_ 1— :_ '_ i — :_ 'C © c © - © © © © © © 1 I ' © 1 I ft Ul Ul Ul LO L 4 r j ru _ i C •D CO - 4 •t> 'Ul L 4 L 4 ru © © _ ru L 4 o r~ Cf C L 4 Ul ft ft— •45 Ul _ cr* 43 _ L 4 ft c- - 4 -4 - 4 Co CO 43 © © © © •CD 30 43 43 © er- rj-. = c- Co — c ru o - Co - 43 L-4 - 43 L 4 — 43 43 L 4 - c- - 4 43 CO •—• Ul o o O o o o O © o o o o © C O o © O o o O O o o © © o © o ru _ i—• ft-_ ft— o o o o o o O © o O o © © © O © o O © o © O . i o •— CO tr- Ul ru © 43 Co •Co - 4 rr- Ul Ul ft ft L-4 ru ru ru ru *— -— _ _ _ ru ru ru •-* .CO -J • f t ru o CO 43 _ .L-4 •Ul Co ru o © _n a c> U4 • 43 CO - 4 CD 43 •— ; ft Co o o -o -o ru Ul CD -4 ft— -~ ru t> — ru 43 *•* 43 c- -4 c- L-I 43 — Ul cr- Ul U4 o o o o O o c O O o O o o = o © © O © O O O 1 O 1 © 1 © 1 c 1 © 1 © 1 © n • • t " • t ' t • • * * ' t ' • -t " • ' i • t ' t - t • t ' • -ft ' ft ' t ' ft " ft ' • '' ft ' « ' t • • ' * ' jC r j ru L-i U4 L-4 L-4 Ul |-J ru ru ru ru ru _ »— _ _ O o © o o © O o _ ft— _ _ o - j 43 ft— *-* _ o -o CO -4 Ul Ll _ CO ft _ CO c- Ul _ _ U4 c- CO _ ul cr- CO CO - J — O -J. ft CO -0 C- -— ru ru o -4 • f t _ G- •Co Ul 43 Ul ru - 4 ru - 4 ru - 4 -43 1 I 1 1 t 1 1 1 I I i r 1 I I 1 I 1 1 I I t 1 l 1 i 1 I 1 o O O o O o o o o o o o o o O o © o o O o o © o © o o © © r> _ o O o O o o o o o o o o o o o o © © © o © O o o © © o — i£ n O CO Co CO Co CO - 4 •Co CO Co CO CO CO CO Co CO CO CO CD Co 43 43 CO cr. CO CO CD CC L 4 c- 43 -J c*- -—- o •43 L-4 ft - 4 - 4 - 4 CO •Co - 4 CO 43 CO 43 43 O O 43 Co CO -*4 - 4 3 -ft o ft L 4 — CO ru 43 C- -4 ft-O -4 -4 0 CO L 4 ru Ul Ul 43 CO ru 43 -4 ru L-4 L 4 o — •—•—•—•—•-•- i 1 i i i i i i r > C-UlftL - 4 r u * — • © • 4 3 C 0 - - 4 C - U l f t L 4 r U ' — Oft— r u L 4 f t U 1 0 - 4 C 0 4 3 © ' r -ft -ft -ft -ft -ft -ft -ft -ft - -ft -ft -ft -ft -ft -ft -ft 'ft -ft -ft -ft -ft -ft -ft - , •. -1-1 I I I I -—.-—;-—:-—--•.— :-—-—:-—:-—:*-*.© © © © © © © © © © © © © © © © •— ru "-j L-I ru ru ru ru •—• — o 43 -o co -4 to LH ft L-I L-I ru •— © © -— ru L-I r~ C > C r J O » ? i . J S U f O r j i : L , l - 4 - 4 0 - J ) o o - - - - - 4 - 4 ' - - - C --4*—.U4 -4 43-4U1 O O U 4 C O 43*— L-4 43 TU ft— .0*- -4 U4.C- ft -4 IU ft— -4 C* 0 © 0 © 0 0 © 0 © 0 © 0 0 0 0 0 0 © © © 0 0 © © © 0 © • • • •• ••• '• • •• *• • • •• -• -n ft— ft— . 0 © 0 © © 0 0 0 0 © © 0 © © 0 0 0 © © © 0 © 0 © © Q r u © c r - - 4 C - u i u i f t f t L - 4 L 4 L 4 r u r u r \ j r u r u - - - — •—•— ruru Ul C- 43 C- --T -4 -— Ul © -4 ,n ft- , 43 CO C- ft>-.C-4C-UlUlU10 3-— Ll COOftft— -4ftU4-— ftft— ft— 43 - 4 0 - — ft— © U 4 f t O C - r u U l - C t O - - 4 U l I I I I I I I I © o c © o o o o © o o © o o o o o © o © o © o © o © © n • •« - « •- - t •• -• - t -ft -• •• •« » -• -ft ft -• •« •• •• ft , . -, , -, -, • I ru ru ru ru ru ru ru ru ru ru ru •—•—-—•— o o o o o © © © r— »— -* — © U 4 U l - - 4 C O - - 4-^C vUlftruO - C D C>ftrU43--4ftru© U 4 ' U " . - 4 O U 4 U l C 0 U1-4-— © C O L 1 - 4 0-U1 3043 4j-4 4 - — - 4 C ) L ' l - - - t > C 3 ' » r i C o l ^ 1 0 C - - - ' I I I I I I I I I I I I I I I I I I I I I I I I 1 I I OOOOOOOOOOOOOOO OOOOOOOOO o OOO .............. ft. ........ ft ft. _^ o o o o o o o o o o o o o o o o o o o o o o o o o o o r i C O - 4 - 4 C O - C - C " - 4 — 4 . - -4' - -4COCOCOCOCOCOCDCaco00COCOCOC0Coa-*. ft- a L4 CO Ul L4 Ul ft- L4 C CO O ft- L4 L4, ft ft Ul Ul -4 Ul ft I V Ul U4 L4 TV ft C O L ^ I C - - C f t U 4 C O - - f t C > 4 a 4 3 U 4 f t 0 4 3 f t — L - 4 C x - - 4 r u - - 4 3 r u i — Ul cac> I • ~ f t - f t _ - . f t - . _ f t _ _ . f t _ _ I 1 I I 1 T I I I ft- •> co - 4 tr- L T ft L 4 ru •— o • 43 co - 4 o ui ft L 4 ru .—-o -— ru ui ft u; c- - j co 43 o r— ft -ft "ft -ft -ft - - . -. - . -, -, •. -. - , -. - . -, •, -. .^ -. - . -, - . - . - T | I I I I ** :-— !-— :-— >* l _ !ft- . _ _ ; _ ! _ : _ : _ l _ ;© © © © © © o © © © © © © © © . -« -. -. -. -. -. -. -. -. -. -. -. -, •. -. -. -. •• -. -. -. -. -. •• •» -. -<-. Ul C- C- O CT- Ul Ul ft ft L-I L-4 r j ft- © -0 CO - 4 O Ul ft ft L 4 ru •— i C O •— L-4 ft r~ CO ft- . r U L 4 _ C 0 L 4 O f t 4 3 r u f t v T C ^ - - 4 - - 4 C 0 - - 4 C 0 4 3 O O O O O 4 3 4 3 O e ftft-4rurjft43Ui43© ft—:ru ui ru L4 -4 f t -4 -—.ru © L-4 L-4 ru ru ca c- L4 - J 0 © © 0 © © © © © © © 0 0 © © © © © 0 0 © © C © © © 0 0 0 • -. -. -« -. -. •. •. -, , -, -, -, -. - , -. -, , -. -. •(-, ruru-— -—_.-— _ _ © © © © © © © © © © © © - : . - o © © © © o © © o L4 © co o Ul L4 ft- © 43 Co - 4 c- cr- ui ft ft L4 L-I ru ru ru ru «-— »— *— *— ru ru ru ru C> C -4 '© ft CO - 4 Ul Ul C- Co © L-l -4 '•— :>C> © C- ft ft— ' © 43 CD CO 43 -— • ft CO I I I I I I I I © © © © © 0 © © © © © 0 0 © 0 © © 0 © © C © © © 0 © 0 © © 0 • *» • ft * t ' t ' t * t - f - f -ft ' t " t -» ' 1 "ft -% 'tl ' t *t "ft -ft -ft " t - » -ft -ft '• *• " 3 w u 4 L 4 L - 4 U 4 U 4 U 4 u 4 r u r u r u r u r u » — - — f t — * — © © o © o o © o - — - — - — * — © ©•— rurururu>— o 43 -4 LO ui •— coc-ft»-coc-uift-ft-uic-co-— ftC-43 OL4f t - C-U1-— . f t f t O U I f t L - 4 - — . - 4 L T O U l C O r U C O f t , " U C O f t 4 3 f t O U i r U ] t 1 1 I I 1 1 1 I I I 1 1 I 1 1 1 1 1 1 1 1 1 1 1 I I 1 0 0 © 0 0 0 O O 0 O O O 0 O O O O 0 0 0 O 0 © 0 © O O O O O .« TC ft- _ O O 0 © CT O 0 O O O O O © O O © © © O 0 © O © © © © O O ft— . '© O 43 43 Co 30 CO CC CO Co CO CO CO CO CO CD CO Cc 43 43 43 43 •43 CO CO CO CO CD •v 0 ft 43 Ul -— Co ft L 4 0 - 43 43 43 43 CO 43 43 CD •CD O O ft— © 0 43 - 4 CD cr 'Ul ft ft c- W CO CO L 4 ui ru U l ft 43 CO Ui 43 O c- CO © 0 C- U4 ft Ul 43 1 1 1 1 1 1 1 1 1 _ > Co - 4 0 - Ul ft L-I ru — O ' 4 3 CO --4 O Ul ft L 4 ru ft—•. 0 ru L-I . f t Ul 0 - --4 CO 43 © 1— I I I I _ ! _ _ • _ • _ : _ _ ._;_._:_•_;_ ^ 0 0 0 ^ 0 0 c ^ c 0 (— L-I ft ft ft ft ft ft ft L 4 U4 rj ft- ft-'© 43 CO -J tr- Ul ft L-I L-4 rj ft- © © _ r j L-I r~ L 4 ' © -Ul - 4 - 4 LH ru O C~ ru C- 43 ft— L 4 ft 0- - 4 C- - 4 CO 43 O © © © CC CO CO 43 43 ft Ul ft _.ru L 4 © ru ft-.v— U4 C> Ul 43 L 4 ft CO - 4 43 - 4 TU Ul C- - 4 CO CC 43 U4 © 0 0 © 0 © C O © 0 © 0 © 0 © 0 © © 0 © 0 0 © © © © © 0 © • -ft -. - , •„ -. -. -, -, -, -, •, -, ., ., ., -, ., ., -"-j »— ft— *~* *— ft—'ft— o © © © © © © © © © © © © © © © © © © © © © © C d 43 - 4 ft ur ft— © -c co - 4 - 4 cr* ui ui ft ft' u* L-i ru ru ru ru *— ft— *— *— »— ru ru ru Cr- >—14) L-l CO Ul L 4 Ul - 4 © L 4 - 4 ru C- ft-.cr- ru CO ft "u © t3 CD - 4 - 4 CO •— ft Co ftlU1COft<^LnL4_--lftftftrUCOIU-OL4_*X>C^--l.'Uru--4*-JOOO'--C . C . 0 . C 0 © 0 © 0 © O C © © © O Q © C © C O O © C © 6 © © n t t ft - » « - • * • * . *t 'ft •% -ft •» -ft - f -ft -% -ft - f ., -% - t - t -ft "t - 2 ru ru ru ui ui ui ui ru ru ru ru ru ru ft- •— •— _ © o © o © © © © _ _ _ _ o ft-4 43 O O O O 4 3 C 0 C - ' U l U I O C 0 C > f t f t - 4 3 C - f t f t - - * L 4 C r C 0 ' — UIC - 4 3 co ft ru ru ui ui •— ru — -4 o © ce co ui -* 43 o ui © — c- ru - 4 L-4 co ui © 1 1 1 « -i 1 1 1 1 i 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 t 1 1 1 o o o © o o o a o o o o o o © o o © o o o o o o o o o o © o • — © o o © o © o o © o o o o o © o o o o O O O O © © O O O O 0043CDCD-4- -4 -4CoCOCOCOCDCOCO(33.COCOC0043430COCOCOCOCCCO 0 » C » r U - * 4 U 4 - a C ^ - 0 " - J i O - C B O - 4 3 0 S 1 1 1 f 1 1 1 1 I > c- LT1 is L-J ru ft •o 40 03 - 4 rC- LT, 4 S L 4 ru ft o ft ru 1.4 i s Jl o 00 43 © r* o » -fe '• - • -'• -'• " '• " '• " ' • -fe " '• -'• -'. - « - 'fe - • '• -'• -'• 'fe » ' •» - - n 1 1 1 i > ft ft ft ft i f t - f t Ift - f t ; — ft o' © © © © © © © © © © © © © 33 • * • '• - • " • - • - • -• « '• • - • • " • " • - • - • - * " • - • - • • • ' • - • - • - • - c. ro L-J L-l L-J L-l 1 4 ru ru ft : f t 0 - 0 43 ro -•4 -c- J i is L 4 rj rj ft © © ft r j L-I r~. 1 L i is C- - 1 i s © 03 is -0 L J ~4 43 ru L 4 LT c- 0 - -4 43 43 o ft ft - 4 -4 - 4 •O -< ui ts —J L-l 1 4 ru 43 03 © -O. ru L> ru 03 C ru — 03 © o- ru L 4 43 — * * .00 33 o © c O O © o © O © O o © © © © © © o © © O O © o n n II ft. ft ft o © o o O © O © © ' o o o © O O O © © © O O o © o a /—»• 1 4 ft o 03 - 4 c- C- 'Jl is i s L 4 L 4 L-l L 4 ru r j ru ft ft ft ft ft ft ft ru ru »-» ft rj © 03 43 G- is J l ru o o> L 4 © - 4 •IS ft. 43 - 4 i — J I is Jl cr- 03 ft 1X2 © *"* CP — Ul - ft ru 43 J l ul 43 01 U l CO Jl G- L 4 -4 43 r-j I -* CC J l oc .'03 - 4 43 -—-3-© o © © c o o © o ft © © © © © O C i © i © 1 © 1 © I © 1 © I © I O o 03 • ' • - fe ' • ' * " i - fe - t • - • ' 't ' • • • • « ' • ' •t - t - t ' t ' 3: © ru r j ru rj ru ru r j r j ru ru ft ft ft ft o O o o o o o o ft ft ft o >• is - 4 CO •o 03 53 is ui © 03 cr- i s ru i - 0 - is ru © L-l J l 03 © 1 4 Jl 03 CO c- •j". c- =• -o ~ • — G- o 43 40 - 4 - o G- 43 -o ru -4 ru -4 ru CO -CO 4. i 1 I i r I I I I 1 1 I t t ! I 1 1 i t < 1 1 1 i I ! T3 o o o o o o o o o o o o o © © © © © o o o © o o © o © n —f o o o © o © o o © o o o © © © © o © © © © © o © © © © o CO o •03 03 33 -1 - J - J -4 03 03 03 03 CO CC 03 •CO 03 03 03 03 03 03 03 03 00 03 s . L-J '03 L-l ft is ft J l •03 '03 o L 4 L 4 J l 'Jl Jl Jl •Jl G- 3- -4 £3- c- J l J l is 42 L-4 is CO ft L-J r j ru C- •03 CO is o ru ft ru Jl 1 4 © ru 14 1 4 - 4 ft 43 1 4 © © ft ru Jl r~ I 1 1 I 1 1 1 1 1 1 ft 3> -4 e- J l i s L4 ru © O CO -4 C- J l i s L4 ru 0 • f t ru L-l 42 J l CP -4 •CO 43 O -n • f t ft , f t . f t • f t i ft • f t . . f t ft I f t © © © . ft ft © 0 I © 1 I © 1 © •• « • -• " 0 - » - • -* -• '* - • -* * -* -• - • " - -» -• - • -• • -• - * » • 0 i s L i J l 'Jl J I 42 42 L-l L-l ru rj ft © -0 CO —4 CP- LH 42 L4 L-l ru ft © © ft ru L4 1— 43 LI J l L4 —- •-J L4 43 is CD © r j is J l 0- - 4 cr- CD 43 © 0 ft ft CO •CO CD 43 0- ft O ru C- J l ru C- •—• 43 G- © s © - 4 - CP 43 J l CO ' C - 42 -4 © © O 0 O c © O O © © © O © 0 0 © O 0 O © © © 0 0 O 0 © ft ft ft © © © 0 © 0 O © 0 0 0 © © O O 0 © © 0 O 0 © n 03 c- 'Jl ui rj © •0 CO -4 c- C- a i is is 42 14 L-4 PJ ru ru ft ft ft ft ft ru ru ru -4 00 ft 0- ft- : -J -4 -4 •CO -4 42 33 -4 ru -4 PU •Co J I pj 43 CO CD 03 43 ft; L4 -4 Cl- JJ L.1 .30 is 43 ft 0 - 43 - 1 O L4 42 L-J ru is ru ru ft 42 -4 CP L4 14 is © CO ru 1 I 1 I 1 1 f 1 0 © © © © © 0 © © © © © © © 0 O © O © © © © © © © © © O © f3 t - • - • * t 1 • • ' • ' ' • " • ' « • • - • • < ' 'fe ' 'fe ' B ' fe ' • ' 'fe " • " • ' s ' fe ' ru r j J! L-J LI L-J L4 ru ru ru ru r j ft ft ft 0 0 O 0 O O O ft ft ft ft O - 4 43 ft ft ft ft O 43 CO -4 J l j i ft 03 CP i s ft Co G- is ft © 14 •0- '.33 ft 14 QP CO cn -4 ft 0- -4 L4 CD CO L i O L4 14 ru 43 — © G- co 42 0 c- 43 42 O cr* " • G-ru CO 1 1 1 I t I 1 ! t t 1 1 t I 1 1 1 1 1 1 t t I 1 1 1 t 1 1 © 0 O O O O © © © O O 0 © O © O O 0 O © © © © © © © © 0 © Cl <- ft ft © © © O O O © © © 0 O 0 0 O 0 O 0 0 O © © © O © © © n i © © 43 43 43 CO CD CD 43 43 43 43 -0 SO CD CD CO 3) 03 CD CD CD 03 'CO CD Co CO CO -p. c- ru ft Co ft ft c- Jl ->l O O 0 ru CD -4 CO CO 03 CO CO 43 CO 03 -4 - 4 -4 G- Ul 0 42 43 ru --4 is 42 43 4] -4 © ft CP ft ft -4 ft -4 ft ru CO 14 43 -SI '43 43 ft 14 © 1 1 1 1 I 1 1 1 1 ft > co -4 c- LT. i s L4 ru ft O '43 CO -41 0 - Jl 42 L4 ru ft O ft ru 14 42 L i CP -4 Co 43 © r -• -'• ' •• -'• ' '• - • " • • -'• -'1 -'. - • '• - • -'• -'» '• " • - • " '• " '• • " • -'• ' » . - •n 1 1 1 ] ft - f t i ft ft t f t I f t ft ft I f t I f t i ft • ft | f t ; f t ' © © © © © C © ©' O O © © © © © • - • - • -» - • - • -'• -'* - • ' « - • - • " • '« " • -• - • - • • * • - • " • ' • - • -fe • " • - n LI L i re- L i J l J I i i 42 L4 L4 r j ft © 43 CO -4 •CP Jl 42 is PJ ft ' f t © © ft L-l i s 1 — © 43 ft ft 43 c- ft -I L4 CD © rj is LH -4 CO -4 Co 43 a 43 43 © © 43 43 O © © Jl ,ru 42 43 CO 14 © 43 43 - L4 0- O c- - © J l c- ru — j 43 © ru © © © © © © © O O © O 0 0 O © O 0 O © © 0 © © O © 0 O © 0 r^ ru ru O O O © © © O O © O O 0 0 0 © © © © O O © a 1— © CO O i ; w ft © 43 CD -4 G* C- Jl 42 42 L-l L4 P J ru ru ft ft ft PU ru ru .3 0 c L4 G- ft ,'Jl L4 42 J l Jl 33 ft .Jl CD L-l CD PJ 43 J J © O •0 43 43 — is 03 O 0- L4 © 0 is 1—- 03 43 ft CO 43 ft O LI PJ O -4 ft © - 4 43 -1 •OS ft -4 43 CC J l i-3 •BJ cr a n f i n > 33 1 T.° - *-* !-—. i t -* 'Ift* lift* 0 C O O O O O O 0 O • " * ' », " • " • " « - t. • • - • " • - • - « « - * - . " • " • • * •• • * n X L-i L*i ra O O -» rj O rj L-i r- 1 c L-l 0 C. L-4 0 L-J O ft-L-J j i c- LT t > •-0 0 O Co -4 -si -< LH LT1 -4 LM c LH W r j -0 ro —J CD CD a. Ul CD 03 -4 0 O O 0 0 O O 0 0 0 O O 0 O 0 O 0 O 0 0 0 O O O O O O n 11 .—» *-* 1—>- 0 O O 0 0 0 O O 0 O 0 O 0 O 0 0 0 O O c- O O ZD 1—11 0 •c 0 0 -4 t> Ul 4- L^ I ru ro rv ru *• • •—*- 1—• ro PO ro c> X; c* C3 . Ift*. • C- k*l i—*- L*J ZD v.n L-J i 0 -4 •**-! ' 0 0 L-J c> 0 W 0 un CO 1= UT ru O- 1—*• w — — L-J O - i O 0 M 03 CO + T3 CO c co r -© ft © ft © © © © © ft c © © O © © © © © © © © © © c - c • © Ci —I • -, - 0 • • " • - fe ' 9 ' • -fe ' fe - • ' fe ' '» - • -« - fe ' • ' fe " fe ' fe " » ' • ' • ' C £ 0 ro ro rj rj ro ro ro rj ro ro rj ft ft ft »— O 0 © © O 0 0 O ft ft ft .— O S 4 CD 0- Oj 4- C O - 4 G - 4 2 P 0 0 03 4 2 r— 4 ! O 4 2 ft ft L - l C P C D ft J4 C P 03 C-3 P J j i C O 4 3 c- 4 3 - 1 L 1 - 4 43 03 - 4 ' — — - 4 © ul G - O 42 0 'Jl © — O — C 3 1 1 1 1 1 1 I 1 1 » I 1 J 1 1 t 1 1 I I 1 C I I X © © 0 O 0 O 0 O O 0 O © © © O © © © O O O 0 O O O © O O • 3C - i 0 0 0 © 0 © 0 © © © © O © © © O 0 O O O O 0 O O © © © n 0 3 43 CD C D C O - 4 - 4 -0. 03 C D 03 C O C O CD C O CO C D C D 03 C O C D 03 C D 03 C O •CO Co C O c Jl Jl - 4 i s 0 © L 4 ru 42 Jl J l ;> G - 0- - 4 —J •03 Co - 4 - 4 - 4 G - •Jl Jl L 4 i s C O L 4 4 3 ru 0 3 0 . 1 4 O 4 3 1 4 © 4 2 0 4 3 •12 a i ru ft- 4 3 4 2 O O J l L-4 1/1 r-Table 6. Windtunnel balance r e s u l t s 0.17-0015 RL.-.0..3(l0)b SOLID WALLS NACA-0015 a i r f o i l s 0015 RE~o'.3(10)6 40LS+P TSUSL ALF C L - 4 . -0'.352 -3'. -0 .252 -2'. -0'. 161 - i ' . -0'. 076 o'. 0 .001 i". 0.'.077 2'. 0'. 1 6 1 $ m 0'.253 0'.352 5. • 0'.4 7 0 6'. 0 ' .59« 7. 0.729 O ' O'.POl *»'" 0'. fi 5 4 10'. 0'.9 05 11'. 0'.95fl 12'. 1', 0 0 3 13'. l'.0 3'! 14'. T.04 6 15'. l'.049 16'. C»'.714 17'. ()'.690 1?'. 0 '.605 19'. 0 ' . 5 O 2 20'. 0'.5R2 CD 0'.0210 O'.O 176 O'.OIS'I O'.O 135 0'.01?6 0'.M?2 O'.O 124 O'.O 134 O'.O 150 0.0170 0'. 0202 0'.0239 0',0?65 0'. 0297 O'.O 336 o'.0105 o',044 1 0". 0511 0.0613 0.0767 0'.2?46 o'.2473 0.2565 0'.2692 0'.2fl'l2 CH0 -o'. 100 -0'.075 -0.051 -0.026 -0.002 0.022 0'. 0 a 6 0.07 t 0'.098 0.125 O'. 151 0.175 0'. 198 0'.219 o',24 0 0 -.257 0'.274 0.286 0.288 0.281 o". 122 o'. 109 O'. 099 0'.097 o'.097 -0 . -0 , 0 . C/4 0 142 0.0139 0.0115 0,0073 0021 0030 0.0071, 0.0O93' 0.0 122 0.0107 0.0 056 -0.0013 0.0042 0.0126 0.0218 0.0271 0.0338 0.0388 0.0378 0.0304 -0 ' . 0597 -0.0713 -0.0600 -0.0608 -0.0592 0015 RE=0.3(10)6 40SS+P TSUSL ALF CL -4 . -0.34 7 -3 .. -0'.250 .*) . -0 ' . 153 -1 . -0 .075 0 . -o'.ooi i . 0'.076 2 . 0'. 157 _ . 0',24 7 4 . 0'.543 5 . 0.4 62 6 . 0'.592 ' 7 . 0'.716 6 . (i',789 9 . 0.8 39 10' 0'.339 11' . 0.939 12' . 0.935 13' . l ' . 017 14' . T.030 15' . 1 .033 16' o'.G92 17' . 0'.633 18' . 0',572 19' . 0.573 20' 0'.573 CO 0'.0202 O'.O 172 O'.O 150 O'.O 139 0'.01'26 O'.O 123 0.0127 0'.0134 O'.OISO 0'.0173 0'.02()9 0.024 8 0'.0230 0'.0312 ' 0352 O'.04o2 0'. 0460 ' 0525 0625 0773 2217. 0'.24(i3 0.2473 0'.2603 0'.2744 0 CMO -0.0 99 -0.075 -0'.049 -0.024 -0.00 I 0.0 22 0.046 0.071 0.096 0.123 O'. 148 0.172 0.19 4 0.215 o'.235 0'.254 0.271 0.283 0'.286 0.279 0.120 0.105 0 .094 0.094 0.096 CMC/4 -0.0146 -0 .0 140 -0.0107 -0.0058 -0 ,0 0 06 0.0 0 35 0.0077 0.0105 0.0120 0,0108 0.0043 -0,0013 0.0033 0.0125 0.0206 0.0285 0.0342 0.039t 0.0395 0.0315 0563 0604 0567 0580 0576 ALF - 4 ' -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 CL -0.353 ~0.?5i -0' . 159 -()'. 075 0'. 0 0 0 C)'.075 0'. 1 5 7 (»'. 24 6 o',34 3 0'.454 o'.580 0'. 709 0'.735 0 .838 0'. 3 P. 6 0.937 0'.98) 1.013 i'.0?5 1'.029 0.653 0'.592 0'.574 0.568 0'. 5 7 0 CD O'.02ll O'.Ol 83 O'.0l60 0.0149 0'.0135 O'.O 135 O'.O 139 ()'.0147 O'.O 163 0.0185 0'.0217 O'. 0259 0'.0285 0'.0321 O'.O 361 ,04y9 ,0464 .0531 ,0629 ,0780 ,2239 ,2373 .2492 ,2598 0.2731 CMO - 0'. 1 0 0 -0.074 - 0 .0 4 9 -0.025 -o'.ooi 0'.022 0 . 0 4 6 0.071 0'.0 96 O'. 123 0.147 O'.l 72 o'.l 94 0'.?15 0.234 o'.253 0,269 0'.231 0'.23 4 0.277 0. 1 06 0.095 0.0 94 0'- 0 9 4 0,095 -0 -0 -0 -0 0 CMC/4 -0 .0137 0 l ? 5 0101 0063 0 0 06 0037 0.0078 0.0108 0.0123 0.0 122 0.0064 0 .0000 0.0038 0 122 0200 0276 0337 0382 0386 0309 0563 0593 0574 056 7 0580 0 0 0 0 0 0 0 -0 -0 -0 -0 -0 T a b l e 6 - 0.17-NACA-0015 0 015 R F - O . 3 ( 1 0 ) 6 50LS+P TSUSL 0015 rHT = 0.3(10)6 70LS+P TSUSL AI.F C l . C O C O -4 ' . -0.344 O'. 0 1 O 5 -0 .097 -3 . -0.245 O'. 016'! -0'.073 • • c * ' -0.15/1 0 '.01/1 zi -0.0 US -il -0.071 O'.O 129 -0.023 0'. 0.005 0'. 0 1 1 6 o'.ooo 1". O'. 0 7 9 0.0112 0.023 0'. ICO 0 0 1 1 5 0.047 z'. 0.250 O'.O 125 0'.072 4'. 0.34 9 0 . 0 1 3 8 o'.o^a 5'. 0'. '1 6 0 0'. 0 1 6 5 0'. 123 6 ' . 0.5 P. 9 O'. 0 1 9 7 0.1/18 7. 0.711 0 . 0 2 3 4 0'. 1 72 e.'f 0.735 0 . 0 2 6 1 0 . 1 9 2 9 . 0.834 o'.02<>5 0 . 2 1 3 10'. 0.881 0'.0333 0'.233 1 t'. 0'.931 0 . 0 3 8 4 0 . 2 5 1 12'. 0>76 0.0440 0 . 2 6 7 13'. {'.0 05 0.0506 0 . 2 7 9 14'. 1 '.016 0'. 0 6 1 0 0.200 15'. 1'. 0 1 9 0'.0766 0 . 2 7 3 16'. 0.663 0.2223 0. 1 08 17'. 0'.589 0 . 2 3 4 7 0.0 9 4 IR'. 0'.564 o'.2'>52 0 . 0 9 2 0.562 0.258 1 0 ' . 0 9 3 20'. 0'.561 O'. 2699 0 . 0 9 5 .0015 RT; =0.3(10)6 601 •C "C./i\ -O'.O 133 -0.0135 -0.0102 -0.0059 -0.0010 0.0039 0.0078 0.0 109 0.0131 0.0116 0.0050 -0.0006 0.0028 0.0117 0.020S 0.0275 0.0328 0 .0379 0.0371 0.0292 -0.0617 -0.0597 -0.0-570 -0.0561 -0'.0561 60L5+P T5U5L ALF CL - 4 . -0.3/13 - 0 . 2 4 4 -2 -0". 1 5 2 - i ' . - 0 . 0 6 7 0. 0.0 0 6 r . {)'. 0 8 3 ?'. O'. 166 3'. 0 . 2 5 6 0'.355 0 ' , ' I 6 6 0 ' . 5 9 2 7. o ' . 7 1 8 0 . 7 9 3 <>'. 0 ' . 8 3 9 1 0 . 0 . 8 8 9 11". 0 . 9 3 9 12. 0 ' . 9 8 1 13'. 1'. 0 1 2 I'K 1 . 0 2 2 15'. l ' . 0 2 ' l 1 '^. o ' . 7 0 3 17'. 0 . 6 0 2 18'. 0 . 5 6 6 I"'. 0 . 5 6 3 20'. 0 ' . 5 6 1 CD 0'.0202 O'.O 17/1 O'. 0155 0'. 0 1 4 1 0.0131 0.0132 O'.O 13'! 0'.0147 O'.O 161 0'. 0 1 8 2 O'. 02 I'I 0'.0253 O'. 0261 0.0314 0.0351 0'.0397 0.04S4 0.0523 0'.0626 0'. 0778 0'. 