wapd-tm-1623
TRANSCRIPT
WAPD-TM-1623
Distribution Category UC-505
IMPROVED APPROXIMATE( FORMULAS FOR FLUX FROM CYLINDRICAL AND RECTANGULAR SOURCES
0. J. Wallace !S. A. Bokharee
Contract No. DE-AC11-88PN38014
March 1993
Printed in the United States of America Available from the
National Technical Inlformation Service U. S . Department of Commerce
5285 Port Rayal Road Springfield, Virginia 22161
NOTE E- l
This document is an interim memorandum prepared primarily for internal reference and does not represent a final expression of the opinion of Westirighouse. VVhen this memorandum is distributed extamally. it ia with the express understamding that Westin$housa make8 no representation as to completeness, accuracy, or usability of information ~coontained herein.
BIZITIS ATOMIC POWER LABORATORY WEST MIFFLIN, PENNSYLVANIA 15122-0079
Operated for the U. S. Dcpartment of Energy by WESTINGHOUSE ELECTRIC CORPORATION
DISCLAIMER
This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency Thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.
DISCLAIMER Portions of this document may be illegible in electronic image products. Images are produced from the best available original document.
WAPD-TM-1623
NOTICE
This report was prepared as an account of work sponsored by the United States Government. Neither the Uni tetl States , nor the United States Department of Energy, nor any of their employees, makes any warranty, expressed or implied, or assumes any legal liability or responsibility for the accuracy, completeness or usefulness of any information, apparatus, produce or process disclosed, or represents that its use would not infringe privately owned rights.
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WAPD-TM- 1623
Improved Analytic F1 ux Formu 1 as for Cylindrical and Rectangular Sources
TABLE OF CONTENTS
I . Introduction .................................................... I 1 . Background . The Approximation of Ono and Tsuro .................
A . An Exact Flux Formula for a Cylindrical Source .............. B . C . 1 . The Functions of Ono and Tsuro .......................... C . 2 . A Sample Problem ........................................
The Approximation of Ono and Tsuro ..........................
D . Extensions of the Approximation of Ono and Tsuro . Approxi- mate Formulas for the Flux at Detector Points Outside the Radial and Axial Extensions of a Cylindrical Source with a Slab Shield .....................................................
Improved Accuracy for the Approximation of Ono and Tsuro .... I 1 1 .
A . Background .................................................. B . CASE I . Slab Shield Parallel to the Source Axis ............ C . CASE I1 . Slab Shield Perpendicular to the Source Axis ......
I V . Approximations o f Rectangular Sources ........................... A . Approximation o f a Rectangular Volume Source by a
Section of an Annulus ....................................... B . Approximation of Rectangular Source with Square C . D . Rectangular Surface Source Sample Problems ..................
Cross-Section by a Truncated Cone ........................... Approximation of a Rectangular Surface Source ............... 1 . 2 . Square Surface Source Problem ........................... Rectangular Surface Source Problem ......................
V . Figures ......................................................... 1
2 Detail of Division of a Cylindrical Source into
Division of a Cylindrical Source into Regions I and I1 ...... Regions I and I1 ............................................
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TABLE OF CONTENTS (Cont I d)
Page
Cy1 i n d r i c a l Source-Volume Approximation Using a Sect ion o f an Annulus w1t.h a Curved Top Surface.............
Bases o f Cy1 inder and Annular Sector.. ...................... Cy1 i n d r i c a l Source Approximation w i t h Detector Point Outside the Ax ia l and Radial Extlinsions o f the Source and w i th a Slab Shie ld P a r a l l e l t o the Source Axis. ......... D e t a i l o f the Midplane o f a Cy l i nd r i ca l Source Approxi- matlon w i th Detector Point Outside the Axia l and Radial Extensions of the Source. .................................... Layout o f A r b i t r a r y Test Problem w i t h Slab Shie ld P a r a l l e l t o the Source Axis..............,....................... .... Cy l ind r i ca l Source w i th a Detectclr Point Outside the Radial and Ax ia l Extensions o f the Source and w i th a Slab Shield Perpendicular t o the Source Axis....... ......... Sect ion of an Annulus Used t o Approximate a C y l i n d r i c a l Source w i th a Detector Point Outside the Radial and Ax ia l Extensions of the Source, and w i th a Slab Shie ld Perpendicular t o the Sourc:e Axis....................... ..... Layout o f A r b i t r a r y Test Problem w i t h a Slab Shie ld Perpendicular t o the Source Axis.... ........................ Base o f an Annular Sector which P,reserves the Area o f t h e Base o f a Rectangular S o u r c e . . . . . . . . . . . . . . . . . . . . . . . . .
Rectangular Volume Source Approximation Using a Sect ion o f an Annulus. . . . . . . . . . . ; I , . .e .~ . .~ .o . . . .o .~ . . . . . . . . .
Square Rectangular Source Approximation Using a Truncated Cone..................., ........................... Rectangular Surface Source w i t h Center Opposite Detector Point... ............................................
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TABLE OF CONTENTS (Cont'd)
V I . T a b l e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1A
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12
Approximate for a Cylindrical Source with a Exact Flux
Lateral Detector Point and a Slab Shield Parallel to the Source Axis.................................................
Improved Ratios of A PPExact roximate Flux
Section II.D................................................ Approximate
P o i n t s Outside the Radial and Axial Extensions of the Source with an Intervening Slab Shield Parallel to t he Source Axis.................................................
Results from the Exact Flux Formula and from Equation
Approximate
Points Outside the Radial and Axial Extensions o f the Source with an Intervening Slab Shield Perpendicular to the Source Axis.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Results from the Exact Flux Formula and From Equation (30)
Using the Algorithm of
from a Cylindrical Source with Detector Exact Flux
(24) for the Problem of Figure 7.. .......................... from a Cylindrical Source at Detector Exact Flux
for the Problem of Figure 10 ................................ The Function Lo(@o, b). ..................................... The Function G(eo, b). ...................................... The Smoothed Function E(eo, b) = G(eo, b)e /eo ............. The Smoothed Function F(eo, b) = F(eo, b)e /eo .............
The Smoothed Function f 2 ( e 0 , b) = F,(eo, b)e / e o ...........
b
b
The Function F(eo, b) ....................................... b
The Function F,(eo, b) .....................................
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TABLE OF CONTENTS (Cont I d l
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48 13
14 The Function R(o,, %,/a,, b ) ................................ 53
15 The Function El ( b ) 58
58 16
58 17 The Function E, (b)
b 18 The Smoothed Function E,(b) = be E,@) ..................... 58
VII. References...........~.............,b...............o.e..o.....o. 59
The Smoothed Function E(4 , eJa, b) = e2/a, b) e b /40 0
.......................................... ..................... The Smoothed Function rl(b) = ble b E,(b)
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WAPD-TM-1623
ABSTRACT
IMPROVED APPROXIMATE FORMULAS FOR FLU> FROM CYLINDRICAL AND RECTANGULAR SOURCES
This report provides two new approximate formulas for the flux at detector points outside the radial and axial extensions of a homogeneous cylindrical source and improved approximate formulas for the flux at points opposite rectangular surface sources. These formulas extend the range of geometries for which analytic approximations may be used by shield design engineers to make rapid scoping studies and check more extensive calculations for reasonableness. These formulas can be used to support skeptical, independent evaluations and are also valuable teaching tools for introducing shield designers to complex shield analyses.
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WAPD-TM-1623
Improved Analytic Flux Formulas for Cy1 indrical arid Rectangular Sources
I. Introduction
Hand calculation methods involving analytic approximations of exact flux formulas and tables of special mathematical functions continue to be useful in shielding calculations since they enable shield design person- nel to make quick estimates of dose rates, check calculations made by more exact and time-consuming methods., and rapidly determine the scope of problems before a detailed soluticln is attempted.
They are also a valuable teaching tool. Solving shielding problems by hand methods can give a shielding engineer a body of experience and a feel for such problems which i s very valuable when the output from black-box type computer programs must be evaluated.
Knowledge of hand calculation methods of radiation fluxes and dose rates is also valuable and even essential in those situations where no com- puter, or no time to use a computer, is available, and a quick answer i s needed.
Several collections o f approximate annlytic radiation flux formulas are available, as are tables o f the required mathematical functions. A par- tial list of these documents is given in Section H of Reference (1). Reference (1) is itself a compilation of useful approximate analytic flux calculation formulas and function tables which were assembled expressly for the use of shielding pel-sonnel. subset of the same material. Reference (1) gives approximate flux formulas for a variety of source geometries and contains tables o f cross-section, spectrum, and build-up factor data as well as shielding function tables and considerable information about these functions. This report assumes that the reader i s at least minimally familiar with the contents of Reference (1).
Reference (2) contains a
Extensive use of Reference (1) has shown that improved analytic approximate formulas are needed for finding the flux
(a)
(b)
at detector points located outside the radial and axial extent of a cylindrical source, and at detector points opposite a rectangular source.
In all cases, the attenuation of a slab shield must be included.
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In addition, more extensive information on the errors in results cal- culated using the cylindrical source approximation of Ono and Tsuro [References (1)-(4)] is needed, and improvement in this formula is desirable.
The material given in later sections of this report meets all these needs. Therefore this report supplements and extends the formulas and information given in Reference ( l ) , and the two reports should be mutually familiar to the user, The use o f this material should enable shielding engineers to make better estimates and quick scoping calcula- tions in many situations and thereby save engineering and computer time.
In order that the reader may better understand the approximate flux formulas given in this report, Section I1 below starts with the exact formula for flux from a cylindrical source at a lateral detector point and then discusses the corresponding cy1 indrical source approximation of Ono and Tsuro [Reference (4)] in detail, ending with a refinement which improves its accuracy in some cases.
Section I11 then presents extensions o f the cylindrical source approxi- mate flux formula which apply to detector points located outside the radial and axial extent of a cylindrical source. Detailed error infor- mation is given for all approximate cylindrical source formulas.
Finally, Section IV discusses calculation of flux from rectangular sources and gives both an exact formula and a new approximation for a rectangular surface source.
All required mathematical function tables are given in Section VI,
11. Background - The Approximation of Ono and Tsuro
A, An Exact Flux Formula for a Cylindrical Source
Figures 1 and 2 show a cylindrical source with a lateral detector point. A slab shield of thickness t is assumed to be parallel to the source axis, perpendlcular to the line OP, and to lie between the source and the detector point P.
The unscattered flux at the point detector P is given by (1)
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where
- sv -
- us -
v =
t =
dVs =
r2-r1 =
4 =
e =
P =
Source s t rength per un i t volume per u n i t t ime
Attenuat ion c o e f f i c i e n t o f the source mater ia l
At tenuat ion c o e f f i c i e n t o f the sh ie ld mater ia l
Thickness o f the sh ie ld
Volume element o f the source
Distance from the volume element t o the c y l i n d r i c a l source surface i n the d i r e c t i o n o f the detector, pro jected onto the base o f the cy l inder . See Figures 1 and 2.
Angle subtended tiy the cy l inder , as seen from the detector po int . See Figures 1 anld 2.
Angle between the s t r a i g h t l i n e connecting the volume element w i t h the p o i n t detector and a s t r a i g h t l i n e passing through the po in t detector arid norma.1 t o the shield. e i s a func t i on o f the height o f the cy l inder . See Figures 1 and 2.
Distance from the volume! element t o the po in t detector.
The i n t e g r a l can be s i m p l i f i e d by choosing the Ono and Tsuro method which regards the po in t detector as the o r i g i n o f the coordinate system (See Reference (4)). Then from Figures, 1 and 2 i t can be ascertained t h a t
(2a) P = r sec 4 sec o
rl = (R+a)cosz4 - cos4 / R Z - (R+a)zsinz+
, , 2 2 2 r2 - rl = 2 cos+ 4 R - (R + a)
dVs = d r d+ (r tan+) dz
sin 4
= d r - d4 (r tan+) de (I- set+ tane)
where subscr ip ts i nd i ca te the v a r i a t i o n i n t h a t d i r e c t on.
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... dVS= dr (- a (r tan@) d+) - (-(r 3 sec+ tane) de) ao
2 2 39
= dr (r sec + d@) '(r sec+ sec ede) 2 3 2 dVs = r sec + sec e drd+de
The angles are given by
= sin-' (R/(a+R)) $ 0
e, = tan-' a/r,sec+
e, = tan -1 a/rlsece
as may be seen from Figures 1 and 2.
By combining equations (l), (2a) and (2e) we may write
exp (-ps (r-rl) sec+ sece) de
The ntegration over r can easily be carried out with the result
00 + = - sv f d + I cose a exp(-b sece sec+)*[l-exp(-ps(r2- r,))sece seC4-1 de 2nus 0 0
where b = pt.
Let G (eo, pt) = I e cose exp (-Ut sece) de 0
(3)
(4)
Then Equations (2d), (3) and (4) yield
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and
G (;, ut) = H(ut) = p cos8 c!xp (-ut sece) de I I '
0
6. The Approximation of Ono and Tsuro - Equation (1) must be solved by numeric integration or quadrature if it is to be solved at all. Ono anal Tsuro were able to derive an ingenious and useful approximation to Equation (1) by substituting a section of an annulus for the cylinder, as shown in Figure 3. To quote from their paper:
"A cylindrical source is replaced by a columnar fragment of cylindrical shell with area of base equal to that of the original cylinder. Fig. 3). The cylindrical shell fragment has six surfaces, two plane side surfaces, a conical top surface, and a bottom surface. Consider a straight line L parallel to the axis of the source cylinder and passing the observation point P. The inner surface is part of a cylinder and passing the observation point P. The inner surface is part of a cylin- der with axis coinciding with the line L and radius equal to a. The two side surfaces contain the line L and are in contact with the original cylinder on both sides. The upper surface is a part of a right circular cone with apex at P, its axis coinciding with the line L, and half apex angle, n/2-eo, such that the conical surface is in contact with the top edge of the cylinder. The bottlom surface is on a common plane with the source cylinder. The outer surface is part o f a cylinder with its axis on L and radius equal to a+mCR, mc being such that the bottom area of the cylindrical shell fragment i s equal to that of the original cy1 i nder . 'I
(See
where
-1 a a eo = tan (7)
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and equation (5) is approximated as
The elevation angle as defined by Equation (8) is measured to the top of the front of the annulus, so that the curved top o f the annular sector lies above the top of the cylindrical source which it replaces. Therefore, the source volume is not preserved by this approximation. approximation.
The volume of the annular sector is then
This helps to make this a conservative
"an - - 3 2 % $0 z [(a+mcR)3 - 8 3 1
To be useful as a hand calculation tool, expressed in terms of mathematical funct in readily usable form.
equation (9) must be ons which may be tabu
Then eq. (9) becomes the approximation o f Ono and Tsuro:
ated
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1. The Functions o f Ono and TSE
From Equations (4) and (11) these funct ions are
de - bijece (a) G ( e o , b) = cose e 0
which i s usua l ly tabul i l ted i n the smoothed ( e a s i l y in terpo- la ted) form
b e G ( e o , b ) = - G(eo, b) e
-
0
and
go J 2 c o w e -bsecede 0
which i s inherent ly i n :;moothed form. r a t i o o f the attlenuatioii o f a s lab sh ie ld 07 th ickness b t o
Lo(# , b) gives the
the at tenuat ion o f an annular sh curved around the detector po in t annular sector source. Figure 4 s lab sh ie ld and the annular sh ie described.
e l d of the same thickness and concentr ic w i t h the shows the r e l a t i o n o f the d which have just been
The d e f i n i t i o n o f LO(gol b) includes a double i n teg ra l . Numeric checks have shown t h a t the value o f t h i s f u n c t i o n i s almost independent of the upper l i m i t on e i n Equation (15) and i s a lso l a rge ly independent o f the source shape behind the shield, provided t h a t the source s t rength i s a constant. o f t h i s func t i on i s no t l i m i t e d t o the approximation o f Ono and Tsuro.
The l i m i t e = 2 ll i s therefore val id, and the use
Tabulat ions of these funlct ions are g iven i n Sect ion V I o f t h i s repor t .
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Any further refinement in source shape or attempt to approximate Equation (1) more closely results in mathe- matical functions which are dependent on at least four parameters. A table of such a function must be voluminous and detailed and i s difficult to interpolate. Problems also arise because functions such as G(eo, b) and the Sievert Integral F(eo, b) are extremely weak functions of the upper limit when that limit is large (greater than 60 degrees). The plots in Chapter Nine of Reference (6) illustrate this.
In contrast to this, the G(eo, b) and Lo($,, b) functions defined by Ono and Tsuro involve only two parameters or independent variables each and are easy to use. Anyone using this cylindrical source approximation therefore owes a debt of gratitude to Ono and Tsuro.
2. A Sample Problem
An illustrative sample problem will now be displayed i n which the approximate flux formula given in Equation (12) i s to be used to find the flux at a detector point 15 cm. from the base of a cylindrical source having of 40 cm. The source attenuat source strength Sv is 1.0, and 1.0 mfp thick. Then
= tan-' E = tan-' 2.67 = 6'
a radius of 10 cm. and a height on coefficient is us = 0.1, the the intervening slab shield is
O = 1.2r
-1 10 -1 = sin - = sin .4 = 23.6" = 0.41r $0 25
= 1.65 and b' = b + p m R = 2.6 mC s c
*41 2 x 3.14 x .1 o L (.41, 1.) lG(1.2, 1) - G(1.2, 2.6)l Q =
= 0.656 x .97 [.368 x .606 x 1.2 - .074 x .48 x 1.21
= 0.586 t.266 - .042] = 0.131
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The flux found by a numeric calculation using the exact flux formula is 0.136, which is in good agreement with the approx- imate hand cal cu 1 at i on.
D. Improved Accuracy for the Approximation of Ono and Tsuro
Table 1 gives the ratios, for a range of problem parameters, of the flux calculated by Equation (12) to the exact flux calculated by Equation (1). The tool for doing these calculations was a special version of the SPAR1 program, which is described in Reference (5). Some of these error ratios are larger than 3.
If the source height a is replajced by a smaller number, according to the following algorithm, the tw3 sets of ratios which are the worst in Table 1 are replaced by the two sets of the ratios which are designated as Table 1A. This gives an improved Ono and Tsuro cylin- drical source approximation whilzh is conservative by less than a factor of 2.15 for the range of problem parameters covered by Table 1.
The height of the front of the annular sector which will preserve volume is
- a ' = -- 3 i i R*aa 2 4 [(a + mcR)3 - a31
0
Set a l l = MIN(2.0 * a ' , !I) and
I I = 0.5 * (a" + a )
Then if
and if # < 0.5 and psR < 2.5 replace a by a ' ' in Equation (8). The
flux may then be found using Equation (12).
< 0.5 and p,R .c 5.0, replace a by a ' ' ' in Equation (8),
111. Extensions of the Approximation of Ono and Tsuro - Approximate Formulas for the Flux at Detector Points Outside the Radial and Axial Extensions of a Cylindrical Source with a Slab Shield Parallel to the Source Axis
A. Background
Exact flux formulas for this situation are given in References (3) and (5). Here, an analogue of the approximate formula of Equation (12) which applies to thls situation will be derived and tested.
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The approximation of Ono and Tsuro was derived for lateral detector points and it breaks down badly for detector points located beyond the axial and radial extensions of the source, as shown in Figures (5) and (6).
The reason for this is readily apparent. model either the top or bottom of the source properly when the geometry is that o f Figure (5). heights h and T = h + a in Figure (5), the approximation of Ono and Tsuro may be made the basis for a simple and usable approximation using the superposition method. The flux from a source of height a which is a distance h above a lateral detector point is assumed to be equal to the flux from a source of height T = h + a minus the flux from a source of height h. There are two cases to be con- sidered: The case with an intervening slab shield parallel to the axis of the cylindrical source (Figure 5) and the case with a slab shield perpendicular to the axis (Figure 8).
Equation (12) does not
However, by properly altering the
These cases are treated in the next two sections of this report.
B. Case 1 - Slab Shield Parallel to the Source Axis The approximate flux formula for this case is given by the following algorithms:
Step 1. See Figure 5.
The height of the superimposed cylinder, that i s , the height of the cylinder of height a combined with the cylinder of height h, is
T = h + a (17)
Find the height T' which will preserve the volume of this large cylinder when it i s replaced by a section of an annu- lus defined to preserve the basal area. This height is given by
3 r R*Ta 2 bo [(a + mcR)3 - a31 T' = - -
where bo and mc are defined by Equations (9) and (lo), respectively.
Step 2. Let TI' = MIN (2.0 * TI, T) and
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T " ' = 0.5 * ((TI' + T)
Step 3. Let Tuse = T.
a a If E < 0.5 and pSR < 5.0 and a < 0.5,
se t TuSe = TI ' ' .
a If i < 0.5 and 1lSR < 2.0 and a < 0.75,
set Tu,, = TI'. (19)
Step 4. The height o f the lower, cy l i nde r i n Figure 4 i s h. the height t o preserve t h i s volume, which i s
Find
T ' h ' = : h i = - .
Step 5. Let hl' = MIN (2,O * h' , h) and
h " ' = 0.5 * (:h" + h)
Step 6. Let huse = h
a If < 0.5 and )lSR < 5 . 0 ,
se t huse = h'l '.
I f < 0.5 and F I ~ R < 2.5,
se t huse = h".
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Step 7. Find
T -1 use e , = tan - a
Step 8. The flux from the cylinder of height a in Figures 5 and 6 is then given by
- G ( e , , b) + G(e , , b + vsmCR} .
I Step 9. Evaluate the accuracy o f the result.
The use of this approximate formula is evaluated in Tables 2 and 3. scopic attenuation coefficient of the source, and is the same as us in Equation (24).
Table 2 gives ratios of results calculated by Equation (24) to results calculated by the exact cylindrical source option o f the SPAR1 program [Reference ( 5 ) ] for a wide range of problem geometries and parameters. the results for the sample problem of Figure 7 calculated by the same two methods.
The accuracy is good for many values of the parameters in Table 2 but this approximation gives low answers for certain combinations of the parametric values as " / a , ala and b increase. The maximum ratios given in this table are less than 3. The low or non-conservative ratios are marked off from the ratios in the range o f 0.88 to 3.0.
I In Table 2, H I = (h+a)/a, and Mus is the macro-
Table 3 gives
These ratios may be used as approximate correction factors for calculations where the problem parameters lie in the range of the parameters used in generating this table. information in this table is therefore very useful.
The
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The behavior i n which nort-conservative o r low answers are generated i s a lso seen i r t Table 3.
The reason f o r t h i s i s eiisy t o f ind : involves on ly Lo ,and G funct ions, and as may be seen from Table 1, G(eo, b) become!; a very weak func t ion o f eo as eo and b increase. I f both e 2 and e 3 [Equations (22) and (231 are greater than $45" and b i s not small, the parameter values and e r r o r r a t i o s o f Table 2 must be used as guide- l i n e s as t o the gleometric: arrangements f o r which Equation (24) i s t rustworthy.
Equation (24)
C. Case I1 - Slab Shield Perplendiculitr t o the Source Axis
The geometry o f t h i s source and sh ie ld conf igura t ion i s shown i n Figure 8. The a p p l i c a b i l i t y o f the approximation o f Ono and Tsuro t o t h i s case i s not obvious.
However, i f an annular sector can be su i tab l y defined which replaces the c y l i n d r i c a l source, the case o f the sh ie ld perpendicular t o the source ax is can also be handled by a superposi t ion method based on the approximation o f Ono and Tsuro. This conf igura t ion i s shown i n Figure 9. A simple a lgor i thm f o r de f i n ing and using such a sector i s as fo l lows:
Step 1. See Figures 8 and 9.
A usable annular sector l'or represent ing t h i s source i s def ined t o have height = 2R and thickness a and the d i s - tance out t o a detector po in t i n the base plane would be h, wh i le the distance the detector p o i n t l i e s below the source base i s a.
Step 2. Find the volume o f the annular sector, which i s g iven by
Van = IT (2R) [ ( H + a ) 2 - h2] @ o / ~ = 2R4,[(h+a)2 - h'] (25)
and the volume o f the cy l inder , which i s V equate these volumes t o determine the angle t$o:
= ~ R 2 a ; and CY 1
T R = - 'o 2 2 h + a '
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2 Step 3. If R I (2h + a ) ,
proceed to Step 4. Otherwi , this approximati n do
(27)
not apply to the problem. See Step 7 below for an explanation of this criterion.
Step 4. Define e = tan-' & and (28 1
-1 a + 2R e, = tan h . Step 5. The flux from the cylinder of height a at the point P I i s
then given by
Step 6. Here again, cases in which e, a both above 45" are likely to give low answers aid the cautions given at the end o f Section 1II.B for Equation (24) also apply to this approximation.
Step 7. Evaluate the accuracy o f the result (see Table 4). This approximation is not applicable to any and all possible variations in the geometry of the source and detector points as noted in Step 3 above.
For practical problems, the angle $o (see Figure 9) should not be greater than 60" or ~ / 3 radians. (27) follows from Equation (26). With this added require- ment , Equation (27) becomes
The inequality
- - - r r R 3 - 2 2 h + a
so that the maximum value of the ratio R/(2h + a ) allowed in the problem using this approximation is
- 14 -
o r R I 3 2 (2h + a ) .
The r a t i o s o f Table 4 were ca lcu lated f o r problem param- e te rs which observe t h i s r e s t r i c t i o n . I n order t o a l low the use o f a l l bu t one o f the problem parameters o f Table 2 i n the generatian o f t he r a t i o s fo r Table 4, whi le observ- i n g t h i s r e s t r i c t i o n , f i r s t r e w r i t e Inequa l i t y (27) as an equation:
- = - * ; then observe t h a t R 3 Q
Subs t i t u t i on i n Equation (31) then gives
h + Q where H I = - Q *
The minimum values o f H ' and a/R used i n compiling Table 2 are 1.1 and 0.2 respect4vely. These values, when subs t i - t u ted i n Equation (32), w i l l g ive the corresponding minimum value o f &/a which s a t i s f i e s the cons t ra in t o f I n e q u a l i t y (27) :
6.25 3 :1 m i n
The other th ree values c l f (i) used i n compil ing Table 2 are 0.5, 1.0, and 2.5; these1 values, along w i t h H ' = 1.1, g i v e the (ala) values 2.5, 1.25, and 0.5 respec t i ve l y [ f rom Equation (32) I .
