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AEDC-TR-69-
VOLUME IV
ARCH e COeY
NOT LOA~
¢
TABLES OF EQUILIBRIUMTHERMODYNAMIC
PROPERTIES OF AIR
VOLUME IV. CONSTANTTEMPERATUREWITH
SPECIFIC HEAT AND SPEED OF SOUND DATA
Herbert S. Brahinsky and Charles A. Neel
ARO, Inc.
April 1969
This document has been approved for public release
and sale; its distribution is unlimited.
VON K~I,RM~,N GAS DYNAMICS FACILITY
ARNOLD ENGINEERING DEVELOPMENT CENTER
AIR FORCE SYSTEMS COMMAND
ARNOLD AIR FORCE STATION, TENNESSEE
PROPERTY OF U. S. AIR FORCE ~DC LIBRARY F40600-69-C-
NOTICES
When U. S. Government drawings specifications, or uther 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 rights or permission to manufacture, use, or s e l l any patented invention that may in any way be related thereto.
Qualified users may obtain copies of this report from the Defense Documentation Center,
| References to named commercial products in this report are not to be considered in any s e n s e as an [ endorsement of the product by the United States .Air Force or the Government.
I
FOREWORD
T h e work r e p o r t e d h e r e i n was s p o n s o r e d by H e a d q u a r t e r s , 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 (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 63101F.
The t a b u l a t i o n s w e r e m a d e 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 u n d e r C o n t r a c t
F 4 0 6 0 0 - 6 9 - C - 0 0 0 1. T h e y w e r e m a d e between J a n u a r y 1966 and J a n u a r y 1968 u n d e r ARO P r o j e c t No. VJ3921, and the m a n u s c r i p t was s u b m i t t e d for p u b l i c a t i o n on M a r c h 14, 1969.
This t e c h n i c a l r e p o r t has been r e v i e w e d and is approved.
E l m e r E. Goins Captain, USAF T e c h n i c a l F a c i l i t y D e v e l o p m e n t D i v i s i o n D i r e c t o r a t e of P l a n s and T e c h n o l o g y
E d w a r d R. Feicht
Colonel, U S A F
Director of Plans
and Technology
ii
ABSTRACT
E q u i l i b r i u m t h e r m o d y n a m i c data a r e p r e s e n t e d for a i r f r o m a
t e m p e r a t u r e of 100 to 15,000°K and f r o m a log p of - 7. 0 to 3.0, w h e r e
p i s ' d e n s i t y in a m a g a t s. T h e s e data a r e t a b u l a t e d at c o n s t a n t t e m p e r a -
t u r e with d e n s i t y i n c r e m e n t e d. The dependent p a r a m e t e r s a r e log P,
Z, C p / R , C v / R , ~, ~E' and A/AA. S e v e r a l s o u r c e s w e r e used in
a s s e m b l i n g the data.
iii
CONSTANTS FOR USE WITH AIR TABLES
T o =
G r a v i t a t i o n a l C o n s t a n t =
1 B t u =
2 7 3. 1 5 ° K
32. 174 f t / s e c 2
778. 158 f t - l b
P o =
,y=
AA -
m~
M o l e c u l a r W e i g h t =
R =
1 g m - c a l = 42, 6 9 8. 8 g m - c m
1 g m / c m 3 = 62. 4283 l b / f t 3
1. 0 a t m
1. 03323 x 103 g m / c m 2
14. 6959 p s i
2 1 1 6. 2 2 p s f
760 m m Hg
1. 013246 x 105 n e w t o n s / m 2
1. 4 f o r AA c a l c u l a t i o n
1087. 334 f t / s e c
331. 419 m / s e c
1. 98726 g m - c a l / g m - m o l e °K
o r B t u / l b - m o l e °R
= 6. 86043 x 10. 2 g m - c a l / g m °K
o r B t u / l b °R
3091. 694 f t 2 / s e c 2 °K
1 7 1 7. 6 0 8 f t 2 / s e c 2 °R
3. 6 6 0 9 9 x 10. 3 a t m / a m a g a t °K
Po = 1. 0^ a m a g a t
4. 4 5 8 4 8 x 10 - 5 1. 2 9 1 4 9 x 10 - 3
8.
2.
