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SS2Kauer* Charles/Approximate Drocedur QC100 -U56 NO. 87-3507 1987 V19

P

C.1 NBSS-P Approximate Procedures for

Calculating Protection From Initial

Nuclear Radiation From Weapons

C. M. Eisenhauer and L. V. Spencer

U.5. DEPARTMENT OF COMMERCE

National Bureau of Standards

Center for Radiation Research

Gaithersburg, MD 20899

February 1987

QC

100

- U 5 6

87-3507

1987

j for:

I Emergency Management Agency

igton, DC 20472

c-2

NBSIR 87-3507

RESEARCH

INFORMATION CENTER

QjytOO

APPROXIMATE PROCEDURES FOR

CALCULATING PROTECTION FROM INITIAL

NUCLEAR RADIATION FROM WEAPONS

C. M. Eisenhauer and L. V. Spencer

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

Center for Radiation Research

Gaithersburg, MD 20899

February 1987

Prepared for: Federal Emergency Management Agency

Washington, DC 20472

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

CONTENTS

Page

I. Introduction 1

II. Source Distribution 2

III. Approach to Shielding Calculations . 3

A. General Approach 3

B. Mutual Shielding Factor 5

C. Barrier Factor 6

D. Geometry Factor 8

E. Attenuation Factor 13

F. Overall Proctection Factors 14

IV. Discussion of INR Computer Codes 15

A. Limitations of Codes 15

B. Description of Subroutines 17

C. Listings of Computer Codes ..... 27

V. Comparison with Monte Carlo Calculations 28

A. Monte Carlo Calculations on Benchmark Structures . 28

B. Combined Components 29

C. AS and FP Secondary Gamma Rays 29

D. Neutrons and Secondary Gamma Rays 32

VI. Conclusions ..... 35

References 36

Tables 37

List of Figures 55

Appendix A. Sources of Data for INR Computer Codes 79

B. Treatment of Mutual Shielding for Neutrons ... 80

C. FORTRAN Listing of Computer Codes .... 82

D. Sample Input Data 118

E. Sample Output Data 121

i i
1
Abstract

In this report we discuss procedures for routine evaluation of the

protection of complex structures against the initial radiations from nuclear

detonations. We describe procedures for evaluating and combining dose

reduction factors for four radiation components: early fission product gamma

rays, air secondary gamma rays generated by neutron interactions in the air,

neutrons, and wall capture gamma rays generated by neutrons through

interactions with nuclei in structural materials. We describe computer codes

developed to evaluate reduction factors for each of these components. The

radiation field in the vicinity of the structure was generated for a 30°

elevation angle for the detonation, as well as a "ring source" averaging over

the points of the compass. Comparisons are made with Monte Carlo calculations

for a series of five benchmark structures.

i i i

I. INTRODUCTION

The purpose of developing approximate shielding procedures is to allow

calculation of shielding in many structures with a simple method that can

be programmed for fast operation on a personal or mainframe computer. In this

paper, we report on approximate procedures developed at NBS to calculate

protection afforded by structures against initial gamma and neutron

radiation. 1 These procedures are modeled on earlier procedures [ 1 , 2] 2 for

estimating protection from fallout radiation, which have proven very useful in

evaluating the fallout shelter potential in the United States.

Calculation of shielding for initial radiation is more complicated than

for fallout radiation because four components, namely, fission product gamma

rays (FP), secondary gamma rays generated in air (AS), prompt neutrons (N),

and gamma rays from neutrons captured in the structure (NG) must be

considered. Under special circumstances other radiation such as prompt gammas

or delayed neutrons may also be of interest. Much of the data base for

procedures discussed here is given in an earlier paper by Spencer [3]; and the

procedures have followed the pattern developed in that paper.

The role of neutrons is more complicated than that of gamma rays for at

least three reasons: 1) neutron reflection from wall surfaces is a dominant,

rather than perturbation effect; 2) neutrons give rise to capture gamma rays

(NG) in the structure, and these are more penetrating than the neutrons

themselves; and 3) the neutron source intensity relative to that of the

initial gamma rays is a function of weapon design. Due to the importance of

neutron reflections, additional procedures have been developed which are based

1 Initial radiation is that which is emitted during the first minute after a detonation.

2 Figures in brackets indicate literature references at the end of this paper.

1
on the accumulated data and experience for enclosures and ducts. To take the

secondary gamma rays produced in the structure into account, additional data

for this component have been generated, on the general pattern of reference

[3]. For relative source intensities we have utilized available data,

beginning with that available in an important report by Auxier et al . [4].

Published and unpublished sources of shielding data used in INR computer codes

are given in Appendix A.

II. SOURCE DISTRIBUTION

In order to compare various techniques for calculating shielding in

structures, it is helpful to establish standard angul ar-energy distributions

in the vicinity of the structure, for the different types of radiation. We

have chosen AS and N distributions from a study [4] requested by the Radiation

Shielding Subcommittee of the Advisory Committee on Civil Defense, National

Academy of Science. These are presented together with the FP angle-energy

distributions [4,5] in Tables I - 1 1 1 . The polar angle in these tables is

defined relative to the direction vector from source to detector.

We have also followed the recommendations of the same study to assume a

ring source of bursts at a fixed angle of elevation. The rationale for

choosing a ring source is that the direction of burst cannot be predicted

beforehand — particularly if the building is likely to be exposed to more than

one weapon. Therefore, a protection factor for a building is averaged over

horizontal directions. The use of a ring source allows the averaging to be

done before the protection factor is calculated. For buildings whose

construction is similar on all sides, the protection is not likely to vary

significantly from this average. An angle of elevation of 30° was chosen as

typical of low air bursts. In order to calculate the protection factor in a

2
building, we start with the radiation dose in air. There is still some

question as to whether the presence of the ground is important enough to be

included in calculating this dose. Although the effect of the ground may be

important in estimating the absolute dose, its impact on the protection

factor, which is a ratio of doses, is small enough to ignore. The calculations reported here assume that the detector with reference to which the

protection factor is estimated is located in a free air medium with no groundair interface present.