- 15 -
WAPD-TM-1623
These values of (ala) are the basis for the parameter values used to generate the error ratios o f Table 4, which clearly shows the geometrical arrangements for which this approximation is applicable. The restrictions on the prob- lem geometry which apply here clearly affect these ratios.
Note that the maximum ratios are less than 3.0. The low or non-conservative ratios are marked off from the ratios in the range 0.88 to 3.0.
These ratios may be used as approximate correction factors for flux calculations using this approximate formula as long as the problem parameters lie within the range of the parameters used to generate this table. given in this table is therefore very useful.
Table 5 gives a comparison of exact and approximate results for the problem shown in Figure 10. reasonably good. than 0.6.
The information
The accuracy here is All the ratios except two are greater
IV. Approximations of Rectangular Sources
A. Approximation of a Rectangular Volume Source by a Section of an Annulus
Provided that a rectangular source is long with respect to it base dimensions and has a lateral detector point, either the approxima- tion of Ono and Tsuro or the new approximations discussed in Section 111 of this report may be adapted to allow calculation of flux or dose rate from such a source.
The geometry of this situation is shown in Figures 11 and 12. The volume of the rectangular source is
vr = ' a 1 a * a 3 (33)
and MR, the factor which preserves area of the the base is
where
- 16 -
(34)
(35)
WAPD-TM-1623
For t h i s approximation t o work wel l , the rectangular source dimensions should be such t h a t
a , >> a , and a , a , .
Then Equations (12),(24), and (30) may be used d i r e c t l y , w i t h M R ~ ~ subst i tu ted f o r mcR and 4o defined by Equation (35). The e - l i m i t s are defined i n the same way as i n the discussions o f Equations (24) and (30), again w i t h mcR replaced by MRa3.
The accuracy o f t h i s approximation w i l l be s i m i l a r t o t h a t o f the approximation o f the corresponding cy1 i n d r i c a l source case. The c loser the shape o f the annular sector approaches the shape o f the t r u e source, the b e t t e r the r e s u l t s ca lcu lated by the approximate formu 1 as.
Approximations o f rectangular sources f o r which the above inequa l i - t i e s are not t r u e are discussed below.
The height a ' which w i l l p'reserve volume i n the s i t u a t i o n o f Figure 12 i s
B. Approximation o f Rectangular Sourc:e w i t h Square Cross-Section by a Truncated Cone
As shown i n Figure 13, the f l u x at. a p o i n t located opposite the center o f t he square end o f a square rectangular source may be found approximately by use o f a truncated cone source.
To preserve the area o f the square end o f the source, the rad ius R o f the near end o f the truncated c:one should be
a 1
f i R = -
and the length o f the truncated cone which w i l l preserve source volume i s then
(37)
(38) 113 a = [a3 + 3a2a3] - a
-. 17 -
WAPD-TM-1623
where V = a ; a 3 is the rectangular source volume. definitions of a, a , , etc.
The defining angle of the truncated cone is then
See Figure 13 for
If b = ut is the optical thickness of the slab shield, p S a is optical thickness of the truncated cone, and
b' = b + p s a .
then the flux at the detector point P 1 is given by
@ = -[E,(b) sV - E,(b') + coseoE,(b' sece,) - coseoE,(b seceo)l P1 2nus
C. Approximation of a Rectangular Surface Source
A rectangular surface source such as that shown in Figure 14 may be approximated by using a disk source if a , L. a 2 so that the source is close to being square. For a square surface source represented as a disk, the disk radius which preserves area i s
Q l r = - - Jn
while use of the radius r answer.
In either case, -1 eo = tan - a
El a 1 - /2 = - will give a c
/7 2 nservat i ve
and given an intervening s.ab shield of optical thicaess b, the flux formula is
- 18 -
WAPD-TM- 1623
(44) wh i le i f b = 0, the f l u x f'ormula i s Q = 'a l og (sec eo).
Now i f an in tervening slab sh ie ld i s assumed i n Figure 14, the exact equation f o r the f l u x a t the po in t P i s [ f rom Reference ( 3 ) ] ,
P
-bsec$ 'a eo Qo Q = - J J s e c ~ e
P = 0 0
where
-1 a1 a , 2a sec 4 Q~ = tan - = tan-' 2a 9 '0
and the maximum value o f eo i s
(45)
(47
I f a , > a , , so t h a t the d isk approximation breaks down, a s imp l i - f i e d approximation o f Equation (4!5) may be w r i t t e n which uses the Lo(eo, b) f unc t i on o f Ono and Tsui-o. This approximation i s
cp = - sa e L (eo, b) sec4 e -bsec$dg 0
p T m o
and i s v a l i d f o r em > Q ~ . the actual source shape i s unacceptably d is to r ted .
Now the S iever t I n teg ra l of the Second Kind i s def ined t o be
Unless Q~ i s small w i t h respect t o e,,
d$ -tlsec$ OO S , ( $ o , b) = b J !;ecQ e
0
Therefore, f o r use i n Equation (48,), def ine
(49)
Tabulat ions o f t h i s func t i on are given i n Sect ion V I o f t h i s repor t . The smoothed form o f t h i s func t ion i s def ined as
- 19 -
b
U
Equation (48) may now be w r i t t e n i n the usable form
The funct ion
i s a lso tabulated i n Section V I . the exact rectangular surface source equation [Equation (45)] g ives
Subs t i t u t i on o f t h i s f u n c t i o n i n t o
I f b i s zero, Equation (48) reduces t o
'a Q = - em log(secgo + tango) P " (55)
where em i s t he l a r g e r angle. ways t o Equation (44).
Equation (55) is then s i m i l a r i n some
D. Rectangular Surface Source Sample Problems
1. Square Surface Source Problem
Refer t o Figure 14. Assuming an in tervening slab s h i e l d o f o p t i c a l thickness b y the exact equation f o r the f l u x a t the detector p o i n t i s
-bsecg secedgde tan * 2a secg
'a secg e Q , = r S s
- 20 -
. . - . . . . - . . . . . .. . . . . . . - . - . . - - - - - .- - - . -
WAPD-TM-1623
or from Equation (54)
where
4o = tan - -1 Q l
2a
Here, let
sa = 1.0, a = 10.0, b = 2.0 mfp, and
Q, = Q 2 = 20
Then the flux, using the exact rectangular source function R ( $ o , k2/a, b), is as follows:
Q 2
a 10 - - = - - 2o 2. Then q'(.7854, 2., 2.) = .5234, and
lr/4 1 Q = - x - x 0.5234 = 0.25 x .1353 x .5234 = 0.0177 P n e2
If the same problem is solved using the approximation of a disk source with area preserved
- 21 -
WAPD-TM-1623
J i 1.77
-1 r em = tan - a = tan-' = 48.50 = .846r
sec 48.5" = 1.51
and
-3.02 - 05 -2 - e E(3.02)] = .5 [.0677 x .723 - 3.02 x .786] # P = + [% ~ i ( 2 ) - 3-02
Q = .5[.0359] = ,0179 . I f the d isk source approximation i s changed t o be conservative, w i t h r = a , 42 , the ca l cu la t i on o f the f l u x i s as fol lows:
P
- - = 1.73 1 - cos 54.6 .579 sec e, =
0*0314 x 0.81 = 0.5 x 0.0417 = 0.0208
F ina l ly , i f the approximation o f Equation (52) i s used, even though, f o r a square surface source,
1 3.46 = 7 [ .0677 x .723 -
- = tan-' a,/2a , - 40 the f l u x i s given by
- 22 -
- - *7854 L0(.71354, 2) x .7854 e -2 - F,(.7854, 2) ll
= .25 x .7842 x .7854 x .1353 x .8819 = .0185
2. Rectangular Surf ace Source Problem
The convention i s t h a t a 2 , t he v e r t i c a l dimension, i s t he longer side. A d isk source approximation w i l l not work i n t h i s case. The detector p o i n t i s . located as i n Figure 14.
Let a , = 20 cm, a , = 10 cm, b = 2 mfp, a = 10 cm, and Sa = 1.0
Then
'rn = .7854r = 450
- tan-' .5 = 26.50 = .463r -1 $ 1 -1 10 tan 2 x 10 - = t a n - = 2a
a,/a = 10/10 = 1 . The f l u x given by the exact l'ormula [see Equations (45) and (54) l i s
Q = - 1 .463 X -1353 Kt.463, I,., 2) = 0.147 X .1353 X -423 P =
(0 = 0.00841
The f l u x from an approximatian founded on i n t e g r a t i n g a l i n e source over the arc a41, i s
P
- 23 -
Q = a4 P
4s a -b - S = - @oe e,F(e,’
51
WAPD-TM-1623
= 0.463 x .1353 x .25 x .8038 = .01262
The flux given by the rectangular surface of Equation (52) is
= 1 x - *7854 lT L 0 (.7854, 2) x .463 x .1353
source approximation
x F,( .463,
= .25 x .7842 x .463 x .1353 x .963 = .0119
- 24 -
V. Figures
- r2 -4 FIGURE 1
Divison of a Cylir,ldrical Source into F!egions I and I1
WAPD-TM-1623
- r SEC # - rz SEC 4
FIGURE 2
1-- Detail o f Division o f C.ylindrica1 Source
into Regions 1 and I1
- 25 -
WAPD-TM-1623
L
FIGURE 3
Cylindrical Source-Volume qpproximation Using a Section o f an Annulus w i t h a
Curved Top Surface
- 26 -
WAPD-TM-1623
4-
FIGURE 4
Bases o f Cy1 iinder and Annular Sector
- 27 -
P i- I
c
WAPD-TM-1623
T
--I- i.
.- e d
7- Q
FIGURE 5
C y l i n d r i c a l Source Approximation w i t h Detector Point Outside the Ax ia l and Radial Extensions o f the Source, and w i t h Slab Shie ld P a r a l l e l t o the Source Axis
D e t a i l o f the Midplane o f a C y l i n d r i c a l Source Approxi- mation w i t h a Detector Point Outside the Axia l and Radial Extensions .o f the Source
- 28 -
FIGURE 6
WAPD-TM-1623
4 0
0 - 5
-I 5
- 2 5
-35'
-45 1
DETECTOR POINTS
I m f p I
tT-+
L -t I O 15 2 5 0
FIGURE 7
Layout o f Arbitrary Test Problem with Slab Shield Parallel to the Source Axis
- 29 -
~
WAPO-TM-1623
FIGURE 8
Cylindrical Source w i t h a Detector Point Outside the Radial and Ax ia l Extensions o f t he Source and w i t h a
Slab Shie ld Perpendicular t o the Source Axis
PI --------- For the approximation l e t H = a, A = h, and
a Mc = K so t h a t McR = a
Then se t L = ZR, equate volumes, and solve f o r $o:
FIGURE 9
Section o f an Annulus Used t o Approximate a Cy l i nd r i ca l Source w i t h a Detector Point Out- s ide the Radial and Ax ia l Extensions o f t he Source, and w i t h a Slab Shie ld Perpendicular t o the Source Axis
- 30 -
WAPD-TM-1623
-.-.e
. DETECTOF? POINTS
F I G U R E 10
Layout o f Arbitrary Test Problem with a Slab Shield Perpendicular to the Source Axis
- 31 -
WAPD-TM-1623
FIGURE 11
Base o f an Annular Sector which Preserves the Area o f the Base o f a Rectangular Source
- 32 -
WAPD-TM-1623
FIGURE 12
Rectangular Volume Source Approximation Using a Section o f an Annulus
- 33 -
WAPO-TM-1623
FIGURE 13
Square Rectangular Source Approximation Using a Truncated Cone
- 34 -
WAPD-TM-1623
FIGURE 14
Rectangular Surface Source w i t h Centered Opposite [letector Point
- 35 -
WAPD-TM-1623
V I . Tables TABLE 1 Approximate Flux for a
Exact Flux Cylindrical Source with a Lateral Detector Point and a Slab Shield Parallel to the Source Axis
R MUS A/R 10.00 .lo .20
B = .20 1.00 5.00 10.00
L / A .20 .50
1.00 2.50
3.88 3.58 2.93 1.83
3.68 3.33 2.63 1.59
3.35 2.81 1.99 1.23
3.22 2.50 1.68 1.11
R MlJS A/R 10.00 .lo . 5 0
B .20 1.00 5.00 10.00
L / A .20 2.50 2.43 2.25 2.13 .SO 2.32 2.22 1.92 1.71
1.00 1.94 1.81 1.43 1.24 2.50 1.34 1.22 1.05 .99
B = .20 1.00 5.00 10.00 R MUS A/R 10.00 . l O 1.00
L / A .20 1.90 1.87 1.78 1.70 .SO 1.78 1.73 1.56 1.41
1.00 1.53 1.46 1.23 1.10 2.50 1.17 1 . 1 1 1.03 1.00
R WVS A/R 10.00 .10 2.50
B = .20 1.00 5.00 10.00
L / A .20 1.45 1.44 1.41 1.37 . 5 0 1.38 1.36 1.28 1.20
1.00 1.25 1.21 1.10 1.05 2.50 1.08 1.06 1.04 1.03
R MUS A/R 10.00 .so .20 B = .20 1.00 5.00 10.00
L/A .20 1.91 1.82 1.69 1.63 ,SO 1.79 1.69 1.49 1.37
1.00 1.54 1.42 1.20 1.10 2.50 1.16 1.08 1.01 1.00
B = .20 1.00 5.00 10.00 R MUS A/R 1 0 . 0 0 . 5 0 . 5 0
L / A .20 1.48 1.44 1.37 1.32 . 5 0 1.40 1.36 1.24 1.17
1.00 1.26 1.20 1.08 1.03 2.50 1.06 1.03 1.00 1.00
B = .20 1.00 5.00 10.00 R MUS A/R 10.00 . 5 0 1.00
L/A .20 1.29 1.27 1.23 1.20 .50 1.24 1.22 1.15 1.10
1.00 1.15 1.12 1.04 1.01 2.50 1.03 1.02 1.01 1.00
E =
L / A . 20 . 5 0
1.00 2 . 5 0
.20 1.00 5.00 10.00 R MUS A/R 1 0 . 0 0 .50 2.50
1.14 1.14 1 1 2 1 . 1 1 1 . 1 1 1.11 1.08 1.05 1.07 1 06 1.02 1 01 1.02 1.01 1.01 1 01
B = .20 1.00 5 . 0 0 10.00 R MUS A/R 25.00 .10 . 2 0
L / A .20 2.45 2.34 2.15 2.08 .SO 2.28 2.14 1.86 1.69
1.00 1.91 1.75 1.41 1.26 2.50 1.33 1.21 1.06 1.02
- 36 -
6 = .20 1.00 5.00 10 0 0
L / A .20 1.75 1.71 1.61 1 55 .SO 1.65 1.59 1.43 1.31
1.00 1.44 1.36 1.17 1.08 2.50 1.13 1.07 1.01 1.00
B = .20 1.00 5.00 10.00
L/A .20 1.45 1.43 1.38 1.34 . 5 0 1.38 1 35 1.26 1.18
1.00 1.25 1.20 1 09 1.04 2.50 1.07 1.04 1.02 1.01
B = .20 1.00 5 00 10.00
.20 1.22 1.22 1.20 1.19
.so 1.19 1.18 1.13 1.10 1.00 1.12 1.10 1.05 1.03 2.50 1.04 1.03 1.02 1.02
L / A
B = .20 1.00 5.00 10.00
L / A .20 1.54 1 46 1.35 1 31 .SO 1.46 1.38 1.23 1.16
1.00 1.30 1.21 1 07 1.02 2.50 1.07 1.03 1.00 1.00
B = .20 1.00 5 00 10.00
L/A .20 1.29 1.26 1.20 1.16 .SO l.2E 1.21 1.13 1.08
1.00 1.15 1 . 1 1 1.03 1.01 2.50 1.03 1.01 1.00 1.00
B = .20 1.00 5 00 10.00
L / A .20 1.18 1.17 1.14 1 . 1 1 . 5 0 1.15 1.13 1.08 1 05
1.00 1.09 1.07 1.02 1 00 2.50 1.02 1.01 1 00 1 00
B = .20 1.00 5.00 10.00
L / A .20 1.09 1.09 1.08 1.07 . 5 0 1.07 1.07 1.05 1.03
1.00 1.04 1.03 1.01 1.00 2 50 1.01 1.00 1.00 1.00
R MUS A / R 25.00 . I O . 5 0
R MUS A/R 25.00 .lO 1.00
R MlJS A/R 25.00 . I O 2.50
R MUS A/R 25.00 .so .20
R MUS A/R 25.00 . 5 0 .SO
R MUS A/R 15.00 .so 1.00
R MIIS A/R 25.00 . 5 0 2.50
WAPD-TM-1623
Improved Ratios o f
Appror,imate Flux Exact Flux
Using the A1gorii)hm o f Section 11.0
E =
L/A .20 .50
1.00 2.50
.20 1.00 5 - 0 0 10.00 R 10.00
MUS P / R .lo ..20 R MUS A/R
L / A 25.00 . 1 0 .50 B = .20 1.00 5.00 1o.00
1.07 1 . 0 2 - 9 5 .93 .20 1.73 1.69 1.59 1.53 .50 1.63 1.58 1.41 1.30
1.00 1.43 1.35 1.16 1.07 2.50 1.13 1.07 1.01 1.00
1.08 i . i a .sa :99 1.10 1.06 1.05 1.07 1.14 1.12 1.07 1.03
B =
L / A .20 .50
1.00 2.50
.20 1.00 5.00 10.00 R 10.00
MUS I I / R . l O .so R MUS A/R
25.00 .lo 1 . 0 0 B = .20 1.00 5.00 10.00
L / A 2.11 2.05 1.90 1.81 1.99 1.91 1.87 1.49 1.73 1.61 1.30 1.14 1.28 1.17 1.02 .98
.20 1.44 1.42 1.37 1.33
.50 1.37 1.34 1.25 1.17 1.00 1.24 1.20 1.09 1.03 2.50 1.07 1.04 1.02 1.01
20 1.00 5.00 10.00 R 1 0 . 0 0
MUS A/R .lo 1 . 0 0 B = .20 1.00 5.00 10.00 R MUS A/R
25.00 .10 2.50 L / A
L / A .20 .50
1.00 2.50
1.66 1.64 1.56 1.49 1.58 1.54 1.40 1.28 1.42 1.35 1.18 1.06
.20 1.22 1.21 f.20 1.18
.50 1.18 1.17 1.13 1.09 1.00 1.12 1.10 1.05 1.03 2.50 1.04 1.03 1.02 1.02
1.15 1.10 1.03 1.00
E = .20 1.00 5.00 10.00 R 10.00
MUS A/R .lo 2.50 .20 1.00 5.00 10.00 MUS A/R
25.00 ,So .20
1.54 1.48 1.35 1.31 1.46 1.38 1.23 1.18 1.30 1.21 1.07 1.02 1.07 1.03 1.00 1.00
L / A .20 .50
1.00 2.50
1.32 1.32 1.29 1.27 1.28 1.27 1.20 1.15 1.20 1.17 1.09 1.04 1.08 1.06 1.04 1.03
L / A .20 . 5 0
1.00 2.50
.20 1.00 5.00 10.00 R 1 0 . 0 0
MUS AI'R .so . :!o B =
L / A .20 .50
1.00 2.50
R MUS A/R 25.00 . 5 0 .50
.20 1.00 5.00 10.00 L / A
' .20 ' .50
1.00 2.50
1.91 1.82 1.69 1.63 1.79 1.69 1.49 1 37 1.54 1.42 1.20 1.10
1.29 1.25 1.20 1.18 1.25 1.21 1.13 1.08 1.15 1.11 1.03 1.01 1.03 1.01 1.00 , l . O O
1.16 1.08 1.01 1.00
E = .20 1.00 5.00 10.00 R 10.00
MUS A/R .so .so B = .20 1.00 5.00 10.00 R MUS A/R 25.00 .SO 1.00 L/A
.20
.50 1.00 2.50
1.48 1.44 1.37 1.32 1.40 1.36 1.24 1.17 1.26 1.20 1.08 1.03 1.08 1.03 1.00 1.00
L / A -20 .so
1.00 2.50
1.18 1.17 1.14 1 . 1 1 1.15 1.13 1.08 1.05 1.09 1.07 1.02 1.00 1.02 1.01 1.00 1.00
20 1.00 5.00 10.00 R 10 .00
MUS A111 .so 1.01) e =
L / A .20 .50
1.00 2.50
. 2 0 1.00 5.00 1 0 . 0 0 R MUS A/R 25.00 .SO 2.50
1.09 1.09 1.08 1.07 1.07 1.07 1.05 1.03 1.04 1.03 1.01 1.00 1.01 1.00 1.00 1.00
L / A .20 .50
1.00 2.50
1.29 1.27 1.23 1.20 1.24 1.22 1.15 1.10 1.15 1.12 1.04 1.01 1.03 1.02 1.01 1.00
E =
L/A .20 .50
1.00 2.50
.20 1.00 5.00 10.00
1.14 1.14 1.12 1 . 1 1 1.11 1.11 1.08 1.05 1.07 1.06 1.02 1.01 1.02 1.01 1.01 1.01
R 10.00
MUS A/R .SO 2.50
6 = .20 1.00 5.00 10.00 R 25.00
MUS A/R . l O .20
L / A .20 .50
1.00 2.50
1.62 1.55 1.45 1.43 1.59 1.52 1.41 1.37 1.50 1.42 1.28 1.21 1.23 1.17 1.05 1.02
- 37 -
WAPD-TM-1623
TABLE 2 Approximate Flux
Exact F l u x
from A Cylfndrlcal Source a t Detec tor Po ln ts Outslde the Radlal and Ax ia l Extenslons of the Source ulth an I n t e r v m l n g Slab S h l e l d
P a r a l l e l t o the S a n s Axis
a/R= .20 Mus*R= 1.00 -------------- Mus= . l o ___-____-_ ---------- R = 10.00 ___----- b= .20 b= 1.00 b= 5 . 0 0 b= 10.00 ______-_______- - - _-__---__------- _--------------- ----------------
H ' / l = 1.10 1.50 2 .50 1.10 1.50 2 .50 1.10 1 .50 2.50 1.10 1.50 2 .50 1 /a
.20 1 08 1.14 1 . 4 3 1 . 0 3 1 .08 1.36 . 9 5 1.00 1.29 .94 1.00 1 .31
.SO 1:09 1.17 3 .87 1 .04 1 . 1 2 3 . 4 2 .99 1 . 0 8 2 .46 1.00 1 . 1 1 2 .03 1.00 1.12 1.22 2 .72 1 .06 1 . 1 9 2 . 3 3 1 .07 1 .20 1 . 6 2 1.09 1.20 1.29 2.50 1 .16 1 . 6 3 1 . 8 3 1 .14 1.43 1 . 3 7 1 . 0 9 1.12 l T ( 1 . 0 3 .97 1 7 1
1 / a
2 .50 1 . 27 1 . z z . 9 s 1.17 1 . I i ;TI 1 . 0 2 .go 1- . 97 I - .os
. 2 0 2 . 1 8 2 .42 2 . 9 8 2 .12 2 . 3 4 2 . 8 2 1 .95 2 .10 2 . 4 1 1 .85 1.94 2 . 1 0
. 5 0 2 . 0 4 2 .15 2 . 3 1 1.94 2 . 0 2 2 . 1 1 1 .67 1 .64 1.55 1.48 1 . 3 9 1 4 1 . 0 0 1 .73 1 .72 1 . 6 6 1 . 6 1 1.56 1 .45 1 .28 1.20 97 1.12 1 .04
1 / a
1.00 1 . 4 1 1 .38 1 . 2 3 1 .34 1 .28 1 . 0 7 1.14 1 .05 . O I 1 .04 .94 3 8 -
. 2 0 1 .70 1 .84 2 .08 1.67 1.80 2 . 0 2 1 .59 1.68 1.79 1.52 1.57 1.58
. S O 1 .60 1 . 6 8 1 . 6 6 1.56 1.59 1 .54 1.40 1 . 3 8 1 . 1 8 1 .28 1 . 18 91
2 .50 1 .14 1.05 [ T I 1.08 .97 '-7 1 . 0 1 , . S i .10 . 9 7 T . 0 1
1 / a . 2 0 1 .34 1.39 1.48 1 .33 1.38 1.45 1.30 1.34 1.35 1.27 1.29 1 .24 . S O 1 .29 1.30 1 . 2 s 1 .27 1.27 1.18 1.20 1 .15 94 1 . 1 3 1 . 0 6 .75-,
1 .00 1.19 1 .15 1.00 , 1 .18 1.10 . 8 8 1.07 98 - 1 . 0 2 88 . 2 8 I 2 . 5 0 1.06 . 9 5 . 7 1 , 1 . 0 4 . 8 8 . b D - 1 . 0 1 784 . 0 8 .98 ;41 . O O
1 / a .20 1 . 9 3 1 96 2 . 0 8 1 .83 1.85 1 .94 1 . 6 8 1 .65 1 .66 1.62 1 .56 1.50 .SO 1 . 7 8 1:72 1.62 1.67 1.59 1.48 1 .45 1.32 1 . 1 5 1.33 1.18 1 .01
1 . 0 0 1 .50 1 . 3 8 1 . 2 2 1.38 1 .25 1 .09 1 .15 1 .03 ; a s ( 1 . 0 7 2 .50 1 .13 1.03 1-1 1 .05 .97 .98 .43 . 9 6 ,--%-IT'
1 / a . 2 0 1 .48 1 . 4 9 1 .48 1.45 1 .44 1 .42 1 .36 1 .33 1.24 1 .31 1.28 1 .12 .50 1.39 1 . 3 4 1 . 1 9 1.35 1.28 1 . 1 1 1 . 2 2 1 . 1 1
1 .00 1.23 1. 13 93 1.17 1 .06 -1.04 . 9 1 e;'::: / % ' T I 2 .50 1 . 0 3 . 9 1 1.00 . 4 9 .95 I .UU . 1 3 .92
l / a
1 . 0 0 - 7 ~ l l l . 0 1 VT .;; . 97 (7 :22 2 . 5 0 :::: '* 1:; ":;; d-! :38 . 9 3 , . 52 .05 . 9 0 1 .32 . O O
. 2 0 1 28 1 .27 1 . 2 3 1 .27 1 .25 1.20 1 .23 1 .19 1 .09 1.19 1 .14
. 5 0 1:23 1 .17 &QZ.- 1.20 1.14 .96 1 .13 1 .02 . l l . 0 7 94
1 /a . 2 0 1 .13 1.11 1 .05 1 .13 1 .11 , 1 .04 1. 12 1 .08 98 1.10 1 0 6 91 , S O . 1 . 10 1 .05 . 9 1 -1.09 1 .03 1 . 86 , 1 . 0 6 ~ . 9 7 . - 6 9 - 1 . 0 3
1 . 0 0 , 1 . 0 5 96 ; . 7 6 1 1 . 0 3 92 . 6 8 . 9 9 , . 8 1 -36 . 9 7 : . 7 2 . 1 6 2 . 5 0 .98 , ,EO . 5 9 . 9 6 1 . 7 2 . 3 9 . 9 3 I . 4 5 .04 . 8 9 . 2 5 . O O
- 38 -
i . ~ .. . . .-
WAPD-TM- 1623
- TABLE 2 ( C o n t ' d )
.20 1.84 1.72 2.05 1.57 1.83 1.93 1.48 1.49 1.75 1.43 1.45 1.89
.50 1.80 1.84 2.32 1.52 1.55 2.07 1.40 1.40 1.57 1.38 1.32 1.33
2.50 1.21 1.20 1.08 1.15 1.09 .92 1.03 .92 -1 .g9 -2-?::1 1.00 1.49 1.74 1.85 1.41 1.58 1.45 1.28 1.21 1.09 1.18 1.08
.20 1.78 1.82 1.95 1.71 1.78 1.87 1 . 8 0 1.01 1.81 1.53 1.50 1.43
.50 1.84 1.81 1.52 1.57 1.!53 1.40 1.39 1.29 1 27 1.13 89 :::: 1:lO .99 (-11.05 . ! D 2 I ~ l 1 : : ~ f i 4 .18 .95 K 5 B .03 1 41 1.31 1.12 1.32 1.21 dh1: 04 * , 9 0 1 4 7 -1
.20 1.45 1.48 1.50 1.43 1.45 1.48 1.37 1.37 1.31 1.33 1.30 1.17
.50 1.37 1.34 1.20 1.34 1.?9 1.12 1.23 1.14 87 1.15 1.02 7-9-1 1.00 1.22 1::; & 1.18 1.07 -80 I 1.08 -A9L:-cl 1.00 .27 2.50 1.04 1.01 r-X7- .42 .97 . .59 .OB .93 .38 . O O
.20 1.22 1.22 1.20 1.21 1.21 1.18 1.19 1.18 JLIO 1.17 1.15 1.02
.50 1.18 1 14 1 18 1.12 .98 1 . 1 1 4 . 0 3 : , 7 7 7 1 . 0 7 9 6 1 . 6 1 1
;:;; ;::: ,I!;: <$1:;; , :;; q-v:;; p;- :;; :;; pi
1 /a .20 1.54 1.53 1.50 1.48 1.45 1.41 1.34 1.30 1.22 .50 1.44 1.38 1.24 1.38 1.29 1.13 1.20 1.10 .94
1.00 1.27 1.17 1.02 1.18 1.04 -95J .77 2.50 1.05 .97 -1.00 '1:; d b .97 I . 8 1 .39
1 /a
1.29 1.24 1.13 1.13 1.02 - .e87
11.00 .B5 -92- 90 I . Z O .66
1.15 1.09 11.05 .94r:!!l
.97 - 8 1 .38
.91 I :re .02
1 /a .20 1.17 1.15 1.08 1 18 1 13 1.08 1.13 1.08 97 1.10 1 04 .90
1 : O O 1:07 .971-8-11:04 J a r 8 7 I :98 I 2 :38 2.50 .98 .54 .98 r 7 2 .35 .92 48 04 :::r:9" ::: 50 1 14 1.07 93 1'12 1 05 88-1 08 9 8 1 :7111.02 9 P J - . 5 6 ?
