transmission of doppler broadened resonance radiation

AEDC-TR-76-12 c

,t~'.~l r, 197a

LzC; f' , .

TRANSMISSION OF DOPPLER BROADENED RESONANCE RADIATION

THROUGH ABSORBING MEDIA WITH COMBINED

DOPPLER AND PRESSURE BROADENING [NITRIC OXIDE 1,- BANDS AS AN EXAMPLE)

1

I i

ENGINE TEST FACILITY ARNOLD ENGINEERING DEVELOPMENT CENTER

AIR FORCE SYSTEMS COMMAND ARNOLD AIR FORCE STATION, TENNESSEE 37389

February 1976

Final Report for Period July 1, 1974 - June 30, 1975

Approved for public release; distribution unlimited.

r W

i

m

!

Prepared for

DIRECTORATE OF TECHNOLOGY ARNOLD ENGINEERING DEVELOPMENT CENTER ARNOLD AIR FORCE STATION, TENNESSEE 37389

propert',t d ~J. $. pit" Foz¢s AF,.DC L|BRARY I"

F40600.17-C-0003

m I

m ~

m

. . . . . ~ - x I . ' " l

NOTICES

When U. S. Government drawings specifications, or other data are used for any purpose other than a definitely related Government procurement operation, the Government thereby incurs no responsibility nor any obligation whatsoever, and the fact that the Government may have formulated, furnished, or in any way supplied the said drawings, specifications, or other data, is not to be regarded by implication or otherwise, or in any manner licensing the holder or any other person or corporation, or conveying any fights or permission to manufacture, use, or sell any patented invention that may in any way be related thereto.

Qualified users may obtain copies o f this report from the Defense Documentation Center.

References to named commercial products in this report are not to be considered in any sense as an endorsement of the product by the United States Air Force or the Government.

This report has been reviewed by the Information Office (OI) and is releasable to the National Technical Information Service (NTIS). At NTIS, it will be available to the general public, including foreign nations.

APPROVAL STATEMENT

This technical report has been reviewed and is approved for publication.

FOR THE COMMANDER

EULES L. HIVELY Research and Development

Division Directorate of Technology

ROBERT O. DIETZ Director of Technology

UNCLASSIFIED REPORT DOCUMENTATION PAGE j READ INSTRUCTIONS

BEFORE COMPLETING FORM

, REPORT .UMaER 12 OOV" "OC"S O" "O J ' S

I AEDC-TR-76 -12

4 T I T L E (and Subtlt leJ J S TYPE OF REPORT & PERIOD COVERED

TRANSMISSION OF DOPPLER BROADENED RESONANCEI F i n a l R e p o r t - J u l y 1 , RADIATION THROUGH ABSORBING MEDIA WITH COMBINED DOPPLER AND PRESSURE BROADENING (NITRIC OXIDE T-BANDS AS AN EXAMPLE) 7 AUTHOR(s) ¢

M. G. D a v i s , W, K. M c G r e g o r , J . D. Few, and H. N. G lassman - ARO, I n c .

19 PERFORMING ORGANIZATION NAME AND ADDRESS

Arnold Engineering Development Center (DY) Air Force Systems Command Arnold Air Force Station, Tennessee 37389 11 CONTROLLING OFFICE NAME AND ADDRESS

A r n o l d E n g i n e e r i n g D e v e l o p m e n t C e n t e r (DYFS) A i r F o r c e S y s t e m s Command A r n o l d A i r F o r c e S t a t i o n , T e n n e s s e e 3 7 3 8 9 14 MONITORING AGENCY NAME & AOORESS~Jf d l l fe ren t /tom C o n t t o | t l n 8 0 l f i c e J

1 9 7 4 - J u n e 3 0 , 1975 S. PERFORMING ORG. REPORT NUMBER

S. CONTRACT OR GRANT NUMBER(s)

10. PROGRAM ELEMENT. PROJECT. TASK AREA & WORK UNIT NUMBERS

P r o g r a m E l e m e n t 6 5 8 0 7 F

12. REPORT DATE

F e b r u a r y 1976 131 NUMBER OF PAGES

81 IS. SECURITY CLASS. (e l th is report)

UNCLASSIFIED

15a. DECt. ASS1FIC ATION / DOWN GRAOIN G SCNEOULE N/A

16 DISTRIBUTION STATEMENT (o! thie Report)

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

17 DISTRIBUTION STATEMENT ( o l the #bllirll©t entered In B lock 20, I ! dJfleeanl from ReporJ)

18 SUPPLEMENTARY NOTES

A v a i l a b l e i n DDC

19 KEY WORDS (Cont inue on reverse aide I f necaaaaty and Iden t i l y by block number)

s p e c t r a r e s o n a n c e b a n d s p e c t r a

t r a n s m i t t i n g m e a s u r e m e n t s ( c o n c e n t r a t i o n ) n i t r i c o x i d e

20 ABSTRACT (Con l lnue an reverse aide I f n e o e a a a ~ and Idan t l l y by bio©k numbe~

The c o m b i n e d D o p p l e r and p r e s s u r e b r o a d e n i n g p a r a m e t e r has been d e t e r m i n e d f o r t h e 0 , 0 T - b a n d o f n i t r i c o x i d e (NO) by c o m p a r i n g m e a s u r e d s p e c t r a l t r a n s m i s s i o n d a t a w i t h t h e c o m p u t e d t r a n s m i s s i o n u s i n g a r a d i a t i v e t r a n s f e r m o d e l . The p a r a m e t e r ( a ' , t h e r a t i o o f c o l l i s i o n a l p l u s n a t u r a l h a l f - w i d t h t o t h e D o p p l e r h a l f - w i d t h ) was f o u n d t o o b e y t h e r e l a t i o n s h i p a " = Cp/T, w h e r e p i s t h e p r e s s u r e i n a t m o s p h e r e s , T i s t h e t e m p e r a t u r e i n K, a n d C i s a c o n s t a n t . The

FORM DD , JAN 73 1473 EO.TION OF , NOV SS,S O.SOLETS

UNCLASSIFIED

UNCLASSIFIED

2 0 . ABSTRACT ( C o n t i n u e d )

v a l u e o f C was f o u n d t o b e 1270 ~ 200 K / a t m . T h i s v a l u e o f C l e a d s t o a o v a l u e f o r t h e o p t i c a l d i a m e t e r o f NO f o r b r o a d e n i n g o f 3 . 5 ± 0 . 3 A. The d e t e r m i n a t i o n o f t h e b r o a d e n i n g p a r a m e t e r p e r m i t s t h e a c c u r a t e c a l c u l a t i o n o f t h e t r a n s m i s s i o n o f NO T - b a n d r a d i a t i o n t h r o u g h t h e h i g h t e m p e r a t u r e , a m b i e n t p r e s s u r e m e d i a c o r r e s p o n d i n g t o j e t e n g i n e e x h a u s t s , i n t u r n m a k i n g p o s s i b l e t h e r e l a t i n g o f t r a n s m i s s i o n m e a s u r e m e n t s t o t h e c o n c e n t r a t i o n o f NO. The a p p l i c a t i o n o f t h e m e a s u r e m e n t a n d c a l c u l a t i o n p r o c e d u r e t o t h e m e a s u r e m e n t p r o b l e m i s d i s c u s s e d .

APSC Anleld AF ! "rein

UNCLASSIFIED

AEOC-TR-76-12

PREFACE

The r e s e a r c h r e p o r t e d h e r e i n was c o n d u c t e d by the Arno ld E n g i n e e r i n g D e v e l o p m e n t C e n t e r (AEDC), A i r F o r c e S y s t e m s C o m m a n d {AFSC), u n d e r P r o g r a m E l e m e n t 65807F. The r e s u l t s w e r e ob t a ined by ARO, Inc. (a s u b s i d i a r y of S v e r d r u p & P a r c e l and A s s o c i a t e s , Inc . ) , c o n t r a c t o p e r a t o r of AEDC, AFSC, Arno ld A i r F o r c e Station, T e n n e s s e e . The work was a c c o m p l i s h e d in the Engine T e s t F a c i l i t y (ETF) , u n d e r ARO P r o j e c t N u m b e r s R32P-54 and R32P-55A. The a u t h o r s of th i s r e p o r t w e r e M. G. D a v i s , W. K. M c G r e g o r , J . D. Few, and H. N. G l a s s m a n , ARO, Inc. The m a n u s c r i p t (ARO Con t ro l No. A R O - E T F - T R - 7 5 - 1 1 5 ) was s u b m i t t e d fo r pub l i ca t ion on June 30, 1975.

Dr. M. G. Davis is an A s s o c i a t e P r o f e s s o r of P h y s i c s at the U n i v e r s i t y of T e n n e s s e e at N a s h v i l l e and consu l t an t to ARO, Inc.

AE DC-T R-76-12

1 . 0 2 . 0

3.0

4 .0

C O N T E N T S

I N T R O D U C T I O N . . . . . . . . . . . . . . . . . . T H E O R E T I C A L D E V E L O P M E N T . . . . . . . . . . 2 .1 D e v e l o p m e n t of T r a n s m i s s i o n F o r m u l a s f o r

C a s e s I n v o l v i n g A b s o r p t i o n L i n e s B r o a d e n e d by F o r e i g n G a s e s . . . . . . . . . . . . . .

2 . 2 R e l a t i o n s b e t w e e n A b s o r p t i o n C o e f f i c i e n t and A b s o r b i n g M e d i u m P r o p e r t i e s . . . . . . .

2 . 3 E x a m i n a t i o n of the B r o a d e n i n g P a r a m e t e r ( a ' ) . D E T E R M I N A T I O N O F T H E B R O A D E N I N G P A R A M E T E R ( a ) F O R T H E NO M O L E C U L E IN T H E P R E S E N C E O F N 2 . . . . . . . . . . . . . . 3. 1 D e s c r i p t i o n of t he E x p e r i m e n t a l A p p a r a t u s . . . 3 . 2 P r o c e d u r e s and R e s u l t s . . . . . . . . . . . DISCUSSION . . . . . . . . . . . . . . . . . . . R E F E R E N C E S . . . . . . . . . . . . . . . . . .

7

8

8

13

14

15 15 22 30 32

I L L U S T R A T I O N S

Figure

1. I l l u s t r a t i o n of S p e c t r a l L i n e S h a p e f o r D i f f e r e n t V a l u e s of t h e Ra t i o of the P r e s s u r e B r o a d e n e d H a l f - W i d t h to t h e D o p p l e r H a l f - W i d t h . . . . . . . .

2. S c h e m a t i c of E x p e r i m e n t a l A p p a r a t u s f o r R e s o n a n c e L i n e A b s o r p t i o n M e a s u r e m e n t s . . . . .

3. D i a g r a m of H e a t e d A b s o r p t i o n C e l l . . . . . . . . .

4. S c h e m a t i c of G a s H a n d l i n g S y s t e m f o r H e a t e d A b s o r p t i o n C e l l . . . . . . . . . . . . . . . . .

5. D i a g r a m of R e s o n a n c e L a m p U s e d to P r o d u c e N a r r o w - L i n e R a d i a t i o n . . . . . . . . . . . . . .

6. (0, 0) B a n d of t h e NO v - S y s t e m O b t a i n e d f r o m D i s c h a r g e T u b e C o n t a i n i n g a M i x t u r e of 12:3:1 (by v o l u m e ) of A:N2:O 2 at 8 t o r r w i t h 2800 v A p p l i e d by U s e of l - m S p e c t r o m e t e r , in S e c o n d O r d e r ( E q u i v a l e n t Sl i t Width, 0 . 0 3 A) . . . . . . .

11

16

19

19

20

20

3

A E DC-TR-76-12

Figure

7.

.

.

10.

11.

12.

13.

P o p u l a t i o n D i s t r i b u t i o n of E x c i t e d Ro ta t i ona l S ta tes of the A 2F- L e v e l of NO in a W a t e r - C o o l e d D i s c h a r g e Tube O p e r a t e d at 8 t o r r wi th 2800 v App l i ed and Con ta in ing 12:3:1 M i x t u r e (by v o l u m e ) of A:N2:O 2 . . . . . . . . . . . . . . . .

E x a m p l e of T r a n s m i s s i o n M e a s u r e m e n t s fo r NO (0, 0) T-Band , as Ob ta ined with a 1 - m S p e c t r o m e t e r hav ing an Equ iva l en t Slit Width of 0 .03 A a. Op t i c a l P a t h L e n g t h f o r A b s o r p t i o n (No~ = 2) . b. Op t i ca l P a t h L e n g t h f o r A b s o r p t i o n

(No~ = 2 .36"x 1017 m o l e c u l e s / c m 2) . . . . . . .

E x a m p l e Set of T r a n s m i s s i o n M e a s u r e m e n t s fo r NO (0 ,0) T-Band, as Ob ta ined with a 1 / 2 - m S p e c t r o m e t e r Hav ing an E q u i v a l e n t Slit Width of 1 . 6 A . . . . . . . . . . . . . . . . . . . .

E x a m p l e of C o m p u t e d T r a n s m i s s i o n f o r NO (0, 0) - r -Band f o r an E q u i v a l e n t S p e c t r a l Slit Width of

@

0.03 A and at Cond i t ions C o r r e s p o n d i n g to Fig . 8 . . . . . . . . . . . . . . . . . . . . .

E x a m p l e Set of C o m p u t e d T r a n s m i s s i o n fo r NO (0, 0) - ~ - B a n d f o r an E q u i v a l e n t S p e c t r a l Slit Width of 1 .6 A and at Cond i t i ons C o r r e s p o n d i n g to F ig . 9 . . . . . . . . . . . . . . . . . . . .

C a l c u l a t e d T r a n s m i s s i v i t y (t) of the Second Band Head of the (0, 0) NO ~/-Band as a F u n c t i o n of the L i n e B r o a d e n i n g P a r a m e t e r (a ' ) . . . . . . . . .

V a l u e s of the S p e c t r a l B r o a d e n i n g P a r a m e t e r (a ' ) as a F u n c t i o n of p / T fo r the (0, 0) T -Band of NO as Ob ta ined by C o m p a r i n g E x p e r i m e n t a l Data with C o m p u t e d Data . . . . . . . . . . . . . .

Page

21

23

23

24

26

27

28

31

TABLES

.

.

D e t e r m i n a t i o n of B r o a d e n i n g P a r a m e t e r (a ' ) f r o m R e s o l v e d L i n e s of the (0, 0) Band of the NO -y-Sys tem,

D e t e r m i n a t i o n of B r o a d e n i n g P a r a m e t e r (a ' ) f r o m the U n r e s o l v e d (0, 0) Band of the NO 1 , -Sys tem . . . . .

28

29

4

AEDC-TR-76-12

APPENDIX

A. C o m p u t e r P r o g r a m f o r t he C a l c u l a t i o n a n d S i m u - l a t i o n of t h e NO (0, 0) 7 - B a n d S p e c t r a T r a n s m i t t e d t h r o u g h an A b s o r b i n g M e d i u m . . . . . . . . . . . .

N O M E N C L A T U R E . . . . . . . . . . . . . . . . . . .

Page

35

79

AEDC-TR-76-12

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

The radiative transfer of Doppler broadened spectral lines, contained within electronic-vibrational-rotational bands, through Doppler broadened absorbing media has been treated in a pre- vious report (Ref. i). In the work reported herein, the radiative transfer of Doppler broadened source bands through media with Doppler and collision broadened lines is treated. In Ref. i, the nitric oxide (NO)molecule was used to demonstrate the technique and to compare experimental data from low-pressure, Doppler broadened absorbing media with the calculated band profiles. In the work reported herein, NO will be used again but at pressures such that collisional broadening by a foreign gas (IN 2) is present. Knowledge of the collisional broadening parameter for NO was found to be uncertain (Ref. 2) so that a major part of the present work was the determination of the broadening parameter to a higher degree of accuracy over a large range of pressure and temperature conditions.

The application of this work is found in the use of spectral line transmission through high temperature media to determine species concentration and temperature in situ. Previously, measurements using this spectral line resonance absorption technique (Refs. 3 and 4) have been made using empirical procedures to account for the finite width of the source lines. The work reported in Ref. I per- mitted the measured transmission to be related to species concentration and temperature in a rigorous fashion when pressure (e. g., collisional) broadening could be neglected. The development in the present report will permit measurements to be related to species concentration and temperature over pressure ranges where the pressure broadening is comparable to, or dominates, the Doppler

broadening.

T h e b r o a d e n i n g p a r a m e t e r (a ' ) as u s e d in m o s t t r e a t m e n t s of s p e c t r a l l i ne b r o a d e n i n g (Refs . 5 and 6, f o r e x a m p l e ) is p r o p o r t i o n a l to the r a t i o of the s u m of the n a t u r a l h a l f - w i d t h and the c o l l i s i o n a l h a l f - w i d t h of the l i ne to the D o p p l e r h a l f - w i d t h . The n a t u r a l ha l f - width can be n e g l e c t e d f o r e l e c t r o n i c r e s o n a n c e t r a n s i t i o n s . T h e o - r e t i c a l e s t i m a t i n g p r o c e d u r e s a r e g e n e r a l l y i n a d e q u a t e to p r e d i c t the c o l l i s i o n a l b r o a d e n i n g and m e a s u r e m e n t s canno t s e p a r a t e the D o p p l e r f r o m the c o l l i s i o n a l c o n t r i b u t i o n s so that the p a r a m e t e r (a ' ) m u s t be e x p e r i m e n t a l l y d e t e r m i n e d . D i r e c t m e a s u r e m e n t of the b r o a d e n i n g h a l f - w i d t h to d e t e r m i n e a ° r e q u i r e s h igh r e s o l u t i o n

AE DC-TR-76-12

s p e c t r a l i n s t r u m e n t s . In the t r e a t m e n t u s e d in the p r e s e n t s tudy, a t h e o r e t i c a l c a l c u l a t i o n p r o c e d u r e is u s e d to p r e d i c t t r a n s m i s s i o n f r o m e x p e r i m e n t a l ' m e a s u r e m e n t s , and thus by i t e r a t i o n of the c a l - c u l a t i o n s u s i n g a" as a p a r a m e t e r , the v a l u e of a" is i n d i r e c t l y d e t e r m i n e d by m a t c h i n g c a l c u l a t e d and m e a s u r e d t r a n s m i s s i o n . The r e q u i r e d e x p e r i m e n t a l da ta w e r e o b t a i n e d by m e a s u r e m e n t of the t r a n s m i s s i o n of D o p p l e r b r o a d e n e d l i n e s in the (0, 0) %-band of NO f r o m a gas d i s c h a r g e l a m p t h r o u g h a t e m p e r a t u r e - c o n t r o l l e d (60 to 1 ,000°F) a b s o r p t i o n c e l l c o n t a i n i n g known m i x t u r e s of NO and N 2 at p r e s s u r e s v a r y i n g f r o m about 0. 1 to 2 a rm.

The r e s u l t s of the t h e o r e t i c a l d e v e l o p m e n t and the e m p i r i c a l l y d e t e r m i n e d v a l u e of a ' a r e a p p l i c a b l e d i r e c t l y to c a l c u l a t i o n s of the t r a n s m i s s i o n of the (0, 0) ~,-band of NO e m i t t e d by a r e s o n a n c e r a d i a t i o n s o u r c e t h r o u g h a b s o r b i n g m e d i a of v a r i o u s NO c o n c e n t r a - t ions , p r e s s u r e s , and t e m p e r a t u r e s . The t e m p e r a t u r e s and p r e s - s u r e s a c c e s s i b l e in the c a l i b r a t i o n l a b o r a t o r y is l i m i t e d , so tha t d i r e c t c a l i b r a t i o n f o r al l p o s s i b l e c o n d i t i o n s is not p o s s i b l e . How- e v e r , the d e t e r m i n a t i o n of a" and the u s e of the t h e o r e t i c a l r e l a t i o n - sh ips b e t w e e n the t r a n s m i s s i v i t y and NO c o n c e n t r a t i o n p e r m i t s e x t e n s i o n to e n v i r o n m e n t s e x p e c t e d at the exhaus t exit of c o m b u s t i o n e n g i n e s and o t h e r d e v i c e s in wh ich m e a s u r e m e n t s of NO c o n c e n t r a t i o n migh t be d e s i r e d .

2.0 THEORETICAL DEVELOPMENT

2.1 DEVELOPMENT OF TRANSMISSION FORMULAS FOR CASES INVOLVING ABSORPTION LINES BROADENED BY FOREIGN GASES

For a single, isolated jth spectral line, the transmission (T-~) of a source line having some frequency distribution (I~.) through uniform absorbing medium of length ~ is given by (Ref. 3 5):

w h e r e u is the f r e q u e n c y and kuj is the a b s o r p t i o n c o e f f i c i e n t wh ich

h a s a f r e q u e n c y d i s t r i b u t i o n i n d e p e n d e n t of Iuj. If the r a d i a t i o n

s o u r c e is m a i n t a i n e d at low p r e s s u r e , the f r e q u e n c y d i s t r i b u t i o n f o r Ivj can be a t t r i b u t e d to the D o p p l e r ef fec t , and is g iven by

AEDC-TR-76-12

-

(2)

w h e r e I~o. is the i n t e n s i t y of the s o u r c e l ine at c e n t e r f r e q u e n c y " 1

(u~) and (AsUj) D is the Dopp le r width at half the i n t ens i ty (half- J

width) of the e m i t t e d s p e c t r a l l ine . The Dopp le r ha l f -w id th of the s o u r c e l ine is g iven by

~ IM2 KT

(Asvj) D = 2v~ MsC2 (3)

In Eq. 3, ~ is B o l t z m a n n ' s cons tan t , T s is the abso lu t e t e m p e r a - t u re of the sou rce , M s is the m o l e c u l a r weight of the e m i t t i n g m o l e c u l e , and c is the speed of l ight .

In g e n e r a l , the f r e q u e n c y d i s t r i b u t i o n of the a b s o r p t i o n coef - f i c i en t (kvj) is g iven by (Ref. 6):

2 • - V

kvj = kv~ -rrl f~ ,2 a e , )2 dy -c~ a + (a);- y

J

(4)

w h e r e

(A aVj)L V ~n/~'~'=~- 2 a - (AaVj) D

(5)

a)j - (A aVj) D

(6)

and y is a d u m m y v a r i a b l e of i n t eg ra t ion . In Eq. 4, ku~ is the a b s o r p t i o n coe f f i c i en t at l i ne c e n t e r fo r D o p p l e r cond i t ibns . J In Eq. 5. (Aavj) L is the L o r e n t z ha l f -w id th (due to co l l i s ion b r o a d e n - ing) of the a b s o r p t i o n l ine and is g iven by (Ref. 6):

9

AE DC-TR-76-12

Z L

(Aavj)L - n" ( 7 )

w h e r e Z L is t he f r e q u e n c y of c o l l i s i o n s b e t w e e n the a b s o r b i n g m o l e - c u l e s and the s u r r o u n d i n g m o l e c u l e s w h i c h l e a d s to b r o a d e n i n g of t he e n e r g y s t a t e s of t he a b s o r b i n g m o l e c u l e s . T h e f a c t o r (~aUj)D is t he

D o p p l e r h a l f - w i d t h of t he a b s o r p t i o n l i n e a n d is g i v e n by

jV2 ~a2 K'I" a

(AaVj) n = 2 ,, - - (8) M a

w h e r e T a is t he s t a t i c t e m p e r a t u r e of t he a b s o r b i n g m e d i u m and M a is t he m o l e c u l a r w e i g h t of t he a b s o r b i n g m o l e c u l e s .

E q u a t i o n 4 f o r kuj c a n be s h o w n to r e d u c e to (Ref . 7):

kuj ku~ Blexp [-((~j + ia') 2] erfc [-itoj + a']l (9)

w h e r e R d e n o t e s t h e r e a l p a r t and i = %/-1. It s h o u l d be n o t e d tha t , f o r low p r e s s u r e s and h igh t e m p e r a t u r e s , a" is v e r y s m a l l and Eq. (9) r e d u c e s to

2

kvj = kvj e-a' (10)

This is the Doppler case examined in Ref. 1.

C l o s e e x a m i n a t i o n of Eq. (9) s h o w s tha t t h e a b s o r p t i o n l i n e h a l f - w i d t h i n c r e a s e s and the a b s o r p t i o n c o e f f i c i e n t at l i n e c e n t e r d e c r e a s e s a s a" i n c r e a s e s , a s i l l u s t r a t e d g r a p h i c a l l y in F i g . 1.

Equations (I), (2), and (4) can be combined to give the transmission of a single line through a medium:

• j-- ,°o,., oF ~", ' t-L ( A ~ -"'j~D ''~ o,,p -lk, C ,. _S~ .~ + (,.~_y~)d,, (11)

If there are other absorption lines which might contribute to the measured transmission of the jth line, Eq. (4) must be replaced by

10

A E D C - T R - 7 6 - 1 2

¢ / l , m i -

>,, i,__ tqO I m

e m

L - ,,:C

o m

q , - -

A

A: a" [] 0- Pure Doppler B: a" = 0.5 C: a° =2.0

(AaUj) D

~)0 Frequency, v, Arbitrary Units

Figure 1. Illustration of spectral line shape for different values of the ratio of the pressure broadened half-width to the Doppler half-width.

] )

AEDC-TR-76-12

2

S : a ' e - Y ku = _1 2 ku~ _ a + ( c o i - y)2 n i ,2 dy ( 1 2 )

w h e r e the s u m m a t i o n is o v e r al l a b s o r p t i o n l i nes , i nc lud ing the j th l ine , which have a f in i te va lue of the a b s o r p t i o n coe f f i c i en t c o n t r i b u t - ing to a b s o r p t i o n of the j th e m i s s i o n l ine. The t r a n s m i s s i o n of the r a d i a t i o n in the j th e m i s s i o n l ine due to a b s o r p t i o n by m a n y l i n e s is g iven by

° - l; " " " } Tj lv~of exp l(-~sV-~> ~ exp ~ k.l,o f . . . . . d v (13) = - . - ~ , a " 2 + (coi-v)2

The tota l t r a n s m i s s i o n (T) in a p a r t i c u l a r f r e q u e n c y i n t e r v a l (e. g . , b a n d p a s s of a s p e c t r o m e t e r o r i n t e r f e r e n c e f i l ter} is g iven by s u m m i n g o v e r all the e m i s s i o n l i n e s in that i n t e r v a l and r e s u l t s in the equat ion:

{ r,<,,-,,~, ~],} { .,,->.,d>. TAr = II°o ~ - - q exp ~ .~ _ ,.,~ o s<'<''<p -[.,,,,.,~,o - , '<,,r ( ,,.2 +~i-:>.,~) <'' ( " " - )

w h e r e the s u m m a t i o n o v e r j i nc ludes al l e m i s s i o n l i n e s which have c o m p o n e n t s f a l l ing within the f r e q u e n c y i n t e r v a l of i n t e r e s t (AV). The t r a n s m i s s i v i t y (t) o r f r a c t i o n a l t r a n s m i s s i o n in a p a r t i c u l a r f r e q u e n c y i n t e r v a l (Au) is then g iven by

tA v o { < q } { c ,',,} [.~_~? ~ (15)

= j j n i a "2 + ( o i - y ) 2

5' I~? f exp dv

In o r d e r to c a r r y out the eva lua t ion of tAv, v a l u e s of kv~ and a" m u s t be d e t e r m i n e d for a p a r t i c u l a r m e d m m and path.

12

AEDC-TR-76-12

2.2 RELATIONS BETWEEN ABSORPTION COEFFICIENT AND ABSORBING MEDIUM PROPERTIES

The absorption coefficient of a diatomic molecule for Doppler conditions at Iine center frequency (kv~) is given by (Ref. 5):

2o2V;--g N.I,, fj,j,, kvo =

rnc 2 (Aavi) D (16)

w h e r e e is t h e c h a r g e on an e l e c t r o n , c i s t h e v e l o c i t y o f l i g h t , m is t h e m a s s of an e l e c t r o n , fj,j,, is t h e o s c i l l a t o r s t r e n g t h o f t h e

a p p r o p r i a t e a b s o r p t i o n l i n e , Nj,, is t h e n u m b e r d e n s i t y of m o l e c u l e s

in t h e l o w e r e n e r g y s t a t e o f t h e m o l e c u l e c o r r e s p o n d i n g to t h e i th t t

l i n e , J is t h e r o t a t i o n a l q u a n t u m n u m b e r of t h e l o w e r e n e r g y s t a t e , a n d J ' is t h e r o t a t i o n a l q u a n t u m n u m b e r of t h e u p p e r e n e r g y s t a t e .