In the calculations of reference [3], the asymmetry of the fission

product source about the detonation point, due to cloud rise, was ignored.

This aspect of those calculations has been criticized [6]; and there is

general agreement that for barrier factors, at least, more precise calculations are required. These have been performed, and are routinely included

bel ow.

III. APPROACH TO SHIELDING CALCULATIONS

A. General Approach

The protection in a building against initial radiation is estimated in

terms of a reduction factor IRF, which is defined as the ratio of the dose D

from initial radiation at a point in the structure to the dose D

Q from initial

radiation at the reference point in free air. If the fraction of the free-air

dose contributed by FP and AS gamma rays and by neutrons is denoted by f

pp

, f^s and f^, respectively, then the reduction factor is calculated from

IRF

D

0 R FP

f

FP

+ R ASf

AS

+ ( R

N + f N

( 1 )

3
where R pp

and are reduction factors for the FP and AS components of the

gamma radiation, and R^ and R^ are reduction factors for the neutrons and the

secondary gammas generated in the structure.

We now consider approximate procedures for estimating the component

reduction factors Rp

p

, R^, R^ and R^. Since the approach is the same for

all components, we drop the subscript in the following discussion.

The general approach which we have taken in developing shielding procedures can be described as follows. We start with the free field dose for each

of the radiation components. We tnen consider the dose at a position on the

exterior surface of the roof or one of the walls of a building. The ratio of

this dose to the free field dose we call the mutual shielding factor, M.

Next, we consider the dose at a point on the interior surface of the roof or

wall, immediately opposite the point on the exterior surface. We call the

ratio of these two doses a barrier factor, 8(X). Next we consider the dose at

some arbitrary point inside the building, with no internal structure. The

ratio of the dose at this point to that on the interior surface of the wall or

roof is called the geometry factor, G, for that wall or roof. Finally, we

consider the dose with any internal partitions or floors in place and call the

ratio of this dose to that in the empty structure the attenuation factor, A.

The reduction factor for each component, i.e., the ratio of the dose at an

arbitrary point in the structure to the free field dose, is then calculated

from the product

R = M . B(X

e

) • G(X

e

,«) • A(X.) ( 2 )

where X is the thickness of an exterior wall or roof and X- is the thickness

e t of an internal barrier. A(X-) may be the attenuation due to the combined

4
effect of several floors and walls for any radiation component. The reduction

factor at a point in the structure for any radiation component is obtained by

summing the expression of eq (2) over the roof and exterior wall surfaces. In

programming calculations in the INR codes some modifications of this simple

product of four factors wera necessary. These modifications will be explained

in section IV.B.

B. Mutual Shielding Factor, M

This factor evaluates the effect of moving the detector from a free-air

situation to an exterior surface of the building. It may include reductions

in exposure due to the presence of nearby buildings. In the simple case of an

isolated building, it is approximated for gamma rays by the integral of the

free-air distribution over the hemisphere from which radiation is incident

divided by the integral over all directions. For a roof, the partial integral

is taken over the upper hemisphere; for a ring source incident on a wall, the

integral is exactly one-half. The roof factor 0.85 has been used for both FP

and AS gamma ray components [3].

The case of neutrons is treated somewhat differently, although it appears

formally the same. Because the contribution from neutrons is not as highly

concentrated along the line of sight between source and detector as is that

from high energy gamma rays, our approach is that of reducing the overall

source strength entering roof or side in accordance with the solid angle

subtended by nearby shielding. This means the introduction of a cosine factor

into the relevant integrals. Calculated in this way, the dose current

entering one side of a building turns out to be 0.47 that of the dosp current

entering the roof.

In more complicated cases where neighboring buildings restrict the angles

from which radiation can reach the detector point, the concept of cut-off

angle is introduced. The source angular distribution for ai r-secondary gamma

5
radiation is peaked in the downward direction at an angle of 30° from the

horizontal. For fission product gamma radiation the distribution is still

peaked but somewhat more diffuse due to averaging over the cloud-rise time.

Furthermore, the I NR gamma-ray source energies are higher than for fallout, so

that INR gamma radiation tends to preserve its original direction. The effect

of this phenomenon is that the photon detector responds as if the walls of the

building were being x rayed with the source radiation. Therefore, we assume

that cut-off angles for the mutual shielding factor can be determined by a

line between the detector point and an important change in a neighboring

building (e.g., the roof line of the neighboring building). For neutrons the

above arguments are not valid. Instead, neutron transport is less sensitive

to the original direction of motion of the neutron. The effect of a

neighboring building is evaluated in terms of the cut-off angle measured from

that building to a point on the exterior surface of the building in which the

detector is located rather than to the detector location, itself. Whenever

there is a cut-off angle introduced by the presence of nearby building, the

factor M in eq (2) is replaced by a difference of mutual shielding geometry

factors which are functions of exterior cut-off angles. The use of figure 17

to determine these factors will be described under the Geometry Factor

section.

C. Barrier Factor, B( X )

This factor is the ratio of dose at the inner surface of an exterior wall

or roof to that at the outer surface of the same barrier. In order to

generate the angular distribution of radiation from a ring source incident on

a barrier, the distributions in tables I - I I I which are a function of the polar

angle 3 (see fig. 1) were averaged over directions of the compass <j>, rotated

6
to a system in which the new polar angle 0 or x is relative to a line perpendicular to the barrier surface, and then weighted by the cosine of the new

polar angle to obtain the current incident on the barrier surface.

Approximate barrier factors for initial gamma radiation were obtained by

one-dimensional transport calculations for the rotated roof and wall sources

in an infinite medium of concrete. In these calculations concrete is substituted for the air that is exterior to the barrier. This introduces an error

of order 10% in the dose, but less in the reduction factor, which is a ratio.