22 l ' l 0.2362 0.24 4 ' i 0.2568 0'.2705 CMO -0'. 1 0 0 - 0 . 0 7 5 - 0 ' . 0 < J 9 - 0 . 0 2 4 o'.ooo 0 . 0 2 ' ! 0 . 0 /18 0 . 0 7 / 1 0 . 1 0 0 0 ' . 1 2 5 O'. lSl O'. 1 7 5 0'. 1 9 8 0 ' . 2 1 8 0 . 2 3 8 0 . 2 5 7 0 . 2 7 3 0 ' . 2 8 ' i 0 . 2 0 5 0 . 2 7 7 0 ' . 1 0 o 0'. 1 0 0 0 . 0 9 3 0 ' . 0 9 4 0 ' . 0 9 5 C M C / ' , -0.0167 -0.0160 -0.0125 -0.0073 - 0 . 0 0 1 4 0.0035 0.0074 0.0114 0.0132 0.0123 0.0075 0.0010 0 . 00^9 0.0 152 0.0238 0.0308 0.0378 0.0 a 11 0 . 0 '101 0.0321 -0.0699 -0.0566 -0.0559 -0.0558 -0.0561 ALF 7. 8'. 9 IOC 1 1". 12'. 13'. 14. 15. 1 (>'. \r. 18'. 19. 20 :. CL -0.345 -0.247 -(>'. 155 -o'.07O 0'. 0 0 i 0,081 O'. 1 63 0,254 0'. 356 0.47 -'I 0'.603 0'.722 •0.784 0>3/l 0.8 8 3 0.933 0'.9 76 {'.0 02 1.012 1 .011 0'.6 39 0'.575 0'.563 0.558 0'.561 CO O', 0 1 O 5 O'.O 1 6 7 0'. 01 a 7 0 ' . 0 1 3 2 o'.ni i s 0'. 01 i 8 o'.o 120 ( ) ' . 0 1 3 0 0 . 0 1 4 5 O'.O 1-65 0 ' . 0 2 0 0 o ' . 0 2 3 3 0 ' . 0 2 6 0 0 ' . 0 2 9 0 0 . 0 3 3 1 0 ' . 0 3 7 6 0 ' . 0 ' I 3 1 O'. 0 ' I 9 8 0 ' . 0 6 0 ' l 0 . 0 7 5 8 0 ' . 2 ? 2 0 0 ' . 2 3 3 3 0 . 2 4 3 4 0 ' . 2 5 5 9 0' 2 6 8 8 CMO CMC/'. - 0 . 0 9 6 -0.0117 - 0 . 0 72 -0.0113 -0.0/16 - 0 . 0 0 8 7 -O'.O 22 - 0 . 0 0 / 4 6 0.002 0.0017 0 . 0 25 0.0056 0 .0 ' !9 0,0091 0'.07'l 0.0122 0 ' . 1 0 0 0.0 135 O'. 126 0'. 0 108 0 . 1 5 1 0.0 04a 0 . 1 7 5 -o .ooot O'. 1 9 5 0'.0053 i)'.215 0.0 138 0'.23/l 0,0211 0.252 0.0281 o ' , 2 6 7 0.0331 0.278 0 . 0 382 0 . 2 7 9 0 . 0 3 7 2 0'.272 o'.029fl 0 . 1 0 1 - . 0 . 0 635 0'.092 - 0 . 0580 0 .092 -0.0565 0'.093 - 0 . 0555 o'.09a -0.0568 0 0 1 5 R F = 0 . 3 C l O ) 6 8 0 1 . 8 + 1 ° TSUSL ALF CL - 4 . -0.334 - 3 . -0.234 ~z\ -0 ' . 145 -1 . -()'. 0 61 6'. 0'. 0 1 0 r. 0.08 7 2'. ( l ' „ 168 3'. 0.26 0 O'. 362 5'. 0'.'I75 6'. 0.606 7;. 0.724 O'. 787 < ()'.828 10'. 0.8 76 11'. 0.925 12'. 0'.967 13'. O'. 992 14'. 1 ,^002 15', 0.994 16'. O.C 21 17'. 0'.S55 18'. 0'.539 CO 0 . 0 2 0 1 0 . 0 1 7 1 0 ' . 0 ] 4 8 O ' . 0 1 3 4 O ' . O 1 2 7 0 . 0 1 2 5 0 . 0 1 2 7 0 * . 0 1 3 6 0 ' . 0 1 4 7 O ' . O 1 7 4 0 ' . 0 ?. 0 3 0 . 0 2 3 3 0 ' . 0 2 5 8 0 ' . 0 2 8 7 0 ' . 0 3 2 6 0 . 0 3 7 1 0 . 0 4 3 1 O ' . 0 4 o 8 O ' , 0 6 0 6 O ' . 0 7 6 0 0 . 2 1 7 0 0 . 2 2 6 2 0 ' . 2 3 7 5 C"0 C"C/4 0.095 p-o . 0 T 3 2 0,069 -0 .0 120 0'. 0 4 il -0.0084 0 . 0 2 0 -0.0!) 47 0'. 0 0 4 0.0014 0'.027 0.0057 0.050 0.0093 0.075 0.0119 a .tot 0.0 127 0'. 125 0,0100 0.150 0.0033 0'. 173 -0.0025 O'. 194 0.0035 0.215 0.0151 0.233 0.0219 o'.251 0.0288 0.267 0.0354 0.275 0.0376 0.274 0.0340 0'.267 0.029t 0.105 -0.0547 0.089 -0.0555 0.009 -0.0540 r j o 43 ~4 o Ul ft Ll ru ft—, ft -ft ' 'a - a ' •k -1 -o o c o = •ft— !-— ... • - • " k 'a ' 'a -'a ' 'k ' 'k ' . * ui Ul Ui Ul o o O © 43 43 LT Cr Co -4 ft— ft-© - 4 rj — 0 3 -J ft— i Co Ul - ru ru Cc O o o © o o o o © © • 1 * » * • a a ' 'k I -k a - i IV ru ru ru ru o o © © © - 4 ui ft L-l »— - J V* Ul ft L4 G 3 - ft :U CO cn ; © ft CO •** •0 o — 43 -— CO ru -© o - © o © o o O a • # * • " • - a ' a • a ' 8 ' a a ' o o o o ft-r j ru ru ru ru 43 3 43 43 t— -4 CO Co c*- Ll LT Ul L4 ft •— LT ru o CO ru I I 1 1 1 O O O O O o o o O © • o o c o © o o © o © • Ul Ul Ul Ul Cr L4 Ll Ll UI rj : cr Jl 3*- CO •V ru 43 •O ft CO c** ft ft o L-l o ru ft CO CO I I I I > © O © © © © © ft © © —J L-4 CO © CO CO C © 43 43 vH ft ft 43 -4--4 ft— .© O © — . Ul - 4 © -4 Ll 43 CO ru © L-i I ' © O O O O O O O © © © © © © L-l 43 C> ft = 0- ft L4 •—ii—!ru L4 ft -1.43 —J -4 —4 ft— ft CD 0*- ft— -*-4 C^-" L4 ft CD ft— CO © 0 © © O O G C © © © C ; 1 I 2 © I ft O : -— -* ft— ft- o o o - i ft ru c - 4 L4 ft— co ru —4 ru o o o o © o © o ft ru © "U ft - 4 43 -I L4 © L4 - 4 L4 CC © © O O O O O O © © © © © O 0 0 © 0 © 0 • © . © © © I I I © © © r> a a . JC © © © O © ft 43 -CO o r u H J U i o ^ O f t - i e CD Ul U! TU Ul L4 Ul — c- Ul :i © CO co r j ft- f t - f t - ~ - - - - ft- , , , © 43 Co -4 O Ul ft L4 rj ft-!©-0 Co -4 (7- Ul ft L4 ru ft-.©ft-,ru L4 © ft- I — Ift— ! © © © © © O © © © © © © © I I © © LT LT Ul C- C*- © © O 43 43 CO Co -4 —4 • "Ul O C- ft- CO ru "U © -4 L4 CO L4 CO — 43 L4 -4—4 Ul ft •—. CO -4 TU fU L4.ft ru w l - f t L-I rj ft-.© © © ft- -j L-I i 43 0- ft ft LT - I © -4 LH ft ft — — Co C> 43 ft © ft 43 O f t © © © © O O © © © © © © O O O © O © O © © O O • •» ".» " " • •• • a -k -k • ( - , ru r u ' u p u r u o o o © o o o o © o o o o © o o o o © © o -4 ui ft L 4 ru --4 c> ui ft ft L-I L-I ru ru ru »-— ft— •— »— ft— •— »-— ft— »— *— — • -3 ft - 4 ; co ru ui -c> ft- 3- ru co J I —, co ui ft ru .u ru 1.4 si - 4 • o c o o 4 3 ' C o© f t — 4 3 r u f t o r u o c o c o - - i f t c o f t 4 3 c 7 - c D C D r u f t — 43 1 1 I 1 I 11 © 0 © 0 0 © © © © © © © © © O © c © . © © © © O O O 0-a ' a a "a ' 'a ' ' a ' a ' a ' 'a ' 'a ' ' a " 'a " a " ft 'a ' 'a ' ' a ' "a ' a ' 'a '1 ' '1 a • a ' a ' - ;"•" © O © ft— — ru ru ru ru ru ru ru ft— p— ft— © © O © © © <--; © O 43 43 43 O — - 4 Co cc - 4 Ul Ul ft— 43 - 4 Ul ru 43 -4 ft ru 0 ru --1 u; 0 - — Ul O - -4 Ul ru © • = ! 'Ul Ul Ul L4 © ft CO ru CC U4 — • ft 43 •Si O © 1 I I 1 I I 1 I 1 1 CO CO © © © O © 0 © 3 0 0 © © O O © © 0 © © © 0 0 © © O O + CSC T3 O © 0 O © © © © © 0 © © O O © © 0 © 0 0 0 0 O O O O Ul Ul Ul 0"- Ll .ft ft L4 ru ru ft— : © C © ft-Ift— ; © c 0 © ft— 'ft— co - 4 0 LT ft L-I ru •—.© ft-iru L-I ft r-ru © © © © © ft— 'ft— ! • - ft -ft "ft "a -k -k "i Ul LT Ul LT C- © © 43 LT LT CT -4 — © • - 4) - 4 L4 . lV - 4 43 43 © O I I I I © © © © © O © © o © © © c •-_-©•© © •k a - . -k - . - k - a - k - . - k - . - . - . -, - . - . - . -o •0 -0 CO CO -4 -4' Ul ft L4 fU • - : © © O ft— "U L4 r --4 ru CO L4 CC •— -0 C- LT LT C" 33 © C- LT ft ft "u -o ru L-4 u i ft ft—. CD ru ft ft — . cr 30 ru L4 LT © © © © 0 0 © 0 © 0 0 © © 0 © O G © © © © © © © 0 • " • " • • ' ' a -a - a -a -a - a - Ci ru ru v ru ru © o © © © © © © © © o © o © o o © © © © o C- LT ft L-' <\i - 4 c- u i x.- L 4 L4 ru ru ru ru •— ft- -— « - •— ft— •— 1— — ru -I ' .T L-4 >— . 0 Ul © ft L-l CO .-I 43 "O ft © - 4 i Jl j-1 'V ru r-u L-4 LT -4 O ft •— ui •— ~ i si LT ru ui ui co co 3- ru 43 ft ru co - 4 •— co c- ru ft ru 0 © © © 0 © © © ' © © O C © 0 © 0 © C © © © I I © o o © 1— r u r u r u r u r u r u r u •— ft- —» •— •— © o © © © o o 43 43 43 43 © - 4 CO CO - 4 U l L-4 -— 43 - 4 U l r u O -4 ft r u © r u ft - 4 43 ft L4 r u L4 ft- ft- © © c- c- U l -4 ft © O O ft 43 ft — .L-4 -4 ."U CO I © r, a " •£ O O I I o o I I © © ' o © I I I I I OOOOOOOOOOOOT . a k -t . . . a a . , - . . . ' , . - . - . . , • , , , . . - x O O 0 0 0 3 0 0 0 0 C O O 0 O O 0 o o o o o o o o o ui ui ui ui -Si ru L 4 . ft n L - I ru ft— :© o © •— i — ;*— o © © © © •—;-—!*-.. L T f t ^ - - 4 - 3 0 - 0 O © C > . ^ L 4 f t - M O C r f t - e r U C 0 f t © ( 7 - 4 3 L 4 L 4 J S W IV ft- 3-- UI Jl 43 43 ru O CD Ul •— CO 43 ft-•—ft-ft-ft-ft-ft-ft- I O 43 Co —4 C- Ul ft.L4 ru ft—.©'43 CO -J-C LT ft L-l ru -—,©•-43ft- W 3 C JIO C* .14-4' ft— i 0 © © © O • - — i © • © 0 © © © © 0 © 0 O © © © Ul a ; U i u : Ul L T c- © c •0 -0 43 CO CO -1 •-4 ' LT L-4 ru — [ © © © C** LT *3*" CO LT ft- — 0 -4 ru -4 L4 -4 . — 43 LT L T C- -4 © - 4 • 33 • L4 - 4 U4 ru ft—.ru Co ft-,ce -4 © 4) ru ru © © ru CO ru ft— 1! © © O © © = © O 0 © © O O 0 © — O 0 c © 0 © © a " *k -'a • 'a " a ""a - a - k - k ' 'a 'a -'a ' 'a - a ' 'a -'a 'a a - a k a ru ru ru ru V O © © © O © © © © O 0 © © O O 0 © L4 c- Ul ft U4 ft- - 4 C- UT ft L-l L4 ru ru ru ru ft— 1— — -— ft— 1— ft— * CO C"- L4 ^4 33 J l = O •L-4 CO L-4 •0 c*-ft © -4 Ul L-4 V •V _-J O • ru *"^ ' " *"* 30 ft- - J Ul 43 Ul - 4 43 cr- 0 Ul - ft— CO - 4 ru J- CO J--v 0 0 © 0 © © © — © O 0 © © © O © © © 1 a " a " a " a ' a ' a "a ' a ' a ' 'a ' 'a ' a ' a ' a ' a * a " 'a ' a "a " a ' a ' a * O O O © ru ru rj ru ru ru ru ft— >— ft-ft— O © O © C 0 Co 43 43 -43 O - 4 CO - 4 c** Si Ll 1— 43 -4 t ru - 1 ft V © ru 0 - L-l ru — CO Ul — 43 co ru ft - L-l ru 43 - CO ru - 1 L4 — ' f t CO I I 1 1 1 ! 1 1 + © © 0 © © 0 0 0 © 0 © © O © © © © 0 © O © © T3 * a * 'a • « 'a 'a * 'a ft " « • "a a a a a 'a a ' a a k ' •« -O O 0 © O © O O © 0 O O © O © O O O © © © - © -(< Ul Ul •Ul Ll '..1 L-J U4 L-4 U 4 ru .V ft—; ! © © © ft-i f t - ! ift- ! © © 0 © co Cr Ul ---^ - 4 J J — CO 0 Ul CO fu L4 ft © Jl ft— L4 • - CO ft © - 4 cr CD Ul ui r j Ul U4 43 •Jl •Co Ul - 4 Co O UJ ft - 4 © ft ft-0 •uM L-J ft I -. "a ' -a ' -a - 1 , 0 1 I 1 © ' O © © ft— t Ul ru L-l 1—. 1 LT ft ft Ul ru 33 n 1 © c © "a 'a a -O © • © © O TJ a -. *— ft— ft— L4 1 ft c- 43 --ft ' 1 O 43 - 4 ^ 1 1 1 © © O Cl a-*a " a " a " 7X O O •— O > ft - 4 © --j 43 ft O © CD 1 I 1 CO © O © n ' -ft. ' "a a • ' 2; "L7 © © 0 0 ft— i f t — ;>-;--.• —11 - © ft Cr ft CO 43 ft-Ul cr h-1 to i p - . r o - M r c o ' - o o r o o - o - i c o c O P J N C N • - N ! — > o c o o or —: —:—<; — i o o ©; rj Pc hi rj o -o &. o o o o o o o o o o o o o o o o o o o o o o o cn r . . • . . . . « . . . . . . . . . . . .. . . . . . . . . . . . . . • in L J O O O C O O O O O O O O O C O O O O O O C O K I I. 1. 1 I. - I o cr i;" o c: o K i r - r; o LP• © on X o- ©-ft c--r- cc in o vr o M ^ . r^ c rj c r> o rj ir N c- ft c c N c- c c i". P J o ft o o c c o c o c ft ft ft ft r j rj rj r j r j n M P i ft -o oc . •. «. •. .. «. ». «. «. .. •. •. ». ». «. •. «. •. •. ». « c j o o o o o o o o o o o o o o o o o o o o o o O . 1 1 1 1 M e o c M * " ~ o- i o n « e r j N c s J ; c s in o;r- ir. i-- rv rv r-- cr -£ cc P o l - - . — , in cr ir1 or -c cr ft ro . . ft ft ft « ft —i ft ft —> ru .-1 .-.-i M cr LT' L I -o r- ft M o c o o o o o o o o o o o o o o © © o o o o o ru 1* U . ». •- • . ». «. • . •. «- •. • L_J O G O O O O O G O O O G O O O O O O O O G G cr — in -c © in o o r- in in e - v o o i n c r r - - o i n K V f t c r - 11 C 1- C N «C " t-1 M — O t— M C - LI ft 1— O ft -0 M m .j M rj »— o o o ft PC t--i — ui o • p- cc cc 0' © ©ft.ft ©'r-ft '-)-•- •- •- •. «. •- •. •. •- «. «. •. «. «. •- • • © © G © G - © © - © © G © © O O © © . © : ft! ftl ftl ft! ft © O I I 1 I I u _ . . . • . « . • . « . « . • . ... « . • . • . . . . • _ j cr i-i r-j —. c ft ro Ni cr in -JO r- oo o- © f t r\i r-i cr in -c r-- s t i l l - . f t ft ft ft ft - i o o I < o o co a-o to in CU © r-H © XI co cr cr ro c- c r p o r - r - i n - f t - c r n o c p f t h P r - o c r o - c r c ^ i l f f C O M ' C f f t i - f u r j i p i n . ' a c M i r i i c . o r o "vi«:« o o o o o orft: •»-*: ft © ©i ft PJ r e - n- M:-- rj -J o ft L4 ru »— © -0 Co o Ul • ft L-4 r u ft— o ft— r u L-4 ft r-• "ft -ft "ft *» • -» -» • '» •• ' -ft -ft 1 i 1 I © o —' Ift— •ft- 'ft— it— . © © © © © © o - © © © © © • ' 'ft. 'ft ft '• ' •» " * • '• • 'ft '• •• • 'ft • -ft - -•• •» • •ft • •» "ft • • n . ft— - J u , Ul ft Ui L~> L-J r u l\l ft— ft— ft-ft— ft— ft— ft— •— r u • -3- • o © L1 -J • © L4 CO ft © Cr i— ICD Ul L-4 M r u L-l •41 J l .CO Ul r u r u Ul — o- r u t— 0- L-J -ft* r j CO Ul © r u 43 Ul Ul Ul u i »—!. a— i © I I 1 I O © © © © •© © © © © © © © © © © o © © © © © o >—' • ' * • • -• • t ' « • t ' • • -I - « * ft ' » -t " ft ' ft ' » -t • 1 ' • • t -ft— r u Ul r u r u r u r u r u r u •— ft— •— ft— © © o © © © o r— • o ru -s © © 43 CD •—. ft r u o -4 •Jl r u © -J ft r u © r u J l --4 © r u 43 — 'CO UJ Ui — <— © CO r u © — 43 — © 3- r u © I 1 I I i I o o © © © © o © © O o o © © O o o © o © © n •JL CO + o © © © © o © © © © © © •© © © © o © © o o o rt X o ft— ; r u Ll w r u r u r u — j ;© © ft—, ift—; ft— 1 Ift— ' © © © c o !*>-.• ft ft-43 w 43 3 - ft— r u Ul CO ft o ft ft— -4 ft o ,_- Co •— J I ft —1 43 Ul • 'u ft r u Ui — • — • Ul r u J I CO - J 43 O Ui 44 U4 r j r u CO I O ft— 'ft -ft I I •© © I I r u L-J I I - 4 O U 1 ftL4ruft-.©43 co-au-LiftL-jru-— O ft— I-— ift— j - — "ft- : © © © © © © © © © © © ft -ft 'ft "ft -ft -ft -ft -ft -ft -ft -ft -ft -ft -ft -ft -ft -ft -4 © ft— •—:© © 43 CO CO --4 O U l ft L-l r j ft- © ft U l — ft- CO rj C- 43 ft CO - 4 L T L4 ft ft C- -4 © Co 0 - ~ ft L4 CO CO ru !> -4 U l i"U L4 CO ru 43 L4 43 ft ' J l © 0 © O C O © © © 0 © © 0 © © © 0 © TL -—OOOOOOOOO OOO OOO UJ ru Co c - U l U i ft uJ L4 u i ru ru -— •— •— *— *— . ui c •—:.n - 4 i © ft co ft © c- — .co o ft L4 L-I C « C 0 3 ' 0 4 ) J L H M \ J - 4 U a ' 4 - : > f t f f ' i O © © ft "ft ' © © L-l ft ft © 43 i o © • -ft -© © Jl - 4 i - 4 'CD i o C3 ru. i-3 Ci cr © fD C cn Ui o 33 \ £ rr, I 11 "45 o • - 2 U l ' l 1 ( I 1 I © © © © © © O © O o © © © o o o © © © © © o © o s—' • ' '• * '1 ' "t ' 't "t '• ' " i • •» • • ' ' t ' ft • '• • ' t ' "ft ' 'ft ' 'ft ' 'ft ' • ' 0-•— ru ui L-4 L4 ru ru ru ru ru -— ft— ft— ft— © © O © © o o ft— o Ul Ul © ft— © co c- ft ru © -4 UT ru © -4 ru o Ul -4 o © •"* - Ul 43 CO Ul L4 ru CO Jl CO — -Jl 43 L4 = Ul — -4 ft Ul I i 1 I I I © r-o o © © © © o © o © © o © © © O © o o © © o o CO CI -I-© o o © © © o o © o o © © © © o © o © © O © n T3 Cr ft— ;ru L-l UJ -UJ ru ru ft— :© © ft—. I- i It— .© o CT © .© ft— 'ft— i->. • 3" ru cr -4 ft TU -4 — ru •Jl --4 'Ji — j Ul *— -4 ft o ft CC —* •JI —-1 ru 0D -43 *— Ul 43 © ft ft cr- CD ca -4 o -4 -4 L4 © 43 © — CO CO i O U I ft L4 IU ft— © ' 43 C 0-4OU1 ft L-l ru ft— !© — S f t — i f t - i f t — i o c s o a o o o o c o a • C C OCT -0 -0 CO CO-4C-© L-i LT ft 43 ft - I ru —J CO - 4 r u c r - © u i © c o r > f t f t © © o © © © © © © © L-I ru LT C-!— ru r u o o o © - © o o o © © - j u i ft ft L-J L4 r u r u r u •— .' 43 JT - 4 "— U. © -4 LT — c r - - 4 f t - 4 r u c o c o 4 3 r u 4 3 ui — U4 C O O O C T ft 'ft -ft *« ' © © O © © c © © ft -ft -ft -ft -t— © © © -I CO — 0-Jl - 4 — .--J © © = o ft -ft 'ft •» ' © © o © 30 Jl LT Ul L4 ru 30 C-© C O © © © 0 0 © © © © © © •— ru ru ru ru ru ru ru ru >—>—*—•— © © C- -0 43 CO 3" ft ru © - 4 Jl L-4 © - 4 co co co o- © ru ru ru — , 43 c © ft oo o o © o o © o o © © © © ft 'ft © © o © © o o © o o o © ui ft-in L4 . u i ru ru •—• JO o i \ ; r o c 7 - c o - u - - j r u j i - 4 - 4 f t - 4 co © -4'ft - - - r u c o j i u J U i f t c o © © « •-• © © ui r u ft- o iru .4 co c •— ru t "t •« • OO'OO •Jl ru o ru ru -4 L4 — I o o o © ft . ft "ft © o o © © © © © CO 'Jl O ft •— © Ul ft— I I I > .ru u i ft r-• 'ft -ft • T l I I I © © © ft -• "ft -Ci r u L-I i-LT ft L4 ft L4 L4 © © © ft ••-•-(-> o o © O •— ft- r u ft -4 © CO ft- o i i I © © © © ft -4 43 -4 L-4 43 I t f © o © n » '* '• .C— © o © rt © >- I— l-s,--4 >— Jl ft 0D -4 ft—-CO 1 I 1 ,t -> L-J . o Co LH 1-7 LJ ru O tft-*. .ru L-J r~ *• o I -t 1 O o o !•—* t>-* ,•—» o •o o C © •© © © © © © © C »—- • ' 'a ' "» ' •* " • * "» •» " • • * ~» • "» ' •« • *• •n j-— o o o CD CD •o LH _Er L-J ru •o •ru L-J i — Ul r j c_> i— rc L-J - j Lsl © - J o _> (V w .LO •—> -+ . ZD • )-* . ru n c. c o o o o o © o w o o © © © © © © © n ft • (J '* ' • "» " '» ' 't ' '• * '• * •» * '» -'* it o rj »•-»" o o o o o o O o © o © o © o © © O © o • " »-•- L*I Ls' i*U ru ru ru • o z — -^1 — - — © --4 J-I ,"U •V L*J • © Ul /—i r j •o w r j >c -i - J »—* © Cc 33 •—ft. -J O I I 1 o w o G o c o o o o © © © c © © © © O © c; . —* o © o © © o © © >— o O o Ul ru o ~-J ft/1. !\) © ru •CTc-' © Co ru "U o 'CO -i 1— © :u w L-J -4 o O r~. I ! f ! I I f~ CO o O o o o o o o o © © o © © © © © © © © CO • • ' • * '» '« • • it '* • ' • • - « m • • + ' o o o o o o o o o o o © © © o © © © © © n T3 o *—. •-J L'i w rj ru ! c o -i '»— : © © © © © i—> ; •— ! Nr. -\J~) > ru CD •— L>J >0 t— OD >— -Cr --J >— *J1 -C: —1 o w -0 Ji J-r o J l Ul o © -u o U4 Ul CO CO r -rO Table 6 0. 34--NACA-0P15 0015 R C s O ' . s d O l d 50XS3P TSUSL 0015 RE = 0'.5(t0)6 70%SSP TSUSL ALF CL cn CMO CMC/4 -0'.342 O'.Ol 99 -0 .100 -o .oi"?.n -0.251' O'.O 169 -0 .074 -0.0107 -2'. -0 .16 2 0.0142 -0 .048 -0.0073 -1'. -0.074 O'.O 132 -0 '.023 -0.0040 o'. -o'.ooo 0'.0124 0 '.oot 0.0008 1'. 0.076 0'. 0 1 2 0 0 .024 0.0051 0'. 1 6 0 0.0 124 0 '.048 0,0078 0.250 O'.O 138 0 '.074 0.0109 1'. 0.337 O'.O 153 0 '.10 0. 0.0144 c r 0'. '13 'I O'.O 177 0 .125 0.0159 (>'. 0.545 0 : .02l3 0 '.150 0.0 123 r. O'. 669 0.0257 0 '.174 0.0 061 8'. 0'.773 0'.030l 0 '.198 0.0045 <>'. 0.8 32 0'.0337 0 .219 0.01 OS 10'. 0 .887 0'.0379 0 .240 0.0186 n'. 0'. 9 .'.| 8 0'. 0 4 32 0 .261 0.0245 12'. 1.010 0.0498 0 .281 0 .0297 13'. T.063 0'. 0568 0 .297 0,0 329 11'. 1'. 1 0 1 0'.064 8 0 .30 7 0.034 0 15'. l ' . 101 0'.0780 0 .302 0.0287 16'. l'.04() O'. 1187 0 '.249 -0 .011 0 17'. 0.721 0.234 1 0 .123 -0,0677 0015 R E = 0'.5C10)6 60%SSP TSUSL ALF Cl. CO CMO CHC/4 -4'. -0.34 1 O'.02ol -0 .101 -0.0153 "3. -0 .253 O'.O 168 -0 .074 -0 ,0103 _ 7» ' -()'. 160 0'. 0 1 4 6 -0 '.049 -0.0084 "\'. -0'.072 0.0133 -0 .024 -0.0057 o'. 0'. 0 0 4 0'. 01 1 9 0 '.002 0.0004 1. 0'. 08 0 0 '. 0 12 1 0 .025 0.0 050 2'. 0'. 166 0'.0127 0 '.051 0.0087 3'. 0.251 0'.0137 0 .075 0.0119 a'. 0'.34 1 0.0153 0 .101 0.0154 5'. 0.437 O'.O 174 0 .128 0.0 174 6!. 0.546 0'.0207 0 '.154 0.0167 7. ()'.671 0*. 0250 0 '.179 0.0101 8'. 0'.775 0.0293 0 '.203 0.0084 «». ()'.835 0'.0328 0 .224 0.0145 10'. 0'.8f,9 0'. 0370 0 '.245 0.0225 11'. 0.950 0.0420 0 .266 0.0294 12'. 1.0 16 0'. 0 4 *18 0 .286 0.0327 13'. T.066 0'. 0554 0 .303 0,0379 11'. 1'. 102 0.0634 0 '.313 0.0392 15'. 1 . 1 02 0'.0795 0 .302 0 .0287 16'. l'.038 ()'. 1206 0 .249 -0.0105 17'. 0'.702 0'.2343 0 .124 -0.0623 ALF CL CD CMO CKC/4 -()'. 34 0 O'.O 197 -0 .101 - O . 0 154 _ T -0'.253 O'.Ol 66 -0 .075 -0 .0 115 -()'. 158 0". 0144 -0 .049 -0 ,0089 -r. -0 .075 O'.Ol 31 -0 .024 -0.0052 o'. 0 , 0 0 6 O'.O 125 0 .001 -0,0007, i ' . O'.O 83 O'.O 120 0 .025 0 . 0 0 4 1 r>' 0'. 169 0'. 0 1 ? 1 0 '.051 0.0 0 79 3 . 0.2S7 O'.O 130 0 ',076 0.0116 <*'. O'. 346 0'. 0149 0 '.103 0.0153 5'. 0'.441 O'.O 171 0 '.129 0.0 177 6'. ()',554 0'. 0 2 o 4 0 .155 0.0 157 7'. 0'.674 0'.024 4 0 '.179 0.0094 8'. 0'.778 ()'.0284 0 .203 0.0077 9'. 0'.832 0'.0320 0 '.223 0.0148 10. 0'.889 0'.0362 0 .24 5 0,0225 H ' . 0'.952 0'. 04] 8 0 '.266 0.0286 12. 1'. 0 1 4 0'.0477 0 '.285 0.0325 13'. 1'.064 0.054 6 0 .300 0 .0355 H ' . l'.(!95 0.0627 0 .310 0.0381 15'. 1.084 0 0 8o0 0 .298 0.0290 16'. 1'. 0 1 9 0'. 1217 0 .24 5 -0 . 010" 17'. 0.69 8 0'.2330 0 .124 -0 .0617 0015 Rl-=0'.5(10)6 80ZSSP TSUSL ALF CL CD CMO CMC/4 -0'.337 0.0215 -0 .101 -0 ,0157 - 3 . -0 .249 O'.Ol 81 -0 .075 -O'.O 119 - 0'. 