T h e n u m b e r d e n s i t y o f t h e l o w e r e n e r g y s t a t e (Nj , , ) u n d e r e q u i -

l i b r i u m c o n d i t i o n s is g i v e n by

hcB°(2J"+1) exP [ -KTh-~c F(J"~a Nj ,, = 2 KT a No

(17)

w h e r e N O is t h e n u m b e r d e n s i t y of t h e m o l e c u l e of i n t e r e s t , B o i s t h e

r o t a t i o n a l c o n s t a n t f o r t h e g r o u n d s t a t e , h is P l a n c k ' s c o n s t a n t , K is B o l t z m a n n ' s c o n s t a n t , a n d F ( J " ) is t h e r o t a t i o n a l e n e r g y t e r m f o r t h e l o w e r r o t a t i o n a l e n e r g y s t a t e .

The value for the oscillator strength (fj,j,,) is g i v e n by (Ref. 8):

vj ",I "" ~j , , j" f j ' j " - - f v % " ~ (18)

Vv,v,, 2(2J"+ l)(2S+ 1)

where fv'v " is the band oscillator strength, v j , j , , is the frequency of the line of interest, Vv,v,, is the frequency of the band head, Sj,,j, is the normalized Hb'nl-London factor for the line of interest, and S is the spin quantum number. Combining Eqs. (16), (17), and (18) gives

" hc ,,~ e2X/"~-n[~"2"h B o v j , J - f v , v , , ~ j - j , N o exp 1 KTa F(J

(19) kv~ = 2(25 + ]) mc 2 RT A vv,v,,(AaVi)D

13

A E OC-TR -76-I 2

F o r a p a r t i c u l a r s p e c t r a l l ine of a g iven m o l e c u l a r s p e c i e s fo r which the v a r i o u s m o l e c u l a r p a r a m e t e r s in Eq. (19) a r e known, v a l u e s of

O kui can be c a l c u l a t e d as func t ions of N o and T a.

F o r the (0, 0) -c-band of NO, Eq. (19) r e d u c e s to (Ref. 1):

kv~ -- 1.603 x 10 -14 ~J'J"N° T 3 / 2 exp [-].4383 F(J")."T a] a

w h e r e the cgs s y s t e m of un i t s is u s e d th roughou t

(20)

2.3 EXAMINATION OF THE BROADENING PARAMETER (a')

Equat ion (7) s t a t e s that c o l l i s i o n a l b r o a d e n i n g of a s p e c t r a l a b s o r p t i o n l ine d e p e n d s on the c o l l i s i o n a l f r e q u e n c y of the a b s o r b i n g m o l e c u l e s with the s u r r o u n d i n g m o l e c u l e s . It can be shown f r o m c l a s s i c a l k ine t i c t h e o r y that the b r o a d e n i n g c o l l i s i o n a l f r e q u e n c y (Z L) fo r an a b s o r b i n g m o l e c u l e of m o l e c u l a r weight (M a) is g iven by

Z L = ~ Z~ = 2~1~ NI~ at'2 2rtKTa . + (21)

where M~ is the mass of the ~th type of colliding molecule causing the broadening, N~ is the concentration of the ~th type of molecule, and a~ 2 is the effective collisional cross section for the broadening process by the ~th type molecule.

Combining Eqs. (5), (7), (8), and (21) results in the equation,

a" = ~N~a~ . ~ (22)

w h e r e A~. is the wave l eng th of the a b s o r p t i o n l ine at l ine c e n t e r and r e s u l t s f r o m the fact that

C A~ = - ~ - vj

By us ing the equa t ion of s t a t e for a p e r f e c t gas,

N~ = 9.66 × l019 P£ T a

w h e r e p~ is the p a r t i a l p r e s s u r e of the ~th type m o l e c u l e in t o r r and T is in K. C o m b i n i n g Eqs. (22) and (24) r e s u l t s in

(23)

it can be shown that

(24)

14

AEDC-TR-76-12

a 5.45 x 1019 [ Ma

= o ~ P£al~ %J ] + M~" 1" ~J t

(25)

F o r m a n y c a s e s , the f o r e i g n gas is c o m p o s e d of ch i e f l y ohe cons t i t uen t , and the c o n c e n t r a t i o n of the a b s o r b i n g gas is r e l a t i v e l y s m a l l . In such c a s e s , s e l f b r o a d e n i n g is neg l ig ib l e , and Eq. (25) r e d u c e s to

I5 ~ Ma] Pa ; .45 × ]0 2 1 + (26)

or Pa a" = Cj ~- (27)

a

where c; 2 is the effective collisional cross section for the broadening

process by the foreign gas, Mf is the mass of the foreign gas, and Cj is a constant for the jth line given by

f M a

Cj 5.4.5 x 10 19 Aja 2 3/] = * M-7 (28)

It is th i s c o n s t a n t (Cj) tha t m u s t be d e t e r m i n e d e x p e r i m e n t a l l y .

3.0 DETERMINATION OF THE BROADENING PARAMETER (a') FOR THE NO MOLECULE IN THE PRESENCE OF N2

The v a l u e of a is f u n c t i q n a l l y dependen t on p r e s s u r e and t e m p e r a - t u r e as shown by Eq. (27). To c o m p l e t e l y def ine a ' , the va lue of Cj m u s t be d e t e r m i n e d e x p e r i m e n t a l l y . Al though Cj depends on the wave- l eng th of the spect r .a l l i ne of i n t e r e s t , f o r m o s t s p e c t r a l bands Cj m a y be c o n s i d e r e d a cons t an t fo r a l l l i n e s in the band and s i m p l y d e s i g n a t e d by C (i. e . , Xj c h a n g e s by l e s s than 0. 1 p e r c e n t t h roughou t the (0, 0) T-band of NO). In th i s sec t ion , the e x p e r i m e n t a l d e t e r m i n a t i o n of Cj fo r a few ind iv idua l l i n e s of the (0, 0) ~,-band of NO and the d e t e r m i n a - t ion of C for the e n t i r e , u n r e s o l v e d band wil l be d e s c r i b e d .

3.1 DESCRIPTION OF THE EXPERIMENTAL APPARATUS

The e x p e r i m e n t a l a p p a r a t u s c o n s i s t e d of a r e s o n a n c e gas d i s - c h a r g e s o u r c e l amp , a hea t ed a b s o r p t i o n cel l , and two s p e c t r o m - e t e r s . The a r r a n g e m e n t of the a p p a r a t u s is i l l u s t r a t e d in Fig . 2.

15

SPECTROMETER

8 &

S E . - ; ~ m

c

i i

"' I I ABSORPTION CEll

SPECTRAL LINE SOURCE

I l l

C)

:0

O~

Figure 2. Schematic of experimental apparatus for resonance line absorption measurements.

AEDC-TR-76-12

3.1.1 Ultraviolet Spectrometers

A 1-m J a r r e l l - A s h g r a t i n g s p e c t r o m e t e r equ ipped wi th c u r v e d s l i t s was u s e d to ob ta in high r e s o l u t i o n data . The g r a t i n g has 1, 180 l i n e s / m m and was b l a z e d for m a x i m u m r e f l e c t i o n at 7 ,500 A. Al l data t aken with the 1 - m s p e c t r o m e t e r was in the s e c o n d o r d e r of the s p e c t r u m . An RCA 1 P 2 8 p h o t o m u l t i p l i e r tube wi th S - s p e c t r a l r e s p o n s e was u s e d as the d e t e c t o r . The i n t e r n a l op t i c s c o n s i s t e d of two f u s e d silLca l e n s e s , each with an f - n u m b e r of 4 .4 . The l e n s e s w e r e p l a c e d as shown in Fig. 2, so that p a r a l l e l l igh t w a s d i r e c t e d f r o m the s o u r c e t h r o u g h the a b s o r b i n g gas and f o c u s e d on the s l i t of the s p e c t r o m e t e r . The 1 -m s p e c t r o m e t e r was o p e r a t e d with a pohysical s l i t width of 10 p, r e s u l t i n g in an e q u i v a l e n t s l i t width of 0 .03 A, which g ives su f f i c i en t r e s o l u t i o n to s e p a r a t e s e v e r a l l i n e s in the T -bands of NO (Ref. 3).

A 1 / 2 - m J a r r e l l - A s h g r a t i n g s p e c t r o m e t e r equipped wi th c u r v e d s l i t s was u s e d to ob ta in low r e s o l u t i o n band s p e c t r a . The g r a t i n g h a d 2, 360 l i n e s / m m and was b l a z e d fo r m a x i m u m r e f l e c t i o n at 3 ,000 A. The e x t e r n a l op t i c s and d e t e c t o r w e r e i d e n t i c a l to t h o s e u s e d on the 1 - m s p e c t r o m e t e r . The 1 / 2 - m s p e c t r o m e t e r was o p e r a t e d with a p h y s i c a l s l i t width of 200 p , r e s u l t i n g in an equ iva l en t s l i t width of 1 .6 A. No l i n e s of NO T-bands cou ld be r e s o l v e d u s i n g th is s l i t width. The 1 / 2 - m i n s t r u m e n t , o p e r a t e d with the 200-p s l i t width, has been u s e d in l i eu of the 1 - m i n s t r u m e n t fo r f i e ld m e a s u r e m e n t s of the a b s o r p t i o n of NO 7 - b a n d r a d i a t i o n (Ref. 4) b e c a u s e it is l e s s s u s c e p t i b l e to v i b r a t i o n and m i s a l i g n m e n t p r o b l e m s .

3.1.2 Absorption Cell

The a b s o r p t i o n ce l l u s e d in th i s r e s e a r c h s tudy was a s p e c i a l l y d e s i g n e d 9 1 . 4 - c m long by 1 0 . 2 - c m - d i a m f u s e d - s i l i c a tube with f la t f u s e d - s i l i c a end p l a t e s and 1 / 2 - i n . tubes fo r gas e n t r y and exi t (F ig . 3). The tube was e n c l o s e d in a c o p p e r s l e e v e which was w r a p p e d with a Calrocl @ unit f o r h e a t i n g p u r p o s e s . A h ighly r e f l e c t i v e a l u m i n u m s h e e t was w r a p p e d a r o u n d the h e a t i n g unit , and the e n t i r e a s s e m b l y was s u r r o u n d e d by t h r e e i nches of insu la t ion . The a s s e m b l y was e n c a s e d in a s t ee l hous ing . T h r e e - i n c h d i a m e t e r h o l e s w e r e lef t in e a c h end of the tube so tha t the l ight s o u r c e could be d i r e c t e d t h r o u g h the ce l l and into the s p e c t r o m e t e r .

T h e h e a t i n g uni t was c o n n e c t e d to a t e m p e r a t u r e c o n t r o l l e r which c o n t r o l l e d the t e m p e r a t u r e of the gas wi th in the ce l l t h r o u g h the m o n i - t o r i n g of s t r a t e g i c a l l y p l a c e d t h e r m o c o u p l e s . The t e m p e r a t u r e cou ld

17

AEDC-TR-76-12

be v a r i e d b e t w e e n a m b i e n t and 1,000=F and c o n t r o l l e d wi th in an a c c u r a c y of +1 p e r c e n t . The p r e s s u r e of the gas in the c e l l was m e a s u r e d by m e a n s of p r e s s u r e t r a n s d u c e r s o v e r a r a n g e of f r o m 50 to 1 ,500 t o r r , with an a c c u r a c y of +1 p e r c e n t .

The gas s y s t e m is shown s c h e m a t i c a l l y in Fig . 4. T h e a b s o r b e r g a s e s cou ld be a d m i t t e d to the c e l l and s e a l e d off by v a l v e s o r cou ld be f lowed c o n t i n u o u s l y . In th is e x p e r i m e n t , the g a s e s w e r e a d m i t t e d and s e a l e d off. The g a s e s u s e d w e r e m i x t u r e s of NO in N2 which w e r e supp l i ed by Scott R e s e a r c h C o r p o r a t i o n as c a l i b r a t i o n g a s e s . T h r e e m i x t u r e s w e r e used : (1) 40 p a r t s p e r m i l l i o n (ppm), (2) 100 ppm, o r (3) 400 ppm of NO. The a c t u a l m i x t u r e s w e r e d e t e r m i n e d to be 40, 99, and 395 ppm, u s i n g a gas c h r o m a t o g r a p h , wi th an a c c u r a c y of +5 p e r c e n t .

3.1.3 Resonance Lamp Source Characteristics

A s c h e m a t i c of the r e s o n a n c e l a m p u s e d as a l ine s o u r c e is p r e - s e n t e d in F ig . 5. The s o u r c e was run u s i n g a 12:3:1 m i x t u r e (by v o l u m e ) of (A:N2:O 2) at a p p r o x i m a t e l y 5 - t o r r p r e s s u r e with an app l i ed vo l t a ge of 2, 800 v. R a d i a t i o n e m i t t e d at the end of the w a t e r - c o o l e d c a p i l l a r y tube was d i r e c t e d t h r o u g h the a b s o r p t i o n ce l l and into the op t i c s of the s p e c t r o m e t e r (Fig . 2). The gas t e m p e r a t u r e in the c a p i l l a r y tube was m a i n t a i n e d at a p p r o x l m a t e l y 320 K by the w a t e r - coo l ing j a c k e t . It is a s s u m e d tha t the d o m i n a n t b r o a d i n g m e c h a n i s m u n d e r t h e s e cond i t i ons is due to the D o p p l e r e f fec t . T h e D o p p l e r l i ne wid th (Eq. (3)) fo r the l i n e s of the (0, 0) %,-band of NO at 320 K is 0. 0005 ~ , so that the a c t u a l width of the l i n e s . i s m u c h s m a l l e r than the e q u i v a l e n t s l i t wid th of the s p e c t r o m e t e r (0 .03 ~) . A s p e c t r u m of the (0, 0) band f r o m the l a m p in which m a n y of the l i n e s a r e r e s o l v e d is g iven in F ig . 6. In o r d e r to e m p l o y the c o m p u t a t i o n a l . t e c h n i q u e d e v e l o p e d in Sec t ion 2 . 0 and the s p e c t r o m e t e r s i m u l a t i o n d e s c r i b e d in Ref. I, it is n e c e s s a r y to de f ine the r e l a t i v e i n t e n s i t y of e a c h l i ne in the band. By us ing a l l the r e s o l v e d l i n e s in the s p e c t r a of F ig . 6, a plot of the r a d i a t i o n in- t e n s i t y d iv ide d by the r e l a t i v e l i ne s t r e n g t h v e r s u s the u p p e r s t a t e e n e r g y ( F j ' ) was m a d e (Fig . 7). The u p p e r s t a t e e n e r g y p a r a m e t e r v a r i e s f r o m the e n e r g y at J ' = I / 2 t o the e n e r g y at J ' = 81 /2 . A m o r e c o m p l e t e d i s c u s s i o n of the e n e r g y l e v e l s of the u p p e r s t a t e f o r the (0, 0) "y-bands a p p e a r s in Ref. 3.

In o r d e r to f ind the r e l a t i v e i n t e n s i t y of t h o s e l i n e s that a r e not r e s o l v a b l e , it is n e c e s s a r y to u s e the c u r v e in Fig . 7. F o r a p a r t i c u - l a r l ine , the va lue of I j , j ,,/ g j , j ,, c o r r e s p o n d i n g to i ts v a l u e of F j , is

found f r o m Fig . 7 and is then m u l t i p l i e d by the a p p r o p r i a t e v a l u e of g j , j , , r e s u l t i n g in a v a l u e of the r e l a t i v e i n t e n s i t y ( I j , j , , ) f o r the J ' J "

18

AE DC-TR-76-12

/--- Quartz Window / F Heat Distribution (Copper)

/ / S Heater Element

/ / / I Reflective Shield

~Steel Housing ~ I nsulation

Figure 3. Diagram of heated absorption cell.

Relief Control Absorption Cell Shutoff Valve Valve [ I vawe

,"re o e Transducer Pump

Calibration to Gas Atmosphere

Figure 4. Schematic of gas handling system for heated absorption cell.

19

A E D C - T R - 7 6 - 1 2

Cooling Water

r-Cooli ng Jacket I n ler~ used Silica Window I(Fused Silica

Wi ndow I I

Electrode ~'J i llary Tube Drain trode

Pump 1 Power Suppl Gas Mixture I n l e t ~ E . _ ~ J

Figure 5. Diagram of resonance lamp used to produce narrow-line radiation.

"E 4

m ~- 3 I , .

. 2 e -

G,) e -

f -

o " o

¢ " m t '~

_~ Resolved ~_ " I , I ~ P22 and Q22 Lines I "

I I ~ I ' ' ' ' I ' ' '

2250 2255 2260 2265 2270

Wavelength, A

Figure 6. (0,0) band of the NO ~,-~ystem obtained from discharge tube containing a mixture of 12:3:1 (by volume) of A:N2:02 at 8 torr with 2,800 v applied by use of 1-m spectrometer in. second order (equivalent slit width, 0.03 A).

20

AEDC-TR-76-12

r "

L _

L _

1.00

0.50

0.20

O. 10 - m

0.05 m

0.02

I I I I I I

0.01 I I i I I I 45, 000 46, 000 47, 000 48, 000

F(J'), cm -1

Figure 7. Population distribution of excited rotational states of the A 21; level of NO in a water-cooled discharge tube operated at 8 torr with 2,800 v applied and containing 12:3:1 mixture (by volume) of A:N2 :O2.

21

AEDC-TR-76-12

l i n e . V a l u e s f o r S j ' j " a r e o b t a i n e d f r o m t h e f o r m u l a s d e v e l o p e d by

E a r l s (Ref . 9) a s g i v e n in Ref . 3. E x p e r i m e n t a l v a l u e s of u-, a s g i v e n by D e e s z i (Ref . 10) w e r e u s e d in t h e s e c a l c u l a t i o n s . ~ h e e x p e r i - m e n t a l v a l u e s of uj a r e m o r e a c c u r a t e t h a n c a n b e c a l c u l a t e d u s i n g the Hi l l and Van F l e c k f o r m u l a a s d i s c u s s e d in Ref . 1. V a l u e s f o r I u j

u s e d in t he t r a n s m i s s i o n e q u a t i o n s ( E q s . (13), (14), o r (15)) a r e t h u s c a l c u l a t e d f r o m t h e v a l u e s of I j ' j ' , / Z j , j , , in F i g . 7.

The distributions of line intensities were measured several times during these experiments using pressures in the resonance lamp ranging from 5 to 15 tort with corresponding changes in the applied voltage and current. No measurable changes in the relative distribution of line intensities shown in Fig. 7 have been found, although the level of intensity may change considerably with the lamp operating conditions.

3.2 PROCEDURES AND RESULTS

T h e p r o c e d u r e f o r d e t e r m i n i n g the v a l u e of C f o r NO c o n s i s t e d of t he f o l l o w i n g s t e p s :

(i) A s e r i e s of l a b o r a t o r y s p e c t r a l a b s o r p t i o n m e a s u r e m e n t s of t he (0, 0) "y-band of NO w e r e m a d e f o r s e v e r a l p a r t i a l p r e s - s u r e s of NO a n d N 2 and f o r s e v e r a l g a s t e m p e r a t u r e s . S e v e r a l s e t s of h igh r e s o l u t i o n d a t a w e r e t a k e n u s i n g the 1 - m s p e c t r o m e t e r to m e a s u r e t h e s p e c t r a l t r a n s m i s s i o n a t t h e v a r i o u s c o n d i t i o n s . A p o r t i o n of t h e r e s o l v e d s p e c t r u m f o r o n e of t h e s e t e s t s is s h o w n in F i g . 8 w i th no g a s in t he c e l l a n d w i th a m i x t u r e of NO and N 2 in t he c e l l . F o r t h e c a s e i l l u s t r a t e d in F i g . 8, t he n u m b e r d e n s i t y of NO is 2 . 5 8 x 1015 m o l e c u l e s ] c m 3, t he p r e s s u r e is 1 .5 a t m , and the t e m p e r a t u r e is 422 K. S e v e r a l l i n e s u s e d to o b t a i n v a l u e s of a" a r e i d e n t i - f i e d in F i g . 8. T h e t r a n s m i s s i v i t y (t j) f o r e a c h of the l i n e s w a s d e t e r m i n e d . D a t a c o m p a r a b l e to t ha t s h o w n in F ig . 8 w e r e o b t a i n e d f o r t h r e e c o n d i t i o n s in t he a b s o r p t i o n c e l l . L o w r e s o l u t i o n m e a s u r e m e n t s w e r e a l s o m a d e wi th the 1 / 2 - m s p e c t r o m e t e r in o r d e r to d e t e r m i n e the t r a n s m i s s i o n of t he u n r e s o l v e d b a n d . E x a m p l e d a t a f o r t h e b a n d t r a n s m i s s i o n a r e s h o w n in F i g . 9 w i th t he o p e r a t i n g c o n d i t i o n s s t a t e d on the f i g u r e . T h e t r a n s m i s s i v i t y at t he s e c o n d b a n d - h e a d w a s d e t e r m i n e d f r o m the d a t a in F i g . 9. U n r e s o l v e d b a n d t r a n s - m i s s i o n d a t a f o r the s e c o n d b a n d - h e a d w e r e o b t a i n e d a t 27

22

A E D C - T R - 7 6 - 1 2

12

10

i 2 6 7

,¢C

a. Optical path length for absorption (No£ : 01 m

T -422K 6 p - 1. 5 atm

6 2

/ 0 I 1 0 2, 264 2, 266 2. 268 2, 2~J~O ~-

Wavelength, A

b. Optical path length for absorption (No £ = 2.36 x 1017 molecules/cm 2) Figure 8. Example of transmission measurements for NO (0,0) -y-band,

as obtained with a 1-m spectrometer having an equivalent slit width of 0.03 A.

23

AE DC-T R-76-1 2

]2

].0

E l

2,200

~--Second Band Head

Temperature. 422 K NO Number Demity:. L31 x 1015 cm-3 Path Length: 9L4cm

Curve Pressure, Concentration, arm ppm Trammisslv~

~ 2 r - 3 / - - 4 /--5

1 L36 55 0.820 ~ ~ 2 LOB 73 0.778 3 O. 71 106 O. 710 4 0.40 188 0.596 t ~ l ~ ~,~ I[~/~1 t , ' i ~ ~ i 5 0.19 3~ 0. 467

2, ZlO 2, 220 Z, 230 2, Z40 2,250 2, 260 2, 270 2,280 Wavelength, A

Figure 9. Example set of transmission measurements for NO (0,0) 3"-band, as obtained with a 1/2-m spectrometer having an equivalent slit width of 1.6 A.

24

AE DC-TR-76-12

c o n d i t i o n s o f p r e s s u r e , t e m p e r a t u r e , a n d NO c o n c e n t r a - t i o n in t h e c e l l .

(2) By using the computer simulation of spectra described in Ref. 1 and utilizing Eq. (14), a series of calculated transmitted spectra for many values of a" was obtained for several values of NO concentration, temperature, and with the spectrometer slit width identical to that used in the laboratory experiments. An example synthetic spectrum for the high resolution simulation is shown in Fig. 10, and an example for the low resolution simulation is shown in Fig. 11. The computer program for spectral simulation is presented in Appendix A.

(3) B y c o m p a r i n g t h e l a b o r a t o r y s p e c t r a t a k e n a t a g i v e n s e t of p r e s s u r e , t e m p e r a t u r e , a n d c o n c e n t r a t i o n c o n d i t i o n s in t h e a b s o r p t i o n c e l l w i t h t h e c o m p u t e r s i m u l a t e d s p e c t r a , w h i c h w a s c a l c u l a t e d f o r t h e s a m e c o n d i t i o n s a n d at v a r i o u s v a l u e s of a ", t h e v a l u e o f a" w h i c h b e s t m a t c h e s t h e e x p e r i m e n t a l r e s u l t w a s d e t e r m i n e d . T h e p r o c e d u r e is i l l u s t r a t e d by c o m - p a r i n g F i g . 8 w i t h F i g . 10 a n d F i g . 9 w i t h F i g . 11. T h e c o m p u t e d s p e c t r a l e d to v a l u e s of t r a n s m i s s i o n f o r v a r y i n g v a l u e s o f a ' , , a s i l l u s t r a t e d in F i g . 12, w h i c h is t a k e n f r o m t h e s e c o n d b a n d - h e a d t r a n s m i s s i o n f o r v a r i o u s a" v a l u e s in F i g . 11. T h e v a l u e s of a" in F i g s . 10 a n d 11 w e r e t h e v a l u e s w h i c h g a v e t h e b e s t m a t c h b e t w e e n t h e m e a s u r e d a n d c o m p u t e d s p e c t r a . T h e v a l u e s w e r e c h o s e n in t h i s w a y so t h a t t h e r e a d - e r m i g h t m a k e a d i r e c t c o m p a r i s o n of t h e s i m u l a t e d a n d m e a s - u r e d s p e c t r a . In p r a c t i c e , t h e a ' v a l u e s f o r a p a r t i c u l a r e x p e r i m e n t a l c o n d i t i o n w e r e o b t a i n e d f r o m p l o t s l i k e F i g . 12, w h i c h w e r e o b t a i n e d f r o m s i m u l a t e d s p e c t r a o v e r a r a n g e o f a r b i t r a r i l y s e l e c t e d v a l u e s of a "

T h e r e s u l t s o b t a i n e d f r o m t h e h i g h r e s o l u t i o n s p e c t r a l a b s o r p t i o n m e a s u r e m e n t s a r e s u m m a r i z e d in T a b l e 1, a n d t h e r e s u l t s f r o m t h e l o w r e s o l u t i o n d a t a a r e s u m m a r i z e d in T a b l e 2. F o r t h e h i g h r e s o l u t i o n d a t a , e i g h t i n d i v i d u a l l i n e s w e r e s e l e c t e d f o r d e t e r m i n i n g t h e v a l u e s of Cj . T h e s e l i n e s a r e n u m b e r e d in T a b l e 2 to c o r r e s p o n d to F i g s . 8 a n d 10. F o r t h e l o w r e s o l u t i o n da t a , t h e t r a n s m i s s i o n a t t h e s e c o n d b a n d - h e a d a s m a r k e d in F i g s . 9 a n d 11 w a s u s e d f o r d e t e r m i n i n g t h e v a l u e s of a '

25

AEDC-TR-76-12

]4

12 I

10

.S_ 8 ¢_

c" O

E E P

i - .

4

Optical Path - 0 ~

Optical Path - 2. 36 x 1017 moleculeslcm2~

!,i! ,L t, Jo,, I ,,

I. 52 2264. 21 2265. 90 2267. 59 2269. 28 Wavelength, )~

Figure 10. Example of computed transmission for NO (0,0) ~-band for an equivalent spectral slit width of 0.03 A and at conditions corresponding to Fig. 8.

26

A E D C - T R - 7 6 - 1 2

1 2 -

, B e-

, m

¢ _

<C

1E

l0

Temperature: 422 K NO Number Density: 1.31 x 1015 cm-3 Path Length: 91. 4 cm

Curve No. a._~_" Transmissivity

1 5. O0 O. 810 / 2 3. 80 O. 774 i /

3 2.48 O. 709 I I

4 1.28 0.594 / , o.,o 0.466 /,I

/ ,~'~'~-Second Band Head !

I I f ] I

1 2 3 4 5

i /

I I

0 2219. 06

Figure 11.

I I I I 2233. 46 2247. 85 2262. 25

Wavelength, A

Example set of compulad transmission for NO (0,0) ~-band for an equivalent spectral slit width of 1.6 A and at conditions corresponding to Fig. 9.

2276.66

27

A E D C - T R - 7 6 - 1 2

Figure 12.

0. 9 - No. 1. 33 x 1015 cm-3

L - 91. 4 cm 0 . 8 -

m

i I I I I I 0 1 2 3 4 5 6

Broadening Parameter, a"

Calculated transmissivity (t) of the second band heed of the (0,0) NO 7-band as a function of the line broadening parameter (a').