1 / a
- 39 -
WAPD-TM- 1623
TABLE 3
Results From the Exact Flux Formula and From Equation (24) for the Problem o f Figure 7
us = 0.1 s, = 1.0 R = 10.
Distance o f Distance o f Slab Shield Thickness Point From Point Below b = 0.0 b = 1.0 Source Edge
Detector Detector b = 5.0
Source Flux Flux F1 ux a z Exact Approx Exact Approx Exact Approx
5 5 5 5 5 5 15 15 15 15 15 15
0 5 15 25 35 45 0 5
15 25 35 45
0.93 0.65 0.33 0.19 0.12 0.082 0.47 0.39 0.25 0.16 0.11 0.08
1.0015 0.70 0.32 0.16 0.09 0.056 0.53 0.43 0.26 0.16 0.10 0.07
0.23 0.14 0.045 0.016 0.0061 0.0025 0..14 0.10 0.053 0.026 0.013 0.0061
0.24 0.19E-2 0.14 0.82E-3 0.037 0.98E-4 0.009 0.91E-5 0.0025 0.88E-6 0.0008 0.81E-7 0.15 0.14E-2 0.11 0.88E-3 0.05 0.29E-3 0.022 0.50E-4 0.009 0.96E-5 0.004 0.18E-5
0.20E-2 0.80E-3 0.40E-4 0.10E-5 0.20E-7 0.50E-9 0.15E-2 0.88E-3 0.19E-3 0.25E-4 0.27E-5 0.27E-6
- 40 -
.- . ... . ..
WAPD-TM- 1623
TABLE 4 --
L/. 8.25 1.31 1 . 1 1 1.10 1.48 1.15 1.08 1.58 1.24 1.07 1.84 1.34 1.08
-:;:--%-I :R .34 .84 7 3 -
L/. 2 . 5 0 1.81 1.24 1.14 1.90 1.34 1.13 2.18 1.54 1.14 2.48 1.78 1.17
93 1.04 1.23 .98
.34 !d ::: :;: ' . 85 .40
1.25 1.92 1.42 1.22 2.41 V.84 1 . 2 2 2.97 2.05 1.28 3.72 2.80 1.38 3.13 1.02 .99 1.08 1.27 Y.01 1.07 1.57 1 08 1.07 1 89 1 23 1.08 8.29 p F . 8 2 - 1 .98 -- 7 2 - 7 8 2 1 ... 98. . 8 8 .!:827. 96 1:05 :84 .98 15.83 .37 .89 . E 8 1 .38 .89 . 8 8 11 .43 .69 :88- .49 .89 , 8 6 7
-. - .SO 2.10 1.82 1.37 2.88 2.12 1.44 3.94 3.01 1.65 5.62 4.32 2.10
1.25 1.37 1.13 1.14 1.79 1.24 1.14 2.31 1.47 1.15 2 . 9 8 1 .83 1.18
;:;; r T t ,I:;: 1.05 %, 1.00 UL+, 1:oo , 1.58 1:;; , :;; .a8 r .e3 . 88 , .75
L/a 8.29 1.18 9 0 9 . 1 32 1 03 93 1.38 1.18 .95 1.39 1 . 2 8 2
31 .25 .34 78.13 .23 . 5 S .78 .24 .$a5 .78 . 2 6 .5S .78 .29 .59 .70
15.83 rn-g: . a 0 . e h ~ g . 4 0 .Lis :;: t :;; ::g 1::: r::; ::;i
L/. 2.50 1.34 1.03 .9S 1 1 1 18 98- 1 58 1.33 1.00 1.82 1.48 1.08
12.50 ' .:! 1;; .4: .:2 . 8 2 r-3 : t i /+;-q1 31.25 .2S .57 .BO .27 .57 .BO 30 .S7 . 8 0 .38 . 5 8 . R O
8.2s . :: : 3 s I 1
1.25 1.49 1.12 .98 1.87 1.3') 1.01 1.81 1.52 1.07 1.98 1.73 1.18 3.13 - ; 8 1 8 . 50 J - + 7 * T ( p & L $ ; :go .87 1.48 1 4 .e(!
8 . e ~ . 9 5 d i , 8 3 1 15.83 .29 .59 .81 .32 .5!l .81 .37 .BO .81 1 . 4 8 . 6 0 .81
L/a . 5 0 1.43 1.15 1.01 1.70 1.45! 1.08 1.93 1.74 1.22 2.28 2.11 1.45
- 41 -
WAPD-TM- 1623
TABLE 4 (Cont'd)
L/a 6.25 1.23 1.00 .99 1 38 1.08 .99 1.44 1.19 1.00 1.48 1.30 1.03 15 6 3 . .89 .13 . 31 : 25 .83 ~ ~ ~ & f ~ 0 7 ~ ! ? ~ ! ~ ~ 5 9 ~ 18.13 .25 .51 .18 .26 .51 .19 .21 .51 . l B .30 .51 .19
L/a
31.25 .21 .eo .ai .ze .EO .ai .3i .eo .ai .3e .eo .ai
2.50 1.44 1.10 1.03 1.66 1.23 1.03 1.19 1.41 1.05 1.93 1.59 1.11 6.25 -3 .76 J ,
A: [-:,-[ .90 85 I 1.09 .63 .83 .67 h m ? 7 e a m s - f .90 1 28 92 90
12.50 .43 . E 8
L/il 1.25 1.60 1.21 1.01 1.92 1.42 1.09 2.20 1.12 1.14 2.55 2.05 1.28 3.13 .86 . 6.25' .52 .r . 86 .63 .e2 .82
.92 1.08
15.63 .31 .62 .82 .33 .62 .82 .38 .62
L/a .50 1.59 1.21 1.13 2.01 1.62 1.20 2.48 2.12 1.31 3..19 2.17 1.88
1.25 1.10 .81 2.50 . 6.25 ' .;:. :;! .67 ,831
H'/L= 1.10 1 . 5 0 2.50 1.10 1.50 2.50 1.10 1.50 2.50 1.10 1.50 2.50 L / i 8.25 1.16 .ai 87 1.29 1.01 .a8 1 - 3 2 1.14 15.63 .58 .63-0 I .71 . e 5 7 0 1 .88 .69 31.25 ' .33 .56 . 1 8 .38 .518 .78 I .49 .51 18.13 .22 .b4 . l l .23 .54 .I1 .25 .54 . 7 1 .29 .54 . l l
L/i 1.25 1.38 1.07 93 1.54 1.23 88 1.58 1.41 1.02 1.60 1.54 1.13 3.13 . . 3 ; 8 n 1 0 3 6.25 .:: .:2 .81 ::: '
.28 .58 . 80 .31 .58 . 8 0 .31 .58 7; r- .59 . 8 0
' 'T 15.63
- 42 -
WAPD-TM-1623
TAE:LE 5 -- Results From the Exact Flux Formula and
From Equation (30) for the Problem o f Fiqure 10
s, = 1.0 R = 10. us = 0.1
Slab Shield Thickness Distance o f Distance o f Detector Detector Point From Point Below 0 = 0.0 Source Edae Source flux Flux Flux
- b = 1.0 b = 5.0
a z Exact Appr3x Exact Approx Exact Aoprox
5 5 5 5 5 5 15 15 15 15 15 15
0
5 15 25 35 45 0 5 15 25 35 45
0.93 NA 0.65 0.43 0.33 0.27 0.19 0.1:' 0.12 0.12 0.08 O.Ot1 0.47 NA 0.39 0.33 0.25 0.2:; 0.16 0.161
0.11 0.11 0.08 0.08
0.23 0.14 0.098 0.062 0.041 0.029 0.14 0.066 0.062 0.048 0.036 0.027
NA 0.11 0.08 0.056 0.039 0.029 NA 0.077 0.061 0.048 0.036 0.027
0.20E-2 NA 0.95E-3 1.1E-3 0.92E-3 0.86E-3 0.76E-3 0.70E-3 0.58E-3 0.55E-3 0.44E-3 0.43E-3 0.14E-2 NA 0.31E-3 0.55E-3 0.39E-3 0.51E-3 0.42E-3 0.46E-3 0.39E-3 0.41E-3 0.33E-3 0.35E-3
- 43 -'
WAPD-TM-1623
TABLE 6
The Function Lo(40,b)
TABLE OF THE SMOOTHED FUNCTION L O ( i . 8 )
R l Y F P l = . 0 1 . 0 5 . 1 0 .20 . 4 0 .BO .90 1.00 1.25 1.50 1.75 2.00 2.50 3.00 ji i i i A D i
,01745 i O O O O O 1 . 0 ~ 0 0 0 .sgggg .99999 ,89997 99998 .99999 ,99994 .99993 ,99991 ,99990 .99998 99999 .e9993 ,04383 1,00000 ,99989 .99999 .99991 ,99994 99978 ,99989 ,89982 ,99953 .99945 99938 .99928 .99911 99895 ,08727 .99998 .99991 .99992 ,99981 ,99934 99905 ,99876 .99849 ,89913 99779 .99745 ,99712 ,98848 ,99580 ,13090 ,99998 ,99979 .99959 ,99921 ,99852 .99795 ,997PO ,99857 ,99579 99503 ,99427 .99352 .99204 .99058 .I7453 ,99982 99962 ,99927 ,89981 99738 ,99817 99502 ,99390 99252 ,99118 .98983 .@a950 98599 99331 ,21817 .99999 :e9941 99898 ,99782 :99598 .99400 ,89221 99048 ,99931 99620 .99412 .99208 ,97902 ,97403 .28190 ,99991 ,99919 :99835 ,99884 .99402 ,99134 ,88878 :98624 ,88318 :99014 97718 ,97423 .98947 .98291 ,34907 ,98988 ,99948 ,99703 ,99432 .e9927 ,89451 ,97992 97547 97004 ,98474 95955 .e5445 94450 93492
99755 ,89528 ,99100 ,99309 ,97558 ,88944 :#E153 :95318 ,84503 ,83712 ,92939 ,91443 .go005 99640 .e9307 ,99081 ,97525 .e8447 .95421 94438 93251 92109 91005 .e9935 ,97895 95942 89498 ,99033 .e8188 98574 ,95102 ,83713 192390 :go811 ,99305 ,87882 ,88475 ,93853 .91410 99324 ,98701 97542 :95435 ,93509 ,91709 ,90009 ,98004 ,86112 ,84319 .92815 ,79441 ,78542 99112 ,99298 196794 .94088 91645 ,99391 ,97299 ,94839 ,82559 .E0427 ,78425 .74784 ,71493 99956 ,97913 ,85901 ,92508 .e9491 ,98791 ,94232 ,81341 ,79693 ,78253 .73997 ,89953 .88429 99159 ,98511 ,83553 ,88499 ,84208 .go489 .77158 .73507 .'10295 ,87445 .E4995 .EO524 ,56907 97058 .94510 .BO108 ,93048 77487 ,72932 .89111 85108 ,91748 ,59879 ,58393 52281 ,49992 95051 .91072 .94743 ,75779 189521 ,84797 .e1048 :57288 ,54189 ,51808 ,49393 ,45781 42873 99281 .E3771 .78513 ,87838 ,81874 ,57821 ,54271 ,50907 ,48169 ,45872 .43905 ,40677 .39110
8 (WFP) = 3.50 4 . 0 0 5 . 0 0 8 . 0 0 8 . 0 0 1 0 . 0 0 1 2 . 0 0 1 5 . 0 0 2 0 . 0 0 2 5 . 0 0 3 5 . 0 0 50.00 EO 00 75 00 ,6 (RAD)
.01749 ,99991 99979 ,99973 ,99968 99957 ,89947 .e9937 .99922 99898 ,99971 ,99920 ,99744 ,99694 ,99618 ,04363 ,99978 199882 .99930 .e9798 :e9734 ,99870 ,99807 ,99512 .e9355 ,99199 .98985 ,98420 .99113 ,97654 .08727 .99515 ,9945i ,98322 .99195 .99942 ,99691 ,98442 ,98071 ,97459 ,96855 ,95887 .93938 ,92814 ,81177 ,13090 .98913 -98769 .e8493 ,98201 ,87642 97092 ,68548 .95744 ,94432 ,93159 ,80696 .87232 85081 ,81996 ,17453 ,99078 .e7823 ,87324 98831 ,95883 ,94919 ,83992 .9263S 90456 .e8374 -84477 .79230 78084 .71822 .21817 ,97010 98822 ,95859 :OS109 ,93849 ,92235 ,90884 ,89880 ,95757 .82944 ,77515 .70953 87023 .e2070
,28190 .95728 :95178 ,94107 ,93082 ,91048 .99117 87289 .84835 90594 ,78909 70519 82835 59897 ,53582
,34907 .92939 ,91619 99838 ,99127 .94906 91918 :79141 ,75329 :e9787 65040 :57492 149432 145491 .40922 .43833 ,89819 ,87278 194729 ,92334 ,77951 ,74041 ,70535 ,85917 ,59590 54583 ,47138 39902 .38551 32791 ,52380 ,94095 ,82334 ,79044 ,76031 70708 68181 .82245 ,17310 .SO938 ,48159 ,39497 ,33296 ,30470 27329 ,81087 ,79123 .79979 ,73081 ,89573 :03845 :58812 ,94910 ,48987 . 4 4 0 0 2 ,39704 ,33970 ,28533 ,28117 ,23124 ,89813 ,73890 ,71427 87058 ,83287 57124 ,52317 49473 .43961 ,39588 ,34781 ,29838 .24986 .22852 ,20498 .79540 .E8553 ,85997 :E1288 .57432 :51357 .48792 143230 .39127 .34293 .30900 .26345 22192 .20313 .18219
,87288 ,83332 .80590 ,55952 ,52180 ,48412 ,42197 .38938 ,35222 .30885 .27910 ,23710 .I9973 .19282 ,18397 1.04710 ,53959 . S I 2 5 1 47004 ,43874 ,39727 ,35170 ,32491 29352 ,25721 ,23179 ,19759 ,16844 ,15239 .13664 1.22173 , 4 6 2 8 1 ,43992 :40309 ,37441 ,33195 .30148 ,17815 :25159 . Z 2 0 4 8 19985' ,18938 . 1 4 2 6 8 ,13059 .11712 1.39828 ,40497 ,38494 ,35270 ,32781 ,29048 ,26378 ,24339 ,22014 19290 ,17382 .14919 ,12493 ,11428 . l o 2 9 8
i.57080 ,35998 ,34217 ,31351 -29121 ,25918 ,23447 .21834 ,18568 17147 15450 .13172 11098 ,10157 09109
- 44 -
WAPO-TM-1623
TABLE 7
The Functi lm G(eo,b) -
TAELE OF THE FUNCTION O ( 8 . 8 1
8 (WFP) = 01 OB 10 20 40 8 0 80 1 00 1 25 1 50 1 75 2 00 2 5 0 3 00 a roan1 - . . .. .- , . 0 174B
,04383 ,08727 .I3090 .I7453 ,21817 .28180 ,34907 ,43833 .B2380 .E1087 .E9813 ,78540 ,87288 1.04720 1.22173 1.39828 1.57080
8 (WFP) = t (RAD) . 0 1745
,04303 ,08727 ,13090 ,17453 ,21817 ,28180 ,34807 ,43033 ,52380 .81087 ,898 13 ,78540 .E7208
1.04720 1.22173 1.39828 1.57080
1728-01 1 6 6 0 - 0 1 4149-01 8290-01 1241t00 1851+00 2058t00 2481tOO 3250+00 4014tOO 474Bt00 B438t00 1098+00 8889+00 7237iOO 8153+00 8807tOO 9179100 9272t00
4.00
1579-01 (429- 0 1 3571-0 1 7134-0 1 l088t00 142OtOO 1789+00 2114+00 2789+00 3438t00 4OBBt00 4838 t 0 0 B174t00 5884 t 00
1170-01 2924 .o 1 1839- 0 1 8739-01 1182tOO 1448100 1727t00 2274+00 2797t00 3289tOO 3747+00 4 18Bt 0 0 4339+00 4885iOO 5383+00 5850 to 0 5750tOO 5757t00
9578 02 2393 01 4780 01 7111 01 9501 01 1182 ' 0 0 1111 i o n
7842-02 1959-0 1 3912-01 5852 -0 1 7771 - 0 1
8420-02 1804-01 3202-01 4788-01 8358-01 7899-01 9413-01 1233t00 1508400 1758tOO 1981tOO 2177tOO 2343*00 2477t00 2853i00 2724t00 2738+00 2738+00
5 0 0 0 - 0 2 1249-01 2493- 0 1 3728- 0 1 4944-01 8140-01 7310-01 9553-01 1184100 1353100 1520t00 1863+00 1781100 1874t00 l988IOO 2028t00 2033t00 2033t00
3894 - 02 9728-02 1941-01 2900-01 3845-0 1 4772-01 5077-01 7402-0 1 899 1-0 1 1042tOO 11eet00 1270t00 1355t00 1419100 1493+00 1515+00 1518t00 1518+00
3033-02 7578-02 1511-01 2257-01 2891-01 3708- 0 1 4409-01 5738-01 8948-01 8024-01 8948-01 9710-01 1031tOO 1075iOO 1123100 1138+00 1137t00 1137iOO
2382-02 5899-02 1177-01 1758 . O 1 2328-01 2883-01
1432-02 3578-02 7132-02 1084-0 1 1407-01 1742-01 2085-01 2889-01 3208 - 0 1 3870 01 4049-01 4348-01 4583-01 4709-01 4 8 4 3 - 0 1 4888-01 4887-01 4887-01
8888-03 2170-02 4323-02 8443-02 8515-02 1052-01 1245-01 1803-01 1917-01 2179-01 2389 01 2547-01 2858-01 2728-01 2784-01 2792-01 2792-01 2792-01
4319-01 8029-01 1292+00
si4i-01 7885-01 1181+00 1570+00 1957+00 2330100 3088tOO 3012+00 4603t00 I1 581 0 0 B787t00 6328t00 8838+00 7178t00 8258t00 8505 t 0 0 8825+00
5.00
1176-03 2934-03 5835 -03 887 1-03 1141-02 1402-02 1049-02 2088-02 1448-02 2724-02 2920-02 3048-02 3121 - 0 2 3158-02 3177-02 3178-02 3178-02 3178-02
iiiS+oo 2143t00 2582+00 3385t00 4183+00 4948tOO 5875t00 8358+00 8993tOO 7574+00 8558+00 9278t00 9710t00 9848+00
9884-01 1152t00 1512t00 18S1t00 2185100 245OtOO 2702+00 2919+00 3100tOO 3348100 3482t00 3485t00 3488tOO
3424-01 4445-01 5370-01 8181-01 8 8 8 8 - 0 1
1854 ii 2271 00 2088 00 3030 00 3354 00 3839 00 3882 00 4234 00 4414 00
.... .. 7428-01 7852-01 8158-01 8472-01 8545-01 8549-01
i102t00 8808+00 7287 t 0 0 7477tOO 7505+00
4482 0 0 4484 00
10 0 0
7919 0 8 1974 OS 3907 OB 5781 05 7500 05 9098 OB 10B3 04 1285 04 1448 04 1545 04 1598 04 1822 04 1831 04 1833 04 1834 04 1834 04 1834-04 1834 04
8549-01
50.00 3.50
B289-03 1318-02 2820-02 3902-02 8152-02 8358-02 7512-02 9830-02 1145-01 1295-0 1 1411-01 1495-01 111 1-0 1 1585-0 1 1809-01 1112-01 1812-01 18 12-0 1
8 . 0 0 8 . 0 0 1 2 . 0 0
1072 -08 2870-08 5275-08 7753-08 1005-05 1213-05 1398- 05 188 1-15 1887-05 1971-05 2021-05 2040-OB 2048-05 2047-05 2047-05 2047-05 2047-05 2047-05
15.00 20.00
3594- 10 8934-10
2 5 . 0 0 35.00 8 0 . 0 0 75.00
4057-34 1141-33 2130-33
3196-03 7979-03 1588-01 2384-02 3117-02 3841-02 4531-02 5781-02 8848-02 7898-02 8340-02 8789-02 9074-02 9234-02 9338-02 9347-02 9347-02 9347-02
4325-04 1079-03 2144-03 3181-03 4178-03 6119-03 B999-#3 7539-03 8758-03 9853-03 1025-02 1082-02 108 1 - 0 2 1089-02 1093-02 1093-02 1083 - 02 1093-02
5852-05 1480-04 2894-04 4280-04 5598-04 8823-04 7845-04 9838-04 1124-03 1218-03 1274-03 1304- 0 3 1318-03 132 1-03 1322-03 1322-03 1322-03 1322-03
5335- 08 1328-07 2818-07 3828-07 4933-07 5908-07 8741 -07 7973-07 8898-07 9053-07 9197-07 9242-07 9252-07 8264-07 9254-07 9254-07 9254-07 9254-07
2421-12 8010-12 1173-11 1091-11 2137- 1 1 2501- 1 1 2783.- 1 1 3131-11
1098-18 2720-18 5260- 18 7475- 18 9279.- 18 1084-15 1159- 19 1258-1s
3358 - 23 8281-23 1580-22 2199-22 2881 - 2 2 2973-22 3181-22 3313- 22 3342-22 3345-22 3345-22 3345-22 3345-22 3345-22 3345-22 3345-22 3345-22 3345-22
1524-27 3748-27 7088-27 9737-27 1180-28 1277-28 1341-28 1385-28 139 1-20 1381 -28 139 1 - 2 8 1391 -28 1391-28 1391 28 1391-20 1391-28 1391 -28 1391-20
1752-09 2544-09 3248-09 3842-09 4328-09 4980-09 5308-09 5431-08 5475-08
2871-33 3351-33 3818-33 3745-33 3814-33 3820-33 3820-33 3820-33 3820-33
. . 3278-11 3325- 1 1 3336- 1 1 3338-11 3538-11 3338-11 3338- 1 1 3338- 1 1 3338-11
.- 1288-19 1295-15 1295- 15 1295- 15 1295-15 1295- 15 1295-15 1295-15 1295-1s
_ _ 5483-09 1485-09 5485-09 5485-09 5485-09 5485-09
~~~. ~~
3820-33 3820-33 3820 - 33 3820-33 3820-33 3820-33 S4iS-ie
.- 1295-15
TABLE 8
The Smoothed Function G(eo,b) = G(e,,b)e b /eo --
TABLE OF THE SMOOTHED FUNCTION EXP(B)*G(S.BJ/B
8 (MFP) .01 .05 .10 .20 . 4 0 .EO - 8 0 1.00 1.25 1.50 1.75 2.00 1 . 5 0 3 . 0 0 0 I R A n l - ... _,
,01749 '
,04383 ,08727 .l3090 .17453 ,11817 .28180 ,34907 ,43833 .52380 ,81087 ,88813 .78540 ,87288 1.04720 1.22173 1 39028 1.57080
. 99995 ,99988 .e9872 .e9712 ,96488 . 9 9 2 0 1 .98850
99995 .99987
.99994 99965
.99994 ,99962 99848
,99058 ,99382 .99051 ,98834 97579 ,90232 . 94860 .e2890 .go514 . 88082 ,85409 .79401 72850 ,85409 58353
99993 99950 99822 9960 1 99291 98893 98408 97180 95815 93722 91514 89007 88218 83189 78402 18993 01438 54872
99892 99g49 99797 99944 99190 98738 88183 88784 95001 92880 90387 87549 84434 81054 73688 85825 58230 51778
.e999 1 ,89943 99772 ,99487 99089 .98579 ,97958 .80391 ,94402 .92013 .89248 .Be140 ,82727 ,78054 ,71183 .e3058 .55554 ,49387
99890 99937 99748 99430 98998 98423 97735 98001 93807 91 180 88158 84778 81091 77182 88887 80813 53287 47350
99989 99918 99715 99359 98863 98228 87457 95517 93072
.e9987 .99888 .99985 99982 99889 99557 99008 98240 97285 98089 93188 89559 85378 80754 75834 70775 85739 58335 48524 42488 37747
99980 99873 99494 98885 97993 98885 9555 1 92255 88224 83804 78584 73289 07988 82778 B3407 45908 40170 35707
9992 1 99883 99288 98738 98034 97181 95038 92348 89 182 85540 81555 77294 ,72855 83888 5559 1 48712 43299
99913 99852 99218 98813 97841 B8905 84583 91838 88185 84289 80039 75539 70905 81739 53523 48872 41884
99905 99820 99147
. 99867
.99700 99488 .99189 . 988OB
..~.. 988BO
,99888 ,99442 .E9130 ,98748 ,97780 .@E544 .a5044 ,83289 . 9 1287 .89048 ,86578
98489 97848 98832 94093 90933 87230 83078 78582 7387 1 89075 59779 51880 45242 40215
.e790 1
.e8828 95448
. 83835
.91993 ,89931 ,87880 82527 .78888 70239 ,83312
,9788 1 .98700 .95288 .E359 1 .91878 .89531 .87 176 .E1845 7S781
90180 .88828 ,83133 ,78143 ,74837 .BO253 ,57933 ,50817 ,45171
.a1011 ,74888 ,87793 .e9112
,82055 .eo885
8 (MFP) 3.50 4 . 0 0 8 . 0 0 8 . 0 0 8 . 0 0 10.00 12.00 15.00 20.00 2 5 . 0 0 3 5 . 0 0 50.00 80.00 75.00 c lodnl - , . ,
,01745 -04383 ,08727 ,13090 ,17453 .218l7 .28180 ,34907 ,43833 ,62360 ,81087 . 608 13 ,78540 .872EO
1.04720 1.22173 1.39828 1.07080
,99977 99857 ,99431 ,98729 ,97747 .98508 . BBO 10 . 9 1382 .88928 ,81903 ,70407 .70928 ,85610 ,80139 ,50881 43888 .38221 ,33979
,99971 ,89842 . 99388 ,98585 .97502 .@I3133 ,94493 .no484 .8B888 ,80272 .74543 ,68734 -83078 .S7770 .e8887
,365110 ,32488
, 4 1 7 ~ 1
,99870 .Be810 ,99242 ,88308 ,970 18 ,95391 . 93458 ,88777 ,83259 ,77203 ,70847 ,84708 . I8982 ,53707 ,45031 .38810 .33784 ,30030
.99984 ,99778 ,99117 .e8029 ,98534 . B4880 ,92440 ,87131 ,80975 .74373 ,87718 ,81348 .555 I 1 . BO349 .42098 ,38088 .31B77 ,28088
99954 997 15 98887 97478 95583 93228 90470 84012 78778 89337 82182 15883 4990s 45120 37838 32201 28229 25092