g m - m o l e / c m 3
g m / c m 3
06254 x 10. 2 l b / f t 3
50592 x 10. 3 s l u g s / f t 3
v i
DISCUSSION
A c c u r a t e t h e r m o d y n a m i c data a r e of obvious i m p o r t a n c e for m o d e r n - day g a s d y n a m i c s t u d i e s. In a c c o r d a n c e with this p h i l o s o p h y , the A r n o l d Engi.neering D e v e l o p m e n t C e n t e r has s p o n s o r e d m u c h of the w o r k of the N a t i o n a l B u r e a u of S t a n d a r d s (NBS) in p r o d u c i n g and p u b l i s h i n g the t h e r m o d y n a m i c p r o p e r t i e s of s e v e r a l g a s e s , an e x a m p l e of which is the AEDC r e p o r t of I-Iilsenrath and Klein (Ref. 1) for a i r. In Ref. 1 the data a r e p r e s e n t e d in t a b l e s of c o n s t a n t t e m p e r a t u r e with the i n d e p e n d e n t v a r i a b l e being log p and the dependent v a r i a b l e s being Z, E / R T , H / R T , S / R : log P, and .Z*. T h e s e data include d i s s o c i a t i o n , i o n i z a t i o n , and s e c o n d v i r i a l c o r r e c t i o n s. The data of H u m p h r e y and N e e l (Ref. 2), which a r e b a s e d in p a r t on the work of Din (Ref. 3), a r e in the s a m e f o r m a t as the NBS data but c o v e r the l o w e r t e m p e r a t u r e r a n g e. T h e d a t a of G r a b a u and B r a h i n s k y (Ref. 4) e x t r a p o l a t e d the e x i s t i n g data to high d e n s i t i e s for the m i d r a n g e of t e m p e r a t u r e s , and t h e s e data a r e a l s o in the s a m e f o r m a t as the NBS data. However, it is d e s i r a b l e to have the above data in d i f f e r e n t f o r m a t s f r o m that n o r m a l l y found in m o s t NBS r e p o r t s , n a m e l y t e m p e r a t u r e v e r s u s d e n s i t y. F o r e x a m p l e , i n t e r p o l a t i o n s at c o n s t a n t p r e s s u r e (Ref. 5) and c o n s t a n t e n t r o p y (Ref. 6) g r e a t l y s i m p l i f y n o r m a l s h o c k c r o s s i n g and i s e n t r o p i c e x p a n s i o n c a l c u - l a t i o n s ; interpolat,ed s p e e d of sound and s p e c i f i c heat data a r e a l s o of g r e a t value. Hence: a p r o j e c t has been u n d e r t a k e n at the AEDC to a s s e m b l e the a b o v e - d e s c r i b e d data in v a r i o u s f o r m a t s by i n t e r p o l a t i n g t h e b a s i c data (NBS f o r m a t ) using the f o u r - p o i n t L a g r a n g e i n t e r p o l a t i o n f o r m u l a d e s c r i b e d by L e w i s and Neel (Ref. 7).
T a b l e I p r e s e n t s t h e s e data f r o m 100 to 15, 000°K in i n c r e m e n t s of 100 deg o v e r a v a r y i n g d e n s i t y r a n g e between a log p of - 7. 0 and a log p of 3.0 in i n c r e m e n t s of 0. 2 in log p, w h e r e d e n s i t y is in a m a g a t s. E a c h s e t of data is at a c o n s t a n t t e m p e r a t u r e with d e n s i t y i n c r e m e n t e d. The dependent p a r a m e t e r s a r e log P, Z, C p / R , C v / R , y, 7E, and
A/AA in t h a t o r d e r. C o n s t a n t s for r e d u c i n g the data to v a r i o u s d i m e n - s i o n a l units a r e found in the n o m e n c l a t u r e.
REFERENCES
. (^) H i l s e n r a t h : J.. and Klein, M. " T a b l e s of T h e r m o d y n a m i c P r o p e r - t i e s of A i r in C h e m i c a l E q u i l i b r i u m I n c l u d i n g Second V i r i a l C o r r e c t i o n s f r o m 1500°K t o 1 5 , 0 0 0 ° K. " A E D C - T R - 6 5 - 5 8 (AD612301), M a r c h 1965.
vii
TABLE I
THERMODYNAMIC DATA AT CONSTANT TEMPERATURE WITH SPECIFIC
HEAT AND SPEED OF SOUND DATA FOR AIR
i x
LOG RHO
-I.
-1,6C
0.8C
LOG P
-5, R
- 3. B 3 6 4
-2. m.
- 8 3 6 4
- 1 , 5 3 6 5
- 1 , 4 3 6 6
- 1 , 2 3 6 8 -I. ° 3 6 9 -0, R 376
- 6384
- 4 3 9 2
- 2 4 1 0
- 0 4 4 5
- I ~ 9 6 O. 3423 0 , 5 2 9 0
Z
l. O O O O
- 3 9 0 9 l.OOO? 1,~ I , ~ 0 9 ~
1, t. P O 0 ~ [.90nD I , ~ 0 0 0 l. O O O 0 1.000~ l.OOqO l.O I. ~ 0 ~ 0
- 3 0 0 0
- 0 0 9 0
- 0 0 0 0
!. 9 0 0 0
- 0 0 0 0 l. O00O ~. 9 9 9 9 ~. 9 9 9 5
- q 9 9 7
- 9 9 R 9
- 9 ~ 8 5 ~. 9 9 R 2 9 , 9 9 6 6
- 9 9 4 7 3.q
- 9 8 8 8
- 9 8 1 4
- 9 6 8 4 ~. ~. 9 2 3 6
I
3 , 4 O L R
4 q ~ 8
4 ~ 1 8
4 9 1 8
4 9! 8 3 , 4 9! 8 ~,3,, 491 8 ~. 4 9 1 8 ~ '. 4 9! 8 3,491a 3.491~ 3.491~ 3 , 4 9! 8 ~ , 4 9! 8
4 9 1 8
4 9! 8
4 9 1 8
4 9 1 8 3. 4 9 ] 8
4 9 1 8
4 9 1 8
4 9 1 8
4 9 2 4 3 , 4 9 3 0 3 , 4 9 3 6 3 , 4 9 4 2 3 , 4 9 4 8 3 , 4 9 7 9
3 , 5 0 4 4 3 , 5 1 4 6 3 , 5 6 1 7 3 , 5 9 5 4 3 , 6 2 0 4 0,
I
V/R
2. 4 B 5 0
2. 4 R 3 5
GAMMA
m.O ].