>~ 0 . 7

.>_

E I /) • - 0.6

I - -

0.5

0.4

Table 1. Determination of Broadening Parameter (a') from Resolved Lines of the (0,0) Band of the NO 7-System

] L i n e N u m b e r ]

] NO, f b l o l e c u l e s / c m 3

i 1 2 a 3 4 5 6 7 8

1 2 3 4 5 6 7 8

1 2 3 4 5 5 7 8

A D s o r b i n g M e d i u m P a r a m e t e r s

2.58 x 10 !5

10.32 x 1015

I

1 1 x 1015

P r e s s u r e , a t m

] 500

1 . 5 0 0

0 , 1 0 2

T e m p e r a t u r e . K

422

I 422

296

,I

I

O. 64 0 . 7 3 O. 70 O, 07 0 . 6 6

I O. 85 O. 82 O. 76

0 19 O. 28 O. 25 0 . 2 1 0 . 2 ] 0 . 5 ] O. 45 O. 27

O. 55 0.56 0 . 5 4 0 . 5 2 0 5 1 0 . 8 4

0.78 0 .59

a

4 . 4 4 . 0 4 . 5 4 . 4

' 4 . 4 4 . 6 4 . 5 4 . 6

4 . ~ 4 . 1 4 . |

4. t 4 , ) 4 . 1 4. ,

0 , 0 0 7 0 . 7 0 . 5 0 , 5 0 . 5 0 . 6 0 . 7

28

AE DC-T R-76-12

Table 2. Determination of Broadening Parameter (a') from the Unresolved (0,0) Band of the NO 7-System

A b s o r b i n g Medium P a r a m e t e r s

NO, M o l e c u l e s / c m 3

1.33 x 1015

7.52 x 1013

1.36 x 1014

3 .314 x 1014

2 .75 x 1015

1.61 x 1015

3.91 x 1015

1.89 x 1015

P r e s s u r e . a t m

0.190 0.395 0.707 1.034

0.721 1.362

0.190 0 .395 0 .707

0 .190 0 .395 0.721 1.034

0.395 0.707 1.034 1.361

0.408 0.721 1.034

0 .395 0 .707 1 .020 1.350

0.190 0.395 0.707

T e m p e r a t u r e , K

422 422 422 422

744 744

l 411 411 411

422 422 422 422

422 422 422 422

744 744 744

296 296 296 296

296 296 296

T, Second Band P e a k

0.465 0 .591 0 .710 0 .777

0 .977 0.988

0.900 0 .942 0 .965

0. 792 0. 870 0.920 0. 936

0. 323 0.436 0.526 0. 586

0. 498 9. 658 0 . 7 5 2

O. 270 O. 330 O. 402 O. 468

0. 370 0. 450 0. 600

a*

0.50 1.28 2.48 3.80

1.00 2.65

0 .30 1 .18 2 .54

0 .34 1.26 2 .63 3 .70

1 .00 1 .84 2 .74 3 .55

O. 34 1.21 2 .22

1.95 2.75 3.77 5.18

1.03 1.65 3.35

29

AE DC-TR-76-12

The t a b u l a t e d v a l u e s of a" a r e p lo t t ed as a func t ion of the r a t i o p / T in Fig . 13, and a s t r a i g h t l i ne g iven by a l e a s t m e a n s q u a r e fit is d r a w n th r ough the poin ts . The v a l u e of C in Eq. {27) {shown as Cj) is equal to the s lope of the l i ne in F ig . 12. F o r the (0, 0) ~ -band

of NO, C is found to be 1 ,270 ± 200 K / a t m . F r o m Eq. (28), the v a l u e of the op t i c a l c r o s s s e c t i o n (a 2) is found to be (9 .5 + 1.5) x 10 -16

@

c m 2. The op t i ca l d i a m e t e r is 3 .5 ± 0 .3 A a p p r o x i m a t e d by T h o r s e n and B a d g e r in Ref. 2 f r o m the e x p e r i m e n t a l w o r k c a r r i e d out by W e b e r and P e n n e r (Ref. 11).

4.0 DISCUSSION

The m a j o r u se fo r the w o r k r e p o r t e d h e r e i n is to d e t e r m i n e c a l i b r a t i o n c u r v e s f o r the t r a n s d u c t i o n of t r a n s m i s s i o n m e a s u r e m e n t s of NO ~ -band r a d i a t i o n t h r o u g h m e d i a c o n t a i n i n g NO to the n u m b e r d e n s i t y of NO in the m e d i a . Such c a l c u l a t i o n s a r e u s e d to ex tend l ab- o r a t o r y c a l i b r a t i o n s at l i m i t e d p r e s s u r e s and t e m p e r a t u r e s to a w i d e r r a n g e of va lue s ; thus a c c u r a t e v a l u e s of the b r o a d e n i n g p a r a m e t e r b e c o m e s a n e c e s s i t y . An a p p l i c a t i o n of the u s e of the c a l c u l a t i o n s to a m e a s u r e m e n t s i t ua t ion is d e s c r i b e d in Ref. 12, w h e r e c a l i b r a t i o n c u r v e s a r e g e n e r a t e d fo r a b s o r p t i o n t h rough the exhaus t of a t u r b i n e eng ine b u r n e r at t e m p e r a t u r e s wel l above those p o s s i b l e in a l a b o r a - t o r y a b s o r p t i o n ce l l .

The u n c e r t a i n t y in v a l u e s of a" p r o j e c t s the u n c e r t a i n t y in the f ina l v a l u e s of c o n c e n t r a t i o n d e t e r m i n e d f r o m the 7 - b a n d a b s o r p t i o n m e a s u r e m e n t s . The e s t i m a t e d u n c e r t a i n t y in the v a l u e s of a" g iven in Fig. 13 is about +16 p e r c e n t . When th i s v a l u e of u n c e r t a i n t y is u s e d to d e t e r m i n e the d e n s i t y of a b s o r b e r s , the p r o j e c t e d u n c e r t a i n t y in the dens i t y is about +10 p e r c e n t and c o n s t i t u t e s the p r i n c i p a l u n c e r - t a in ty in the r e s o n a n c e a b s o r p t i o n t e c h n i q u e fo r c o n c e n t r a t i o n m e a s - u r e m e n t s t h r o u g h u n i f o r m m e d i a . A m o r e a c c u r a t e v a l u e of a" would c o r r e s p o n d i n g l y r e d u c e the p o s s i b l e u n c e r t a i n t y in m e a s u r i n g the c o n c e n t r a t i o n of NO. H o w e v e r , e x p e r i m e n t a l e r r o r s in m e a s u r e m e n t s of th i s n a t u r e would p r o b a b l y l i m i t the u n c e r t a i n t y to no b e t t e r than ±5 p e r c e n t so that p u r s u i t of a b e t t e r v a l u e fo r the c o n s t a n t C is p r o b a b l y not w a r r a n t e d for p u r p o s e s of m e a s u r e m e n t .

T h e e x p e r i m e n t a l w o r k f r o m which the d e t e r m i n a t i o n of a" was m a d e u t i l i z e d m i x t u r e s of NO in N 2. Thus , the f o r e i g n b r o a d e n i n g gas is N2. The q u e s t i o n a r i s e s as to w h e t h e r o t h e r g a s e s wh ich migh t

30

A E D C-TR-76o12

7

6

5

t ~

q )

4 I= s ._

a .

e -

"E 3 q,t

8 L -

e ~

2

0 0

sym r-i

0

I I I I

High Resolution Data (Average) Low Resolution Data Second Band Peak

O

8 / o ° O

CO

a" - cJ~ , C - 1270 + 200 K/atm

1 2 3 4 ' 5 p/T x 103, atm/K

Figure 13. Values of the spectral broadening parameter (a') as a function of p/T for the (0,0) T-band of NO as obtained by comparing experimental data with computed data.

6

31

AEDC-TR -76-12

be found in c o m b u s t i o n gas s t r e a m s , such as CO 2, H20 , CO, e t c . , m i g h t have s i g n i f i c a n t l y d i f f e r e n t b r o a d e n i n g c r o s s s e c t i o n s . B a s e d on the r e s u l t s p r e s e n t e d in Ref. 5 fo r CO, the b r o a d e n i n g c r o s s s e c t i o n fo r NO is not b e l i e v e d to be s i g n i f i c a n t l y d i f f e r e n t fo r o t h e r m o l e c u l e s than f o r N 2. E x p e r i e n c e with m e a s u r e m e n t s in a b s o r p t i o n c e l l s l o c a t e d in s a m p l e l i n e s in wh ich m e a s u r e m e n t s of NO c o n c e n - t r a t i o n m a d e by o t h e r m e a n s a g r e e d we l l wi th the v a l u e s o b t a i n e d by the a b s o r p t i o n t e c h n i q u e (Ref. 12) a l so g ives c o n f i d e n c e to the un i - v e r s a l i t y of the b r o a d e n i n g p a r a m e t e r wi th d i f f e r e n t m o l e c u l e s .

The i n d i r e c t m e t h o d of d e t e r m i n i n g the b r o a d e n i n g p a r a m e t e r u s e d in th i s s tudy is b e l i e v e d to be a va l id a l t e r n a t i v e to the u s e of h igh r e s o l u t i o n s p e c t r o s c o p y to m e a s u r e l i ne s h a p e s and thus d e t e r - m i n e the p a r a m e t e r d i r e c t l y . H o w e v e r , the m e t h o d r e q u i r e s the u s e of a good m o d e l f o r the r a d i a t i o n s o u r c e and fo r the a b s o r b i n g m e d i a , and a high s p e e d d ig i t a l c o m p u t e r to a c c o m p l i s h the c o m p l e x n u m e r i - ca l c a l c u l a t i o n s .

F i n a l l y , a s i g n i f i c a n t r e s u l t of the w o r k r e p o r t e d h e r e i n is the i m p r o v e d va lue of the e f f ec t i ve c r o s s s e c t i o n (o r d i a m e t e r } f o r co l - l i s i o n a l b r o a d e n i n g of the g round s t a t e e n e r g y l e v e l s of NO. T h e v a l u e of the e f f e c t i v e b r o a d e n i n g c o l l i s i o n d i a m e t e r (3 .5 + 0 .3 /~) d e t e r m i n e d in th i s w o r k o f f e r s c o n s i d e r a b l e i m p r o v e m e n t in u n c e r - t a in ty o v e r the b e s t known p r e v i o u s e s t i m a t e of T h o r s e n and B a d g e r (Ref. 2) of 3 .8 + 1 ~ .

REFERENCES

.

.

.

Davis , M. G . , M c G r e g o r , W. K . , and Few, J . D. " S p e c t r a l S i m u l a t i o n of R e s o n a n c e Band T r a n s m i s s i o n P r o f i l e s f o r S p e c i e s C o n c e n t r a t i o n M e a s u r e m e n t s : NO -y-Bands a s an E x a m p l e . " A E D C - T R - 7 4 - 1 2 4 (ADA004105), J a n u a r y 1975.

T h o r s o n , W. R. and B a d g e r , R. M. "On the P r e s s u r e B r o a d - ening in the G a m m a B a n d s of N i t r i c Oxide. " The J o u r n a l of C h e m i c a l P h y s i c s , Vol . 27, No. 3, 1957, p. 609.

M c G r e g o r , W. K . , Few, J . D . , and Li t ton , C. D. " R e s o n a n c e L i n e A b s o r p t i o n Method fo r D e t e r m i n a t i o n of N i t r i c Oxide C o n c e n t r a t i o n . " A E D C - T R - 7 3 - 1 8 2 (AD771642), D e c e m b e r 1973.

32

AEDC-TR-76-12

.

.

.

.

.

.

10.

11.

12.

M c G r e g o r , W. K. , Se iber , B. L . , and Few, J . D. " C o n c e n t r a - t ion of OH and NO in Y J 9 3 - G E - 3 Engine Exhaus t s M e a s u r e d in Situ by N a r r o w - L i n e UV Abso rp t i on . " P r o c e e d i n g s of the Second C o n f e r e n c e on the C l i m a t i c Impac t A s s e s s m e n t P r o g r a m , C a m b r i d g e , M a s s a c h u s e t t s , N o v e m b e r 1972, p. 124.

Mitchel , A. C. G. and Z e m a n s k y , M. W. R e s o n a n c e Rad ia t ion and Exc i t ed A toms , C a m b r i d g e U n i v e r s i t y P r e s s , C a m b r i d g e , M a s s a c h u s e t t s , 1971.

P e n n e r , S. S. Quan t i t a t ive M o l e c u l a r S p e c t r o s c o p y and Gas E m i s s i v i t i e s . A d d i s o n - W e s l e y P u b l i s h i n g Co. , Reading, M a s s a c h u s e t t s , 1959.

J e f f r i e s , J . T. Spec t r a l L ine F o r m a t i o n . B l a i s d e l l P u b l i s h i n g Company. 1968.

Ta tum, J. B. "The I n t e r p r e t a t i o n of I n t e n s i t i e s in D i a t o m i c M o l e c u l a r Spec t ra . " The A s t r o p h y s i c a l J o u r n a l . S u p p l e m e n t No. 124, Vol. 16, 1967, p. 21.

E a r l s , L. T. "Ro ta t iona l S t r eng th F a c t o r s fo r 2£--27r T r a n s i t i o n s . " Phys i ca l . Review, Vol. 48, 1935, p. 423.

Dee zs i , I. "A Recen t Ro ta t iona l A n a l y s i s of the ~ - B a n d s of the NO M o l e c u l e . " Acta Phys i ca , Vol. 9, 1957, p. 125.

Weber , D. and P e n n e r , S. S. " In t ens i t y M e a s u r e m e n t s in the v - B a n d s of NO." J o u r n a l C h e m i c a l P h y s i c s , Vol. 26, 1957, p. 860.

Few, J. D. , B ryson , R. J . , McGrego r , W. K. , and Davis , M. G. "Eva lua t i on of P r o b e Sampl ing v e r s u s in Situ Opt ica l T e c h n i q u e s fo r N i t r i c Oxide C o n c e n t r a t i o n M e a s u r e m e n t it, C o m b u s t i o n Gas S t r e a m s . " P a p e r p r e s e n t e d at T h i r d Jo in t C o n f e r e n c e on Sens ing of E n v i r o n m e n t a l Po l lu t an t s , Las Vegas , N o v e m b e r 1975.

33

AE DC-TR-76-12

APPENDIX A COMPUTER PROGRAM FOR THE CALCULATION AND SIMULATION OF THE

NO (0,0) 7-BAND SPECTRA TRANSMITTED THROUGH AN ABSORBING MEDIUM

The c o m p u t e r p r o g r a m i n c l u d e d in t h i s a p p e n d i x was d e v e l o p e d to c a l c u l a t e the t r a n s m i s s i o n of a b a n d of s p e c t r a l l i n e s f r o m a p a r t i c - u l a r m o l e c u l e t h r o u g h an a b s o r b i n g m e d i u m c o n t a i n i n g the s a m e m o l e c - u l a r s p e c i e s . T h e a p p r o a c h m a y be u s e d f o r any m o l e c u l e , but t h e l i n e s t r u c t u r e and a n g u l a r m o m e n t u m c o u p l i n g a r e so d i f f e r e n t f o r e a c h s p e c i e s t h a t a s e p a r a t e p r o g r a m is u s u a l l y n e e d e d f o r e a c h m o l e c u l a r s p e c i e s . In t h i s a p p e n d i x , t he c o m p u t a t i o n a l p r o c e d u r e is d e s c r i b e d f o r the NO m o l e c u l e .

DESCRIPTION

T h e p r o g r a m is s e p a r a t e d into two s t e p s . Step 1 r e c o r d s a l l input da ta and c o m p u t e s t he t r a n s m i s s i o n of the r a d i a t i o n due to e a c h s o u r c e l ine . Step 2 p r o c e s s e s t h e s e da ta and g e n e r a t e s t he s i m u l a t e d s p e c t r o m e t e r o u t p u t s i g n a l . The p r o g r a m is c u r r e n t l y b e i n g r u n on t he IBM 370-165 c o m p u t e r ; X - Y p l o t t e r da t a a r e p r e s e n t e d on t he CALClVIP 765 p l o t t e r .

PROGRAM STEP 1

T h e f i r s t p r o g r a m s t e p is d i v i d e d into f o u r p a r t s :

Part 1 - Input Data

P a r t 1 c o n t a i n s the v a r i o u s COMMON and DIMENSION s t a t e m e n t s f o r t he p r o g r a m . If m o r e than 500 e m i s s i o n l i n e s a r e to be c o n s i d e r e d , a m o d i f i c a t i o n of the p r o g r a m wou ld be n e c e s s a r y . V a l u e s of AA, a ' , T a, T s, and f and v a r i o u s p lo t c o n t r o l p a r a m e t e r s a r e input . D e t a i l s of the input da t a and f o r m a t a r e d i s c u s s e d in the f o l l o w i n g p a r a g r a p h .

Part 2 - Spectral Line Calculation

Cards identifying each emission-line to be considered are read. For each line, the rotational energy of the upper electron state F(J')

is computed via SUBROUTINE FUPPER, and the rotational energy of

35

AE DC-TR-76-12

t h e l o w e r r o t a t i o n s t a t e F ( J " ) is c o m p u t e d in S U B R O U T I N E F L O W E R . T h e H S n l - L o n d o n f a c t o r is t h e n c o m p u t e d in S U B R O U T I N E H O N N U M . T h e v a l u e of I o vj is f ound by i n t e r p o l a t i o n f r o m F i g . 7. T h e c u r v e in

F i g . 7 is an input to t h e p r o g r a m .

0 F o r the (0, 0) T - B a n d of NO, t h e v a l u e s of kv i a r e g i v e n by Eq. (20) a n d a r e c o m p u t e d in P a r t 2.

Part 3 - Line-By-Line Transmission Calculation

In P a r t 3, t he t r a n s m i s s i o n (Eq . (13)) is e v a l u a t e d f o r e a c h l i n e . S i n c e k v is a f u n c t i o n of v, m a n y t i m e - c o n s u m i n g e v a l u a t i o n s of k v a r e a p p a r e n t . In f ac t , if t h e r e a r e n n o d e s u s e d in t h e n u m e r i c a l i n t e g r a t i o n , t h e n n m 2 e v a l u a t i o n s a r e r e q u i r e d w h e r e m is t h e n u m b e r of l i n e s b e i n g c o n s i d e r e d . If the p r o g r a m v a r i a b l e A L L O W is s e t to z e r o , t h e p r o g r a m w i l l s u m o v e r a l l t h e l i n e s , i . e . ,

m

. = k ( A - l ) i~' kv, i=l vi

To save time (although at the expeuse of some accuracy), another

o p t i o n is a v a i l a b l e . T h i s op t i on is s e l e c t e d by s e t t i n g A L L O W >0 . B y c o n s i d e r i n g the j t h s p e c t r a l l i n e , t h e s u m E k v is w r i t t e n as :

1 i J+Ju J-JE

~i kvi = ~ kvi + ~ k i=j i=j-1 vi (A-2 )

Note that the index in the second sum decreases. The indices Ju and Je are chosen so that the contributions of the (j +ju)th and (j - je) th

lines are as small as desired. The exact criterion used is

and

k vj+j u

J-Ju i= ~j kvi

< ALLOW (A-3)

k j Vj_j u

j-jr • ~- kvi i=j-1

< ALLOW

@

In effect, only those lines in a chosen neighborhood of uj are c o n s i d e r e d .

(A-4)

3 6

AEOC-TR-76-12

If a" = 0, no c o l l i s i o n b r o a d e n i n g is c o n s i d e r e d and kui is c a l c u -

l a t e d f r o m Eq. (10). If a" > 0, then kvi m u s t be g iven by Eq. (A-4) .

S u b r o u t i n e WFUNC e v a l u a t e s the func t ion

R{exp [ - (e j + ia') 2] erfc [-ioJj + a']

wh ich is c o n t a i n e d in Eq. (9) and l e a d s to the d e t e r m i n a t i o n of kuj.

T h e s u b s e q u e n t e v a l u a t i o n of the i n t e g r a l in Eq. (13) is done n u m e r i - c-ally u s i n g the t r a p e z o i d a l r u l e .

Part 4 - Data Storage

Thi s p a r t w r i t e s p r o g r a m c o n t r o l da ta as we l l as w a v e n u m b e r and s o u r c e l i ne t r a n s m i s s i o n data onto a d i sc f i l e fo r p a s s a g e to Step 2.

P R O G R A M STEP 2

Step 2 p e r f o r m s the p lo t t ing func t ions of the p r o g r a m . T h e m a t h e m a t i c a l and p h y s i c a l c o n s i d e r a t i o n s a r e p r e s e n t e d in d e t a i l in Ref. 1.

The p r o g r a m f i r s t r e a d s in the v a r i o u s c o n t r o l p a r a m e t e r s f r o m Step 1. Then , the f i r s t se t of v a l u e s of vj and ~ a r e r e a d in T h e s e da ta c o r r e s p o n d to the f i r s t v a l u e of No s u p p l i e d to Step 1. All fo l low- ing c u r v e s wil l be p lo t t ed a c c o r d i n g to the s c a l e f a c t o r d e t e r m i n e d f r o m the in i t i a l c a s e . G e n e r a l l y , the c a s e N o = 0 (no a b s o r p t i o n ) is c a l c u l a t e d f i r s t , and al l o t h e r p lo t s a r e r e f e r e n c e d to th is c a s e (Fig . 1).

If I P L O T I = i , then z e r o s l i t width p lo t s a r e p r o d u c e d (Fig. 2).

If I P L O T 2 = i , a s e p a r a t e plot is p r o d u c e d fo r e a c h v a l u e of No as wel l as the f ina l c o m b i n e d plot .

The c o n g l o m e r a t e s p e c t r a l p r o f i l e is c o n s t r u c t e d as fo l lows : A l i ne wi th a he igh t p r o p o r t i o n a l to the s p e c t r a l i n t e n s i t y is d r a w n at A i + i / 2 A k x fo r e a c h s p e c t r a l l ine and a t r i a n g u l a r s l i t f unc t ion of b a s e width 2Ak~ is c o n s t r u c t e d about tha t l ine . To a r r i v e at the c o n g l o m e r a t e p r o f i l e , the c o n t r i b u t i o n s f r o m e a c h l i ne at a g iven v a l u e of ~ a r e s i m p l y added .

37

AEDC-TR-76-12

PROGRAM VARIABLE DESCRIPTION

The following var iab les a re used in the program:

Mathemat ical P r o g r a m Symbol Variable

T'j TJ(J)

o

vj WO(J)

(A sVj)D DWJ

(A aVj)D DWL

Iu~ E(J)

? EO(J)

kui CAY(1)

EL

a" AP

T s TE

T a TA

~A SLIT

N O ENO

V" IVU

##

V IVL

J " RJPP

Usage

Transmission of spectral line, j

Center wavenumber of jth spectral line

Doppler width at half maximum intensity of jth spectral line

Doppler width at half maximum absorption coefficient kv~ of the absorption line J

Intensity of source spectral line

Intensity of source spectral line at center wavenumber

Absorption coefficient for the ith line

Absorption path length

Collis ional broadening parameter

Source gas temperature, K

Absorber gas temperature, K

Equivalent slit width

Total number density

Upper vibrational state

Lower vibrational state

Lower rotational state

38

Mathemat ical Symbol

Sj "j,

F(J')

F ( J " )

m

P r o g r a m Var i ab le

w(I)

NUP

NLO

BRANCH

IPLOTI

IPLOT 2

YHGT

D E L P L T

s(J)

FU

FL(J)

ALLOW

NLINES

AE DC-TR-76-12

cs_q_e

Nodes for n u m e r i c a l in tegra t ion (Eq. (I))

Upper spin state

Lower spin state

Line branch designation

For zero slit width plots, set IPLOTI = 1 otherwise = 0

For separate N O plots, set IPLOT2 = I, otherwise = 0

Maximum height of spectral plots, in.

Scale for abscissa of spectral plots, A°/in.

H~nl-London factor for jth line

Rotational energy of the upper electron state

Rotational energy of the lower rotational state

Relative error (see Eq. (i0))

Number of emission lines

39

AEOC-TR-76-12

DATA INPUT

All data is input to Step I.

CARDS i

Column 1 F(J')

F O R M A T ( 2 F 1 0 . 0 )

C o l u m n 11 (Iu~/Sj,,j')

T h e f i r s t c a r d s e x p e c t e d by t h e p r o g r a m a r e v a l u e s of (Iu~/Zj,,j') v e r s u s F u j , o n e d a t a p a i r p e r c a r d . T h e c a r d s s h o u l d b e a r r a n g e d

in o r d e r o f i n c r e a s i n g F u j . A b l a n k c a r d m u s t f o l l o w t h e f i n a l d a t a

c a r d of t h i s g r o u p . T h e d a t a f o r t h e s o u r c e l a m p u s e d in t h e m e a s - u r e m e n t s s h o w n in t h i s r e p o r t a r e g i v e n in T a b l e A - 1 .

CARD 2 T I T L E CARD FORMAT (20A4)

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

CARD 3 DELPLT FORMAT (FI0.0)

CARD 4 SLIT FORMAT (FI0.0)

CARD 5 AP FORMAT (FI0.0)

CARD 6 TA FORMAT (FI0.0)

CARD 7 TE FORMAT (FI0.0)

CARD 8 EL FORMAT (FI0.0)

CARD 9 YHGT FORMAT (FI0.0)

CARD I0 IPLOTI FORMAT((II)

CARD ii IPLOT2 FORMAT (Ii)

~KCARDS 12 FORMAT (3X, AI, 2Ii, IX, F4.0, IX, FII. 0)

T h e s e c a r d s a r e t h o s e w h i c h d e s c r i b e t h e s p e c t r a l l i n e s to b e c o n s i d e r e d .

40

AEDC-TR-78-12

C O L U M N 4 B R A N C H (P , Q, o r R) F O R M A T A1

, C O L U M N 5 N U P F O R M A T I1

C O L U M N 6 N U P P F O R M A T I1

C O L U M N 8- 11 R J P P F 4 . 0

C O L U M N 1 3 - 2 3 WO F l l . 0

T h e s e c a r d s m u s t be a r r a n g e d in o r d e r of i n c r e a s i n g w a v e - n u m b e r WO. A b l a n k c a r d m u s t f o l l o w t h e l a s t l i n e d e s c r i p t i o n c a r d . T h e d a t a f o r t h e NO (0, 0) T - B a n d a r e g i v e n in T a b l e A - 2 .

C A R D S 13 FORMAT (FI0.0)

These cards contain the values of ENO to be considered. All plots

will be scaled to the plot representing the first value of ENO in this

g r o u p .

SAMPLE CASE

T h e c a s e to b e c o n s i d e r e d h e r e is t h e (0, 0) NO T - b a n d w i t h c o l l i s i o n a l b r o a d e n i n g c o n s i d e r e d . T h e f o l l o w i n g v a l u e s w i l l b e u s e d :

a ' = 1.5 T a = 420K

T = 320 K

1~ = 91 cm o

AA = 1.6 A N O = 0., 1 x I015, 1 x 1016 cm "3

YHGT = I0 in. O

DELPLT = 6 A/in.

The equations and constants used for computing the upper and

lower energy states and the I-r6nl-London factors are discussed in

Ref. 3 and are repeated here for completeness.

41

AEDC-TR-76-12

F o r t h e u p p e r s t a t e ( S U B R O U T I N E F U P P E R ) ,

F" = T~ + G" * F~ [] = 1,2

w h e r e

T~ = 43965.7 cm "I

w h e r e

where

G" = ¢ o ~ ( v ' + 1 / 2 ) - ¢OeXe(V .- 1/2) 2

¢o e 2374.8 cm -!

x ' = 15.45 cm "1 ('De O

F~ = B~(J '+ 1 / 2 ) ( J ' - 1 / 2 ) + Dv(J '+ 1 / 2 ) 2 ( j ' - 1 / 2 ) 2

F~ = B , ~ ( J ' + l / 2 } ( . [ ' + 3 / 2 ) ~ - By( j ' ~ 1/2)2(J " - 3 / 2 ) 2

B v = B _ " - ae(V + 1 / 2 )

• 1.9977 cm -I B e =

a" = 0.0198 cm -I

D v = -6.2 x 10 "6 cm "I

For the lower state (SUBROUTINE FLOWER),

F"= T~ + G" + F~ n = 1,2

T~= G••= 0

w h e r e

and

F I = B~[(J + I./2) 2 - I - u] + DvJ •'4

F~ = B~[(J"+I/2) 2 - 1 + u] + D~'(J"+I) 4

u = J"+ I./2) 2 - Y -

Yv = A/By

A = 124.2 cm "l

= - a (v "+ I/2)

-I Be = 1.7046 cm

a c = 0.0178 cm "I

D v = -4.8 x 10 -6 cm "l

42

AEDC-TR-76-12

The HBnl-London factors are given in Table A-3.

The emission lines being considered can be read from the data card listing which follows. The plots produced by this case are shown in Fig. A-I. Many other calculations as well as comparisons between actual and computed spectra are presented in Ref. I.-

43

AEOC-TR -76-12

NO

0 . 0 + 1 . 0 0 + 15 1 . 0 0 + 16

T e - 320 K

T a - 4 2 0 K

- 9 1 . 0 c m

a" = 1.50000

Maximum Height, in.

i0.00 6.97 1.84

1 .000 0 . 8 0 1 0 .289

/A

2219 .06 2 2 3 1 , 0 6 2 2 4 3 . 0 6 2 2 5 5 . 0 6

0 W a v e l e n g t h , A

Figure A-1. Spectral test case.