1 6 0 0'. 0156 -y .04 8 -0 ,0078 -!'! -0 .069 0'. 0 1 4 1 -0 .023 -0 .0057 or. 0 . 0 0 6 O'.O 131 0 .001 -O.OOOI r. O'. 079 0'.0127 0 .025 0 .0056 - i * <-. 0 . 166 O'.O 122 0 . 0 5 0 0'. 0 0 8 4 3. 0.254 O'.O 129 0 .075 0 , 0 1 t 3 1'. 0'.34 4 O'.O 144 0 '.101 0 ,0147 5'. . 0'.4 39 O'.O 164 0 '.128 0.0174 6'. 0'.553 0.0193 0 .153 0 .0143 7'. 0'.672 0'.0251 0 .178 0 .0090 8. 0.774 0.0267 0 .20 1 0 ,0068 «>'. 0.831 0'.0298 0 '.223 0 .0145 10'. 0'.883 0'. 0.338 0 .24 3 0,0221 11. 0'.943 ()'. 0 383 0 '.263 0 .0285 12. 1'. 0 0 8 0'. 0 4 4 6 0 '.284 0 .0333 13'. T.054 0.0505 0 .297 0.0352 H ' . l'.078 0.0582 0 '.304 0 ,0370 15'. 1.060 0'.0786 0 .282 0,0188 16'. ()'.717 0'.2075 0 '.113 -0 , 0753 225 T a b l e 6 " 0.5O-HACA-OOI5 oois Rir=o'.s(i0)6 SOLID WALLS CD 0.0267 0.0229 0.0198 O'.O 178 O'.O 16*1 0',0161 0.0160 0.0174 O'.O 192 0.0226 0'.0266 0'. 0318 0.0362 0'. on io 0.0470 0.05/16 0.0625 0'.0721 0'.0f.23 .0'. 0 94 9 0". 113fl 0'. 1 '17 <7 0'. 1726 0'.1926 0'.2178 0015 RlZ = 0'.5(i"0)6 40ZI.S + P TSUSL R C = U . 5 C 1 0 ) 6 . I O Z S S T - P T S U S L ALF CL -0.367 -0 .269 mm T» ' -0 .170 - r " -0 .077 0'. -o'.ooo r. (>'. 076 ?.'. O'. 167 0'.266 < 0'.369 5'. 0 .495 6. 0'.6 2'l 7'. 0 .767 e'. 0.852 9'. 0 .917 10'. 0'.993 11'. l'.073 12'. 1 i 4 8 13'. 1'. 217 11. f'.266 15'. i'.2c,a 16'. 1 .281 17'. r.2'18 IB'. 1'. 2 1 0 19'. 1'.165 20'. 1.139 CMO CHC/4 ALF CL CD CMO CMC/4 -0 .099 - 0'. 0 0 « 2 -4'. -0.350 0.0233 -0 '.090 -0.0078 -0 .07'l -0 .0075 „ 7 ' -0 . 26 2 0'.019S -0 .071 -0.0065 -0 .049 -0 .0 066 -2'! -O'. 170 O'.O 168 -0 .047 -0.0049 -0 .024 -0.0051 - f . -o'.oei O'.O 149 -0 .023 -0.0033 -0 .0 02 -0.0014 o'. -0.005 O'.O 136 -0 .001 0,0 0 02 0 '.020 0.0008 r. O'. 0 65 O'.O 136 0 '.019 0.0034 0 . 0 4 4 0.0025 O'. 148 O'.O 139 0 '. 0 a 2 0.0054 0 .071 0.0048 it. O'. 236 O'.O 153 0 .066 0.0074 0 '.097 0.0062 4 . 0'.326 O'.O 174 0 .089 0.0090 0 '.126 0.0038 0'.4 27 O'. 0206 0 '.113 0.0079 0 .149 -0.0040 6'i 0'.545 0.0253 0 '.135 0.0013 0 .174 -0 .0!44 7'. 0'.677 0 0 3 1 0 0 .157 -0.0092 0 '.197 -0 .0 117 8'. 0'.765 0'.0361 0 .176 -0.0113 0 .220 -0.0038 o'# 0'.823 o'.04o5 0 .197 -0 .0049 0 .24 3 0.0009 lo'] 0'.885 0'.04r>9 0 .218 0.0017 0 .267 0.0054 H'. 0 ,958 0'.0533 0 .24 0 0.0059 0 .208 0.0084 12'. T.019 0'.0602 0 .257 0.0083 0 .306 0 . 0 1 0 7 13'. l'.086 0'.0687 0 .273 0,0039 0 .320 0.0126 l-'l'. 1.143 0'.0785 0 .289 0' ,0U8 0 .325 0.0120 15'. t". 186 0.039 1 0 .299 0,0116 0 .304 -0 .0069 16'. 1'. 2 0 0 0'. 1020 0 .302 0.0110 0 .274 -0.0298 17'. {'. 193 0.1256 0 2^9 -0 .0103 0 .257 -0.0308 ie'. l ' . 147 0'. 1572 0 .246 -0.0340 0 .24 3 -0.0429 19. 1 .099 0'. 1733 0 .225 -0.0444 0 .232 - 0 . 0 496 20'. 0'.940 0.3485 0 .150 -0.0970 ALF -4' -1 . O'. l', 6, 7'. R, 9'. i o ' . 11'. 12'. 13'. 14. 15'. 16'. 17'. 18'. 19'. 20'. CL -0.353 -0.262 -O'. 168 -0.079 -O', 007 O'. 066 O'. 1 4 6 0.235 0.327 0.427 0.550 0'.684 0',775 0.8 34 0,897 0'.971 l'.0 37 1 .09 7 1'. ir>6 {'.197 1 '. 2 1 4 .1.20 3 1 .160 {'.104 l'.064 CO ' 0243 02()8 0174 0157 014 1 0139 0 14 2 0155 0170 0205 0247 0304 0357 0 4 01. 0.0459 0.0540 O'. 0615 0'.0702 0'.0799 0.09O7 ' 1031 1268 1571 1789 3502 CMO -0'.094 -0.071 - 0'. 0 4 6 -0.023 -0'.002 0.020 0.042 0'.065 0.090 0.114 O'. 137 0.159 0.179 0. 199 0.220 0.24 2 0.259 0.276 0'.290 0.302 0'.304 o',28 0 0'.24 8 0'.228 0.146 CMC/4 -0 ,0 073 -0.0060 -0'.0()48 -0.0035 0.0001 0.0032 0,0056 0,0072 0.0091 0.0087 0.0013 -0.0087 -0.0113 0 0 48 0006 0052 0063 0 091 0097 0,0113 0.0 099 0,0119 0.0 351 0.04 28 0,1292 o 43 Co -4 CT- Ui ft L-l fU »— © •— • — " — ' » — C-J ft T~ CO CO co r j r j ft -j'C- cn ft t-i r j •—-• cr* cc LH ru rj L-J ft CO ft ru 43 co co - 4 • • © - i c-l*W 4} S> •rj L4 ! in ft 'CO -4 . o LH iO c O © © —. o o o © © © © © © o © © o © O © © © © © o II L4 ft— ft— ft— © o © © © © © © © ec- © O © © © O © © © © © rd o © -4 ft ru 43 ro -4 c- Ul ft L-l L-l ru ru ru - — f— • — ft— ft— t— >•— ru « -L'4 •V -4 'Ul Co L T ft c* -4 © L4 Co L-4 o Ul © c- ft L-4 L-l ft -4 ' 43 L4 L l L-J o ft— L4 ru •—• -4 © ru © L4 o C- *-— J l © *— ru L4 43 ft •Co ft— 43 «—ft I I 1 • © O O © o © © O © © © © © O © © © © c © © © © © •© © n t ' a * 8 ' • ' • - 1 -ft -• ' '1 • ft ' t ' 8 " t " ft -'f a -a " » -8 " • • ' t • ft ' • • or ft— ru ru ru ru ru ru ru ru ru ru ft— ft— ft— »— »— o o o © © © © © © o © >— ft 43 o CO - 4 J I L-i •— -43 - 4 C- L-l — *c c ft ru © ru ft - 4 43 L 4 LT © L 4 ru - L T — - ••1 ,o CO CO o CO LT .*•* - i w4 ° © ru L T © — ^ t 1 I 1 I I t 1 I 1 *-4 © © o © © © O o o © © © © © © © © o © o © © © O © •-> I— Ti CO O O © O © o © © o © © © © o © © © o © o © © © o © rt + 43 ft Li ft— ft— 1 — .'ft— : © © © © ft— : © c C ft— I O © © © © © © © --. T3 ft L 4 © J l •CO L 4 o 43 c*- L4 L4 © Co ru 43 © CD C"-L 4 © L4 ft c- CD ft - 4 ' C - ru c- CO 43 ru •— ft-43 Ul o L 4 -— 43 Co ru © L 4 -J ru © ft ru ft •H 03 C 03 ru •— ft— ft— »— »— »— ft— ft— ft-ft— 1 I 1 1 > o 43 Co - 4 c- J l ft L4 ru ft— o 43 CO - 4 - * K Ul ft L 4 r j ft-t © ft— .ru L-I ft r~. » • • •> " '• -'ft -' . -'• ' '• -•• • • ' ft - -. -a a " a 'a "a " ft -' • 'a " • "a —T I I I 1 1 © © ft— , ft ' — . •ft- :—-. •ft- Ift— .ft- - © © © © © © © © © © © c © © © © n © • -'» -ft -» " ft -a ft - • " ft -• -a ' « -a a ' a -ft ' » a " 'a ' a ' a • a " a ' a ' • * •— Cc © ft-ft— ft— — ft— . © © 43 CO CO - 4 • J l ft L4 ru ft-' © O © ft— ru L-l r—. UI 43 Co Co Co CO L 4 CO •— LT Co ru O CO ft rj ru L4 C- © *-4 cr* "3" LT CO LT - 4 J l 43 ru CO o -4 L — o - 4 - 4 ' — 43 CO J l J l CC c- -CC - 4 • © Ul O © o © o © o © o © O © O © © © © © o O c © o ll C4 ft— —ft ft— ft— © © o © © © © o o © o o © © © © © © © © o © L4 - J J l ru o CO - 4 c- J l J l ft L-4 L4 L4 ru ru ft— —ft ft-ft— ft-ft— ft— ru ru a " © LT "*J J I © CO JO 43 •£• ft— I J l 43 ft ft ft © - 4 • J l ft ul fcT •4 © ft J l Lrt - 4 J l ft— 43 Ul •— © LT 43 o 43 L4 c* ft ru •— M -4 L4 ru — © ru . — i 1 i I < I © © © © © © © © o © © © © © O © o © o © © © © © © c r> —. t ' •i " • ' t • 'ft " a ' 'a ' 'a * a ' 'a " a - a • a ' a " a ' a ' a ' 'a " a ' a ' a ' ' a ' a ' a a " 0-»— rj ru ru ru ru ru ru ru ru ru ft— ft— r - ft— ft-O o O O O © O © © © L-4 ru ft - 4 43 43 CO - 4 J l L-4 ft— 43 - 4 J l L4 ft— 43 cr* ft ru © ru ft - 4 C Ul (**> © ft 0= C- 43 4". — or CO CC 3= Co 43 CO ft © cr L-l . © ft— ru 3*" -— ' — 1 1 i 1 1 1 I r I I [ X © © o © © © © © © O o o © O © o O o © o o o © © © o ; ft— © © © © © © © © © © © o © o © © © © © © © © © ' © e L 4 •—:•—•—;•—;© © © © © . — '© © c © © © © = © © © 1 U l r u - — -— •— . " U © - 4 3 0 3 U l f t - f t O C o r u 4 3 4 3 C O C r L 4 © r u f t 3 - : •— 0 - C o U l L n - 4 L 4 C ^ f t L 1 3 D C O - — *rc* o o w rj e 4: 4 ) S-l-l Cl ' i f o o ft— Ln + 0 CO CC I-U-— . - f t - v - f t - f t - f t - f t - I 1 1 I > O 43CO"-Jt->Ul ft L 4 ru •— O 4 3 C O - 4 0« Ul ft L-i rj •—,©•— ru L 4 ft r" a -ft 'ft -ft - . -ft -ft - . -ft - . - . - . - . a a "a a **. - . "a '. - . -. - *tl I I I © © • © © » — I— '.*—.-— :© © © © © © © © © © © © © © © © © a -a -ft -ft * . - a ft " . - . - . ~. - . a - a " a -ft ' a a - a ' a *a a a • . T l Ul LT Ul O © © © C -0 43 CO CO - 4 rj- Jl ft L-l TJ >- '© © © ft- r j L 4 ! ~ 4 C* C -*4 — LT ft ft— 0- ft— LT © LT -vi LT L"4 L4 ft CT* —! O rj- LT —- L 4 CC © Or ft O "U 43 ru ft- L 4 ft©Cftft L 4 ft - 4 • — , - 0 43 Ul © •- ft-© © © © © C O © 0 0 © © © © © © 0 © © © © © © © © a *a - a "a -a -a - a -a "a - a - a -ft 'a "a - . - . -ft -a -a -a : - rt r v r u r j f t - * - © © o © © o © o © * © o © © © o © o © © © © c 3 Ul Ul — 43 -O O- 'Jl Ul ft L-4 Ll L 4 ru ru • — *— ft— — i — —• • — ft- i — ft- ru CO ft • — --4 ft - 4 *-4 © ^4 ^ ft © cr- L-l 4 ) C- ft V 'U — - J rj ft - 4 ' — > » - Co 0 - 43 ft- ru ft- ft 43 o 'Jl Ul Ul 3 - c- c- ru CD r j 43 • — 43 - 4 ft L T I I I I o © © © © © © © c © © o © o o © o © o o © o o o © n B ' a "a ' a " a ' a ' a ' a "a ' a "a a ' a "a "a "a "a "a "a "a "a a *a *a ' C i 0 o © © ru ru ru ru ru ru ru •— -— — •— o o o © o o © o © o Co CO Co Co L-4 - 4 - 4 3- ftUl— 4 3 - 4 C - U 4 . — 4 3 - 4 f t r u © — ftc-co - 4 ft — © - 0 • — — L 4 43 ft Ul CD 43 © 43 — 4 ft © - 4 ft ft CO .— . f t 43 1 I I I I I I I I I I © © O © © © 0 0 © 0 © 0 0 © 0 0 © 0 © © © © © - " * > © 0 O © © - — O © © © © © 0 © © © © © © © © 0 0 © © © © 0 cr o- ui c- © •— :•— :•— I*—:© © © © © ft-J—i© © © c © © © © v . . » w 1 l \ J L J - 4 f 4 - 4 l I l * - - 4 ^ £ ^ W O H C - 4 4 ! - l \ l s e C I ' e •«4rj43JiL4Liijiru--co--ft- •— LTI L - I c w ru C -4 -4 - o ru D ru 1 i • I > o 43 CO - 4 43- Ul ft L-l ru - — © 43 Co -41 Ul ft UJ ru ft— .© *— ru L-J ft a - a a *a ' a *" 'ft 'ft -» " a '• •• a ' '. - • " a ' "a - a 'a ' 'a a 'a • '• •a a •a ^1 © 1 i 1 1 o © © © ft-ift* Ift— 'ft- *— i ft-© © © © o © © © © © © © © © © © © © ft- a * a - t '• -'a - ft • ft -ft » - • * a - • ft a - a - a ' 'a ' 'a • a ' a - a 'ft a ' a •- » —-* Ul cr* - 4 © ft-ft-Ift— .ft— '© 43 •0 CO CO - 4 Cr- Ul ft L-J ru ft— © © © —ft ru L4 r— Ul L4 rj L T ft— L4 © L T 4> L4 -4 ft- L T -4 ft rj ru L4 L T - J © -4 c- J I L T CO ru ru .CO L T L T CO - ru Ul 43 - 43 - 4 '33 -4 '_ © = --4 • — *"* _ ro rr O © o © © = © © © O o © © O © © © © © O © © © © rr, II a ' a ' a a 'a • a " • -a ' a * a - a ' 'ft -'a " a - a "• 'a a ' a " a - ft * a 'a » ' • a - o 11 © ru ru ft-.ft— .© © © © © © © © © © O © O O © o © © o ©• © C3 . © a - co - 4 ft ru 43 CO - 4 Ul ft ft L4 L-J L4 ru ru ft— ft— ft-ft-ft-ft— ft-ft— " J a Ul •Jl -4 " 4 . - 4 'L-4 L4 L T -4 •43 L-4 ft © ' ji —. .CO c?- ft t L l 3- 43 ru L T o 43 — ft cr* ru 43 ft Ul 43 — - 4 -1 Ul L4 L-4 ru 43 — — ru c = © UJ --v © I I 1 I © o © © © © © © © © © © O © •© © © © © C © © © O © © O '—' o a a ' 'a 'a ' 'a ' 'a ' a ' a ' a ' a ' a * a " a ' a ' a ' a" " a 'a -'a ' 'a " a " ' a " ' a ' ' a ' a — CT-© ft-ru ru ru ru ru ru ru rj ru ft— ft— ft- ft— ft-O O © o © O O O © © 43 T J •ui Co 43 Co cr Ul L l •— - 4 Ul 01 ft-43 c- ft ru © ru ft --4 43 - 4 Co LT - 4 •ru r — ;L4 t— .Ui CO ft c- - I CO 4) CO CC LT ft— CO ft —• • — .— c- © ft © I 1 I 1 1 1 t I i 1 I n © r- O © © o © © o o o © o © O © o O © © © o O o © © O CO + •a co tzz co © © © © © o © © © o o o © © © © © © © © © © o © o < - i - 4 .co L4 . f t - :© ft-1— !•—.-—.'© © © © © © ft-.•-.;© © c © © © © ©"->.-ru U. 43 -> -Jl JT ft— © Co ft © --4 -*4 ru © © 43 G-* ft © ru 'Jl r> *-4 ft i f t 4 . 0 9 O - B « , J l W O N C > S W 4 f t ! 0 I W 3 l N O C , - 4 co + co CZ 03 r-K3 cn' 227 T a b l e 6 - 0.5O-NACA-OOI5 0 0 1 5 Rir = 0 ' . 5 ( i 0 ) 6 5 0 X S 3 + P T S U S L 0015 RE = 0.5ii '0)6 70KS3+P TSUSL ALF -4' -3 _ •> -1 0 1 4 5 6 7 o «_> 9 10 1 1 12 13 I'I 15 16 17 18 19 20 CL -0.353 -0',261 -0'. 169 -0.081 -0'. 007 0'. 066 0'. I'I6 0.238 0.324 0.426 ()'.5-'l7 0.671 0.759 0'.818 0.877 0.94 3 1'. 0 15 I '.075 0 I I 3 1 l ' . 173 1'. 187 1.172 r. 1/13 i ' .083 o'.870 CD 0 ' . 0 2 3 9 O ' . 0 2 o 2 O'.O 1 7 3 0 . 0 1 5 1 0'. 0 1 '11 O'.O 13V 0 . 0 1 3 7 0 . 0 1 5 0 0'. 0 1 7 1 0 ' . 0 2 0 3 0 ' . 0 2 / ) 9 0'. 0 3 0 6 0 . 0 3 5 5 0 . 0 4 0 2 0 . 0 4 5 5 0 ' . 0 5 2 0 0 . 0 6 0 1 ' 0 6 3 1 0 . 0 7 7 3 0 . 0 8 7 6 0 . 0 9 9 6 0 . 1 2 3 0 0'. 1 5 1 0 o'.o 17/1 0 ' . 0 3 2 7 CMO -0.093 - 0'. 0 7 0 -0.0/17 -0.023 -0.001 O'.O 19 0.0/12 0'.066 0'.090 0.113 0.136 0.157 0'. 177 0.196 0.216 0.236 0.256 0.271 0'.235 0.296 0.29-0.27'1 0.2/12 0'.223 0.1/12 CHC/4 -0.0063 -0.0059 -0.00/(9 -0.0034 0.0003 0.0032 0.0 061 0.0 07 7 0.0097 0.0088 0.0017 -0,0089 -0.0097 -0 ,004 1 0.0012 0.0 05/4 0.0083 0,0098 0110 0119 0097 0107 0366 0290 -0.0614 ALF CL - 4 . - 0 . 3 5 0 *" .'J . - 0 . 2 5 7 -2 . - 0 . 1 6 7 -1 . ~(>'.0 78 0 . -o' .ooi i . 0 ' . 0 0 6 2 0'. 1 5 0 3 . 0 .237 4 . 0 . 3 2 6 5 . 0 . 4 2 4 6 . 0 . 5 4 6 7 . 0 ' . 6 7 1 8 . 0 ' . 7 5 5 9 ' . 0 ' . 8 1 2 10' . ' 0 . 8 6 8 11' . 0 . 9 3 0 12' . 0 . 9 9 7 13' . T . 0 5 2 1 4 ' l ' . 1 0 3 1 5 . i ' . 133 1 6 ' 1, 1 3 8 17'. 1'. 1 1 1 18'. T . O 5 0 19'. 0 ' . 6 4 5 20'. 0 ' . 6 2 0 CD 0'.0238 0'.0202 O'.Ol 73. O'.O 153 O'. 0138 0'.0134 0'.0137 O'.O 148 O'.O 164 0.0194 0'.0258 0'.0290 0.0337 0'.0380 0 .0429 0'.0490 O'. 0559 O'. 0658 0'.0714 0'.08o2 0'.0940 0.1202 O'. 1445 0.2537 0'.2785 CMO -0.094 -O.07O -0.045 -0.0 22 0.000 0.021 0.044 0.068 0'.092 0'. t 15 0.138 O'. 158 0.178 0.199 0.217 0'.236 0.254 o'.270 o'.233 0 -.292 0'.285 0'.253 0'.227 0.093 0.094 CMC/4 0'.0075 0.0065 0 .0042 0.0024 0.0006 0.0 193 0.0 066 0.0092 0116 0112 0 04 3 0 0 68 -O'. 0068 0.0001 0047 0090 0116 0 143 0 158 0.0174 0.0095 -0.0166 -0,0294 -0.0774 -0 .0733 0015 Rir = 0'.5(10)6 60%SStP TSUSL ALF - 4 . 6. 7'. 8'. 9' . 10'. 11'. 12'. 13'. H ' . 15'. 16'. 17'. 18'. 19. 20'. CL -0.354 ~0'.261 -0 . 169 -0. 081" -O'. 004 0.068 O'. 150 0'.24 0 0'.327 0'.427 0.547 0'.677 0.761 0',8 18 0.878 0.941 T.0 09 i'.074 l ' . 126 r. 164 1 . 175 1.15 1 r.112 1.062 0,742 CO 0'.0258 O'. 020 1 O'. 0174 O'.O 153 0.0141 O'.O 139 O'.O 140 O'.O 152 O'.O 172 0'.0202 0'.0247 O'.030l 0'. 0 3 4 6 0'.0391. 0'. 0 4 4 6 0'.05f)8 0.0583 0'. 0668 0'.0757 0'. 0 8 6 0 0'.0985 O'. 1249 O'. 1498 0'. 1719 0.3052 CMO CMC/4 •0.095 -0.0073 •0.071 -0.0069 •0'.047 -0,0049 •0.022 -0.0026 •0.000 0.0007 0.021 0.0042 0.04 4 0 .0069 0'.068 0.0089 0.092 0.0115 0.117 0.0114 0'.138 0.0033 0.160 -0.0059 O'. 180 -0.0062 0.201 0.0 0 05 0.22 0 0.0060 0.24 0 0.0 10 1 0.258 0.0 126 0*275 0.0143 0.290 0.0164 0.299 O'.O 165 0'.297 0.0122 0.270 -0.0100 0'.24 3 -0,0289 0.219 -0.0418 0'.103 -0.0941 0015 RE = 0'.5ClO)6 80%S3 + P TSUSL CD 0'.0255 O'. 0204 O'.O 175 0.0155 0'.0141 O'.O 135 O'.O 136 0". 0144 0'.0160 O'.O 186 0'.0222 0.0265 0'.0298 0'.0334 O'.0.376 0'.0422 0.0432 0'.0554 0'. 0624 0'.0721 0.0802 0'. 1147 0.2212 0'.24.3 4 0'.2664 ALF CL - 4 . -0.342 - 3 . -0.252 -2'. -0.160 - 1 . -0.074 0'. o'.ooo f. 0'. 0 71 2. O'. 154 3. 0'.24 0 l\\ 5'. 0.329 0'.427 6'. 0'.548 7". 0'.670 8'. 0'.74 7 9'. 0.799 10'. 0.854 11'. 0.913 12'. 0.974 13'. l'.023 ^'f f.071 15. 1'.094 16'. 1.084 17'. 1.0 42 ie'. 0'.526 19'. 0'.565 20'. u',593 CMO CMC/4 -()'.092 -0.0074 - 0 . 0 6 8 -0 . 0 0 5 8 - 0 . 0 4 3 -0 .0039 -0 . 0 2 1 -0 . 0 0 2 3 0'.002 0.0017 0 .023 0.0052 0 . 0 / 1 6 0 .0075 0'.069 o . o i o o 0 .093 0.0110 0 ' . U 7 0.0115 O'. 139 0 .0043 0'.158 -0 . 0064 0 .178 - 0 . 0 0 5 6 0.197 0.0018 0 .216 0.0075 0 .233 0.0107 0'.251 0 . 0 142 0 .265 0'. 0 159 0 .276 0 . 0 162 0'.282 0.0172 0 .264 0.0013 0'.231 -0.0224 ()'.084 - 0 .0560 0 .085 -0.0664 0'.088 -0.0710 r v ^ » — » — » — * - + • - - . C°, ^ ^ ^. ^ °„ ^ » O 'Jl ^ W PJ »- O Z ru U i £ ift "» it-* j — • © © © © © © © o © © = I o 1 o 1 1 o o o ru L-J L-t L-J L-l r j r j >-* - © - 0 •o CO --I •cr- Ul L-l ru O *% t ru •r". >—» l/l r j LH Li i i w L-J c- - J -0 »— Ji c- CO c- rj t— r j L-J s*n •CO CO **-( - s i - j —J LH -o c L-i 4 ; L1 Co - J . - 0 - j Ul CO UJ 4-- — i CO o o o O c o C! o © o c © © © o © © © © o o o o o o 3^ rr, •» -'» -» '• * 'ft - '« -'« -'ft •t 'ft -' i •» • •t " '• • o 11 ru r j *"* —* ftft ft* © o © © © o o © © © © © © o o o o o o o — —- - J — ru © - 3 CD - 4 c- ui Ul 4* L-J L-l ru l-J *— r — ru ru i — - 'L-l L-l L-l -0 ^4 •c- Li J l - 4 • © Ji •CO ft* ft :co L..T •J\ c* •CO •J\ s/l ru 0 - —* - 0 •o LI L-l U l L-J L-J J l - 0 - 0 © — *-i J l o- ru ru »-» CO UJ »—\ I i I 1 j »—- ; o o o O © o o O o o o © © o o © © © © G o © o o o o o • • • • • '• ' •§ - 1 -# • • ' t - a - • -ft " ' t ' t -' t • ft - • •• « --» * • ' •» • • • " ' * ' • 2; rj r j r j L-l L-J L-J Ul rj ru rj r j r j ft ft* ft P— © o O o o o o o o o — o ru — o CO c- — rj o - 1 Ul L-J .— CO C7* j i ru o rj -*4 •o "** . CO LH CO .LH C- r j L-J L-l ft* • Co - J LI r j Co L 1 ru © Tj J\ -0 o i I i I 1 I ! 1 O o . o • o o O o o o © © © o o © O © © • O o o O o o o n o o o o o o © © © © c o o © o © o • © • * o :» o o * o * o o CO -+ c i L-l Ift- 1 ro ru r j ft* ; — i ft*: o © © © ft-; ft- t — -' ft— ; o o c -3 L-J •Jl ru ftft ru L-l ft CO CO j i "u -cr ru o - J . Ji J l L-J © --4 o ru O CO ru - 4 L-l Co o ui ru -J ~4 Ul *- Ul X. o W w CO cr CO !~ r - J ^ r - ^ - r - f - — ftft- — ft I i I i o o o c o->ic-ui*=L-jru © -o co ->i cr- j i is L-J ru •— © — ru L-I •*= r*. • -. -. -. -. -» -. -• . -. -. - . - • •« - n i i i i ft ' f t Ift -ft ft i f t ft Ift I f t Ift |ft i© © © © o © © © © © •© © © © ' • -. -. -. -« -. -. -. -. -. -. - . -. -. -. •« -• •« •• - n L-J L-J L-J L-I — -- L-J L-J rj — • © -o cb co o j l L-i r j ft© © o ft ru L-I r~ - J D C ^ C > ^ f t f t O L - J L 1 C - C - - C - C 0 f t C - r j - 0 C 3 - J K C ~ J C ^ > I c o L - i o a i j i c c w w w - o j j c L n a j j J i c - r j c - f t ' C - L ' i - j © © O C © © © © © © © 0 © 0 © © © © © © © 0 © © © • * » • • * • • • •» •* -t *• -« -» -» •• •» -« -» -i *t -t -» -r~i rorjfL'ft* — ft-ooocooooooocoooooooci -o t © --J L-! ft -o cc — j c- j l i : £- L-l L-l ru ru — >— — ft •— >- ru ru. M » - J * o c J S a t J 5 ui a m 3 —ie- ru -o - J 'C- LU s> co J I <3 -0 CO O Jl -0 -0 Jl J= CO CO CO © Co j ; J l Jl Ji ft Jl ~J LI Jl ru I I I I I © C © 0 © C © - © 0 © 0 © © © 0 0 © © 0 © © © © © © O " • "t -f "« "t 't •» 't *• -» "1 't "t -f "0 't -« '« 't ' r j rj rj L-I ui U J L-J J J U J rj rj ru ru r— ft © 0 0 0 0 0 0 — © jiMCoorufijiuJft-coc-L-iftCoC-L-i©--! — ru©rj'Ji--Jo j i ft ru -o Co co o ft.ft.--j * - . j ; ft*:cr- o ru Ji c- Co L-J © L I o - J ru t i l l 11111 o o o © © o o o o o o o © o o o o © o o o o © o o r ) o o o © o o © o © o © o o o © o o o © o © o o © © r > o Ji rj o © ru J J L-J rj rj •—•:•—.!o © o •—:•—!—,'© © © © ft;—;— c w c « C D ' j - ' i i \ j o - J L J i L J - - i > - - j n j i \ i o s e > - c o - J : J i * ! J 1 L T . J l C ^ O - O f t J L - J f t - e - - 4 C > - 4 f t ^ O f t ' J i - j ; r u ^ ft3 Si tr !-• n) 1 o it • ~-J I O 0 8 CO r -r-Co r j f t f t f t f t f t f t f t f t f t f t f t I I I I > 0 o cs - j c- u i Ji L-I r J ft: © -o co --j o j i J i L-J ru •— o — ru L-I Ji r— . - . -. -. -» -. -. •» -. . . -. -. -. -. -. -. -. -. - . -. -. -. - - n i i i i t ft Ift 1 f t , f t ft 1 f t ft V- Ift Ift iO © © © © © © © © .© © © © .