999 I 4 99852 98819 989 34 940 19 91838 885 18 81117 730 I3 850'19 578 30 11118 457 14 412 t o 343111 294 ' iZ 257 10 229 17
99934 99589 98371 98394 83732 90483 88781 78398 89825 81282 53838 47558 42391 .38 179 31819 27274 23884 21213
,89919 .e9494 .98002 .95598 ,92387 ,88523 ,84187 ,74087 .85151 .5852 1 492 18 ,43275 .38510 .34885 ,28888 24761
99893 99337 97393 94291 90225 85431 80189 89222 58998 50384 43482 38107 3388 1 30493 25411 21781 19058 16941
99888 99181 98790 93019 88158 82544 78937 84581 54093 45728 39322 34424 30801 27541 22950 19872 17213 15300
.e9818 98889 ,85805 .BO570 -84291 ,77317 ,70214 ,57155 .48825 .39213 ,33833 ,29431 .28181 ,23564 .I9820 ,18817 ,14715 ,13080
99742 98404 93877 87118 79080 70843 82803 49105 39708 33122 28392 24843 22083 19874 18582 14198 12421 11041
9989 1 98097 92750 84951 75928 80839 58492 4530 1 3840 1 30344 28009 22758 20230 19207 15172 13005 11379 10115
99815 97639 91122 81895 71685 81918 53407 40789 32883 27238 23347 20428 .18158 18343 13819 11073 10214 09079
21088 . 19259
- 45 ' -
WAPD-TM-1623
TABLE 9 b
The Smoothed Function ( a o , b ) = F (eo ,b)e / eo
TABLE OF THE SMOOTHED FUNCTION EXP(S)*F(O.B)/O
B ( M F P ) - , 0 1 ,05 , i o .20 .40 . 8 0 . 8 0 1 0 0 1.25 1 . 5 0 1.75 2 . 0 0 2 . 5 0 3.00 4 (RAD)
,01745 ,04383 .On727 ,13090 ,17453 .21817 ,28180 ,34807 .43833 ,52350 ,81087 ,59813 ,78540 ,87288
1 ,04720 1.22173 1.39528 1.57080
1 (YFP) 4 (RAD) . 0 1745
,04383 ,08727 . I3090 ,17453 ,21817 ,25180 .34807 ,43833 .52350 ,81087 ,89913 .78540 ,87285
1.04720 1.22173 1.39525 1.57080
1 . o o o o o . o o o o o . 89998 . 99907 .S8995 99992 .89988 .a9878 .98987 .e9951 .98931 ,90907 ,88878 .e9842 ,99743 .e9582 ,98253 .97328
1.00000 .99998 ,98894 . 89988 ,98974 . 99980 .89942 . 89895 ,88834 ,09755 ,98858 . 99538 ,98393 .98215 ,98729 ,97848 .98453 .el385
. 99999
.99997 ,98997 .89971 .Be848 . B982O .SO884 .98791 .e9859 ,885 1 1 ,89317 ,99080 ,98792 98443 ,97482 .9599 1 .93257 ,98443
. 89988 . 09994 ,99975 ,89943 ,99898 ,99940 ,99708 ,88583 ,89337 .e8027 ,99543 .98178 ,87813 . 95933 ,95113 ,92343 ,87723 ,79598
.99998
. 98987
. 99949 ,89985 ,89798 . 99880 . e9537 .99188 .E8583 .Be071 ,9732 1 . 884 18 ,95334 .a4048 ,80713 ,85987 .79 145 .70774
99997 99881 89924 99828 99594 99520 89307 88757 98038 87133 85032 94715 93159 91335 88739 80801 72795 84831
. 98898
.89975 ,99888 ,9977 1 .e9582 ,8938 1 .@SO78 .88348 ,97398 .e8211 . e4775 .e3072 ,91080 ,88778 ,83140 ,78038 .E7857 ,80385
.98985
. 98988
.e9873 ,99714 .Be481 ,98203 .e8850 ,97844
.OS308 ,93549 ,01484 ,88094 85387 ,78870 ,72113 ,83897 ,58810
98780
,89994 ,89980 ,8984 1 89843 ,88384 .88005 .88558 ,97443 ,95988 ,94198 .82080 ,88573 ,88733 ,83543 .78 188 ,87927 ,59864 ,532 15
.89892 ,89952 . 898 10 89571 ,98238 . e 8 8 0 9 .a8284 ,95948 ,95222 ,83111 .BO815 ,87741 ,84488 .80912 ,72898 .e4373 .56550 ,50275
99991 89944 89778 99500 99112 88513 98003 98453 94488 92050 892 18 85983 82382 78458 89840 81317 5378 1 47805
89990 99937 89748 89429 88988 98417 97724 95985 83722 91012 87858 84298 90378 75168 87274 58857 51398 45888
.e9997
.e9921
.89593
.E9288
.e8735
.ea029
.97189 ,85003 ,82287 . 88002 ,85283 . 8 1 1 2 1 ,78887 ,72015 ,82885 .54241 .47484 ,42209
,89985 .99905 ,99820 .89148 . 98498 ,87843 . 9882 1 ,94059 .SO855 ,87078 .e2819 .78 189 ,73320 ,58352 ,58826 ,50707 ,44378 .39445
3.50 4 . 0 0 S . 0 0 8.00 8 . 0 0 1 0 . 0 0 12.00 16.00 20.00 25.00 35.00 50.00 5 0 . 0 0 75.00
,99982 . 99889 .Be557 .E9005 .Be238 .87280 ,08078 ,93132 ,88483 .E5234 ,80915 ,75477 .70289 ,85131 ,5558 1 .47788 ,41824 ,37177
. 99980 ,98873 ,99494 .88855 ,97981 . 88880 ,95540 .S2223 .88191 ,83488 .78342 .72985 ,67637 .82258 ,92802 .45344 .we77 ,35288
,99875 . 89841 ,98389 ,98594 ,87900 ,98127 ,84482 ,90453 ,85500 ,80148 ,74350 ,88485 ,82741 ,57385 ,48292 , 4 1 4 1 1 .35235 ,32208
,89970 .e8810 ,99242 .88308 ,97014 .US388 .83445 .E8747 .83182 ,77082 ,70779 .e4505 ,887 15 .53418 ,44747 ,38383 .33588 ,29839
,89959 ,98747 .88992 ,97752 ,88054 .a3934 .B1435 ,85518 ,78783 .7 1887 ,84893 .!I8172 .Liz385 ,47351 ,38522 ,33877 .a9542 .a8348
.99949
.e9893 -88743 .87209 .99112 , 82522 ,89505 ,82508 ,74787 ,87018 ,19700 .53181 ,47599 ,42927 ,35799 ,30877 .28842 ,23880
99938 ,98520 . 88495 . 88853 ,84187 ,81150 ,87551 ,79708 .71233 .e3008 ,55573 ,49103 , 4 5 8 8 0 39538 ,3295 1 ,28244 ,24713 .21987
,99924 ,99525 ,99125 .e5880 ,92830 . 88153 .85005 ,75849 .E8534 .57951 .SO581 .a4523 .39634 .35879 ,29733 ,25485 .22300 19822
,89899 ,89359 ,87514 .94549 . 80848 85029
,80830 ,70225 .eo091 ,51423 ,44448 38985 34846
,31183 ,25988 ,22273
19489 . 17324
99873 99212 988 10 93270 88581 83102 77230 55439 54873 48538 40041 35058 31184 28048 23373 20034 17530 15582
99823 88900 85722 80809 84552 77808 70791 57798 47425 39738 34085 29828 265 12 23881 19884 17044 14913 13258
,99747 ,98435 ,83990 ,87338 ,79387 .71047 .E3049 .a9542 ,40084 ,33439 28854 .2508 1 .22284 ,20085 .I5721 ,14332 ,12540 . 1 1 147
99595 98127 92887 85183 75229 57 198 58871 45650 36692 30588 282 19 22941 20392 18353 15294 13109 11471 10198
.99821 ,87869 .91229 82091 ,71951 822 17 ,537 10 ,41048 ,32894 ,27414 ,23499 ,20550 . 18278 ,18448 . 13707 . 1 1 749 ,10280 .09138
TABLE 10
The Function F (eo,b)
TABLE OF THE FUNCTION F ( e . 8 )
B I Y F P I I - 0 1 .05 . l o .20 .40 . 6 0 . 8 0 1.00 1 2 5 1 .60 1.75 2 0 0 2 5 0 3 0 0 i iRnbi . 0 1745
,04383 .OB727 . 13090 ,17453 ,21917 .a8180 ,34907 .43833 ,52380 ,81087 ,89813 ,79540 ,87288 1.04720 1.22173 1.39828 1.57080
1728-01 4320-01 8840 -0 1 129e*oo 1728*00 2180+00 2592t00 3455tOO 4318+00 9181+00 8044tOO 5905+00 7788t00 8825+00 1 0 3 4 t O l 1205tOl 1372t01 1514+01
1550-01 4150-01 8301-0 1 1245t00 l580tOO 2074t00 2488tOO 3317tOO 4144t00 4988+00 S791tOO 8510tOO 7428tOO 8238tOO 9835tOO 1138+01 1281+01 1385t01
1578-0 1 3948-01 7895-01 1194+00 1578tOO 1972+00 2388t 0 0 3 1 5 2 i 0 0 3935+00 4715tOO 5490tOO 8258+00 7021tOO 7773t00 9238tOO 1081+01 1178t01 1229+01
1429-01 3572- 0 1 7143-01 1071t00 1427t00 1783t00 2 138t 00 2848tOO 3549t 00 4245tOO 4933t00 5812tOO 5277+00 8928+00 8155+00 9237 tO 0 1003t01 1024+01
1170-01 2824-01 5847-01 8784-01 1188+00 1458+00 1747tOO 2320tOO 2988tOO 3442t00 3985t00 45 12.00 BO18IOO 5502100 8388tOO 7040100 7407400 7452+00
8578-02 2394--01 4788-01 7172-01 9548-01 1182+00 t427+00 .. 1882100 2348100 2791t00 32 1 8 t 0 0 .. 3529+00 4015tOO 4374+00 4985t00 5404t00 5578+00 5589iOO
7842-02 1980-01 3917-01 5888- 0 1 7810-01 9740-01 1185400 1543tOO 1810t00 2284+00 2801+00 2920t00 3214t00 3481t00 3912t00 4174r00 4258t00 428 1 t 00
84 2 0 .. 0 2 1505-01 3208-01 4802-01 8388-01 7982-01 9520-01 1258t00 1553 t 0 0 1838t00 2102t00 2350100 2574+00 2773tOO 3077t00 324 lt 0 0 3282+00 3283tOO
5 0 0 0 -02 1250-01 2495-01 3737.01 4989-01 8188-01 7393-01 8745-01 1200100 1413100 1811100 1792t00 1952too 2088100 2288tOO 2378100 2395t00 2395t00
3894-02 8731-02 1943.-01 2909-01 3885-01 4 8 1 0 - 0 1 5741 -01 7551 -0 1 9271 -0 1 1088tOO 1235t00 1357+00 1481tOO 1578tOO 1703tOO 1755t00 1752t00 1782+00
3033-02 7578- 02 1513-01 . . 2283-01 3008-01 3739-01 4459-01 5851 -0 1 7153-01 8379-01 9476-01 1043tOO 1124*00 1190+00 1273t00 1302+00 I305+00 1305+00
2352-02 5901.02 1178-01 1781-01 2338-0 1 2908-01 3482- 0 1 4533-01 5934-01 5449- 0 1 7283-0 1 7984-01 8543-01 8995-01 9534-01 9898-01 9712-01 8712-01
1432-02 3579-02 7141-02 1087- 0 1 14 15 -0 1 1758-01 2 o s i - 0 1 2722 01 3305- 0 1 3925-01 4275-01 4849-01 4 9 4 3 - 0 1
5442- 0 1 5442-01
8888-03 2170-02 4328-02 5481-02 8958-02 1051-01 1258-01 1835-0 1 1874- 01 2270-01 2518-01 2718-01 2857-01 2970-01 3057-01 3084-01 3085-01 3085-01
B (YFPI = 3.50 4 . 0 0 5 . 0 0 8.00 8 . 0 0 1 0 . 0 0 12.00 1 5 . 0 0 20.00 25.00 35.00 50.00 8 0 . 0 0 75.00 i (RAD) . 0 1745
,04383 ,08727 .13090 .17453 ,21817 .28180 ,34907 .43833 .52380 ,81087 .e8813
,87280 1.04720 1.22173 1.38828 t.57080
.78sao
5270-03 1315-02 2824-02 3914-02 8178-02 8408-02 7598-02 8817-02 1179- 0 1 1348-01 1485-01 159 1-0 1 1887-01 1718-01 1758-01 1783-01 1783-01 1783-01
3188-03 .. 7892-03 1590-02 2370-02 3132-02 3871-02 498 1-02 siee-oz 7045-02 8005-02 8785-02 9330-02 9715-02 9951 -02 1 E t 3 - 0 1 1011-01 10 15-0 1 1015-01
1178-03 2935-03 5843-03 8895-03 1147-02 1413-02 1687-02 2127-02 2517-02 2828-01 3050-02 3221-02 3320-02 3374-02 3407-02 3409-02 3409-02 3409-02
4325-04 1080-03 2147-03 3190-03 4197-03 5158-03 8084-03 7870-03 8998-03 1001-02 1072-02 1117-02 1143-02 1155-02 118.2-02 1182-02 1182-02 1182-02
5853-05 1450-04 28S8-04 _... . . 4292 - 04 5824-04 8875-04 . . 8030-04 1001-03 1153-03 12% - 0 3 1325-03 1382-03 1380-03 1388-03 1388-03 1388-03 1388-03 1398-03
7820-08 1975-05 3912-05 5777-05 7538-05 Bl84-05 1 0 6 4 - 0 4 1308-04 1482- 04 1583-04 1855- 04 1588-04 1887 - 04 1701-04 1702-04 1702-04 1702 0 4 1702-04
1072- 0 8 287 1-00 5281-05 7774-05 1010-05 1222-05 1 4 1 0 - 0 5 1709-01 1910-05 2027-05 2088-01 2110-05 2118-05 2120-05 2120-05 2120-0s _ _ 2120-06 2120-05
5335-09 1328-07 2819-07 3938-07 4955-07 5950-07 5808-07 8088-07 8881-07 9282-07 8452-07 9508. 07 9522-07 8525 - 07 9525-07 9525-07 9525- 07 9525- 07
3594-10 8937-10 1754-09 2551-09 3251 - O B 3888-08 4387-09 5053 -09 5404-09 5550-09 5598-09 6807.09 5509-09 5808-09 5600-09 5808-09 9508-09 5509-09
2421-12 5012-12 1175-11 1898- 1 1 2147-t1 isis-1; 2809-11 3172-11 3331-11 3384- 11 3397- 11 3399- 1 1 3389- 1 1 3399- I 1 3399-1 1 3399.- 1 1 3399-11 3399- 1 1
1098-18 2721-15 5257- 18 7495- 18 9318-18 1070-15 1189-15 1272-15 1305- 15 1312-15 1313-15 1313-15 1313-15 1313-15 1313- 15 1313-15 1313-15 1313-15
3358-23 8284-23 1582-22 2205-22 2572-22 2980-22 3184-22 3342 - 22 3373-22 3377-22 3377-22 3377-22 3377-.22 3377-22 3377-22 3377-22 3377-22 3377-22
1524-27 3749-27 7098-27 9752-27 1155-28 1284-28 1350 - 28 1395-28 1402-28 1402-25 1402.25 1402-25 1402-25 1402-25 1402-28 1402-25 1402-25 1402-28
4897-34 1142-33 2133-33 2878-33 3384-33 3835-33 3785-33 3838-33 3845-33 3845-33 3845-33 3845-33 3845-33 3845-33 3845 33 3845 33 3845-33 3945-33
- 46 -
WAPD-TM-1623
TABLE 11 The Smoothed Function P,(e,,b) = F,(eo,b)e b /e,
UNCTION Expie)
. 1 0 . 2 0
, 0 0 0 0 1 1.00004 .00029 1.00021
* F Z ( O . B ) ,
.40
1 .00003 1 .000 18
1 . 00172 1 .00301 1,00478
1.01232
1.03849
1,08034
1.11181 1 . 05850
8 . 0 0
i .ooo7e
I . ooe9o 1 , 019313 1. ozooe 1. owe8 1 . o e ~ e ~ 1.11e02 t . i 1 m e
/O
.BO
1 . O O i l O Z 1.00013 1.OOll51 1 . 00 'I 14 1. 00203
1.00415 1.001IO5 1 .01210 1.0 1783
1 . 031~73 1 ,03789 1.04803 1 . 011133 1.01280 1.00484
.eo I92
10.00
I . oo:iie
1 . ozme
TABLE
1 (MFP) * 4 (RAO) . 0 1741
,08717 ,13090 . I 7 4 1 3 ,21817
.34907
,043e3
,28180
. 8 0
1 . 0 0 0 0 1
1. 00021 1.OOOS7 1.00100 1.00155 1.00221 1.00381 1.00172 1. 00779 1 . 00981 1 .Of148 1.01238 1.01189 1.00278
,97140 .89818 .80100
12.00
1 . ooooe
1 0 0
1 00000 1 00000 1 00000
89988 99998 98984 98998
99903 90792
99288 98804 98074
90340 8 1872 72859
19.00
neeel
oseo1
w e 2
1 25
99988 89992 99988 99928 99870 89784 99898 98440 88078 88584
87058 95919 94440 90097 83302 7437 1 88 128
2 0 . 0 0
9 m e
1 50
99987 99884 99938
99742 89594 99410 88925
97403
94919 93191 81070 85358 77518 88821 eiooa
9985e
8 8 m i
em03
25 00
1 75
89878 98904 99785
98395 98123 88414
geese
meis
87485 88148
eoezi a t w e 7 2 ~ 3 e4037
94730 92870
97940
58923
35 00
99828 88931 95840 91049
79302 71377 1 8 4 5 1 48045 40279 34911 30238
24191 20158 17279 111 19 13439
esoze
ze879
1 75
2 .00 2 . 5 0 3 . 0 0
98985 99992 99990 99988 99852 98937
90713 99571 99429 99873 e9809 99748 00114 1 00102
00218 I 00229
00721 1 00140 01044 1 00828 01878 1 01082
004eo 1 00408
.- - 13578 i83i . i 44421
1 . 0 0 e .00 5 0 . 0 0 8 0 . 0 0 75 .00 . . . .. - ,
,01741 ,04363
,13090 ,17453 ,11817
,34907
.11087 ,19811 ,78140
1.04720 1.22173
. o w 2 7
.ze180
. me33
.e2380
.once
1 .39eze 1 .e7080
.98871 ,89941 ,99388 ,98581 .97408 ,98122 .94472 .BO422 ,88132 . some ,74100 .e8202 ,014 1s ,17014 ,47904 ,41078 ,35843 .31950
89878 ,98243 ,97030 ,93523
,77935
,15889 ,47381 ,40799
,31758 28583 23819
,20417 . 17865
lS8BO
. m e 9 ,83868
. e e m
.3s7ze
98001
99141 ,90884 . 97oee .81174 .95129 .92190 ,88070 ,93332 .78112 . 7ze.47 ,117121 .e17ez ,12241 ,44838 ,39134 .34871
TABLE 12
The Furiction F,(en,b)
1 . 0 0 2 . 5 0 3 . 0 0 (RAD) .0174S
,09727 .13090 ,17413 ,21817
,34907 ,43031 ,12310 .E1087
,78140
1.04720
,04513
. m e a
. e m i s
. anee 1.a217a I . m e 2 e 1.17090
1728-01 4321 - 0 1
18(10-01 4112-0 1
1249+0#
209I+OO 2518tOO
4282+00 8212+00 1188+00 722lrOO 8328+00 9128+00 1233+01
2173+01 3113tOI
cui-01
lee8 + o o
338e+oo
1004toi
1179-01 3949-01 79011-01 1187+00 1197+00 1988+00 2394+00
4945t00
0831tOO
8884+00 1111+01 1484+0 1 1947+01 2427+01
azi8+oo 4oee+oo eeee+oo 7 8 e ~ + o o
1429-01 3873-01
1074+00 1438+00 1798+00 2l13+00 2901+00
4482+00 1218+00
7027t00 '7988tOO 10 14+0 1 1272+01 1880+01 1753t01
7 i m - 0 1
3eee+oo
e124+00
1170-01 2921-01 5814- 0 1 9790-01 i174+00
1717+00 2319+00 2981+00
4212 + 0 0 4917+00 ~ 0 8 + 0 0 1320+00 7834+00 9428+00 1082+01
I ~ B + O O
~ I J O ~ + O O
i t i e + o i
8S70-02 2395-01 4792-01
7842-02
3822-01 1888-01 7860-01 9818- 0 1 1179+00 l174+00 1972t00 2371+00 2772t00 3173+00 3173+00 3968+00 4719+00 1333iOO M3S+OO
12.00
198 1 - o 1
ses3+00
!1421-02
:l210-01 11819-01 (1421-01 l1021-01
1284+00
1 9 2 Z k O O :!238+00 :!110400
.l149+00
~1205+00 ~ ~ 2 1 o * o o
1 1 . 0 0
ieos-01
111930-0 I
i e o i t o o
i!851+00
:ie78+00 w m o o
5000-02 1250-01 2489-01 3748-01 4884-01
7478 - 0 1 9945- 0 1 1238100 1478tOO 1714+00 1941k00
e.238-01
21e8+00 ~JBI+OO
mteroo 2703t00
2875tOO 2978100
3884-02 9734-02
2817-01 3884-01 4848-01 5807 - 0 1 7705-01
1138100 1313100 1479100
1773t00 188S+OO 2113+00 2138+00 2138+00
184e-01
0507-0 1
ie33+00
3033-02 758 1 - 02 1511-01 2270-01 3 0 1 9 - 0 t
4110 - 0 1 1870.01 7380-01 8717-01
1127+00 1237t00 1334+00 1477+00 1143t00
1554+00
3788-0 t
iooe+oo
ise4+00
1433-02 358 0 - 02 7150-02 1070-01 1421-01
9 1 1 2 - 0 1 2777-01 3407-0 1 3994-01 4S28-01 4998-01 1387-01
$ 7 ~ 9 - 0 1
17 18. o 1 e i o 7 - 0 1 ezze-01 8235-01 8235- 0 1
8 0 , 0 0
8888-03 2171-02 4334-02 8480-02 ne0 1 - 0 2 1089 -0 1
new-o 1 1300t00 1737+00 !2177+00
7 105-0 i 950s-s 1 1201+00 144WOO 1931400 242BtOO 2928tOO 343S+OO 3949100 4474rOO
1274-01
2 0 3 4 - 0 1 2388 01
2914-01
1887-01
2ee3-01
3118-01 3288-01 3434-01 3472-01 3474-01 3474-01
9 7 i i 0 1 w o e - o i 9188-Ol 8374-01 1004*00 1ooEi+oo
770PtOO 777fi100
B O ~ Y + O O 7oe11+oo
iiii+ii 1134+00 1139+00 1 1 3 9 t 0 0
5 0 . 00
1300+01 17OB+OI 2390t01 489eco I
3.80
1270-03 3191-03 1517-02 79e4-03 2127-02 1192-02 3921-02 2377-02 1204-02 3148-02 ems-02 3801-02 7081-02 &KW-OZ 1001-01 1211-01 1401-01
1701-01 1804-01 1877-01 1947-01
iseo-oi
iseo-oi ieeo-ot weo-of
e (MFP) 4 (RAD) . 0 1741
,08727 ,13080 ,17413 ,21817
,34907
.E1097
,78140
1.04720 1.22173
,04383
.zeieo ,43833 . e2380
.e9813
. 87zee
i.3eezs i .570eo
4 . 0 0 1.00
4328-04 1080-03 2149-03 3199-03 4218-03
7824-09 9211-03 1038-02 1123-02 1180-02 1211-02 1233-02 1243-02 1244-02 1244-82 1244-02
1108-03 m i - 0 3
8 . 0 0 2 0 . 0 0
3104-10 8940-10
2 5 . 0 0 3 1 . 0 0 7 5 . 0 0 e.oo i n e - 0 3
e811o-v~
1eee-02 2180-02
2936-03
8720-03 1112-02 1424-02
2189-02 1940-01 3211-02 3417-a2 3892-02 3 m - w 310e-02 3e91 - 0 2 3 e ~ 1 - 0 2 3881-02
10 00
107%- 0 1 3917-01 179:1~01 717:1- 0 1 9230 09 107!1-04 1331-04 1110-04
17111-04 17511- 04 1772- 04 17 TI - 04 I7711 - 04 177U-04 17711 - 04 17711 - 04
m n - o e
1~411-04
1124-27 3710 -27 7106-27
4818-34 1142-33 2 135- 33 2885 ~ 3 3 3378-33 3854 -33
1813-01
2902-04 4301- 04
0027-04
weo-04
eesz-04
1072-01 21172 - oe m e - o e 7788-01
~ I O 1 1 - 0 1 1131-08 1421-01 1739-01 1855-01 2087-01 2117-01 2187-08 2188 .os 2200-05 220 1-08 2201-01 2201-01 2201-01
Ij331-08 1329-07 :LB13-07 :I849 - 07
!1984-07
11230-07 !l074-07
!l787'07 13016-07 !l819- 07 'D820-07 ' W Z O - 07 '1820-07 1820-07
, ise0-07
w e - 0 7
! ~ s z e - o ~ ! m e 0 7