1 , 4 0 ~ 5 1 , 4 0 4 5 I. 4 0 4 5 i • ¢,
- 4 0 4 5 1.40" 5 1.4P l. 4045
- 4 n 4 5
- 4 0 4 5 1.401.
- 4 0 4 5 I ° 4 0 4 5 1.4C
!. 4 0 4 5 !,4('-' ]. 4 0 4 5
4 0 4 9
4058
1.409o
- 4 1 8 7
- 4 4 0 0
GA MMA-E
I.
1.401S
I.
I.
1,401R
I ,
I. 4 ~ 1 6
I. 4 0 1 ~
I .49 !~
I.
I .4016'
1.4o I .4C I. 4 0 2 1
- 4 0 7 3 1. 4 0 2 ~ I. 4 0 2 7 I. 4027 1 , 4 0 Z 3 I. I. I. I.
- 4 0 2 3 I ° I. 1, I. 3 9 7 7
AIAA
0.6C
n.6~ 9.6C
~. D. ~.
- 6 0 5 4
- 6 C 5 4 0.6P ?.6C
9.6C ~.
- 6 ~ 5 4 0.6C 3.6~ 0.~C
- 6 0 5 4
- 6 9 5 4
- 6 0 5 5
- 6 3 5 5
- 6 0 5 5
- 6 r 5 6 ,~.6C 9.6C 0.6C ?. 6 ~ 5 3
- 6 0 5 1
- 6 0 5 0 ~. 6 9 4 g
- 6 0 4 0
- 6 0 3 4 0.6=
- 5 9 8 9
- 5 9 5 3 0.5' ?.
LOG RHO
LOG P
- q 3 5 4
- 7 3 5 4
- 5 3 5 4
- 6 , 1 3 5 4
- 9 3 5 4
- 7 3 5 4
- 5 3 5 4
- ~ 3 5 4
Z
l.O00n
l.OOO
!. 0 0 0 0 !. 9 0 0 0 l. O 0 0 0 1.009~
T ~ CPIR n.@
- 4 9 2 8
- 4 9 3 3
- 4 9 3 3
- 4 9 3 3
- 4 Q 3 3
- 4 9 3 3 3.. 4 9 3 3
- 4 9 3 3
- 4 9 3 3
CV/R
- 4 g 4 7
- 4 9 4 7
. 4 q 4 7 ?. 4 9 4 7 ?.
- 4 g ~ 7 2.4~
2. 4 9 4 7
GAMMA
I .40Dl !. 4 9 0 3
1.403~ I. 1.40,') 1,40D 1.4C !. 4 0 0 3
GA
I
l 1
M M A - E
.4nlO
1. 4 n 1 4
I , 4 0 1 4 I , 4 n 1 4 I.
A I A A
P. 8 5 6 1
~. 8 5 ~ I
n. 8 ~ 6 1
- 8 5 6 1
LOG RHO
- 8 n -3. -3.~ -3. -3.~n
- 6 0 -!. 4 0
- 2 9
- 3 0
- 8 0 -0.