© © r j L-I L-J L-I L-I ru r j •- c © -o co - j c- J I •= L-I ru <— o © 0 •— r j L-J r~ LI ft Ci Li L-I -O L-l Cf CD © P J Ji - J O O L-J rj L-l L-J i l ft CO - 0 - J - 4 a r j a o J I i J I r j -0 u rj c- u c- J ; U J I c c- co c ui c co s. © C © 0 0 © © © © O O C O O O O © 0 © 0 © © 0 © 0 . * -» -« *» ** *• -• *» -< -» -• -1 -» - i - v *• •• *• -« ** -» - n ro r u f t f t ft*ftO©o©oo©oo©oooooooo©c? 1 c - J i u c j) co - J o- C J l i w f j rj M >- - •* -* ft ,M ru Ji --j-ft .L-i v :> s- a j s a a L-I . 1 -o U l —:o - j - s - - J - C O —'—-O C O J i L - l J i r j f t - O f t f t J i L - l ^ © C O C l - f t - - J © L - i O L l ^ L - l C O 1 1 1 I I © © © © o © © © © o o © o o © © © o © o © © © © o r i ' • * -» « -. "I "t •• • ' t "t • • -« • "t - » - • "t . • • r j r j ru ui L-I J I L-J rj r j rj ru fj »— ft •— »— © © o o © o o © ft © — c - - c r j ^ i i \ j o - c - J J " i r-u o cc c- — »— o cr- Ji rj o ru L I --1 o © CO --I L-l O Ji CO ft L-l O --I C" L-J © O C- TU CO L-l o ,'U J l O C- ft. I l l ( l i t o o o o o o o o © © © © © o o o o o © o o o © o © r - > © O 0 © © 0 0 © 0 © 0 © © © 0 © 0 0 0 © © © 0 0 0 0 j i L-J o ft iru L-I r J rj rj ru -—.—.© © —;—:—;»—;»—.© o o o »— j*— j —^-© f t C D C o - j © c o c > j ; f t ^ i \ j c > © f t L ^ - - J J i r u ^ f t j i c o f t - t j i ^ f t - 3 L J 4 i J ) C ' - 0 C > - J ^ C - > - J l C ) O " - - i l C ) J 3 C - 4 C » - 0 J l II o J l ci co NJ NJ 00 nj»—•—>—•—*—•— I I I I > o j M s i c- 'Ji £ u ru - o o a s ^ u; c u rj • - o - r v c r • -. •• -. -. -. •• -. -. • -. •-. -. •. •. -. -. -. -n I I I I I o O ft- ift-* It-* ;ft— !.— ift— Ift— ift-* I O c o G cr o o o o O O O O O G O O • • -. -. -. -. -. •. . -. -. -. -. -. -. -. -« -. -. -. -. -. •• -. rt ~ - 4 'tu ru ru rj >-• ,o -o CD c o - 4 c - ui ft L-4 P J o o o >— ru L-4 r~ Ui ft- L-4 T J UI C- L-4 - 4 T J ft -4 43 L-4 0 - CO C*- L-4 P J L-4 ft C- O - 4 3- C- CT-O -4 J l 14 ft* , G 43 L 4 L4 ru Ul ru Ln L 4 P4 C- Co ft ft C"- Ul 00 43 Ul rj o c o o o o c o o o c o o C o o o o 0 o o o o o 33 m II L-l o o o o o o o o o o o o o o o o o o o C3 o ft— .0 c- L-I ft-o o Cc -4 c- Ul Ul ft ft Ul ru ru ru ft— »— ft— ft-* ft— ru ru • • CD ru u- ft L l r— ' f t ft Jl •cc ru cr ft— ' f t CO ft o CO C> c- -4 Co ft— . f t Ul O L-4 ru 00 o L4 -4 o ru rj 43 Ul 0- o 0- c- — 43 0- 43 0- o Ll " UI \ 1 1 | I t o c o o o G o o o o o C o o o o o o G o G o o o c f l • ' '• - i • '• • • " 't ' 't ' 8 ' • - • - a ' i ' • - a ' ft ' i -'ft - 1 ' • ' t - • * '8 • t ' 'ft ' 1 • zz cr ft— ru rj rj U J L4 ru rj ru rj rj ru ft-ft ft— ft-. ft-o • f t o o o o o o o o o ro c- 42 ft— ft— 43 •Co 3 - ft ru o Co cr- ft ft— 43 -4 ft ru o ru ft -4 43 Ul 43 -4 L.1 — O CO — ft Ul -4 • — L4 Ul CO Ul O cr UJ rj ru o ru 0- C* I l 1 l I 1 i 1 Mi o o o o o o o o o o o o O o o o o O o o o o o o o T~ ' rt — • J : co o o o o o o o o o o o o o o o o o o o o o o o o o o + - 4 U4.»— ;ru LJ UJ .ru ru ru ru •— . ; G o • - ; — > - 1 — ; o o o o •— n-» i - * , . u ft-*ft-ft-C0ft-ft-C0CPL4rUft00-3-l\;CC43CPL4C0Oft--4OL4ft L4 -4 0- *04C43fU43CrUiUlPjru—4CDU4ftro ft-.ft- Ul — ft v l u l —1 . CO cz CO ft- ft- ft- ft- ft- ft- I 1 I I > ui ft L4 ru ft— o 43 co -4 c- ui ft L-I ru ft—iO'*— ru L4 ft r -. - . - . - . - . -. -. - • . -• • -» -t - n o • Ul - 1 ft-ft— L4 0.983 •o ft • CO 43 J l o • CO L4 Ul 0.776 o ft " -4 ru Co o II • c-o o Ul Ul -4 ft ' L4 o L-l Ll O o ft -ru ru • LH ft 0.076 0.009 -0.062 1 ft '• CO 1 p; Ll 43 1 o L4 L4 Ul n i~ 0.1637 O • -o Jl -4 . 0 • • o LJ 43 o ft -o U l Jl ru o • -o U ' L4 O c ft -o ru 43 0-o t -ru Ul c ft -o ru Ul 1 o ru CD o ft • ..CO CD O O Ul C * ' o L-l ru o o -4 • * o o « o ft— o '» -o ft— 43 o • o ru 04 o ft o 43 O • -o -4 43 O ft -o ru ru Ul o o o • ' o -4 CC G ru O t ' ru Ul L4 c 8 ' ru o ru ui ft— o '• ' rj Ul o « • 43 QL i • CO o c 8 ' ft— G t ' O •» •• ru . o O •t • o 43 C-O 'ft ' o -4 L4 o 8 ' O Ul o o 't • o ru Co o 'ft ' o o I '8 ' o I o 'ft o 01 43 1 ' t ' o < o i ' O CO CO rt o I o o o o o o o o o o o o O o o o o 1 o I o I o . . . . . . . . . . . • . • . _c o o o o o o o o o o o o o o o o o o o o o ft L4 L-I u i . r u r u ft- :•— 1>— ; r u r u io o o o •- ;->. — i r U i \ l i ' \ 3 C 0 U l O f t O L 4 O O — J f t O U l f t - f t C O f t — ft PU L4 o O- ru -4 — -4 43 U4 »-• ft 43 Ul ft C- Ul Ul -4 ft O O Co -4 C- Ul ft L4 r u •— O 43 CO -4 0 - Ul ft UJ PJ ft-ft— Ift— ift- .'ft— ift- ift— .ft— Ift- ift- i f t O - O O O O O ft O O O P J ru L-J L-I L-J PU ru >—.o -o -o co - 4 c- u, ft L-J P J ft- O O co ft- ru o c- o L 4 0 - co o ru 0 - co L I ru ru L4 3-ft-.L4 r u r j C - f t O O C - o r u O C c r U f t C O U l - 4 - 4 - 4 - - ; I I I I > 0 ft- ru L 4 ft r~ •« -• •• -• -. - n 1 I I I I 0 0 0 0 0 . - . -. •• -• - n O o ft—.ru L-J T~ ft— CO —4 —J —1 ft L4 - 4 . ft • - . o o o o o o o o o o o o o o o o o o o o o o o c o •rt 11 ru 0 0 O 0 0 O 0 0 O ' 0 0 0 0 O 0 0 0 O O 0 0 U l O 0 ft— 0 -43 Co - 4 0- U l ft ft L J L-! ru ru ft— ft-ft— • —* ft— ru ru « J I O 'CC - 4 :-4 • ft L4 ru ru L-l c- 43 L 4 - 4 '-— I J I 0 00 Ul J I J l c- CD ft— IU1 U l 0 43 CO 43 U l — — ru ru 0 - 0 O L 4 43 0 - 4 ru 43 ru ru ft — ru ui »—ft' 1 1 I 1 1 0 0 O 0 0 0 0 O 0 0 O 0 O O 0 O 0 0 0 O 0 0 0 O 0 0 r> w « -' » ' t ' % • ft ' • - ft ' t - • -'• ' • • " • " 't 1 't ' • • * - » -'• ' • ' » ' * - t ' '. * • ' ' zz 0 -r j ru ru L 4 L-4 U4 ru ru rj ru r j 0 0 0 0 0 0 O 0 0 0 U J ft CO O -— ft— 43 - 4 U l U4 •— 43 - 4 J l L-l ft-CO c- ft ru 0 ru ft - 4 I-— 43 - 4 - J - 4 ru J I CO 00 CO CO - 4 - 4 - 4 L l U l 43 0 L 4 1— *-» .L4 - 4 •ru - 4 U l 1 1 1 I 1 1 1 Ml 0 0 0 O O 0 0 0 0 0 0 O O O O 0 0 0 0 0 0 0 O 0 O rt r-CO 0 0 0 O 0 0 0 0 0 0 0 O O O O 0 0 0 0 0 0 0 O 0 0 rt -*-ft ft ft— i o rj ru • j »— ;— I ft-Ift— :o O C O ft-ift— i ft-I-— 1 0 0 0 C 0 ft-I-*.- 13 (3- L 4 0 OS IU 3 - ft-43 - 4 ft L4 —1 ru O - 4 U l c- ft »— 0- ru ft O- 43 ft— ft O c- 0 - U l ft U l U l 43 c- Jl *— ft ft - 4 •ul U l c- 0 - 4 - 4 ft ft - 4 04 CO —4 • c r 1-ro 33 cr. n . , o o o co cz co 1 i 1 I > -4 U l ft U l ru ft— O • 43 CO - 4 0 - U l ft 04 P J ft— . O ft— ru L-l ft I --n 0 1 1 1 I 1 0 0 ft— ift— 1— l i- i ft-I— 10 0 ' O 0 0 O 0 G G G G O 0 O O 0 ft— • ' '.ft * • * ft ft -. -• - • -• -ft -. -. -• - . * • -. ' « -a ' ft -. • ' • ' 0 ft-LP. ft— .ft- .1—' < G G - 0 CO CO - 4 cn ft L-I ru ft-G O O — rj L-l r~ U l L 4 wl ft ft— -4 G ft -4 G ft 0 U l ru ru L 4 c- G - 4 c- L n O ft— 4; 0 — . f t U l G L 4 L4 CO ft 43 ui U l •* 0 ru U l ru ru c- 33 33 rn O 0 0 0 O O 0 O G G 0 0 0 O O 0 0 O 0 c 0 n 11 . - n 11 0 ft-0 0 0 •ft O 0 O O O O 0 0 0 C - O 0 0 O 0 0 0 ro 0 . - ft— •0 -4 - 4 Cr- L.1 U l L 4 L 4 ru ru ru »— ft— ft— ft-ft-ft-ft— ru ru * ui c- ru CO 0 IU C"- G ft CD ft 4; -3- ru 0= c> •_n t U l - 4 — i f t U l 1—. 43 ru U l 43 43 L.1 O CO ft 0 - ru L l 00 CO ft U l 6 - 4 — 0 U l .—«.• 0 1 1 1 1 0 O 0 0 0 O G O O G O G G 0 G 0 G c G G G G c n 0- • '• • ft ' • • • ' • ' ft ' " ' '• ' ' * a - » * * ' "t ' • ' • ' •t • a 'a ' a ' a • — 0-ru ru ru ru ru ru ru ru r - ft— ft— r— •ft- G 0 O 0 O 0 O O 0 0 J I CO CO CO - 4 J I U l »— 43 - 4 c- UJ ft— 43 - 4 ft rj O ru ft 0 - 43 00 c- 0 -4 — . 0 L l 43 43 43 CO O 43 CO L l — - 4 • f t 0 — 43 — -4 • 0 0 is; 1 1 1 1 5-S 0 0 O 0 0 0 0 0 O O 0 0 0 O O O 0 O 0 O O 0 rt T~ CO . •* • ' I Ul + 0 0 0 0 0 0 0 O O O O 0 O O O 0 O 0 O O 0 O t-13 0 ru ru ru ru rj ru ru ft-, IO O ft— •ft— iru ft— ift— I G O 0 O G -— 13 0 0 X 43 CD -4 ft ft-U l CD -4 ru 0 0 0-ft •43 L 4 U4 3 - CO ru ft - 1 43 -4 •JI ft ru 0 3- -c ;\> ft ft U l c- co U l 04 43 ru - 4 J l ft— —i cz cr. L O r j — — ftft-ftftH-ftft i i i i >• o O Co S C 1 Jl C L*J PJ r - O O CO SI C i.T J i W W — .© ft .ru l-l J i ~ • -. -. -. -. -. •• . •. •-. -. -. -. •. -. •. -. -. -. -. •• -. -. --n I i I I i o ft ii— i f t ft ft ift ft ft . 0 © © 4 = o o o © o o © © o o © ci . -. -• -. -. -. -. -. -. -. -• -. •« -. -» -. -. -r, • J — I ' J N N ru - " c j) a a «i ( M l £ w P J » : c c o >• rj i-i r~ r j c- i'j c u n u ^ J o w c co - i c- i H> >-• ru 1-1 in a - j - j c L-J J> o c co c r j - J J I j) c a 'Ji J) i r j w - J 'Ji ci 0 P J CO O © O O © O © O © O © © O © C © O O © © © © G © © • •. -ft -ft •• -• -ft •• -• -ft -ft -ft •. •« -ft -1 •• -ft •• •. -o r j f t f t f t f t o o o - 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 •0 CD j i j.; o o co -j o J I J I j i j i i.-i r j ro ft ft ft ft ft ft ft ru ru Co J J - J O JO • 0- J l C r - J ' J J M ? 1 - 1 ? D i a O i c i . l v l C i ru ft ru rj ft - i ^ c> c» P J o ft ft J i o i.-j co o o ft J J ivi J I co t 1 j 1 1 o o o c o o o o o o o o o o o o o o o o o o o o o r i « '< 'ft ' » -ft 'ft 'ft * • ' « *t 'ft " t "ft • • *» "t *• "ft " t 'ft "ft "ft " f "t X ft ru ru r j 1-4 J J ru rj rj rj rj ft ft ft ft . 0 o o o o o o o o o o 1,1 - J J J >- o o - - i 'Ji u rj J J - 1 j i w - a c- i M o r j i ~ i o j i ui :u j i ru ui ft j i —1— i © -j -j - j c> w J ) I M J ftft,JI 00 I-J -j I I I 1 1 I I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 o o 0 . 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 si J J . 0 ftirj rj rj ru ru ftftift;© o »— i h - i n . ; — i — c 0 0 0 ft:^' j i j j c o i j - i c t u i - a - j i - r w o - i - J j i . v j M i s - j o m c c o s o c - j a c o o f t o s r o o c ft>-i s i ft i«i ru ru s i c-i o 1-1 j i cr o o J i cu n 11 CO CO + -I co c C l I— ft-_ftftftftftft t I I 1 > s i o J I J i c-i ru ft o JO co - je* ui .e n ru ft© 1—,ru L-J J i r— • . - . • ' . - . ~ . - . - . • . - . " • ' . - . - T l J i l l O O f t Ift I f t I f t O O O O O O O O O 0 0 0 0 0 0 0 0 o • -» •» -• •• -• "• -* 1 •» •* - * ' • •• ' • ** *• •* '» -* ' O ft LH O — l O O -0 O CO ^ I s T C - L i © L-l r j ft'O c o - N w r . Ul c c- a a i a r j c» J ; i-i c i r j r j i-i i - 1 c c in - i — j >— : - - i j i r j o J I o J I j i s i -o cc J I j i J I o J J -o J I J J J I ccj 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 n . - . - . - . - . - . - . • . -m -. -. -. -. •. •• •. -o Ii ru 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 o o o o c j o ru -o o- J l J i J i J= L-l L-' L-J rj ru 1— ft ft ft ft ft ft >— rj • " c L-I • co ru --1 ru - J L-I ft is i v i JJ c- c-- L-I u - J c c J I i J l Co JJ L-l L-J L-J 0- LT CD ft L-J CO J l Co CP CP PJ CO O- J l JJ — t i l l o 0 0 0 0 O O O O O O O O O O O O O O O O O O O 1 ~% *» ' • '« "• "ft "ft "* '« '» '• "• -1 "ft -ft *o -ft -ft - Ci c-0 r j ro r j ru ru ru rj ft ft ft ft ft o o o o o 0 0 o o c C O J i - J | - J ? J T L - l f t J J - - J ' J l L - l f t J J s l J i r j O f t J i C - J J ^ C ^ J J J J O J I ^ O - J J J J J C O - ^ J l f t C o j l ' J l j J f t - J - o co 0 1 l i l t Ml 0 0 0 0 0 0 0 0 0 0 0 0 0 0 . 0 0 0 0 0 0 0 0 0 co 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 + j i o c-i LJ . jJ.ru rj ru I-.I-IO — .ftirj — ift.'o o o o o <— is.. -0 L - l ? f t J i L - J J J C > . O C > f t - J L - I J J O - J | J i - 0 J i r u L n j J O J i P J , M -j.w - J 'ji ui ru in a - o iu c- 'Ji ? o a - j i in -< CO CO P J 1 t I 1 > 0 J ) Co s i • cr-Ul J i L-l ru 0 J J CO n J i L co L-J -4 ft i - 4 c i c- i rj r j rj 1-1 c- o - 4 -1 o- c-N ' ID J J p -o a - -rj - i j i c- cc j i —.00 co c c- J J ru co c-0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 > •• -• -• •« -. •• -• -. -• •» •• -. -« •• •• -. -• -• -o ru ft o o o o - o o o o o o o o o c - o o o o o o o o in ru J J cc --4 c* c- Jl Ji Ji L-i 1-1 L-* ru ru ft ft ft *-— ft *— ru ru L-l ft.'J) Jl O O l-l CD . V 3 i-l C OI ftlCC -~IJ1 - J ! C - CO ft • J! ro ca ft o o co CP 0 J I ~ J •-- co ft •-• r j - J L-J J J i l L-I cr- in 0 1 1 1 I 0 0 0 0 0 0 0 0 0 0 o o o o o o o o o c o 0 0 0 • -ft -ft -ft ft •• -ft ft -ft -ft •• -ft •• •• -ft -ft -ft -ft -ft -ft -ft -ft '» • i 0 r j rj L-J r j P J ru ru ru >— ft ft ft ft o o © o © o o o o © J J - J . J J o co M ir, U J ft J ; - j Jl L-J J J CP Ji ru o ru si o J S ; J N o a i - J a o 3 S - J J a c- w cc J I w - w - - i w a 1 f i l l 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 « « -» 'ft '• • '• '« « « '* '• '« "• « - • « • ' • • < • « 'JL O © 0 0 © 0 © © © © © © 0 © © © © 0 © 0 © © 0 0 j i © ru L-i.LJ.Lirj ru r j >—io © ft-:ft;ftii—;o © o o 's,• S ' J l S - W O O S t O C C M M l j O J J C M - l - J I U i S f t L - 4 J i j - r i j L ' i r j s - o o o w r j c - t s j i f t - f u o o o c - r - w c -XI rr, It C l co co CO r-ro o IV — —ft-ft-ft-ft-ft-ft-ft-ft- l i t O'O cn -4 o a u r j i . . c - a co - j p u i c i-i r j - o r j u '-*_'•"•_'•-*_:•-"_''—_."— — ' — I— 10 o o o o.o o o o o o o o o o ui cn on ui ft L-I ru — •= o co -~i -,-ono a c U1C U l v l £ I U £ O O O O O O O O C O O O O O O O O G O O O O O O O — ft- — — ft— ft-0000000000000 O O O O O O ru.oOft:[j-oa-4?r/jiEWL'[rjruft-ft»ft*--ft*ft-ruru ft ru iv ru r> L-J s co o ru -.J" -4'— Jl ru o -4'C- cr- -4'4; >-;JI ft- j j r u c r . O f t f t W o c o 4 i - u 0 5 M - - i f t f t . o r u - - j u i w o o f t * w i -i I I I I G G C G O G O O G O O C O O O O O O O O O O C O O - " - . t *« 't * • "t * i ' t 'ft - • •* " t * • -* *• ' « '% '• '• *l ' t ' * ' » * 2 r u ru r j r u r j ru ru ru ru ru ru ft-* — «-* o o o o o o o o ft- o — r u r u r u r u i v — — — o o 4 3 C D C > f t — 4 3 C P f t r j o r u u i - - 4 o 43 o L4 rj ru o co u i — .Co ft co cr LT ru co ft 43 ui o ft --4 ru co ft f I ! I I I I I 1 I I I I I I I o o o o o o o o o o 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 • ft . -. . • ft ft -. . . » . •« • - ft . ft ft . ft . . "£ ft— ft— ft— ft— ft— O O O O O O O O O O O O O O O O O O O O O ui r j ru ft— 'o -0 -4 43- ft L4.ft—io o ft— ,'ft—.'•—:ft—:»— :o o o o o o — 1-**.. C o C o U 1 4 3 U l P U — J f t C 0 f t - U l ftUlruUlUlftft- 43C->— f u U l C o o f t o o - 4 r j - 4 - - ? a J : u i u i - - r j o £ i \ j w w w o c - j i f t - -JO-1 I 1 1 3> 43 Co -4 • C - Ul ft L4 ru ft— o 43 CO -4 c- Ul ft Ul ru ft— o ft— ru L-l ft f— • -• ' •* -• *• -ft *• -ft -ft -• -ft ' 'ft -ft " •ft -ft *• •• -» • -. - . • ".• -n 1 I 1 1 o ft-Ift- ft— I-— .'ft— it— ift— ii— ift— ift— 'ft— I O o o O O o o C o o o o o c •ft -ft ' '• 'ft -» 'ft •» • 'ft • 'ft - " -'ft 'ft -'ft ' '• ' 'ft • -ft ' •ft ' 'ft -ft •ft • •n ft-C- Ul LT Ul U i ft ft L-l rj ft— • O •0 ri- c- Ul L-l ru o o ft— ru L4 r- Ul ru ft ru ft LJ - j G ft— ru ru ru L4 ft— -4 LT L4 ru o 43 o CO -4 - i 43 LT ru co -1 -J 43 -4 - ru LT U-i C- . ft UJ - c ru ft 43 o UJ Ul ft o o c o o O O C o o o O o o o O o o O O o o o o r?t • -'ft 'ft -'ft. -'ft 'ft -'• '• ' '« - • -ft -'ft '• • ' • " ft -'» 'ft ' « 'ft 'ft • '» - ft. o ti ru ft— ft— ft— ft-* o O o o o o o o ft o o o o o o o o o o o ft— • *— 43 O ru o 00 -4 c- c- Ul ft ft L4 ru ru ru ft— *— , . ft-ft— ft— ru ru 9 ' 13 C TP -I L-J co CO co ru ft C" t— I f t Co ft o 'CO 0- Ul Jl ' J - 43 ru o • CO 3- Ul UJ — -1 PU UJ *— ft— Co PU CO CO UJ CP - Ul Ul UJ 43 Ul -I Ul *—ft I 1 I i o o c o o o o o o o o o o o o o O o o c o o O c . c o w • ' zc o-ru ru ru ru ru ru ru ru rj ru ru ft— ft— ft— ft-ft— o o o o o O o •— o ft— ft- ru *— ru ru ru — ft— o o 43 43 Ul O -4 Ul ru o ru ,-- -4 o o Ul o c- L-l LT ft— ru — o — -4 o — o CD 43 o ft — ft -4 ru ru 01 i 1 1 i I ,- I • • 1 I 1 I I 1 I , o r-o o o o O o O o o o o o o o o O O o o o o O o o o ft-* ft- ft- — — — ft— o o o o o o o o o o o o o o o o o o n CCl Ul L4 PU L4 rj o 43 Co G-ft L4 ft—i c c a o o o o o o o o • - i N f t -CO G- Ul .u ru CO CP Jl L4 43 ru cr Ul 43 43 CD Ul ,-— ru ft-Ui -4 CO ft— ft > •— C- Ul CO -4 UJ C- c- UI -4 ru ru — U4 o PU -ft ft-L4 Ul Ul Jl -4 p— 01 1 o PUft-ft-ft-ft-ft-ft-ft-ft- — ft- i i i i > O 43'Co-4C-UlftL-irUft- O 43C0-4C-UlftL4rUft—,o - ft— r u L - l f t r -ft- -ft- ! — Ift- i»— 'ft- I*- Ift- ;ft— J O O O O O O O O O I I I o o o o Ul Ul LH Ul ft CP L4 L-l ft- LT 40 ft-.Ul ft ft-i L 4 L 4 T J — O CO C i r u L 4 LT o ft ru 43 »-43 03 -4 C> CO o • UJ ft ft I ft L 4 L T J l ft ru O O O O O O O O O O O O C O C O O ru ft— ft— ft— ft—. a— 43 c UJ ru - I iL4 O 43 L4 CD O Ul O L 4 - * : 0 O O O ft— 43 CD —4 C -o ji - J ? -4 •Cr O LT O- Co O O O Uc U l ft o ru ft ui ui 43 o o ' ru rj r j — o o • •• -o o O o ft-n-ft C - O O 43 ru ft i—.-4 o c o o » -» •» • o o o o .LD CP • CO CO I I o o • -• -o , P J L4 |— 43 43 ft r u o o • •• 'O o o C3 ru ru Jl LT C- CD i 43 - 4 C- CP UJ 43 O O O O O O o o o o o o o o o o o rj ru ru ru ru »— ru ru ru ru 43 O LT Jl LT I I I I I o o o o o rj ru ru ru ru rj ft- ft- ft— o •— 43 O .' J 43 • I I I I o o o o o ft CO -I I I I O O O ' L 4 .ru r j ft- ,'c • Ul C o Jl ru Ul >— C- Ul Ul o o o o o O -4 I- ft Ul O CP o CP o 43 O CO L4 L4 O O O ft— I O O I Ul L4 'Jl ' Jl O UJ O o • ft O o 0 O 1 - ft ' O o -4 L4 o o I I o o o o O O o o — o PU ui 43 •— -4 >-« I I o o o o I I o o o t ft ' X O ft- o -4 O -4 ft-. I I o o o ft L4 U l CO o o ft— ; c O 00 U l c-O O o o o o o o U! ru L 4 Ul PU O ft -4 o o o O ft—,'\ • 43 ft- ft — UJ c ft-Ul nct n fl O o co CO co c u> 1 I 1 1 > 43 CO -•4 C-. U l ft L 4 r-j ft— o 43 CO - 4 C- U l ft L 4 r u ft— • o ft— • r u L4 ft r -' • - » - « '* •ft -ft • 'ft 'ft "ft "ft -ft "ft -ft -ft -ft -ft -ft • • - I I •• ' • -n ft— ft-ft-•ft- •ft— Ift- :_ . = c C ~ c o O I o c I 1 1 O • t " ft -' • " '* '* - • 'ft 'ft -'ft ' * • 'ft ' • - " 'ft • ft -'ft-ft '• • • * 'ft -•ft •« "ft ' • ' ' w L-J L-l ft L - l LM r u ft— o 43 43 •CO - 4 O ' J l ft L-l r u ft-; c - . o G ft— r u L-: I -- 0 43 G ."1 O L4 c - 43 43 r u U l - 4 U l L4 ft- ft ft ft c - ft— 43 43 CO CO LH 43 L-J CO L4 • CO CC L 4 CO 43 •— U l *-° U l c - r u 43 r u 43 43 ft . c o r u O O O o re- o o O O fC- o o o O o o o O c O O O o G a • 'ft ' ft -ft • ' • 'ft - li -• -ft -h -• * ft -• • - a " ' • - • 1 'ft ft -' • » O ft— ft-.»— ft— o o o o • o o o o o to- o o O o O o o o o O - 4 U l r u G 43 CO - 4 - 4 o u" ft ft U ! r u r u ft— ft— ft-ft— ft— ft— ft— r u r u o 43 G CO 43 43 43 ft— ft— .ft - 4 •ft— Ift CO L-l 43 - 4 U l •J l J l 3*. 30 ft-J l o 0 - r u L-l CD -1 - 4 * - " 43 CO •0 L 4 r u r u 0 - CO — Co o - — ~ 1—-o o o o o o o o o o o o o O O o o o o o o O G 12" r-> o 43 43 CO - 4 G- U l ft r u ft—, I G G ft-•ft— Ift—1 'ft- -ft-I O o o G o G ft—. !