2 2 6 7 . 0 6 2 2 7 9 , 0 6

44

AEDC-TR-76-12

Table A-1. Data Cards for Sample Case

V Column 1

4 5 1 0 0 . 1 . 2 5 4 5 2 0 0 . . 9 2 4 5 3 0 0 . . 6 8 4 5 4 0 0 . . 5 4 4 5 5 0 0 . . 4 5 4 5 ~ 0 0 . . 3 ~ 4 5 7 0 0 . . 3 3 4 5 8 0 0 . . 2 8 4 5 9 0 0 . . 2 5 5 4 5 0 0 0 • • 2 3 4 6 1 0 0 . . 2 0 8 4 6 2 0 0 . .19

4 6 3 0 0 • . 1 7 5 4 5 4 0 0 . .158

4 6 5 0 0 . . 1 4 5 4 6 6 0 0 . . 1 3 2 5 4 6 7 0 0 • . 1 2 46800. . I I 4 6 9 0 0 • •1 4 7 0 0 0 . . 0 9 2 4 7 1 0 0 . • 0 8 4 4 7 2 0 0 • . 0 7 7 4 7 3 0 0 . . 0 7 4 7 4 0 0 . . 0 6 4 4 7 5 0 0 . . 0 5 8 4 7 6 0 0 . * 0 5 3 4 7 7 0 0 . . 0 4 9 4 7 8 0 0 . . 0 4 4 4 7 q 0 0 . . 0 4 1 4 8 0 0 0 . . 0 3 7 4 8 1 0 0 . . 0 3 4 4 8 2 0 0 . * 0 3 1 4 8 3 0 0 . . 0 2 8 5 4 8 4 0 0 . . 0 2 6 4 8 5 0 0 . . 0 2 ~ 8

4 8 6 0 0 . 4 8 7 0 0 . 4 8 8 0 0 . 4 8 9 0 0 . 4 < ) 0 0 0 . 4 9 1 0 0 . 4 9 2 0 0 . 4 9 3 0 0 . 4 9 4 0 0 , 4 9 5 0 0 . 4 9 6 0 0 . 4 0 7 0 0 • 4 9 8 0 0 . 4 9 9 0 0 . 5 0 0 0 0 . 5 0 1 0 0 . 5 0 2 0 0 • 5 0 3 0 0 . 5 0 4 0 0 . 5 0 5 0 0 . 5 0 6 0 0 . 5 0 7 0 0 . 50800.

• 0 2 1 8 • 0 1 9 8 o 0 1 8 . 0 1 6 5 • 0 1 5 • 0 1 3 8 • 0 1 2 6 • 0 1 1 5 • 0 1 0 5 • 0 0 9 7 • 0 0 8 8 • 0 0 8 1 . 0 0 7 4 • 0 0 6 8 • 0 0 5 2 . 0 0 5 5 . 0 0 5 2 . 0 0 4 7 . 0 0 4 3 • 0 0 3 9 . 0 0 3 6 • 0 0 3 3 * 0 0 3

45

AE DC-TR-76-12

Blank Card SPECTRA TEST 6 , 1 . 6 1 . 5 4 2 0 , 3 2 0 ,

Table A-2. Spectra Test Case

CASE

9 1. r - B r a n c h (Column 4) 1 o . [ - -NUP (Column 5) o [ r -NUPP (Column 6) 0 J ] | I--RJPP (Co'lulnzn 8-1"1)

P 2 ( 1 0 , 5 ) 4 4 0 5 2 . 0 3 P 2 ( 1 1 . 5 ) 4 4 0 5 2 p 0 3 P 2( 9 , 5 ) 4 4 0 5 2 , 0 3

• °Pl 2 ( 1 2 , 5 ) 4 4 0 5 2 , 7 8 P 2( 5 . 5 ) 4 4 0 5 2 , 7 8 P 2 ( 1 3 . 5 ) 4 4 0 5 4 , 2 2 P 2( 7 , 5 ) 4 4 0 5 4 . 2 2 P 2 ( 1 4 , 5 ) 4 4 0 5 6 , 1 6 P 1 2 ( 6 . 5 ) 4 4 0 5 6 . 4 9 P 1 2 ( 1 5 , 5 ) 4 4 0 5 8 . 3 3 P12 ( 5 . 5 ) 4 4 0 5 5 . 5 0 P 1 2 ( 1 6 . 5 ) 4 4 0 6 1 . 3 0 P 1 2 ( 4 . 5 ) 4 4 0 6 1 , 7 7 P 1 2 ( 1 7 - S . ) . . _ 4 4 0 6 4 , 6 6 P 1 2 ( 3 , 5 ) 4 4 0 6 5 , 4 0 P 1 2 ( 1 5 . 5 ) 4 4 0 6 8 . 6 9 P 1 2 ( 2 . 5 ) 4 4 0 6 9 . 6 0 1 : ) 1 2 ( 1 9 . 5 ) 4 4 0 7 3 , 2 1 P 1 2 ( 1 . 5 ) 4 4 0 7 4 . 2 6 ; )22( 3 , 5 ) 4 4 0 7 7 , 5 8 P 2 2 ( 4 * 5 ) 4 4 0 7 7 . 9 5 P22 ( 2 , 5 ) 4 4 0 7 7 . 9 5 Q I 2 ( 4 , 5 ) 4 4 0 7 7 , Q 5 Q12( 2 . 5 ) 4 4 0 7 7 . Q5 P 1 2 ( 2 0 . 5 ) " 4 4 0 7 8 . 5 9 P22 ( 5 , 5 ) 4 4 0 7 8 . 5 9 I )22 ( 1 , 5 ) 4 4 0 7 5 . 5 9 Q12( 5 . 5 ) 4 4 0 7 8 . 5 9 0 1 2 ( 1 . 5 ) 44078.s-9 P 2 2 ( 6 . 5 ) 4 4 0 8 0 , 3 2 0 1 2 ( 6 . 5 ) 4 4 0 8 0 , 3 2 P22 ( 7 , 5 ) 4 4 0 5 2 . 3 3 Q12( 7 . 5 ) 4 4 0 8 2 . 3 3 P 1 2 ( 2 1 . 5 ) 4 4 0 8 4 , 3 3 P 2 2 ( 5 . 5 ) 4 4 0 8 4 . 8 3 0 1 2 ( 8 , 5 ) 4 4 0 5 4 , 5 3 Q22( 1 . 5 ) 4 4 0 5 6 . 1 5

R I 2 ( 1 . 5 ) 4 4 0 8 6 . 1 5 1:)22( 9 , 5 ) 4 4 0 8 7 . 9 8 0 1 2 ( 9 . 5 ) 4 4 0 8 7 , 9 8 Q22( 2 . 5 ) 4 4 0 8 9 . 5 6 R I 2 ( 2 , 5 ) 4 4 0 8 9 , 5 6 P 1 2 ( 2 2 . 5 ) 4 4 0 9 0 , 2 8 P 2 2 ( 1 0 , 5 ) 4 4 0 9 1 . 5 6 Q I 2 ( 1 0 . 5 ) 4 4 0 9 1 . 5 6 Q22( 3 . 5 ) 4 4 0 9 3 . 3 9 R12( 3 , 5 ) 4 4 0 9 3 . 3 0 P 2 2 ( 1 1 . 5 ) 4 4 0 9 5 . 7 0 Q 1 2 ( 1 1 , 5 ) 4 4 0 9 5 . 7 0 R22( 1.5.) 4 4 0 9 6 , 8 2 P - i ~ . ( 2 3 . 5 ) 4400-7. i 8- 0 2 2 ( 4 , 5 ) 4 4 0 9 7 , 6 5 q 1 2 ( 4 , 5 ) 4 4 0 Q 7 , 6 5 P 2 2 ( 1 2 , 5 ) 4 4 1 0 0 , 4 5 Q 1 2 ( 1 2 . 5 ) 4 4 1 0 0 , 4 5 Q22( 5 . 5 ) 4 4 1 0 2 , 7 2 R I 2 ( 5 . 5 ) 4 4 1 0 2 , 7 2 P 1 2 ( 2 4 . 5 ) 4 4 1 0 4 , 5 9 P 2 2 ( 1 3 , 5 ) 4 4 1 0 5 . 7 2 Q 1 2 ( 1 3 , 5 ) 4 4 1 0 5 . 7 2 R22( 2 , 5 ) 4 4 1 0 5 , 7 2

22 (__6. ~ _ ) 4_4_ z_oe._ 1 7 R I 2 ( 6 - 5 ) 4 4 1 0 8 . 1 7 P 2 2 ( 1 4 , 5 ) 4 4 1 1 1 . 5 0 Q I 2 ( 1 4 , 5 ) 4 4 1 1 1 . 5 0 P 1 2 ( 2 5 , 5 ) 4 4 1 1 2 , 3 4 R22( 3 , 5 ) 4 4 1 1 3 . 5 2 9 2 2 ( 7 . 5 ) 44114.15 R12( 7 . 5 ) 4 4 1 1 4 , 1 5 P 2 2 ( | 5 . 5 ) 4 4 1 1 7 . 8 4 Q 1 2 ( 1 5 . 5 ) 4 4 1 1 7 , 5 4 P I 2 ( 2 6 e S ) 4 4 1 2 0 , 7 1 Q22( 5 , 5 ) 4 4 1 2 0 , 7 1 R12( 8 , 5 ) 4 4 1 2 0 , 7 1 R 2 2 ( 4 , 5 ) 4 4 1 2 1 . 5 2 P 2 2 ( 1 6 , 5 ) 4 4 1 2 4 , 7 ' 4 Q 1 2 ( 1 6 , 5 ) 4 4 1 2 4 . , 7 4 Q22( 9 , 5 ) 4 4 1 2 7 e 6 8 R12( Qe5) 441274.68 .p.! 2(27..5_) 4~.!.2_9.98 R22( 5 , 5 ) 4 4 1 3 0 . 4 2 P 2 2 ( I T e S ) 4 4 1 3 2 . 1 6 Q | 2 ( t 7 , 5 ) 4 4 1 3 2 . 1 6 Q 2 2 ( 1 0 , 5 ) 4 4 1 3 5 . 3 ! R I 2 ( l O e 5 ) 4 4 1 3 5 . 3 1

45

A E DC-TR-76-12

Table A-2. P 1 2 ( 2 8 0 5 ) 4 4 1 4 0 , 1 3 P 2 2 ' ( 1 8 0 5 1 4 4 1 4 0 , 1 3 0 1 2 ( 1 8 o 5 1 4 4 1 4 0 0 1 3 R22( 6 0 5 ) 4 4 1 4 0 0 1 3 0 2 2 ( 11o51 4 4 1 4 3 , 4 4 R ! 2 ( 1 1 0 5 ) 4 4 1 4 3 , 4 4 P 2 2 ( 1 9 o 5 ) 4 4 1 4 8 0 6 8 0 1 2 ( 1 9 o 5 1 4 4 1 4 8 0 6 8 P 1 2 ( 2 9 , 5 ) 4 4 1 4 9 0 8 3 R22( 7 0 5 ) 4 4 1 4 9 . 8 3 0 2 2 ( 12o51 4 4 1 5 2 0 1 7 R 1 2 ( 1 2 0 5 ) 4 4 1 5 2 , 1 7 P 2 2 ( 2 0 o 51 4 4 1 5 7 , 7 3 0 1 2 ( 2 0 , 5 1 4 4 1 5 7 , 7 3 P 1 2 ( 3 0 0 5 ) 4 4 1 6 0 0 4 6 R22( 805 ) 4 4 1 6 0 0 4 6 0 2 2 ( 1 3 0 5 ) 4 4 1 6 1 , 3 2 R12( 13051 4 4 1 6 1 0 3 2 P 2 2 ( 2 1 0 5 ) 4 4 1 6 7 0 3 1 0 1 2 ( 2 1 , 5 1 4 4 1 6 7 0 3 1 0 2 2 ( 1 4 o 5 ) 4 4 1 7 1 0 1 9 R12( 14o51 4 4 1 7 1 , 1 9 R22( 9051 4 4 1 7 1 0 1 9 P I I ( 9 0 5 ) 4 4 1 7 6 0 8 5 P l l ( 8 , 5 ) 4 4 1 7 6 , 8 5 P22 ( 22051 4 4 1 7 7 o 2 8 0 1 2 ( 2 2 o 5 1 4 4 1 7 7 0 2 8 P 1 1 ( 1 0 0 5 ) 4 4 1 7 7 , 2 8 P11 ( 7 , 5 ) 4 4 1 7 7 , 2 8 P l t ( 11051 4 4 1 7 8 , 5 3 _ P ! . 1 . ( 6 0 5 ) . 4 4 1 7 8 , 5 3

I 1 1 1 ( 1 2 o 5 ) 4 4 1 8 0 0 5 8 P ! 1 ( 5 0 5 ) 4 4 1 8 0 0 5 8 0 2 2 ( 1 5 , 5 ) 4 4 1 8 1 0 3 8 R12( 15o51 4 4 1 8 1 , 3 8 R 2 2 ( 1 0 , 5 1 4 4 1 8 3 0 0 2 P 1 1 ( 1 3 , 5 1 4 4 1 8 3 0 0 2 P l I ( 4 , 5 ) 4 4 1 8 3 0 0 2 P 1 2 ( 3 2 0 5 ) 4 4 1 8 4 0 0 8 P 1 1 ( 1 4 0 5 1 4 4 1 8 6 0 0 7 P l 1( 3e5) 441~6e O? P 2 2 ( 2 3 , 5 ) 4 4 1 8 8 0 1 6 0 1 2 ( 2 3 o 5 1 4 4 1 8 8 0 1 6 P 1 1 ( 1 5 0 5 ) 4 4 1 8 9 0 8 0 P 1 1 ( 2 , 5 ) 4 4 1 8 9 0 8 0 0 2 2 ( 16 ,51 4 4 1 9 2 , 1 8 R 1 2 ( 1 6 , 5 1 4 4 1 9 2 0 1 8 P 1 1 ( 1 6 0 5 ) 4 4 1 9 4 , 2 9

ConlJnued

p t 1 ( . 1 . _s.I...44. 1.9.4_...~.t_ / 2 2 ( 1 1 , 5 ) 4 4 1 ' 9 4 o 9 3 P 1 2 ( 3 3 , 5 ) 4 4 1 9 5 0 9 1 0 1 1 ( 2 0 5 ) 4 4 1 9 7 0 0 8 P 2 1 ( 2051 4 4 1 9 7 0 9 8 0 1 1 ( 3o5) 4 4 1 9 7 , 9 8 P21 ( 3051 4 4 1 9 7 o 9 8 0 1 1 ( 105) 4 4 1 9 7 0 9 8 P21 ( 1 , 51 4 4 1 9 7 0 9 8 P 2 2 ( 2 4 0 5 ) 4 4 1 9 9 0 2 1 0 1 2 ( 2 4 , 5 ) 4 4 1 9 9 0 2 1 P 1 1 ( 1 ? 0 5 1 4 4 1 9 9 , 2 1 0 1 1 ( 4 , 5 ) . 4 4 . 1 9 9 , 2 j ;:)21( 4 , 5 ) 4 4 1 9 0 . 2 1 0 1 1 ( 0 , 5 ) 4 4 1 9 9 , 2 1 1:)21( 0e5 ) 44199021 0 1 1 ( 5 , 5 ) 4 4 2 0 0 0 1 3 I121( 5 , 5 1 4 4 2 0 0 0 1 3 0 1 1 ( 6 , 5 1 4 4 2 0 2 0 3 6 P21 ( 6051 4 4 2 0 2 0 3 6 9 2 2 ( 1 7 , 5 ) 4 4 2 0 3 0 4 9 R I 2 ( 1 7 , 5 ) 4 4 2 0 3 0 4 9 R I I ( 0 , 5 ) 4 4 2 0 3 , 4 9 Q 2 l ( 0 , 5 ) 4 4 2 0 3 , 4 9 P ! i ( 1 8 0 5 1 4 4 2 0 4 0 9 6 Q 1 1 ( 705) 4 4 2 0 4 0 9 6 P21 ( 7 0 5 ) 4 4 2 0 4 , 9 6 R I I ( 105) 4 4 2 0 6 , 0 3 0 2 1 ( 1 , 51 4 4 2 0 6 0 0 3 R 2 2 ( 1 2 , 5 1 4 4 2 0 7 0 8 1 0 1 1 ( 8 , 5 1 4 4 2 0 8 , 3 8 P21 ( 8051 4 4 2 0 8 0 3 8 R I I ( 2 , 5 1 4 4 2 0 9 , 6 9 9 2 1 ( 2 , 5 ) 4420~)069 R21( 005 ) 4 4 2 1 0 0 6 9 P 2 2 ( 2 5 0 5 ) 4 4 2 1 1 0 2 1 0 1 2 ( 2 5 o 5 1 4 4 2 1 1 0 2 1 P 1 1 ( 1 9 , 5 1 4 4 2 1 1 0 2 1 0 1 1 ( 9 0 5 ) 4 4 2 1 2 , 2 5 p 2 1 ( 9 0 5 ) 4 4 2 1 2 0 2 5 R11( 3 0 5 ) 4 4 2 1 3 0 8 1 0 2 1 ( 3 , 5 ) 4 4 2 1 3 , 8 1 0 2 2 ( 1 8 o 5 ) 4 4 2 1 5 0 4 6 R 1 2 ( 1 8 , 5 1 4 4 2 1 5 0 4 6 0 1 1 ( 1 0 o 5 1 4 4 2 1 7 0 0 0 P 2 1 ( 1 0 0 5 ) 4 4 2 1 7 , 0 0 R21( 1051 4 4 2 1 7 , 6 0 P 1 1 ( 2 0 0 5 ) 4 4 2 1 7 , 7 3

47

AEDC-TR-76"12

R I I ( 4 . 5 ) Q21 ( 4 0 5 ) R 2 2 ( 1 3 o 5 ) 0 1 1 ( ! 1 o 5 ) ; ) 2 1 ( 1 1 , 5 ) P 2 2 ( 2 6 0 5 ) 0 1 2 ( 2 6 o 5 ) R I I ( 5 , 5 ) 0 2 1 ( 5 , 5 ) R 2 1 ( 2 , 5 ) P ! ! ( 2 1 0 5 ) 0 2 2 ( 1 9 o 5 ) R I 2 ( 1 9 o 5 ) Q i I ( 1 2 , 5 ) P 2 1 ( 1 2 o 5 ) q l l ( 6 . 5 ) 0 2 1 ( 6 0 5 ) P 1 1 ( 2 2 , 5 ) R 2 1 ( 3 0 5 ) R 2 2 ( 140 5) Q l 1 ( 1 3 o 5 ) P21 ( 1 3 . 5 ) P 2 2 ( 2 7 . 5 ) 0 1 2 ( 2 . 7 , 5 ) R I I ( " 7 , 5 ) 021 ( "7, 5) 0 2 2 ( 2 0 . 5 ) R I 2 ( 2 0 , 5 ) P l ! ( 2 3 0 5 ) 0 1 1 ( 1 4 , 5 ) P 2 1 ( 1 4 o 5 ) R21 ( 4 0 5 ) R 1 1 ( 8 , 5 ) 0 2 1 ( 8 0 5 ) R 2 2 ( 1 5 , 5 ) Q I I ( 1 5 o 5 ) P 2 1 ( 1 5 , 5 ) P 2 2 ( 2 8 , 5 ) 0 1 2 ( 2 8 o 5 ) P 1 1 ( 2 4 e 5 ) R I I ( 9 , 5 ) 0 2 1 ( 9 0 5 ) R 2 1 ( 5 0 5 ) 0 2 2 ( 2 1 . 5 ) R 1 2 ( 2 1 , 5 ) Q I 1 ( 1 6 * 5 ) I) 2 1 ( 1 6 o 5 ) P 1 1 ( 2 5 , 5 )

Table A-2. 4 4 2 1 8 , 5 5

4 4 2 2 0 0 7 8 4 4 2 2 2 , 2 4 4 4 2 2 2 , 2 4 4 4 2 2 3 0 9 5 4 4 2 2 3 , 9 5 4 4 2 2 3 0 9 5 4 4 2 2 3 , 9 5 4 4 2 2 5 0 1 4 4 4 2 2 5 . 2 6 4 4 2 2 8 . 0 0 4 4 2 2 8 , 0 0 4 4 2 2 8 0 O0 4 4 2 2 8 0 O0 4 4 2 3 0 . 2 3 4 4 2 3 0 0 2 3 4 4 2 3 3 , 2 4 4 4 2 3 3 , 3 1 4 4 2 3 4 , 4 7 4 4 2 3 4 0 4 " 7 4 4 2 3 4 0 4 ? 4 4 2 3 6 0 8 6 4 4 2 3 6 , 8 6 4 4 2 3 6 . 8 6 4 4 2 3 6 , 8 6 4 4 2 4 1 , 1 3 4 4 2 4 1 0 1 3 4 4 2 4 1 0 6 8 4 4 2 4 1 , 6 8 4 4 2 4 1 0 6 8 4 4 2 4 2 , 1 1 4 4 2 4 4 0 3 0 4 4 2 4 4 , 3 0 4 4 2 4 9 0 1 0 4 4 2 4 9 , 1 0 4 4 2 4 9 . 1 0 4 4 2 5 0 , 1 7 4 4 2 5 0 0 1 7 4 4 2 5 1 . 3 1 4 4 2 5 2 , 0 5 4 4 2 5 2 , 0 5 4 4 2 5 2 , 0 5 4 4 2 5 4 , 5 2 4 4 2 5 4 , 5 2 4 4 2 5 7 . 5 4 4 4 2 5 7 . 5 4 4 4 2 6 0 0 9 3

Continued R I I ( 1 0 , 5 ) 4 4 2 6 0 , 9 3 0 2 1 ( 1 0 . 5 ) 4 4 2 6 0 . 9 3 R 2 1 ( 6 , 5 ) 4 4 2 6 1 ,"79 P 2 2 ( 2 9 . 5 ) 4 4 2 6 4 0 2 4 Q 1 : : ) ( 2 9 , 5 ) 4 4 2 6 4 , 2 4 R 2 2 ( 1 6 o 5 ) 4 4 2 6 4 , 2 4 0 1 1 ( 1 . 7 , 5 ) 4 4 2 6 6 , 44 P 2 1 ( 1 7 , 5 ) 4 4 2 6 6 , 4 4 0 2 2 ( 2 2 , 5 ) 4 4 2 6 8 , 6 5 R 1 2 ( 2 2 . 5 ) 4 4 2 6 8 . 6 5 R I I ( I I , 5 ) 4 4 2 5 9 0 9 2 0 2 1 ( 1 1 . 5 ) 4 4 2 6 9 0 9 2 P 1 1 ( 2 6 , 5 ) 4 4 2 7 1 . 5 3 R 2 1 ( 7 0 5 ) 4 4 2 7 2 0 4 9 0 1 1 ( 1 8 . 5 ) 4 4 2 7 5 , 9 8 P 2 1 ( 1 8 . 5 ) 4 4 2 7 5 . 9 8 P 2 2 ( 3 0 . 5 ) 4 4 2 7 8 , 9 6 Q 1 2 ( 3 0 , 5 ) 4 4 2 7 8 , 9 6 R 2 2 ( 1 7 . 5 ) 4 4 2 7 8 , 9 6

0 2 1 ( 1 2 . 5 ) P 1 1 ( 2 7 . 5 ) 0 2 2 ( 2 3 0 5 ) R 1 2 ( 2 3 . 5 ) R21 ( B . 5 | 0 1 1 ( 1 9 , 5 ) P 2 1 ( 1 9 . 5 ) R I I ( 1 3 . 5 ) Q 2 1 ( 1 3 , 5 ) P 2 2 ( 3 1 . 5 ) 0 1 2 ( 3 1 , 5 ) R 2 2 ( 1 8 , 5 ) P 1 1 ( 2 8 , 5 ) R 2 1 ( 9 0 5 ) Q ! ! ( 2 0 0 5 ) P 2 1 ( 2 0 , 5 ) 0 2 2 ( 2 4 , 5 ) R 1 2 ( 2 4 0 5 ) R I I ( 1 4 . 5 ) Q21 ( 1 4 , 5 ) P l 1 ( 2 9 , 5 ) 0 1 1 ( 2 1 . 5 ) P 2 1 ( ? ! , 5 ) R 2 1 ( 1 0 , 5 ) P 2 2 ( 3 2 . 5 ) 0 1 2 ( 3 2 , 5 ) R 2 2 ( 1 9 . 5 ) R I I ( 1 5 , 5 )

4 4 2 7 9 . 6 5 4 4 2 8 2 . 6 9 4 4 2 8 3 0 2 8 4 4 2 8 3 . 2 8 4 4 2 8 3 . 2 8 4 4 2 8 6 . I 0 4 4 2 R6e i 0 4 4 2 9 0 0 1 2 4 4 2 9 0 . I 2 4 4 2 9 4 , 3 8 4 4 2 9 4 , 3 8 4 4 2 9 4 , 3 8 4 4 2 9 4 , 3 8 4 4 2 9 5 , 7 9 4 4 2 9 6 . 8 7 4 4 2 9 6 , 87 44298,56

4 4 2 9 8 , 5 6 4 4 3 0 1 , 17 4 4 3 0 1 , ! .7 4 4 3 0 6 , 5"7 4 4 3 0 8 , 2 2 4 4 3 0 8 , 2 2 4 4 3 0 8 , 2 2 4 4 3 0 9 0 89 4 4 3 0 9 . 8 9 4 4 3 1 1 . 1 3 4 4 3 1 2 . 8 2

48

AEDC-TR-76-12

0 2 1 ( 1 5 o 5 ) 0 2 2 ( 2 5 0 5 ) R 1 2 ( 250 5 ) P 1 1 ( 3 0 0 5 ) 0 1 1 ( 2 2 , 5 ) P 2 1 ( 2 2 • 5 ) R 2 1 ( 1 1 o 5 ) R ! 1 ( 1 6 o 5 )

0 2 1 ( 1 6 , 5 ) P 2 2 ( 3 3 0 5 ) Q 1 2 ( 3 3 o 5 ) R 2 2 ( 2 0 0 5) 0 2 2 ( 2 6 • 5) R ! 2 ( 2 6 0 5 ) P 1 1 ( 3 1 o 5 ) 0 1 1 ( 2 3 . 5 ) P 2 1 ( 2 3 o 5 ) R 2 1 ( 1 2 o 5 ) R 1 1 ( 1 7 0 5 )

0 2 1 ( 1 7 o 5 ) o 2 2 ( 3 4 0 5 ) Q 1 2 ( 3 4 0 5 ) R 2 2 ( 2 1 • 5) 0 1 1 ( 2 4 o 5 )

P2 ! ( 2 4 0 5 ) 0 2 2 ( 2 7 0 5 ) R 1 2 ( 2 7 0 5 ) P I ! ( 3 2 • 5 ) R 2 1 ( 1 3 o 5 ) R i 1 ( 1 8 0 5 )

0 2 1 ( 1 8 o 5 ) 0 1 1 ( 2 5 . 5 ) P 2 1 ( 2 5 , 5 ) P 2 2 ( 3 5 0 5 ) 0 1 2 ( 3 5 o 5 ) P l I ( 3 3 0 5 ) 0 2 2 ( 2 2 0 5 ) ( ~ 2 2 ( 2 8 0 5 ) R 1 2 ( 2 8 . 5 ) ~ 2 1 ( 1 4 . 5 ) R i l l 1 9 o 5 ) 0 2 1 ( 1 9 o 5 ) 0 1 1 ( 2 6 0 5 } P 2 1 ( 2 6 • 5 ) P 1 1 ( 3 4 0 5 | ; ) 2 2 ( 3 6 , 5 ) 0 1 2 ( 3 6 0 5 ) R 1 1 ( 2 0 0 5 )

Table A-2. 4 4 3 | 2 0 8 2 4 4 3 1 4 o 3 5 4 4 3 1 4 o 3 5 4 4 3 1 9 0 6 9 4 4 3 2 0 o 2 8 4 4 3 2 0 . 2 R 4 4 3 2 1 • 38 4 4 3 2 5 0 1 2 4 4 3 2 5 . 1 2 4 4 3 2 6 0 2 0 4 4 3 2 6 0 2 0 4 4 3 2 8 0 2 2 4 4 3 3 0 0 6 2 4 4 3 3 0 0 6 2 4 4 3 3 2 o 9 2 4 4 3 3 2 0 9 2 4 4 3 3 2 0 9 2 4 4 3 3 5 . 2 2 4 4 3 3 7 . 9 7 44 337 * 97 4 4 3 4 3 o 0 1 4 4 3 4 3 0 0 1 4 4 3 4 5 • 86 4 4 3 4 5 • 86 4 4 3 4 5 • 86 4 4 3 4 7 0 4 5 4 4 3 4 7 0 4 5 4 4 3 4 7 0 4 5 4 4 3 4 9 0 5 1 4 4 3 5 1 0 4 6 4 4 3 5 1 • 46 4 4 3 5 9 . 8 1 4 4 3 5 9 . 8 1 4 4 3 6 0 0 3 8

4 4 3 6 0 * 38 4 4 3 6 1 • 81 4 4 3 6 3 0 6 1 4 4 3 6 5 0 0 0 4 4 3 6 5 o 0 0 4 4 3 6 5 0 0 0 4 4 3 6 5 , 5 5 4 4 3 6 5 0 55 4 4 3 7 4 ° 1 2

4 4 3 7 4 , 1 2 4 4 3 7 7 o 0 9 4 4 3 7 8 . 4 9 4 4 3 7 8 0 4 9 4 4 3 8 0 0 2 1

Continued 0 2 1 ( 2 0 . 5 ) R21 ( 1 5 o 5 ) R 2 2 ( 2 3 . 5 ) Q 2 2 ( 2 9 0 5 ) R 1 2 ( 2 9 . 5 ) Q 1 1 ( 2 7 0 5 ) 1 : : )21(27o5) P 1 1 ( 3 5 0 5 ) R 1 1 ( 2 1 0 5 ) 0 2 1 ( 2 1 o 5 ) R 2 1 ( 1 6 0 5 )

I ) 2 2 ( 3 7 o 5 ) 0 1 2 ( 3 7 ' o 5 ) Q 2 2 ( 2 4 o 5 ) R 1 2 ( 2 4 . 5 ) R 2 2 ( 2 4 0 5 ) Q 1 1 ( 2 8 0 5 ) P 2 1 ( 2 8 0 5 ) P l 1 ( 3 6 0 5 ) R 1 1 ( 2 2 0 5 ) 021 ( 220 5) R 2 1 ( 1 7 o 5 } 1 : ) 2 2 ( 3 8 0 5 ) 0 1 2 ( 3 8 o 5 ) Q 2 2 ( 3 1 0 5 ) R 1 2 ( 3 1 0 5 ) R 2 2 ( 2 5 0 5 ) 0 1 1 ( 2 9 0 5 ) P 2 1 ( 2 9 0 5 ) P 1 1 ( 3 7 0 5 ) R l 1 ( 2 3 0 5 ) 021 ( 230 5) R 2 1 ( 1 8 o 5 ) P 2 2 ( 3 9 0 5 ) 0 1 2 ( 3 9 o 5 ) 0 1 1 ( 3 0 , 5 ) P21 ( 3 0 . 5 ) 0 2 2 ( 3 2 . 5 ) q 12( 3 2 0 5 ) R 2 2 ( 2 6 0 5 ) P I t ( 3 8 0 5 )

R 1 1 ( 2 4 0 5 ) 0 2 1 ( 2 4 ° 5 ) q21 ( 1 9 . 5 ) 0 1 1 ( 3 1 0 5 ) P 2 1 ( 3 1 0 5 ) 0 2 2 ( 3 3 0 5 ) R I 2 ( 3 3 0 5 )

4 4 3 8 0 • 2 1 4 4 3 8 0 0 2 1 4 4 3 8 2 • 3 1 4 4 3 8 2 0 9 3 4 4 3 8 2 • 9 3 4 4 3 8 9 0 2 3 4 4 3 8 9 • 23 4 4 3 9 3 • 03 4 4 3 9 5 0 56 443 95 • 56 4 4 3 9 6 • 6 0 4 4 3 9 7 0 04 4 4 3 9 7 0 04 4 4 4 0 I • 4 5 4 4 4 0 1 0 4 5 4 4 4 0 1 . 45 444 04 • 77 444 04 • 77 4 4 4 0 9 . 5 0 4441 I • 51 4 4 4 1 1 0 5 1 4 4 4 1 3 • 0 5 4 4 4 1 6 • 27 4 4 4 1 6 0 2 7 4 4 4 2 0 • 73 4 4 4 2 0 . 7 3 4 4 4 2 1 0 0 2 4 4 4 2 1 0 0 2 4 4 4 2 ! • 0 2

4 4 4 2 6 0 6 t 4 4 4 2 8 0 O l

4 4 4 2 8 • O l

4 4 4 3 0 0 5 6 444 35 • 89 4 4 4 3 5 0 89 444 3 7 0 7 7

4 4 4 3 7 • 77 4 4 4 4 0 , 2 3 ' 4 4 4 4 0 0 2 3 4 4 4 4 1 0 2 6 4 4 4 4 4 * 4 0

4 4 4 4 5 • 0 5

4 4 4 4 5 0 0 5 4 4 4 4 8 • 65 4 4 4 5 5 0 0 9 4 4 4 5 5 • 09 4 4 4 6 0 0 4 5 4 4 4 6 0 e 4 5

49

AEOC-TR-76-12

T a b l e A - 2 .