- 4 0
- 2 0
- 3
0.~ ~. 6 0
- ~ 0
1, 1,
- 3 0
- 2 0
- 6 0
- 8 0
- 0 0
LOG P
- I. 9 5 9 0
- I. 7590
-I • 5590
- I • 15g
- 9 5 9 0 - 0. 7 5 go
- 5 5 9 1
- 0 , 3 5 9 1
- 3 , 1 5 9 1
- 0 4 0 6
- 4 ~ 9 R
- 6 4 0 4 O, 8 4 0 1 1.03o
- 2 3 8 9 I.~
I. R 3 6 9 - 0 3 9 3
- 2 5 0 7
- 4 9 1 8
- 3 6 3 8
- 1 3 1 1
Z
I , ~ 3 0 n I , ~ 0 0 0 1, !,OOOO 1, ! , 0 0 3 0 ! , 0 3 0 0 1.003 n !. 3 3 } 0
!. 3 0 0 0
- 3 o 3 3 I. ~ 9 3 3 !. 3 0 3 0 1,000~
1, ~,
- 9 9 9 9
- 9 9 9 9 ~ , 9 9 9 8
- 9 9 9 8 ~. 9 9 9 8 ~. g 9 7 q
- ~ 9 9 2
- 9 9 7 5 ~, ~. 9 9 3 9
- 9 9 2 3
- 9 9 1 2
- 9 9 6 7
- 0 2 3 3
- 1 2 4 8 1,
- 3 3 5 l 12,
T~ £PIR
- 5 0 4 2
- 5 9 4 2
- 5 3 4 2
- 5 0 4 2 3 , 5 0 4 2
- 5 ~ 4 2
- 5 3 4 2
- 5 0 4 2 ~ 3. 5 3 4 3
- 5 0 4 4
- 5 0 4 4 3 , 5 0 4 6 ?. 5 0 4 8 ~. 5 0 5 6
- 5 0 ~ q
- 5 ~ 6 6
- 5 3 9 5
- 5 1 1 4 3, 3,52O
- 5 2 9 8
- 5 4 6 0
- 5 7 3 9 3 , 6 1 6 8
- 6 8 5 3
- 7 9 8 6
- 9 9 5 t
- 2 9 0 9
- 5 8 5 2
- 0 1 3 6
- 7 4 3 7
- 4 9 7 0
- 0
3n CV/R
- 5 0 2 6
- 5 0 2 6
- 5 0 2 6
- 5 0 2 6
- 5 C 2 6
- 5 0? 6
- 5 ~ 2 6
- 5 0 2 6
- 5 0 2 6
- 5 0 2 6
- 5 0 2 6
- 5 0 2 6
- ~ C 2 6
- 5 ~ 2 6
- 5 0 2 6
- 5 0 2 5
- 5 0 2 6
- 5 0 2 7
- 5 0 2 6
- 5 0 2 5
2.s
Z. 5 1 4 6
GAMMA
l. I D r : 2
4002 1.40C
4 0 r > 1.40"~ 2 !. 6 0 0 2
4 0 ~ 2
I. 1, 1.
- 4 0 0 3
- 4 0 C 4
- 4 0 0 3 1, 1.400S 1, 1, 1,
- 4 0 1 6
- 4 0 3 0
- 4 0 1 7
I. 4 C 9 2 I. ~ 1 3 0 - 4 2 1 3
- 4 3 2 7
- 4 5 2 6
- 4 8 4 3 1.54!
- 6 1 6 7 1, 1, 1, 3, 0,
GAMMA-E
I ,
I • 3997
I • 3 0 9 8
I ,
I ,
I. 3 9 9 g
- 3 9 9 5 I. 3 9 9 5
- 3 9 9 6 I , 1. 3 9 9 5 1 , 3 9 9 3 1 • 390. !. 4 0 0 5
- 4 0 1 8 I. 4 0 3 4 I. 4 C 5 5 1, 1,
1 , 4 6 8 4 1, 1.60~, I. 7 7 2 0 2,
- 8 8 3 1
- 6 3 4 3 D.O
A/AA
I , ~ 4 7 9
l o 0 4 7 7 t. 0 4 7 7 1 , 3 4 8 1
- 2 4 8 5
- 3 4 o 6
- 3 5 3 5
- 3 5 4 9 !. 3 5 9 8
- 0 6 9 0 !. 3 9 6 0
- 1 2 0 2 1, 1,
- 8 5 2 7
- 4 8 2 1
LOG RHO
- 6. 8 0
LOG P
- 5 , P 3 4 3
Z
l.O
I... o h
1.00~ n
T~ C P / ~
- 0
- 5 3 t 2
- 5 3 0 1
- 5 3 0 4
- 5 3 0 4
- 5 3 0 4
- 5 3 C 4
- 5 3 c ~
- 5 3 9 4 3,
- 5 3 C 4 3o
3V/R
GAMM~
O,O
- 3 q 4 4
- 3 9 4 4
- 3 q 4 4
G A M M A - E
1.3q
- 3 q s n
- 3 9 5 0 1 , 3 9 5 1
- 3949
A/AA
1.2ORl
- 2 C 7 9
- 2 0 8 0
- 2 0 7 9 !. 2 o 8 n 1.2oao 1.20eo !. l.?nRO
- 2 0 7 9
LOG RHO
-l. O -0.
LOG P
- 2 3 4 3
- 0 3 4 3
- 8 3 4 3 -2. -2.
- 2 3 4 3 -2. -1,834] -1. -1.
- 0 3 4 1
- 8 3 4 1 -0. -0,
- ~. 2 3 4 0
- 0 , ~ 3 4 0 ~. D. 3 6 5 9
2.1B
2. q 9 2 2
i
Z
l. O00n
t.O00O
1 , o 0 0 r
L.~O
l.nO
I.OOO
l.O
I.?