-<-.' J l 43 Co 43 o 43 c- »— r u CO- o u ; ft— - 4 J l ft t— 43 0 - r u ft— ft - 4 o ft C0 ft- 43 ft ft— • c * CO ft CO ft - 4 - 4 O U l O o O r j 43 CO ft— - 4 L4 ft- ft- ft- ft- ft- ft- ft- 1 I I I > c- ui ft L-I ru • - o o co -4 c- ui ft L4 ru — o •— ru L4 ft r-• - . -. - . - . - . - • - . - . - . • - . - . - . - . - . - , --n • i i i i ft- , , — ft- i— .w- G O O O O O O O O O O -O G O G . - . - . - . - . - . - . - . - . - , - . - . - . - . - . - , - . - , -(-j »— ft— ' G O G 4 ; CO CO - 4 •C~- Ul ft L-l ru ft— G O O ft-rj L-l -— L4 ru o JI . O L4 CC ru LT ft ft m in c- 0- -1 G Co -I c~- c-rj L4 Ul in ru •ui ru *— • 43 - 4 • — LH Ul L4 cr- O ft— -1 43 -4 o o o o 0 O c 0 0 O O 0 G G O 0 G O O 0 O rt o o o o 0 O 0 0 0 0 O 0 G O O 0 O O O 0 O 0 c- Ul ft ft L4 U.1 L4 L4 ru ru ru ft— ft— ft— ft-ft— ft— ft— ft— ru ft ft-•J ! G ' CO ft ft—. IG Cr- . 4 G - 4 : f t L4 ru ft— .ru L-l O CO L-l o- ft— Ul •O t— Ll •"~ 00 L4 LT — O Ul Ul C- — C0 O CD 00 o o c — C G O O 0 G G 0 O G C O 1 O 1 1 1 c r> * • t * ft » - t ' ft '-I ' 1 • - t ' » ' % * » " ft ' » - t ' » ' 1 * ll -• 1 • :i ru ru ru ru ru ru |-J ft— ft— »— ft-1-* O O 0 O O O O O 0 0 o o o o 0 G 4> • 3 O ft ru - 4 ft ru O -— ft C"- 43 0 - - 4 cr- 0 ft L4 O cr — Ul ft ru CO — 43 - 1 ft CO — 43 Ll I 1 » 1 f > 1 t I o o o 0 0 G O 0 O 0 O 0 0 O O O O O O O O 0 o o o 0 0 O O 0 O 0 O 0 0 O 0 0 O O O 0 O '. c r-> ft ft L-l .Ul ru O O 0 « 1 ft— I— 1 it— Ift—-! i 'ft— 1 IO G G O G ft— •s. • - 1 ft 43 »— ru CO O Co ru - 4 43 43 cr L4 1— 43 ft O L4 - 4 O ft o Ul Ul 0 •— c- *— -O - 4 O ft-0 43 L 4 ft 1— ft— ir— ru ft Ll 43 CO - J O Ul ft L 4 ru ft- o - 4 3 CD - 4 C- Ul ft L 4 ru ft-ft "ft -ft- -ft -ft -'• -ft -ft -ft -ft -ft -ft ->. -» -_ ,- . -—J | -*J*— Ift— Ift— Ift- Ift— -O O G O O O O O G O ft ft ' ft ft L-l ru ru •— O 43 CC *-4 > CT- LT ft L4 ru ft— c -4 43 3- — ft - 4 G ru L l n -4 CO 0 - LT ft ft Ul ft 0-ft—.43C---4—4CCTUC Co ft— C- ru ft •— .00 — It— . -4 G I I I I > .O *— TU L4 ft r— • -• - T l I I I I 0 0 0 0 0 ft ••» -ft ft -ft - f l o •— ft- r u L4 i~ •-U G 43 43 CC ft- ft-; 43 ft 43 G G O O G O G O G O O O G O G G O O O O ft—'ft— — •— ft— O O O G O O O O O O O O O O c o u n L 4 - U G 4 3 C o - 4 C - u . f t f t L 4 r u r u r u f t - » — f t -ft L 4 ft c 03 Ul ft ft Ul 3- 43 ru Ul 0 ft G -4 . J l ii.' C O U J 4 3 * - — ft-40-"-44343-4OUlft-— ru C o — J 4 3 G G G O G O O G O O G O G O C G O G O • -» '» "* 'ft "• 't ' 1 "t '1 *t *t t •» -f -fl -» -» -» • ru ru ru ru ru r j ru ru ru ru >—>—--•-•— 0 0 o o *— ft— rjft— ft— — ft— OOO4303C-ftft— 43i0-ftru Ul -4 -ft— - 1 — 4 L 4 ft-,-4-ft O 3> ft L4 1—;C0 L4 CC Ul O I I I I < ( ( I I I I O O O O O O O O O O O O O O O O O O O I I t O O O -—ft— * —— O O O O G O O O O O O O O O O ft— i r u G G CO -4 O ft L-J ft—.'G O ft— Ift— ft— !•— ;•— IG o 4 3 0 4 3 r u — I U l > - - 4 i — 3 - f t U l v — ftJlL4OCD0-C - f t f t C O 0 C D ' " 0 L 4 4 3 - 3 0 f t f t O 4 3 O C - - C D 4 3 ' -O O O ft— I G O O O CD IU L4 -I O ru - 4 -o ft c-I o 0 • cc o o i-3 tu CT fD cn G O O G « -» '• -• -• * rt O O G O O C3 ft- 1— •— ru ru ui a- co ru ui ru L4 c- o ui I I I I I. o 0 0 0 0 0 0 w 1 - ft 'ft - a ' t ' 0 -O O O O O O ru ru J I - 4 43 ui . 0 o cn 43 30 P i II •—I fl " G I—\ — I ON -Nl Ul o M : r -co + -0 o 1 I 1 1 > Co -4 *-> LH ft ui ru ft— 0 ' 43 CO -•I C - Ul ft Ul ru ft— 1 0 ru L-l ft r~ • *• • - • - • • ' ' • i» -fl *• •» -fl -» ' -• - • '» ' • 'a "a *• • "» ' •~n 1 1 1 I 1 0 '•— '•— i»— ii— •ft— i — ift- O G C G G O G c G 0 G G G G G G G • •» " ' • -» • • ' • •ft ' ' • ' 'fl '• " • •• • 'ft -'ft • •• -•» •ft 'a •• • • "a 'a • 0 ft-ru L4 rj ru »— 0 0 43 CO -4 Ul ft L4 ru »— ' C G G ft— .ru L4 r- Ul •0 ft— -4 L4 CO ru Ll 03 G ft 13- ft ft ft ft ft- n c ft- <3 CO Co -4 cr c- 43 L-i -— ' — G 43 ru rj 43 *-•Ul 0 0 G O O 0 O O C 0 0 O O 0 G 0 0 0 G G O O O rn 11 *— ft— O O O 0 O O G 0 0 G O 0 O 0 0 O O G O O O 03 ft—1 L4 G 43 CO -4 c- c Ul ft ft L4 ru ru ru ft— - — ft-ft-ft— ft— ft— ru ru « -O IV •— IL-J LH cc G ft -4 '— !J1 43 ft G -4 •ui t Ul ft c- Co ft- •Ui G ru -"- *"* ru Ll 30 0 - ft o- - — Ul 0- 0- Ul •CO ru 0 Ul I — *—V ft* i c O G G 0 C G G —; O O 0 0 O 0 0 c 1 I G I G 1 G 1 G r. • O A • « ' fl ' • * » ' » " fl ' fl " • '» " » - • - • ' • ' * • 1 * t • a " a ' 'a ' a ' a ' u: cr ru ru ru ru ru ru ru r j ru 1— ft— 1— ft-ft-O G 0 0 O 0 O O O 0 0 ft-— • — G 0 0 0 43 CO c- t ft— o- ru ft ru ^1- -4 43 c- ft— •-* ru 43 L4 Ul ru 0 ft ru ru 0 CO - -4 '- *- • O ru v l — Ul -4' 1 1 1 1 1 I • 1 1 1 1 1 I M! 0 0 0 0 O 0 0 0 0 0 0 0 0 0 O O 0 0 O 0 O O O 0 •— -*- CO G 0 0 0 O 0 c 0 0 0 0 0 •0 0 O G 0 0 G 0 O O O 0 + 00 .30 - 4 ' Ll Jl L-l ru G c 0 ft—' 'ft— i 'ft— 1 Ii— 1 Ift— I G G G G O O G •--.' Ui ft cv- 3- CO G 1 4 »— 0- ru -4 L4 c- C ft ft- 43 0- Ul O ru O CO . ft c- Ul ft~ ui O Ul O 0 Ul ru - 4 ' O UJ ru •Jl Ul C- 43 ru 43 c* ft c-co ro CO s i ru o • J J ro s i o LH J i L-l P J — i O • '• *• 'ft • '• -_* I f t I f t ft io • -'ft 'ft 'ft *• • * 'ft - • • '» -* X : l-J 7_ L-l L-l rj P J ft G G - 0 r j o 2 L i j; L-4 LH CD o P J - 4 - J •35 CD CP L-J Co O CP o © o O O O © O O c © o • f t ft o o O o s i L-J ft* o -0 Co - • J c- c- J l o o 00 J J s | , -.4 . - J •CD o V w J l o o J I CO o J i L-l *-i J J o co - j c- J I L-J rj ft i O ft I I 44 > r j i-i c r-o o o o • -• '* -< cc s i . o m J l C- i : CJ . J l L-4 O O I O O O O O : l-J PJ ft , C ft i m ? • j i JI •—. j i ft o s i —J 1 I I O O O • I "ft 'ft - 1 ft PJ L-J I 0 Co Co 1 CC Ji O O O O • 'ft -ft -ft -O O O O O O O O O O O O O fi j i l-l ru 3- O L-l s i ' 0 - ft o P J a -si'.n in J I J i co m © © © © © O ft ru P J - I C ! : O -O —J Jl c-U J P J o o o o ' © o O o o o o © o o o o o O o a " 'I ' 'ft 'ft ' * ' 'ft "ft 'ft ' '• ' • - ft '« "t ' •ft ' '1 • 'ft -'ft ' 'ft ' > -r j r j -u r j PJ r j r j ru ru rj r j o c o o ft i— ft ft ft »— ft o o o - 0 CC L> J l ft J J CP J i ru o J i -0 CO s | o l-i r j C- c- s i ft o -0 --I i - i X J i I 1 l 1 1 i I I i l • o o o o o o O o o o o O o o o o o O o o ft ft o o o o O o o o o o o o o o o o o o ft. ; © JO J J CB s i 'CP Jl J i r j o o o ft ift :*— ;i— .ft o L-J o JJ J l CO 3 - •j) o o L-l JJ PJ 3 - . \ J IT, Jl J i ft j j CP o PJ s i Co o L-J CO CP ft .—-PJ o J i s i J l Co Jl w rj o I I o c o o O P J I o o • 'ft o o o o I-J ru O ft I I I o • • • • :< O O O O fi Si J J JJ J i - 0 I I I O O O O • ft • ZK O O O O O O - I N ' Ji* Cc o i J i O JJ — ft ft ft ft ft- ftv- I I I I > - j c- n J i L-I ru >— .o J J co s i a- n J i i-i r j >— o ft ru i-i J i r~ io o o o ru r J .ru jj o o ft'ft •= - j -ij o o j i --j o P J - - J 4i l-l.l-l 30 s i L-l LH s i CP o o • -ft -J l Ji o o o o o o o o o o o ft o O - J o c-Ji Ji • O O O O O CP J l X: J i I-.' O J i CO PJ CO — J i C* ru PJ O o L-4 ru L-l J J - 4 L-4 O O ru — c -g - 4 O O © • -ft i i ru j i j i —1 J i o o ft -ft ' o o I 1 O O O O ft o o o Jl C- ft o J i CD 1-4 L-l I I I o o o . -• -» - n ft ru i-i . i — CO CO -J cc c J l O O O O ft -ft -ft -ft -O O O O LP. l-l ft CO PJ P J V c--4 l-l CO i O c : ft * ft ' ru r J o o i I I I o o * - • ,- o o CP 3 -cs J J — J i o o o o o o o o o o o o c o o o o i r j ru r j rj r j »— o o o o l O CC CP J i o I I I I I O O O O O • « "* • a O O O O O J l J i 14 ft : 0 PU •— O s | J i O O J l O CD •JJ Co o O ' • « i o o J i ru ; j o o o •» •* o o Jl o C- CO 3= 03 co ru o o JJ s i o ru o o • •» • o o o- w U4 w O O O O - i ru o ru 3 - i i ft .ru o o o o o o o » -• -• -o o o o o ft ft PJ O JJ L- l 0 - s i J i • I I o o o o • - » - . • 3C o o o o Ji - I J J c-1—n t i i o o o o o o o o ft i C o o ft CO l-l o o o co J I o o o o O © CT S.' ru o J J j i o J ; J J r j t I 1 -1 o i-3 O o CO S I c- J l J i L-I ru »— o J J co S I CP in J i l-l ru © ft i i - ' J L-l t i r - a> "• -. *• -ft -• -• -• 'ft -ft -ft "ft • •ft -ft -ft -ft -ft --ft "ft '« ' -ft cr i i — I 1 1 1 1 t—• (B ft- lp— -.ft I f t ' f t :•— •— i i — ' O o o o o o o •o o o o o © © o ft '• • 'ft '• -'ft '» -• '• ' •• 'ft "ft ' 'ft 'ft "• -ft 'ft -ft -'ft -ft ' -• -'ft ' '• ' • ft r. C l in j i — — J i l-l PU r.j i — ' O 0 Co - J c- in L-l ru ft o o ft rj r j L-J t~ »-— CO J J s i ru cn s i O ft l-J LI s i s i L'l j i X; j i Ci CP- ru o o •0 . 3 ru CO -ru o *•* CD l-l C- i S CP J l o l-J J l ru CD ft • ru L-J " f t CP J l I o o o o o o o o o o o o o o o O o o O O o c o © © CJJ n o • -ft ' 'ft -•• -'ft " • ' 'ft -'ft *• ' 'ft -'ft " 'ft 'ft ' ft '» -« -ft • '» - ft 'ft ' • -'ft -'ft ' • « -o II CP. Pu ft ft .1— 'ft- -— o o c o o o o o o o o o o o o o © o O o ft. s i o •CD J l L-I ft o J J CD - J c- J l J l j i L-l ru ru ru ft ft ft ft— ft. ft IV PJ • -o L-l o ru J J CP Xi L-4 J i •Jl CP o L-l c- J J - i ft- • CO O J l J l — : J i O 1 l-l C- ft ~i o o — J j J l s i J J CO CP o - I CO ft - •Jl L-J - i J l © s i ft% ft 1 1 1 i 1 o o o O o o o c c o o o o o o o o o o o o o O o o © © o t ft t • '« • 'ft * ft • ft - ft -ft ' ft ' ft - ft -'ft - t " • -'ft - ft ' » " t " ft * t • ft - » * ft " 0 -r j PJ ru ru ru ru ru Pu r j r j PJ ft ft ft . f t ft o o c o © © o o ft* O 1— ru •— ru ru ft ft 1— ft o o J J CD c- Xi ft J J CP j i ru o ru J l - J © o J I o J J t— . © J J n L-l ft . s | l-l s i • J i l-l O Co J i --I L-l O J i c- PU - J l-J J l o i I I I 1 I i I I 1 1 1 i I 1 1 o •sn o o o o o o o o o o o o o o o o o o o o o o © o O o CO CO ft— ft ft »— ft o o o o o o o o o o o o o o o o o o © o O -ft ru ' f t • f t I O o Co ~ J • J l J i ru ft. ' © o ft I f t , Ift ' w. ;— ; :o o c © © o ftjS , u s i c- CO s i c- J l •^ I-J ro ft © JJ CO s i c- in fi L-l ru o ru L-l fi LF ft I f t 1 — ift • f t L — • f t 1 © c = © o o © o • © o o 1 I o i 1 o o l-J L-l L-J PJ ft ••- I O JJ -0 CD -si •c- in o L-l rj ft •o o © — •PJ L-4 r~. J l o L-J O J l JJ L-J CP CD ft J i c- J i j i X: i i fi- in s i ft JJ •CD CO s i ft i J i — Cc J l ro PJ •CO - L-4 . 3 - »— '•- ,'J1 LS ru -= l-J l-J -1 © JJ X3 o o = © o © o o o O o © © O o o © © o © o © o n ft o © o o o © © © © O o © o o o o © o o o O ft-ru o o CO - J c- CP 'Jl J i J i LJ L-l ru ru ft ft — ft ft ft ft PJ PJ ft X-- s i • X2 J i - J CD ft . f i -4 L-l s i • ft "Jl —• .CD c- xi fi fi L<1 s| • o fi o J J c» J> PJ CP JJ - Co •-* n ru CO l-l r j ~j o ru L-l - o ft I 1 1 1 1 O © o o o o o o o © © © © c © © © o o o © © © © n 3C CP ru ru PU ru ru ru PU r j ru ft ft ft ft ft O © o o © O o o o © o — ft ft o o o o o j ; CO c* UJ ft JJ cs fi PJ o PU fi --I JJ 30 3 s ru ru JJ JJ 3 - J l 1 - ' • CP o © JJ c- l-l -•1 ' J i —• o L-l - J ft* ~i -4 1 i i l I I 1 1 1 I 1 1 t i-C o o o o o o © o o O o © © o o o o o o O o o o o C/> m '» ft '• '* * ' -ft ft ft - 'ft 'ft •« ft • '» ft ft •ft 'ft » « •ft m CE CO O o o © © o o © o O o o © o o © o o o o o © © O + CO CO CO S i 'CP fi L-l ft I O o o ft Ift ift I f t . ift ; © o o o © o © -s • w l-l ft o O - J J i JJ -4 L-l J l ru 'Jl J l j i ft CO 3 - ru ft J i CP JJ J i CO J i ' • J CO J i o s i ru J l CD JJ ft ru ft ft' o J J JJ JJ J i o s l CD co '. 7. 1 .096 0. 0 4ci4 0.215 -0.0559 7-'. fi'. 1 . 189 0".0506 0.24 1 -0.0530 fi'. <>'. 1 .267 0'.0567 0.263 -0'. 04 c »5 9. 10. 1 .331 O'. 0645 0.231 -0.0471 10'. 11. 1 .377 0'. 074 1 0.291 -0.0473 11'. 12. 1 .393 0.0921 0.289 -0.0548 12'. 15:. 1 .176 0'.2304 0.14 2 -0.1547 13. CL •0.345 •0.24 1 •0.134 -0.024 0.'. 0 8 6 0', .92 0'. 296 0'.4 03 0.506 0'. 6 1 0 0'.71 3 o'.m i 0'.907 O', 99 3 l'. 091 1'. 1 79 1'.265 T.326 T.363 l".394 1.186 CD O'. 0194 O'.O 180 0'. 0 1 7 1 O'.O 168 O'.O 172 0'. 0 179 O'.O 193 0.0212 0'.0233 O'. 0259 0'.0289 0'.0326 0'. 0370 0'.0425 0'.04 78 0.0534 0'. 0594 0'.0 672 0'.0773 0'.0959 0'.234S CMO -0.158 -0 . 133 -0.106 -0.078 -0.051 -0.023 0.003 0.031 0.0 58 0.037 0.114 0 .14 1 0. 166 0 . 1 9 0 0.215 0 .239 0 .263 0.230 0.29 0 0.289 0'. 1 4 6 SOLID WALLS CMC/4 -0.0723 -0.0728 -0.0727 -0.0723 -0.0717 -0.0706 -0.0699 -0 .0689 -0 .0673 -0.0645 -0.0625 -0.0607 -0.0591 -0.0574 -0.0551 -0.0524 -0.0491 -0.0466 -0.0465 -0.0546 -O'. 153T. JOUKOWSKY RE = 0'.5(10)6 SOLID WALLS ALF CL CD CMO CMC/4 -7 . -0.34 6 0'. 0195 -0 .159 -0.0733 -6 . -0-.24 1 O'.O 1*3 -0 .133 -0.0732 -5 . -0 .13 4 O'.O 174 -0 .106 -0 .0726 -4 . -0.024 O'.O 165 -0 .078 -0.0723 . 0.086 O'.O 166 -0 .051 -0.0718 . 0,193 O'.O 179 -0 '.023 -0'.0709 -1' . 0.297 0.0192 0 .003 -0.0703 0 . 0'.4 03 O'. 0205 0 '.031 -0.0689 1 . 0.5 03 0.0223 0 .059 -0.0674 2' . 0.613 0'.0246 0 .037 -0.0651 3 . 0.713 0'.0273 0 '.114 -0.0628 4' . 0'.8 13 0". 0307 0 .141 -0.061 1 5' . 0'.90H 0'.0349 0 .166 -0.0593 6 . t'. 0 03 0'.0415 0 .191 -0.0579 7' . T.094 O'. 0469 0 .215 -0.0556 e ' r. ia6 0'.0525 0 .24 1 -0.0524 9' T.266 O'. 0584 0 .263 -0.0495 10 . 1.331 O'. 0660 0 .231 -0.0467 i f 1.376 0'.0770 0 .292 -0 .0 469 12' . 1 '.401 0'.0943 . 0 .29 1 -0.0540 13' . f. 173 0'.2357 0 .146 -0.1518 Table 7 J O U K O W S K Y K E : - 0 ' . 5 ( l O ) 6 "UO/SSS + P T S U S L A L F CL CO C! *0 r . M C / 4 - 7 . - 0 . 3 3 1 0". 0 1 3 9 - 0 . 1 5 5 - 0 . 0 7 3 4 - 6 . - 0 ' . 2 2 7 O'.O 1 7 3 - 0 . 1 2 9 - 0 . 0 7 2 2 - 5 ' . - 0 . 1 2 5 O'.O 1 5 7 - 0 . 1 0 2 - 0 . 0 7 1 0 - 4 . - 0 . 0 1 8 O'.O 152 - 0 . 0 7 6 - 0 . 0 7 0 3 - 3 ' . 0 ' . 0 8 5 0'. 0 1 5 7 - 0 . 0 4 9 - 0 . 0 6 9 4 : / . 183 0 ' . 0 1 6 1 - 0 . 0 2 3 - 0 . 0 6 8 3 0 ' . 2 8 2 O'.O 1 6 9 0 . 0 0 3 - 0 . 0 6 7 1 o . 0 . 3 8 1 O'.O I 3 7 0 . 0 2 9 - 0 . 0 6 5 6 f . 0 . '1 7 7 0 ' , 0 2 1 2 0 . 0 5 4 - 0 . 0 6 4 1 2 . 0 ' . 5 7 2 0 . 0 2 3 8 0 . 0 8 1 - 0 . 0 6 1 4 3 . 0'. 6 6 6 0 ' . 0 2 7 2 0 . 1 0 6 - 0 . 0 5 8 9 0 , 7 5 5 0 . 0 3 0 9 0 . 1 3 0 - 0 . 0 5 7 5 5 . 0 ' .8 ' I5 0 , 0 3 4 7 0 . 1 5 4 - 0 . 0 5 5 4 .^ 0 . 9 3 2 0'. 0 4 0 0 0 . 1 7 7 - 0 . 0 5 3 5 7'. 1 . 0 1 4 0', 0 4 5 0 0 . 2 0 0 - 0 . 0 5 1 5 8". 1 . 0 9 9 0'. 0 5 0 7 0 • 2 2 - 0 . 0 4 9 2 9 . 1 . 1 7 1 0 ' . 0 5 7 0 0 . 2 4 3 - 0 . 0 4 6 3 1 0 ' . 1 . 2 3 9 0 ' . 0 6 4 2 0 . 2 6 2 - 0 . 0 4 3 8 1 1 . 1 . 2 8 2 0 ' . 0 7 2 7 0 . 2 7 3 - 0 . 0 4 2 6 12 ' . 1 . 3 0 9 o ' , 0 8 5 5 0 . 2 7 5 - 0 . 04 m 0 . 6 6 3 0 ' . 0 2 7 7 0 . 1 0 5 - 0 . 0 5 9 7 ''. i . 1 3 4 -0'.0-'l70 0.2 3*'. - 0 , 0 . 1 1 4 0 . 2 5 3 - 0 . 0 4 2 9 1 0 . 1 . 1 8 8 .d'. 0 5 2 5 0 . 2 5 3 - 0 . . ' 3 9 - . 0 . 2 6 9 - 0 . 0 4 2 9 11 ' . r . 2 2 4 0'. u 6 21 .0 .2/. 1 - 0 . l l " / i q 0 . 2 7 1 - 0 . 0 4 7 4 1 2 . 1 . 2 3 7 ( . ' . 1263 i) . 2 5 0 - 0 . 0 1 0 . 1 2 5 - 0 . 1 4 3 3 13 ' . 0 . 9 6 3 0 . 1 9 7 1 0 . 1 0 7 - 0 , 1 3 6 9 Table 7 J O U K O W S K Y RiT = 0 . 5 C l O ) 6 5 0 A L F C L CO C MO -'!'. - 0 . 3 2 4 O ' . O l 78 - 0 . 1 5 1 -':>'. - 0 ' . 2 2 5 0'. 0 1 6 2 - 0 . 1 2 7 - 5 ' . -() ' . 1 2 0 O'.O 1 5 2 - 0 . 1 0 1 " q > - d ' . O 19 O'. 0 14 9 - 0 . 0 7 4 ** .'j . 0 ; . OP.5 O ' . O l '!3 -o . 0 4 7 0'. 1 8 3 0 . 0 1 5 4 - 0 . 0 2 1 0 ' .?77 0'. 0 1 6 7 0 . 0 0 3 o. 0'.375 O'.O 1 8 2 0 . 0 2 9 i ' . 0'.4 6 8 0 ' . 0 2 0 6 0 .053 o ' . 564 0 . 0 2 3 4 0 ' . 0 3 0 3 . 0 . 6 5 3 0'. 0 2 6 2 0 . 1 0 4 0 ' . 746 0 ' . 0 2 9 6 0 . 1 2 8 5'! 0 ' . 8 3 2 0 ' . 0 3 3 l 0 . 1 5 1 6 . 0 ' . 9 2 1 0'. 0 '10 0 0 ' . 1 7 6 7 . 1 ' . 0 0 2 0 ' .0 ' l^5 0 ' . 1 9 8 ?•'. l ' . 0 P 2 0 . 0 5 1 2 0 . 2 1 0 9'. {'. 1 5 6 O - . 0 5 7 7 0 . 2 4 0 io'. 1 . 2 1 5 0'. 0 6 4 8 0 . 2 5 7 i r. \ ' . 2 6 0 0 ' . 0 7 3 9 0 . 2 6 8 12 ' . 1 . 2 8 8 0 ' . 0 8 6 3 0 . 2 7 1 13 ' . 1 . 0 5 7 0 . 2 0 7 ^ - 0 . 1 3 0 Jf : i iSr ! . !S .?7> O'.O 1 7 7 - ;l . 1 5 2 - c. - 0 ' 2 2 ? O ' . O l 6 6 - 0 . 1 2 6 - O - . 1 2 3 o'. 0 1 6 0 - 0 . 1 0 1 - '. - O ' . O 18 0'. 0 1 4 4 -o . 0 7 3 _ 7 ' 0 ' . 0 8 4 0'. 0 1 4 7 - 0 . 0 4 7 _ J O'. 131 O'.O 1 5 5 - 0 . 0 2 2 - l ' l 0 - . 2 7 6 O'.O 1 6 7 0 . 0 0 3 0 . 0 ' . 3 7 1 O'.O 1 7 9 0 ' . 0 2 8 f. 0'.4 6 7 0 ' . 0 2 0 3 0 . 0 5 3 2' . 0 ' .561 0'. 0 2 3 1 0 ' . 0 7 9 3'. 0 ' . 6 5 3 0 . 0 2 5 9 0 . 1 0 4 n'm 0 ' . 7 ' l ) 0' .029 3 7 0 0 ' . 1 7 4 7'. 0 ' . 9 9 3 0 ' . 0 4 2 7 n . 1 9 7 (V 1 ' . 0 7 6 0 ' . 0 4 3 3 0 . 2 1 8 9' . 1'. 1 4 3 0 ' . 0 5 4 7 0 . 2 3 9 io'! i ' . 2 ( ) 5 0 . 0 6 2 3 0 . 2 5 5 i r. f . 2 5 2 O'. 07 04 0 . 2 6 7 1 2 . T . 2 7 7 O' .OS 15 0 . 2 6 8 13 ' . 1 . 0 5 5 0 ' . 1 9 5 0 0 , t 2 8 •,;3.Si-P T S U S L J O U K O W S K Y C M C / 4 A L F C L 0 . 0 7 1 2 - 7 ' . - 0 ' . 3 2 5 0 . 0 7 0 6 - 6 . - 0 . 2 2 1 0 . 0 6 9 8 — I" '* - 0 ' . 1 19 0 . 0 6 8 9 "4 • - 0: . 0 1 6 0 . 0 6 8 2 ** -> • ( ) ' .087 0 . 0 6 6 6 -? : 0'. 1 8 5 0 . 0 6 5 7 0 ' . 2 3 J 0 . 0 6 4 1 0 ' . 3 7 4 0 . 0 6 2 3 i . 0'. 4 7 1 0 . 0 6 0 3 *>' 0 ' . 5 6 3 0 . 0 5 7 9 ji, 0 . 6 6 0 0 . 0 5 6 6 0 ' . 7 4 6 0 . 0 5 4 7 5'. 0 ' . 8 3 2 0 . 0 5 2 6 6'. 0 ' .9 16 0 . 0 5 0 6 7 . . ( ) ' ,998 0 . 0 4 8 3 e'.' i ' . 0 7 4 0 . 0 4 5 4 9'. 1'. 1 4 3 0 . 0 4 2 3 1 0 . T . 209 0 . 0 4 1 9 11 1 . 2 5 2 0 . 0 4 5 9 12 ' . l ' . 2 5 2 0 . 1 3 6 3 13 ' . 0 ' . 9 9 5 / .SSt -? ' T S U S L JOIJKOwSK Y C ' - : C / 4 A L F C L 0 . 0 7 2 0 - 7 ' . - 0 ' . 3 1 6 0 . 0 7 0 4 - 6 ' . - 0 . 2 1 8 0 . 0 7 0 0 . - 5 . -(>'. 1 1 6 0 . 0 6 8 7 - 4 ' . - O ' . O 14 0 . 0 6 7 8 - 3 ' . 0'. 0 8 9 0 . 0 6 6 8 0 . 1 8 5 0 . 0 6 5 4 -r. 0 ' . 2 7 9 0 . 0 6 3 9 o'. ()'. 5 7 4 0 . 0 6 2 6 r. 0 ' . 4 7 0 0 . 0 6 0 1 2. 0 ' . 5 6 2 0 . 0 5 7 6 7 ' - * • 0 ' . 6 5 5 0 ' . 0 5 6 0 4 . ( i ' .74( l 0 , 0 5 4 0 5 . ( i ' . S 2 7 0 . 0 5 2 2 6'. 0 . 9 0 9 0 . 0 5 0 0 y\ 0 ' . 991 0 . 0 4 7 6 8'. 1 . 0 6 5 0 . 0 4 4 2 9'. i ' . 1 3 7 0 . 0 4 2 1 io : . i"'. r->4 0 . 0 4 1 2 1 I. ii '.230 0 . 0 4 6 0 12 ' . l ' . 2 4 6 0 . 1 3 7 8 13 ' . 0 ' . 9 9 8 Wt" = 0 .5ClOj6 70-/ , - SS + P T S U S L CMO C M C / 4 0'. 0 1 8 2 - 0 . 1 5 6 - 0 . 0 7 5 1 0'. 0 1 7 0 - 0 . 1 2 9 . - 0 . 0 7 3 3 0 . 0 1 5 8 - 0 . 1 0 3 - 0 . 0 7 2 7 0 ' . 0 5 0 2 - 0 . 0 7 6 - 0 . 0 7 1 5 O'.O 154 - 0 . 0 4 9 - 0 . 0 6 9 9 O'.O 1 5 8 - 0 ' . 0 2 3 - 0 . 0 6 9 0 0 ' . 0 1 6 7 0 . 0 02 - 0 . 0 6 7 7 O'.O 1 8 9 0 . 0 2 6 - 0 . 0 6 6 4 0 . 0 2 1 5 0 . 0 5 3 - 0 , 0 6 4 3 O ' . 0 ? 4 1 0 . 0 7 8 - 0 . 0 6 1 8 0 ' . 0 2 7 1 0 . 1 0 4 - 0 , 0 5 9 a 0'. 03 0 0 0 ' . 1 2 8 - 0 . 0 5 7 5 0'. 0 3 3 4 0 . 1 5 1 - 0 . 0 5 5 3 0 ' . 0 3 7 0 0 ' . 1 7 4 - 0 ' . 0 5 3 0 0 ' . 0 4 2 4 0 . 1 9 6 - 0 . 0 5 1 1 0 . 0 4 7 5 0 ' . 2 1 7 - 0 . 0 4 8 2 0 ] . 0 5 3 3 0 . 2 3 8 - 0 . 0 4 5 2 O - . 0 6 0 3 0 . 2 5 5 - 0 . 0 4 3 2 0'. 0 6 9 3 0 . 2 6 6 - 0 . 0 4 2 5 0'. 0 3 0 0 0 . 