R 2 2 ( 2 7 o 5 ) 4 4 4 6 2 0 0 7 P l 1 ( 3 9 0 5 ) 4 4 4 6 2 0 7 1 R I 1 ( 2 5 , # ) ) 4 4 4 6 2 , 7][

. . . . . . . . . . . . . . . . . . . . . . . .

0 2 1 ( 2 5 o 5 ) 4 4 4 6 2 0 7 1 R21 ( 2 0 , 5 ) 4 4 4 6 7 0 1 6 0 1 1 ( 3 2 o 5 ) 4 4 4 7 3 0 1 5 P21 ( 3 2 0 5 ) 4 4 4 7 3 0 1 5

" 0 2 2 ( 3 4 o 5 ) 4 4 4 8 1 0 2 6 R 1 2 ( 3 4 , 5 ) 4 4 4 8 1 0 2 6 R I 1 ( 2 6 , 5 ) 4 4 4 8 1 o 2 6 0 2 1 ( 2 6 , 5 ) 4 4 4 R I 0 2 6 R 2 2 ( 2 8 • 5 ) 4 4 4 8 3 0 4 0 R 2 1 ( 2 1 o 5 ) 4 4 4 8 6 0 4 1 0 1 1 ( 3 3 • 5 ) 4 4 4 9 1 0 7 5 P21 ( 3 3 • 5 ) 4 4 4 9 1 , 7 5 R I 1 ( 2 7 0 5 ) 4 4 5 0 0 • 0 9 0 2 1 ( 2 7 , 5 ) _ . 4 4 5 0 0 ° OQ 0 2 2 ( 3 5 , 5 ) 4 4 5 0 2 , 6 1 R I 2 ( 3 5 , 5). _ 4 4 5 0 2 , 6 1 . R 2 2 ( 2 9 0 5 ) 4 4 5 0 5 0 2 4 R 2 1 ( 2 2 0 5 ) 4 4 5 0 6 0 1 3 0 1 1 ( 3 4 o 5 ) 4 4 5 1 0 0 9 2 P21 ( 3 4 • 5 ) 4 4 5 1 0 0 9 2 R I I ( 2 8 , 5 ) 4 4 5 1 9 . 4 7 0 2 1 ( 2 8 • 5 ) 4 4 5 1 9 0 4 7 0 2 2 ( 3 6 • 5 ) 4 4 5 2 4 0 5 5 R 1 2 ( 3 6 , 5 ) 4 4 5 2 4 • 5 5 R 2 1 ( 2 3 , 5 ) 4 4 5 2 6 • 75 R 2 2 ( 3 0 o 5 ) 4 4 5 2 7 , 76 0 1 1 ( 3 5 o 5 ) 4 4 5 3 0 o 6 7 P 2 1 ( 3 5 o 5 ) 4 4 5 3 0 0 6 7 R l 1 ( 2 9 o 5 ) 4 4 5 3 9 , 7 4 0 2 1 ( 2 9 , 5 ) 4 4 5 3 9 , 7 4 0 2 2 ( 3 7 o 5 ) 4 4 5 4 6 0 7 6 R I 2 ( 3 7 0 5 ) 4 4 5 4 6 0 7 6 R 2 1 ( 2 4 • 5 ) 4 4 5 4 7 0 8 0 R 2 2 ( 3 1 o 5 ) 4 4 5 5 0 0 8 9 0 1 1 ( 3 6 o 5 ) 4 4 5 5 0 , 8 9 P 2 1 ( 3 6 o 5 ) 4 4 5 5 0 0 8 9 R11 ( 3 0 , 5 ) 4 4 5 6 0 0 3 8 0 2 1 ( 3 0 • 5 ) 4 ¢ 5 6 0 0 3 8 0 2 2 ( 3 8 o 5 ) 4 4 5 6 9 e S 6 R 1 2 ( 3 8 0 5 ) 4 4 5 6 9 , 8 6 R 2 1 ( 2 5 , 5 ) 4 4 5 6 9 0 86 Q l l ( 3 7 • 5 ) 4 4 5 7 1 0 9 3 P 2 1 ( 3 7 o 5 ) 4 4 5 7 1 , 9 3 R 2 2 ( 3 2 o 5 ) 4 4 5 7 4 0 0 3 R ! 1 ( 3 1 , 5 ) 4 4 5 8 1 • 7 3

Concluded 0 2 1 ( R 2 1 ( 0 2 2 ( R 1 2 ( 0 1 1 ' ( P 2 1 ( R 2 2 ( R I I ( 0 2 1 ( R 2 1 ( 0 1 1 ( P 2 1 (

3 1 o 5 ) 4 4 5 8 1 . 7 3 . . . . . . . . . . . . . . . . . . . . . . . . . .

2 6 o 5 ) 4 4 5 9 1 ° 5 3 3 9 ° 5 ) 4 4 5 9 3 • 4 6 3 9 . 5 ) 4 4 5 9 3 o 4 6 3 8 . 5 ) 4 4 5 9 3 • 4 6 3 8 0 5 ) 4 4 5 9 3 0 4 6 3 3 • 5 ) 4 4 5 9 8 • 17 3 2 , 5 ) 4 4 6 0 3 o 5 8 3 2 , 5 ) 4 4 6 0 3 • 5 8 2 7 0 5 ) 4 4 6 1 4 0 4 1 3 9 o 5 ) 4 4 6 1 5 o 72 3 9 . 5 ) 4 4 6 1 5 . 7 2

R 2 2 ( 3 4 , 5 ) 4 4 6 2 2 . 9 7 R I 1 ( 3 3 0 5 ) 4 4 6 2 6 0 1 6 0 2 1 ( 3 3 * 5 ) 4 4 6 2 6 , 1 6 R 2 1 ( 2 8 o 5 ) 4 4 6 3 7 ° 85 R 2 2 ( 3 5 0 5 ) 4 4 6 4 8 0 2 2 R I 1 ( 3 4 , 5 ) 4 4 6 4 q o 12 0 2 1 ( 3 4 , 5 ) 4 4 6 4 9 , 1 2 R 2 1 ( 2 9 , 5 ) 4 4 6 6 1 . 8 6 R 1 1 ( 3 5 • 5 ) 4 4 6 7 2 , 7 6 0 2 1 ( 3 5 o 5 ) 4 4 6 7 2 , 7 6 R 2 2 ( 3 6 o 5 ) 4 4 6 7 3 , 9 4 R 2 1 ( 3 0 0 5 ) 4 4 6 8 6 , 5 9 R 1 1 ( 3 6 o 5 ) 4 4 6 9 7 , 1 2 0 2 1 ( 3 6 o 5 ) 4 4 6 9 7 0 1 2 R 2 2 ( 3 7 ° 5 ) 4 4 7 0 0 o 0 2 R 2 1 ( 3 1 ; 5 ) 4 4 7 1 l o 6 9 R 11. ( . .3705)_. .4472.20 - 14 0 2 1 ( 3 7 , 5 ) 4 4 7 2 2 0 1 4

. R_22_( 3s.. 5 ! __44 7~_7_. 04.. R211 3 2 , 5 ) 4 4 7 3 7 • 4 6 R 1 1 ( 3 8 , 5 ) 4 4 7 4 7 , 3 7 0 2 1 ( 3 8 o 5 ) 4 4 7 4 7 , 3 7 R 2 2 ( 3 9 , 5 ) 4 4 7 5 4 0 4 3 R 2 1 ( 3 3 o 5 ) 4 4 7 6 3 0 2 8

__R U. (_3.?. _5. ) _~47_7 3_. ~_3_ 021 ( 3 9 0 5 ) R21 ( 3 4 , 5 ) R21 ( 350 5 ) R 2 1 ( 3 7 0 5 ) R2 ! ( 3 8 , 5 ) R21 ( 3 9 , 5 )

4 4 7 7 3 , 4 3 4 4 7 8 9 o 81 4 4 8 1 8 o 2 6 4 4 8 7 4 o 81 4 4 9 0 4 • 54 4 4 9 3 4 0 5 1

B l a n k Card

0 . 0 o 0 0 0 E 1 5 . O 0 0 E I 6

5 0

AEDC-TR-76-12

R22 ffi

Q22 =

TABLE A-3 HONL-LONDON FACTORS FOR 2Z -* 27r TRANSITIONS INTERMEDIATE BETWEEN HUND°S CASES (a) AND (b)

(2.1"'+ 1) 2 + ( 2 J " + 1 ) [ Y ( Y - 4 ) - ( 2 J " + 1)2] '~4(4J"2+ 4 j " + 1 - 2Y)

( 2 J " + l)[(4J "'2

8(J " '+ 1)

+ 4 J " - 1) + I Y ( Y - 4)+ ( 2 J " + l)2}"t'~(8J "'3 + 12J "'2 - 2.1"+ 1 - 2Y)]

P22 =

RI2 =

QI2 ffi

8 J " ( J ' " + J)

• "5t(4j,, 2 ( 2 J " + 1) 2 ÷ ( 2 J " + I)[Y(Y - 4) + ( 2 J " + 1) 2] + 4 5 " - 7 + 2Y) 8J'"

1)2]'~'t(4j,, 2 (2J " '+ 1) 2 - ( 2 J " + I ) [Y(Y - 4) + ( 2 J " + + 4 J " - ? + 2Y) 8(J '" + 1)

( 2 J " + 1)[(4J " ' 2 + 4 J " - i) - I V t V - 4) + (2J'" -½

+ 1)21 (8J "'3 + 12J ' ' 2 - 2J'" - 7 + 2Y)]

P12 =

R l l --

Q I I =

8 J" (J ' " + I)

.,~ ( 2 J " + 1) 2 - ( 2 J " + 1)[Y(Y - 4) + ( 2 J " + 1) 2] (4J "'2 + 4 J " + 1 - 2Y)

8J""

.½ (2.1"+ 1) 2 + ( 2 J ' : + I ) [ Y ( Y - 4 ) + ( 2 J " + 1) 2 ] (4j " ' 2 + 4 J " - 7 + 2Y)

8(J"+ 1)

-½ (2.1"-,- ])[(4j " ' 2 - 4 J " - 1) + IY(Y - 4) + ( 2 J " * 1)2} (8J "'a + 12J " ' 2 - 2 J " - 7 + 2Y)]

8 J " ( J ' " + 1)

P I 1 =

R21

Q21

-½ ( 2 J " + ])2 + ( 2 J " + 1)[Y(Y - 4) .,- ( 2 J " + 1) 2 ] (4J " 2 + 4 J " + 1 - 2Y)

8 j e,'

( 2 J " + 1) 2 - ( 2 J " + ] ) [Y (¥ - 4) + ( 2 J " + ] )2"J '~(4 j "2 + 4 J " + l - 2Y) 8 ( J " + 1)

= ( 2 J " + 1)[(4J " ' 2 + 4 J " - 1) - I Y ( Y - 4 ) + ( 2 J " + 1)21"~(8J " ' 3 + 12J " ' 2 - 2 J " + 1 - 2Y)]

8J (J + 1)

P21 -½

( 2 J " + 1) 2 - ( 2 J " + I ) [ Y ( Y - 4 ) + ( 2 J " + 1) 2 ] (4J " ' 2 + 4 J " - 7 + 2Y)

8J'"

w h e r e y = A / B v

51

A E D C - T R - 7 6 - 1 2

T H E P R O G R A M

I V G L ~ V ~ L 2 1 R A l k D A T ~ ' = 7 S l ? 8 0g~O4b~48

c

C P A R T | PN4T& PARIr & P A R I I P A R T | PARlr I PARTI P A R T | ~ , . e * * e , e e . _ e e e e _ e e e , , . * * ~ 4 , • • , , e e t b be b e e t e e e , e~ . * * e , • e_ee_eeo e e e e e e o e o o , o e e o e , e e e e , e e , C

| f iTF .GERb4 P • G e R , E L A h K I INTEGER* 4 BRAN(. H 0 ; R E N S I O N S(SOO) = F L ( S t , GJs l ICCSG0J tP . ID (50O)

n. ,~_EN .S.!ON ~ * q S ( 20 J o = . e N s t o ~ K o ( s o o ) DATA P / e P e / • Q / e G e / s R / e R 4 / DATA 8LANK~Te * / COMNQNJPARERdJq-..DNUT 19CONS Td eC C k s ] r 3 , wO eEOc KO e k L | kES O[141=N-S'IO"--N b( 50GJ ,E (SGO' ) ,C .AY(~UO) sUAT' (600") , P . J ( S O O I e T . J ( ' S O O )

. ¢_,. ~._._~E_RA...% 7 ( 2.0_e . ~ . ? : - J., t ) ALLOW: c O 0 |

"C AL.L F UNC( XDUM ) I R 2 2 L " -~-"

| ¥ U = 0 1 VL= G

. . . . . . . _R_I~AD ( .b , ,.,]Ib I= )HEADS 3 6 6 FORMAT ( ~ Q A 4 )

READ( 5v 36 JOE.i.PL T READ( 5 , "46 ) S L IT Dt .AM: SL. | T REAl3( 5 , 3 6 ) AP READ( 5 • 3 6 J I"A READ( 5 • 3 6 | TE~ READ( .Es 3 ~ ) E L R E A D ( S e 3 6 ) V H G T R i ' A D ( " J ? G 0 | [ P L O T 1

70o FORMAT ( -';[ ( ) 37 Ft~RMAT ( | | e 2 F 1 0 . G)

C I : * t~O 1 ~=..D-- 1 4 / T A * * ( &* D 0 / 2 eOG)

C 2 = " 1 . 4 3 8 3 ~ G / T A C.UNST 1=-" 2 * D 0 * D S Q R T ( Di.GG( 2"•DO ) ) "- C O N S T ~ : 1 . 3 G T D - 7 4 S O R T ( T E ) C G N S T 3 = I e 3 G 7 D - 7 * S Q R T ( I A ) C.U NS T 4= 3 .F..-- 7 * S O R T ( T ~ ) IIR [TIE( 6~ 87 )HF.ADS,AP

~'17 FORMAT(IH|e;~OXe2OA4*(OJle3HAe~eFTo4J c C ~ * ~ * ~ * * ~ * * * * * ~ i * i * * i i t * b t t i t i l i l l i ilii*ii~*iilii*~**illi*liliO*li~lii~lli~lli ¢ PARTa PARTa PART= PAaTa PART= PARr= PA.TZ P ~ = ¢ * e ~ * e e , e , , , e e ~ e e ~ . , e e , e _ee ,..e_e _e_o_***¶, ? e , . ? , e , e , ¶ e e eeeeeeeeeeee,eeoeee?eee,eee,eee~o~ c

J = ! 749 RE AU (-5 • t )8RAI~;H ' ,h IJP ~-fi't"C ,R J-PP e b(: ( J )

(P ( ~JRANCHe F'DoI:)IL.ANK JGO TQ JPP'=AJPP

I i=GRRAT ( J X o Air o | t j ] I • J J (o IF4o0 o | X el; ! 1 o 0 ) ' I F (E t r4ANCHoE0oP |GO T0 I G |F(URANCPoEQoQ)GQ TC 2C,

5 2

A E D C - T R - 7 6 - 1 2

IV G LEVI~I . o ~ o ~ , s 2 1 M A I k OATE as 7 S i 7 8

c;.-. F-U~ER ~t v~ ;;~i; ;JPP+i .F~ ) . . . . . . . . .

_ C.A_LL HGNNUN| I VUelVL.eNUP_ eN. LOeJ_I:P4.1. 9.J.P.II_.I_~_~_S_(..J._J.J. GO TO tOO

. .~p_URmATI4F~O. OI • . .

20 . (.ALL. F t ~ P P E R I I V U * N U P * J P P e l l :b ) C A ' ' HON~UN( Z v u : i w , . , ~ , u p , P , l . c , jpF_,.J_p.p_, ~?_.,.s_.t.J.J .~ .. G~ TO IGO

10 CAL.L F t ~ P P E k ( I ' e U , N U P e J P P - I ~F iJ | C A L L PIONNUN| [ V U g | V L . e k t , P ~ N L r . , J P P - - | s J .Ope | i S ( J | |

l (JO CALL. FLOM: .R( I V L * N L C e J P P , F L | J ) I J :O (J ) R S ( J | * F U N C ( F U ) t N | TE | 69 i 0 | ) J e I, f4~ANCH 9NUP •NL.C e J P P • F U * F L ( J ) • i O ( JJ • S ( J ) * E G ( J J) . . . . . . . . . . . . . . . . . . . . . . . . .

I O I F U R N A I ( 2 X , 1 3 e 2 X I A I • I t e | 1 • •1 e , [ = . • 8 | e • a F U a e e l D | b e e e b X • OFLme e D | 0 • 8 e 1 5 X • e I u = e •1,1) t 6 e l d e EJI• ° S J : e • D I 4be 8 , . ~ X • eE;O Jm e c O | 6 0 8 )

J=J4 .1 GO 1"0 7 4 9

.3 CUkT | N U E NL. IrNF-SmJ-- i

81)O R E A D ( b e 3 o , P . . N D : S G O ) ~ N C DU b ~ i : i ~ N L I N P - S r ¢ = C I I S | [ ) * E. , I IP(C2*FL.( i l I KO| [ ) : U * E N U

6 g 1.1.1 NT l N L+i- C

(. " P A R | 3 P A R T 3 PAR | 3 PART3 PART.~I PART~ PAR|.'~i Pddqlr 3

C

| S A V E : 1 N I N T = 4 C NP | : N | I~T~ | I' AI~T('JP: 0 eD U TAt*; 'O T : @ e D 0 DU 2 U 0 J : I e N L Z N E S L I I J : C G N S T - ) e ttU ( J ) Ui[-L.T A t I : C U N 5 T 4e 80 | J ) AZ J = • U ( J |-DF..L T A t UZ J : a n | J )+DP..LTA I D | CT=I',Z J - A Z J Ot:L.:O | S T / N | N T a)U 7(J(,C | : l e N P l W( I | = A Z J # ( 11-- |)*DP..L. P . ( i ) : l : O ( J ) • Ir.XP(--((kI(I)-mC(JJ)eCChSTJI/i)tlJ)•*2) IP(E:NOeI,: ,Q=QeJGG TO b744 ,?

J L E F T : O SI. ,ML=O. -'- ~Mi, l : 0 e I [ = J

1 1 0 8 b w L : C ~ . F . S T J * m Q ( l | J I I - ( A P e E U I 0 * I G O I"0 1 | 6 C ,'~r.. TA=- 'CONr-T 1 * ( i ( i ) - - i C ( I ! | ) / O I L ~. ALL. ".F uNC ( L~E T A , APe Tr. RM ,U • . k S ) C', T~J l l O l

| l ; J O l ~ . l . M : L ~ P | - - I ( , , I 1 1 - I G ( l l I I I C t . ] K S T I / D I L I 1 1 2 1 I I O I - ~ C ~ , ! INt . ' -

TNP..tv:K(.( I I .) •'TL~iid

53

AEDC-TR-76-12

I V G L~'Vt: l . ~l l 14AIk I ) A I r: ~ 7 | | ' / 8 0 ~ 1 / 0 i ~ 4 1

| F ' ( J L S : P T o ~ ' G o I ) G L m TG | i G ~ SbMHa S L,MR4.TN J: IV l ¥ | l I O ( ElJeGTelI([IoAklIoI"NEIIoECI.O.)GQ I 'C 1 1 0 7 | P ¢ I i o ~ G o J ~ . I I ~ S I G O 1 0 | 1 0 7 I F C I I . . 1 4 J I ) e L T o d Z J ) G G TG 3 3 5 6 0 I F ( A d S | T N & I / S U N I N | e L E o A L L C i b | G C TG i | 0 7

331150 (.UNT IN L,4~ II:I 14'I

GU To | I G 8 1 1 0 1 JLF.P r~, I

i [ = J - - 1 I I ' I J . I : Q . I I G Q ICl I l l 3 GU I U i l i b

I Iuqli CUNT |Nk,P. S 4.ML= bt, ML+ TNE It I F I v , CII I 1 ) . L . I ' , I ( i ) * A N D e i h l " l l o t " G o d ' o IGG l r o 7 @ 1 3 I f - I i l . i : Q , I I G G TU 741,13

ll'liUlll I,GT.AZJIGI TC 3311JI IIIAu$1TN' It/.SUNLI.LL,ILLCIJIGI I n lull

3551)I I.I.I~ I I NI,,E

llall-I G(, Y(J i l U ( t

? O I 3 f~UkT I N U I GU Ti ] ?OUO

~744]P .5 UIt~.m t~ e 5t , M N = O .

7Gt~tJ ( .A ' f ( i ) :~ t . .NL#SUNR ";UN I : : ( , .OU ~UMd~I 4~ oO U i I L L ~mlJl: I . J ~ e L) O UU 'VU4,1I, i . = t , N P i

~G(Ju O A I ( ! ) . : E l ! l e L X P I - - C A Y ( I | e E L ) OU ~ O i i s l e N I N T lil.ltl l a b l . k | 4,IIcL2011'LJA TI 1 ) t 'OA T | 14' I I I

V0U I .ll~,lel~mbtdJ, l i l4,UL.L.21(s- ( i J 4,k:l 14' 1 ) i I J | J ) : r-4.,I M.d T J I J | : S U M | I A I , T u P : I A U T O P b T J | J ) T AI, rJU | : TAUUU T4.F. J ( J J

2 0 0 g U h i ll~ll.l: (.

C PA~ T*) /-JAH 14 PA(,I 14 PAMT4 PAHT4 PART4 I IART4 PART4

C T~ (.= 1A t. 1UP,~ T~u,4U I A4. PHA:. II./~Q-- I A U i l k | T t . ( I . , ~ '4E) [ A o | r . eLh( .o ,*L,TAt , oALFHA

~ U F I . , I e N A T ( / / o ~ e eTA :ze , O l LJo.IlelIJi e *Ir.a e e l l l l l . e U e l IXe e k C a e eDl lbeU.el l~l io I L n e e eiJ | G*UO = ~ , * / * . ~ A * e |AU , I I e~lJ, Go~j 8.OK l OALIIHA~s | i O l b e 6 J

viler | I i : l, -51) ) bL. [ 1' . P l . T V II h Qi-I. I ~ A sb~'/PJI l oL,1LAId • VH~bT * A L I h i l l ) e ~.NO s • I L e I"A , i - L e | I:~.LJY I e l PL( .TZ U eL ll,l'~ e AP ,ulna, I A ~ • o I,-t.AU ~-

uIJ ~ 4 3 1 l = l . l ~ . l l ~ t - l ~

54

A E D C - T R - 7 6 - 1 2

iV • LEV~-L Z | FUhC DATE s ? S i t e

FUk'CII'|ON F~NC( XI. D ' R ' : N S ' O h XO AT A t_' 0 C) o .~_O_~!*J_~.O_OJ._ DATA I m S T / O /

_ J ~ s LR._s_r :eg.__o+ !p_o TO , [F IXeJ .TeJ IOATA( | | ) G O TQ 2@O OQ IO . I : . I , N P I

. . . . . . . . . . . . . . . . . . . . .

II:¢XDATAIIIeL.Ee)I.AND.IIDAIA|I4,1IeGEoXJ)GO TO I g 10 C~NT ! NI.JE

PUNCh ( YDATA( N'P )--YDA lr~tl Nlil'~" J ' l | JI~-XI)Alr-A~ NID"~-I S'( ,liOA,'lr A ( NP Ji--XDATAINP| J J 4,V _ *.U. A .T.A.( NP )

O ~ O e v * 4 S

R~TURN 20 FUNCa(YDATA||*I|~YOATA.~(iJ|t|XDATA(I~|)--XDATA|||It(X--XOATA||J|

e ~ V D A T A ( ' | ) RETURN

2oo ~ L ~ = c VOATAC 2 J~VDA rA~; I ) * | i ; x o ~ i ~)~CX~ATA|EI--XDATA( I ! I+TDMTA( I J RETURN

I G O IOU I s l + l O O O N + A O I b , 2 I X D A T A I I J , ¥ D A I A ¢ I ~ .

2 F Q R N A I ( E F | O e O | [FIXOA|A(|)eEQe@eUG)GQ TO 3

|UO CUNT|NUE 3 CUhT|NUE

N P = I - - ! NPImNP-- I J R S | : | NETU~N ENO

56

A E D C - T R - 7 6 . 1 2

I V G i .P.VEt. 2.1 FIJPPER DAlr , : m 7 8 1 7 8

. . . . . . . . . . . . . . . . . . . . . . S I , JSROUT| I~ F U I : P E R ( V e N • J | h O £ X e / = )

C (.