I.~
1. 6 8 5 o
1 1. 0 3 8 q
T ~
CP/R
3. 5 3 0 6 'i
3. 7 8 O 4
4 , C 3 2 8
D,C
CV/R
2 , 5 3 2 C
GAMMA
I~
GAMMA-E
1,394q
1 , 3 q 5 1
A/AA
1 o 2 0 9 4
1. 2 3 4 C
1.2R
1. 3 3 7 o
LOG RHO
- 3 0
- 6 , 8 0
- 6 , 6 0
- 2 0
- 6 , 3 0
- 5 , 8 0
- 5 , 6 0
- 4 0
- 2 0
LOG P
- 6 , 7 3 7 4
- 5 3 7 4
- 3 3 7 4
- 1 3 7 4
- 9 3 7 5
- 7 3 7 4
- 5 3 7 4
- 5 , 3 3 7 4
- 1 3 7 4
Z
l.DO
L.~OOO
'T--'~
CPIR
O,O
3. 5 9 C 7
3. 5 8 7 q
3. 5 8 7 q
: V / R
2 , 5 8 6 q
2. 5 R 6 9
2 , s R 6 g
~. 5 q 6 9
SAMMA
1.3B
GAMMA-E
1.3e6R
1 , 3 R 6 6
1. 3 q 6 5
A t A A
LOG RHO LOG P Z
- 6 0 - 4. 2 5 8 2 1. 0 0 0 0
- 4 0 - 4. 0 5 8 2 1. 3 0 3 0
- 2 0 - 3 , 8 5 8 3 1 , 9 3 ~ 0
- 3 , 8 0 - 3. 4 5 8 3 1 , 0 0 0 0
- 3 , 6 0 - 3. 2 5 8 2 1. 0 0 0 0
- 3 , 4 0 - 3. 0 5 8 2 1,
- 3 , 2 0 - 2 , 8 5 8 3 1 , 9 0 0 0
- 3 , 0 0 - 2 , 6 5 8 2 1,
- 2 , 4 0 - 2 , 0 5 8 2 1. 3 0 0 n
-2.2~ -1.8580 1. 3 0 0 n
- 1 , 8 0 - 1 , 4 5 8 0 1 , 0 0 0 0
- 2 0 - 3 , 8 5 8 0 1. 0 0 3 1 -1-,30 -9,6579 1,
- 8 0 - 0. 4 5 7 9 1 , 3 0 3 1
I. ~ 0 2.1681- 1 , 3 6 2 5
i:
T = &oo CP/R ~ ~VIR
- 5 6 0 3 2 , 6 6 0 3
3. 6 6 n 4 - , '?. 6 6 0 3
3 , 6 6 0 4 ~ i 2 , 6 6 0 3
GAMMA
1~
1. 3 7 5 q
I~
I..
GAMMA-E
1.376g 1,
I. 3 7 6 3
L , 3 7 6 7 ;
I. 3 7 6 7
I , 3 7 9 7
l , S l l l 1,60~ 1,
2 , 0 9 3 T
A / A A '
1 , 4 6 q 5
I o 4 6 9 5 I, 4695- 1 ..46q' I • 469- I ..4695- I = % 6 9 " 8 -
LOG RHO
- 0 0
- 8 0
- 6 9
- ~. 4 0
- 2 0
- 3 0
- R 0
- 4 0 -5.
- P O -4.
LOG P
-b, -5, -5,7Q
- S. 5 9 1 3
- 3 9 1 3 -5.
- 4 , 7 9 1 3
- 5 9! 3
Z
I,OODO
I,~
1.qO
L. 3 0 3 0
I.~
T= 700
CP/R CV/R
3. 7 4 5 8 2. 7 4 5 B
GAMMA
I. 364.
GAMMA-E
I°
AIAA
1. 5 B 0 7
LOG RHO
C.O
LOG P
- q 9 1 3
- 7 9 1 3
- 5 9 1 3
- 3 ~! 3
- 1 9 1 3
- 2 , ~ 9 1 3
- 7 9 1 3
- 5 9 1 3
- 3 9 1 3
- 1 9 1 3
- I. 9 ~ I I
- l. T g l l
- I. 5 ~! I -1.
- I. 1 9 1 1
- O , q g l l -0, -0. -O.#qlO
- 1 9 0 9
- ~ 092
3 • 6094
I. ~ 1 0 4 1. 1. !. 6 1 5 6 1. - 0 2 6 8
- 2 3 8 7
- 4 5 8 1
- 6 9 2 3
- 9 5 5 3
- 2 ~ 0 5
- 3 4 6 3
Z
!.3D#o
3 0 3 3 1.39o
0 9 9 0
0 0 3 0
0 O D O l. O0~O l. O
0 0 0 0
0 0 0 0
L.O~DD 1.09~ 1.09~
1.00~
- 3 0 0 2
- ~ O O 4
- 0 0 3 6
!. 3 0 2 6 I. ~ 0 4 0
1.010n
- ~ 4 2 5
- 0 7 1 5
- 1 2 0 5
- 2 1 2 3
- A 0 1 6 1.8~
- 6 6 1 3
T -
- 7 4 5 7
- 7 4 5 7
- 7 4 5 7
- 7 4 5 8 3 o 7 4 5 3 3.7#
- 7 4 5 7
- 7 4 5 7 3 , 7 4 5 8
- 7 4 5 7
- 7 4 5 7
- 7 4 5 8 3,. 7458 3j 7 4 5 6
- 7 4 5 6
- 7 4 5 6 3 , 7 4 5 6 3 , 7 4 5 0 3 , 7 4 6 3 3 , 7 4 6 2
- 7 4 6 4
- 7 4 6 7
- 7 4 7 8 3,
- 7 5 3 2
- 7 5 5 0
- 7 6 2 1 3.77o, 3
- 7 9 6 ~
- 8 1 8 7
- 9 5 0 9
- 0 7 3 6
L,. 2646
:V/R 3 A M ~ A GAMMA-E A/AA
2 o ~ 5 8 1. 3 6 4 2 1. 3 6 4 6 1. 5 8 3 5 ~. 7 # 5 8 1. 3 5 4 2 1.3549!. 5 8 0 7
- 7 ~ 5 8 1. 3 6 6 2 1. 3 6 5 1 1. 5 8 ~ 7 2.7~58 1. 3 6 4 2 1. 3 6 5 1 1.
- 7 ~ 5 8 1.3642 1.3650 1. 5 8 0 7
- 7 4 5 8 1,3642 1.3659 1.
- 7 4 5 8 1. 3 6 4 2 1.3659 1.