The error introduced by the substitution of a concrete backing for the

interior of the structure, that is, behind the detector, is expected to be

still smaller because gamma rays are reflected from other structural

materi al s.

The barrier factors calculated for initial gamma radiation are shown in

figure 2. As expected, the AS gamma rays are generally more penetrating than

the FP gamma rays because they include higher energy photons. Furthermore,

the two AS curves are rather similar. The two curves for FP gammas would

also be similar due largely to the choice of a 30° angle of elevation for the

gamma ray sources. But cloud rise has the consequence of depressing the wall

curve and raising significantly the roof curve, thus making the latter much

less steep. The data from which these curves were derived were obtained using

a gamma ray adjoint moments program written by G. L. Simmons [7], and a

distribution construction program written by L. V. Spencer [8],

Barrier factors for neutrons and for the capture gamma rays which they

produce in the structure are shown in figure 3. These data correspond to

Snyder-Neufel d [9] dose weighting factors for the neutrons, and Henderson [9]

weighting factors for the gamma rays. These were generated by ANISN calculations for the roof, and DOT calculations for the walls [9]. They are based on

7
calculations for slabs and therefore do not include any neutrons reflected

from behind the detector. The contribution from reflected neutrons is evaluated by a reflection factor added to the geometry factors (see section D.2).

D. Geometry Factor, G(X .w)

1. Unreflected component . The geometry factor is the ratio of the

exposure at an arbitrary distance from the inner surface of an exterior wall

or roof to the exposure at the surface. A cumulative integral over the

angular distribution of radiation emergi ng from the surface is required to

estimate this factor. Calculations used to approximate this integral for

gamma rays, however, give the cumulative angular distribution over the

incident radiation. The two integrals are equal only for the radiation not

scattered in the barrier. But, in view of the fact that unscattered and

smal 1 -angl e-scattered components dominate the dose for the source energies and

barrier thicknesses of interest, we believe that the calculated integrals

represent an adequate approximation for this application. For neutrons,

integrals were taken over angular distributions of emerging neutrons.

A polar reference axis for specifying the cumulative angular distribution

of the incident radiation must be selected. For a ring source incident on a

horizontal roof, the vertical direction is the obvious choice. Cumulative

angular distributions are expressed in terms of the solid angle fraction

subtended by the roof. Figure 4 shows these geometry factors for the air

secondary gammas. In this figure and in some of the following figures, as

well as elsewhere in the text, thickness of barriers are given in units of

pounds per square foot (psf) of concrete. The sharp rise in the curves for

thin barriers shows the effect of the concentration of photons at 30° angle of

elevation. The higher values of the curves for thick barriers and small solid

angle fractions indicate the increased importance of radiation traveling more

nearly perpendi cul ar to the roof slab. Similar curves for FP gamma radiation

8
are shown in figure 5, and for neutrons and neutron-capture gamma rays (in the

structure) in figures 6 and 7, respectively. The single curve for neutrons is

a good approximation for all thicknesses.

For radiation incident on a vertical wall, the choice of a reference

direction is not so obvious. Figure 1 shows two possible directions: the

vertical direction, normal to the roof, and the horizontal direction, normal

to the wall slab. Since cumulative integrals over polar angles are correct

only for circular source areas and cylindrical symmetry, one tries to choose

the direction which most closely approximates this. We feel that most large

buildings with story-heights small compared to wall-lengths can be better

approximated by a cylindrical wall with a vertical reference axis rather than

a series of four circular walls, each with a horizontal reference axis. The

symmetry of the ring source about the vertical direction provides an additional reason for choosing a vertical axis as the reference direction.

Geometry factors for walls are approximated by the product of two

functions. The first function G^Xe.u), given in figures 8-11 is an integral

over the region of polar angles subtended by the walls of the structure. The

second function, G

2

( Xe

,

4

> Q

) , varies with the limits on the azimuthal angle <j> 0 (see figs. 13-16) for each wall. The sum of values of this function for each

of the walls of a structure is therefore dependent on the shape of the

bui 1 di ng

.

Geometry factors G^Xe,^ are plotted as a function of the solid angle

fraction tu subtended by the ceiling (or floor) rather than that subtended by

the walls. Therefore, for increasing values of w the geometry factors in

figures 8-11 decrease. Note that the horizontal scales in figures 8-11 are

semi -log scales in the quantity (1 - w) . The curves for AS gammas show a

steep slope near w = 0.5, due to the concentration of photons at the 30°

9
angle of elevation. The corresponding curves for FP gammas are shown in

figure 9, and for neutrons and capture gammas (in the structure) in figures 10

and 11, respectively. Note again that figure 10 does not include reflected

neutrons.

When the detector is on the same story as the radiating walls, a geometry

factor for radiation from portions of the walls above the detector plane must

be added to a geometry factor for portions of the wall below the detector

plane (see fig. 12a). When the detector is on the story below, geometry

factors must be estimated for the solid angle fractions subtended by the

ceiling of the higher story, and the floor of the higher story, and the two

subtracted (see fig. 12b). A similar subtraction is required when the

detector is on the story above the radiating walls.

Geometry factors G

2 (Xe,oj) for AS gamma rays and for a single wall are

plotted as a function of s i

4

> 0 in figure 13. The curve for zero thickness in

figure 13 is proportional to the angle <j> 0

. The line for 36 pounds per square

foot (psf) of concrete is nearly proportional to sin<f>

0 and is therefore

equivalent to the prediction for thick walls in the fallout methodology. 3 The

higher geometry factors for thickness greater than 36 psf show the effect of

increased peaking in the angular distribution, relative to the direction

perpendicular to the wall surface. The curves for FP gammas (fig. 14) are

almost a duplicate of this set. Corresponding curves for unreflected neutrons

and wall capture gammas are presented in figures 15 and 16. The single curve

that approximates the function G 9 for neutrons for all wall thicknesses is

proportional to the azimuthal angle subtended by the wall.