2421- 12 8014- $ 2 117e-11 1700-11 2187-11 2131-1 1 2834-1 1 3215-11 3387- 1 I
3461-11
3484- 11
3448- 11
3484- 1 1 3484- i I
3484- 1 i 3484- 1 1 3484- I I 3484- 1 1
ioe8-ie 8273-1e 7 s i s - i e
1 178- le 1287- (e
133t-ie
2722- I 1
9 3 1 7 - 1 1 1077-11
1322-15 1330-18
1331-11 1331-11 1331-15 1331-11 1331-15 1331-19 1331-15
3388 -23 8287-23
2211-22 1884-22 1718-08
2558-09 3271-09
i i i e - i 7 i e83 -22
3408-22
3007-22 3208-22 3372-22
3410-22
3S80-Oi 4409-08 5127-09
._ 3788-33
3870 - 33 3870-33 3870-33 3870-33 3870-33
3883-93 ( l i i 7 - 0 4 1020-03 1184-03 1303-03 1382-03 1428-03 1481-03
1405-03
14ei -03 ~ e e - 0 3
S i i i - 0 2
8338 -0 2 7218-02
9238-02 9948-02 1047-01 1082-01
5567-09 s w o - 0 9 1725 09 1739 -09
_ _ 34 10 - 22 34 10-22 3410-22 3410-22 34 10 -22 3410-22 3410.22
5741-09 5741 .OB 1741-09 1741-09 1741-09 5741-09
%TO-33 3870-33 3870-33
i i t 4 - 5 8 1414-26
3 i 7 8 - 3 i 3870-33 3418-22
WAPD-TM-1623
TABLE 13
The Smoothed Function K($,,a,/a,b) = R($o,a,/a,b)e /$, b
p ( R A D ) . o 1741 ,04363 ,08717 . 13090 ,17453
,34907
,12380
,78140 ,87268
1.04720 1.17080
.zeta0
. 43833
.e1087
L2IA = 8 (YFP) 8 7 (RAD) . 0 1748
,08727 . I 3 0 9 0 ,17413 .26180
,32380
,18140 ,87260 1.04720 1.57080
. o m s 3
,54807 ,43833 .e1087
w o o - o z 4eee-01 8013-02 1008-01 1003-02 4999-01
1029-01 1 0 2 4 - 0 1 5051-02 5047-01 1117-02 1112-01 1212-01 5208-01 5342-02 1337-01 1510-02 1 1 0 5 - 0 1 6727-02 5721-01 8317-02 6350-01
8231-01 8229-01 2596tOO 1231t01
e 8 ~ - 0 2 eooe-01
. 0 1 . oe . 10 . 0 5
1144t00 1144tOO 1247t00 1211too 1258too 1212too 1 96+00
1370+00 1423+00 '1978t00 1891+00 2039+00 1811tO1
21 . I 5
1328t00
2410+00 2411t00 1458100 1463tOO 2474t00 2106100 2811 too 26 13t 00 2694t00 2797tOO 3094t00 3308100 3980100 2374t01
.so
.05
3987100 31881 0 0 3596tOO 3eo7too 3e22too 3ee7too 3732tOO 3820t00 3931t00 4081iOO 4489+00 4797t00 5689tOO zeeatoi
.78
. 0 5
4631t00 4837t00 4646tOO 4659t00 4879t00 4735100 4817t00 4927tOO 1211+00 5768100
7198tOO 2909r0 I
1 . 0 0 . 0 5
~soe.9100
e 129 t o o
8 9 4 8 + 0 0 8950t00 8963tOO 8985tOO 9016t00 9105+00 9234100 8405100 9114100 989erOO 1068*01 1 117+Ot 1261 t O 1 3114+01
2 . 5 0 - 0 5
1186tO1 1 188rO 1 1188401 11e0101 1193t01 1203t01 1217t01 1238t01 1260tO1 1289*01 1370t01 1424t01 1174t01 380 1 t0 1
5 . 0 0 . 0 5
1303*01 1304tO1 1305101 1307101 1311401 1321+01 1335t01 1354t 0 1 1378t01 1408101 1489t01 1543r01 1692tO 1 3803101
7 10 . 0 5
1384101 (365 + O 1 1368tO1 1368tO1 1372t01 1382tO1 1396tOl 1 4 1 1 + 0 1 1439101 (4691 0 1 1 1 5 0 t 0 1 1604+01 1752t01 3953t01
1458+01 1417t01 145860 1 146Ot01 1484r01 1474rOl 1488tO1 11071 0 1 t630t0 1 1880t01 1 8 4 0 1 0 1
1841tO1 4024+01
ie94toi
1488101 1488t01 1488101 149010 1 1493t01 1103t01 1617t01 1538 I 0 1 1560t01 1589tO 1 1669tO1 1722tO1 1869t01 4045+01
1500t01 1500+01 1509101 1504t01 1508101 1517tOl 153 I t o I 1150101 1174t01
1682+01 1738to 1 1881tOl 4054t01
i e 0 3 t o i
1 1 0 8 t 0 1 1108tO1 1 1 1 0 ~ 0 1 1512t01 1516t01 1525tO 1 1539t01 1518 I O 1 158 1 t o 1 1611tO1 1690101 1743+01 1888 t o 1 4059+0 1
I O . 0 0 . 0 5
2 0 . 0 0 . 0 5
3 0 . 0 0 . 0 5
4 0 . 0 0 . 0 5
5 0 . 0 0 . 0 5
6000-01 4996-01 1244tOO 2449tOO 3584t00 4828t00 8888tOO 1168tOl 1271101 1329101 1401t01 1420t01 1427r01 1431t01 1 0 0 3 - 0 1 4999-01 1244t00 2450+00 3588*00 4830t00 8890400 1188401 1278101 1329tOl 1401t01 142Ot01 1428t01 1431t01 1012-02 5008-01 1246tOO 2454t00 3592tOO 4838t00 89OZtOO 1170t01 1177rOl 1330t01 1403t01 1422t01 1429t01 1432t01 8028-01 8024-01 1250tOO 2482tOO 3B03t00 4652*00 8923tOO 1172t01 1279101 1332101 1405+01 1424tOt 1 4 3 1 t 0 1 1435t01 (1090-02 8048-01 1258t00 2473tOO 3e18t00 4671t00 8912tOO 1175t01 1282tO1 1338t01 1408t01 1427t01 1434+01 1437r01 1114-02 1 1 1 0 - 0 1 1272t00 2503tOO 3882+00 4728t00 9038t00 1184+01 1291t01 1344t01 1418tO1 1435t01 1442t01 1446t01 8208-02 1203-01 129StOO 2548t00 3726tOO 4804tOO 8180*00 1197401 1304101 1357101 1420t01 1447101 1414t01 1458101
849s-02 5493-01 1367+00 2887+00 3922tOO 5050t00 9532tOO 1236101 1 3 4 3 t 0 1 1395+01 1468t01 1483+01 1490t01 1493401 1709-02 1704-01 1419+00 2787tOO 4064+00 5221+00 9791*00 1264t01 1370101 1422tO1 1491t01 1108tO1 1115t01 1 1 1 8 t 0 1 e31S-02 6312-01 1569r00 3074t00 4467100 1719t00 1050101 1336t01 1441t01 1492401 1559r01 1575tO1 1581t01 1 5 8 4 t 0 1
8119-02 8101-01 1007tOO 3887tOO 5193t00 7087+00 1227t01 1513t01 1814t01 188ltO1 1722101 1736t01 1741t01 1743+01 8551-01 4881tOO 8829tOO 1269tOl 1518101 1896tO1 2187+01 2427+01 2502+01 2538101 2578+01 2588+01 2591r01 2593t01
e334-0~ e m - 0 1 i~zetoo m o 8 t o o 08tit00 4eiztoo e324100 i z t m o i 1321roi 1374toi 1445t01 t4e)tot 1470101 1473101
e7e.o-02 e7si-01 1877too 327etoo 4751too eoe9too 1097toi 138stoi 148etoi t s ~ ~ t o i 1 e o ~ t o 1 i e i e t o i ie25toi iez7+01
LZ/A * . 0 1 . 1 0 . 2 1 .50 .75 1.00 2 . 5 0 1 . 0 0 7.50 10.00 2 0 . 0 0 30 00 40.00 50.00 fj !!WE! I .IO .IO , 1 0 .10 . t o . 1 0 . 1 0 . 1 0 . 10 . I O . I O . I O . 1 0 . 1 0
' F i i i s .043e3 ,06727 ,13090 ,17413 .28180 .34907 ,43633 . s23eo .et087
,872ee .78540
1.04716 1.57080
1 0 0 0 - 0 2 6003-02 80 11-02 8027-02
1111-02 1 2 0 2 - 0 2 1321-02 1484 - 02
swe-02
ee88-oz e m - 0 2 8893-02 7965-02 3454-01
499s-01 4999-01 5008-01 1023-01 1044-01 1107-01 5 197- 0 1 1320-01 1479-01 5681-01
6684-01
2969t00
szee-of 7981-0 1
1243f 00 1144+00 1246t00 12sotoo 1155tOO 1271tOO 1293t00 1323tOO 1383100 1413t00 1817tOO
1970tOO 5902*00
issotoo
2448fOO 2440100 2413tOO 2460t00 2471tOO 2801tOO 1544tOO 1602tOO
2774+00 3049100 3244t00 3821tOO 9040tOO
2e78too
3680tOO 358 2+ 0 0 3588100 3108t00
37 17t00 3800100 3907tOO 4043t00 4427t00
1416100 1115to1
3 e i ~ t o o 365etoo
413981 o o
4eietoo 4622+00 4829 too 4842tOO 4860t00 4714t00 4790t00 4893t00
8193tOO 5662 t 0 0 9988t00 6908*00 1270t01
sozetoo
8812+00 8815t00 8817100 8847tOO 8871t00 885St00 9071tOO 9224t00 8418tOO 9658t00 1031101 1074+01 1187r01 1706t01 .
1147r01 1147tO1 1 1 4 8 t 0 1 115oto1 1153t01 1161tO1 1113r01 1189t01 l208+01 1233r01 1297t01 1338101 1449101 1899+01
124310 1 1 1 4 3 r 0 1 1244r01 1248101 1249tO1 1257t01 1268tOt 1284t0 1 1302t01 1328+01 1387t01
1528tO 1 1957101
14zet01
1288+01 1288+01 1289t01 129 It0 1 1294tO 1 1302+01 1313tO1 1327 tO 1 1346t01 1368tO1 1427t01 1466t01 1584+01 1982tO1
1342tO1 1342+01 1343+01 134St 0 1 1341t01 1355t01 1365t01 1379t0 1 1396tOl 1417+01 1473t01 1509t01
2008*01 ieoa+oi
1363tOl 1353+01 1314+01 t356 t O 1 1358 to 1 1385101
1389tOl 1406t01 1427+01 1482t0 1 1517 t O 1
2013tOl
137eto1
i e o e t o i
1356+01 1358*01 131740 1 1359t01
1389t01 13794 0 1 1392 1 0 1 14OBt01 1429+01 1484+01 1519t01
2014+01
138 1 t o 1
$81 t t o i
1357+01 1357+01 1358+01 l36Ot 0 1 1383tO 1 1370*01 1380*01 1393t01 141OtOI 1 4 3 0 t 0 1 1485*01 1520101 161 1 1 0 1 2014101
,0436 5003-02 4998-01 1244t00 1446t00 3574t00 4604tOO 8671t00 1107t01 1184101 1218101 1248101 1150lOl 1250i01 1251tO1 ,06717 8011-02 5007-01 1146t00 2450t00 3980100 4811t00 8881t00 1 1 0 8 t 0 1 1185r01 1217t01 1147t01 1251t01 1211tO1 1251101
i q a m R O Y R - ~ ~ sn?i-oi imo+oa Z ~ B ~ + O O 35811too 4e23too 8EQQtoo 1toe+oi i i a s t o i 1 z 1 8 t o 1 1248101 izsztof 125zto1 i253toi . .---- ,17453 Siii-ii Siii-ii iiiitii iiiitii ieiitii iiiitii i i i i t i i i t i & i i iiiitii iiii+ii iisiiii iikitii iisitii iisitir ,28180 SIOS-02 5101-01 1269tOO 2495tOO 3843100 4890100 8794t00 l118+01 1195t01 1226101 1216tO1 1259t01 IZBOtOl 1260101 ,34901 1101-02 5188-01 1280100 2536tOO 3700tOO 4761tOO 889BtOO 1128t01 1204t01 1234101 1263t01 1167t01 1267t01 1267t01 ,43833 8306-02 5301-01 1318t00 2590+00 3777t00 4818100 9029lOO 1141+01 1215t01 1245t01 1273t01 1278t01 1277tOi 1277t01 ,12380 8451-02 1410-01 131St00 26BltOO 3877tOO 4978t00 9197t00 1156tOl 1229101 1259tOl 1286tOl 1289t01 1 2 E O t O 1 1289t01 ,61087 6641-02 5639-01 1402tOO 27SOtOO 4001tOO 1 1 3 O t O O 9403tOO 1175t01 1247t01 1171b01 1301tOI 1 3 0 4 i 0 1 1304t01 1304tOl ,70140 6183-02 8178-01 1134t00 3001tOO 4349tOO 1551tOO 9942t00 1223t01 1291101 1317t01 1340t01 1342tOl 1342tO1 1342101 ,87286 6162-02 6113-01 1827t00 3175t00 4588tOO 5835t00 1029tO1 1253101 1318101 1343101 1384+01 1386t01 1388+01 1366tOI 1.04720 7678-01 7661-01 1898100 3871tOO 5255t00 6609t00 1114tO1 13PStO1 1383101 1405t01 1423t01 1424tO1 1425+01 1425tOl 1.5'1080 1855-01 1738t00 3771tOO 8177tOO 7882tOO 8158+00 1177t01 1426t01 1465+01 1480b01 1492r01 I493tOl 1493+01 1493t01
'/A (YFP) I RAD ) . 0 1741 ,04363 ,08721 ,13080 ,17453 .26180 ,34807
,62360 ,81087 ,78540 .87266 ,04720 ,37080
,43833
. 0 1
.40
1 0 0 0 - 0 2 8002-02 1 0 1 0 - 0 2 1023-02 1 0 4 1 - 0 2 1093-02 1189-.02 1289-02 1398 - 02 1560-02 6008-02
7116-02 1037-01
e313-0~
. I O
.40
4991-01 4998-01 5001-01 6018-01 5038-01 1058-01 11BJ-01 5 2 6 4 - 0 1 1392-01 6114-01
8303-0 1 1141 -01 1012+00
eooo-oi
. 2s
. 4 0
1242too 1143t00 1245t00 1248tOO 1252tOO 1285tOO 1284+00 1309tOO 1340100 1380100 1480100 1884 +DO I767+ 0 0 1343*00
.so
. 4 0
2440tOO 2441tOO 2445t00 2451tOO 2459t00 2484100 2119too 2587 t O O 2827tOO 2702t00 2908t00 3045tOO 341 1 t O O 4083+00
.71
.eo
3518t00 3863tOO 3571tOO 3583t 00
36671 0 0 3733 t 0 0 3817+00 3921tOO 4200tOO
4855 t 0 0 1387t00
385ei o o
3e18too
43a3too
1 . 0 0 . 4 0
4568tOO 4569t00 45751 0 0 4588t00 4600 t 0 0 4643 tO 0 4703tOO 4783100 4883100 5008*00 5338t00 9550100 6074r00 e385+00
2 50 . 4 0
8383100 8398 t 0 0 8404t00 8417t00 8435t00 8489t00 8564+00
8781t00 8924t00 8274t00 9476t00 9900100 9178*00
neet roo
5 00 .40
1035+01 1035t01 103St01 1037t01 1038t01 1043+01 1048101 10161 0 1 1085t 0 1 1075t01 I100 t o 1 1 1 1 3 r 0 1 1138+01 10I8t01
7 50 . e o
1085t0 1 1 0 8 1 + 0 1 1086t01 1087601 1088tO1 1091 t 0 1 1098+01 1102101 1110101 1118t01 1 I38t01 1149t01 1189+01 1 0 3 1 t 0 1
10 0 0 . 4 0
1 1 0 1 1 0 1 1 I O l t 0 1 1102+01 1103101 1104101 1107101 1 1 1 1 t O 1 I 1 1710 I 11244 01 1131t01 1 1 4 9 t O f 1158101 1177t01 10451 0 1
20.00 . 4 0
1 1 1 1 * 0 1 1111tOl 1 112+01 1113t01 1114+01 1116+01 1120 t o 1 1125t0 1 1 132to I 1 139tO 1
1 165+0 1 1182tO1 iO48t01
1 19eto1
3 0 . 0 0 . 4 0
1112101 1 1 12 tO1 1112t01 11 13t0 1 11 14tOl 1117101 1121t01 1125tO1 1132+01 1 1 3 9 6 0 1 1156tO1 1185101 1182101 1048tOl
40.00 . 4 0
1112+01 1 1 1 2 i o 1 1IlZtOl 1113t01 11 14rOl 1 1 17tO1 1 121tO 1 1126tO1 1132+01 1139t01
1 m + O 1 1182tO1 1048401
ti~et01
5 0 0 0 . 4 0
1112101 1112r01 1 1 12+01 1113101 1114r01 1 117tO1 1 121 t o 1 1 1 2 6 i 0 1 1 1 3 2 i 0 1 1 1 3 9 t 0 1 1 158t 0 1 1165b01 1182101 IO48 e 0 1
L2/A = . 0 1 . 1 0 . 2 1 .SO .79 1.00 2 . 6 0 5 . 0 0 7 SO 10.00 20.00 30 0 0 4 0 . 0 0 5 0 . 0 0
,# IRADI ,01741 1 0 0 0 - 0 2 4995-01 1142*00 2435tOO 3941iOO 4134r00 8138100 9741iOO 1007t01 1 0 1 5 + 0 1 1018+01 1 0 1 8 t 0 1 1018101 1 0 1 8 t 0 1 .04363 1002-01 4997-01 1242tOO 2436lOO 3142tOO 453S+OO 8138tOO 9741100 1007t01 1015101 lO18t01 1018401 1018tO1 1 O l B t O l .On717 11009-02 5003-01 1244lOO 2439460 3546+00 4540t00 8143100 8741tOO 1017+01 1015101 1019tO1 1019tO1 lOl9rOI 1 0 1 9 r 0 1 ,13090 1020-02 5011-01 1247tOO 2444t00 3814+00 454St00 8153100 8710+00 1007t01 1018tOt 1 0 1 9 t 0 1 1019t01 tOl9tg1 1 0 1 9 * 0 1 ,17453 eo3e-02 5030-01 1zsotoo z4mtoo w e 4 + 0 0 4581+00 81eetoo 9758+00 I O O B I O I io is to t i o i e t o t ioietoi toisto! t o i e i o i .ze180 1081-oz 1076-01 izez+oo 2473+00 3593too 459e+oo 8203too 8778100 foogiol 1017r01 t o z o + o i i o z o + o t 1020+01 i o z o t o i ,34907 1146-02 8141-01 1278100 1503t00 3635t00 4846400 8254+00 8807100 1011101 1018+01 1022t01 1 0 2 2 t 0 1 1022tO1 1022101 .43833 5233-02 1227-01 1299*00 2543tOO 3689+00 4711t00 8319100 8842100 1013+01 1020101 1023t01 1 0 2 3 t 0 1 1 0 2 3 t 0 1 1023101 ,52380 1343-02 5336-01 1326tOO 2594t00 3759t00 4792400 8397100 988lr00 1016601 1022101 1025tO1 1025101 1025101 1025101 ,81087 1478-02 5471-01 1359100 2656tOO 3842100 4890400 8485tOO 9921t00 1 0 1 8 1 0 1 1 0 2 4 4 0 1 1026+01 1028tOl 1028tOl 1028401 ,78540 8942-02 5 8 3 4 - 0 1 1447100 2819+00 4019tOO 5138100 8678100 9991100 1022401 1027401 1 0 2 8 + 0 1 1028tOI 1028101 1 0 2 B t O l ,87286 6 0 8 0 - 0 1 8070-01 1509100 2923400 4194tOO 5287+00 8771100 1001t01 1 0 ? 2 + 0 1 1028101 1028101 1028t01 1028401 1028101 1.04720 8693-02 6679-01 1651400 3178100 4509100 5610t00 8893100 8972100 1015101 1 0 1 B b O I 1020+01 1020101 1020101 1 0 2 0 1 0 1 1.57080 7551-02 7452-01 1770100 3178100 4262tOO 5102tOO 7405100 R129t00 8244k00 R270+00 8279100 8279100 8279t00 8279tOO
8 (YFP) = .eo .eo .eo .eo .eo . B O .eo .eo .eo .eo .eo .eo .eo .eo
- 48 -
WAPD-TM- 1623
- TABLE 13 [Cont'd) TABLE OF THE SMOOTHED FUNCTION EKP(5 ) tR(P .L2 / , I .B I /~
L2/A 8 (MFP) # (RAD) . 0 1745
,04383 ,08727 ,13090 .17453 .28180 .34907 ,43853 ,12380 ,81087 ,78540 .17288 1.04720 1.57080
.01
.80 .IO . B O
4904-01 4996-01 5002-01 501 1-01 5025-01 5083-01 5118-01 8190-01 1281-01 5391-01 5878- 0 1 8852-01 (1288-0 1 8047-01
.25
.80 .50 .80
.75
.80 1 . 0 0 .80
1 . 5 0 .80
5 00 .80
0115100 921s+oo 9218t00 9217100 92 19 + 00 8223100 9228tOO 9228100 9228tOO O21eroO 0158100 9085100 1887t00 8830tOO
7.50 .80
i o . 0 0 .80
9489100 9489tOO 9489 6 00 9488,OO 9487100 9483t00 9458 + 0 0 9 4 4 5 t 0 0 9429iOO 9403t00 8313100 0238+00 8987+00 8909tOO
20. 0 0 .80
9482100 9482tOO 948 1 4 0 0 9480100 9479t00 8474100
3 0 . 0 0 .80
9482t00 9482tOO 9481rOO 9480100 8479600 9474tOO
4 0 . 0 0 .80
8482100 9482tOO 948 1 100 9480100 8479100 9474t00
50 00 .80
0482.00 9482100 9481t00 948OtOO 9479100 9474100 9487+00 9455t00 8437100 941lrOO 93 l 9 t O O 9243+00 8991100 8912t00
5000-02 8002-0 1008-02 8017-02 8031-02
1241100 1241100 1243t00 1245tOO 1248tOO 1258+00 1271tOO 1 89IOO
1338+00 1407100 1450+00 1548t00 1454 tO 0
1 3 1 1+00
243OtOO 243 1 t 00 2434+ 00 2438100 2444100
3525100 3528 I O 0 3530100 3538100 3544100
4 5 0 0 t O O 4501*00 4505t00 4512100 4522tOO
7895t00 7888600 7899100 7905100 7Bl3100
9427tOO 9427100 9427iOO 9427+0@ B4>8tbO _ _
5089-02 8124-02 8197-02 8288-02 S398 - 02 8815-02 8882-02 8282 - 02 8104-02
1 4 8 2 t i i 2487tOO 2520tOO 2581t00 2BlltOO 2738tOO 2810100 2973t00 2854t00
3588tOO 3802t00 3847+00
.. 4550100 4590t00 484 1 t 00 4703tOO 4778tOO 4950100 5044100 5207t00 4330100
- . .. 7935 r o o 7985100 8001 t o o 8041 t O O 9082 ' 00 8145 100 8152 100 8080 00 8290 00
.. 9424tOO 9419t00 841 1t 0 0 9397100 O375rO0 9290t00 9217400 8989t 0 0 8898tOO
9487tOO 9455t00 9437toO
9487t00 9455t00 9437+00
9487tOO 9455100 9437t00
_ _ 3701t00 3788iOO 3928*00 4018+00 4199100 3507tOO
941lrOO 9319100 9243+00 8991 t o o 89 12i 00
9411+00 9319100 8243100 8991tOO 8912t00
9411100 9319100 9243t00 8991+00 8912tOO
!/A .Ol 1.00
5000-02 5002-02 5008-02 5014-02 1025-02 5057-02 8103-02
. I O 1 . 0 0
4994-01 4995-01 5 0 0 0 - 0 1
.25 1 . 0 0
1240100 1241+00 1242t00 1244t00 1247t00 1254 t 0 0 12854 0 0 128DtOO 1297t00 1318tOO 1389+00 1398+00 1458t00 1252+00
.so 1.00
2425tOO 2428t00 2428t00 2432t00 2437t00 2451100 2471+00 2497t00 2528100 2587tOO 2858t 00 2705tOO 2791tOO
.75 1.00
3510tOO 3511t00 35 14 t0 0
1 . 0 0 1 . 0 0
4487+00 4488t00 4471100 4478600 4484t00 4505tOO 4535t00 4572tOO 48 18+ 00 4888tOO 4773iOO 4819tOO 4854t00 3803100
2 50 1 00
7888.00 7889.00 78704 00 7873< 00 7878 0 0 7889 0 0 7895( 0 0 77051 00 77114 00 7711100 78854 0 0 78051 00 73804 00 5505i 0 0
5 . 0 0 1 . 0 0
8758t00 8758tOO 8758100
7.50 1.00
8897t00 8897100 8894t00 8891t00 8885tOO 8870100 88481 0 0 8813100 8789r00 87 10 t O O 8533tOO 8408400 8037r00 5957iOO
10.00 1.00
2 0 . 0 0 1 . 0 0
30.00 1 . 0 0
8924t00 8923100 8921+00 8S18tOO 8911iOO 8894t00 8888*00 8934tOO 8787t00 8728100 8548t00 8417t00 8047+00 5983t00
40.00 1.00
8924+00 8923100 892lt00 8918tOO 8911+00 8894100 8881t00 8834+00 9787 t 0 0 9728100 8548iOO 8417t00 8047tOO 5963r00
50 0 0 1 . 0 0
89l9tOO
8918100 8912t00 9908100 8889tOO 8885 t 0 0 8830100 8784tOO 8723+00 8544tOO 8415tOO 8045100 5982100
8918100 9924100 8923t00 8921tOO 8918tOO
8924100 8923t00 8921+00 8918tOO 891 1 t 0 0 8894iOO B 8 8 8 t 0 0 8834100 8787tOO 8726100 8546tOO 8417kOO 8047t00 5983t00
. a l i i 5
.04383 -08727 .... _ .