- 7 4 5 8 1. 3 6 4 2 1. 3 6 5 9 I.~B ~. 7 4 5 8 1. 3 6 4 ~ 1. 3 5 5 I 1. 5 8 9 8
- 7 4 5 8 1. 3 ~ 4 l 1. 3 6 5 2 1.58~
- 7 4 5 6 1. 3 6 4 2 1. 3 6 5 2 1. 5 8 0 8 ~. 7 4 5 6 1. 3 6 4 2 1. 3 ~ 5 2 1. 5 ~ D 8
- 7 4 5 8 1. 3 6 4 3 1. 3 6 5 3 1. 5 8 1 0
- 7 4 5 5 1. 3 6 4 5 1. 3 6 4 9 1. 5 ~ 0 7
- 7 4 6 1 1. 3 6 4 2 1. 3 5 5 6 1. 5 8 1 2
- 7 4 5 8 1. 3 6 4 4 1. 3 6 5 7 1. 5 ~ 1 3
- 7 4 5 6 1. 3 6 4 6 1. 3 6 5 7 1. 5 8 1 4
- 7 4 6 3 1. 3 6 4 7 1. 3 6 9 2 1. 5 8 3 6
- 7 4 5 1 1. 3 6 5 3 1.3703 1. 5 8 ~ 6 2.7462 1.3652 1. 3 6 9 0 1.
- 7 4 8 0 1. 3 6 5 8 1. 3 7 0 6 !.586n 2.7#92 1. 3 6 6 2 1. 3 7 3 5 1. ~. 7 5 0 8 1.3676 1. 3 7 8 2 1.
- 7 5 1 9 1. 3 7 3 1 1. 3 ~ 5 8!. 6 0 0 6
- 7 5 1 7 1. 3 7 3 7 1. 3 9 8 9 1. 6 1 2 5
- 7 5 4 4 1.3783 1. 4 1 8 3 1. 6 3 2 1 ?. 7 4 0 3 1. 3 8 9 0 1. 4 4 8 ~ 1. 6 6 2 5
- 7 6 8 7 1.3947 1. 5 0 2 8 1. ?. 8 0 3 8 1. 4 0 9 l 1. 5 9 3 2!. 8 P 7 7 2 , 8 0 0 R 1,4330 1. 7 5 2 4 1. 9 7 1 9
- 8 2 4 2 1. 4 4 2 4 2. 0 5 4 # 2. 2 9 5 6
- 9 1 8 1 1. 4 0 8 0 2. 6 5 0 ~ 3. 3 1 2 5
- 1 9 2 7 1. 3 3 5 7 3. 6 1 1 1 4. 7 4 8 2 ~. 1 2 0 6 0. 0 0. 0 3. ~
l OG RHO -7.DO
- 8 0
- 6 ) -6.
- 2 0 -6.
- ~. 8 0
- 6 0 -5.
- 2 0 -5.
- 8 0
LOG P
- 6 l ~ 3 3 3
- ~ 3 3 3 -6. 1333
- ¢ 0 3 3 3
- 7 3 3 3
- 5 , ~ 3 3 3
- 5 , 3 3 3 3
- ~ 3 3 3
- 0 3 3 3
- 4.? 3 3 3
- 5 3 3 3
- 3 3 3 3
Z
l.qO !.
1.0OOP
L.~O 1.000o
- 0 0 0 0
- 0 0 0 0
- 9 0 0 0
- 0 0 0 0
T ~ CP/R
3.R2q 3.82RS 3.82R
~.82R 3.82R~ 3,R
- R 2 8 6 3. 8 2 q 6
- 8 2 8 6 ~. 8 2 8 5
SV/R GAMMA GAMMA-E A/AA
2.8286 9.0 O.O 3. )
?.9286 1.354q 1,3528 1. ~.8286 !.3535 1.3543 !.
- 8 2 R 6 I. ~ 5 3 5 1.3~40!. 6 8 3 0
- 8 2 8 6 1. 3 5 3 5 1. 3 5 4 4 1. 6 8 3 2
- 8 2 8 6 1. 3 5 3 5 1.3541 1.
- 8 2 8 6 1. 3 5 3 5 1.3543 1. 6 8 3 2 2,8286 1.3535 1.3543 1.
- 8 2 ~ 6 1. 3 5 3 5 1. 3 5 4 3!. 5 8 3 2
- 3 2 8 6 1.3535 1.3561 1.6R
- 8 2 8 6 1. 3 ~ 3 q 1. 3 5 4 4 1. & 8 3 3
- 8 2 8 6!. 3 5 3 5 1. 3 5 4 3!. 6 8 3 0
LOG RHO
-I.
- I. 0 0
LOG P
- I. 8 8 1 9
- I. 6 8 1 9
- I. ~ 8 1 q
- n ~ l q
- 0 , 8 8 1 9
- 6 8 1 8
- 4 8 1 8
- 2 8 1 8
- P 8 1 7 3, 0.318/+
- 5 1 8 3
- 1 1 9 9 I.~
- 5 2 3 0
- 7 2 6 1
- 1 3 9 2 2.~52/+ 2.57/+
- 8 1 1 4
- 3 7 5 6
- 8 3 7 6
- ~ 2 5
Z
1.DOOO
1. ] 3 3 0
l,O
- 0 0 3 3
l. O 0 0 1
- 3 0 0 1 !. 3 0 0 2
- 0 0 0 3
- 3 3 3 7
- 0 0 1 2
- 0 3 3 0
- 3 0 4 7
! , 0 1 9 2
1.353/+
1 , 1 3 9 0
- 2 4 3 5
- 3 0 9 3
- 6 6 8 6
T= 903
CP/R 3V/R
- q 0 7 3 2.