3 In the methodology for calculating fallout protection this information is not

available and it is arbitrarily assumed that for thin walls the geometry

factor is proportional to <j> 0 and for thick walls it is proportional to si n <j> Q

, where

Q is the azimuthal angle between a line perpendicular to the wall and

a line arawn to one end of the wall. This implies that at the center of a rectangular building with thick walls, the relative contributions of the long

and short walls is equal to the ratio of their lengths.

10
The expression of the geometric effect as a product of a polar and an

azimuthal factor was made possible by a remarkably good approximation of

separability evidenced by the data. The assumption of separability was made

in the fallout methodology only because of the lack of data on the azimuthal

dependence. It was later supported by Monte Carlo calculations [10]. Current

evidence, still somewhat limited, also points to this approximation as

justifiable in the cases of unreflected neutrons and wall-capture gammas.

When the incident gamma radiation field is limited by the geometry of

both the building in which the detector is located and an exterior structure,

the product M • G(X ,a>) in eq (2) is replaced by a difference of geometry

factors. For example, figure 12 shows a detector position for which the

incident field of radiation through the first story wall is limited by the

solid angle fraction defined by the first floor of the ceiling of the first

story and the solid angle fraction a/' defined by the presence of an exterior

structure. The combined interior and exterior geometry effects in this case

are approximated by the expression

This procedure is not applicable to neutrons and wall -capture gammas, however.

For these radiations one simply applies a factor M obtained from figure 17,

which records the part of the upper hemisphere not blocked off, in terms of an

upper hemisphere free-field geometry factor for neutrons. This factor is

applied equally to upper and lower hemisphere reduction factors.

2. Reflected component . The contribution from gamma rays reflected from

structural material behind the detector is of the order of 10% and is

neglected in these calculations. However, the contribution from reflected

neutrons is of the same order as that from unreflected neutrons and must be

taken into account.

(3)

11
For many enclosures an adequate rule for this is simply to calculate the

unreflected neutron reduction factor, including all contributing walls and

roof, and multiply by a (total /unrefl ected) factor (1 + p Q

) which we take here

to be 3. This assigns to the reflected neutrons twice the dose contributed by

the unreflected components, a value obtained by several rather different

calculations using Snyder-Neufel d dose weights. Problems arise when an

important wall surface subtends a rather small solid angle fraction, as shown

by a) in the sketch in figure 18. The sidewalls and endwall then act as in a

closed duct, to contribute a dose attenuated by geometry and by one or more

albedo factors. We then multiply the unreflected component directly from

the given wall surface by a factor (1 + p + p g

). Here p and p g

, the contributions from sidewalls and endwall s, respectively, are evaluated for w and to ,

as presented on figure 18. We should note that this approach ignores variations in the length-to-widt+i ratio of a source wall; but calculations have

indicated that these reflection factors vary only weakly with this ratio.

In a building with many windows the reflected neutrons will not make such

a large contribution. To account for this effect we have made the reflected

contribution dependent on the relative window area on the story in which the

detector is located. One then multiplies the reflected neutron components p

and p gby (1 - w) and (1 - w ), respectively, where w

&

is the fraction of

endwall solid angle subtended by windows, and w is the fraction of sidewall

solid angle subtended by windows, so that the detector does not receive

reflected neutrons from a window. The I NR codes assume a central detector

location. Furthermore, for wall sources, w is assumed to be zero, since the

floor and ceiling are two of the "side walls," and w

g

is approximated by FW,

the fraction of wall perimeter occupied by windows. For roof sources or

contributions from upper (or lower) stories, where the floor (or ceiling) is

12
the "end wall," w

g is assumed to be zero and w is approximated by FW.

However, in basements below grade, the full reflected contribution is assumed,

regardless of the window configuration on higher stories.

E. Attenuation Factor, A(X^)

This factor is a ratio of the exposure with interior structure in place

to the exposure in an empty building. In the INR calculations it often does

not appear as an explicit factor.

J For all types of roof radiation the

thicknesses of all horizontal barriers above the detector, including the roof,

are added to obtain a total thickness X

Q

. The product of the barrier factor

B(X ) and the attenuation factor A(X^) in eq (2) is replaced in the calculations by a table-lookup of the roof barrier factor B(

X

0

) . The variables of

the geometry factor are X

Q and uj, the solid angle fraction subtended by the

roof. Similarly, for all types of wall radiation, the thickness of all

vertical interior partitions is added to the exterior thickness to obtain a

total thickness Xy. A single table-lookup is then used to obtain a wall

barrier factor.

For gamma rays, the attenuation of radiation from walls of the next

higher story through a ceiling to a detector, say, in the basement, is evaluated by an attenuation factor A(

X

0

' )

.

Figures 19 and 20 give the attenuation

of AS gamma and FP gammas, respecti vely , from a ring source for different

incident polar angles e

Q

. Each curve contains information for the energy

spectrum at that angle. In order to apply these curves to a basement

detector, we could estimate the average angle to the upper story walls and

interpolate for the correspondi ng value of cosq

0 and the thickness of the

ceiling. However, these curves were approximated in the INR codes by the two

roof curves from figure 2. The adequacy of this approximation is discussed in

section V.C.

13
For neutrons and secondary gammas the attenuation is accounted for by

adding the thickness of the ceiling (or floor) barrier to the thickness of the

interior and exterior walls of the upper (or lower) story to obtain the argument for the wall barrier factor.

F. Overall Protection Factors

A much-used concept in fallout shielding studies is that of the

Protection Factor (PF). To apply this to initial radiations, one must choose

one or more standard mixtures of the different source components. The

difficulty of this is quickly seen in the variety exibited in figures 10-13 of

Auxier et al . [4]. Nevertheless some patterns do emerge which may provide

useful reference for this purpose.