5008-01 3918tii 3525t00 3544tOO 3570t00 3804t00 384S+OO
.. 8754100 8750*00 8740t00 8722t00 8897t00 8881tOO 8811t00 8 4 5 2 t 0 0 8332tOO 7978100 5918tOO
. 13090 ,17453 .a8180 .34907 ,43833 ,52380 ,81087 ,78540 .87280 ,04720
5019-01 5051-01 5 0 9 8 - 0 1
8011tOO 8894tOO 8888t00 8834+00 8787tOO 8728100 8548tOO 8417t00 8047+00 59831 00
5181-02 5234-02 5320-02 8534-02 5858-02 5918-02
5154-01 5227-01 5313-01 5525-01 5848-01 5901-01
_- .- . - 3893tOO 3800t00 3854 t 0 0 3929tOO 3149t00
1 1 .57OeO 5208-02 5170-01 2309tOO
L2/A - . 0 1 .10 .25 .SO .75 1 . 0 0 2 50 5 00 7 50 1 0 . 0 0 20.00 3 0 . 0 0 40 0 0 50 0 0 8 (MFP) 1.25 1.25 1.25 1.25 1.25 1 . 2 5 1.25 1.25 1.25 1.25 1.25 1 . 2 5 1.25 1.25 b (RAD)
,01745 5 0 0 0 - 0 2 4993-01 124OtOO 2419*00 3481t00 4428tOO 7404+00 8288bOO 8348100 8357iOO 8359t00 8359t00 8359100 8359100 .04383 8001-02 4994-01 1240100 2420tOO 3491t00 4427+00 7404tOO 8285+00 8347r00 8358100 8358r00 8358100 8358t00 8358400 ,08727 5005-02 4898-01 1241+00 2421+00 3493+00 4429tOO 7403tOO 8281rOO 8342r00 8352r00 8353iOo 8353100 8353t00 8353400 .I3090 5011-02 5004-01 1242100 2424t00 3487t00 4432tOO 7402100 8255t00 8335r00 8344100 8348100 8348t00 8348100 8348t00 .17453 1019-02 5011-01 1244t00 2427+00 3501t00 4437tOO 7399+00 8248tOO 8325100 8334tOO 8335iOO 8335t00 8335tOO 8335100 .28180 5043-02 5038-01 1250+00 2437t00 3514tOO 0450100 7383tOO 821nrOO 8295iOO 8304t00 8305tOO 8305t00 8305100 8305+00 ,34907 5078-02 5088-01 1259100 2452tOO 3531t00 8487100 7381tOO 8180100 8252tOO 828OiOO 8281t00 8281t00 8281t00 8201100 ,43833 5118-01 5110-01 1288t00 2489100 3553tOO 8488100 7381+00 8127+00 8193100 8200100 8201100 8201t00 8201t00 8ZOltOO .52300 8108-02 8180-01 1280100 2490100 3577+00 K i 1 1 t O O 7332t00 8057t00 8118100 8124t00 8125t00 8125tOO 8125+00 8125t00 .e1087 5228-02 5218-01 1294+00 2513*00 3804t00 0534t00 7287tOO 7987*00 8022tOO 8028100 8028400 8028+00 8028+00 8028iOO ,78540 5358-02 5347-01 1324t00 2582+00 3852t00 8585t00 7130100 7713400 7757+00 7781*00 7782t00 7782tOO 7782+00 7782r00 ,87288 8421-02 5411-01 1338t00 2582t00 3608100 .1582tOO 7005100 7539t00 7579tOO 7583tOO 7584t00 7584t00 7584t00 7584'00
1.04720 5512-02 5497-01 1358+00 2591+00 3835400 ,1471+00 8828+00 7077+00 7110t00 7114tOO 7114100 7114r00 7114tOO 7114400 1.57080 4487-02 4442-01 1081t00 2010tOO 2755100 3334t00 4788bOO 5088t00 5108100 5110tOO 5110tOO 5 1 1 O t O O 5110+00 5110+00
TAOLE OF THE SMOOTHED FUNCTION EXPl8)tR(#.L2/A.BI/#
LZ/A
9 Kj .01745 .04383 ,08727 . 13090 ,17453 .28180 .34907 ,43833 .S2380 .e1087 ,78540 .E7288
1 . 04720 1 .S7080
. 0 1 1 .50
. 10 1.50
. 21 1.50
12381 0 0 1239t00 1239tOO l24OtOO 1242*00 1245t00 125Ot00 1258t00 t 283tO 0 1270+00 1281t00 1283t00 1288100 9813-01
, . 5 0 1.50
2413tOO 2413t00 2414tOO 2418*00 2418tOO 2424400 2432tOO 2442t00 2452 to 0 2482t00 1474tOO 2470tOO 2418+00 17*8t00
.75 1.50
1 . 0 0 1.50
2.50 1 . 5 0
7 m a 1 0 0
5 00 1.50
7843100
7.50 1.50
7892tOO 7891tOO 7885100 7874400 7880+00 7818t00 7758100 7878t00 7577tOO 7451t00 7117100 e904 t 00 8372400 4482+00
1 0 . 0 0 1 . 5 0
7897+00 7895100 7889100 7878t00 7884tOO 7822t00 7781t00 788 1 tOO 7579t00 7453100 7119100 8905100 8373+00 4401+00
20 00 ' 1 50
7897t00 7895t00 7889100 7879+00 7884t00 7822t00 7782 t 0 0 788 1 i 00 7579t00 7454tOO 7119tOO 8905t00 8373tOO 4483*00
3 0 . 0 0 1 50
7897 t 00 7895t00 7889100 7879t00 7884r00 7822iOO 7782t 0 0 788 l+OO 7579iOO 7454100 7119tOO 8905+00 8373r00 4483r00
40 0 0 1.50
7897100 7895tOO 7889tOO 7879100 7884t00 7822t00 7782tOO 788lt00 7579t00 7454+00 7119t00 6905t00 8373100 4483 t 0 0
50.00 1.50
7897t00 7895100 7889100 7879t00 7884t00 7822tOO 7762tOO 7881t00 7579t00 7454400 7119100 8905*00 8373t00 .3483*00
5000-02 5001 - 0 2 5003-02 5007-02 5013-02 5028-02 5049-02 5074-02 5104-02 5135-02 5189-02 5203-02 5159-02 3957-02
4993-01 4994-01 4998-01 5 0 0 0 - 0 1 5005-01 8020-0l
3472tOO 3472t00 3473t00 3475100 3477tOO 3484tOO 3492+00 3502tOO 3511+00 3519tOO 3513tOO 3493tOO 3381 t 0 0 2468tOO
4388100 4387t00 4387+00 4389100 4391 100 439eto0 4402t00 4407tOO 4,1 1 o t 00 4408t00 4'373t00 4327t00 4 143tOO a!l8r+oo
71sitoo 7155too 7150t00 7143100 7123100 7091t00 7048 t 0 0 8984100 8902+00 8857 1 0 0 848a+oo
.. 7842t00 7838100 7828r00 78 131 00 7773t00 77 let00 7840tOO 75421 0 0 7420t00 7093100 8881IOO
-._. _ . 5041-0 1 5087-01 5095-01 5128-01 5179-01 5191-01 5145-01 3937-01
e o i o r o ~ 4247+0Q
.... .. 8353100 4488100
L2/A = .01 .IO . 25 .50 .75 1 0 0 2.51 5 . 0 0 7.50 1 0 . 0 0 2 0 . 0 0 30 00 4 0 . 0 0 5 0 . 0 0 8 (MFP) = 1.75 1.75 1.75 1.75 1.75 1.75 1.7'3 1.75 1.75 1.75 1.75 1.75 1.75 1.75 I (RAOI
. o i i i s ,04383 ,08727 . 13090 .17453 .28180 .34907 ,43033 .52380 .81087 ,78546 .87288 1.04720 4.57080
5000-02 5000-02 6001-02 5003-02 8008-02 8013-02 8022-02 5032-02 5 0 4 1 - 0 2 5048-02 5031-02 5000-02 4850-02 3580-02
4992-01 4993-01 4994-01 4998-01 1998-01 8005-01 50 14-0 1 6024-01 5032-01 5037-01 1021-01 4989-01 4838-01 3585-01
.IO 2 00
4992 - 0 1 4991-01 4992-01 4992-01 4991-0 1 4990-01 4987-01 4981-0 1 4970-01 4951-0 1 4172-01 4901-01 4585- 0 1 3278-01
1238t00 1238t00 1238t00 1239t00 1239tOO 1241tOO 1243t00 1245tOO 12 *e+ 0 0 1247iOO 1241tOO 1232+00 1191 t o o 8719-01
.?I 2.00
2407+00 2407tOO 2407tOO 2408t00 2400+00 2411tOO 2413tOO 2415tOO 2415100 2412tOO 2391+00 2366tOO 2287t00 1034tOO
. I O 2 . 0 0
3443rOO 4347t00 4341100 4347t00 4348t00 4345100 4342t00 4337tOO 4328t00 43 12 t 00 4287tOO 4193t00 4 113t00 388Ot00 2122*oo
1 0 0 2 . 0 0
4 3 0 8 + 0 0 4308tOO 4307tOO
7477t00 7475100
7507t00 7505t00 7497100 7484100 7488+00 7413tOO 7339100 7240t00 7117100 8967t00 8579 t 0 0 8339t00 5781kOO 3898+00
7.50 2 . 0 0
7 175 100 7172t00 7183100 7148100 7128t00 7084kOO 8977100 ~8882+00 (1720100 8549100 8118*00 5859r00 5287100 36 131 00
7509tOO 7507t00 7499t00 7488t00 7488400 7415tOO 734Ot00 7242+00
7509t00 7507tOO 7499tOO
7509100 7507r00 7499t00 7488100 7488100 7415100
7509+00 7507tOO 7499 t 00 7488*00 7488t00 7415tOO
7509100 7507+00 7499tOO 7488+00 7488100 7415t00 7340100 7242tOO 7118tOO eea8r 0 0 8580100 8340100 5789tOO 3999+00
50 00 2 . 0 0
3453 t i i 3454t00 3454t00 3494100 3455t00 3.94100
7486tiO 7455tOO 7438,OO
7488100 7488+00 7415r00
.. -. 7387100 7314tOO 7219+00 7097t00 BB4BIOO
734itii 7242t00 7118100 8988*00 8580 t 0 0
7346tii 7242+00 7118bOO 89e8tOo 6580100 8340t00 5789t 0 0 3899100
7346+ii 7242t00 7118+00 8888t 0 0 858 0 t 0 0 8340t00 5789t00 3999+00
.- 3452t00 3447t00 3438+00
. - .. 7118100 8988 t 0 0 858 0 t 0 0 8340t00 5789r00 3999tOO
IO 00 2 0 0
7178tOO 7178t00 7173100 7173100 7184+00 7184tOO 7149100 7149t00 7065+00 7127t00 7127+00 7085t00 8977r00 8977t00 8883tOO 8883*00 8720+00 0720100 8549t00 6 5 4 9 t 0 0 8118100 8118+00 5859t00 5859t00 5267100 5267tOo 3813tOO 3813100
3383t00 33341 0 0 3180100
-. 8555tOO 8328t00 5758t00 3991tOO
ejiitii 5789100 3999+00 2249+00
LZIA 1 (YFP) b (RAD)
,01741 ,04383 .om727 . 13090 .I7483 .28180 .34907 ,43833 ,51380 ,81087 ,78540 ,87288
1.04720 1 ,57080
. 0 1 2 . 0 0
5000-02 50 00 - 02 8000-02 1000-02 5000-02 4999-02 4998-02 4990-02 4979-02 4980 - 02 4882-02 4813-02 4178-02 3280-02
.75 2 . 0 0
3435100 3435100 3434tOO
8.00 2 . 0 0
' 2 0 . 0 0 2.00
3 0 . 0 0 2 . 0 0
7 178 k 00 7173t00 7184tOO 7140100 7127t00 7085t00 8977t00 8883*00 6720100 8549r00 8118*00 5859t00 5267r00 3613t00
40.00 2.00
1237 t 00 1237COO 1237tOO 1137100 1237100 1238tOO 1 2 3 8 b O O 1234100 1230100 1225100 1204100 1 185+00 1124tOO 8012-01
2401100 2401 too 2401too 2400tOO 2400t00 2398tOO 2384400 2398t00 2379t00 2385t00 2313+00 2270t00 2134100 1508*00
8720100 0718r00 8712tOO 8701t00 8885t00 8 8 4 0 t 0 0 8574r00 8488+0O 8373100 0232tOO 5858r00 5623100 5070t00 3482t00
7157tOO 7155100 7148t00 7131*00 7109100 7049100 8982t 0 0 8849r00 8709100 8539100 8110+00 5852lOO 5281 t O O 3809IOO
7178100 7178*00 7173100 7 184100 7149tOO 7127tOO 7085400 1977100 8883t00 8720 IO0 8549100 8118100 5859t00 52137 I O 0 361Rt00
7i7310i 7184tOO 7140IbO 3433t00
343 1 t 0 0 342BtOO 3417400 3484+00
4304100 4301+00 42JO+OI 4274100 4251 + O O
. . . .. 7127tOO 7085t00 8977t00 8883tOO 8720100 j384too
3358t00 3282 + O O 3188100 2987t00 2074600
45 i7100 4Ill10O 40 Z8100
_ _ 8549t00 8 1 1 8 t O O 5859t00 5267*00 3813400
3917too 3813t00 25'l8*00
- 49 -
WAPO - TM- 162 3
0 IOW ,11749 . 04193 . 08721 . 13090
4011-01 4010 - 0 1 4017-01 4083-01 4011-01 4a10-0l 4015-01 4118-01 4850-01 4 1 8 9 - 0 1 4398.01 4499-91 4 1 1 1 - 0 1 2154-0 1 I . s i o i i
1121.ee
.. 40oar00 4141 I 0 0 4 8 1 1 t00
4 0 8 2 - 0 1 4.11-a1 4991. I 1 4 1 1 1 0 1 4813 0 1 4790-01 4902 0 1 4 3 8 1 . 0 1
01141 04393 08127 11am0
2111a W o e 1 43931 9Y390 91011 11540 81199
1 0471e 1 51010
. 114113
1 0 4 I t 0 0 2500 I 0 0 2113*00 1440.01
1 1 2 0 0 1 7492 0 1 0 1 9 4 # I .
1118-eI i i i o - 0 i
- 50 -
WAPO-TM-1623
TABLE 13 (Cont'd) - -
L l I A 0 IWFPI f IIAOD)
0 114s 04303 0 8 1 1 1 13980 Il4S1 10111 34007 4au33 513W 01807 78140 8llW
I 04110 I 5101t
0 1 1 0 . 0 0
4198 - 0 1 4981-02 4849-02 488?-01 4802-0 4S11-01 42?3-01 3132-02 3¶?4-@2 3111-01 100 1-01 23s 1 - 0 1 le61-02 1 3 0 1 - t l
I 0 1 0 . 0 0
4813-tl 480l-tl 4125-01 4883-01 4118-01 4547-tl 4lS1-@1 3911-0 I 3ss5-t I 3203-t l 2s10- t 1 1331 - 0 I 19St-01 1 3 0 0 - t I
1s 1 0 . 0 0
1111te0 11081t0 1100*0t lI8S100 lIO4*00 1101+t# 1134*tt 8sll-tl 8037-01 1119-01 0 1 1 5 - ~ 1 SO08-~l 4730-01 3113-01
1 s0 1 0 . 0 0
3140100 3131 S O 0 3703100 3041.00 3¶14*9t 3314r00 3122110 1 8 4 1 t t 0 1sss01e 2283O.t 1826100 1841r00 1373.00 9 1 % - 0 1
3 0 . 0 0 IO. 00
3140100 3731 600 3 1 0 3 + 0 8 3848+@0 3¶14.0@ 3 3 1 4 + t 0 1111r00 1841000 2sss 1 t 0 2183+00 1110+00 1041400 0 1 3 1 0 t 9150-0 I
TABLE
04303 08711 13000 114S3 10181 34897
.4au33 ,51300 01087 7.3.. 8 i i e
I 04120 I 51080
L Z l A -
2 O t i i 34907 43033 Slau1 01017 78149 17200
1 04720 I 61019
L 2 I A = 0 I W C I .