- 9 0 7 2?. 9 0 7 2
- 9 3 7 2 2. 9 0 7 2
- 9 0 7 2 2. 9 0 7 2
- 9 0 7 2 2. 9 C 7 2 3.9073 2. 9 0 7 2
- 9 9 7 3 2. 9 0 7 2
. 3. 9 0 7 3 2. 9 0 7 2 3. 9 0 7 2 2. 9 0 7 2 3 , 9 0 7 2 2, 3. 9 0 7 2 2. 9 0 7 2 3. 9 0 7 2 2 , 9 0 7 2 3. 9 3 7 3 2. 9 0 7 3 3. 9 0 7 5 2. 9 0 7 9 3.9071 2. 3. 9 0 7 5?. 9 0 7 7 3.907/+ Z. 9 0 7 6 3. 9 0 9 7 2 , 9 0 7 3 3.9976 2. 9 0 5 6 3. 9 0 7 0 2. 9 0 5 9 3. 9 1 C 4 2. 9 0 7 7 3. 9 1 3 ~ 2. 9 0 7 6 3.9157 2. 3. 9 2 / + l 2. 9 1 0 2 3. 9 3 4 6 2. 9 1 2 7 3. 9 4 4 2 2. 3.9701 2. 9 1 2 2 4. 0 2 3 3 2. 9 3 0 9 4. 0 5 8 3 2. 9 3 9 5 4. 0 8 9 9 ~. 9 1 9 8 4,1L12 2. 9 3 6 5 6.1371 3. 0 1 9 7 6. 2 6 2 6 3. 2 7 6 6 0,3 4. 0 6 1 4
GAMMA
- 3 4 4 n
- 3 ~ 4 ' ~ 1.3/+
- 3 4 3 9 1.3/+
- 3 4 4 0
- 3 4 3 9
- 3 6 4 0
- 3 4 3 9
- 3 4 4 0 1.3/+
- 3 4 3 9
- 3 4 3 8 !. 3 4 3 9
- 3 4 4 ~
- 3 4 4 q
- 3 4 4 5
- 3 4 5 8
- 3 4 8 4
- 3 6 3 3
- 3 7 2 7
- 3 8 0 5 1./+ I./+ 1,
e.O
G A M M A - E
I./+
A / A A
1,778g !, 1, 1,
1.77~q 1,77B
- 7 7 9 2
- 7 7 q L 1,
- 7 7 8 7 I. 7"~ 1,
- 7 7 8 8 1 , 7 7 8 9
- 7 7 8 8 1.779/+ 1 , 7 7 9 7
- 7 7 9 7 !. 7 7 9 8 1,
- 7 7 q l 1, 1,
- 7 9 3 8 1,
- 8 3 8 4
- 8 7 6 8 I • 9423
- 3 5 4 8
- 2 4 4 5 2,
- 3 6 6 6
- 0 6 1 4
- 3
LOG RHO
LOG P
- 6. P 364
- ~ 3 6 4
- 6 3 6 / +
- 5 , 4 3 6 4 - 5.? 36/+
- 5 , 0 3 6 4 -/+, 8 3 6 4
- 6 3 6 / +
- 4 3 6 / +
- 236/+
1.30Dq I.~
l. DOOO
1 , 9 0 0 3
1.300~
T= I
CP/R CV/R
3,9814 2. 9 7 q 9
- 9 7 Q 7 2 , 9 7 9 9
- 9 7 9 7 2 , 9 7 9 9
- 9 7 9 9 " 2. 9 7 9 9
- 9 7 9 8 2. 9 7 9 9
- 9 7 9 8 2, 3,9797 2. 9 7 9 Q
- 9 7 9 7 2. 9 7 9 9 3 , 9 7 ° 9 2. 9 7 9 9
- 9 7 q 7 2. 9 7 9 9 3 , 9 7 9 7 2. 9 7 9 9
GAMM&
GAMMA-E
A / A A
**!. 8 6 o 5 t. 8 6 9 4
- 8 6 9 5 '
- 8 6 9 3 t. 8 6 9 5
- 8 6 9 3
- 8 6 9 5
- 8 6 9 4
- 8 6 9 4**
9
LOG RHO
Z
1. a 9 2 o
- 9 0 3 1
1 , 0 0 7 q
1. 3 3 5 6
- 3 6 1 8 LOG RHO LOG P Z CP/~ CV/R GAMMA
- -4.
- -6.
- -6.
- -~,O
- -3,
- -3.
- -1.