C .c

0 9 J 0 6 S 4 6

F.L.I=CTklON STATE_FOR A G | V I = k V | O R A T I O N A L S l r A l r E E V J e A G | V ~ ' N S P | N S T A T E C N | • AND A GE~k~N R n T A T | C / ~ A L S T A T E ( J )

INTEGER R E A L * 4 J J = J | N D E X ~ e s T : 4 3 g o 5 * 7 V lE:s2JT4 e0 M E X E : l e , . 4 6 O i - = | e S g T 7 A L P } , . * _ E : . o I s a . . . . I J V ~ - b e 2E-- 6

GO T O ( I • 2 J oN | . . . . I F N : O V * i J + e g | * ( J ' - oS)I~OV4)( J 4 e S | * O t ? . * ( J " e S J ) * 0 2

GO i ' 0 3 ..~ F N : O V * t J.*.__b) *C J * | • 5 _)_* .O VOC.J~: S_) .* e.2.eC_J_* : . .S) , e 2 "4 C.ONT | NU~

G:: b E * ( IP4eS )-.-Ill~XEO( ¥ t e 5 } , 4 2 F : T ~G #FN Ri~ TURN EI~D

5"7

AE DC-T R-76-12

IV G ~ V E ~ 21 H G ~ U N UAT~ = T ~ l T ~

~UUROUI INE HUNNbN|N~Peh~PP~bGAk~NLGANeJFeJPP~IE~H0hL| SUUROUT|N~ HONN~N C A L ~ L A T ~ S TH~ HONL--LO~DCh FACTCN ~HE~E

C hUP=UPPER V I B R A T I O h A L bTAT~ _~ .. NUPP:L0WER V I ~ R A T I O N A L STATE C MEGAN=UPP~R 5 P | h ~ T A ; ~ C MEGAI4.=LU~R S P i N bTAT~ C j : j o e

C l ~ : | FQ~ P U~ANCHe : ~ FCR G 8~AkCHe ~3 FOR R ~ A k C H C

~EALO4 J J : J P P + e 5 T | : 2 e # J ~ | e

T J : I . / S U R T ( T 3 e 3 * ~ g e 3 ÷ ~ 2 ) J U = | U ÷ ! GO T U | 2 o 2 e 2 o A ) e J ~

2 CUNT[N~E GO T O ( ~ | g ~ ) e N E G A h

21 ~ONTIN~E Gb T 0 1 2 ; I , 2 1 ~ ) , ~ E G A N

211RN~N=Tg+;l~T3~(4e~J#J÷4eOJ÷le--i46eS) O~NOH=Oe~J G~ TO 1 1 1 1 1

2 1 2 RNU/4=T2-TI~T3~|4o~JOJ÷4e~J÷Ie-146e6)

DL~UM=ee0J G~ TO | t i l l

~2 CGNTLN~E GU T O | ~ Z I , 2 ~ 2 ) ~ N E G A ~

O ~ N O H : 8 6 # J G~ TO 1 1 1 1 1

2 2 2 RNUH=T2*TI~T3e|4e~JeJ*4e*J'-7÷I4~eS)

D~hOM=Se*J . . . . . . G O - T O - I I I - I - I . . . .

3 C O N T I N ~ GG T O | ~ J e 3 2 ) ~ N E G A N

3 | ~ U N T | N ~ GO T O i 3 I | ~ 3 1 2 ) ~ M ~ G A M

J E t RNUM=Tl~(|4~J~J--4~J--iJ÷T3~(OetJ~43÷12e~J~J--2e~J"-Te÷14&eSJ) 0~NOM=~e eJ t | J ~ J e ) . . . . . . . . . . . . . . . . . . . . . . . . . . GO TO I I l l l "

J 1 2 R~UM=Tl~(~e~J#J@4.~J--le--T3~(Oe~J~tk$@12e~J4~--2e~.l-Te÷14@eS)) U ~ N O M = E e # J ~ I J + i e ) G~ TO l l l l l

32 CONTINU( GO T O | 3 ~ I ~ 3 2 2 ) ~ E G A N

D£NON=Oe e J $ ( J ÷ | e ) GC TO 1 1 1 1 1

322 RNU~l~(i4.eJeJ~eeJ,-le|÷T3el~eeJee3+12oeJ~J--2oeJ~lo--i46eb))

GO YU 1 1 1 1 1

GO T O K 4 | e 4 2 ) , M E G A ~ • ! C~NT|N~E

G~ T U ( 4 1 1 e 4 1 ~ ) e N E G A N

Og#'O0/4~S

50

AE DC-TR-76-12

I V ~ ~ k V ~ L

4 | |

4 1 2

~ 2

| l l l ~

~ , ~ I

~' 1 I'IG N N L. ~'

~ N U M : T ~4"1 I I T 3 1 ( ~ e W J 4 ' J { 4 e I J - - T a ~ 1 4 O e : ~ | L , IENUM=d e 41( J + I o )

GJJ I 'U | I L | i l

s<N~M= T 2 - - T I O T ~ | 4 • ~ J O J + 4 e ~ , ~ - 7e 4"l, d lCe ~J DL. '~ut4= J" . t / ( J + | )

Go., ' I '~ 1 1 1 1 1

L~ .NT [ NL, I-

GIJ T J ( 4 ~ = | e 4 ~ ; ' ; o~V,:¢jAM

.(NL, M:l-~--1/O134|~e*JOjt~elJt|e--J4~tCeb| DI~ ,h, L I M : b e4~| J.4 I • ]

• aL, TU I / i l l

' ;~,L,.4= [ < ÷ T I I' r J ~ ( q + $ J ~ J ) q . • j + | e - 1 4 l ~ e b J L J ~ k L J I d = t : . ~ [ Jt~ | . )

C J N T I N ~ L

[ P = ( O J - N L J M . I ' U e t J J G L r E ~ ] 1 hL.h.l.. -~ r~ hi U M,/Ul" N.J M I l L I' ~, I~ N

H ~ N L = t; •

~ c T U K N

E k l )

UAT~.

t @~#U6#45

6 0

A E D C - T R - 7 6 - 1 2

I V G L I - V L L • . ! Wi: 'Uh(. UATP. = 7 : ) l ? b U . ) , # ' O 0 1 4 S

S t.dHtJ~., T | NI= b F U N C { XP gYi" el i I t T*~ ) W ' ( Z ) |

X I - I Y F A*,tE THI" HJ'AL AI~,~ I f ~ A G I k A R Y P A H T b OF THr. ARGUME~,T "a i ,W- ~ A~.. THI- HEAL A h J Z IdAGINARY P A R T 3 OF TI lE F U h ' ( . T | O h ~u|Z):LXP(--Lo~')~'I<F4..|--IZ| (~E~" I~ ,ATiO~AL EUREAU CF "~TAhrJAE.~S i-ANULJ..J~)k LIF MATH~.NAJ ' ICAL Pl~b,a. .T lChS, PAGE; ~ 'V7)

J,,qPL 1 t. i T ,t F A L e | ; ( A--I', eL,-Z ) t l ( 7 ) 2 LuMPLJ- X# I o Z C J m C * J o L S + T i , : 2 , T 3 W ( Z ) 3 ( - U M H O N / I A L I L r - / Z | "41Q 4L, • 2 ) o.~ ( 4 U J BY | 31 } t S ( Z | 4 U 1MI~-N ~" I 'JN ~ ( ~ ) W ( Z ) 5 EI 'LAG=O W ( Z ) b IF ( .~ ,PeLTe@.) I [ ' J -AC,= IFLAG~L W(Z ) 7 I I ' ( Y F ' t ' T * U e ) J I ~ L A G = I F L A G ~ * 3 W I Z ) 8 A I=DALt~'( XF ) W ( Z ) 9 Y I= [JA" I '~( YF ) W ( Z ) 10 It'(XIeGLeJeCJO'JeONe'I|eGbe3e[JO)GQ TG I W(ZJ I I

l | : l ~ e V I + l W ( Z ) 1; ' J J = i O t X I + I W i Z ) 13 | E l = l i t 1 W ( Z ) 14 J J i = J J + l w ( Z ) | b O 0 IG K : 1 , 2 W ( Z ) | 6 ~' I .=( -' i I 1 , J J * ~ ) - " t f | • J J l B K ) ) e ( x i - - x ( J J l ) ) / | X ( J J | - - X ( J J | | ) 4 . ~ ' ( | i , J J I , K ) W ( Z ) 1 7 /-'~= ( Z ( I i 1 . J J * K ) - - Z ( I i l , J J l . K I ) e ( ' ~ l - - X ( J J | ) ) / ( A ( J J ) - A ( J J i ) ) W ( Z ) 1 8

0 4 ' Z ( I l | , a J J I oK ) W ( Z ) I U

i U * | X ) = 4 .' I - - / : ~ ) e ( Y l - Y ( l I I ) ) / | y ( El ) - V ( i I i | ) + z 2 i ( Z ) 2 0

W I = e ( I ) V f l Z ) 21 W~.=a( ,~ ) W t Z ) 2 2 [ F ( I F L A G el= G e G ) Rf'- l ~ k l ~ N ( Z ) .,53 Gu TU( 1~JU,~O( . , 3C t . o4QG) • 1 F L A G W ( Z ) 2 4 H~- T U r N B t Z ) 2 ~,

I | F I X l e G T e ~ * ~ O e U ~ e Y I * G T , o , U O ) G C TC 2 W ( Z ) 2 6

J= ( b , i J C~ | * I . )G J ~ i ( Z ) 2 7 Z~=.DI .MPl . +~ l ~ 1 . Y l | W I Z ) 2 8 Z S : Z ~ . * Z C W I Z ) 2~ T l : • 4o I " | J ~'L) { , / ( Z b - • 1 ; L 1 ~:-~bDU) W ( Z ) 3 0 r'~:e~,~J99"J21Loo/(Z~'-leit~44'~270uI I I Z ) 31 l J= • U U ~= c: ~ J d(* qO U / ( Z ,~-- ~" = ~"2 :)J 4 J 7UO ) W ( Z ) 3 2 i~.-" J • Z (..~ | I | # T 2 + T J ) W I Z ) 3 3 w l : ( tuL t J ~ . U N J b | tt~. ) ) l , , ~ W ( Z | .34 d ~: = ( L)CCNJG ( ~ ( . ) - - tt~.) l J4~e : G U W ( Z ) 3 e" l~J" ( I FLA(~ mr. Oo G ) I,C'.- I UkN W ( Z ) 3b ' GU T~)( IO~J,~:Q~.,3Ct,,4G4. I e | F L A G B I Z ) 3 ?

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, 7 1 7 2 6 7 ~ 0 , 0 5 2 2 2 4 © U ~ * . 3 e l J S G D O , . 2 ~ S b O O d C * . 2 3 ~ 2 3 ~ b G e . 2 C u c J g ~ b •

. ? 1 7 5 d S U ~ . . 4 ~ S b ~ l U O , , ~ t U 3 ¢ 3 ~ U , . ~ o + E ~ O D G ,

. 4 7 1 ~ S J D U , . 3 = / ~ 3 7 b U e . ~ 6 3 1 g ~ D O , . 2 d 2 2 0 ~ b O * , I + 5 7 1 7 0 + ,

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. 4d?b~OQOe 04=O~790Oe

. J o U T g g O o e . 3 4 2 2 U b b U e 0 2 d ~ 4 1 7 0 0 , , ~ 7 0 ~ 4 b D O , , 2 3 0 3 0 U O O * . 2 2 1 ~ 3 D ~ + , 2 1 4 1 7 2 D 0 ~ WIZ ) 121 0 1 ; 3 0 1 ~ d e - , 1 8 7 5 0 6 0 U , o l D | e b b 0 0 0 I ( Z ) 122

W I Z ) I Z 3 WIZ ) 1 2 4

0 ~ 6 3 2 2 3 0 0 , . b | 4 8 ~ 2 D O . . S ? L T I ? O O o I | Z ) 125, , 4 ~ T b 2 1 D d l + 4 3 V S | ~ D O * . 4 1 4 1 9 1 U 0 * N I Z ) 12.~ . 3 b l J 3 b D + e , 3 3 3 9 4 2 D 0 , , 3 1 0 O O I D O , I I Z ) 127 0 2 7 7 4 1 2 0 0 , 0 ~ b 5 8 ~ 0 0 0 , 0 2 5 ~ 0 ~ D 0 1 N | Z ) 128 0 2 2 7 4 U ? D O , 0 ~ i 9 3 4 7 0 0 , 0 2 1 | 8 0 0 D 0 , WIZ) 129 . l g i d i U U O . . i 0 5 9 2 4 D O * e i U O J b l O O e I I Z ) 1 3 0

e ( Z ) 1 3 1 U ( Z ) 1 3 2

, b U d J ~ D d e , b b g 2 3 0 D O t 0 5 3 3 5 8 1 D 0 , ~ ( Z ) 133 0 4 4 4 4 J 4 U O t . 4 1 9 7 0 6 U O , 0 ~ ? ~ 1 6 0 0 , W(Z) 1 3 4 . 3 4 0 2 4 | D 0 , . 3 2 4 2 2 ~ D 0 , , J O ~ 4 6 3 0 0 e t ( Z ) 135 . 2 7 1 4 7 ~ D O e , ~ 6 0 5 9 8 0 0 , e 2 5 0 4 6 9 0 0 0 H | Z ) 136 . 2 2 3 g S Z D O , , Z i b 2 1 9 D O , . ~ O U 9 6 1 0 0 e I ( Z ) 137 . i ~ g b b 4 U O e , 1 U 3 ~ S 0 0 0 , , 1 7 8 6 4 9 D O , . i ( Z ) . E 3 0

. ~ 4 ~ T J g D O e , : 2 0 1 9 2 0 0 1 0 4 9 2 2 8 9 D 0 1

. 4 1 U g ~ S O 0 , . 3 ~ 7 9 0 6 D 0 , , J T O J 4 l l ) O o

. 3 ~ F ? ~ b O d , 0 3 1 J 2 7 3 D O * 0299dO4OOe

. 2 o 4 7 1 0 ~ * 02~4~b4DOo 0245U~OOOe

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. 1 ~ ? 1 7 0 ~ 0 * . i ~ i 6 o ~ 0 0 e 017644?DOe

0 4 8 9 7 1 0 D 0 , 0 4 b g 4 8 0 D O * . 4 4 9 2 4 6 D O e . J g A ~ 3 b D O , 0 3 7 4 5 1 8 0 0 e , 3 5 8 0 4 3 D O e . 3 i 4 | ? b O O o , 3 0 | 2 ~ 4 D d , e 2 8 9 2 0 8 D O * 0 2 5 7 2 3 7 D 0 J 0 2 4 7 8 b i D O e * 2 3 9 0 2 7 0 0 0 . ~ | ~ 3 ~ 0 0 e . 2 U 0 5 8 | 0 0 , 0 2 0 2 0 1 3 0 0 e e 1 8 4 3 6 2 U O , 0 | 7 9 0 8 4 0 0 , 0 1 7 4 0 7 4 D O e

, A 3 0 2 7 1 D O o " 0 4 1 8 # 3 6 D 0 , 0 3 o 3 g b 7 0 0 o 0 3 b O I 8 2 0 0 e . 2 9 ~ 7 4 1 0 0 e 0 2 8 8 5 1 9 0 0 * . 2 4 9 i S | D O e e24D~SbUOs 0 2 1 0 6 7 0 U 0 * . 2 0 4 | 6 0 D U .

W | Z ) 139 W t Z ) 140 U | Z ) 141 w ( Z ) 1 4 2 W ( Z | 1 4 3 V ( Z ) 144 W|Z ) 145 U ( Z ) 1 4 6 W ( Z ) 1 4 7 W(Z) 1 4 8 W(Z) 149 8 1 Z ) 1 5 0 W(Z) 151 W | Z ) 152 V ( Z ) 153 U ( Z | | 5 4 NCZ) 1 5 5 W¢Z) 156

o 3 3 6 7 9 9 0 0 , W | Z ) 1 5 8 , 2 7 7 8 6 5 0 0 e W(Z) 159 , 2 3 2 4 8 2 D 0 ~ W i Z ) 160 . 1 9 7 9 8 2 O D e W | Z ) 161 ' o 1 7 1 4 5 2 0 0 . V ( Z | 1 6 2

, 3 7 J | 5 3 0 0 9 , 3 6 ~ 3 8 6 0 0 , , 3 6 3 0 2 0 " D 0 , . 3 3 S 7 2 1 0 d * 0 3 2 5 4 4 6 D 0 o . 3 1 5 0 6 4 D O * , 2 6 4 7 3 1 0 U e . 2 7 5 1 7 4 0 0 m 0 2 6 5 Y 6 7 0 0 o , 2 4 0 5 7 ~ D O e e ~ 3 2 d 6 | D O t e 2 2 5 5 0 3 0 U e . 2 0 5 4 5 7 D O e . | 9 9 4 0 2 D 0 o , 1 9 3 6 3 4 D O e 0 1 7 7 ~ 1 U 0 0 . 0 1 7 3 1 4 7 D O e . L b 8 6 0 2 D O *

W(Z) 163 W | Z ) 164 wCZ) l b g W ( Z ) 1 6 6 U ( Z ) 1 6 7 W(Z1 1 6 8 W(Z) I b g UCZ| 170 W¢Z) 1 7 i WlZ1 172

64

AEDC-TR-76-12

I v G L k V ~ L ~ i

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& , l ~ 3 ~ U i b O e , i 0 1 4 ~ 4 D 0 /

DATA Z I ~ /

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t . 2 2 3 ~ 4 2 0 0 . , I V ? 8 2 7 0 0 ,

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0 2 1 J 2 2 J ~ .

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DATA Z I ~ / • . I d S J ~ g D d , • . | ~ u o 3 b O ~ + • . 2 1 1 0 + 7 D 0 ,

• .20111500, • . i d 3 ~ 3 ~ D O , • o l o : I ~ O D O * l . 1 4 + . l o O U /

O~TA L I T /

I . 1 7 . + + + + 0 0

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+ . l : ~ l l ~ O + + -

l . 1 4 1 + C I U J / UATA Z I + /

8LK DA[A

. 2 l ~ i 3 b D O ,

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. 2 7 7 4 0 7 0 0 ,

. 2 G b T b G U ~ , e l T ~ C C ~ O Q e

0 2 5 7 ~ 7 4 0 d e e ~ 3 ~ S t J O O t . ~ 6 0 2 1 3 D 0 , . 2 ~ b � ~ U G . 01S945~D0~ . I ~ 4 S C 3 D O *

. ~ S 4 3 1 0 0 e 0 ~ 5 4 7 8 4 b G ,

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. 1 ~ 2 S b 3 0 0 .

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e 2 2 ~ 3 6 2 b O o . 2 6 4 8 9 5 b O . . 2 ~ 8 6 9 5 0 0 . ° 2 | 3 ~ 8 6 0 0 , . 1 8 8 Z 0 8 0 0 . , 1 6 ~ b 0 2 ~ 0 ,

0 | ~ 2 4 7 D 0 , 0 2 3 0 6 7 8 0 0 , ° 2 2 3 7 1 0 0 0 , . 2 0 3 6 8 4 0 0 0 , i ~ 2 1 1 ~ D d , o 1 6 ~ 4 8 P b O 9

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bATE :n 7.5170 0 9 / 0 6 / 4 5

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£ 2 7 0 1 9 9 0 0 , ° 2 7 6 6 9 3 0 0 . . 2 4 7 6 2 8 0 0 o . 2 1 6 4 2 8 0 0 ~ 0 1 8 g 0 7 2 0 0 9 . 1 6 6 3 4 2 D 0 ,

* 2 3 9 7 ~ 3 0 0 . * ~ 5 3 4 6 | 0 0 m 0 2 3 3 8 1 3 0 0 . . Z O 7 9 1 2 D Q , . 1 8 . 3 5 9 9 0 0 e 0 1 6 2 6 8 1 0 0 ,

. 2 0 4 6 6 2 0 0 , o 2 3 1 3 8 S D 0 , 0 ~ 0 1 9 2 0 0 * ° 1 9 9 3 1 5 0 0 , . 1 7 7 9 8 5 0 0 ~ 0 | 5 8 8 8 3 0 0 0

0 1 7 3 8 6 5 0 0 , 0 2 1 0 6 6 4 0 0 . 0 2 0 6 9 0 2 0 0 * . 1 9 0 7 1 7 b 0 , 0 1 7 2 2 7 6 D 0 . . 1 ~ 4 9 7 b D 0 1

. 1 4 7 2 7 2 0 0 +

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. [ ~ 4 0 1 2 D O e

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.z+++sg9o. w(z+_+~9 * 2 5 3 6 9 7 D 0 * i ( Z ) I T S

_ . o 2 1 6 ~ 9 0 0 0 m l Z ) 176 0 1 6 9 0 1 4 0 0 , V l Z ) I T T 0 | 6 5 5 4 6 0 0 9 N I Z | | T 8

e I Z ) 1 ? 9 . . . . . . .~z) !s~

0 2 8 3 4 4 3 0 0 o WIZ) | 0 1 ._ ~ . . | 7 5 2 1 [ ~ o W(Z) 1 8 2

0 2 4 1 2 3 3 0 0 0 U I Z ) 183 0 2 1 0 5 8 7 0 0 0 W I Z | 184 0 1 8 4 1 6 5 0 0 0 I ( Z ) 185 • 1 6 2 3 1 0 0 0 , m l Z ) 186 " " - m ' l Z ) 187

WCZ) 188 . . . . . . . . . . . . . . . . . . . . . . 0 2 0 7 9 0 0 0 0 s W | Z ) 1 8 9 0 ~ 5 0 8 5 8 0 0 , N I Z J 1 9 0 • 2 2 8 T 3 3 0 0 e I I Z ) 1 0 1 e 2 0 2 8 1 8 0 0 * I | Z ) 192 0 | 7 9 | 3 1 0 0 ~ N ( Z ) 193 0 1 5 8 9 1 b D 0 0 W|ZJ 194 . . . . . . . . . . . . . . . . . . . . . . .

W i Z ) i g 5 W I Z ) 190

. 2 1 5 ? 1 1 0 0 ~ I l Z ) 197

. 2 3 0 8 2 6 0 0 e M ( Z ) | 9 6

. 2 | 6 3 4 0 0 0 0 I ( Z ) 109

. 1 9 4 9 4 T b 0 , U ( Z I 2 0 0

. 1 7 3 0 5 4 0 4 ) , W~Z) 2 0 | . 1 5 ~ 1 0 9 0 0 o V ( Z ) 2 0 2

W | Z ) 2 0 3 V ( Z ) 2O4

. J d o g 8 4 D b e W | Z ) 2 0 5

. ~ 1 1 8 4 6 0 0 J WIZ) 2 0 6

. 2 0 4 1 T 7 0 0 0 W(Z) 2 0 7

. 1 8 7 0 4 3 0 0 e M | Z | 2 0 0 e | 6 d 0 7 4 0 0 * W | Z ) 209 e | b 1 7 5 3 0 b . W(Z) 2 [ 0

I ( Z ) 2 | | V ( Z ) 2 1 2

. l b l ¥ 0 2 0 0 , M ( Z ) 2 1 3 * 1 9 4 0 4 9 0 0 , I I Z i 214 * ! ¥ 2 3 4 7 G 0 , M ( Z ) 2 1 5 . 1 7 g 1 7 2 0 0 , WlZ) 2 1 0 0 1 6 J J 3 0 0 0 e u ( Z ) 2 1 7 014UO3000J i ( Z ) 2 1 8

e c z ) 2 1 9 W ( Z ) 220

. i 3 g ? 1 7 0 0 o M I Z ) 221 0 1 7 7 5 1 3 0 0 * I ( Z ) 222 0 1 8 0 9 3 3 0 0 , V ( Z ) 223. , 1 7 1 3 9 0 0 0 0 V ( Z ) 2 2 4 . l ~ 7 ~ b E U O * W ( Z ) 2 2 5 . 1 4 4 2 4 3 b 0 1 N ( Z ) 2 2 6

WIZ) 2 2 7 B ( Z ) 228

65

AE DC-TR-76-12

IV G t.P..VI::L -'1

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OATA Z 4 ~ • e 5 F O U q ~ D O e . 4 ~ 7 7 4 4 0 G e e 4 3 J 4 4 ~ 0 0 , e 3 7 7 0 6 U O O e e J ~ | b 3 5 0 0 *

UI.K I~ATA DAT~ : 7 S 1 1 8 O ~ r O b / 4 :

t o~z i i5-~ t o l Z ) 454

i ( Z l 46e t o l Z ) 451 W I Z ) 451 I I Z i 45~ NCZ) 46C toCZ) 4 6

• . J 0 2 4 3 2 0 0 , 0 2 ~ 1 3 6 0 0 e e 2 3 0 o ~ o O U , 0 2 0 0 1 5 5 0 0 , e t + 5 0 0 ~ O e . . . . ~(.Z).46._2. * e J 6 0 o c O D O e o l 2 0 b E | U O o 0 1 3 6 7 U 6 0 0 e o l ~ 4 ~ 3 b D O e 0 | | 3 6 2 0 0 0 0 $ e | U S U ~ 4 0 u t o O g S b 6 i U O i e O ~ e O O | 0 O t e O 8 1 2 4 5 0 0 e o O T S t g o 0 0 1 • eO0~740UU0 0 0 6 4 8 4 2 D O e e U 6 0 4 0 9 0 0 9 o O ~ b 3 ~ | D d ~ eObZ741DOe • e u s g 4 1 ? O U e o04~JE4DGg e 0 4 3 0 U ~ 0 0 1 . 0 4 1 0 6 4 0 0 1 e O J 8 7 2 8 O O e • , 0 3 0 2 7 7 0 0 /

UArA Z 4 9 / • . ¢ O U 4 | ~ U O I .S~ZV3~OUe . S b ? : 6 g u o o . 4 0 2 | 0 4 0 0 . * J b 5 0 0 2 D O e • 031qd2~DOe , 2 0 0 2 g 0 ~ 0 t e 2 5 0 5 3 2 0 0 1 0 ~ 4 7 ~ 9 0 0 t 02@2429000 • . I b Z g 2 2 D U e * 1 6 5 0 6 8 0 C * . 1 0 U 8 7 7 U U , e 1 3 Y O b l O O e 0 1 2 0 9 7 1 0 0 e • . l I b ~ g 4 O U e . 1 0 6 3 5 ~ 0 0 , * U g S | O 3 O O e e U g 0 7 | O 0 0 t o O U S 0 6 8 G O e • .UFSOS~DUe . 0 7 2 b ~ C O G e eO677U~UOe e 0 0 3 3 4 2 0 0 1 0 0 ~ 9 ~ 9 8 D 0 , • e O ~ 5 0 i ~ O ! e 0 ~ 2 2 3 ~ 0 G 9 e C 4 g l S b O U 9 e 0 4 6 3 | 5 0 0 o e 0 4 3 7 0 0 0 0 9 • e 0 4 1 3 0 ~ 0 0 /

CATA Z ~ U / • e 6 1 0 1 4 c 0 0 0 . ~ J o d e T D G e e S F 2 7 7 J D U e e 4 1 0 4 9 1 0 0 , e 3 7 1 U 1 3 O O e • e 3 3 1 ~ 4 4 0 d t 1 2 ~ b b g 2 0 ~ l e Z b 6 4 2 7 U O e e 2 4 0 0 5 7 0 0 o *ZEFOUSOOe • 0 1 9 6 7 o ~ 0 G , . 1 7 8 9 g O D b e e l O 3 2 ~ 1 D O e 0 1 4 9 3 7 0 0 0 0 . 1 3 7 0 1 2 0 0 , • * 1 ~ 0 0 0 2 0 U o o | 1 6 1 ~ 4 D b e 0 1 0 7 ~ 4 0 0 0 e * 0 ~ 9 4 2 7 0 0 e 0 0 ~ 2 2 0 1 0 0 5 • e O d 5 o 4 ~ O e . 0 8 0 0 0 q ~ , e 0 7 4 7 1 2 0 0 , eO6Udg4DOt eOo~500D~e • . 0 0 1 4 8 0 0 0 9 e 0 5 7 8 1 1 0 0 0 e 0 5 4 4 3 ~ 0 0 1 . 0 5 1 3 3 0 0 0 5 . 0 4 d 4 U S O O e • 0 U 4 ~ = 1 0 0 /

u ~ r A Z ~ l / • . o 0 7 1 ~ 6 0 0 9 e 5 3 8 0 5 5 0 0 ~ 0 4 7 8 V 9 1 0 0 ~ o 4 2 7 2 2 5 D U e e 3 0 2 1 0 ~ 0 0 0 • e 3 4 ~ U / ~ 0 ~ e ~ C ~ 5 3 0 0 0 , 0 2 7 d 4 4 ~ e 0 2 5 2 0 2 4 0 0 e e2~U75MDOe • . 2 U ~ 2 | g O O e e l g O 0 3 b O 6 ~ e 1 7 3 8 ~ D d l 0 1 o 9 ~ 3 1 0 0 J e | 4 6 7 | 2 0 0 e • . i J b ~ 4 ~ U d , . 1 2 4 V 5 4 0 0 e . 1 1 5 7 0 2 0 0 e e l O F J b J O 0 ~ 0 0 9 ~ 2 4 0 0 1 l e d W 2 g g + U d l eO~bdOlOOv e 0 0 1 1 6 2 0 0 1 e O P O u 2 1 O O e 0 ~ 7 1 3 ~ 4 0 0 e • o J U F @ 2 4 0 U e e C b J O f f O O O t o d ~ g S ~ & D O t e U 5 6 1 1 8 0 O e e 0 5 3 0 4 1 0 0 t

UATA ~ 2 ~ • o = V 3 7 u i ~ d e eO320GgDUo . 4 7 7 4 3 0 U 0 , e 4 2 9 ~ 7 5 0 0 0 e3Ub777DOe • e J 4 9 2 ~ o 0 0 J o J i ~ | ~ e O O e 0 2 d o 8 1 ~ D O t e2ob84?OOe e 2 3 7 8 0 0 0 0 o • o ~ 1 7 J G ( O O e e J g g O S b O O e e | 8 ~ 7 4 2 D O e e 1 6 8 1 0 1 0 0 9 e 1 5 5 0 0 0 0 0 1 • 0 1 4 ~ 3 0 5 0 0 j . 1 3 5 7 1 1 ~ 0 , e i 2 3 1 ~ 7 O U e + 1 1 4 4 9 5 D 0 e e l O 6 b S O O O e • 0 0 ~ 9 ~ 3 0 0 j . o g J O ~ D O ; e O 8 7 | l b U U o e 0 8 1 7 0 0 0 0 9 " e 0 ? b r S J G O + • m d F ~ 2 ~ U ~ l 0 0 6 8 0 3 1 U O e eOO418000e 0 0 0 0 6 3 9 0 0 o e O ~ b J O O e

QATA Z 2 J 7 • e : 7 ~ J ~ F D O e e 5 1 f f Z ~ U ~ g e s o g i ~ f f D d e + 4 l b o b T O O e 0 ~ 0 6 4 1 2 0 0 e • o 3 ~ | 2 g ~ C e e 3 1 ~ l O b O e e 2 g J ~ = i O U + 0 ~ b 0 7 5 7 0 0 + 0 2 4 4 2 ~ 5 0 0 e • e J ~ S | ~ U U , e ~ O ~ i C S O 0 * e l ~ 8 7 U O O e e J T ~ 2 7 | O O e e l o 2 1 d O O O e • e l ~ d ~ U ~ O @ + . | J ~ 4 4 1 ~ O e e l ~ u d ~ O e e l ~ O ~ D O s e l i ~ 7 6 O D O e • e | u : q 1 1 0 0 , e d g e T b ~ O b e o O ; 2 ~ 0 2 D O e o 0 8 6 ~ b D O e 0 0 0 1 7 7 3 0 0 9 • oUT~U~¢O@t e O T ~ = J U O e e U b S ~ | 7 ~ O e e O b 4 8 ~ O O O e e 0 6 1 4 4 0 0 0 8 • . U = d ~ q J O d /

UATA Z ~ 4 /

t o ( Z l 4 6 ~ . . . . .w |Z l 4 6 4

I ( Z | 4 6 5 l i i ) 4 6 6 i ( Z ) 467 I I I Z I 466.'