Very high megaton (MT) detonations are apt to be based on energies

provided largely by the fission process; and shielding at greater distances

from the detonation becomes important. These aspects, together with the 1 MT

data of reference [4], figure 12, suggest using a high MT reference reduction

factor such as the following:

IRF

g

= 0.5 R fp + 0.2 R as

+ 0.3 ( R^

+ R

NG ) (4)

Where it is understood that R.. always includes the wail capture gamma-ray

component.

Similarly, low kiloton (kT) detonations can feature neutrons generated by

fusion reactions, with only a limited fission component. The neutrons

generate a substantial air secondary component, however. This is illustrated

in figure 10 of reference 41, and suggests a representative combination such

as the following, for low kT cases:

14
IRF (5)

n

- 0*6 (R^ + R^q) + ^.2

^AS

+ ^FP

The more general problem of mixed cases should not be ignored, and hence

we tentatively suggest even-balancing for an intermediate, or "other"

reduction factor representation:

IRF

0

( 6 )

This is consistent, more or less, with figures 11 and 13 of reference [4].

These three combinations, translated into reciprocals, can perhaps serve

to cover any possible requirements for "IPF's." Note that by choosing three

such representations , a full set of values can be used in combination, without

loss of information about the three radiation components.

IV. DISCUSSION OF INR COMPUTER CODES

A. Limitations of Codes

The present version of the INR codes (INRG6 for gamma rays and INRN6 for

neutrons) has several limitations, some of which may have to be modified in

the future.

15
1.

Codes calculate contribution from roof and from walls of the same story,

story above, and story below the detector location . Contributions from

walls of stories more than once-removed from the detector are assumed to

be negligible.

2. Codes calculate protection at a central location of each story . The

concepts used for the central detector can be extended to off-center

detectors, as is done in the PFCOMP code. The extension requires

significant increase in coding because four solid angles are required for

every solid angle calculated for the central detector. Unless more

experimental data or Monte Carlo calculations become available for

comparison, this refinement does not seem justified.

3. A limited number of configurations of interior partitions are included .

Interior partition configurations are limited to a rectangular central

core or a central corridor, extending the length of the building.

4. Each story of a building must be approximated by a square or rectangle .

5. Windows are assumed to have the same configuration on opposite sides of a

bui ldi ng .

6. Linear interpolation between tabulated points on linear or log scales is

used . The number of tabulated points for barrier and geometry factors

should be increased so that interpolation is more accurate.

7. The ceiling attenuation factor for AS and FP gamma rays is approximated

by the roof barrier factor . The ceiling attenuation factor for AS and FP

gamma rays should be made dependent on the average angle of incidence of

radiation rather than approximating it by the roof barrier factor.

8. The contribution from windows of the story above is overestimated . A

better calculation may require more input parameters.

16
B. Description of Subroutines

INTRPB Calculates barrier factors for four walls and overhead barriers by

interpolating on tabulated values

Input

XTAB(ll) tabulated values of barrier thickness

X( 5) array of barrier thicknesses for four walls and

overhead, in units of pounds per square foot (psf) of

concrete

BTAB(11,4) tabulated barrier factors for roof and walls for two

types of radiation

Output

B(5,2) barrier factors for air secondaries and fission product

gammas ( I NRG) or neutrons and capture gammas (INRN) for

four walls and overhead

Remark:

The number of tabulated values of barrier thickness is currently

assumed to be 6 in the neutron code and 11 in the gamma-ray code.

INTRPG Calculates geometry factors G

L and G2 for four walls, and geometry

factor G for overhead, by interpolating on tabulated values.

For roof geometry factors linear interpolation on 1 og G _vs. log <o is used. However, for side-wall G

1 geometry factors, linear interpolation on log G _vs. log ( l-o») is used. For side-wall G

2 geometry

factors, linear interpolation on log G vs.. log sin<j> is used.

Common

:

ZTAB(6) tabulated value of barrier thickness

YTAB(11,2) tabulated array of values of to and sin^

GTAB(6,11,6) tabulated array of geometry factors for walls and

overhead.

Input:

X( 9) array of barrier thicknesses with X(n + 5) = X(n), psf

Y(18,2) array of values of u> and sin<j> defining each surface

17
Output:

0(9,2) geometry factors for ai r-secondary and fission product

gammas (INRG) or neutrons and capture gammas (INRN)

with four values of G 1# one value of G, and four values

of G

2

.

Remark

The number of tabulated values of barrier thickness is currently

assumed to be 6 in both neutron and gamma codes.

» GEOM Calculates values of m and sin<j> for four walls from input linear

dimensi ons for story.

Input

HI height of portion of wall above detector plane, ft

XL length of story, ft

W width of story, ft

Output:

0M( 4) solid angle fraction subtended by equivalent circular

ceiling associated with each wall

SPH 1(4) value of s i n for each wall

SECTOR Calculates values of the array Y (see INTRPG) for the upper and lower

portions of a partial story (sector)

Input:

IL parameter indicating whether to neglect (IL = 0) or calculate ( IL = 1) values of Y for the lower portion of

the wal 1 . HU height of portion of wall above detector plane, ft

HUR height of roof above detector plane, ft

HL height of portion of wall below detector plane, ft

XL length of story, ft

W width of story, ft

18
Output

:

Y( 18,2) array containing values of u in the first column and

sinrjj in the second column. The first 9 entries are for

surfaces above the detector plane; the remainder are for surfaces below the detector plane.