- -C,
- -0, - 0, - 0.~ - 0. - 0. - 1. - 1. - I , - 1. - 2 , I.BO - 2. - 2. - 2, - 3. - - L O G P - - I , - - - - - - - - 3 ~ - - 2 , - - - - 2 , - - 2 , ~ - - ~ - - - - - - - - 1 , ~ - - I n - - - - 0 , - - ~ - - 0 ~ - - - D 3 ~ - D - 0.96~ - 1. - 1 , - 1. - 1 , - 1 , - 2 , - 3 , - 1. 1.303D - 1,30~ - 1, - I.~ - 1. - 1. - I.~ - 1 , - 1, - 1. - 1,30~ 1 , 0 0 ~ - 1.OO 1 3 3 ~ - 1. 1 , 3 0 3 ~ - 1. - I.~ - 1. - 1. - 1. l.OOOg - 1 , - 1 , - l , ~ - 1 , - 1. - 1, - T= - 3.9797 CPIR : CVIR - 3 9 7 9 8 2. - 3 , 9 7 9 9 2 , - 3.9797 2. - 3 9 7 9 8 2. - 3 9 7 9 7 2. - ~ 9 7 9 8 :? , - 3 , 9 8 0 0 2. - 3 , 9 7 9 8 2 , - 3 9 7 9 8? , - 3,9799 2. - 3.9798 2. - 3.9797p~,.,? - 3 9 7 9 8 [ I' - 3 9 8 0 0 2 , 9 7 a - 3 , 9 7 9 8 2. - 3 , 9 7 9 7 2 , - 3 , 9 7 9 9 2. - 3 , 9 7 9 6 ~ , - 3 9 8 0 6 2 , - 3 , 9 8 C 5 ?. - 3.9798 2. - 3 , 9 8 1 3 1 2. - 3,9811 2. - 3 9 8 2 8 2 , - 3 9 8 5 8 2 , - 3 , - 4 0 0 8 5 2.9R - 4 , D ~ 2 7 2 , - 4 , D 6 0 9 2 , - 4, 1205 3 , - 6 , - 4 , 2 9 2 1 3 ° - 4 3 2 6 4 3, - O.O 4 ~ n - 1 , GAMMA - 1 , - 1 , - 1 , - 1 , ~ - 1 , - 1 , - 1 , - 1 , - 1 , - 1 , - 1 , - 1~ - 1 , - 1 , - 1 , - 1 , - 1, - 1, - 1 , 3 5 ~ - 1 , - 1 , - 1, - 0, - 1 , G~MMA-E - 1 , - 1 , - 1 , - 1 , - I - I , - 1 , - 1 , - 1 , - 1. - 1 , - I , - 1 , - I , - 1 , 3 3 ~ - 1 , - 1 , - 1 , - 1, - 1 , - 1 , - 1 , - I , ~ - I , - I , 1.361R - 1 ° - 1 , - 1 ° - 1 , - 1. - 1. - 2 , - 3 , - 0 , - 1 , A/AA - 1,86' - 1 , - 1 , - 1 , - 1 , - 1, - 1, - 1 , - 1 , - 1. - 1 , - 1 , - 1 , - 1 , - 1 , - 1 , - 1 , - 1, - 1. - 1 , 8 7 D - 1 , - 1 , - 1, - 1. - 1. - 1. - !.89D - 1 , - 1 , - 1 , - 2 D - 2. - 2 , 3 # - 2 , - 3 , - 5 , - T= O ° ]
- 6 8 0 - 6 1 9 5 0 1 0 3 0 9 4 , 0 3 6 4 3 , 0 3 6 6 1 , - 7 9 3 - 6 , 3 9 5 ~ 1 0 0 0 0 O.O 3 0 3 6 6 O,O
- 6 , 6 0 - 5 9 9 5 ~ 1 , 3 0 0 0 4 , 0 3 6 7 3 , 0 3 6 6 1 ,
- 6 , 4 0 - 5 , 7 9 5 0 1,30DO 6 , 0 3 6 6 3 , 0 3 6 6 1 ,
- 6 , 2 0 - 5 , 5 9 5 n 1 3 0 3 0 4 0 3 6 5 3 0 3 6 6 1 ,
- 6 , 0 0 - 5 3 9 5 0 1 0 0 3 3 4 0 3 6 6 3 , 0 3 6 6 1 ,
- 5 , 8 0 - 5 , 1 9 5 O 1 0 0 0 9 4 , 9 3 6 7 3 , 0 3 6 6 1 ,
- 5 , 6 0 - 4 9 9 5 9 1 , 0 0 0 0 4, C368 3 ,
- 5 4 0 - ~ 7 9 5 0 1 , 3 0 9 0 4 , 0 3 6 6 3 0 3 6 6 1 ,
- 5 2 0 - 4 5 9 5 0 1 , 0 0 ~ 0 4 , 0 3 6 5 3 , 3 3 6 6 1 ,
- 5 , 3 0 - 4 3 9 5 0 1 , 3 0 ~ 0 4 , 0 3 6 6 3 0 3 6 6 1 ,
- 4 , 8 0 - 4 , 1 9 5 C 1 3 3 0 0 4 , 0 3 6 6 3 0 3 6 6 1 , - 0. GAMMA-E - 1, - I ¢ - I , - 1. - 1, - 1.32~ 1 , 3 2 8 L - 1,3_;' - 1 , - 1, - 1 , - 3 , A/AA - 1 , - 1 , - 1 , - 1 , - 1 , - 1 , - 1 , - 1 , -! , - 1,. - 1 ,