2 6 0 - 0 . 0 4 7 5 0'. 1 9 2 5 0 . 1 1 0 - 0 . 1 4 0 7 R F = 0 . 5 C 1 0 ) 6 8 05 .SS+P T S U S L CO CMO C M C / 4 0'. 0 1 7 0 - 0 . 1 5 2 - 0 . 0 7 3 4 O'.O 154 - 0 . 1 2 6 - 0 . 0 7 1 7 0'. 0 1 4 3 - 0 . 0 9 9 - 0 . 0 7 0 4 O'.O 1 3 6 - 0 ' . 0 7 3 - 0 . 0 6 9 5 O'.O 1 3 3 - 0 ' .04 6 - 0 . 0 6 8 2 0 . 0 1 4 0 - 0 ' . 0 2 2 - 0 . 0 6 7 3 O'.O 154 0 . 0 0 4 - 0 . 0 6 5 4 O'.O 1 6 7 0 . 0 2 9 - 0 . 0 6 3 3 O'.O 1 8 0 0 ' . 0 5 5 - 0 . 0 6 1 4 0 . 0 1 9 9 0 ' . 081 - 0 . 0 5 8 6 0'. 0 2 2 6 0 . 1 0 6 - 0 . 0 5 6 7 0 . 0 2 5 7 0 . 1 2 9 - 0 . 0 5 4 4 0'. 0 2 3 6 0 . 1 5 2 - 0 . 0 5 2 5 0 ' . 0 3 3 5 ' 0 ' . 1 7 5 - 0 . 0 5 0 5 0 . 0 3 7 4 0 . 1 9 7 - - 0 . 0 4 8 5 0 ' . 0 4 2 6 0 ' . 2 1 7 - 0 . 0 4 5 6 0 . 0 4 7 5 0 . 2 3 3 - 0 . 0 4 2 7 0 . 0 5 4 9 . 0 . 2 5 4 - 0 . 0 4 0 5 0 . 0 6 3 0 0 . 2 6 2 - 0 . 0 4 0 5 0'. 0 7 4 2 0 . 2 5 9 - 0 . 0 4 7 0 0'. 18 72 0 . 1 1 5 - 0 . 1 5 6 1 T a b l e 8. Q u a n t i t i e s d e r i v e d f r o m b a l a n c e r e s u l t s . 0.25 W a l l .. C l a r k - Y . m Re = ctro 0 . 4 5 ( 1 0 ) 6 X ac d a a mo s o l i d 0.1011 -6.42 0.231 0.0276 -3.12 40%LP .0970 -6.45 .233 . 0263 -2.96 50%LP .0958 -6.48 .229 . 0263 -3.00 60%LP . 0954 - 6 . 54 . 228 . 0263 -3.02 70%LP .0947 -6.60 . 255 .0265 -3.11 80%LP . 0940 -6.67 .229 .0259 -3.25 40%SP .0967 - 6 . 5 1 .228 .0267 -2.99 50%SP .0952 -6.52 .230 . 0261 -3.03 60%SP . 0944 -6.57 .231 . 0257 -3.09 70%SP .0917 -6.36 . 277 .0245 . -2.77 80%SP .0906 -6.46 .228 .0250 -2.90 0.39 C l a r k - Y Re = 0 . 5 ( 1 0 ) 6 W a l l m X d C M a ac d a u mo s o l i d 0.1032 -6.28 0. 235 0.0275 -2.86 40%LP .0956 -6.16 .229 .0261 -2.66 50%LP .0936 -6.22 .230 .0254 -2.73 60%LP .0914 -6.35 .227 .0251 -2.79 70%LP .0903 -6.40 .225 . 0250 -2.87 80%LP .0882 -6.54 .223 . 0246 - 3 . 0 1 40%SP . 0952 - 6 . 1 9 .227 .0261 - 2 . 69 50%SP .0941 - 6 . 2 1 .230 . 0256 -2.72 60%SP .0923 -6.30 . 233 .0249 -2.78 70%SP .0917 -6.36 .227 .0253 -2.84 80%SP .0912 : -6.45 .222 .0255 -2.92 0.53 C l a r k - Y RE = 0.5 ( 1 0 ) 6 W a l l m c*i 0 X d C M a ac d a u mo s o l i d 0.1044 -6.42 0. 235 0.0278 -2.97 40%LP .0944 -6.27 .231 . 0256 -2.73 50%LP .0932 -6.35 .234 . 0250 -2.79 60%LP .0917 -6.39 .230 .0249 - 2 . 8 1 70%LP .0907 -6.43 .232 . 0245 -2.90 80%LP .0889 -6.55 .226 .0246 - 3 . 03 40%SP .0938 -6.29 . 233 .0252 -2.73 50%SP .0928 -6.32 .233 .0250 -2.75 60%SP .0920 -6.35 .232 . 0249 -2.76 70%SP .0907 -6.39 .231 .0246 - 2 . 82 80%SP .0895 -6.47 .227 . 0246 — 2.96 T a b l e 8 ( c o n t ' d ) . 0.66 C l a r k - Y Re = W a l l . . m otic, s o l i d 0.1074 - 6 . 33 40%LP .0947 - 6 . 02 50%LP .0931 - 6 . 14 60%LP .0909 - 6 . 19 70%LP .0899 - 6 . 16 80%LP .0884 - 6 . 31 40%SP .0932 - 6 . 05 50%SP .0930 - 6 . 19 60%SP .0915 - 6 . 11 70%SP .0902 - 6 . 18 80%SP .0887 - 6 . 17 0. 66 C l a r k - Y Re W a l l m Ctl 0 s o l i d 0.1124 - 6 . 28 40%LP .0989 - 5 . 95 50%LP .0974 - 6 . 03 60%LP .0962 - 6 . 09 70%LP .0955 - 6 . 09 80%LP .0930 - 6 . 21 4 0%SP .0982 - 6 . 00 50%SP .0976 - 6 . 00 60%SP .0946 - 6 . 13 70%SP .0934 - 6 . 11 80%SP .0924 - 6 . 16 0 . 5 ( 1 0 ) 6 0.234 0.0283 -2.74 .234 .0250 - 2 . 4 1 .235 .0245 -2.50 . 224 . 0249 -2.50 .226 . 0244 -2.57 . 219 . 0247 - 2 . 8 1 .232 .0248 - 2 . 4 1 . 224 .0255 -2.53 .229 .0246 -2.46 .228 .0244 -2.57 .222 .0245 -2.68 ..0 (10) 6 dC„ X ac da " a mo 0.243 0.0287 - 2 . 82 .238 .0257 - 2 . 4 1 .238 .0253 -2.49 .235 .0253 -2.55 .231 .0255 -2.58 .228 .0251 -2.82 .235 .0259 - 2 . 4 3 .237 . 0255 -2.49 .233 .0251 -2.60 .230 . 0250 -2.62 .255 .0253 -2.76 240 T a b l e 8 ( c o n f d) . 0. .17 NACA--0015 Re = 0.3 (10) 6 W a l l . m ct i o X a ac d a m o s o l i d 0.0982 0.03 0.230 0.0251 0.08 40%LP .0958 .04 . 231 .0245 . 04 50%LP .0957 • - 0 . 0 1 .232 . 0243 - .01 60%LP . 0961 - .04 .227 .0249 .00 70%LP .0967 - .02 .233 . 0244 - .08 80%LP .0960 - .10 . 236 . 0240 - .16 40%SP .0967 .04 .232 .0245 .04 50%SP .0963 .04 .230 .0247 .03 60%SP .0954 .00 .232 . 0243 - .01 70%SP .0958 .00 . 231 .0245 .00 80%SP .0956 - .04 .229 .0246 - .05 0. 34 NACA--0015 Re = 0 . 5 ( 1 0 ) 5 W a l l m Cti o X d C M a ac d a 0 m0 s o l i d 0.0993 0.01 0. 236 0.0266 0.02 40%LP .0945 .10 .231 .0258 . .07 50%LP .0941 .07 .233 .0255 .02 60%LP .0929 .04 .234 . 0251 - .01 70%LP .0927 .03 .233 .0251 - .04 80%LP .0927 - .07 . 234 .0251 - .13 40%SP .0929 .06 .236 .0249 . 03 50%SP .0925 .04 .237 .0247 - .03 60%SP .0924 .01 .230 . 0253 - .03 70%SP . 0928 .01 .231 .0254 - .04 80%SP .0925 - .01 .233 .0251 - .05 0. 50 NACA-•0015 Re = 0 . 5 ( 1 0 ) 6 W a l l m X d C M a ac d a u mo s o l i d 0.1036 0.04 0.252 0.0249 0.07 40%LP .0940 .14 .250 . 0228 .07 50%LP .0935 .13 . 249 .0227 .04 60%LP .0936 .12 .249 .0227 . 03 70%LP .0924 - .01 .247 .0226 - .01 80%LP .0906 - .04 .246 .0223 - .16 40%SP .0933 .14 .250 . 0226 .07 50%SP .0929 .14 .249 .0226 .07 60%SP .0929 .12 .246 .0229 .02 70%SP .0921 .20 . 249 .0226 . 00 80%SP .0913 .06 .247 .0224 - .08 T a b l e 8 ( c o n t ' d ) 241 0. 67 NACA--0015 Re = 0 . 5 ( 1 0 ) 5 W a l l . m • - -a io X d C M a ac d a 0 m 0 s o l i d 0.1080 -0.03 0.214 0.0264 0.01 40%LP .0954 0. 25 . 219 .0228 .13 50%LP .0945 .22 .219 . 0226 . 06 60%LP . 0940 .13 . 211 .0232 - .01 70%LP .0915 . 09 . 212 .0225 - .12 80%LP .0891 - .04 . 210 . 0221 - .31 40%SP .0960 .22 .214 .0234 .10 50%SP .0935 .22 .216 . 0226 .07 60%SP . 0928 .23 . 215 . 0226 . 07 70%SP .0921 .16 . 212 .0227 .00 80%SP .0902 . 05 .211 . 0223 - .18 0. 67 NACA-0015 RE = 1 . 0 ( 1 0 ) 6 W a l l m X ~=i—Mn a ac d a 0 m 0 s o l i d 0.1114 - 0 . 08 0.226 0.0259 - 0 . 08 40%LP .0981 .29 .213 .0241 .15 50%LP .0969 .25 .208 .0242 .25 60%LP .0952 .23 .213 .0233 . 08 70%LP .0940 .19 . 213 .0230 .00 80%LP .0922 .04 . 208 . 0230 - .18 40%SP .0975 .22 .213 . 0239 . 11 50%SP .0962 .27 .211 .0237 .14 60%SP .0943 .22 . 212 . 0232 .06 70%SP . 0935 .17 .214 .0229 .00 80%SP .0935 .16 .210 .0232 - .05 T a b l e 8 ( c o n t ' d ) . J o u k o w s k y Re = 0.5.(10) 6 W a l l . m a i o • X ac ' dc7M° ' a m0 s o l i d # l 0.1059 -3.78 0.236 0.0275 -1.14 s o l i d # 2 .1056 - 3 . 78 .236 . 0274 -1.14 s o l i d # 3 .1055 -3.77 .236 .0274 -1.14 40%LP . 0988 - 3 . 74 . 233 . 0260 - 1 . 02 50%-LP .0975 -3.77 .234 . 0256 -1.07 60%LP .0965 - 3 . 83 .232 .0255 -1.07 70%LP .0958 -3.88 .230 .0254 -1.15 80%LP .0954 -3.98 .230 .0254 -1.29 40%SP .0984 - 3 . 80 . 232 . 0259 -1.09 50%SP .0970 - 3 . 80 .233 .0255 -1.10 60%SP .0965 -3.80 .232 . 0254 -1.10 70%SP .0968 - 3 . 83 .231 .0257 - 1 . 04 80%SP .0959 - 3 . 85 .230 .0256 -1.14 T a b l e 9. P r e s s u r e c o e f f i c i e n t s f o r NACA-0015 a i r f o i l R E r l . 0 + ( i 0 ) 6 S O L I D W A l . L S O.feT-wACX-OOIS 0(115 A L " - ' . X / C o'. 0 0 . 2 0 . « 1. o 1'. 5 ' •I . 9 T>' c 2 ' . 9 1'. 9 7 , i . 8 1 2'. H ' 1 ' . 1 1 7 . 3 a 1 . 0 0 c ' . 7 7 J o ' . 5 5 i o ' . 1 5 1 - 1 ' ' . 0 - i 3 - o ' . i o o - o , 3 3 6 - 0 . 1 8 3 2 9 . 7 ' 'J'! 7 3 9 . 6 1 9 . 5 5 9 , 5 t « , i 7 -l 2 P, ^ u 9 7 ' ] o 0 . ? 0 . 3 1 '. 0 1 ^ • "V - i -? . ^ 2 . ' i l ' . 1 ( ' , « J«'.8 ?. it. fl' 2 9 . 7 ij 9 . 5 6 O , 1 7 9 , 2 r.5 r 9 6 ' ] 9 C, - o . : -'i i - o ' . 5 2 5 - C ' ' . 5 u 9 - 0 . 1 H 3 -O . ^ - i i l l - 0 '. 2 f 9 - f c ' . 2 2 1 - 0 '. i -'I 3 - 9 '. .1 ;i c 0 ' . 0 9 3 Cl'. 7 6 0 tj'rr,?.'J (I . ! 7 2 0 '. 0 1 2 « ' . 1 6 1 • 0 . 2 7 1 •<-•'. 3 3 1 i. ' . -'i 7 0 0 '. 5 7 7 o . ' . 5 9 3 o ' . 5 9 i ' J ^ u 9 0 . 3 5 7 « ' . 2 1 6 « ' . 1 1 3 o'.o 8 8 o . « 7 1 0 ' . " 7 7 0 . i l n 7 - 0 . 3 6 7 - o . L ; 'i 5 - o ' . i , (.-•.; - 0 . 7 0 '.5 - 0 . 8 -'I .'| - o .Kr-"/ - 0 , 8 ' K | - 0 . * 2 3 - 0 ' . 7 ? ' . - 0 . 7 6 5 - 0 . 7 2 3 - 0 . 7 0 7 - 0 . ( .31 - 0 . 1 , 3 0 - 0 . 6 ,"• 9 - 0 . 5 7 1 • i i . ' . J l - o . : . ' i ; ' - 0 . 2 3.1 - 0 '. 1 !. 3 -0.017 O.Ol . ' l 0 . 9 5 8 0 . 8 5 9 0 . 5 5 u 0 ' . 3 7 7 0 . 2 3 0 C l ' . 1 2 0 O , 0 « 3 -- 0 . 1 5 , - ' - 0 . 3 3 0 - 0 . 1 ' l f l - 0 ' . - / • / 3 - 0 . 3 8 3 • 0 . 2 8 a • 0 . 1 7 a • 0 . 1 2 t • • 0 . 0 5 3 . • 0 . 0 7 3 0 ' . 5 ? 7 - 0 ^ 5 1 - 9 , 6 ' 1 . 3 - 1 . 0 i l 0 - l ' . 1 7 6 - l ' . 2 7 5 - 1 . 2 9 I - l ' , 3 0 2 - 1'. 7 5 - 1'. .-: 1 3 - 1 j. l a s - 1 0 1 8 - 1 . 0 6 1 - 1'. 0 0 'J - O ' . ' . i ) 1 - o'. 9 a 4 - o ' . n ft 3 - 0 > 1 6 - ' / . 7 6 9 - 0 ' . 7 1 1 - 9 ' . 6 1 3 - 0 ' . 5 1 , 1 -O'.'IOS - 0 ' . 3 0 3 - 0 '. 114 0 3 f l o.°. a 9 3 2 *;'. I i l 6 - 0 c 9 a • 0.1-0591 - 0 . '16 1 - 0 . 3 1 3 - 0 . 2 1 5 - 0 . H 7 1 0 , 0 6 . 3 0 . 7 6 5 0 . 0 3 9 0'. 911 0 . 1 0 9 0 . fl 2 1 0 . 7 3 H 0 , A 6 2 0 . 1 3 7 0 . 1 5 0 0 . 0 1 1 - 0 . 0 0 1 - 0 , 1 1 2 • 0 . 1 1 7 • • o . o d t • - 0 . 0 6 6 • • 0 . 0 3 0 0 . 0 3 7 •1 , 0 . 0 0 1 0 . 2 0 1 0 . 0 6 0 . 4 2 7 0 . 6 7 4 0 8 1 ».? ' . 3 9 6 a o o - 3 ' . 0 2 1 - 2 ' . 9 / i f l - 2 ' . 9 0 7 6 1 5 - 2 ' . 7 1 r t - 2 ' . .306 1 5 1 - 1 . 3 5 5 - t ' , , 7 2 2 - l ' . 5 9 1 - r . ' i 8 7 - 1 . 3 7 0 -r. 3 0 9 - 1 ' . 2 1 2 -r. 155 - l ' . 0 9 9 - 0 ' . 9 7 7 - 0 ' . 0 6 9 - 0 . 6 9 6 - 0 ' . 5 3 7 - o ' . 3 a v - 0 ' . 2 5 1 - 0 ' . 0 9 3 o'. 02-1 0 ' . 3 0 0 0 ' . 6 6 8 0 ' . 9 fl 1 1 ' . 0 0 5 0 ' . 9 b 9 0 '. 9 1 S 0 '. 3 6 7 0 ' , 6 6 0 ' . 3 6 1 C . 203 0 ' . 0 6 0 O'. 0 2 1 • 0 ' . 0 2 2 • 0 ' . 0 2 2 • 0 . 0 1 1 . O ' . O H • 0 ' . 0 5 0 • - 1 0 - 2 . 1 0 1 - 3 . 5 7 3 - 3 . 9 1 2 - 1 . 0 3 5 - 3 . H 1 5 - 3 . 7 0 1 - 3 . 5 0 7 - 3 . 3 » 8 - 3 , 0 2 U - 2 , i i i - 2 . 1 9 9 - 2 . 0 3 D - 1 . ( 1 5 5 - 1 . 7 3 2 - 1 . 5 * 9 - 1 . 1 9 1 - 1 , 3 f l 9 - 1 . 3 1 7 - 1 . 2 3 5 - 1 . 0 9 6 - 0 . ' ) 7 ft - 0 . 7 1 8 - 0 . 5 / 3 - 0 . 1 0 9 - 0 , 2 5 0 - 0 , 1 0 2 . - 0 , 0 2 5 - 0 , 2 r i l 0 , 2 5 2 0 . 8 1 7 0 , 9 f l 5 1 , 0 0 1 0 , 9 9 1 0 , 9 6 5 0 , 8 0 6 0 . 5 0 9 0 , 3 3 9 0 , 1 6 0 0 . 1 1 1 0 . 0 3 2 O . O O l - 0 , 0 0 9 • 0 , 0 0 9 . • O . O O f l . 1 2 - 3 . 3 0 2 - 1 > 1 2 - 5 . 3 0 1 - 5 ' . 1 1 2 - ' ( . 7 7 3 - l ' . 5 1 8 - • ' 1 . 3 6 3 - " ' . 2 3 5 - 3 . 2 1 0 - 2 . 9 0 2 - 2 ' . 5 7 9 - 2 . 3 1 7 - 2 . 1 1 7 - 1 > 3 f l - 1 ' . 7 71 - 1 . 6 7 1 - l ' . 5 5 8 " 1 ' . ' I 5 1 - 1 . 3 6 3 - 1 . 1 9 9 • l ' . 0 5 6 - 0 . 8 1 0 - 0 ' , 5 9 f t - 0 . 1 1 0 - 0 ' . 2 5 1 - 0 . 1 1 8 - 0 , 1 0 2 - 1 , 0 1 5 - 0 . 2 9 7 0 . 6 1 6 0 . 8 8 3 0 . 9 7 0 1 . 0 0 0 1 . 0 1 1 0 '. 9 1 3 0 . 6 1 2 0 . 1 6 2 0 . 2 6 2 0 . 2 1 1 0 . 0 9 3 0 ' . 0 3 1 o'.OOh ' 0 . 0 1 5 • . O ' . O f l O • 11 -'I . 5 5 5 - 6 . 3 3 0 - 6 , 5 7 3 - 6 , 1 9 1 - 5 . 7 7 C . - 5 , 1 6 1 1 - 5 , 2 6 2 - 5 . 1 5 9 - 3 . H H 9 - 3 , 3 1 1 - 2 , 8 9 8 - 2 . 5 7 3 - 2 , 3 5 1 - 2 . 1 3 5 - 1 . 9 1 1 - 1 . 8 2 0 - 1 , 6 7 5 - 1 , 5 6 7 - 1 . 1 5 3 - 1 . 2 7 3 - 1 . 0 9 2 - 0 , 8 0 3 - 0 , 5 5 5 - 0 , 3 9 5 - 0 . 3 0 8 - 0 . 2 5 6 - 0 , 2 2 5 - 1 , 8 0 1 - 0 . 9 1 7 0 . 3 2 7 0 , 7 0 9 0 . 8 7 1 0 , 9 5 7 0 . 9 9 8 0 , 9 7 2 0 . 7 3 5 0 . 5 5 i ) 0 , 3 1 3 0 , 2 8 1 0 . 1 3 1 0 , 0 1 3 0 , 0 0 2 • • 0 , 0 5 0 . • 0 , 1 1 7 • - 1 6 - 5 ' , 5 6 7 - 7 . 1 6 8 - 7 . 5 7 1 - 7 . 0 0 6 - 6 ' . 5 ' l 3 - 6 ' . 2 8 6 - 6 . 0 8 1 - 5 . 1 1 3 - 1 ' . 2 1 6 - 3 . 5 3 2 - 3 ' . 0 8 5 - 2 . 7 1 5 - 2 ' . 1 3 2 - 2 ' . 2 0 1 - 1 . 9 7 0 - I . 8 2 6 - I ' . 6 3 6 - l ' . 1 9 7 - 1 . 3 7 1 - 1 . 1 1 7 - 0 , 8 9 6 - 0 . 6 7 0 - 0 . 6 1 8 - 0 . 5 8 3 - 0 ' . 5 6 2 - 0 , 1 9 0 - 0 . 1 0 3 - 2 ' . 5 7 6 1 7 1 O i l 5 5 3 7 7 ' i 9 0 3 9 8 0 0 0 5 0 ' . 8 0 0 0 . 6 3 0 0 . 3 9 9 0 ' . 3 2 2 0 . 1 5 2 0 ' . 0 2 1 0 . 0 3 3 0 . 1 1 0 0 . 2 0 7 ALPHA X / C °'2 0 , 2 0 . 1 I ' .O J ' . 5 1 ' . 9 2 . 5 2 ' . ' 1 . 9 7 ' . 1 9 ' . 8 1 2 ' . " 1 1 . 8 1 7 . 3 2 0 . 2 2 2 . 3 2 1 . 8 2 7 . 2 2 9 . 7 3 ' ( ' . 7 3 9 . 6 '19'. 5 5 9 . 5 6 9 ' , 3 7 9 . 2 8 8 ' . 9 ' 9 7 ' , 0 0 . 2 0 ' . 3 1 . 0 1 ' . 5 2 . 0 2 ' . 1 2 . 9 1 ' . 9 9 ' . 9 1 1 . 0 2 1 ' . 8 2 ^ ' . 7 1 9 . 5 6 9 ' . 1 7 9 . 2 8 8 ' . 5 9 6 ' . 9 R F = l ' . 0 * ( ' l O ) 6 2 1 l O ^ L S Oi» U P P E R , S O L I D L O K L H ; P L u - ^ U H 0 . 9 4 0 1 . 1 2 0 1 . 3 0 1 1 . 4 5 2 1 . 5 4 1 1 . 0 0 2 0 ' . 7 3 8 0 ' . 5 6 8 0 ' . 2 0 6 - 0 ' . 2 ' I 9 -( . ' ' . 1 2 6 - 0 , 2 0 3 - 0 . 2 6 9 - 0 ^ 1 1 2 - 0 . 1 7 9 - 0 ' . 5 0 9 - 0 . 5 3 0 - 0 ^ 5 1 1 - 0 . 5 0 1 - l l ' . 1 9 9 - 0 ' . . ' I 8 1 - 0). - I ti fi - 0 , 1 1 8 - 0 , 1 3 3 - 0 , 1 1 2 - 0 , 3 7 6 - 0 . 3 0 5 - '•>'. 2 Z 9 - » ' . 1 7 7 - o ' . 1 1 1 - o ' . 0 2 1 0 ' . 1 0 9 o ) , 7 5 7 0 . 5 6 8 0 ' . 1 6 5 - o ' . o o i - 0 ' . 1 5 7 - o ) , 2 6 1 - 0 , 3 1 5 - 0 . 1 6 3 - 0 ' . 5 5 0 - 0 ' . 5 6 5 • 0 ' . 5 0 9 • 0 ' . ' 4 3 « • 0 ' . 3 3 6 •ll'f\9Z • 0 . 1 1 6 • • 0 ' . 0 3 1 • 0 ' . 1 0 9 0 , 9 1 . ' | 0 ' . 1 6 7 0 ' . i 5 3 - 0 . 2 1 8 - 0 , 1 1 7 - 0 . 5 " 0 - 0 . 5 9 2 - 0 . 6 1 3 - 0 . 7 2 0 - 0 ' . 7 1 1 - 0 . 7 2 5 - 0 ' . 7 0 3 - 0 ' . 6 8 i - 0 . 6 5 9 - 0 . 6 3 3 - 0 . 6 0 7 - 0 , 5 7 6 - 0 . 5 5 1 - 0 . 5 2 5 - 0 . 1 7 9 - 0 ' . 1 3 3 - 0 ' , 3 1 5 - 0 . 2 7 3 - 0 , 2 0 1 - 0 . 1 0 9 - o ' . o i i 0 . 1 2 2 0 . 9 6'j 0 . 8 6 3 0 . 5 3 9 0 . 3 6 1 0 . 2 2 5 0 . 1 1 7 0 ' . 0 -10 • 0 . 1 1 5 • 0 . 3 1 1 • 0 . 3 7 6 • 0 . 3 7 1 • 0 , 3 5 5 • 0 . 2 6 3 • 0 . 1 5 0 • 0 . 0 9 3 • 0 . 0 2 1 0 . 1 0 7 0 . 6 2 3 - 0 ' . 0 6 1 - 0 ' . ( i 2 u - 0 ' . 8 0 6 - 0 ' . 9 1 0 - l " . 0 1 2 - 1 ' . 0 5 8 - l ' . 0 7 8 - T . 0 7 3 - 1 ' . 0 2 2 - C . 9 6 0 - 0 > 1 9 - 0 ' . 8 6 3 - 0 ' . H 1 6 - ' j ' . 7 7 0 -<>'. 7 3 9 - 0 ^ 7 0 3 - 0 . 6 6 2 -f>' . ( ,36 - 0 ' . 5 7 5 - 0 ' . 5 2 3 - 0 '. '! 1 0 - 0 ' . 3 1 3 - 0 ' . 2 2 5 -<>'r 1 3 3 - 0 . 0 2 0 0 ^ 1 1 9 0 . 9 9 3 0 ' . 9 1 3 o'. n o a 0 . 6 3 9 o ' . 5 3 S 0 ] . 1 2 7 0 . 3 1 5 •0', 1 2" - 0 , 0 9 7 - 0 . 1 8 9 - B ' . 2 1 1 - 0 ' . 2 1 1 - 0 ' . 2 0 5 - 0 ' . 1 3 3 - 0 ' . 0 9 2 - 0 ' . 0 1 5 0 ' . 0 9 3 0 . 1 2 7 - 0 . 7 8 ! - 1 , 1 6 9 - 1 . 5 1 1 - 1 . 5 3 I - 1 ' . 6 1 3 - 1 . 6 1 2 - 1 . 5 9 7 -l'.'nn - I . 3 « 9 - 1 , 2 5 1 - 1 . 1 6 3 - 1 . 0 6 5 - 0 , 0 9 8 - 0 . 9 2 I - 0 . 8 3 0 S 2 3 7 8 1 7 5 1 6 7 3 5 9 6 .'16 7 3 5 3 • 0 . 2 5 5 • 0 . 1 5 2 • 0 . 0 2 S O . i - i t 0 . 3 7 0 0 . 9 8 3 0 . 9 6 3 . 0 . ' * 7 5 0 . 7 8 2 0 . 6 8 9 0 . 6 1 7 0 . - 9 5 0 . 1 2 7 0 . 0 0 3 • 0 . 0 8 5 • 0 . 1 0 5 • 0 . 1 0 0 • 0 . 0 6 1 • 0 . 0 1 1 • 0 . 0 ) 3 0 . 0 S 5 - 0 . 0 2 7 0 . 1 4 3 0 . 3 2 7 8 1 0 1 2 11 1 6 - 0 ' . 6 6 3 - 1 . 5 H - 2 ' . 5 5 6 - 3 , 7 0 3 - a ' . 9 3 1 - f . 7 7 8 - 2 . 8 2 8 - 1 ' . 0 2 8 - 5 . 3 1 3 *b . 6 17 - 2 ' . 1 6 3 - 3 . 1 7 5 - 1 . 2 9 1 - 5 , 5 0 9 -h ' . 7 5 6 - 2 ' . ' 1 0 0 - 3 . 2 5 1 . 1 '. 2 2 8 - 5 , 2 3 0 - 0 ' . 2 3 2 - 2 ' . 3 7 9 - 3 . 1 5 1 - 3 . 9 5 2 - 1 , 8 1 9 _ r ' . 7 7 9 • i? ' ^ r . z - 3 . 0 - 2 - 3 . 7 7 6 - 1 , 6 1 1 - l j . 5 0 2 - 2 ' ! i 7 6 - 2 , 8 9 9 - 3 ' . 6 2 3 -•I , 1 3 6 _ r . 1 2 0 - 2 ' . 1 8 9 - 2 . 7 6 6 - 3 , 1 6 1 - 1 , 3 1 3 - a . 6 5 1 - l ' . ' ' 6 8 - 2 , il 2 9 _ (i ' . 8 5 3 - 3 , 2 2 3 ' . 7 5 5 - l ' . 7 1 7 - 1 . 9 8 5 - 2 . 1 0 2 - 2 , 7 5 3 - 3 . 1 0 7 - f . 5 5 7 - 1 . 7 9 6 - 2 . 1 0 5 - 2 . 1 0 8 m 2 ', 6 9 n - l ' , 3 9 7 - 1 , 6 3 3 - 1 . 8 9 1 - 2 . 1 6 5 . ~> . 1 0 3 - 1'. 2 9 0 - 1 . 5 1 0 -r . 7 3 5 - 1 . 9 ^ 9 - 2 , 1 5 6 - l ' . 1 9 7 - 1 . 3 8 2 - i ' . 5 9 7 -1 , 7 8 3 - 1 . 9 S 6 - 1'. 1 1 5 - 1 . 2 7 5 -r. . 1 5 3 - 1 . 6 0 3 , 7 6 1 - l ' . 0 5 3 - 1 . 2 0 9 -1; . 3 6 6 -1 . 5 2 0 -r . 0 6 3 - 0 . 9 9 7 - 1 , 1 3 2 -r, . 2 5 9 - 1 . 1 1 2 -1' . 5 0 1 - 0 ' . 9 3 0 - 1 , 0 5 0 -1', . 1 9 2 -1 . 3 0 8 -1 . H I - 0 ' . 8 8 9 - 0 , 9 '.> 1 - 1 , , 1 2 0 - 1 . 2 3 1 -1 . 3 1 3 - O ' . 7 9 6 - 0 , 3 « 7 - 0 , , 9 8 7 - 1 . 0 7 6 -1 . 1 3 9 - 0 ' . 7 0 9 - 0 . 7 7 5 - o ' , , 8 6 1 - 0 . 9 3 7 - 0 ' , 9 7 9 - 0 ' . 5 1 9 - 0 . 6 0 1 , 6 5 9 - 0 . 7 1 5 - 0 ; 7 "• 2 - 0 ' . 1 2 0 - 0 . 1 5 3 - o'. , 1 8 9 - 0 . 5 2 9 - 0 , \- 1 7 - 0 ' . 3 0 8 - 0 . 3 3 0 - 0 . 3 5 1 - 0 . 3 5 9 - 0 . , 1 1 2 - 0". 1 9 0 - 0 . 1 9 2 - 0 ' . 2 0 2 - 0 . 2 0 1 - 0 ' . •2 •« - O ' . 0 5 6 - 0 , 0 1 9 - o ' . 0 5 9 - 0 , 1 0 6 - c . 1 9 3 0 ' . C 7 2 0 , 0 5 8 0 . 0 1 3 - 0 , 0 5 1 - 0 . 1 5 7 0 '. 1 9 9 0 . 0 0 7 - o . h l B - 1 . 3 8 6 . 2' 2 1 3 0 ' . 7 8 2 0 , 1 1 1 - 0 . 0 1 2 - 0 . 5 8 1 - 1 . 2 5 2 0 > ) 9 7 0 , 9 0 6 0 . 7 3 1 0 , 1 7 2 0 ' . 1 2 5 0 ' , 9 9 2 0 , 9 8 7 0 . 9 2 1 0 . 7 9 2 0 . 5 7 3 0 ' . 9 1 6 0 . 9 9 2 o'. ' ••38 0 . 9 2 1 c . 7 7 3 0 ' . 8 9 0 0 , 9 6 2 r. 0 0 3 0 . 9 7 3 0 . 8 9 1 • C' . 6 2 f. 0 , 9 3 6 o'. 9 9 5 1 . 0 0 1 0 ' . 9 6 3 C ' . 6 3 3 0 , 7 7 3 o'. 8 8 5 0 . 9 6 7 0 . 9 9 1 0 ' . 3 1 5 0 , 1 9 7 o' 4 6 2 9 0 . 7 1 0 0 ' . 8 11 3 ' . 1 9 6 0 . 3 ' M 0 . i i i>5 0 , 5 6 5 0 . t : ^ 5 0 ' . 0 7 2 0 , 1 3 0 o'. 2 8 5 0 . 3 7 9 0 . 1 1 9 0 . 0 3 6 0 . 1 1 0 0 . 2 3 1 0 , 3 1 7 0 . 3 8 8 0 ' . 0 0 0 0 , 0 6 3 0 . 1 2 6 0 , 1 8 3 0 . 2 2 8 0 ' . 0 0 6 0 , 0 1 3 0 . C 7 5 0 , 1 0 6 0 ' . 1 3 1 O ' . O l 1 0 , 0 3 7 o'. 0 5 u C . 0 6 9 0 . 0 7 9 C . 0 ' 1 7 0 , 0 1 3 0 . O i l 0 , 0 1 1 0 . 0 2 3 0 ' . 0 7 H 0 , 0 6 3 0 ' . 0 3 9 O . O O S - 0 . 0 1 9 0 . 7 8 5 0 . 9 5 3 1 . 1 2 8 1 . 2 9 5 1 . 4 3 2 f il L Table 9. (cont'd) 0.61-NACA-oci5 0015 RE=!'.0*(10)6 50ii.S OAR UPPER/ SOLID LOWER) PLENUM 0015 RE = l'.0*(10)6 604LS -OAR UPPER, SOLID LOWER; PLENUM A L A 0 ? 1 6 ,< /c 0 , 0 1 . 0 06 0 .913 • 0 .635 0 , i ? 2 C 1 0 .791 0 . 1 3 1 - 0 .05 7 -0.764 Q , 1 0 .56 1 - 0 .107 -0 ."30 -1.15 0 ; . 0 .199 - 0 . 3 " 6 -0 .307 -1.4 8 0 1 c 6 " u 8 - 0 .116 -0 . 9 4 2 -1,552 1 9 • 0 137 - 0 .535 -1 .030 -1.603 r -(; 209 - 0 . 5 8 6 -1 .030 -1,573 -i j 9 - 0 276 - 0 . 6 3 3 -1 .071 -1.547 , 9 - 0 ,'121 - 0 .715 -1,071 -1.439 7 . 1 - 0 « 3 - 0 .730 -1.009 - 1.325 <> . 6 - 0 .5 0 1 - 0 . 7 15 - 0 / . 5 2 -1.312 \2 . 1 - 0 .519 - 0 . 7 00 - 0,900 -1.135 I -!< , 8 - 0 5 1 4 - 0 .'.71 - 0,859 -1 .047 1 7 , 3 -e 5 0 9 -6 ,648 -0 .812 -0.975 P.'J . 2 - 0 .'! Q t| - 0 .607 -0 .750 - 0 . 8 9 8 P. 2 . 3 - 0 6 8 3 -0 .581 -0,735 -0 . 846 t p. - 0 13 7 - 0 , 5 3 5 -9.68 3 -0,805 ? ~f - 0 1 4 2 - 0 . 5 3 5 -0 .64 7 -0.754 29 , '7 - i ' •'12 6 - 0 .509 - 0 . 6 16 -0,723 , 7 - 0 3 8 5 - 0 ,468 -0 ,554 -0,651 , 6 - 0 3 6" -a .421 - 0,497 -0.573 , 3 - ii 3o2 - 0 . .3 2 9 - 0 . 3!'. 8 - 0 . 4 5 5 . 5 -0 - i 7 /; - 0 - 0 .295 - 0 . 3 1 7 6 0 . 3 - . 0 1 3 7 0 3 ~ 8 a 54 3 0.771 , -1 - 0 •j • i 3 0 0 4 3 9 0 . 6 8 8 2 , 9 - 0 3 0 7 .0 , 0 5 2 0 356 0,621 tl , 9 - 0 .4 5 3 -0 .133 0 1 4 4 0.400 9 , 9 - 0 ' 5 •'! 