Subroutines called:

GEOM

INPUTT Input routine data storage for tabulated barrier and geometry

factors

Input/Output:

IPR print index: (IPR > 0), print all tabulated barrier

and geometry factors

0MTA6 tabulated values of solid angle fractions

SPTAB tabulated values of s i

n

43

Common

:

XTAB tabulated values of barrier thickness

BTAB tabulated values of barrier factors

ZTAB barrier thicknesses for which geometry factors are tabul ated

GTAB tabulated values of geometry factors

0MRTAB( 17) tabulated values of solid angle fraction for duct data

(INRN.only)

RTAB( 17,2) tabulated values of duct attenuation (INRN,only)

0MSTAB( 17) tabulated values of solid angle fraction for mutual

shielding (INRN.only)

XMSTAB(17,2) tabulated values of mutual shielding (INRN.only)

19
* TEST Calls in input data for building parameters

Input

:

TITLE (20A4) Descriptive title for building

IW, ID, IPR, IMS, IP, HI, HS( >0) , HT, HD, HR, FW, HIU, HIL, XL, W

(515, 5F10.2/5F10.2)

Indices

IW Window index

IW = 0 No windows

IW = 1 Windows on all four sides

IW = 2 Windows on two long sides

ID Detector index

ID = 0 Sub basement

ID = 1 Basement below grade

ID = 2 Basement - partly above grade

ID = 3 First story of multistory building

ID = 4 Second or higher story

ID = 5 Second or higher story, but immediately below roof.

ID = 6 First story, immediately below roof.

IPR Print index

IPR = 0 Suppress printout of input tabulations and some geometry factors

IPR > 0 Print this information

•Je TEST is replaced by CETE1 (for neutrons and secondary gammas) and CETE2 (for

AS and FP gamma rays) in program written by R. Lyday for FEMA. His

subroutines CHARLI and CECARD are used to relate input data in the SANDINR

system to input parameters required by the INR codes.

Code will overestimate contribution in this case if detector is below grade.

For calculating geometry factor, code assumes grade level is at detector

level. If detector is above grade, code does not calculate contribution

from below detector plane and contribution will be slightly underestimated.

20
IMS Mutual shielding index

IMS = 0 Set mutual shielding equal to 0.5 for walls, 0.85

for roof gamma rays, and 0.58 for roof neutrons.

IMS > 0 Determine mutual shielding from heights of

neighboring buildings.

IP Index for configuration of interior partitions

IP = 0 No interior partitions

IP = 1 Four-sided core configuration of interior

partitions

IP = 2 Central corridor extending the length of the

bui 1 di ng

Linear dimensions (Relative to floor of this story, in units of ft)

HI Ceiling height

HS(>0) Sill height

HT Height of top of window

HD Detector height (Not actually used in INRG code, where test

is made on HL. Used for mutual shielding test in INRN

code

HR Roof height

FW Fraction of perimeter occupied by windows

HIU Height of story above

HIL Height of story below

XL Length of building

W Width of building

XLM(4F10.3) Length of first plane along each wall of building (not

used in INRG code)

WM(4F10.3) Width of first plane in direction perpendicular to each

wall of building

HM(4F10.3) Height of SECOND plane on each side of building

After reading in these data, codes call subroutine INPUTT to read

in tabulated shielding data. Codes then read in:

21
RFSTOR

Wall Thicknesses (psf)

XE ( 5E 10 . 3 ) Thickness of each exterior wall (L = 1,4) and of roof

plus intervening ceilings (L = 5)

XI ( 5E10 .3) Thickness of each interior wall (L = 1,4)

XUE( 5E10 - 3) Thickness of each exterior wall of story above

(L = 1,4)

XU I ( 5E10 . 3 ) Thickness of each interior wall of story above

(L = 1,4) and of ceiling (L = 5)

XXLE(510.3) Thickness of each exterior wall of story below

(L = 1,4)

XXLI ( 510.3) Thickness of each interior wall of story below

(L = 1,4) a-nd of floor (L = 5)

Calculates the reduction factor for the four walls and overhead of a story

Input: (Barrier thicknesses in psf, linear dimensions in ft)

IW index to indicate configuration of windows

HI story height

HIU height of story above

HIL height of story below

HS average height of window sills above floor

HT average height of top of windows above floor (HT>HS)

XL length of story

W width of story

X(9) array containing values of four wall thicknesses and

overhead thickness, with X ( n + 5) = X(n). Thickness

includes that of intervening interior partitions.

XU(9) array for thicknesses of four walls of story above and

total overhead thickness (XU(5)), with X(n + 5) = X(n)

XXL(9) array for thicknesses of four walls of story below, with

X(n + 5) = X(n)

FW fraction of the length of the wall that is occupied by

wi ndows

22
XMS( 5,2) mutual shielding factor (INRN only)

ID detector index, indicating basement, first story, etc.

IPR print index

IMS mutual shielding index (INRG only)

IP index for configuration of interior partitions

WM( 4) width of area at grade level perpendi cul ar to each wall

(INRG only)

HM( 4) height of building nearest to each wall (INRG only)

HD detector height (absolute or relative to floor of this

story; but definition must* be consistent with that of HR

and HM)

HR roof height (absolute or relative to floor of this

story; but definition must be consistent with that of HD

and HM)

XI ( 5) thicknesses of interior partitions

XUI ( 5) thicknesses of interior partitions of story above and

of cei ling ( XU 1(5))

XXL 1(5) thicknesses of interior partitions of story below and

of floor ( XXL I

( 5)

)

Output:

RF (5,2) reduction factor array for four walls and overhead, for

ai r-secondary and fission product gammas (INRG) or neutrons and capture gammas (INRN)

Subroutines called:

INTRP8

SECTOR

INTRPG

GMSHLD ( INRG only)

INTRPR ( INRN only)

23
INTRPR Interpolates on tabulated reflection factors for neutrons to obtain a reflection factor for tne "side" and "end" walls of the room. Here

"end" refers to the surface opposite the one through which the

radiation enters and "side" refers to the remaining four surfaces.

Input

:

0MRTAB(17) list of solid angle fractions at which reflection

factors are tabulated

RTAB(17,2) reflection factors for 17 solid angle fractions for

"side" walls (K=l) and "end" walls (K=2)

TAUR(5) solid angle fraction subtended by the four walls (1=1,4)

and ceiling (1=5). Values of TAUR are calculated in

RFSTOR, assuming detector is centrally located,

vertically as well as horizontally. Thus the solid

angle fraction subtended by the "end" wall is always

equal to that subtended by the source wall, and the same value is used for each of the two reflection factors.