I I A O I 0 114) 04m3 O I l l ? 1308t (?IS3 10180 34107 4-33 5130t 01101 18541 812-
1 04710 I ¶?090
OF THE YOOTWO F u C T l ~ E X P I 8 I * R I ~ . L l , A 8 l I j
0 1 I O 15 SO 75 1 00 2 !IO 5 00 1 SO 10 0 0 1 0 00 30 00 4@ 0 0 5 0 0 0 15 0 0 IS 00 15 0 0 15 00 I5 t0 IS 00 15 110 IS 00 I5 0 0 I S 0 0 IS 0 0 I S 00 I5 0 0 IS 00
4 9 M - t 2 4919-02 4918-01 4 8 1 9 - 0 1 4 0 8 0 - 0 1 4330-t2 3 1 IO - 0 1 341s-01 3004-tl 108 I - 02 Y1#.-.1 1099- tl lS13-02 10S8-tl
4001-t I 4144 . 0 1 4884-01 4185-01 4OS3-01 4305-01 3818-01 3441-tl 3t31-01 1WI-01 l#*J-01 118S-tl IS1 1 - t 1 1.47-01
3 1 1 l * 0 0 3080I00 3 0 1 1 + 0 0 2988+Ot 1 8 J 8 I 0 0 100 11 00 1381100 1090100 1819+tt 1¶18*0@ lY54r.a lll9*00 0401-01 0271- 0 I
3 l I l 1 0 0 3099400 3051100 2988k00 1898t00 200 I 100 1 3 8 1 + 0 t 1080*1t 1028190 lS98.tO 1154.a. Ill*+t0 0400-0l 0 2 1 1 - 0 I
IlIl100 30091t0 30¶1+Ot 1909*90 1 8 9 8 I 0 0 1001+0t 138lO.t 1090100 1818101 tser*tr 1Y5.raa l l29.00 9408-01 0271-01
488s-91 48? I -tl 4811-01 41S3. 0 1 4Sl8-01 4114-02 aula-01 3111-02 108O-tl 1311-02 IO I1 - 0 1 1035-t1 1303 - t2 w14-03
4950-01 4120-01 4143-01 47Ie-tl 4531-tl 4010-01 3512-01 3 W I - t I 1we-01 130s-91 1118-01 lOl8-0l 1349-01 8980-01
11811t0 11?8100 IlSSO00 1113101 1081.00 8137-0 1 1818-01 135s-01 0310-tl 1481-01 41?1-01 3148-01 3208-01 1138-01
1718*@t 2114000 1055 + 00 1811*00 1413rt0 1213.00 lalor t 0 lOSl.t0 141s10e l114+t0 8043-0 I a500- t I ?1¶0-*1 4712-01
4914-01 4803-0'2 40sl -tl 4001-02 4408 - tl 3132-02 330 I -tl 1841-02 1 4 1 4 - t Z 200m-t1 1018-01 1 4 W - 0 2 1114-02 80W-03
4938-01 4 9 0 1 - t 1 4103-01 4030-tl 4411-01 3111-01 3323-tI 110s-t1 2380-01 2 # S I - 0 I low-91 1440-01 1100-01 10@1-#1
I I O O ~ ~ ~ 1159r.1 1134190 1084.00 1043r00 8107-tI 1828-01 W l 4 - 0 1 5010-t1 4831 0 1 31W-tI 3389-01 2814-01 1813-01
1441100 2418100 2374rt0 11801t0 1173100 1191090 1013*00 I IS1 100 11¶0.00 9890-11 1 1 0 3 - 0 1 0933-01 S l l l - 0 1 1851 - 0 I
244¶*09 2428100 1374100 1 1 8 O + t 0 2113b10 18.8000 10131 09 13¶1+00 11s0*00 9890-0 I 1 1 0 3 - 0 1 0933-t1 s i71 . e l 3811-01
Y44S.00 1419800 1314100 2280100 2 l 1 3 l t 0 I9891t1 1013r00 I m b 00 IlS0~00 9810 t l 1 1 0 3 - 0 1 0833-01 S711 . 0 1 38s I - 0 I
244¶*00 14211.t 2374ltV 1180100 1 1 1 3 1 0 0 1898100 1013+00 1 3 5 1 ~ 1 0 I150 $00 9890.01 1 ? 0 3 - 0 1 0933-01 Sl?l-Ol 3851.01
- 51 -
WAPD-TM- 1623
TABLE 1 3 (Cont'dl
L21A 8 l l ? C l I 11Ml
#114¶ 04ma W721 13018 17453 2OlD8 341e7 43033
010.7 78540 D l 200
1 #412# 1 51.10
5 2 m e
8 I W P I f 1110)
8 1745 1747*0# 1124600 1847+## 1531+** 13S. l *#~ 11*8b## 1732-#1 7#53-#1 5894-01 5044- # I 3923-#1 3531 - # 1 2 0 4 2 - 0 1 1ss2 - 0 1
I l 4 1 t 0 0 1724.01 1 8 4 1 * 0 # 1531400 1393tee 11#8.00 8 1 3 2 - # 1 7 0 5 3 - # 1 5 8 8 4 - # 1 5 # 4 4 - 0 1 3923-01 3 1 3 1 - 0 1 2942-01 1982-81
1303*## 1 l # D * # # 1132-01 7 # 5 3 - # 1 S884-#1 5 # 4 4 - # 1 3923- # 1 353 l -#1 2 * 4 2 - # 1 1981 - e 1
. I . 51#1#
20 oe 8 0 . 0 0
1597+0# 1572+00 1488*00 1380+0@ 1223.eo 9480-#1 134O-# 1 5 9 I 1 -# 1 49 IS-. 1 4 2 1 1 - # 1
3 2 8 0 - 0 1 3 2 8 0 - 0 1 32110-01 2952 0 1 2 9 5 2 - # 1 2 9 5 2 - 0 1 2 4 8 0 - 0 1 2461-01 1 4 0 0 - 0 1
2952-0 1 1401- a 1
IMU
5 7 5 . 0 0
1430+## 1 4 0 2 * 0 0 1310+*# 1180+## 1035ta0 7732-#1 S 9 1 1 - # 1 4737-#1 3940-01 3314 - # 1 2832 -01 2381-01 1974-01 13 18-0 1
1 so 7s 0 0
1 0 0 0 15 0 0
20 e 0 7 5 . 0 0
1430 0 00
30 0 0 79 00
50 0 0 1s 0 0
1430600 14O2.00 1310+00 1 1 8 # t # # 1035*#8 7732-01
4737-01 3948-# 1
1 1 3 ? - 0 1 2309-01 1914-01 1318-01
191* -at
3384-0 t
1430+00 1402+0# 1310*00 11E#.OO 1035**# 7732-0 1 5911-01 4731-#1 3948-#1 3384-0t 2532-#1 1309- 0 1 1914-#1 1 3 1 8 - 0 1
1430reo 1402*00 1310100
1401.00 1310100 11a8r88 .- 1035+##
3452-01 40#1-#1 2D77-#1 3934-#1 2400-#1 3287-81 1111-#1 25%-01 1728-#1 2 3 # 1 - # 1 1438-01 1517-#1 9S19-#Z 1218-#1
.... ~. 1974-#1 1316-01 1 5 7 # 1 #
- 5;1 -
WAPD-TM-1623
I l
1033-03 2180-01 4321-02 ._.- _. 0511-00 1s21-*1 ~ .- . 1 7 1 1 - 0 1 2111-01 4271-01 1328-81 3298-01 8414-01 l 8##-0 l 4419-01 111'7-01 2308-01 8131-01 2114-01 1100-01 3480-01 8 8 0 1 - 0 1 4931-01 5990-01 1 8 Y l - 0 I 1*20*e I
l e 08
YI4S-02 8318-02 ( 8 7 7 - 8 1
04303 08711 1301e I1483 20180 348#7 43833 82300 01#81 18840 1 1 2 M 04710 S1.80
.. 2400+00 11s140e 4 IBO+00 381 I e0 I
50 05
4085-02 I 0 1 1 - 0 I 2031-01 3OM-01 4 105-0 I 0234-0l 1401 -0 I
t i r i . 0 1 0305401
2e e0 OS
2320-01 5117-01 lIO4+00 174eta0 l337*00 3521tet 4144rW 5911t0e 7 3 0 @ 0 e 1003 t @ 0 IlO5+@l 133l.@l l l l 5 . 0 l 3853+# I
1 0 . 0 0 IO
1302-#4 2 0 1 1 - e3 ~ i m i - e 3
1411-0 I 2882-01 448o-el 150.0
17 453 20110 34101 43033 52300 ole11 18540 I1 208
I 04720 1 57010
.- 820 I - 0 3 8314-03 1214-02 1 1 1 1 - 0 1 r i i r - i i 1139-02 3311-02 4 1 2 1 - 0 1 5011-02 1014-82
2730-01 3311-01 41 10-0 I 8804-01
i i i e - i i 0 1 I 0
1191-04 191s-03 3#5#-#3 5154-03 1 8 1 3 - 0 3 1211-e2 1843-02 2 1 0 2 - 0 1 2518-02 3144-02 4451 - e2 5215-02 1541. 0 1 480m-el
L2 /A 5 IWPI
(11101 0 I145 04303 0 8 7 2 1 13010 11483 20110 34801 43033 5230e 01087 18540 81200
I e4110 I 57010
I0 . I 0
7810-03 1114-02
5148-02 7800-01
3154 -02
.1¶ . I0
1884-02 481 1 - 0 2 91.0-02 1 4 1 I - 0 l 188Y-@l 3010-@l 4015-01 5225-01 0 4 5 0 - 0 1 7110-01 Ileeree 1 3 l l . @ 0 I 800*00 8381t00
5 oe I0
1 0 . 0 0 I 0
so 0 0 IO
.. 2043t00 3013.0e 4148*#0 5240re0 0315400 1582. e 0 1014101
5418 e 0 0074.00 790treo lO55.*l 1200ret Is18.el 1 8 C J + ~ l
l I S l * 0 1 I48 I $ 0 1 18ll.*l
L21&
f ::z 01145 04383 08121 13090 I1453 20180 34807
S P J O I llle81 71540 11200
I 0472e I 51010
43033
. * 1
. 2 0
1145-04 1181-03 358 I - 0 3 5388-03 ?2l1-#3 1094-01 1184-02 1 8 H - 0 2 233.-*1 i m a - a z 3 1 1 0 - 0 2 4811 - e2 8584-02 1385-01
2¶ 1 0
s oe 20
1 1 1 8 - 0 2 4443 - 8 2
5180-@4 1403-03 2031-03 4101-03
1138-03 12.8-02 1541-02 111s-01
saaa-oa
5844-#3 1402-01
1288-01 3 1 2 1 - 0 1 04.5- 0 I
l 3 # I - 0 l 3252-01 8500- 0 I #788-@l l303.00 1900 4 0 0 2022*00 3293r00 3113 $0 0 4084.00 0085*@0 0115400 8300+#0 1101+e1
1451-a2 303s-e2 128 I - t 2 1018-01 145%-@ I 2220 - 1 1 3004-01 3821-01 4104-01 5051-@1 1842-01
5344-01 1338-01 2010-01 4024-01 5382-01
08721 13090 I7453 20180 34001 1201-01 431133 1510-01 5230e 1813-01
78543 3183-@2 3158-0l 01081 2211-02 2274-01
iwi - i I
I . i 4 7 i i 1 . 5 1 @ 8 #
. @ I145
. e8117
. 04303 4714-#3 I I W - 0 3 23#8-#2 3002-02 4 1 I 8 -e2 7213-@1 1148-#2 1252-01 1533-01 1834-01 2515-01 2107-01 3038-#l 8424-01
2333 -02 5833-#2 1109-0l l l 5 o - e I 2348-01 3553-0 I 419s-01
7193-02 1941-01 3800-01 5851-01 7802-01 lIl9t00 l 58 t t00
13080 17453 1 1 1 8 0 341*7 43033 52300 .Ol01? 18540 2511-02 11280 2 1 1 2 - 0 1
57010 w i s e a n i ( i - w
0010-0l 1453-01 8003-01
1 I 8513-02 iiii+ii
- 53 -
WAPD-TM- 1623
TABLE 14 (Cont'd). TIdLE Of TM T U C T I O N RII.L2fA.Bl
L2/A * 0 1 10 25 50 15 1 0 0 2 50 5 00 7 50 10 00 20 00 30 00 40 00 50 00 4 I M P ) .BO 80 80 80 8 0 80 80 8 0 8 0 80 80 80 80 80 L IRAO)
01145 . 04303 . 0 8 1 2 1 .13090
4m33 s i r i i
.a1081 ,18540 81100
1 0 4 1 2 0 I .51080
3911 - 03 9115-03 1051-02 2048-02 3041-02 59w-e2 8028-02 t018-81 1241 - 0 1 1410-01 2003-01 2295-01 2949-01 ~ a a - 0 1
1900-02 4100-02 0542-02 1434-01 1911-01 1890-01 390 1-0 1 404 1 -01
1105-01 9054- 0 I 1102100 1 J I I t 0 0
ams-eq
i a i ~ + o e
2105-01 0914-01 1384-01 108*-01 2179-01 4198-01 5050-01 7 149-0 1 8101-01 1034100
1515+00 191Ot00 1539+00
t38ateo
3519-02 8 8 1 5 - 0 2 1107-01 2814-0 1
5353-01 1 199-0 I 9098-01 1100It0 1311*00 114lt.0 1978100 2450400 30588r00
J I ~ I J - ~ ~
0 1 9 l - O l 1548-01 3097-01 4049-0 I 0200-01 9335-01 1249100 1509*00 1801600 1218t.0 l 8 1 4 t 0 0 3190100 3193t00 4440*00
1 1 1 1 - 0 2 1801-01 3814- 0 1 5411-01 7230-01 1 @ 8 5 t @ 0 1441600 1809100 2 1 1 0 + @ 0 1530100 3231100 3580 b 0 0 4 I 7 1 r e 0 4811+00
7393-02 1848- 0 1 JOOO-01 5S44-*1 7392-01 1 tosr00 1417*00 1845100 2111rmt 2513t00 1278100 3014r00 4 2 1 0 * * 0 4868.00
7410-02 1850-01 3113-01 5589-01 1424-01 1113to0
1852t00 1 2 1 8 6 0 0 258 1100 3287100 3022100 4219100 4877rOO
~ m a + o o
7430-02 1859-01 31 18-0 I 5570-01 1434-01 1 1 1 5 + O O 1485tOO 1854tO0 221#+00 1 5 8 3 t 0 0 3 a a s w 31124 t a o 4 1 3 1 r O O 4879+00
1 4 3 0 - 0 2 1859 - 0 1 31 18 - 0 1 5575-01 1434-01 1 115t00 1485r lD 1 854 t 00 1 1 1 0 + 0 0 1583600 3 1 8 9 t 0 0 3 0 1 4 b 0 0 4231*00 4870.00
i m a - 0 2 1859-01 31 1 8 - 0 1 5510-01 1434-01 1115+00 1485+00 1854600 1 1 1 0 * 0 0 15831 00 3289+00 3014tOO 4 2 3 1 + 0 0 4879 0 0
01145 04303
.08711 . 1 3000 ,11453
,34907
,52300 ,01081 10140 812W 04120 57000
i a im 43133
3210-04 aeaa-04 1007-03 1415-03 3221 - 03 4871-03 0553 - 03 1285-03 1008-02
1598-02 1811-82 2219-02 3009-02
ii9a-w
3201-03 8011-03
' 1005-01 2412-02 3223-01
0544-01 8174-02 1007-01 1 I 8 4 4 1 1580-01 1813-01 1173-01 2988-01
4aa5-02
1904-03
3917-e2
8004-02 1208-01 1025-01 2054-01 1499-01
39w-01
5011-01 1135-01
i s s 2 - w
smoo-oa
zaa2-01
r4.w-r 1
1557-02
1791-01 1 1 1 1 - @ 1 1¶04-01 1301-01 3173-01 4009-01 4812-01
1014-01 808 3- 0 1 1015*00 1334100
3a94-02
31aa -0 1
2254-02
1118-01
22a3-01 34 13-0 1 4515-01 5180-01 7021-01
1090t00 1231r*0 1514.00 l 8 1 @ + 0 0
sa31-w iasa-ei
aaso-01
4924-01 1231-01 2402 - 0 1
4928-01 1401-01 9881-01 1231r00 1485t00 11336D0 22lSt.0 2441600 1835*00 3181t00
mss-ef
5113-02 1428-01 2855-01 4281-01 5105-01 8 5 4 2 . 0 1 1130t00 1415*00
1951100 2400*00 2098 * *e 3090r00
i a s e w
3 4 4 2 ~
1 1 1 7 - 0 1 1432.01 2882 - 0 1 4192-01 5'118-0 1 8501-01 1138600 14 11+ 00
IOO0b00 2489 I O 0 2 1 0 2 r 0 0 3091+00 3445+00
i o s a 1 ~
5 1 3 0 - 0 1 1432-01 2884-01 4194-01 5711-01 85W-01 1139t00 1418t00 1093+00
2409*00 2102.00 3100.00 3440*00
w a i t o e
p IRA01 01145 04 383
. wiii I3090 11453 20180
1 04120 1 . 5 1 0 8 0
2500-04 0292-04 1251 - 0 3 1819-03 2510-03 3182-03 587e-83 8388 - 0 3 1153-03 914a-03 1285-02 1 355- 02 1854-02 20 1 1-02
2401-03 0244-03 1250-@2 1071-02 zs@o-a2
5009-82
7141-02 9 131 -02 1203-01 1353- 0 1 1049-01 1909-01
a i i i - w a31a-ti
1210-02 3025-02
9090-01 1214-01 1828-01 2452-01 3087-01
4390-01
0450-01 1774-01 0045-01
a053-02
3 i m - 0 1
57as-01
T A l L L O f THE F U K T I O N Rlb.L2/A.~l
L2/A
9 IZZI . 0 1145 ,04313 . 08127 . 1 3090 ,17453 .lo190 ,34907 43033
01081 18540
1 04120 1 ,51080
.513ae
onao
. e 1 1.50
1841-04 4809-04 9142-04 1402 - 03 1851-03 2031-03 3932-03 4940-03
0998-03 9094-03 1013-01 1205-02 1391-02
~ w a - t i
10 1 . 5 0
1944 ~ 0 3 4802-03 9118.03 1400-02 1949-02 1933-02 392s-01
5953-02
1011-01 l I 0 1 - @ 1 1380-0 1
4m3a-oa
a m - 0 1 9 0 i a - t ~
25 1 . 5 0
4814-03 1200-02 2414-01 3623-02
727s-02 91 38 -02 1123-01
1731-*1
2499-01 1903-01
m3a-02
wia-01
124a-01
3ma-ei
50 1.50
0391-0 3 2350-02 4101-02 105s-02 9411-02 (416-01 1194-01 1377-01
3350-01 4335-01 4909-01
0194-01
zoaa-et
saoa-ei
i i 4 a - o 4ms-02 8 1 3 4 - 0 1 1311-01 1151-01 1030-01 3531 - 0 1 4441-0 I 5 300- 0 1 0 3 0 1 - 0 1 8211 - 0 1
1091+00 1 2 0 + 0 0
o 1as-0 1
3 1 0 2 - 0 1 925s-01 1811 - 0 I 2770-01 a7ae-01 5545-01 1 3 8 1 - 0 1 9203-01 1100+@0 1215*00 1004480 11s ir00 1980100 2154+00
4114 0 1 1 0 4 3 - b I 2880 -0 1 3120-*1 4163-a 1
8253-01 1024.00 1218*00 1404+00 1145+00 18S5r00 2133t00 2299tD0
a n z - 0 1
I 00 I 50
1108-02 4111-02 8543 - 0 2 1202-01 1110-01 2108-81 3418-01 4291-01 5152-@1 0 0 0 8 - e I
8420-01
lW48tb0
ioa3-01
ea82 - e 1
P 50 1 50
2 1 8 8 - 0 2 8909-01 1393-01 2088-01 2 7 8 2 - 0 1 4101-0 I 5 5 2 3 - 0 1 0 8 0 0 - 0 1 8 100-0 1 9408-01 1151t00 1102600 1407t00 1489r00
5 00 1 50
3054-02 1035 - 0 1 1s20- 0 1
3043-01 454 1-01 0 0 1 0 - 0 1 7438-01 8811-01 1011.00 1243400 1340 e00 1484t00 1500+00
mea - 0 1
4 1 8 0 - 0 2 1045-01 1088- 0 1 31 3 0 - 0 1 4168-*1 8 2 2 9 - 0 1 8202-01 1025t00 1219600 1405ree 1141400 1890+08 21.34600 1 3 0 0 + 0 0
i 5 0 S - i i i s i i i - i c 0 0 4 5 - 0 1 0015-01 7418-01 1478 0 1 8855-01 8855-01 101Ot00 1 0 1 0 b B 0 1241.00 11.1*1. i J a i + i i i J i i + i i 1489t00 1489.00 1Sllr00 1571+D0
40 0 0 5 0 00 1 50 I 50
3075 (2 3075-11 7687-02 1887-b2
L I / A . . 0 1745 . 04383 . 08121 . 13@*0 . 17453
,34801 ,43033 ,52388 01081
,18540
1 . 04720 1 .11080
! Z! - . z a w
.enoa
.#I 2 . 0 0
10 1 . 0 0
25 2 . 0 0
50 2 . 8 0
15 1 . 0 0
1 00 2 . 0 0
1 00 2 0 0
5 00 2 00
7 5a 1 00
10 00 1 . 0 0
2s 00 2 00
J 0 . 0 0 2 00
40 00 2 . 0 0
50 00 2 . 0 0
- 54 -
WAPD-TM-1623
. 01145 ,04303 . (I727 . laom0 . I7453 ,20180 .34007 .43033 .52300 O l 0 # 7 70540
. #71M I W 1 2 @ 1 570ma
1103-05 ll5@-@4 l77@-@3 l700-@4 17@7-03 4125-03 311#-04 3173-03 8845-a3
3422-03 a555 - a3 I l O - 0 2 2502-02 3412-02 5090-@1 0153-@2 #30#-@2 9124-@1 114@-@l l 3 # # - # l 1504-01 1045-01 tow-0c
4000-03 1217-02 2 4 3 2 - 0 1 3044-02 4850-@2
058 1 - 0 1 1185-0 I I 4 @ 3 - @ 1 1008-0l l#0@-0l 2ama - a 1 2 2 1 0 - 0 I 1334-01
n 3 e - m
0004-03 1510-a2 301m-02 4537 - a2 0031-02 ma.2-02 l l # 0 - 0 l l 4 O # - # l 1135-@l Irn81-0l 24@0-@1 2558-@l 2155-0 I 2815-0l
0488-@3 2311 4733-02 1 a78 - 0 1 040a-a2 0 # 3 - @ l l#20- a I 2232 - 0 I 20@4-@1 2130-a1 3458-01 3840-@1 3851-0 1 3912-01
0401 ~ I3 2373-02 4 1 3 8 - 0 2 1 0 8 0 - 0 2 0 4 0 8 - @ 1 l 3 # 4 - # l 1 8 2 8 - @ l 2234-@l 2000-@1 2038-@l 3400-at 3042 - @ 1 3#53-@l 3914-01
14#1.@3 I 3 7 3 - 0 1 4138-a2 1010-02 I400-01 I304 - a 1 l # 2 # - @ l 1234-01 2000-m I 1 0 3 8 - @ l 3400-@l
3053-0 I 3 # l 4 - 0 1
m41-01
0 m - u 0408-03 2 3 7 3 - 0 1 2373-@? 4138-@2 4 1 3 # - @ 1 7am0.02 1 0 8 0 - 0 2 8408-02 04@#-@2 l384-@I 1304-01 1828-01 1818-01 2234-@1 1234-01 20W-01 2O@O-bl 2030.@l 2038-01 3400-@1 340@-01 3041-01 3042-01 3053-01 3853-@l 3914-01 3914-@1
0408 - 03 2373-02 4738-02 7088-@2 04@m-@Z 1314- 0 I 1828. 0 1 2 1 3 4 - 0 I 2oae-0 1 1938-@1 3481-a I
3853-01 3914-01
m4i-ai
LZ/A - @I 10 25 sa 5 00 7 50 10 (0 1 0 00 30 @ @ 40 00 SO 0 0 0 (WPI - 3 a0 3 aa 3 a0 3 00 3 :: ; :: : :: 3 00 3 00 3 00 3 aa 3 00 3 0 0 3 aa 4 , a m i
I miiw @471@
I .57@00
L l I A 0 IMFPI
lam) 01745
. em727
. l3@#0
. I7403
. 20l10 ,34107 43033 . 5230a
. O I 0 0 7 ,11040 #llIO
I. a411a I 57am0
. oama
4344-a5 l0#0-04 2 l 7 @ - 0 4 314#-04 4322-(4 044a-a4 asa4-04 l04#-@3 1117-03 1411-@3 1707-03 1820-03 1m01- e3 200m-03
D l 3.5a
2039-01 0985 - 09 1315-04 In# - e4 20 15- a4 3##4-@4 5lao-a4 0202-04 1333 - 04 # I # # - 0 4 ## 35. a4 1#31-@3 I 087.03 1112-03
4339-04 ((14-03 2105-a3 3242-aa 4313-03 0427-03 8488-03 l047-@2 1234-02 140m-az 1 1 0 1 - 0 1 l # 1 4 - @ 2 l#55-@2 200a-02
I @72- 03 10#@-@3 0354-ao 001m-03 I 007 - a2 l500-@2 18#7 -@2 25m-02 304m-az 3477-b2 41m5-02 4407-02 4803-02 4#00-02
2000-03 Sl01-@3 1031-01 l544 -@1 2@54-@2 305n-a1 4aal-a2 4900-02 omw-02 MIS-a2 7##0-@1 #482-02 8@04-@2 021#-@2
m11-03 1 3 0 2 - 0 3 I45e-02 1184-02 2ma3-01 4318-02 wmm-02 00m3-01 #2l4-02 0320-@2 1112-01 1170-01 1148-01 1260-01
! S i c - i i i 9 i i - i i iiii-ii 1104-ao 3415-02 rrw-ai 2@40-02 3###-01 5417-01 2414-(2 4578-01 0335-02 2543-02 4#00-@1 0032.02
3 O I 5 - @ 3 9034-03 1804-12 17.a-01 3189-02 5332-02 1a13-e2 8000-01 100m-01 l 1 4 Y - # l I 3 S 2 - 0 l 1125- 0 I 15113-01 1521-01
I 00 3.50
1155-03 '5380-03
I O @ # - 0 2 :I I 3 4 . @ I :llot-a2 4130-01 $1044- @ I 5805-@2 fI583-#2 7 1 4 1 - 0 1 1 # 8 1 - @ 1 I I108-01 t1352-02
i o i s - o a
521m a 3 I 3 0 4 02 2003 a2 3##l 02 5102. a2 1034. 02 0070- 02 l l l 4 - # l l 4 0 # - @ 1 l518-@1 9832-0 I l m I 2 - a l 1991-01 20 13-01
2 50 3 50
3912-03 1523-03 I 5 a I - 1 2 1241-02 2m7a- I 2 4318- 12 5003- I1 588# - 12 7#3#- I 2 8824- I 2 1000- I 1 Ia43-111 l a 7 o - o l 108 l - t l l
5381-03 1344.02 1083-02 4@08-02 5317-82 7855-01 1025-0 l 1240-01 1443-01 I O 14-0 I l#00-@l 1040-01 2 0 3 t - 0 1 2a4m-01
5 00 3 . 5 0
3 @ 1 7 - 0 3 7000-13 1533-01 22mm-02 3032-02 4405-02 5800 - a2 7.10-02 n a m - 0 1 8#51-@2 l O 1 0 - 0 l l o 5 o - a l I###-@l to95-0l
5383-03 1345-02 1584-#2 4a I I - a z 53l#-@2 785#-02 lo25-al 1240- 0 I l 4 4 4 - # l 1015-01 l80# - a I I 9 4 # - 0 l 2031-01 2 @ 5 0 - @ 1
1 sa 3.5a
3077-@3 1087-03 l533-@1 2 1 0 # - @ 2 3033-@2 4484.02 580 I - 02 7 @ 1 @ - @ 2 naan-a1 8050. aY I02@ 0 t l@SO-0 1 l e e # - 0 1 I 00s - a 1
5383-@3 I345 - a2 1 0 8 4 - 0 1 4 0 1 1-02 sal#-02 7851-@2 I@25-@l 1240-0 l 1444.01 I O I S - 0 I 1808-01 lS40-01 2831-@1 I o 5 a - a I
0 . 0 0 3 so
3 0 1 1 - @ 3 7087-03 IS33 .02 2180-0 W33-02 4460-02 5 8 0 1 - 0 1 70I@-Ol 8bO#-@2 805#-@1 l @ 2 0 - @ 1 l 0 s e - 0 1 l O O 9 - 0 l 1081-01
5303 .a3 1345-02 1084-02 4 a l ( - a 2 53l#-@2 785#-@2 l a l 5 - a l l240-@1 1444-01 I O l 5 - @ 1 l80m-a I 1 0 4 # - @ I 1031-@1 2050-at
Y O 00 3.5a
3077-03 1087-03 1533-02 2288-02 3@33-02 4400-01 580l-@2 1 @ 1 0 - # 2 8000-@2
l 0 2 @ - @ l IO50-0I 108#-@l lD95-@ 1
8esrn-o~
53m3-03 1345-02 1084-@P 4al I - 0 2 salm-01 1#58 - 0 1 I 0 2 5 - 0 l 0 4 0 - 0 1 1444-01 l o I 5 - a l 1800-@1 1040-@l 2031-Bl 2 0 5 0 - @ l
30 00 3 . 5 0
3077 - 03 7087.03 1533-02 ) I # # - 0 2 3033-01 4400.02 580l-@2 7 a I 0 - 0 1@0#-@2 8#50-02 1 0 2 @ - @ I l o s e - 0 1 1an0-01 1 009- 0 I
5383-03 1345-01 2084-@2 4 a l 1 - 8 1 53 I1 - 02 18S#-02 l 0 2 5 - 0 l 1140-01 1444-a I 1015-01 IO01 - a t 1040-01 20 3 t - a I 209a-*l
4 a a0 3 50
3077-*3 1081. a3 l533-#? 2909-02 3033-@1 44w-a2 580 I - 0 2 7010-02 aoo0-e2 ass#-02 l 0 2 0 - 0 l 1050-0 l 1081-01 ioe5-01
S383.03 I345 0 1 2814-03 4011-02 53Irn-02 785#-01 I 0 1 5 - 0 l 1 ? 4 0 - @ l 1444-01 I O I S - 0 1 I 8 0 8 - a I 0 4 0 - * 1 1131 - a I 1 0 1 0 - 0 1
5 0 @ @ 3 50
1077 a3 7087-@3 lS33 I?