- - w ( z ) " ~ ' ~ t o IZ ) 4 7 0 t 0 ( Z ) 471 ! t o ( Z ) 4 7 2 W(Z) 4 7 3 t o ( Z ) 4 ? 4 • ( z ) 475~ t o , - , i i Z l t o ( i ) 4 7 e I I Z ) 4 7 9 t o ( Z ) 4 8 0 i ( Z ) 451 to (Z ) 482 t l ( Z ) 4 8 3 t i l Z ) 484 aCZ) 4 0 ~ toKZ) 4 5 6 t o i Z ) 4 8 7 t o f Z ) 408 t o (Z ) 4 8 9 V l (Z ) 490 Iv ( Z ) ' 491 W(Z | 4 9 2 N ( Z ) 4 9 3 W ( Z ) 494 l l | Z ) 4 9 5 to (Z ) 4gb S ( Z ) 497 I ( Z ) 4 9 8 W(Z) 4 ~ 9 to (Z ) 500 W(Z I 501. i ( Z ) 5 0 2 VCZ) 5 0 3 i l Z ) ~04 to (Z ) 5 0 5 to(ZJ 5 0 o t o ( Z ) 5 0 7 i ( Z ) 5 0 8

70

A E B C - T R - 7 6 - 1 2

IV G L ~ V ~ L ~1 dLK DAIA UAT~ : ?51FU O ~ l O b l 4 b

• . J ~ u J l O u . . J 2 . ~ 6 d u O , , 2 ~ 3 b ~ 7 U O . . 2 7 0 0 4 u D 0 . e ~ 4 o 2 O O i t o ~ Z d ~ T O O t . 2 1 1 3 ~ 3 U 0 ~ e | Q ~ J V H O O t e lSOVbTO0~ e lO?~b3OO~ t , 1 ~ : ; 7 5 U ~ , 1 4 ~ i ~ 7 ~ , . 1 3 6 3 2 6 D @ , . 1 2 0 3 ~ 3 D ~ v . I I S I ~ u C O s # . l l U ¢ ~ J O O e , l ~ 3 7 b o U ~ e O Q 7 4 ~ D ~ e O g l i U b O O ~ eUUb37U~O~ • e U d I 4 ~ 7 U U o e l ? l ; J ~ D ~ o . U ¢ 2 7 ~ 2 D O e , U b O a b 3 O O t eOob2~bCOe

. : i ~ l i J D O e e ~ 7 ~ : J b U U ~ e ~ Q U O : D O e e 4 0 = O 2 3 O O t e37411UOOt e ~ 4 e l d O ~ o e ~ l d ~ 2 ~ b ~ e 2 ~ q ~ : O O e e 2 7 1 u l ~ O b 0 e 2 b O b ~ g G b ; e~J IUb~DG~ e 2 1 4 ~ 2 ~ U ~ e | 9 ~ 4 1 6 D U ~ . | d 5 2 V ~ O O e e | 7 ~ 4 Z 3 C O 0

# e a u U G ( d U d t ~ l ~ 7 U b ~ . I ~ L d 3 D U ~ e i 3 1 | U b D O e e1220bOOO~ • I L o 2 ~ U U O . e l C d J ~ D b e . A U I ~ I ~ U O . . O g l O l ~ O O . . ~ 9 U ~ b l O U e . U ~ g O ~ t e O ~ , , ~ e e O ~ T U ~ e e U T ~ 5 ~ 3 0 ~ e oDo~U34D~o

# . ~ o J ~ l U O e o 4 ~ I T ~ J U G e e 4 ~ | U T b D O e e 3 Y | b b ~ O U e o3b3U2UOOo , J J ~ 7 ~ U D U , e31J@S7DO~ e2~UO~TO~. . 2 T O v l 6 O O . e2~O~23DOs . 2 ~ J I ~ i D U . . 2 | c ; ~ 4 D ~ . . 2 O ~ G b T D U . . | 8 o 4 ~ 3 D ~ . . 1 7 b ~ b 2 C O .

t . l u 4 J q ~ O U s . l ~ J 7 7 J U ~ t e I ~ ¢ U : A D O t . 1 3 b i l 3 O O e e |Z68U3DOe e l i ~ 2 % e b d ~ e l I I ~ U 2 D U e e l U b ~ 4 ~ O U e e U ~ U T U D U e eOv4J4JOO~ . C o ~ 2 2 ~ J ~ .UU447~DG~ o O U O U b l b Q i eU?~9~OOOe . O ~ Z l ~ O O .

~ATA Z ~ 7 / • ; ¢ : | ~ o 4 D O e . 4 2 ~ | ~ U ~ t e4UOUJ?DOe e J T b g l X D O ~ e3518u3DOe

. 3 2 ~ 7 7 7 0 0 e ~ 3 C ~ S O D U ~ . 2 d O ~ | T D O * e Z ~ T J T U O ~ , e24~55OD~e ; e~JJOGQbUo e ~ | 7 0 ) o U O ~ e~U3494DUo e |~O3U4OUe . 1 7 8 2 7 : 0 0 ,

• 1o¥092Du~ . l ~ b T ¢ : U C e e * 4 7 ~ 2 6 D U t . 1 3 8 4 1 2 D O e o | 3 U ~ O 2 D O I t e 1 2 2 7 2 3 D d ~ . I I U 7 4 4 D G ~ e l U ~ 2 7 7 D ~ , e lU32UUDOD eU97713DOe

• UVg~41DO, . O ~ T T ~ D U , .OU32oCDUe . 0 7 V U b ~ D O t * 0 7 5 1 ~ 1 0 0 e

U~TA Z ~ 8 / • e~2038U~Oe * 4 0 U ? 4 3 D O e . 3 8 G | b | D O . e 4 0 9 3 | ~ O O 9 o3~80~ODUI • e J I ~ b ~ 4 D U t * 2 ~ 9 2 1 l D O e e2UOO4bOOt e 2 ~ 4 1 8 O U e * 1 4 ? O l 2 O O t

• ~ J I ~ 3 U ~ . . 2 | 7 ~ 3 D b . e203~47DU~ ; l Y I 3 o b U O ~ . | T Y T o 2 C Q e + e l u d g ~ O U O I e i S ~ 9 ~ O O I . 1 4 ~ I F 4 O u e o J A I O 4 ~ O O J o I ~ 3 0 J 3 G O o • . 1 2 = 5 ; O D O . . I i f f t 7 4 D G . . 1 1 2 2 4 3 C U . 0 1 U 6 2 6 0 D O . . l O 0 0 8 ~ D O . • e O ~ 4 Q Q ~ e .O~CbbGDOe oUd~ I43GUD o U ~ I g ~ D U e oU7?gU2OOJ

DATA ~ / • J ~ l ~ l O U e o ~ 7 o ~ | 4 D O e oJS¥721DOe e34247~DOe . 3 ~ 4 9 6 b U @ , • 3O7bOQDO* . 2 ~ d O 1 3 D O * e2741~OOOD e 2 5 8 4 3 1 D U e . 2 4 3 4 3 9 G d *

• e 4 2 V 2 4 4 0 0 * . 2 1 5 0 E T D { . . Z O 3 2 7 2 D U v . 1 9 1 ; 7 1 U 0 . e l~O42bCOe • o l T o ~ V g D O e o I ~ G A ~ T D O t e l o l l ~ O D O e o 1 4 3 0 O 3 D O t o13623~DOe • e l ~ T b J I O d e . | ; | l | ~ O e e | | 4 7 b | C Q , o | O ~ d 2 7 D U D . I U 3 2 8 ~ 0 0 . t . 0 9 8 | C 7 D u , e O ~ J 2 ~ D G e oOUb73bDOe e D ~ 4 4 9 3 0 0 ~ . U ~ O ~ l g D O 0 • e k T ~ T g 4 O O /

DATA Z~O/ e 3 6 4 4 J ~ D 0 9 . J S J Q e o D O e e 3 4 0 U ~ O O ; . 3 2 b ~ 7 3 D O e 0 3 1 1 1 0 1 U O e

# e ~ O ~ 4 O ~ e 2 ~ 1 3 ~ D O e . ~ 6 O u ~ D U e e ~ b 2 o d J U O ~ e2JgOoTDOe e 2 2 6 0 4 6 0 U e , 2 1 3 0 5 O U O e e 2 u l ~ l i O U e 0 1 9 0 8 2 1 O O e . l ~ O J o T D o t

; .&TG534DO~ . | b | J U O D O e e | 5 2 6 3 7 D O , e i 4 4 ~ l O D O e e l ~ b g O U D d . e | ~ 7 8 ; U ~ e o | 2 J | { ~ J G I e l | b ~ 5 8 ~ O t e | | [ O O 3 O d o e l O S S l V D O e

$ . I U ~ 3 ? ~ D O , * O g 5 6 5 8 U U * *O~ I@37DO. . O u u F ~ 4 D U t .OU2609UOe • . O T U u t S D u /

DATA Z ¢ i /

wCZ) DO9 w ( Z ) b l O w ( Z ) 511 w ( Z ) 51~ . ( Z ) b13 w ( Z ) 5 1 4 w l Z ) h i 5 w ( Z ) 5 1 o W | Z ) b | 7 U f Z ) 510 WCZ) I~!9 w ( Z ) ~2U re(Z) 521 W(Z) "-22 WIZ) b 2 3 W(Z) 5 2 4 W(Z) . b 2 5 W(Z) ~ 2 o W(Z) ~27 W(Z) 5 2 8 ~ ( Z ) 529 i l Z J b30 N ( Z ) 531 W I Z ) .~32 W(Z) 5 3 J t e l Z ) 534 w ( Z ) ~ 3 5 W(Z) 53(= U ( Z ) b37 d ( Z ) 538 m ( Z i 53Q W(Z) : 4 0 ill ( Z ) b41 WIZ) b42 re (Z) b43 W( Z ) ,~¢,4 a ( Z l ~45 I ( Z ) 54o w ( Z ) 547 w,(Z) 54ts w ( Z ) b4,~ m ( Z ) bbu W(Z) b51

w ( Z ) 5";3 m I Z ) 5~4 W(Z I bS~ w ( Z ) 55r w ( Z ) ~,=7 w ( Z ) 5 5 8 i ( Z ) 559 W(Z) 5bu w ( Z ) 5 o l W(Z) oh2 w ( Z ) 563 w ( Z ) 564

7]

AEOC-TR-76-12

| V G L E V b L 21 bLK D A | A DArE : 7 5 1 7 0 0 9 S 0 t ) / 4 ~

• 0 3 4 0 0 2 6 0 ~ e . 3 3 1 5 f f 3 0 G . . J 2 1 J 3 2 D O e 0 3 0 9 d 3 1 0 0 , . 297529DOm * . A E 4 7 8 6 D ~ o 0 2 7 | b e l O O e 0 2 b 9 0 3 | D 0 1 0 2 4 6 J g b D O 9 . Z J 4 U U b O U I * 0 2 2 2 2 1 3 0 0 o 0 2 | 0 8 C b D O e * i V 9 ~ d A U U e e l d g b A Q O O , * i 7 9 0 8 1 D U 0 * . | 7 0 J T I D Q , . 1 C 1 5 7 2 D C , 0 | 5 3 2 7 4 0 0 , . J 4 5 4 0 7 0 0 8 . 1 3 8 1 0 0 0 0 , * 0 1 3 1 1 8 0 0 0 , 0 1 2 4 6 7 4 D G 0 . L i D + b T O O , * 1 1 2 d l O D O e . 1 0 7 4 0 8 0 0 , * * l O 2 3 2 ~ O * * d ~ 7 5 5 4 D O o *G~3U~ADUe * 0 8 8 d ~ T D O e oO8405gOO* * 0 0 8 1 1 1 3 0 0 /

DATA Z c 2 / 4

* . 3 1 ~ 0 7 3 D 0 o . 3 1 | D e b U G , 0 3 0 3 8 0 4 0 0 8 . 2 9 4 ~ 7 # D 0 + 0 ~ 8 4 3 2 7 0 0 t • o2734EADO, . J 6 2 3 C 6 D O e o 2 5 i O I b O o , o 2 3 9 7 Y 2 D O , . 2 2 8 7 0 3 D 0 9 * * ~ I F Q O 4 O O I 0 2 ¢ 7 4 4 2 D ~ + e 1 9 7 3 o 6 D d * .LUTPOSDOm 0 1 7 8 4 7 8 D 0 . • . I b g h ~ i O O + 0 1 ~ 1 3 4 3 D U , * | b 3 4 2 g c o e . I A b g J u D O . 0 1 3 8 8 5 6 0 0 e l . | 3 2 1 ¢ 4 D 0 o . 1 2 5 8 4 g D U o 0 1 1 9 6 9 1 0 0 . 0 1 1 4 2 7 2 0 0 , . 1 0 ~ 0 7 3 D 0 0 • o10Jb?TOOo 0 U 9 9 2 0 ~ 0 t o094U22DOs e O 9 0 0 J | D O o eUDb677DOe

*DSJ~44DUJ DATA Z ~ 3 /

• .AMU408bU0 eAbJ ;dAOO+ 0 2 8 7 7 7 1 D U . e A ~ 0 2 J ~ D U , . A 7 | 7 1 0 D U , • * ~ 0 2 4 9 ~ 0 0 s 0 2 ~ 2 8 4 4 D 0 , . ~ 4 2 9 ~ F G d + * 2 3 2 9 ~ 8 ~ 0 8 0 2 2 3 0 3 7 0 0 9 • 0 2 1 ~ 0 3 D ~ . 2 9 3 ~ 9 2 D C + . 1 Q 4 4 1 0 D 0 e e | 8 5 ~ 4 6 D 0 8 0 | 7 6 6 2 7 0 0 8 * * |OD~CgDO9 e lbOODObO, . | ~ 3 | ~ l O O , e I 4 0 0 0 V D O e . 1 ~ 9 2 1 7 D 0 0 • 0 1 3 2 7 7 3 0 0 + 0 1 2 6 0 6 7 D 0 , . l J O U d S O O o . 1 1 6 4 1 3 0 0 , 0 1 1 0 2 3 6 0 0 e • * 1 0 ~ 3 3 ~ D 0 e * |CO~CSDG, . 0 9 6 J J O O O , 0 0 9 2 1 0 9 0 0 0 . 0 ~ 8 ~ 3 D 0 1 * . 0 ~ 4 0 ~ 8 0 0 /

DAIA z e 4 / • . 2 8 1 0 ~ 6 D 0 ~ . 2 7 7 7 9 5 D u + *~7~G6~Dde . 2 0 0 8 6 5 D 0 . . 2 ~ 9 7 7 5 D 0 o • * 2 ~ 1 ~ 3 0 0 8 0 2 4 ~ b | T D O . 0 2 3 4 ~ S ~ D O J * 2 2 0 1 | | 0 0 8 0 2 1 7 2 1 ~ 0 0 + • 0 2 0 8 3 7 ( D 0 8 * l S ; O ¢ G O U 9 * l ~ l 1 3 3 D U e . l + ~ 8 4 U O O o . | ? 4 0 1 4 ~ 0 8 ~ _ . l b T G T ~ U O e * | ~ 0 4 b O G o . L S A ~ Z o U U , . 1 4 5 7 ~ 1 D 0 9 . 1 ~ 2 2 9 D 0 8 * . 1 3 3 0 4 ~ 0 0 , o 1 2 7 1 6 1 D C . . | 2 1 5 0 9 D 0 , . l 1 6 2 5 8 D O e . l i l 2 l D D O e * * l U O + 3 o D 0 e * 1 0 1 ; ~ 1 D 0 9 . 0 9 7 0 0 1 D 0 9 . 0 ~ 3 0 2 3 D 0 , . 0 U 9 6 0 8 D 0 , • . 0 ~ 5 ~ 9 2 D 0 /

DATA Z 6 ~ / • * ~ 5 2 2 0 0 , * 2 ~ J A O l O C * * 2 ~ 9 ~ 3 5 0 0 , . 2 5 4 4 7 8 D Q ~ . ~ 4 8 5 0 0 D O ~

. ~ 4 1 ~ | 4 0 0 ~ * 2 J 4 7 1 4 D G , 0 2 ~ 7 1 Z g D U , 0 2 | 9 3 0 2 D 0 , 0 2 | | 3 4 9 D O 9 • 0 2 0 3 J + D D U . . | , 2 4 3 8 D O . . 1 8 7 6 0 0 D 0 , . 1 7 9 9 b S D O . . I 7 2 0 X O D O . * 0 1 6 5 2 H I D U . . L S ~ A S S O O , 0 1 5 1 5 7 0 0 0 . . 1 4 5 1 2 0 D O . . | 3 8 0 3 3 D 0 9 * * 1 3 3 0 1 5 D d e * J ~ ? J e 3 U G 9 . 1 2 | U 7 2 D O o . l l b 8 3 4 D O , . l l l ~ 4 Z O O e • . i 0 7 2 8 b U 0 8 * lU~ f fS~OOo 0 0 9 8 0 4 8 D 0 0 0 0 9 4 ~ 4 0 0 0 ~ e 0 0 0 8 4 2 D 0 ~ * * 0 8 7 2 2 7 D 0 /

DATA Z ~ 6 / - - + - . 2 5 | ' ? 2 3 D 0 ; - ; 2 ~ O ~ G D C . . 2 4 7 ¢ 9 2 0 0 8 . 2 , 3 0 4 2 D 0 . . 2 J 8 0 9 2 0 0 .

* . 2 3 2 4 2 0 0 d , , 2 2 ~ ! S 0 0 C , . 2 1 9 5 4 6 0 0 , . 2 1 2 o 1 4 D O e . 2 0 5 5 0 4 0 0 ~ • . | 9 0 3 0 7 ~ D e * 1 S I O 9 9 D C 0 . 1 8 3 9 4 J O O ~ 01FO88VDO0 e | O ~ U 7 7 0 0 , * . 1 0 3 2 3 7 0 0 . . I ~ 6 0 V A D O . 8 1 5 0 3 ~ 9 D 0 , . 1 4 4 2 4 ~ D O s . 1 3 8 3 0 8 D ~ , • . 1 3 2 ? ~ 0 0 0 , . L ~ 7 3 0 ~ O O , 0 1 2 2 1 Z I O O e . | | 7 | 6 4 D 0 e . 1 1 ~ 4 2 8 C 0 ,

DATA Z e T / • * 2 3 ~ 4 0 3 D 0 , * 2 3 0 1 8 7 D 0 + . 2 3 5 8 3 8 D 0 , * 2 ~ 2 ~ 0 ~ D 0 * . 2 2 8 3 3 7 D O t @ 0 2 ~ J 4 8 2 D O * * 2 1 8 0 7 7 D 0 9 * 2 | 2 2 4 7 0 0 j e 2 0 6 1 0 3 D 0 8 * | 9 9 7 4 4 D O * * 0 1 9 3 2 5 5 0 0 e . | e 0 7 C ? O O , * | D U l o J O O e 0 1 7 3 6 7 0 D 0 , . 1 0 7 2 7 D C O e • * l o U g + b D O , 0 1 0 4 8 7 2 D G ~ . 1 4 0 0 1 0 D O e . 1 4 3 1 4 7 0 0 . . 1 ~ 7 ~ 0 9 D 0 ,

* . L u ~ a 2 2 D O . * I C A I 3 b D G e . 1 0 0 1 3 3 D 0 e * 0 9 0 3 0 9 0 0 , .OUAb~TUO, • 0 ~ 8 9 1 7 0 D 0 /

DA~A ZOO/

w l Z ) 5 0 5 w l z , ) 5 0 6

u ( z ) 5 6 8 v i ( z ) Doe w ¢ z ) 5 1 0 w l Z ) 571 V l (Z ) 572 I I Z ) .~73 Ill ( Z ) 5 7 4 W l Z ) 5 7 0 w ( Z ) 570,.. w ( Z ) 577 W I Z | 570 I | Z ) 5 7 9 V ( Z ) 580 w ( Z ) 581 w ( Z ) ' ; 82 u ( Z ) 0 8 3 w ( Z ) 584 w ( Z ) 5 8 5 u ( z ) 5 8 6 w ( z ) 5 8 7 v ( ZJ 5 8 8 W(Z) 58g W(Z) 5 g o w l Z ) 5 9 1 B I Z ) 092 i D l Z l 5 9 3 t l ( Z ) 594 W | Z I 5 9 5 u l Z ) 5 9 6 w I Z ) 5 9 7 t~ lZ ) 5 9 8 u I +," ) ~,gqJ . I Z ) 6 0 0 W l Z ) QOl w I Z ) 602 tv(Z ) 6 0 3 t v l Z ) 6 0 4 w | z ) QO.~ V ( Z ) 6 0 6 UCZ) 601# w ( Z ) b u s w I Z ) (~O9 V ( Z ) * t O tD(Z) b | 1 W(Z) b 1 2 v ( Z ) 6 1 3 N | Z ) 6 1 4 WCZ) 6 1 5 W(Z) 6 1 b w t z j 6"17- Il l |Z) 6 1 6 l l ( Z ) 619

V ( Z ) (120

72

A E D C - T R - 7 6 - 1 2

IV b L ~ V b L 21 ULK DATA " ' D A T b : 7 5 1 7 ~

* e J J d J 5 5 0 0 . * 2 2 7 4 5 ~ G , . ~ 2 ~ 5 ~ U D 0 ~ e ~ 2 2 8 0 0 0 0 , e ~ 1 9 2 6 8 0 0 ~ • * ~ 1 5 0 V 3 U O e . 2 1 G 3 d F D O e e 2 O b 2 5 8 U O e * l V 9 8 0 4 D O , e i g 4 1 1 | D O e • . l ~ f f 2 f i d O ~ , e I ~ 2 3 1 1 D G o e l r 6 3 2 ~ D O e e | 7 0 3 5 7 0 0 * e I o 4 4 3 8 D O e • . | b D b O 4 D @ , ° ; ~ f f ~ U G I * ~ 4 ? 2 ~ D O , _ , ~ | 4 | d S I D O . o | J 6 5 7 1 D O o • 0 1 3 1 4 6 9 0 0 , * 1 2 6 5 2 ~ D 0 , . 1 2 1 7 6 ~ U Q e * 1 | 7 | 6 0 0 0 e . 1 | 2 7 7 ~ 0 0 , * 0 1 0 8 5 q ¢ D 0 , ° I G q 4 ~ U D b e * 1 0 0 6 ~ 1 0 0 . *ODDS?bOO, . O V 3 3 1 U O O , • . o E g ~ 8 D D /

DATA Z 6 U / * 0 2 1 8 3 ~ U D ~ , 0 2 1 7 7 2 ~ 0 6 0 . 2 1 6 1 8 1 0 0 , 0 2 1 3 ~ 5 6 0 0 0 0 2 1 0 8 4 3 0 0 , * * 2 0 7 2 3 2 0 0 , . 2 U 3 1 1 ~ 0 0 0 * | g 8 6 9 4 0 0 , 0 1 9 ~ 7 4 1 0 0 , . | 8 8 6 3 ~ 0 0 e

- i - - 0 - 1 6 d 3 5 4 ~ 0 ~ - ~I-77VSQDO'3----;I?24EODO;-'%-16-699000;"~|61519000- • . l S b O g g O 0 , e I E O 7 ~ U O G e * | 4 5 5 1 8 0 0 . * i 4 0 3 9 5 0 0 . * 1 3 ~ 4 d 3 O U e • 0 1 J d S ~ 3 0 0 , . 1 2 : d ~ | O G e * 1 2 1 J O J O O e . 1 | 6 9 1 1 0 0 t . | 1 2 6 7 6 6 0 e • * l O D ~ g ? O O * 0 1 0 4 6 7 4 0 U 9 . l O O g O b o O , . d D r 2 0 4 0 0 t * 0 ~ 3 6 1 0 0 0 , * . 0 9 0 4 7 g D U /

U A I A Z T O / * 0 2 0 V 3 7 7 0 0 ~ 0 2 0 ~ d 5 4 D U , * 2 0 7 ~ 7 7 0 U . 0 2 0 5 6 0 7 0 0 , e 2 O 3 O I 4 D O e • * i Q ~ d 7 3 U O e * 1 S 6 2 6 ~ 0 0 , * | g 2 Z S b U O e e ! 8 7 9 2 7 0 0 . 0 1 8 3 3 4 4 6 0 , • 0 1 7 8 5 6 e 0 0 , 0 1 7 J a 5 4 0 0 , 0 1 6 8 6 5 1 D 0 , . | 6 3 6 0 3 0 0 . * | ~ 8 5 4 7 0 0 t • * 1 ~ 3 ~ 1 5 0 0 , e l i ~ 3 4 D U 9 * 1 4 3 0 2 6 0 0 , o | 3 8 d U 7 0 0 , 0 1 3 4 0 9 4 C 0 . • * | ~ U 4 g U U U . * 1 2 5 0 2 T D O e * i Z G b U d D O . e l l b 4 8 4 D O e * l | 2 4 1 0 0 0 g • * i U 0 4 ~ 3 0 0 9 * 1 0 4 7 0 7 U C , * i O I O S O C U . * 0 9 7 5 4 6 0 0 . * 0 9 4 1 6 8 0 0 , * ° G g o g ~ i D O /

DATA L T I / * e 2 U l | ~ ? O 0 , 0 2 6 0 7 4 ~ 0 0 , * l g g b b g D O , * l U 7 9 0 0 0 0 e e | Q S T J 2 0 0 , • * i ~ 8 4 0 0 , * l ~ g T g f f b C . * l d 6 2 3 9 D O e * 1 8 2 3 6 8 0 0 . o 1 7 8 2 4 3 6 0 0 • . 1 7 3 g | o D O e * i e ~ 4 4 5 0 6 . 0 1 6 4 d 6 6 0 0 . * 1 6 0 2 2 3 0 0 , 0 1 5 5 5 ~ i 0 0 , • . | b U O U 0 0 0 , * | 4 ~ Z 3 0 U O . * 1 4 l b t O D O . o 1 3 7 1 | 3 0 0 0 0 1 3 2 6 6 7 0 0 0 • . i 2 d J l ? G O . e | ~ 4 0 7 1 D G , ° | l g G 3 6 D O , . 1 1 5 ~ | 9 0 0 , * I | Z u Z 3 O O , • * | 0 8 ~ 4 ~ U U o . i C 4 6 0 G ~ U e e 1 0 | 0 7 6 0 0 , e U ~ 7 o 7 4 D U , oUU4, , J9500 , • * Q ~ | 2 3 6 0 U /