5 - 0 .303 - 0 ' 083 0.132 j 8 - 0 5 5 6 -() . 3 3 5 - 0 171 0 . 0 1 1 - 0 ] 5 1 1 -0 .360 - 0 , 3 3 3 - 0,081 ! 7 -'/ •17 3 -0 .3'-''I - 0.328 - 0 . 1 0 0 £ - 0 ' 3 3 3 - 0 .257 - 0 / 8 7 -0,094 , 1 - 0 ' 199 - 0 .138 -'•>, 1 l<> -0,058 7 ' / , 2 - ( / 1 i 6 -0 . 0 '•'• 2 -0.073 -0.033 p v , 5 - 0 ' 0 2 R -0 .0 15 : O' 000 - 0 . (10 7 96 . 9 ()' 117 0 .109 0.103 0,091 c -0 .023 0 . 1 4 5 0 .326 0. 530 L 8 10 12 14 16 -0'.656 -1.510 -.2.4 98 -3,630 - 1 ' 763 -f.768 -2.80a -3.93! - 5.180 - 6 ' 367 - 3.142 -3.151 - 1.212 -5.392 -6' 542 - 2 ' . 375 - 3.270 - 1.119 - 5.107 - 6 ' 0 25 -2'.355 -3.151 -3'.92l - 1.718 - 5 ' 637 - 2 ' . 331 -3.021 -3'. 734 -4.490 - 5 109 - 2 ' . 251 -2.902 -3.517 - 1.330 "\ 259 - 2 ; 1 7 3 -2,777 -3.417 - 1,210 - 4 ' 69 0 - 1 . 9 3 9 - 2.450 - 2.610 -3.132 _ i' 6 4 1 -l'.721 -1,956 -2.316 -2.687 035 -1.513 -1.780 -2.077 -2.350 - 2' 601 - l ' . 358 -1.629 -1.854 -2.080 - 1 ? 270 - l ' . 259 - 1 . 1 6 4 -1.693 -1.873 - 2 ' 053 - f . 17B -1.354 -1.558 -1,702 -1 8 67 -1.077 -1,260 -1.397 "1.557 670 - l ' , 025 -1 . 193 -1.311 -1.453 -1 . 57 7 - 0 ' . 968 -1. UO -1.231 -1,319 - f . 1 5 3 - 0 ' . 9 0 6 -1,037 -1'. 1«3 -1,26! - l ' . 341 -0'.864 - 0,975 - l ' . 080 -1.163 -1 216 -0'.766 - 0,871 - 0 / 5 6 -1.028 -1. 075 - 0 ' . 6 7 7 -0.762 -0'.82b - 0,893 - 0 . 93d -0'.527 - 0.596 -O.t.39 - 0,651 - 0 . 67 2 - 0.407 - 0 . 4 1 5 - 0.^73 - 0.191 - 0 . 48 1 - 0 ' . 2 98 -0,315 - 0.332 - 0,328 -o'. 320 -0'. 179 - 0.135 - 0 . 1 6 7 - 0,183 - 0 . 212 - n'. 0 4 1 - 0,040 - 0 , 0 1 7 - 0.060 -0. 160 0 ' . 081 0.064 0 ' . 0 2 6 - 0.028 - 0 . 13', •121 - 0 . 0 0 6 0 009 0.005 96,9 0 . 115 0 .11 R 0.107 0.088 C L -0. 026 0.147 0.328 0.529 8 10 12 14 16 -0'.665 -1.529 -2.507 -3,583 -4 .719 -l'.787 -2.765 -3'.916 -5.063 - 6 324 - 2', 1 5 0 -3.136 - 1 . 1 9 5 - 5,300 -6 427 -2'. 374 -3.229 -4.076 -1.997 -5 962 -2,358 -3.079 -3.839 - 1.62 1 -5 5 4 9 -2'.332 -2.992 -3.653 -4.3S0 _ C 240 - 2', 2 4 4 -2.642 -3.498 -4.241 - lj 204 -2'. 1 66 -2.729 -3.374 -". 103 -*r 480 -T.932 -2,4 00 -2.663 -3,075 527 -T.724 -1,900 -2.265 -2.602 „ 1 918 -r. 1 9 1 -1 .740 -2.007 -2.263 - 2 505 -1 '. 34 0 -1,581 -1.316 - 2 , 0 06 „ 3 1 74 -r.252 -1.H7 -1.651 -1.826 . 1 0 7 3 - l ' . 153 - 1 . 3 3 9 -1.506 - 1,636 -1 782 - l ' . 055 -1.215 - 1.373 -1.487 " 1 612 -1.013 -1.118 -1.284 -1.389 - 1 4 78 - 0'. 9 5 1 -1,071 -1.161 - 1.296 - 1 369 -0'.853 - 0 , 9 9 4 -1.104 -1.194 -1 266 - 0', 8 3 6 -0.912 -1.042 -1.122 - l ' luS -0'.753 - 0 . S 3 9 -0.903 -0,967 - l ' 039 - 0 '. 61.0 - 0.736 -0.794 -0.834 -0' 87 4 - 0'. 5 0 1 - 0,5n6 -0.608 - 0 . 6 1 9 - •) ' 651 -C'. 390 -0.4 2 2 - 0 '. 4 4 3 - 0 . 4 59 - 0 ' a ! 5 - 0 ' . 3 ; i! -0,2!>9 - 0 '. 3 0 9 -0.239 - 0 2 6 5 - 0 ', 1 6 1 - 0 , 1 6 5 -0.159 -0,145 -0, 172 -0'.032 - 0.026 -0.030 -0.043 131 0'. 0 8 8 0,082 0'. 0 4 2 -0.006 - 0 ' 0 9 0 0'. 19 3 0 . 0 0 5 -0.619 -1.337 143 0'.784 0,143 -O'.O 15 -0.556 - i ' ! 173 0'.997 0.906 0.728 0.172 0 . 1 4 3 0'. 9 9 7 1.001 0.930 0.78 5 0. 592 0'.955 1 .004 0 . 9,8 6 0.913 0 . 78 3 0'. 8 8 8 0.973 0'. 9 9 7 0.975 c. 9 0 0 0'.831 0,937 0.997 1.001 0 . 96 5 0'. 6 4 9 0.7R5 0'. 9 0 4 0.960 1. 0 04 0'.363 0.510 0'. 6 1 6 0,741 - 0 998 0'. 2 1 8 0.361 0'. 4 S 6 0.585 0 ! 685 0 '. 0 8 8 0.201 0.310 0.100 o'. 488 0 ' . 062 0,160 0.253 0.343 0 . 427 0'. 0 2 0 0 . 088 0.150 0,215 0 . 277 0 ' . 0 26 0 ,067 0'. 099 0.143 c . 164 o ' . o n 0.O62 O'. 083 0 , 1 07 0 ' . 132 0'.072 0.072 0 . 066 0,071 o'. 0 6 6 0'.09£ 0,093 0 ' . 0 68 0.045 0 . 019 0.769 0.935 1.088 1.228 1. 305 Fable 9. (cont'd) 0-fc"I-NACA-0015 0 01-5 RE=1.0*(iO)6 70SLS OAR UPPER, 30LID LflWER) PLENUM ft 10 1 2 001S Rf=l'.0*(iO)6 ALPHA 0 2 II 6 Y./C 0 .0 e ' . 997 0 , 90 j 0'.571 ft'. 0 9 7 .2 7 30 0 . a-i a -0'. 1 4/J -0.791 0 , 1 r. •'! 3 0 . i19 -0,50 0 -1.17 2 1 . 0 1 77 -0 . :i 8 - 0 ,5 8 3 - 1 . • j 0 s 1 r 0 0 9 -o. •1 2 1 -(;'. "95 -1 ,5o 1 1 /) 119 " 0 , 5 '13 - 1 / 9 fl - 1 . 6 1 8 2 CT 22 6 - 0, 57 3 -1.111 - 1 .582 2 \ 9 288 -0 .62/1 - l ' . 109 -1.561 1 , 9 .[ -) -t - 0 . 7 00 -l'.Of'.R - 1, 1 ? 3 7 , -1'. I; 9 i-; -0 , 7 1 1 - 1 / 3 7 -1 .38 0 V . 8 - '• ^ 5 1 5 -0 . 7 05 -0.969 -1.1*3 12 - o . "3 0 - 0 , (,90 -0,933 -1.090 11 . 5 1 1 - 0 , (•, 6 0 - 0 r 6 7 1 -1.009 17 . 3 - 0' 5i>5 - 0 . 1,19 - 0 . fl 0 9 -0.937 20 n - o ' . •J9i| - 0 . 59/| -<>'. 758 -0.860 22 - ° , 17 9 - o ' . '-.7 a -0^717 - 0 , 8 0 9 z-. , (•'• .•j c- 3 - i . r r- T -0,6(10 -0,751 p y . 2 _ f, 'l 4 3 - o . 517 -0,63" -0,717 2 9 , 7 - o ' . '12 7 -0 . .19 3 -1,598. - 0 . 6 7 fi T ^ . " -0'. 3 9 0 -0 . «5l -0.536 -0.599 r r, , • J 3c-0 - 0 . 105 - 0 / 1 7 9 -0.533 19 11) ^ - o . 3 1 9 - 0 , 3 6 6 -0.105 -'•/• 331 - o . 23« -0^28.3 -0.302 (jl '.i - o . ! '",.9 - o , 16 1 - 0 .195 -0,205 7 9 .2 - o . 0 9 2 -0 . 0 9(1 -0'. :197 -0.103 f l ? , 9 - u ' . o o i 0 . 0 2 2 o / u 0.020 97 . 0 d] . I 2 J 0 . 1 11 •j . i s o 0.153 0 .2 «!• 77S 0 , 968 0/197 o. a 19 0 . 3 0. 595 0 . 866 1,007 0,977 1 .0 <;'. 3 0 2 0 . 551" 0,853 0.977 1 , 5 o ' . o -*3 0 , 3«3 0,7 1? 0.89 0 2 . 0 123 o ' . 315 0 5 8 9 0 . H 0 8 ? , :i - (J „ 3 26 0 . 131 0 . a fl 6 0.721 2 | 9 298 0 . o /' 3 o / o a 0,611 il ,9 f -: 7 - 0 . 121 0,202 0.110 9 ,9 -0. c.3 0 -0 . ?8R -0 035 0.169 11 , a - o . 551 -0 . 31 9 -0 133 0.0/11 C . f, -<•', 'l 9 9 -0 . 3 « / l -0.19S -0.057 29 7 - c , -!6B -0. 331 -0'. 195 -0.062 1 ri c: - c . 233 -0'. 154 -0,057 6 9 . II - 0'. 179 -0 . 126 - 0 'r 0 9 2 -0.U31 79 .2 * 0'. 112 -0. a 75 -0.056 -0,005 8.°/ r - c' ",19 0. J06 0'. 0 I 6. 0, 020 96 .9 120 0. 123 0'. 119 0.112 C - o - 0 2 2 0. 145 0. 348 0. 518 I -0.651 -f.753 -2.111 -2.331 -2'.2R7 -2.292 -2'.211 -2', 105 -l'866 -1 .665 - 1 ', 1 5 H - 1'. 3 1 j - 1'. 2 I 1 -1'. 1 21 -l'.022 -0',970 -0^898 -o',656 -0 -0 -1.553 -2.807 -3.119 •3.196 •3.061 -2.962 - 2 . fi 2 2 -2,719 -2.371 -i.900 -1 ,6°3 -1.532 -1 .337 2 7 8 1 8 5 1 0 2 0 2 9 7 7 9 7 1 1 - 0 ' . 6 2 a - o 1 7 a - O - . 3 5 9 - 0 ' , 2 1 5 - O ' . I ' l l - 0 ' . 0 1 7 O'. 1 0 8 0 . 1 9 1 0 ' . 7 7 1 0 ' . 9 8 9 n'. 9 9 1 0 ' . 9 5 2 0 ' , 6 9 5 0 ' . 8 3 « 0 ' . 6 a 1 0 ' . 3 7 2 0 ' . 2 3 2 0 ' 1 0 2 " . 0 7 1 035 035 015 087 l 13 • 0 , 9 1 1 • 0 . B 9 1 • 0 . 8 0 1 • 0 . 6 9 2 • 0 , 5 1 1 • 0 . 3 3 6 • 0 , 2 l ; 7 • 0 . 1 1 8 • 0 . 0 0 3 0 . 0 9 6 • 0 . 0 1 8 0 . 1 2 2 0 . P. 9 1 0 , 9 8 7 1 . 0 0 3 0 . 9 7 7 0 , 9 1 0 0 . 7 9 5 0 , 5 2 6 0 , 3 7 0 0 , 2 1 5 0 . 1 7 3 0 , 1 0 1 0 , 0 7 0 0 . 0 8 0 o.oao 0,111 5 3 9 9 1 a 0 1 8 ? . 2 l 6 0 6 1 1 3 3 . 3 1 0 2 . 5 6 0 • 2 . 2 2 1 1', 9 3 5 1 . 7 2 2 1 . 5 9 7 1 . 1 1 1 1 . 3 0 U T .227 1'. 1 3 9 1 . 0 3 5 0 . 9 8 3 o' .n'sn 0 . 7 3 8 0 . 5 5 6 O'^^S 0 ' . 2 6 5 0 . 1 1 9 0 . 0 2 0 O'.OSl 0 . 6 3 1 0 . 0 1 1 0 . 7 0 9 0 '. 9 0 1 0 '. 9 7 1 0 ' . 9 9 5 0 ' . 9 9 5 0 . 9 1 7 0 ' . 6 7 7 0 . 5 1 1 ' 3 3 1 2 B 2 1 7 8 1 2 6 1 0 5 0<>/l 0 . 7 4 8 0 . 9 1 1 0 . 0 8 1 1 . 0 6 5 11 • 3 . 5 6 8 - 5 . 0 2 1 - 5 , 2 0 6 •'1 . 9 3 1 • 1 . 5 1 6 -'1 . 2 6 3 • 1 , 1 5 1 - 1 . 0 1 1 • 3 . 0 0 9 - 2 . 5 3 7 • 2 . 1 5 3 • 1 . 9 1 0 • 1 . 7 1 8 • 1 . 5 5 2 - 1 • 1 , 3 9 7 • 1 . 3 0 9 • 1 . 1 9 0 • 1 . 1 2 2 • 1 . 0 2 1 • 0 , 8 7 9 • 0 , 7 6 0 • 0 , 5 5 7 • 0 , 3 9 2 • 0 , 2 - 1 7 • 0 . 1 0 7 • 0 . 0 2 1 0 , 0 1 3 •1 . 2 7 3 • 0 , 5 8 3 0 , 1 5 3 U . 7 6 ' 1 0 . 9 0 1 0 . 9 7 1 1 . 0 0 8 0 . 9 9 2 0 , 7 7 1 0 , 6 2 1 0 . 1 2 7 0 , 3 7 5 0 . 2 5 1 0 . 1 6 8 0 . 1 1 2 0 . 1 1 6 0 . 0 8 S 1 . 1 9 5 . 1 6 ALPHA 0 p 1 X / C 0 ' /) '. 6 6 0 0 .0 0 -.999 0 ' , S 8 ' 5 5 8 5 6 J . 1 2 6 • 0 2 O'. 7 7 3 0 . '11 2 -0 1 16 6 . 2 2 9 0 1 0 ' . 5 3 0 0 . 1 o.-i -0 /I 7 6 5 .76/1 1 0 ' . 1 7 0 - 0 . 3 8 7 -a 8 1 2 5 . 3 0 0 - 1 5 - 0 ' . 0 2 6 - 0 . 1 3 1 -0 " 5 5 5 . 1 0 ' l 1 9 - 0 ' . 1 6 0 -0 , 5 6.'l -1 0 5 3 1'. 9 3 9 2 5 - 0 ' . 2 3 2 - 0 . 6 1 1 -1 0 6 9 1 . 0 6 1 2 9 - 0 ' . 3 9 9 - C , 6 (17 -1 . 0 7 1 3 . 3 7 5 1 .9 - 0 ' . ' I 2 7 - 0'. 7; 9 _ 1 0 6 9 2 ' . 6 9 9 7 ,11 - o / j o a - 0 . 7 2/1 -0 . 9 8 6 2 . 3 2 7 9 ft - 0 . 5 1 0 - 0 , 7 0 3 -0 ."30 2 . 0 2 3 1 2 . 1 - o ' . 5 2 5 - O . h R R .0 . 8 8 3 l'.aoi 11 . 8 - 0 ' , 51 0 - 0 , ( , 5 7 -0 . 8 3 7 1 . 6 1 6 1 7 .3 - 0 ^ . 5 0 5 - 0 . 6 3 6 -0 . 7 7 5 f. 1 5 0 2 0 . 2 - 0 . 1 8 9 - 0 ' . S 8 5 -0 . 7 1 8 1 . 3 3 7 2 2 . 3 - O ' 1 6 9 - 0 . 5 7 5 - 0 . ( . 8 2 1 . 2 3 9 21 Q .') . •'! :l 3 - 0.51/1 - 0 ' 6 5 2 1 ' . 111 2 7 \z - 0 ; . ' i J 3 - 0 . 5 1 3 - 0 , 6 1 0 l ' . 0 3 2 2 9 . 7 - 0 . 1 2 2 - 0 . 1 8 3 - 0 , 5 7 9 0 . 8 8 3 31 . 7 - 0 , 3 8 6 - 0 . 1 1 1 - 0 . 5 1 8 0 ' . 7 1 3 3 9 . 0 - O . 3 1 0 - 0 . 3 9 5 - 0 . - ' i56 0 ' . 5 0 1 1 9 , 5 - o ; , 3 7 3 - 0 . 2 9 7 - 'j .3 5 8 0 . 3 1 6 59 , 5 - 0 . 3 1 1 - 0 , 2 2 5 -0 . 2 5 5 0 ' . 2 1 3 6 9 7 - 0 ^ 1 3 0 - 0 . 1 5 8 -0 . I 7 « 0 ' . 1 2 9 7 9 -> - 0 , 0 8 3 - 0 . 0 7 1 -0 . 0 8 5 0. 0 9 3 8 8 .9 0 . 0 0 5 ' O ' . O ? : • 0 0 3 8 0 . 0 6 2 9 7 . 0 O'. 1 3 1 0 . 15 0 0 , 1 5 7 2 . 1 2 1 0 . 2 o'. 7 9 3 . 0 / 1 7 3 0.99 1 l ' . 1 8 7 0 . 3 O'. 6 0 S 0', S 8 0 l ] , 0 0 2 0'. 1 0 8 1 . 0 0 ^ 3 2 1 0 . 5 3 7 0 , 8 3 7 0 . 5 6 2 1 , 5 0 , 0 5 2 0 ' . 11 7 0 , 6 9 8 0 . 7 6 / 1 . 0 - 0 . 0 9 8 0 . 2 7 3 0 . 5 8 5 0 . 8 9 3 r> . 1 - O ' . 1 9 1 0 ' , 1 6 5 0 / 1 7 6 0 . 9 ' i ' l 2 , 9 - 0 ' . 2 5 8 0 . 0 9 - 5 0 . 3 9 9 0 . 9 9 1 1 , 9 - 0 / 1 0 7 - 0 . 0 8 7 0 / 8 8 0 . 8 1 1 9 . 9 - 0 , 5 1 5 - 0 . 2 6 6 - 0 , 0 3 3 0 . 6 9 7 11 . 8 - 0 , 5 3 0 - 0 , 3 1 3 - 0 . 1 3 1 O', 1 9 0 . 21 , 8 - 0 , 1 7 9 - 0 . 3 2 8 - 0 ' . 1 8 3 0 . 1 5 1 2 9 . 7 - 0 . •'! 1 3 - 0 . 3 0 7 -0 , 1 8 3 O ' . 3 3 0 1 9 r - 0 '. 2 91 - O ' , 2 3 o - 0 .112 0 '. 2 1 7 . 6 9 , 1 - 0 / 5 5 - 0 . 1 1 2 - 0 . 0 8 0 0 . 1 7 0 7 9 .2 - 0 , 0 9 3 - 0 ' . 0 5 6 -0 . 0 1 9 O'. 1 2 9 es ,5 0 . 0 0 0 o'.ali 0 . 0 2 3 0 . 0 6 7 9 6 .9 O'. 1 2 9 . 0'. 1 3 0 0 . 1 2 6 1 . 2 8 4 c L - 0 . 0 1 2 0 . 1 5 5 0 . 3 3 4 80*LS OAR UPPER. SOLID LOWFRj PLENUM . 6 8 10 0 . 055 0,855 3 38 5 38 605 621 62 1 571 121 305 181 0 88 995 933 855 811 752 71 1 661 571 511 385 2 76 1"3 085 029 158 8 3 0 970 "86 918 8 15 7 16 66 0 153 181 0 6 0 0 33 019 019 012 002 0 31 122 0.523 ,757 ,8 6 2 •3.109 •2'. 362 •?'. 300 •2'. 213 •2.11/1 • 1 ', 6 5 t • l ' . 665 ,112 ,373 ,131 , 05 1 ,989 ,922 ,S71 •0.798 .712 . 619 566 »l\ ?. .323 ?15 .09 1 .028 ,13 1 .120 .710 0^967 r,oo3 .962 19 1 0 ^869 :.pa .109 26 0 0 . O'. 0 ' . 0 ' . 0 ' OU 120 100 061 061 0 95 100 126 0.736 -1 ,659 -2.882 -3. Hui - 3 . 3 3 1 -3.016 -2.913 -2.783 -2.633 -2.369 - 1 .866 -1,628 -1 .172 -1 .306 -1.203 -1.099 -1.000 -0,961 -0.815 -0.821 -0,736 -0.60 1 - o . ; i 3 h -0 .296 -0.171 -0.073 0.062 0. 150 -0.093 0.368 0.876 0.985 ,005 1.000 .985 0,829 370 .111 ,269 ,233 0.155 ,129 .121 0,135 0,160 0.889 12 1 1 2 . 6 2 9 - 3 . 5 5 1 3 . 9 5 3 -1 ,999 1 . 1 R 5 - 5 , 0 8 2 3 . 9 6 B - 1 . 7 6 6 3 . 7 1 7 - 1 , 3 7 3 3 . 5 2 5 - 1 . 1 9 2 3.310 - 1 , 0 7 8 3 . 3 H - 3 . 9 7 0 2 . 3 8 7 - 2 , 8 7 3 2 . 1 1 9 - 2 . 3 1 0 1 . 8 1 5 - 1 . 9 3 7 1 . 5 9 1 - 1 . 7 2 5 1.119 - 1 . 5 3 9 T .290 - 1 . 3 7 9 r. 125 - 1 . 2 0 3 I . 0 5 8 - 1 . 1 2 5 0 ' . 9 5 0 - 0 , 9 9 1 0 . 9 0 1 - 0 , 9 1 8 0 . 8 0 6 - 0 . 8 2 0 0 , 7 1 3 - 0 . 7 0 6 0 . 5 7 1 - 0 . 5 6 7 0,110 - 0 . 1 0 6 0 . 2 6 0 - 0 . 2 5 1 0. H 2 - 0 . 0 9 1 0 . 0 1 8 - 0,008 0 '. 0 7 0 0 , 0 '19 0 . 1 2 6 0 , 0 6 0 0 . V 2 1 -1 . 1 3 6 0 . 1 0 6 - 0 . 6 6 0 0 ' . 66 7 0.100 0.RH5 0 . 7 2 6 0 ' . 9 6 1 0 . 8 7 6 0 . 9 9 7 0 . 9 5 9 f. 0 0 2 1,000 0 . 9 5 0 0 , 9 9 0 0 . 7 0 3 0 . 8 2 1 0'.518 0 . 6 6 9 0 . 3 8 1 . 0 , 1 8 3 0 ' . 312 0 , 1 3 1 0 ' . 2 1 5 0 . 3 2 6 0 ' . 1 8 3 0 , 2 1 5 0 ' . 1 6 2 0 , 2 0 1 0 . 1 5 2 0 . 1 7 8 O'. 1 5 2 0 , 1 1 2 0 . 9 9 4 1 . 1 0 8 CN P , a L". J 3 L * p; a c* a c ^ L " -o - c c r v i a ? f o t N C - N - . i ? -c a e; 3 CT — — — — — — — — O ' I 1 t I I I O C C CZ o c o o o o o o o o o o o o o o o o o o o •o cr r - — t> r j r.: rj —• .-"i — — — r j cr cr- -C >i cr- r- o ~ c o u~ cr- c? —* c cc C ^ r rj ~ ~ ^ N .r rr v, ,-1 p. r, _ ^ r. c h c ^ ^ , n r , r j pj r__ , X- LT -T CT- i f P . c C r r j - c cc r -r - r - -~ r - — ~ x N c i r 7 r j P . r j M - o- r h c 3 ^ K I M r j j r . ru — r ; „ _ _ o o o o o o o o o o o o o o o o o o o c o o o o o _] 1 1 1 1 r 1 1 1 1 t 1 1 1 1 1 1 1 1 ^ o o r- o to i^: — T . M i - ^ 1 L ' : c N N f " f 7 L" C o c " ,*- j"' [-*. d r i t-~- -C cr. r j j ~ , v a > 11 - o CMC N J i," a 1 » i r- 0 r-~ £ P J in x M i / i x i-i i" , 3^ « « r o te ic P J ^ I-J - ,x c i)' P J c n o K r- ir> \r. -c ro r j —• • a a; ^ 1" ^ i i r j pj r j r j r j - —* rr c -r tr i r o i 1 1 i J r 1 1 1 -™ rv. • 1 1 1 r 1 1 1 • - - ir. ir- — <-j t-. —• — o z~ «x. cr. — — — — — — — c- 0 0 1 1 1 t 1 t - — - * O O O O O O O O O O O O O G O O O O O O O O O O " O 1 1 1 1 ( 1 j t 1 1 f 1 r 1 T — o j-i c — ^ - - O i r c - c r o o r - i ^ — r - r - c r ^ r ^ o o o r r c c . 3 o ' i f rt cr N C O « f'j i i ; o M J o C; ^ H p tc b" ~ i l 1 •' c K - 7 N - o cr a: •- -o c i f ;.- 1-1 r j a i « r . - c N LA r i ru r\j P J p.- r\j ru P J rv - H - — ' O O O O O O O O O O O O O — ' O O O O O O O O O O O O > 1 I 1 r t 1 1 1 1 1 1 1 1 z? r £ N - ^ O N C C — o- 3 P C O 4 IP a' O - C PJ P . -""L \ ' O' O (•". /. .0 o rr c- M ^ ? : J n C cc N ••: - 1,1 C n o cr r~ C -c x — =: r-l r j — — c o —• r-i —. o c o o o o o — —• r j — 0 0 c o c c o o o o o o c . 0 0 0 0 o c c o o o * o " o * o " o " o 1 < > 1 • I 1 l f 1 t l 1 1 1 1 l t 1 1 r-j f- c — T c- cr r c: c- r - r -o r c u" c rv ^•. v j - ^ A : zr J~ —• ' J o o o o 1 1 1 1 1 ' i « i ' c M - o - 3 w o c o ^ . c I-"I ir. cr r c in • fi •£ o- v cr r" rv — — r - rvj cc r,- rr r • ^: « r i r- rvj ; o c o o o o o o o o o o o o o l 1 l 1 1 1 t 1 1 1 l 1 t - ~ o • " c cr - « c o n r P i ? ( - . 3 i - i o c •? t c P J ^ PJ - o c- o c -c r . o 1 - - a: — o o o c c ^ a a 1 - --r r ; r: — - • -. — P . r. !•* f — in 10 r i i-i f\; — — o O O ». ^ • . «. «. . . «. * . . . « . v 0 0 rr o o o o 0 0 . 0 0 o o o o o o o o < 1 1 i 1 1 t 1 1 I 1 l 1 1 1 1 1 1 • 1 - r - o o o o o o o o o o o o t I 1 I I I I o f- ;-"\ o c - . o n: — - c f. — • —. a- — r ; t-- r~ K O K , . . „ W -.. " - " - - • - • cr 11 ^ x fi rj n t> o o « - 11 c cc ro c c C b"- PM — c o o — o o — o o o • r- cc c c- p" «. •. •-u o o o c I 0- ~C r- ir-X C PJ n ff 0 0 o - r c O O O O O O O O O O O O O - ' — " O O O O O O O O O O O * I • a.- a- o 1 O A . — —• — • r t 1 1 1 1 1 1 r j o c o x « cc c n o 3 o r— cc o o o X' C - P J -f b" n IT X rr iT->J IT O —< r-1 o; r-' X fj c. f» o O r? rr Ti o r- IT r1 O L~> C - * o c ; o — —. — — — , - 1 0 0 0 0 0 0 MC- —C- C " pj 0 0 0 - *• *• *- ** *• '- *- •- K «- »- •. «. «v O O O O O O O O O O O O O O O O O I t I I — O O O O O O O C O O • " • " " I t * r • r - o ir> ru o cc 0 0 1 o c s n o " a- o ip L"' o L I i r i * ^ ^ L I LP t i t i 1* I T i n r * i \ ; M • •. « .. ... »„ ., . N C l - l U H O h i C M C M Oj M C M CO (-1 K i - l « cr CO A j O O O ~« A J P J ~4 o — - * P J r j M M rr o ii"! ti" -o o N N C cc cj> « f^ rj M ^ o N c o- o £ N W - ^ K ( V 5 t ; C C - C O IT. CT — CC * - t — rj N S h - c c ^ X - ^ r v r ; d IT. i r o IT c — J r ~ . » . « . t . - a . U . ^ - — a- ^. >L ~ r j ^ - ^ n x ff - 1 or, L " l»* IT P - cr N rr 1^ 1 c x '•j x - a ^ " i r~. o er a a L i K ! o f . r , -r - N N c c o m L i rr x t-t M A ; ru a f\.' - « « o o c cr cr o c o-arc t c cc cc tt-c o o o o o o o o o o o o o o o o o o o o G O o o o o o o o o t I — o o o o I I I 1 I t c a : u s o c j cr up c *c s o « x o r c - c r - ^ M N x x c * N o f > —• r; s x c; n « i-i r ; s P J N r i o x « c rr A : cr — rr PJ o c X N \ C u", r; ^ p j P J — o O" C o c T . ^ r i cr fu - r j c Aj c J i C- PJ £ C C C !1 i ' , r r i Pj r ; — •3 IT. • r i P.- Pj . o o o o o o o o o o o o o o o o o o o c o o o o o o 1 I r 1 I r . . . . . . . . o — -c P J M -c ir- M t-i ; i J : O rr o cr A J CT *> ^~ PJ IP, N C O • — c- r - M f- X ai O Pj — O c — U". cC - T o cc PJ — o cr J " 'J~ IT -c • >i « o cr ic r^ -0 u*- ir ~ M Aj ro —• o o c. cr r~ i.i =r r\J P J A J P^ P J . - J . to -C -rr cr '.,i r- r - . ' ~ ~ -JT -r; c _ — — — " O O O O O O O O O O O O O O O O O O O O O O O O O O O 1 I I I •£ O C CT- C C - IT 3 N O ^ If 3 X P , N - C- P j M If rj X ^ C PJ ^ A.' I T ^ X M a~ P J ^ m o o a ru P J r - cr AJ -3 cc o M ir- ff- 1*1 •£• M - C CT CJ ^ S C* r - tc c-t* o f-- u" n P J — c CT- x l - -C J ; L* - T — to rv —* O O C S ; *-* P J — — — — n . u AJ r . — o — — — —— — — — o o o o 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0*0*0 o 0 0 1 1 1 1 1 1 1 1 1 t 1 1 1 r 1 1 1 1 t 1 1 1 1 1 r o O ^ « L P i X « * ^ O C \ ' N r * i X i r t c C c T ? , C i r N - C S i ^ , S 5 P s . ' C T ^ « •c L P -rr L P -JT c — P J LI-, O r j no P J y ic M o o pj — cr P J r - i>- o -JZ o -c x — PJ X TJ PJ « C C ? X X N X ^ i L1 c; C r P ' K r j ^ ^ - ^ - - - - • - - - — -o o - c - c* X s o - - - - . 3 i X C Pj X ~ * — — ' — O O O O O O O O O O C O O O O O O O O O O O O O O O O O O O I t I 1 1 1 t 1 I f 1 1 1 1 1 ; 1 i 1 i 1 , CT N Aj S Jj ti* r - o c P - rr- )>- ; . CC U " — O L"-• J 3 -C •£ sO -C , O MO- .2 : X C PJ X -"t 0- i f m 3 C v* C . j , -, -j , , , "• — i f cr r j or o cr M —• cc — « - o cc c r j P J r* . — - - - ~ ~ j r j — o o o o n 0 0 0 o o o o — — < "i X ? - PJ M O ' / i N M j 3 C 0- I ^ / ro j- ^ • • -• rr r i M r o o o o o o o o o o o o o o o o o o o o o o o o o o o o o " I l l l l * " I I I t I o o o o c-> o c Pj cr c cr re c N - r j c t o c — i". o i : c c « — c - c r o r r . — f-* ci r- . * L' A J cr PJ CC — — Cf O • w - ! f o " r-~ — r— • r r? cj cr t i t i r i r j —.- — o : M rr LP. M O rC O c- cr- iT tr Pv r - — O O — M r-l P J Pj • 1 s C P ; K I Pj r j 1 •c 1- n L ' n: 1 —t t O O O O 1 I I I I O O O O O O O O O C C O O O I I I I I I I I I I I I 1 f O O O O O O O O O C O O O O O I t 1 o — -j-- i r P J —• — if. rr J ; x. -5 'ji 3 r i p j « - « • e M P J Jj E c — - i ; c 1 ~ t~ o — c c i - o c sr. cc - 1- cr — cc t i P J -C cr n —- —* ac K J O o: c t - o r rr r C 1 c « P J 11 M 10 K * r'i rP f-*1 r-" r M r j P J — O O O O C i - - CC L * rr r-" r k ^ ».•-*. t. s. « . » . * . t. ».•••.*. «v « . • . « . « . V • . « . * . *. ».»-•.