Output

:

RH0(5,2) reflection factor for four walls (1=1,4) and ceiling

(1=5), for "side"walls (K=l) and "end" wall (K=2).

NMSHLO (INRN only) Calculates the mutual shielding factor for neutrons

incident on the roof and walls of a building. The solid angle

fraction of open sky is calculated at the center of the roof and at

exterior points at detector height at the center of each of the four

walls. (For a detector below grade the exterior points are also below

grade, although, physically, they should be at grade level or higher.)

Mutual shielding factors are then interpolated from curves for either

the roof or walls. A factor of 0.5 for the walls and 0.58 for the

roof is included in the mutual shielding factor for neutrons. Reduction factors are multiplied by mutual shielding factors in the RFSTOR

subrouti ne.

24
Input: (in units of ft)

XLM(4) length of area at grade level parallel to each wall

WM(4) width of area at grade level perpendi cul ar to each wall

( INRG only)

XL length of building

HM(4) height of building nearest to each wall (INRG only)

W width of building

HD detector height (absolute or relative to floor of this

story; but definition must be consistent with that of HR

and HM)

HR roof height (absolute or relative to floor of this

story; but definition must be consistent with that of HD

and HM)

Internal Variables:

TAUM(5) Solid angle fraction of open sky for each wall. Areas

for calculating solid angle fractions are projected on

to the horizontal plane at the height of the building

nearest to each wal 1

.

TAUMRF(5) Solid angle fraction of open sky for each quadrant of

roof. Areas for calculating solid angle fractions are projected on to the horizontal plane at the height

(HMAX) of the highest nearby building.

Output:

XMS(5,2) Mutual shielding factor for walls (J = 1,4) and roof

(J = 5), for neutrons (1=1) and neutron capture gammas

(I = 2). Mutual shielding factors for neutron capture

gammas are assumed to be equal to those for neutrons in

the current version of NMSHLD.

Subroutines called:

INTRPR

Remark: See Appendix 3 for more detailed description of mutual

shielding for neutrons.

25
GMSHLD ( I MRG only) Calculates mutual shielding factors for gamma rays through

roof and walls of building. As viewed from the detector, the nearest

building limits the amount of open sky. For each side of the building

the intersection on the wall of the plane formed by the nearer edge of

the roof of a nearby building and the detector is determined (i.e.,

the edge of the "shadow"). Mutual shielding factors for sections of

the walls below this intersection are set equal to zero. For example,

if this intersection (shadow edge) is at a height halfway between the

window sill and top, a ratio is formed of the contributions from above

that intersection and from the whole window. This ratio -- the mutual

shielding factor -- is applied as a correction to the window contribution. If the shadow intersects the roof, rather than the wall, then

the intersection (instead of the real roof edge), determines the size

of the effective roof on that side. A factor of 0.5 for the walls and

0.85 for the roof is included in the mutual shielding factor for both

types of gamma rays. Corrections for mutual shielding are applied in

the RFSTOR subroutine.

Input: (Linear dimensions in units of ft, barrier thicknesses in psf)

WM(4) width of area at grade level perpendicul ar to each wall

HM( 4) height of nearest building to each wall

XL length of building

W width of building

HD detector height. (Absolute or relative to floor of this

story; but definition must be consistent with that of HR

and HM.)

HI height of the story

HL height of portion of wall below detector plane

HIU height of story above this one

HT height of top of window

HUR distance from detector to roof. HUR is set equal to

HR-HD in the RFSTOR subroutine.

26
XW(9) thickness of walls

Y ( 18,2) solid angle fraction and sin<j> arrays

GP (7,18,2) geometry factor for up to 7 different contributing

sections of wall, different sides -- upper and lower

, and 2 types of gamma radiation.

IW window index: IW = 0 no windows; IW = 1 windows on four sides; IW = 2 windows on two long sides.

Output

XMSW(4,5,2) mutual shielding factor for four walls and roof for

air secondary gammas (M = 1) or fission product gammas

(M = 2). Corrections for walls of same story (J = 1),

windows of same story (J = 2), walls of story above

(J = 3), and windows of story above (J =4).

Subroutines called:

SECTOR

INTRPG

C. Listing of Computer Codes.

FORTRAN listing of subroutines of the INRG6 and INRN6 computer codes are

shown in Appendix C. Data input for sample neutron and gamma programs are

shown in Appendix D. Finally, output for the same sample programs are shown

in Appendix E.

27
V. COMPARISON WITH MONTE CARLO CALCULATIONS

A. Monte Carlo Calculations on Benchmark Structures

Since several approximations have been made in the derivation of eq (2)

and in the determination of the component functions, it is necessary to check

the results either with experiments or with more rigorous calculations.

Experimental checks of approximate procedures for predicting fallout shielding

were extensive. However, there have been no systematic experiments developed

to either predict or check theoretical procedures for estimating protection

from initial nuclear radiation. Therefore comparisons must be made with

independent calculations.

The approximate procedures of eq (2) will be applied mainly to three

dimensional structures with rectangular roofs and walls. Monte Carlo calculations probably offer the most promising approach for obtaining accurate and

independent results for a small number of configurations.

Unfortunately we have available only one set of Monte Carlo calculations

with which we can compare our calculated reduction factors. The Monte Carlo

calculations considered here were performed by Beer and Cohen of MAGI [11,12]

under subcontract to NBS and FEMA. Although the Monte Carlo method is a

rigorous one, its application to any particular problem may contain errors due

to poor sampling techniques or inadequate modeling of the geometry of the

problem. Therefore, discrepancies between NBS approximate procedures and MAGI

Monte Carlo calculations do not necessarily imply that the procedures are

inadequate.