UAIA Z T ~ / • . l ~ o J O b u e * | ~ J ~ 0 0 , 0 1 ~ J 7 6 0 U , 0 1 9 0 9 1 5 0 0 , o l f f d g b l D O , • . l ~ 6 ~ 3 2 O d e e I ~ 3 7 L ~ D ~ m * 1 ~ 0 5 3 ~ 6 0 e . 1 7 7 0 6 1 0 U , 0 1 7 3 3 4 0 0 0 e t . | o ; 4 1 d D O e * | ~ J 3 ; O 0 , ° 1 6 1 1 4 5 0 0 . * | b ~ 7 2 0 0 . 0 1 5 2 5 5 3 0 0 0 • , ~ 4 f f ~ i F O U , e [ A J f f e ~ O e * I ~ : U H ~ U * 0 | 3 6 ~ 3 5 0 0 , e I 3 | | A b D O e • * 1 2 7 U 3 1 0 0 t , [ 2 3 ~ J U O e . I i ~ 0 6 U D O , 0 1 1 5 2 3 3 0 0 e * 1 1 1 5 0 3 0 0 e • * | U T U U I ~ U ~ e l C ~ 7 O ~ O . * 1 0 0 ~ 6 9 D O e * O ~ ? 0 8 U O O e 0 0 ~ 4 : 0 ~ 0 0 ~ • . U ~ 1 4 3 4 0 0 /

D~r~ ~ 7 3 / * | d o T O ¢ D O , ,|ba¢~l~O, * i o o b J O O O , * 1 6 4 ~ o A O O e . | d ~ 6 ~ b D O e

• o i d b 4 d G O O e * I 7 7 9 7 0 0 0 , . I ? b | 2 U D d , 0 1 7 2 0 ~ 3 D 0 , * | 6 8 6 J 7 D D J • . I o b U 7 ~ D u , . | ~ 1 3 4 ~ D u o * i ~ T b U 2 D O , 0 1 ~ 3 5 6 7 0 0 . 0 1 4 9 ~ 7 2 0 0 w • * l ~ b b 4 b D O . e l 4 1 ~ l ~ b ~ e * 1 3 7 ~ d U D O e * 1 3 3 4 9 6 ~ 0 e * 1 2 g ~ 4 f l O O e • * 1 2 5 6 ~ 0 0 0 , * 1 2 1 ~ 4 0 D 6 , * 1 1 8 0 ¥ g 0 0 . ° 1 1 4 4 4 2 D 0 , . l | O ~ 7 b ~ O . • * 1 0 7 4 0 J D ~ e * 1 0 4 0 2 7 0 ~ . . l b O 7 ~ l D O , * O g F o 7 5 D d 9 * O ~ 4 4 g v D o , • . Q D I = ~ J D U /

~ATA Z 7 4 / * . | a ~ G ~ u , . i e O U ~ l ~ U o 0 1 7 ~ 3 6 ~ D 0 , 0 1 7 U 2 4 5 6 0 e , 1 7 6 7 | 5 0 0 e • 017¢UOffDU, e | 7 2 o C ~ D U . * l T O O O b U O , . 1 6 7 | ~ 4 0 0 e 0 | b 4 | 3 2 6 0 e @ . [ o U f f e ~ U U e . l ~ F q ~ C D b e ° 1 5 3 9 4 ~ D O e 0 | 5 0 3 ~ 0 0 ~ , . 1 4 o b ~ D O , • e 1 4 ~ 6 ~ 2 0 0 , . 1 3 ~ 1 2 0 0 0 , . | 3 b J ~ T D O , . 1 3 l o O g D o e . 1 2 7 0 9 2 0 ~ g • * | 2 q 2 I U D O e . 12UoOODO, * | 1 7 0 4 5 0 U e * 1 1 ~ b 6 0 0 0 e * l l O l b ~ D d e • * IOUU2FDOo * | U 3 b ~ 6 D U , o t U O A J 3 D U , * O V F 3 o U D d , * 0 0 4 3 9 6 0 0 e • * d g l § | J D O /

U ~ ; A L 7 ~ /

qlJ(Z 9 6 2 1 W ( Z ) 6 2 2 w ( Z ) 6 2 3 .w!z.) .6~ If (J[ I 6 2 5 w | Z | 6 2 6 i ( Z ) 6 2 7 V f Z ) 6 2 6 wKZ) 6 2 9 W(Z) 6. t0 I I ( Z ) 6 3 J i C Z ) 6 3 2 N ( Z | 6 3 3 i g (Z ) 6 3 4 I ICZ) 6 3 S . V I Z J 6 3 6 i ( i l 6 3 7 l l ( Z | 6.36 U ( Z I 6 3 9 l l l Z ) 6 4 0 I l l (Z) 641 W | Z ) 6 4 2 WIZ) 643 I f ( Z ) Q44 "*( Z ) 6 4 6 w ( Z ) 6 4 6 WCZ) 647 I ( Z ) 64,H, I f ( Z ) 6 4 9 I ( Z ) 050 I ( Z ) " o51 i ( Z ) 6 5 2 W(Z I 6 5 3 111(7) 6 5 4 rd (Z) a b b

I ( Z ) 6 6 6 w l Z J 6~7 i I Z ) 6 5 8 w ( Z ) o b g l i ( Z ) 660 WIZJ 6 6 II W(Z) 6 6 2 i i Z I 6 6 3 II ( ,7.. ) 61~4 I ( Z ) 6 6 6 I ( Z ) 66~ W(Z) 6 6 7 i ( Z I 6 6 6 I ( Z ) 6 6 9 WIZ) 6 7 0 I ( Z ) 0 7 1 N ( Z ) o 7 2 t I Z ) 6 7 3 t l ( Z J) 6 7 4 ' W ( Z ) 6 ? 5 w ( Z ) 6 7 6

?3

A E D C - T R - 7 6 - 1 2

iV G L E V E L 21 BLK DATA DAll'-i~"--m 1 .511 '6 09~04v~6S

. 1 7 6 3 6 2 0 0 ~ - . 1 7 4 1 f 1 2 D 0 , . 1 7 3 5 4 2 0 0 , . 1 7 2 5 6 5 0 0 0 . l ? l l D l O 0 ,

• . 1 5 6 6 5 8 0 0 J . 1 5 3 7 6 . 8 0 0 . 0 1 5 0 4 9 0 0 0 , . 1 4 7 1 4 1 0 0 . . 1 4 3 7 1 7 0 0 0 • . 1 4 0 2 3 9 0 0 . . 1 3 6 7 3 1 0 0 . * 1 3 3 2 0 9 0 0 * 0 1 2 9 6 9 1 0 0 * 0 1 2 6 1 9 2 D 0 ,

14161'3 1141Z1 i | Z ) tJ lzJ 6811 I l l l 61i~11

• 0 1 2 2 7 2 . . 4 1 ) 0 , . . . l l g 2 g 6 D O , . 1 1 5 9 1 9 D 0 0 0 1 1 2 6 0 2 D 0 , 0 1 0 g . t 4 9 D O * • . 1 0 6 1 6 6 D 0 6 . l C 3 0 f i T D O o * l O O 0 2 6 D O * . 0 9 7 0 7 3 0 0 * , 0 9 4 2 0 2 D 0 , • , 0 ~ 1 4 1 3 ~ 0 / M I Z I 68-11

DATA Z T 6 / v C z J 684; • . 1 6 8 8 3 0 ~ 0 ~ * 1 ~ 8 6 4 5 0 0 * . 1 6 ~ 1 0 2 0 0 , . | 6 7 2 ~ 2 0 0 , . 1 6 0 9 9 0 0 0 ~ M I Z J 6 0 ~

. 1 6 4 4 5 6 0 0 , . ! 6 2 O 3 3 0 0 , . 1 6 0 5 4 8 0 0 9 . 1 5 6 2 2 7 0 0 , . 1 5 0 6 9 6 0 0 , M ( Z ) 6 ~ 1 • . 1 ~ @ 8 0 0 . . 1 5 0 1 2 4 U 0 , . 1 4 7 1 3 2 0 0 e 0 1 4 4 0 3 8 0 0 e 0 | 4 0 8 6 ~ 0 0 , U I Z | 0 ~ • ~ . 1 3 7 6 2 ~ D 0 0 _ . . 1 3 . _ 4 ~ I _ 5 4 0 0 , . 1 3 1 0 5 6 D 0 , . 1 2 7 7 6 5 0 0 , . 1 2 4 4 6 0 0 0 , e l Z l 6 8 8 • . 1 2 1 1 d ~ O + , . l i T g 4 0 D O , . 1 1 4 7 3 5 0 0 0 * 1 1 1 5 7 6 0 0 * 0 1 0 8 4 7 4 D 0 o I l Z ) 61~ . • . i 0 5 4 3 1 D 0 , . 1 0 2 4 5 1 0 0 * . 0 9 9 5 3 8 0 0 , . 0 9 6 6 9 6 0 0 * 009~J12700* M I Z ) 6 9 0 • 0 0 9 1 2 3 0 D 0 / N I Z ) 691

DATA Z T T / M ( Z | 6 ~ • . 1 6 3 6 6 2 D 0 * . 1 0 3 4 g 0 0 0 o . 1 6 . . t 0 1 1 0 0 o , i 6 2 6 1 1 0 0 e * 1 6 1 1 1 1 0 0 *

* . 1 4 U 2 7 1 0 0 , . 1 4 6 6 3 7 D G , * 1 4 3 8 7 0 0 0 0 * 1 4 1 0 1 4 0 0 0 . 1 3 0 0 6 7 0 0 * • * ! 3 5 0 5 6 0 0 , _ . *1319@g000 . * ! 2 6 0 1 3 0 0 * . | 2 f i 6 1 2 0 0 * . 1 2 2 ? 0 9 0 0 0 • . I 1 9 6 1 7 0 0 ~ . 1 1 6 5 4 5 0 0 . o 1 1 3 5 0 3 0 0 0 . 1 1 0 5 0 0 0 0 , . I 0 7 5 4 0 0 0 ~

" * 0 1 0 4 6 3 1 0 0 , . 1 0 1 7 7 7 0 0 , * 0 9 8 9 8 1 0 0 * * 0 9 6 2 4 7 0 0 * , 0 9 3 6 7 7 8 0 ,

w | Z ) 6 9 3 v ( Z | 6 9 4 E ( Z I 6 9 8 mCZ) 6 9 6

W I Z ) 6941 * . O g O ~ 7 3 D O /

QATA Z T U / * ' . 1 ~ e ~ 0 ~ - . I ~ . - - - ~ e ~ 3 - ~ O . - - ~ S T S I : O D . . I S 6 6 1 6 0 0 .

. ~ . ib~26000~__?J~376..GD.__Oe _ ~ 1 5 2 0 . 1 4 D 0 , . 1 S O l O 2 D O e . 1 4 7 9 8 5 0 0 , * , 1 4 5 7 0 3 0 0 , , 1 4 3 2 7 7 0 0 , 0 1 4 0 7 2 7 D 0 0 , 1 3 6 0 ? 4 0 0 e * 1 3 5 3 3 6 0 0 * 4 . 1 3 2 5 3 0 0 0 o * l ~ g 6 7 4 0 0 6 . 1 2 6 7 8 2 D 0 e * i 2 3 6 6 9 0 0 * . . | 2 0 9 4 7 0 0 0

W I Z ) 6 9 g WCZ) ? 0 0 + ( Z | T O I D i l l 70J l W i l l 7 0 3 W I Z I ~04

* . i 1 8 0 2 7 0 0 e . I 1 5 1 2 0 0 0 . . 1 1 2 2 3 4 0 0 , * 1 0 9 3 ? 7 0 0 * . 1 0 6 6 6 6 0 0 e * . 1 0 3 7 7 1 0 0 , ,1~1C440__0~... ~ 0 9 0 3 6 2 0 0 * . 0 9 6 7 3 4 0 0 , * 0 9 3 1 6 2 0 0 o • . O U U b 4 9 0 0 /

DATA Z 7 9 /

m i l l 7 0 8 l l Z | 7 0 6 V l Z | 7 0 ? W I Z | 7 0 0 m l Z ) 7 0 9 I l Z ) 7 1 0

* , | 4 2 2 7 6 0 0 , , 1 4 0 0 3 g D 0 , , | 3 7 6 ~ 0 0 0 6 * 1 3 5 2 1 8 0 0 m , 1 3 2 6 7 1 0 0 o .* .E~UU~4DU* . 1 2 7 3 6 4 0 0 , , 1 2 4 6 7 3 0 0 0 , 1 2 1 9 3 5 0 0 6 , 1 1 9 1 6 2 0 0 e * . 1 1 6 4 2 5 D 0 , . A I J 6 7 3 0 0 6 . 1 1 0 9 3 5 0 0 e . 1 0 8 2 1 6 0 0 6 . 1 0 5 5 3 0 0 0 6 • . 1 0 2 8 7 5 0 0 . . I C O 2 ~ O D G * * 0 9 7 6 8 8 0 0 * e 0 9 5 1 6 3 0 0 * . 0 9 Z 6 6 6 D 0 * * . G V O 2 b b O U /

DATA Z e O / ' "

w l Z ) 711 I ( Z J 7 1 2 W(ZJ 713 I ( Z ) 7 1 6 I ( Z ) 7 I S I ( Z ! 7 1 6

* . i 4 g g g 2 D U , . | 4 g ~ 7 1 0 0 , . 1 4 9 5 1 0 D 0 , . 1 4 8 9 1 3 0 0 , * i 4 8 0 8 8 D 0 o * . 1 4 7 0 4 4 0 U , . 1 4 5 7 S 2 D 0 , . 1 4 4 3 4 6 0 0 . . 1 4 2 7 2 1 0 0 , . 1 4 0 9 3 1 0 0 * • " ~ A 3 U g g 3 D O ~ " . 1 ~ 6 9 2 2 0 0 , " . 1 3 4 7 3 5 0 0 , . 1 3 2 6 4 6 0 0 , , 1 3 0 0 7 6 0 0 , * . 1 2 7 6 3 3 0 0 1 . 1 2 5 1 3 3 0 0 , . 1 2 2 5 9 | D 0 e . 1 2 0 0 1 b O O e * 1 1 7 4 2 2 0 0 o • . I 1 4 ~ 1 7 D 0 , . 1 1 ~ 2 1 2 0 0 , . | 0 9 6 | 4 0 0 , . i 0 7 0 3 1 D 0 . e | 0 4 4 6 9 0 0 0

* . 0 8 ~ 8 2 ~ 0 0 / END

U ( Z | 717 l l ¢ZJ T i e U t Z ) i r l g re(Z) 720 e l ( Z ) 7 2 1 l l ( Z ) 7 2 2 W(Z) 72.1 I I | • ) 724

?4

A E D C - T R - 7 6 - 1 2

i v G ~ V E L i l M A I ~ ~ATE : ? b l # o O 9 # i i / | U

~ 1 ~ 7

C U U 3 ~

C L C C

C L C

U E M ~ N S I O h H ' : A D $ i 2 @ ) DiMJ-'~,al3r~ ~ , T S T O i ~ ( 3 , ' ) o c h S T L & I 3 b ) •TAI. , .~T1`(3@| u I M ~ . N S i U N ANGle r 'S )0 ) • H T ( ~ ' : U U i , P L C I , X ( - ' . ~ u O ) giJl,.r.TY ( - ~ S t # 0 i t

• XIJL T ( ,~ ) • Y P L ' / ( 4 ) •dl.,/'-I- ( J UGrJ) N C A ~ E : -'j | oTA,.e It= i .~rMAA:- - I U0Ge m k l T ~ ' | c • ~ 1 ~ , 2 7 | I'L,F.4A r ( 1 1 , 1 / / / )

L A L L P L U i | G e w - | 2 * * J ) t .A l .L .PLUT( 0e • - 1 | • : • 2 3 J

~* .A~ IN ~ J ~ T ~ U L PANAN~T~H~

RL;AU ( 2. C, ~-/~rJ: 41"J~q ) S L ] T t H L T N | h I I=LTNAX •DF-LPLT • D L A ~ I Y I q G T e h L i i~,l"$ • ~"NOi i l L i TA• I~L.• i P L U T I , | P L G 1 -~ ,W eL i,k ~ • Ai , l l t I Ml: i • I 'AU • l I- r.A O S

T i , I A F = ( - i ) l i t . l ~ 2

Hr-AU ] h I A V ~ N ~ , M U c R . I [RAI~SMISSEON P A i . q S . COI~,VERT IAVI-NUNBE.qS Tu WAVI:LF__NGTh ANO 13P..T(-'RMi~,E I~AX|I~U~ "lrI~AI~,SNJSS[r,N

UO d 3 7 | C A k l O = i , l ~ L i k r - S hlL, AD | ~=0 |ANG( I C A R ~ i • H T I I CARD) I F | HT( I ~ A I 4 1 D ) . L T e 0 w JHlr( [ ( , .AkU| : U * STMAX=AMAX I I STMAX I H T i ]CARD ) | ANG( | CAJ41)ia=( | o E ~ U S ) / A N G I i (,Ak~UJ

8 3 7 CONT |N t , E NLASE=~ .CASEt i I I : N L i h E S

P&. I'M | N : A N G ( I ) Pi.. T M A X = A N G | | I I i I D E : - ' . I D L . A N P i T H [ N : P L T M | 1~"-2 • i l [ 0 " : PLTMA Jt : P L lrMA , I t+2. l l l l [ D~ I )~ .LTA : b T MA X / t ; .

3,~, LUNT INUE

PRO~UCP. lrHl~ ZP~RU S L I T i I~JTH PLGTS iHF .k | P L O T i a I

I P I I P L O l r i e E O e O J G U |U o o O O I T,= ST~ I PL T MA X'-IJL T,~| k i / U k L P L T [ L G = T b S T i~. G= I L G t ; ~ L ~ = I L G ~ P I . T I 4 I : P t . TN i N XPLlr ( 4 I~-D~LPL. T YPLT/, 3 I : O * Y P L T ( 4 )mO~" LTA dOUZIr. : YPLT I 4 J l | C* (, ,Al i AJiJ S I l l * t l i le • Ilia Ill l l - - | iHLGl lOe t X P L T I I 3 1 *XPLTI I4 ,1 r i O * ) Y,I=,i.T i I I*'l Oe I)O 5 0 l : h l l l

"/5

AE DC-TR-76-12

]iV G LbVI~L 21 M A I N

Gu TO g 9 ! 7 7 | JL:KKOUNI"- !

N : / E T T R A F : . ~ T R A F SDLAM OG 8 8 [ - - - I o k

8 d I~.i.0T,X| | ) = P L G T X ( | ) * T I R A F TEST= I PL. TNA X- -PLTM| h J / U E L P L ~ | L G = T~- ST | L G = | L G + ~ RLG= I L G

C C C C

8 0 0

S u |

~ b 3 9 5

C C C

6 6 0 0 2

4 ~ 4 L C C

" O g / l | / I S

/O~'-TERMIN/: Thk. MAXIMUM VALtJE C/; TH f" SPECTRAL CLJmV I~ AND | F T H | S I--, TPE F I H S T CUkVE ~.OMPUTI-'D. THL= y A X I S SCAL i: FACTOR I S CALCULATED

SF)NAX : : ' - | 0 U * Di) tS0U X : I t N I F ( P L G 1 r Y I I r ) e L I [ e S P M A , V . ) G O TG 800" : ) P M A X : P L O T Y | ir j ~.(JNT |NUE I F ( ] STA~Tef -U e i J OraL ~ P : S P N A X t 1fHGT

P L U T Y | N~ | ) = 0 . P L O T Y ( N + 2 I = O E L Y P PL, UT X (N+ | ) = P L TM i N PLGTX( N+ 2 J = D [ : L P L T VAL HA X= II 0e OPLOT Y( N~2 J bO D53(~ ~' M U N D A Y = I s N ]F (PI .O TY( MONOA Y ) • GT * VA L~A,~) PLCTY (NONDAY) 4V JkLNA& CUN 1" IN ~E N P ~ = N + 2 VlI<IT/:(40)NP2,(PLOT,~CL),PLC/Y(L)eL=|,kp2I

PRUt)UC/: A SEPARATE PLOT FOR EACH VALI~F. OF iF.k0 ElF | P L O T 2 m |

| P ( ZPLOT2eEQeOJGO 16 ~bCGZ CALL A . ~ | S | U e t U e , O A t t - I L t6LGo0e,PLGlrX(N+II)ePLOTX(N~2JD|0eJ) CALL b y J 4 1 ~ . O L | o § t ; • 0 9 0 1 0 l N O = J t 0 e l 3 ) ~.ALL P L T F L T ( o ( } e ~ ' 0 0 r - 0 • e [ k C o G * t 3 ) ( .ALL L | N , - ( PLCJTJCtPL-~[YgNt I t U t l ) CALL P L U T ( R L G ~ 2 e , O e C t - - J ) " t.~JN T |N~E I S T A ~ I : O "CArdS [R ( NCA S I" ) : T A U hT ~'TQH | NCA '~'E l : SPMA X / D / : L Y P ENbTOR(NCA$ f- )=ENO GO rO ~ d 3 a ~ LONT INUE

PkODUCb THi: 4F]~NAL SPECTRA F L C |

~.ALL AX i S ( C • sue t * l lA vr--LEkGTH *,--IL 0 ,RLG t O . , P L T M | N o Ur-LPLlr e i O , J) t .ALL SYM: IUL | • c ' t S * ( ~ , . l tHEAU. .c tO, t 8 0 ) L A L L '**YI.16OL( e ' t ~ * 5 * * | t I T F ' : * * O * t 3 ) ~.ALL N~,~4uER i - - U * t - t J . ~- U , t T F . , 0 . , - -1 ) CALL SYMUUL( e S t ; e 3 t • ! , e | A : e , ( J e t 3 J L A L L NU(4DERIL-U• t - - ( Joe - -Co i T A t O J s - l t ) ( .ALL S Y M U G L ( e . ~ , 5 . 1 t e . I , ~ t L = r o g e r 3 |

77

A E D C - T R - 7 6 - 1 2

I v G L~VLL

7b

| 5 0

4g~5 4997

21 MAIN UATE m ? 6 I l a

CArL NUNt:~R(--0e , - Q o w - - 0 , e E L I 0 e e l ) CALL 5YNBQL(e.'~•~'eg••Ee3HA*=•0**3) CAI.L NUNB*'I~|--O, •--~*m--Oe eApRIINtoOe oSJ) , CN.I.. S Y N 8 O L ( - - , . ~ e ~ ! 1 5 , 6 , 7 , , I * * ...NQ. _..M.AX HT_...lr_A_U_*oO,.,I_.gJ) CALL SYNiS0L( - - . 2 t JS71 .~oS . .~bse | ,e | X N ) ° , 0 * * 1 3 | UI3 7U I= IoN( .AS~ Y t l : 8 , ~ - , I...Oi CALL PL IF I . T ( - - e J I . , g I I f o Y I o e l e J : k , I I i l I I ( i | IO* e:~l • ,.ALL N~MEI~:R( * 4 ; l g l 4 t Y I l e . l * I ' I ISTC;R( I I oOe o; l l CALL ;~t.Nk:~R(leOlll~rlo¥lteleTAL,:~ll;(lJ,Oe?3).. CQNT|NUE ENOI = IL l [ 40 Rt= It.iNO 40 R EA~ ( 4 C, END=49Y ... | N P 2 , ( PLOT 1 ( L ) , P L Q I Y I L l o L a I *NPd?. J) N=NP2--2 CALL:..L INE.(P.L.O. T x ,PLOTY, .N , l •0 , | | GO lO l f O CALL.. PLO.T( RLG~'~• * 0 • *--3J. CALL P L o l r ( u . 0 , g s t ; ) STOP ~NO

O ~ I i / 1 8

78

AEDC-TR-76-12

NOM ENCLATUR E

ui, u. J Ivj

kuj, ku i

1]

I o o vj

Y~, Y? 1

(A S u liD,

(A sUj)D

K

Ts

hl s, Ma

C

ku~, k o • u i

a

Y

tO

(AaUj)D"

(AaUi) D

T r a n s m i s s i o n of s p e c t r a l l i ne ( d e s i g n a t e d j) t h r o u g h a m e d i u m , i n t e n s i t y un i t s

-1 W a v e n u m b e r of the i th o r j th s p e c t r a l l ine , cm

I n t e n s i t y of s o u r c e s p e c t r a l l i ne at w a v e n u m b e r , uj, i n t e n s i t y un i t s

A b s o r p t i o n coe f f i c i en t fo r the s p e c t r a l l i ne at wave- n u m b e r , vj o r u i, cm -1

A b s o r p t i o n pa th length , c m

-1 W a v e n u m b e r , em

I n t e n s i t y of s o u r c e s p e c t r a l l i ne at c e n t e r w a v e n u m b e r , o vj, i n t e n s i t y un i t s

C e n t e r w a v e n u m b e r of the i th o r j th s p e c t r a l l ine , -1 cm

Doppler width at half maximum intensity of the ith or jth source spectral line, cm-i

Boltzmann's constant, 0.6952 cm -I K -I

Temperature of gas in light source, K

Mass of molecules in light source and absorber, respectively, gm

Velocity of light, 3 x 1010 cm/sec

Absorption coefficient at center wavenumber, • -1 cm

O vj or u i,

Spectral line broadening parameter (ratio of collisional to Doppler line widths)

Dummy variable of integration

2(u.- vq) Doppler frequency function, J J

(AaUj)D

Doppler width at half maximum absorption coefficient, ku_?, of the ith or jth absorption line, cm-I

J

79

AEOC-TR-76-12

(~aVj) L

Z L

Ta

TA u

Av

e

m

Nj ,,

f j ' j ,,

h

Bv o

j ,t

F(J "9

No

f • $• v v

u j , j ,,

V • i • v v

~j,,j ,

S

N~

Lorentz width at half maximum intensity of the jth absorbing spectral line, cm -1

Effective collision frequency for spectral line broadening, sec- 1

Temperature of absorber gas, °K

Transmission over the frequency interval &v t h r o u g h a m e d i u m , i n t ens i ty un i t s

T r a n s m i s s i v i t y o v e r the f r e q u e n c y i n t e r v a l Av; r a t io of inc iden t to t r a n s m i t t e d in t ens i ty

W a v e n u m b e r i n c r e m e n t , c m - 1

E l e c t r o n i c cha rge , 4 .80 x 10 -10 esu

E l e c t r o n m a s s , 9 .11 x 10 -28 gm

N u m b e r d e n s i t y of m o l e c u l e s in the l o w e r s ta te , J ' ; c m - 3

O s c i l l a t o r s t r e n g t h fo r the t r a n s i t i o n f r o m the uppe r s t a te J ' to the l o w e r s t a te J "

P l a n c k ' s cons tan t , 6. 625 x 10 -27 e r g sec

Ro ta t iona l cons t an t for the vth v i b r a t i o n a l s t a t e (g round s ta te , v = 0), c m - 1

Rota t iona l quan tum n u m b e r fo r the l o w e r s t a te

Rota t iona l e n e r g y of the J " t h r o t a t i o n a l s ta te , c m - 1

Tota l n u m b e r dens i ty of m o l e c u l e s , c m -3 0

Band o s c i l l a t o r s t r e n g t h fo r the v ~. ,v t r a n s i t i o n

W a v e n u m b e r of the l ine c o r r e s p o n d i n g to the t r a n s i - t i o n v ' J ' - ~ v " J '~ c m -1

W a v e n u m b e r at the b a n d h e a d of the (v ' , v " ) band, -1 a m

Rota t iona l s t r eng th , o r HGnl-London fac tor , f o r the v ' J " - v " J " v i b r a t i o n a l - r o t a t i o n a l t r a n s i t i o n

Tota l e l e c t r o n spin quan tum n u m b e r

N u m b e r dens i t y of m o l e c u l e s ~ o t h e r than the a b s o r b - ing m o l e c u l e in the a b s o r b i n g m e d i u m , c m - 3

80

AEDC-TR-76-12

2

~.? ]

P.~

C. J

C

Effective collisional cross section for the broadening process by the £th type molecule, cm 2

Mass of the ~th type molecule, gm

Wavelength at line center of the jth spectral line,

Partial pressure of the £th type molecule, torr

Mass of the fth type molecule, gm

Line broadening constant for the jth spectral line, K/torr or K/atm

Average line broadening constant for all spectral lines in a given band, K/atm

cm

81

transmission of doppler broadened resonance radiation

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