*. ^ V. «. «. i . ». < O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O - ^ I I • I I I I I I I I I I I I I I I I I 1 I I I I I I • t" M i' o J J J : r j r j x s r j e i' X N c ff c c c N C s c - T P J c> r x N - r c L " cc o o cr c cr r cc c r - o; — t - 1- L."- I-I — =c f» P J r-i M r - P J ru o o t"1 — M t-i ,T -r-i J - O ^ i-r: —• o O — — . V P. .V (V A Pv P. — — • — — o O O O - r-1 C t - Li" A, — O O O — O — O O O O O O O O O O O O O O O O O O O O O O — O O O O O O C O C 1^ C (••- S X — LT - ' r- • - - - CC P.' i."1 I o cr o — — • > o o o o o o o o o o o 0 0 0 0 0 0 0 — ---> 0 0 I I I I I I I I I 1 I I 1 I t I 1 J I I t — f- ff O M P J o M cr -*r cj r „ o o 03 i r c? cr LA —» o r - M o cr pj t-T Pj r - p j r. o o L ' c o A i x i i ' i p r r ^ i r c c : C - x r - o y - ^ c c c - - r - — > IT- S Aj Pj I" r : c r - -P J C C L ^ . - r r j — 0 0 — — — — — — — — — o o o o o o c o o o o o o o o c 0 0 > 0 0 0 0 0 0 0 0 0 " " " i i - O M C- — cr t PJ L P C c: cc -z 1* 1 1 1 T r N t o o — ffLPOiniri-oyLni/iuitntn c o > — r-1 U l h- ff M O M oD M CC M c j ^ X H f j K * M cO n'—WcC AJ o ' f f "ff " o P j V j *— j - « P j P j M M C - C L f i l T i O - O N N C C c C O — P J P J M l j l O r - c c f f f f 247 Tab le .10. ( c o n t ' d ALPHA -7 -5 y./c o' .o - c ' . i:.'> %T, ' - ' i " o ' . l O/H.Q 0'."K". 1 . 7 <>..". (.5 ' J . ' . ' X i 3'.3 0 / . 8 7 0 / . 3 8 5 .0 O / i 17 0.1 7o 7. 1 0,279 0.O56 9'.9 o ' . l ' I ' . - 0 . 0 ' l f l 1 . s 0 ^ 0 r. ,7 - 0 . 1 1 1 18'. 6 - U . 0 4 H - 0 . !"? 23 .5 -O ' . l l ' l - f l'.?3o 2 8'.5 - o ' . l ' I a -0'.?<.;>. 33.il - 0 / 8 6 - 0 . 3 7 9 3f'.'.'3 - 0 . 1 " 3 - 0 . 2 7 7 '13'.5 - O / K ? -0.,-".;' 48 .5 -0 . 167 -0.23'? 53'. 5 -(>'. 156 -0 . 209 sr.'.s -0]. 137 -0 . 1 0 6 63 .5 - 0'. 1 09 - 0 ' . I 5 11 68 .5 - 0 / 7 8 -0 . I 20 73.5 -0 . 0 5 9 -0 . 107 78'. Ti -(j ' ,0'i2 -0 . 027 B3 ' . 5 0 . 0 2 0 O.n 'U RS.5 0 / 158 O'.O'U 9 3 . 5 -0 . 0 6 9 -O'.o76 l'.7 -? ' .283 -T . .I55 i ' ,2 -T .871 - i . ; :« 1 8.3 - 1 / 3 " -0 . 9 0 7 12'." -0 . 9 2 9 -0 . 699 20'.7 - 0 / . 5 5 -0.49.8 29.0 -0 / 1 7 2 - 0 . 5 1 9 39.7 -0 , 2 9 6 -0 . 209 50'.5 -0 , 1 8 2 -0 . 1 1 2 61',2 -0 , 0 8 2 -0.0 29 72.0 0,001 0 .043 8,3.8 0 , 0 5 2 0.09.1) 91 .0 0, 1 0 5 . 0'. 1 37 96 .0 0 .088 0 .103 C L - 0 . 3 2 7 - 0 . 1 2 7 li 50'i[ !1 n,\P UP0F.7, -3 • 1 1 0'." .'12 1 . 002 0'. 7 8 9 o',84 1 0 . .'1 8 " -O'. 0 79 o'.30 1 - 0 . I 0 8 - 0 '. 6 3 0 0 \ •, 1 1 - 0 . 3 '! -0'. 763 - 0 . 0 9 " -0 , 8 0 7 • - 0 '. 7 5" -O'. 1 8 8 - 0 . 4 3 9 - 0 '. 7.1 0 - 0',35ft - 0 . '19 2 -O'. 733 -0J.3O1 -0.3'" 0 - 0 , - 0 . •'1" 7 '10 7 - 0 '. 7 0 3 - 0 '. 6 7 6 -0 ' , 5 7 " - 0 . 5 1 'I - 0'. 6 4 7 -0',37" - 0 . 0 8 0 -O'. 6 0 0 - 0'. 3 8 11 - 0 . 078 - .V. 57 9 -o'.367 - 0 . •'155 - 0 . 5 3 " - 0'. 3 (13 - 0 . • 1 1 5 - 0 . 4 " 7 - 0', z 0 2 - II, 376 -O ' . ' IV i - 0 '.278 -') ' . 3" 1 -1 .372 - 0', 2 .'1 7 - 0 . 3« 5 - f l ' . 3 05 -0 ' .215 - 0 . 2 ? 6 -0' .250 -0 ' . 156 - 0 . 156 -0'. 1 39 -0'.091 - 0 . 1 10 -O'. 1 '12 -0'.03S - 0 . 06 1 -fl ' .0S7 o'.nts 0. 000 -0 ' .022 0^021 - 0 . 0 8 5 0 .011 -0.0 65 -O'. 0.03 -0' .079 -0' 715 - 0 . 130 0'.333 -0 .781 - 0 . 365 - o ' . o o i -O', 582 - 0 . 3 0 i -0 ' .052 -0 /181 - 0 . 268 -f)'.066 - 0 , 3 6 0 - 0 . 3 0 6 -n ' . 056 - 0 . 2 3 6 - 0 . 128 -O' .Ol 'J - 0', 11 5 - 0 . 060 O'. 0.'l3 -0,0,76 0 . 0 3 3 0'. 0 8 il 0 n 2 " 0 . fl 8 0 O'. 117 0 , 086 0 . 10 1 O'. 1 76 0 , 123 0. 167 O'. 2 02 0 168 0. 192 0'.237 0, 126 0. 1«7 O'. 1 68 0. 081 0. 273 0 .468 SfH.Tr> L nwF.'f • K L F . M U I 3 5 7 0.25 1 -11'. 5 5 9 - 1 . 6 5 0 - 0 . 8 0 4 -1 .771 -2 . 8'XI - 1 . 2 5 | - 1."31 - 2 . (> '* 3 - 1 . 2 ' . " - 1 . 7 1 6 - 2 .2 « 3 - 1 . 1 5 " - 1 '. 5 6 3 - 3 . 0 M - 1 . 0 7 5 - f . 4 1 1 -1 .729 - 1 . 0 0 8 - 1 ' . 386 - 1 . 4 8 7 -0 . 910 - 1.10 7 - 1 , 3 0 3 - 0 . 8 5 5 - 0 . " " 5 -1 .154 -0 . 787 - 0 . 9 1 0 - 1 .052 - 0 . 7 1 5 - 0 . 8 1 7 - 0 . " 3 l -0 .661 -O'. 777 - 0 . 8 5 6 -0 . 6 2 '1 -0'.r,«7 - 0 . 7 7 6 - 0 . 5 1 3 - 0'. 6 1 1 -0 . 665 - 0 . 4 7 7 - 0 . 5 5 5 -0 .587 - 0 . 1 2 9 - 0 / 1 7 3 -0 . 5 0 8 - 0 . 3 5 7 -0 . 401 -0.4 33. - 0 . 2 " 5 -0'. 329 - 0 . 3 ' i l -0 .231 -0 . 2 4 2 - 0 . 2 6 9 - 0 . 1 6 8 - 0'. 1 8 7 - 0 . 3 0 3 -0 . 1 ()/| - 0 . 126 - 0 , 1 3 9 - 0 . 0 3 9 -0 . 058 - 0 . 0 7 6 - 0 . 0 1 3 - 0 . 0 3 0 - 0 . 0 3 9 - 0 . 0 6 8 -O'. 064 - 0 . 0 5 2 0.683 0 '. 1 3 5 0.983 0.30 5 0 '.543 0,741 0,169 0 .352 0.51 7 0.110 0 .265 0.413 0 .082 0'. 1 97 0.309 0 .090 O'. 182 0.279 0 , 1 1 6 0'. 192 0.268 0 . 1 4 3 0'.205 0.264 0 . 1 6 7 C . 3 I 3 0.262 0. 198 0'.232 0 . 2 7 ? 0 . 2 1 5 0'.243 0 .27? 0 . 234 0'. 253 0.272 0 . 1 8 3 0'. tvu 0.205 0 .652 0. 809 0.986 9 11 13 .. 2' " 4 5 -4 . 2 '11 -0 .924 - 4 . l l « -5 . 35? - t .4 0? -5'. 4 52 - 4 . 1 6 4 -P .936 9„7 -3 .250 -0 . " 1 5 30 0 _ -> , 6 3 6 -0 . 8 7 3 _ 2 0 0 o- - 2 .305 -0 . « 5 1 - l ' . 759 -1 .970 -0 .'•51 - l ' . 5 0 6 -1 .666 -0 . 87? - 1 '. 3 0 7 -1 .418 -0 .87? - 1 . 158 -1 . 3 3 3 -0 .651 - 1 '. 0 1 6 - 1 .059 -0 .3 30 - 0 . 93 0 -0 .956 -0 .829 -0'. 8 1 6 -0 .830 -0 . 8 29 -O'. 721 -0 . 7 1 4 -0 .6 08 -O'. 6 1 9 -0 .606 -0 .7 99 -O'. 529 -0 ,S17 -0 .776 - 0 . 4 3 8 -0 . 4 1 « -0 .755 -0'. 34 7 -0 , 3 2 « -0 .729 -0'. 2o7 -0 ,36 0 -0 .710 -0'. 206 -0 .211 -0 .663 t o o -0 .167 -0 .638 -0 .081 -0 . 1 37 -0 .617 - 0 . 049 -0 . 1 05 -0 .549 - 0 . 045 -0 . 0 6 ? -0 .5 15 0. 985 0 .915 0 .98 2 0'. 871 0 .94 1 0 .831 O'. 65« 0 .751 0 .633 O'. 539 0 .629 0 .5 14 O'. 113 0 ,487 0 .39 4 O'. 362 0 ,427- 0 . 33? 0. 335 0 . 3 8 ? 0 .299 0'. 318 0 .35 1 0 .254 0'. 3 07 0 .351 0 .231 0 . 309 0 .32 3 0 .217 c'. 0'. 299 0.302 0' .174 28 8 0 .282 0 .130 0'. 217 0 ,191 -0 .010 1. 125 1 .214 1 .012 JOUKOWSKY RE=.5(iO)6 60XLS fl.«,l! UPPER, SOLID L0WER*PLENUM A L P H A -7 -5 -3 1 3 5 7 <> 11 13 X / C O'.O -0'.ll'4 0 . 5 8 6 0 ' . «53 1 .000 0*.7B5 0 . 2 4 1 -o ' . 5R7 -1 .673 -3'.0~10 - 4 . 3 3 9 -0 . 8 7 0 O'.'l 0^.973 0.996 0 /<35 0 . ' ;74 -0'. 105 -0 . 871 - l ' . 8 0 3 -2 . 9 2 2 -'4'. 157 - 5 . 3 1 3 -1 .250 l'.7 0 , 8 5 4 0 ' .628 0,294 - 0 . 1 23 -o ' . 637 -1 .2.45 - 1'. 914 - 2 . 6 7 9 -3 ' .459 - 4 . 153 -0 . 921 3'.3 0 , 5 8 0 0 ' .520 0.001 -0 . 3 5 3 -o ' . 7 8 ' i -1 .258 -1.7 ' IS - 2 . 2 8 7 - 2 . 9 S 5 - 3 . 1 8 a -0.7 « h 'i .O 0/111 0 . 1 7 2 - " ' . 1 06 - 0 . 4 15 -0 . 778 -1 . 1 71 - 1 ' . 559 - 2 . 0 55 -2 , 2 7 6 - 2 . 6 1 0 -0 ' . 6 t3 7'. 1 0 , 2 7 8 0 . 0 5 ' l -0 ' .199 -0 . 161 - o ' . 7 5 ° -1 .070 -1 .385 -1 .731 -1 .986 -3 . 2 6 6 - 6 . 7 8 1 9'.9 0, 149 -0 . 0 5 2 -0 ' .?69 -0 . 191 -n ' .736 -0 . 9 9 6 - 1 .273 -1 .479 - l ' , 7 4 5 -1 .943 -0 . 791 IZ'.S 0 , 0 5 2 - 0 . 120 -0' ,305 - 0 . 4 8 9 -0'.7,V1 -0 . 91 1 -1 . 1 10 -1 .297 -1 .506 -1 ,690 -0 ' . 83? IP.'.6 -0 / 150 -0 . 200 -0].351 -0 . 5 0 8 -o ' . 67o -0 . 8 4 6 -0 .987. -1 . 15S -1 .296 -1 .399 -0 . 7 9 6 23'.5 -0 , 1 1 7 - 0 . 2 4 ? -0 ,377 -0 .51 1 -O'.6<|5 -0 , 791 -o ' . 905 -1 .045 -1 . 153 -1 .214 -0 . 8 1 9 2R.5 -0 , 1 5 3 -0 . 26(1 - 0^373.-0 . 490 - o ' . 6 0 ' l -0 . 7 0 6 -0 . 806 -0.9?S -0 . 9 9 6.-1 .(136 -0 . 7 9 6 33'.6 -0 , 181 -0'.?7'1 -0 , 373 -0 ,473 -0 . 5 8 3 -0 . 674 -o ' . 759 -0 , 853 -0 , 9 2 2 -0 , 9 4 0 -0 . 8 0 U 38'.5 - 0 / 9 2 -0.375 -0 . 360 -O/14I -p ' .545 -0 , 6 0 9 -l)'.691 -0 . 760 - 0 . 8 2 5 -0 . 8 1 7 -0 . 7 9 3 'I3'.5 - 0 / 8 . 3 -0'.?5? -0),331 - O . ' U O -o ' .501 -0 . 5 3 7 -0 . 6 0 5 -0 . 665 ~0 ' .70'I -0 . 6 9 3 -0 . 7 9 5 ' IR.5 -0 ,U>9 -0'.?33 -0 , 3 9 3 -0 . 37O -o ' . 427 -0 . 171 -0 ; .531 -0 . 581 -o ' , 61 1 -0 , 5 9 0 -0 . 7 8 0 5 3 . 5 -0 ' . 15« - 0 . 2 1 3 -0 . 2 7 3 - O.334 -0 ' .374 - 0 , 1 16 -0 .461 -0 .50 ' J -0 . 514 -0 . 4 9 9 -0 . 7 3 8 5R'.5 - 0 / 3 7 - O . I 8 0 -0 ' .?37 -0 . 2 7 3 - o ' . 303 -0 , 351 -0 .3'?7 -0 , 421 -o ' . 430 -0 , 4 0 4 -0 . 7 1 0 63'.5 -0 , 078 - 0 . 131 -0 - ,203 -0 . 2 1 6 -o ' . 247 -0 . 2 8 3 -0 . 3 1 3 -0 . 335 -o ' .341 -0 . 3 3 0 -0 . 7 2 7 6R',5 - 0 , 078 -0 . 122 -0J.147 -0 . 151 - o ' . 187 -0 . 21 1 -0 . 2 3 7 -0 , 250 - o ' . ? 6 9 -0 . P 5 1 -0 ' .680 73 .5 -0^955 -O'.09.'l -0 . 081 -0 . 1 0 5 - o ' . l ' U -0 . 161 -o ' . IRO - 0 . 193 - 0 . 199 -0 .200 -0 . 6 7 6 7R'.5 -0 , 041 - 0 . 9 1 6 -0',031 -O.O*-? -O'.OR'I -0 . 0 9 5 - O . l l R - 0 , 1 23 -0 . 140 -0 . 162 -0 . 6 4 2 03^.5 0^035 0 .045 0 , 0 2 7 0 .005 - o ' . 016 -0 . 034 -0 . 051 -0 . 064 -0 . 0 8 3 - 0 , 12? -0 . 6 1 0 8fi'.5 0 , 0 6 5 0 .047 0 . 0 3 7 0. 017 -O'.OOS -0 . 0 0 8 -o ' .021 - 0 . 0 3 0 -0 . 047 -0 .095 -0 . 5 7 0 'J.S -dj.056 -0 . 0 6 5 -0 '.i)68 -0 .O72 -o ' . 073 -0 , 068 -l) ' .049 -0.02.3 -0 . 0 5 9 -0 .074 -0 . 5 4 4 l'.7 -2].247 -1 .406 - 0 / , 7 8 - 0 . 1 1 0 0 ' .345 0 . 6 9 1 0 . 8 9 7 0 . 9 9 8 0 . 9 R 7 0 , 9 1 1 0 . 9 9 0 fl',2 - l ' , e i « -1 .275 -0 . 7 4 6 -0 . 3 4 2 o ' .016 0 . 3 1 5 0 . 5 5 7 0 , 7 4 3 o'.879. 0.9(17 0.8?9 8'.3 - 1 , 1 16 -0 . 3 9 5 - 0 / 5 5 9 -0 . 381 -O'.OIO 0 . 1 8 0 o ' .366 0 . 5 2 3 0 ' .661 0 , 7 5 5 0 . 6 1 9 12'.« -0 , 9 0 7 - O . 6 8 0 -0 , 464 -0.24.3 -o ' . 063 0. 130 0'.?75 0.4 )8 0.545 0 . 6 3 U 0'.5I5 20'.7 - 0 ^ 6 1 7 -0 . 486 -0 , 3'I1 -0 . 1 8 9 -0 ' .051 0 ,08? 0 . ? 0 1 0 . 3 1 6 0 ' . «16 0 . ' l " 3 0. 396 ?9'.0 -0 , 1 5 9 -0 .343 -0 , 218 - 0 . j I 9 - o ' . O O i 0.0"3 0. 188 0 . 2 « 7 0.36.3 0 , 4,79 0 . 328 3'»'.7 -0 . 2 8 ? - 0 . 195 - 0 , 1 0 0 -O.11U8 o ' .043. 0. 1 37 0 . 2 0 3 0 . 2 7 2 0 . 3 5 3 0 .367 0 .288 50'.5 - 0 / 6 0 -0.0 " 3 -0 , 027 0. 01 3 0 ' .085 0 .152 0 . 3 1 3 .0.270 0. 316 0 , 3 5 9 0 . 2 6 5 6l'.2 -0 , 074 -O'.0?l 0 , ,KlO 0 . 087 0'. 1 19 0 , 1 75 0 .222 0 . 2 7 0 0 . 309 0 . 3 4 ? 0 . 2 3 5 7?'.0 OJ.0.1 7 0 . 05 3 0,0"5 O.135 o ' . 1 7 i 0 . 2 0 3 o ' .?43 0.2RO 0 .307 0. 329 0 . 2 1 6 a?'.8 0, 070 0. 095 0, 131 0 .165 0. 197 0 , ? 2 ? 0 . ? 1 9 0.?71 0.391 O.3O4 0 . 1 6 7 9l ' . ( J (1,116 0 . 1 n 1 0 , 1 7 2 O.?0| 0 ' .25t 0 . 2 3 " 0.358 0 .230 0 .394 0 .291 0 . 1 3 7 9(,'.9 6 .097 O' . l l ' l 0. 130 0 . 1S2 U. 17 a 0.19.1 1)'.200 0 . 2 1 4 0 .216 0 . 3 0 0 -0.0 1 7 C L - 0 . 3 1 4 - 0 . 1 20 0. 087 0.278 0 .472 0. 653 0 .823 0. 985 1 . 1 1 9 1 . 204 0. 9S19 24 8 T o b . K ; 1 0 . (cont'd) J 011K (1 •1 '•(• = -. S CI 0 1 TOtlS DAW I IPPEM, S f 1 L , , - , i . n i , f - - « » P i r M l « A l . PHA -7 -S - I 1 X / C 5 7 q , 3 0 . 0 - 0 1?7 0 . S . H 7 0 > 5 3 0> , : o 47S - o ' ' . . ? - o % " a "I'^V: - ' » • • ' « -o.78> 1,7 o / o o 0 - . , . a , „ , , . , , ". - ; , u « - 3 . 3 3 s - t . t i a 3 , i ",569 o'.J,M 0 / 0 6 - 0 ~ ,55 - 0 ' 7 7 5 ' • - . ->,"<" - 1 . 1 3 8 - 0 . 7 7 0 7,1 o.? (.6 0 . 0 3 0 - o , , o 3 . , , . , , 5 7 - n ; 7 3 7 ' - • ' • ' " - • • ' - • > - - • • < « • * - ° - 7 0 3 "'.'> 0^ I ' l l -0 . 1,3? -!)':.73 -o ' . - l''0.- 0-7-V „ ' " -r1' - 0 . 7 0 7 I*,-' " 0 " - . - M J , - 0 l 3 0 - « : , M 5 l o - ' ^v ' ! o ' ^ ; " - ! ' ^ " - 1 . ^ " 0 . 7 1 7 1 8 , 6 -0,052 - 0 . . 9 6 - 0 > 1 .tul't I'-'^ -]-'.43» -0,476 -0'.483 -0.4 M -0.715 58.5 - 0 / 3 2 -0 . 188 -<)'..?«! -0.286 - o'.?99 - 0 . 3 1 0 -0.365 -0.593 - o ' . o o i -0 . 576 -0.7 17 63^.5 - 0 , 1 06 -0 . 158 -0'.?08 - 0 . ? I 4 -0'.?37 -0.?73 -0.?89 -0.315 - 0'. 31 7 -0.30! -0.705 6K'.5 -0^.070 -0 . ( 2 1 - 0 / 4 6 -0 . 1 43 -0'.176 -0.206 - 0 . 2 2 ? -0.23 1 -0 .24 1 -0.23 1 -0.667 73'.5 -0,055 -0 . 105 -0/177 -0 . 105 - 0 / 28 - 0 . 1 49 - 0 : 163 - 0 . 172 -0.M 73 -0 . 183 -0.646 78.5 -0,000 -0.O29 -0,050 -0.055 -0.075 -0.090 -0.093 -0.107 -0.111 -0.143 -0.627 83.5 0^.028 0'.'J"6 0,037 0 .005 - o ' . 006 - 0 . 026 -0.034 -0.050 -0 . 059 -0 . 1 1 4 -0.587 88.5 0,060 0.')5n 0'.039 O.n?? o ' . 007 0, 00 1 O'.OOO -0.014 -o'.034 -0.084 -0.551 93'.5 -(/.055 -0. 067 -0'.075 -0.065 -0J.065 -0 .050 -0'.034 -0.O29 -0/>17 -0.057 -0.515 l'.7 -?'.226 -1 .41? -0 ' . ( , 7 2 -0. 1 04 o'.357 0.693 0 .903 0.991 0.979 0 .909 0.99O 1.2 -l].81« -1.268 -o'.74,3 - 0 . 339 o ' . 022 0 . 328 O.KbZ 0.748 0'.882 0 .94 1 0 .823 8.3 - 1 / 2 6 -0.89u - 0 / 5 4 -0 .232 -0'.035 0. 131 0'.573 0.535 0'.669 0.764 0.625 1 2 ' . 4 -(.']. 890 -0.6 "3 155 -0.34 2 - o ' . 046 0 .130 o ' . 283 0.4?9 o ' . 549 0 .64 6 0'.5 2 ? ?0'.7 -0.646 - 0 . 1 8 7 -0',3'I3 -0.178 - o ' . O I ? 0.1)94 0.2 1 7 0.326 o'.4?6 0.500 0.401 29.0 -0,464 -0.338 -0/120 - 0 . 1 1 0 -o'.OO? 0.101 O'.?04 0.292 o'.37d 0 .437 0.353 J°',7 -0.287 .-0.201 -O'.l 0 2 -0.015 o'.OSt 0.130 o'.?l? 0.28! o'.34B 0.397 0.506 50l5 - 0 / 6 9 - 0 . 1 03 - o'.0?4 0.047 o'.O"! 0. 158 0'.?23 0.277 0. 329 -0.277 0 .277 bl'.2 -0,073 -0.02? 0 / 3 5 0.093 o'.1?5 0. 1 79 ()'.?.',3 0,281 o'.319 0.346 0.247 72'.0 C',008 0 .048 o'.096 0. 112 o'.l78 0.207 o'.?59 0.237 o',321 0,3 3 3 0.339 8.7'.8 0,063 0 .092 0 / 32 0. 1 70 0.303, 0,223 0'.358 0.281 0.306 0.310 0. 178 9l'.0 0 / 1 0 0. 1 39 0 170 0.203 0'.33? 0.212 0.269 0.237 0.306 0.299 0.190 96'.0 0.093 0. 109 0. 132 0. 161 0 '. 1 7 1 0.200 o'.?lO 0.224. o'.230 0 ,207 -0.004 C L -0.314 - 0 . 1 1 9 0.089 0.276 0.467 0.647 0.813 0.968 1.098 1.117 0.952 J O U K O W S K Y H E = . 5 0 0 ) 6 101:1.3 OAR U P P E S , SOUS lnw ER,P l E N U H A L P H A - 7 -5 -3 -V t -, X/C 3 - 1 1 3 r, 7 9 11 ,3 ;;; 1;H / " - f l s " i s ; :ws zr,i « , I U J - 9 . 1 1 , . ' - 0 . 4 3 5 - 0 . 7 6 4 - 1 . 1 6 0 - 1 . 5 6 1 - 2 . 0 6 1 - 2 . 2 1 7 - 2 . 5 6 1 -0 . 5 8 O 7 , 1 0 , 2 6 5 0 ' . ( )50 - 0 , 1 9 9 -0 . 4 6 2 -0 . 7 4 9 - 1 . 0 6 3 -l'.Jril - 1 . 6 3 3 - f . 9 8 7 - 2 , 1 8 9 - 0 . 5 9 7 9 . 9 0, 1 4 7 - 0 , 0 5 3 - 0 . 2 6 9 - 0 . 4 9 1 - o ' . 7 ! 7 - 0 , 9 8 1 ) - l . ? 5 r t -1 . 0 3 1 - 1 . 7 0 5 - 1 . 0 8 4 - 0 . 5 9 " ; 13J.5 0 , 0 4 6 - O . I l " - 0 ' , 3 ' . ) 5 - 0 . 4 9 3 - 0 ' . 6 7 5 -0 . 9 0 0 - l ' . 0 6 3 - 1 . 2 4 0 - l ' . 1 4 7 - 1 , 6 0 5 - 0 . 6 0 6 18^ 6 - 0 , 0 5 2 - 0 . 1 8 1 - 0 ' . 3 4 5 - 0 . 5 0 0 - f> ' .658 - 0 . 8 3 8 - 0 . 9 3 4 - 1 .H 7 - 1 . 2 6 5 - 1 , 3 1 7 - 0 . 6 0 1 23,5 - 0 , 1 1 3 - 0 . 2 3 9 - 0 ] , 3 7 0 - 0 . 5 1 1 - o ' . 6 ? f a - 0 , 7 6 0 - 0 . 8 7 3 - 1 .00 1 - 1 . 1 0 4 - l . t ' 1 3 -0.63.5 28.5 - 0 / 5 1 - 0 . 2 3 0 - 0 , 3 6 6 - 0 . 4 8 1 - 0 . 5 8 4 -0 .68-1 - 0 . 7 7 6 - 0 . 8 8 2 - 0 ' . 9 6 9 - 0.O63 - 0 . 6 3 3 33'.6 - 0 ^ 1 7 8 - 0 . 3 6 9 - o ' , 3 6 0 - 0 . 4 6 6 - 0 ' . 5 3 7 - 0 . 6 1 4 - 0 . 7 2 7 - 0 . 8 0 4 - f l ' . H R O - 0 . 8 5 1 - 0 . 6 3 9 38'.5 - 0 , 1 8 5 - 0 . 2 6 5 - 0 ' . 3 4 7 - 0 , 4 3 2 -0 . 5 1 2 - 0 . 5 8 7 - 0 ' . 6 5 3 - 0 . 7 1 7 - 0 . 7 7 2 - 0 . 7 2 0 -0'.fe«5 17/.5 - 0 , 1 7 6 - 0 . 3 5 0 - 0 ' . 3 2 8 -0 . 3 9 O - 0 ; i 6 6 - 0 . 5 1 3 - 0 . 5 5 3 - 0 . 6 2 8 - 0 . 6 4 1 - 0 . 6 1 4 - 0 . 6 5 4 '18,5 - 0 , 1 6 6 - 0 . 2 2 1 - 0 J . 2 9 2 - 0 . 3 6 2 - o ' . 3 9 6 - 0 . 4 5 0 - o ' . 4 9 ? - 0 . 5 3 9 - 0 ' . 5 5 6 - 0 . 5 0 4 - 0 . 6 5 8 53.5 - O . l ' o - 0 . 3 0 4 - 0 ' . 3 i , l - 0 . 3 3 8 - 0 ' . 3 3 5 - 0 . 3 7 8 - o ' . i i l l - 0 . 4 5 4 - o ' . 4 6 1 - 0 . 4 2 8 - 0 . 6 5 4 58'.5 - 0 / 2 6 . - 0 . 1 7 0 - 0 ^ . 3 3 7 - O . 2 7 1 - o ' . 2 8 2 - 0 . 3 2 3 - u ' . V i i i - 0 . 3 8 0 - 0 . 3 7 5 - 0 . 3 " 3 - 0 . 6 4 9 63).5 - 0 , 1 0 1 - 0 . 1 3 6 - 0 . 2 0 0 - 0 . 3 0 3 - o ' . , ? 1 8 - 0 . 2 5 7 - 0 . 3 7 8 - 0 . 2 9 1 - o ' . 2 9 4 - 0 . 2 7 4 - 0 . 6 5 8 68.5 - 0 , 0 6 5 - 0 . 1 0 9 - 0 ' . 1 2 4 - 0 . 1 3 5 - o ' . 1 5 5 - 0 . 1 9 ? -0 . 2 0 6 -0 . 2 2 3 -0 . 2 0 7 -0 . 2 0 4 - 0 . 6 3 8 73,5 - 0 ^ 0 4 6 - 0 . ' J 3 , - | - 0 ' . 0 6 9 - 0 . 0 9 5 -0'. 1 0 6 -0 , 1 3 0 - o ' . l l ? , - 0 . 1 6 4 - O ' . l ' j l - 0 . 1 6 8 - 0 . 6 U ? 78.5 - 0 , 0 2 9 - 0 . 0 0 6 - 0 , 0 2 1 - 0 . 0 4 6 - o ' . 0 5 ' > - 0 . 0 7 5 - O ' . O B S -0 . 0 9 6 - 0 ' . l ) 9 8 - O . l ' l ? - 0 . 6 3 1 83'.5 0 , 0 3 6 0.05.3 0 . 0 3 9 0.0 1 9 0 ' . 0 0 6 - 0 . 0 0 8 -o'.0 1 8 - 9 . 0 3 9 -0'. 0 4 7 - 0 . 1 1 5 -0 . 5 8 9 8R'.5 0 , 0 7 0 0 . 0 6 0 <)].0(13 0 . O 3 6 0 ' . 0 3 7 0 . 0 1 5 o ' . 0 0 3 0 , 0 0 1 - o ' . 0 1 9 - 0 . 0 8 5 - 0 . 5 4 ? 93'.5 - 0 / 1 4 8 - 0 . 0 3 ( 1 - 0 . 0 5 4 . - 0 . 0 6 1 - 0 ' . 0 5 3 - 0 , 0 2 9 - o ' . 0 2 o - 0 , 003 - 0 ' . 0 1 7 - 0 , 0 6 8 - 0 . 5 2 5 l'.7 - 3 . 1 6 9 - 1 . 3 ' I 6 - O / . 1 0 - 0 . 0 6 3 0 '.3';2 0 . 7 1 4 0 ' . 9 I 1 0 , 9 9 2 0 ' . 9 6 7 0 , 8 9 9 0 . 9 « 4 U'.Z - 1 ^ 7 7 9 - l ' . ? l i - 0 , 7 1 5 - ' " ' . ? 7 6 0'. 0 5 2 0 . 3 4 3 ( ) ' . 5 8 7 0 , 7 6 3 0 , 6 8 3 0 . 9 5 6 0 ' . 8 1 ? 8'.3 - 1 , 9 9 3 - 0 , 8 3 6 - 0 . 5 3 8 - 0 . 3 5 9 - o ' . O K , 0 . 2 0 8 0. 3 9 7 0 . 5 5 5 0 . 6 8 1 0 . 7 6 1 0 ' . 6 2 1 1 2 . 1 - 0 , 8 8 6 -0,1,1.7 - O / 1 3 3 - 0 . 3 2 5 - 0 ' . 0 3 2 0 . 1 4 6 0 ' . 3 1 4 0 . 4 4 7 0 ' . 5 7 1 0 . 6 9 5 0 . 5 0 ? 2 0 . 7 - 0 / , | ? -0 .46.1 - 0 . 3 1 2 - 0 . 1 7 2 -O ' . 0 ? 0 0, 1 0 8 o ' . ? 3 8 0 . 3 4 0 0 . 1 4 2 0 . 5 1 0 0 . 3 8 8 ?9'.0 - 0 , 1 4 7 - 0 . 5 1 9 -0].207 - O . O " ? . 0 ; . O 1 6 0 , 1 1 9 o ' . 2 1 5 0 , 3 0 6 0 . 3 9 1 0 , 4 4 0 0'.335 3r''.7 - 0 , 2 7 1 - 0 . 1 8 ? - 0 . 0 8 7 -11 .1 )36 0 ^ 0 6 9 0 . 1 4 6 o'.?2(. 0 . 2 8 7 0 ' .3(>3 0 . 4 0 ? 0 . 2 9 7 50 .5 - 0 . 1 5 4 -0.O33 -0^.0 1 1 0. 0 5 5 0'. 1 0 9 0 . 1 7 4 o ' . ? 3 a 0 . 2 3 7 0. 3 4 6 0 . 3 7 ? 0 . 2 6 7 6 l'.2 - o ' . O f . 3 - O ' . O O I 0 / ' | 8 0 . 1 0 1 0'. I ' l l .0 . 1 9 7 0'..•"•'5 0 . 2 9 1 0 . 3 3 8 0 . 3 5 1 0 . 2 3 3 7?'.0 0 ] . 0 I 7 0'.!)67 0 . 1 1 ? n ' . 1 5 0 o ' . l 9 6 0 . 2 2 ? 0 ' . ? 6 4 0 . 2 9 9 o ' . 3 3 1 0 . 3 4 ? 0 . 2 2 1 8 2 . 8 0 / 7 6 O ' . l l ? 0 / 4 1 0 . 1 8 0 0 ' . 3 3 3 0 . 2 3 7 0 . ? 6 8 0,?'I1 0 . 3 1 9 0 . 3 1 7 0. 1 6 8 9 1 .0 0 / 1 8 0 ' . l 5 l 0 . 1 8 3 0 . 2 1 ? 0 ' . 3 1 6 0 . 3 5 1 o ' . 3 8 3 0 , 3 9 7 0 . 3 1 9 0 , 3 0 6 0 . 1 30 «6'.0 0 . 0 9 9 0 / 2.8 0'. 1 4 3 0 . 1',9 0 . 1 9 1 0 . 2 0 5 0 . 3 2 1 0 . 2 3 3 c ' . 2 4 2 0 , 2 0 7 -o'.Olu Cj - 0 . 3 0 4 - 0 . 1 0 7 0 . 0 9 7 0.28'J 0 . 4 7 2 0 . 6 5 1 0.8L6 0.966 1 . 1 0 2 1 . 1 6 4 0 . 8 3 1 .o. • - ly T B . - rYB., + TA..y - TB..v = usine. , j i j £ k ^.. mi v j i ? ] i p > ] i p i 3 (2) k m (4) 2 (6) J (8) 2 (9) i=l,NWS (43) ? ( B i U + B J L ) a j + ^ k ^ U ^ L * + r I ( A . U + A . L ) + I ( B . U + B . L ) y p + I ( A . U + A . L ) V p = - U ( c o s 6 u + c o s G J J (11) m ( 1 3 ) J (15) J (17). j (18) L=NSUl+(k-l)NSPS U=L+NSPS-1 (45) ? ( BJD + B JL ) aj + ^ k I ( A n ^ + A n L ) + r I ( A . U + A . L ) + ? ( B . u + B . L ) y p + £ ( A . U + A . L ) V p = -U