3033-az 4 4 W - 8 1 5801-01 l o l o - # ? 8000 02 895#-@2 1020 @ I 1050 . a I IO89 @I 1005 ( 1
m e ai
,01745 l50#-00 I S M - 0 4 3#34-@4 1 5 1 4 - ( 4 1053-03 l285-@3 1744-1'3 1771-@3 Illl~01 1771-03 1 1 1 1 - 0 3 l7?1-03 I 1 7 1 0 3 1 1 7 1 - 0 3 .E4303 3#03-05 3083-@I 083@-04 l8#@-03 203@-@3 3212-03 4350-13 4 4 2 1 - 0 4423-03 4 4 I 3 - 0 3 4423-03 4423-03 4413-03 4413.01 0#127 7971-05 1.51-04 1082-a3 31SY-a3 a2a9-03 8 4 0 1 - 0 3 1115-13 8118-@3 8817-113 8817-03 8 1 1 1 - 0 3 0817.113 1 1 1 1 - 0 1 8 1 1 1 - 0 3
L 2 I A 9 ( W C )
(Moo) . @ l74¶ . 0 4 a m . am717 .13ama
11453 . .. .201#0 . Ji iw .43033 .5230a . O l e 8 7 ,71540 . #71W
I . t4720 I ,07080
0 1 ¶ . a @
5#71-00 1400 -a0 202#-@5 4372-@5 57e1-85 #520-@5 1105-04 l333-@4 1531-04 1084-04 W12-04 1 W I - 0 4 2017-@4 2W2-04
25 5.00
1443-a4 mas-04 7 W l - 0 4 l@73-@3 1421-03 20rnI-03 2711-03 320m-03 3150-03 4147-03 4072-a3 4112-03 4#l0-03 4#30-03
90 0 . m
2741.04 om..-04 1301-03 za37-03 20#7-@3 3#03 - a3 5134-03 011#-@3 7010-@3 7#@8-03 #75#-#3 #000-@3 8177-03 # l # l - 0 3
.15 s.aa 31W-04 0478-04 1881-03 2 I I9 -@3 3730-@3 5475-03 7.w-03 #¶@I-03 0714-03 W O # - @ l I l # P - 0 2 1222-01 1243-01 l144-@2
I oa 5 00
4'510-04 l143 -@3 227m-03 3:1em-03
0!5##-03 0401-03 I l l l m - a l l I O l - @ 2 l:ll3-b2 14 I 2 - a2 l445-@2 1407 ~ @ I ldlo1-02
~ w - o a
1.5a 5.ae
5ma3-aa 1174-01 1030 - a 3 4 3 1 4 - 0 5770-03 #42#-@3 loml-at l2#7-a I 1455-0 I 158s-t I I731 .0 I l172-@ I 1704-0 I 1100-0 I
5 aa 5.00
5#4#- 04 1405-03 2#5# - 03 4400-b3 ¶#lo-03 8417-@3 1001-01 1115-01
100¶-@1 ll40-@2 l 7#@-@2 lm.I-0a l#04-@1
1 4 e a - a ~
7 50 5 me
504m- 04 1405-03 2#5#-@3 44ao-aa 5rnlO-03 #4#7-@3 I @ # O - @ 2 11#5-@2 1403-01 191¶-@2 1740-(2 l7#@-@2 I # @ Z - @ 2 1#@4-@2
la. 00 5.0@
5m40-04 1405-03 2050-03 44ao-03 5#1#-03 04m7-03 l@##-@2 1200-01 1403-01 15*3-02 I 7 4 I - @ P 1780-a1 l # @ 2 - 0 2 I8(4-@2
3a 00 5.0a
0#4#-04 l4#5-@3 205#-@3 4400-03 S#IO-@3 #4#7-03 l@#0-@2 I N S - 0 2 1403-02 1s03-0* l740-@1 17ma-02 1 1 0 1 - 0 1 l#@4-@2
40 00 S . 0 0
5#4#-@4 l4#5-03 I%#-a3 44#0-@3 58 l # - b3 # 4 # 1 - 0 l 0 # # - @ 2 l I # ¶ - 0 2 1403-02 11m3-02 1140-@2 1780-02 1ma1-02 I 0 W - 0 2
5 8 l # - @ 3 8487-03 10##-@2
04m3 a0727 laam0 17403 20100 34007
. s2na ala#? 7OS4. #71W
I W72@ 1 57au
43033
2155-05 5303-05 1012-04 l5##-@4 2 1 $2 ~ a4 30##-04 3#13-@4 4742-04 1370-04 5m75-04 0407-@4 w00-a4 MW-04 0080-04
52W-85 1323-04 2935-04 3#27-@4 01ms-04 75#5-@4 we3 .a4 1 183-03 l¶1#-@3 l44@-03 loma-03 l 0 1 4 - @ 3 IO34 -@I IO35-@3
*##e-05 24m3-04 4W7-@4 74w-04 8771-04 1427-03 1833-03 2183-03 241a-03 200a-03 2m45-03 mmm-03 3 0 3 0 - @ 3 3032-@3
130m-04 34 I O - 04 oma4-e4 l 0 0 - @ 3 t33#-*3 le51 - 0 3 250 1-03 2172 - 03 3JS3-aa Je42-@3 3907-03 4032-03 4008 - a3 4a70-a3
20w-011 5 0 4 l - o ~ l la03-0: l 1402-0:1 190a-a:1 1150- @:I
4212-0:l 47?7-a:l OI44-0:l 053 1 - 0 3 5003-0:1 504 I -@:I 6043 .@:I
mm-o:~
2017 . a i 5000-@4 10@7-03 14#7-03 1#73- t3 2lOb-03 3038. 03 41#4-@3 479@-@J 5 l 5 7 - @ 3 5544 - e3 1010-03 w54-a3 se50-#3
1@17-a4 5000-04 1 0 0 1 - 0 3 I 4W-03 1073-03 28aa-03 42m4.03 4 7 0 1 - 0 51s7- 03 5544-03 5010-03 5054-@3 wise-03
m3m-03
2027-a4 500a-e4 1001-03 1491-03 iwa-03 zoea-03 m3o-w 4284-03 4700-@3 5157-03 5544-@3 50 I O - 03 w54-a3 wise-03
1027-a4 5@00-@4 ( (07-03 I407 - 03 1973-03 2000-03 3030-@3 4204-03 4790-@3 5l57-@3 5544-03 W I O - 0 3 5954.03 5050-03
2.17-04 50oa-aa 1 0 0 1 - 0 3 1491-03 l@73-@3 1#0@-@3 303#-@3 4204-aa 47#0-@3 5157-03 s544-03 SOW-03 5OS4-@3 w60-03
2027-04 5ooa-a4 l@01-@3 l407-@3 l#73-03 l80a-03 3mm- 0 3 4284-03 47m0-03 5l51-@3 5544-@1 5010-03 5054 - 0 3 sese-01
2027-04 5000 04 I 0 0 1 - @ 3 l4#7 l#73-03 2 8 0 0 - 0
- 55 -
WAPD-TM-1623
TABLE 14 (Cont'd)
50
110a - a0 D112-#0 I zaa - a5 lots-a5 24ao-a5 2882-#5
3133-#5 3*15-*0 4#01-#5
4aoa-a5 4#08-#5
i e . a o
439 I - eo
3433-eo
4a05-e5
7 5e i m ae
29OD - a0 1 4 0 2 - 0 0
40 a0 10 ma
29OD-00 1 4 # 2 - # 0 1401-05 2108-#5 2l32-05 4alo-05 494D-#5 5019-#5 0#14-05 0331-a5 O5l# -05 0520-*5 053a-a5 8530-#5
50 00 10 00
2908-#0 1 4 0 2 - 0 6 1401-05 2101 -05 2832-05 40le-05
2 5a I # ma
2901 -a0 1 4 0 # - # 0 l401-#5 Zl08-#5 283 1 -#I
I314-Oi 1843-#5 254l-OS
l401-#5 1401-05 2101-#5 2lOD-#5 2132-05 2132-#5
1401-*5 2 loa - a5 2132 - a5
l451-#5 2108-#5 2832-05
iiii-ii i i i i - e 5 4941-*5 4#48-@5 5020-# I 5029-*5 0#14-#4 0#14-#5
i i i i - a s 4940-*5 5029 a5 0#14-#5
4948-*5 5029-05 0#14-05 0331-05 05 IO- 05
,43033 . 02%* .01*81 .1054# B l 2 M
I #412#
0331-#¶ 6331-@5 0510-#5 051#-OS 0510-#5 0525-0s
0331 -a5 6520- 05 01 i e - 01 050D-@5
0525-a5 0528-@5 5529-as
r s r i - a s 0530-05
5lD#-#5 52D@-@5 I 5 1 W # 93i4-#1 82la-ao
1187-12 441 I - I2 DlDl-I2 O D 2 - I I
971a-ll 2432- I #
911@-1l 2432-10 4116- I # 0952- IO 88.6-11
918a-11 2432-10 4175-10 OS52-IO 8890- la Ilm4-aa 1380-#9 1415-09
9780- I I
4170- I # 0952-1# 11.6-10
1 4 3 2 - * e 911a-I1 1 4 3 2 - 1 0
9710-11 2432- 10 4115.10 0951-10 8890-10 l184-## 1385-#9 1415-09 l521-#9 I54 1 - 09 1545-09 1545-09 t545-#9 1545-a9
918#-Il 2432- IO 4110-1# 0852-I@
. 4 1145 a4303 . O D 1 2 1 l3aBa
l l B 1 - I I 4431- I 1
4248- 1 I la5l-la 2a18-la 3#3l-I# 3888-l# 0254-l#
0015- I @ o m - i a
I1453 mI8a 348W 4am3 5230# elal l 7054a 81200
I . a412a 1 . 5l#D#
i s i i - a i I54 1-00 I54S-@D 1545-a8 1545-09 l545-0#
15ii-ii 1541-0 1545-09 154s-ae 1545-#9 1145-as
l521-#9 I541 -09 1545-0s
l54l-@9 l545-#9 l545-#9 1545-OD 1545-09
2 8 2 1 - 1 3 1#24-l3 1314-12 19DD-12 2121-12 3333-12 3185-12 4aa8- I2 4W4-I2 4104-12
4 1 IO- I3 1112-12 2202-l2 3315- I2 4208-12 0531-12 0292-II 0034- I2 0153-12 0183- I2 ElOD- I2 0189-l2 0189- I2
5510- 13 1385-12 ¶ 1 0 1 - l ¶ 3914-12
584D- I3 1453- I2 214@-l2 4 l # 4 - I2
5915-13 2117- 12 4150-12 5201- 12 OD@*- 12 1DIl-I2 8224- I2 8301-12 D390- I2 8 4 # 2 - I2 84#2- I2 8 4 @ 2 - I2
i 4 i a - n 5DZO-I3 1412- I2 2171- I2 4150-11 5251. I2 08#0- I2 lOlO.12 8224- I2 8301 I2 8390- I2 8 4 * 2 . I2 04m2- I2 1402- I2
5925-0 1412- I2 2 8 1 1 - 12 4158-12 5207- 12 0905-12 7119-12
8301-12 8395- I2 8402-12 8402- 12 8 4 0 2 - 12
8214- 12
5925- 13 1412- I 1 2811- 12 4150-12 5201- 12 0900- I2 7819-12 8 2 2 4 - 1 1 8301. I2 8390- I2
5925- I 3 1411.12 2877- I2 4150-12 5201- I2 0900-l1 1819.12 8224- 1 1 e301 - 12 8390-12 8402- 1 1 8 4 0 2 - 12
I IDl- I3 2D14- I3 5121 - 13 D42D- I3 l a l l - 12 1414-12 IO1 I - I2 ll@2-l2 1135- I2 1744- I2 1145- I2 1145-12
. @ 1745
. #Dl21 13a9a ,11453 .1019a .341#1 ,43033
. 0 I #Dl
.1854#
.81200
e4303
.5230e
ini-ii 0519-10 1393-12 771i- ti 1118-12
8132- I2 1 2 1 # - 1 Y ._
1951-12 7157- 12 1951- I2 1951- 12
.- 8304- I2 8310-12 8 3 1 0 - 1 1 8310-12
4 l#D- t i 4101-12
8401-12 84e2- I2 8402- I2
- 56 -
WAPD-TM- 1623
TABLE 14 (Cont 'd) -
L l / A 0 1 I0 15 50 75 I 00 2 50 5 0 0 7 50 10 00 20 00 30 00 40 00 50 0 0 0 I W P I 35 00 35 00 35 00 35 00 35 00 I5 00 35 0 0 35 0 0 35 00 35 00 35 00 35 0 0 35 0 0 35 00 1 I1101
01745 5 4 1 2 - 1 1 5410-11 1152-17 1871-17 1127-17 11W-17 2187-17 1117-17 2217 I7 2217 17 2217-17 2207-17 2287-17 2117 17 04303 1301-11 1341-17 3102-17 4100-17 5517-17 5Od7-I7 5007 17 5007-11 5007-17 5007 17 5007-17 5007-17 5007-17 5007 17 (a711 2031-11 2000-17 0015-11 1418-17 1008-10 10 l Ib - IO 1087-10 1081 IO 1017-10 087 10 1087-10 I017 IO 1017-10 1017 IO 13000 3707-11 3710-17 8580-11 1353-10 1522-10 1598-10 1503-10 1¶03-10 1503-10 1503-10 1503-10 1503-10 1503-10 1503-10 17453 4011-11 4017-17 1070-10 1000-10 1884-10 11:11~10 1144-10 1044-10 1844-10 I144 IO 1144-10 1844-10 1144-10 1144-10 20110 5130-10 0841-17 1351-10 1124-10 1313-10 1430-10 2444-10 2444-10 1444-10 1444-10 1444-10 1444-10 1444-10 2444-10 34107 0500-11 0405-11 1471-10 1310-10 2000-10 ZoFb-IO 2004-10 2004-10 1004-10 1004 10 1004-10 1004-10 2004-10 1004-10 43033 0010-88 0511-11 1 0 1 1 - I O 2314-10 1070-10 2727-10 2735-10 2730-10 2135-10 1735-10 2735-10 1735-10 1735-10 2735-10 51300 0141-11 W35-I7 1531-10 1381-10 2085-10 1743-10 1751-10 2751-10 2751-10 2751-10 2701-10 2701-10 2751-10 2751-10 01017 0741-11 0041-11 1031-10 a401-IO 2017-10 2 7 U l - I O 2753-10 2753-10 2753-10 2753-10 2713-10 2103-10 2753-10 2753-10 78540 0740-11 0 0 4 1 - 1 1 1832-IO 1401-10 1018-10 2705-10 2753-10 2713-10 2753-10 1753-10 1703-10 1753-10 2753-10 2753 10 17200 0740-18 0041-17 1532-10 2401-10 2088-10 27W-IO 2753-10 1713-10 2753-10 2753-10 2753-10 1153-10 1713-10 2753-10
1 04720 0741-11 0042-11 1032-10 2401-10 2080-10 2705-10 2753-10 1753-10 2753-10 2753-10 1753-10 1753-10 2753-10 2753-10 1 57080 0741-18 0042-17 1532-10 2401-10 2000-18 27t5-10 2753 IO '2753-10 1753-10 2753-10 2753-10 2753 10 2753-10 2753-10
L P / A 0 1 10 25 50 75 I 00 1 50 5 00 7 50 10 00 10 00 30 00 40 0 0 50 00 1 I W C ) - 50 00 50 00 50 00 I0 00 1 0 b b 50 0 4 50 00 0 0 00 50 00 50 0b 50 00 50 00 50 40 5 4 00 6 (Rano)
01745 1171-15 1043-1b 3083-14 1434-¶4 S831-¶4 5877 I4 511b ¶4 5110 1 4 5 1 1 * - ¶ 4 518b 1 4 #18.-¶b 5110-14 5110-¶b S1am-14 04303 4i4i-ii 4is. i -54 i i i e - 5 4 iaii-zj ii5i-i3 i i c o - i a i isi- ir i i s i - z a iiii-is iiii ii iiii-ii i i i i - ir tiii-ii iiii-ij 01727 7127-25 7700-24 1143-13 1503-13 2748-23 2770-23 2772.23 2772-13 1772.23 2771-23 2172 23 1772-13 1772-13 2772.13 13010 1148-14 1414-13 Sa)¶-23 3117-13 3835-¶3 3114.13 31#6-¶3 3100-13 3116-¶3 3100-13 3100-¶3 3100-13 3161-13 3811-¶1
10180 34107 43033
1015-14 1701-24 1710-24 1713-24 1721-14 q719-¶4
1510-13 1004-13 1011-23 1014-23 1084-13
. - . 1OU-13 1722-14 1084-13
3543-23 3130-23 3101-23 3774-23 3774-23 3174-13 3774-13
5455-13 0500-23 1510-13 5510-23 5510-23 5510-13
5115-¶3 S I 8 1 - 13 5180-23 5111-13 S8BI - I3
5501-23 5170-23 5833-23 5140-23 5840-23 5s4*-23
5585-13 5178-13 5130-23 1141-23 1843-23 5843.13
5070-13
0842-13 5143-23 Sa43 - 13 1.43-1)
ssn-za
L2 /A 0 I Y F P l
I I A O I 01745 04363 01717 13000 17453 10110 34107 43033 51300 eiea7 7a540
1 570a0
17200 1 04720
0 1 0 0 . 0 0
70 17-30 1175 18 3550. 28 4804-10 5170-18
7123-28 7120-18 7120-21 7120-21 7120-28 7110-18 7120-29
ea35 - 11 i 0 a s - 2 8
10 0 0 . 0 0
7417. ¶1 18% i i 3407-11 4700-21 5722-21 0001-21 O s 0 b - m er41-ii 0 1 4 4 - 2 1 0144- 11 0 8 4 4 - 1 1 0144-21 0844-18 0944-2a
25 0 0 . 00
io3a-m 4 e a i - z a 104 1-28 1053-27 000-27 1405-17
1510-27 1517-27 1517-27 1527-17 1527-37 1527-27 1517-27
1591- 17
I 0 0 0 00
2313-21 5003 ~ 11 1071-27 1415-17 1775-17 2000-27 1 1 3 2 - 2 1 1143-27 2144-17 1144-27 1144-21
2144-27 1144-47
2144-a7
1 00 1 0 0 0
lb40-m 6005-28 113?-17 IW'5-17 t i e l - i7 2 1011- 27 2141-27 215.1 -27 2251-17 ¶¶5'1. ¶7 _._. -. 225!1-27 2 25!1. 27 221!1-17 125!1-17
2255-17 2255 17 2155-27 2255- 2 1 ¶lS5-¶7 .... - 2255-27
5 00 0 0 . 0 0
2440-2a 8eeo-m
~ 0 - 2 7
1137-27 1505 27
1101 17 1244-27 1255 ~ 17 1255-17 1255-17 1251- 27 1255-27 1251-27 1255 - 17
1137-27 I505 1 7
2108-17
1251-21 2255-17 2251-27 2 255 - 27 2155-27 2255-27 1255-27
1170 27
2244.27
10 00 1 0 00
2440-11 0000.20 I 137 - 27 150¶-21 070-27 2 101- 27 2244-17 2255 17 2255-17 2255-27 2155-17 1255~17 2255- 17 1255 ~ 17
2 0 . 0 0 0 0 . 0 0
2440-21 0000-28 1137-17 1505-21 1870 -27 2 I01 - 27 ¶¶4b-17 iZ55-ii 1255 - 27 2255-27 12S5-27 2255-17 ¶¶55-17
30 00 0 0 00
1440-2a
ia7v-n
2244-27
60.0 2 1 1137-27 1505 27
2101-01
2155-27 2115.27 2255 17 1155-17 1255-27 2255-27 2255-17
40 0 0 0 0 0 0
0 0 4 0 - ? 0 1137-27 l¶05-17
2108-27 2144-27 2255-21 1255-27 2255-17 2255-27 1255-27 1255-27 2255-17
2440-2a
1170.27
50 00 60 0 0
2440 21 6006 21 1137-27 156S.17
1109-27 1 1 1 4 . 2 1
1a7e 27
- 57 -
WAPD-TM-1623
TABLE 15
The Function E, (b)
oiooo 2959t01 04000 2881+01 05000 2481+01 00000 2295+01 07000 2151+01 08000 2117411 .__ . 10000 1823101 20000 t223+0t 3 0 0 0 0 9057t00 40000 7024600 50000 5598r00 80000 4544+00 80000 3lOO+00
I 00000 2194*00 1 zsaoo 1 4 6 4 ~ 1 50000 1000+0* 1 75000 0949-01 1 90000 5820-01 2 0 0 0 0 1 4890-01 i s a w 0 ~ i s i - @ i ? 00000 1305-01 3 50000 6970-02 4 00000 3779-02 5 00000 ( ( 4 8 - 0 2 8 0 0 0 0 0 3801-03 8 0 0 0 0 0 3787-04
10 00000 4157-05 12 SO000 1773-08 15 00000 t918-07 4 7 5anno 13131-01 . . - - - - . 20 0 0 0 0 0 9014-10 25 .00000 5348-12 30 00000 3021-14 35 00000 1753-tS 46 00000 1037-18 45 00000 0225-21 S0 00000 3703-23 55 00000 232t -25 8 0 00000 14J8-21 135 aoooa 8941-30 7 ~ . 0 0 0 0 0 3515-34
t 0 0 . 0 0 0 0 0 3884-45 150.00000 4152-07 200.00000 8815-19
TABLE 17
The Function E,(b)
0lYfPl 0 1 0 0 0 02000 .OJ00@ .0401# 05000 06000
. e 7 0 0 0
. 08000
. 10000
.20000 30100 40000 sa000 80000 80000
1 00000 1 15000 1 .5000# 1 75000 1 90000 i oooma - . . . . . . 2 . 1 0 0 0 0 3 00000 3 50000 4 00000 ..... s.00000 8 . 00000 8 . 00000
IO. 00000 t 2 . 5 0 0 0 0 15 00000
35 00000 40 00000 45 00000 50 00000 55 000ae 80 00000 0s 00000 75 00000
I 0 0 00000 1st 00000 200 00000
L 2 l I l 9497b00 @ t J 1 + 1 0 8817+@0 8535+00 8 2 7 8 + @ 1 8 0 4 0 r 0 0 7818.00 7810+00 1 2 2 5 + 0 0 5742r00 4891+00 3894.00 J206+00 2782r00 200**00 1485r00 1035r00 7310-01 52 11-0 1
3753-01 1980-01 1884-0 1 s102-e2 3190-01 9985-03 3183-03 3414-04
4271-01
ia35-05 2508-00 1818-07 12S8-01 9433-10 5172-12
TABLE 16
The Smoothed Function
E,(b) = be E,(b) b -
B l Y F P l 01000
.02000
. 0 3 0 0 0
.04000
.05000 08000 0 1 0 0 0 08000
. 10000 1 0 0 0 0 3 0 0 0 0 40000 50000 80000 80000
1 0 0 0 0 0 1 25000 t 50000 1 75000 1 90000 2 00000 2 .50000 3 00000 3 5 0 0 0 0 4 00000 5 00000 8 0 0 0 0 0 8 . 0 0 0 0 0
10 00000 1 2 . 5 0 0 0 0 t 5 . 0 0 0 0 0 17 SO000 20 i i i o o 2 5 . 0 0 0 0 0 30 00000
35 0 0 0 0 0 40 00000 4 5 00000 so. 0 0 0 0 0 55. 0 0 0 0 0 I30 0 0 1 0 0 - . . . . . 8 5 . 0 0 0 0 0
t 0 0 . 0 0 0 0 0 75.00000
150. 00000 100.00~00
0 . LXP t 0 I * E I I 8 I 04075 08845 09148 1 1 I83 (2972 14823 18148 17588 20 t 4 8 29887 38878 4 0 1 3
98904 98899 99018 9934 1 99505
TABLE 18
The Smoothed Function - E,(b) = bebE,(b)
BtYfP) 01000 02000 0 3 0 0 0 04000 05000 08000 07000 08000 10000 2 0 0 0 t 30000 4 0 0 0 0 50000 8.000 80100
1 00100 1 25001 t 50000 1 75000 1 so000 2. 00000 2 . 50@0@ 3. 00000 3 50000 4 00000 5 00000 8 00000 0 00000
10 0.000 1 1 so001 t 3 . i o o o o 17 50000 2 0 . 0 0 0 0 0 2s eoooe 30.00000 3 5 . 0 0 0 0 0 40 00000 4 5 . 0 0 0 0 0 50 00000 s5 .00000 ii. 00001 85 . 0000I 75. 00000
100.00000 1 s 0 . 8 0 0 0 0 200.00000
B.tXPtII.E2IBI 00959 0 1883 02728 03553 04351 05123 05870 08595 07985 14027 18997 23131 28927 30194 35780 40385 45151 49142 52537 54345 55489 00297 8 4 0 4 87247 89847 73944 77038 0 1 4 1 1 84481 87143 89038 90444 91531 93102 94182 94989 95509 98041 98422 98738 97000 97214 97585 98177 90777 99080
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WAPD-TM-1623
VII. References
1. 0. J. Wallace, "Analytic Flux Formulas and Tables of Shielding Functions," WAPD-TM-1453, June 1981.
2. K. Shure and 0. J. Wallace, "Comriact Tables of Functions for Use in Shielding Calculations,," Nuclear Science and Engineering, 56, pp. 84-89 (1975).
3. 0. J. Wallace, "Semi-Analytic Flux Formulas for Shielding Calcula- tions, 'I WAPD-TM-1197, May 1976.
4. H. Ono and A. Tsuro, "An Approximate Calculation Method of Flux for Spherical and Cylindrical Sources With a Slab Shield," J. Nuc. Sci. and Tech., 2, X6, pp. 229-235 (June 1965).
5. 0. J. Wallace, "SPAR1 - A Semi-Analytic Point-Kernel Computer Program for Shielding," WAPD-TM-1196, June 1976.
6. D. Van Nostand, "Reactor Shieldin'g Design Manual," T. Rockwell, Ed., Princeton, NJ (1956).
tU .S . GOVERNMENT PRINTING OFFICE 1993-709-001-41005
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