A series of structures of increasing complexity were selected as benchmark structures to test the adequacy of the approximate procedures. They were

designed to approach in complexity a typical multi-story dormitory building.

Cross section and elevation sketches of these structures are shown in

28
figures 21 and 22. Figure 21 indicates a structure that contains a basement

ceiling (elevation view), and windows on two sides (plan view). These

structural details are given in table IV.

B. Combined Components

First we present a comparison of the overall protection factors

calculated by NBS and MAGI for the high and low yield combination of

components discussed in Section III.E. This comparison can be made only for

structures 4 and 5 since MAGI did not calculate reduction factors for neutrons

in structures 1 through 3.

Table VI shows reduction factors for the four radiation components and

for overall reduction factors according to the weighting factors shown in

eqs. (4) and (5) of Section III.F. Comparisons are made for structures 4 and

5 at central positions in the first story and basement. The first fact to

note is that the first story provides protection factors of 2 to 4, while

basements provide protection factors of 6 to 20. Secondly, the NBS estimates

of reduction factors are up to 40% higher than those of MAGI and are therefore

conservative, in that they estimate less protection. The computer codes

generated by NBS therefore seem to predict reasonable estimates of reduction

factors. Reasons for di screpancies with the MAGI Monte Carlo calculations and

possible improvements in the NBS computer codes are discussed in the following

sections

.

C. AS and FP Gamma Rays

Monte Carlo calculations were made by Beer and Cohen [11] to determine

reduction factors for AS and FP gamma rays incident on the five benchmark

structures. In a preliminary exercise the roof barrier for ai r-secondary and

29
fission-product gammas was determined. Comparison of these results with those

estimated from figure 2 is shown in table V. The agreement between the two

methods for this simple configuration is within 10%.

Now we turn to comparisons for the benchmark structures. Tables VII

through XII give comparisons of reduction factors for AS and FP gamma radiations calculated by MAGI and NBS for centrally-located detectors (x = y

= 0)

in the five benchmark structures. We consider first, structure #1. The

comparisons shown in table VII indicate reasonably good agreement for the AS

gamma radiation, but the NBS calculations for the FP gamma radiation are as

much as 46% higher than the MAGI calculations. The discrepancy is probably

due to the calculation of geometry factors, since the calculated barrier

factors for the roof show only a few percent discrepancy. The NBS geometry

factors may be high because of the approximation, discussed earlier, of

integrating over the incident angular distribution rather than the emergent

angular distribution.

Structure #2 includes windows. Since the contribution from windows

involves merely an integral over portions of the source angular distribution,

the two methods ought to agree well. The observed discrepancies for the

basement are due to insufficient characterization by the computer codes of the

geometry of the windows on upper stories. The code assumes erroneously that

the windows of the upper story extend from the tops of the windows of the

detector story to the top of the upper story, thus accounting for a larger

window area than intended from the input data. Comparison of the contributions from the walls shows the same discrepancies as observed in Structure #1.

The approximate procedures do not predict any differences in roof dose

between structures #1 and #2, because of the presence of windows in

structure #2. The Monte Carlo calculations, on the other hand, seem to show

about a 5% decrease in reduction factor because of leakage of gamma rays

through the windows.

30
In structure #3, the main effect of the basement ceiling is to reduce the

dose in the basement. Table IX shows that NBS calculation for the roof is

still high, but that the wall results also differ by about 35%. To examine

the effect of the ceiling barrier we take ratios of the contributions calculated by MAGI for structures #3 and #1. We then compare these values with the

NBS attenuation factors interpolated from figures 19 and 20. Table X shows

the results. The agreement for the component from the roof is reasonably

good. The agreement for radiation from the wall, however, is not as good.

The main reason for this is that the barrier factor of the ceiling was

originally made dependent on the average angle of incidence of the photons on

the upper surface of the barrier. When the computer code was written, the

roof barrier was substituted as a simplification. Table IX shows that the

approximation results in a reduction factor from the walls that is lower by a

factor of 1.9 for air secondaries and by a factor of 3.2 for fission product

gammas. The approximation made in the INR code is conservative and tends to

overestimate reduction factors or underestimate protection.

Structure #4 is similar to structure #3 except that it contains windows.

Comparisons of the contributions to a basement detector from the walls and

windows of the first story calculated by the two methods are shown in

table XI. Both calculations predict a lower wall contribution in structure #4

than in #3 because of reduced wall area. The window contribution calculated

by NBS for the air secondaries and the fission product gammas is much larger

than that calculated by Monte Carlo. This is the largest discrepancy in the

comparisons we have considered. The attenuation in the basement ceiling as

calculated from ratios of entries in tables VIII and XI is in reasonable

agreement for the wall sources. Furthermore, the attenuation for window

sources calculated for air secondaries by MAGI is ( .0098/ .0693) = .141, not

31
too different from the value of .165 calculated by MAGI for wall sources.

However, the attenuation predicted for fission product gammas is

( .0010/ .0409) = .024, considerably lower than the value of .065 calculated by

MAGI for wall sources. Therefore, the MAGI results for windows are believed

to be about a factor of 2.5 too low, reducing the discrepancy from a factor of

13 to 5.2.

Figure 21 shows multistory structure #5. Because of the many stories,

the roof source is not expected to contribute to the dose on the first story

or in the basement. However, since the ambient source radiation is directed

downward, walls above the first story may be expected to contribute to the

dose at these points. Table XII shows a comparison of the contributions from

the first, second, and third story walls to detectors on the first story and

in the basement. Both calculations indicate that for ceiling thicknesses of

57 psf, the first story is the major contributor. Contributions from higher

stories increase the dose by about 1/3 for AS gamma rays and 'are almost

negligible for FP gamma rays. These increments would vary with the geometry

of the building and the thickness of the ceilings. Agreement between the two

types of calculations is good for the first story and, for the basement, a

factor of 2 to 3 better than for structure #4. This reinforces the argument

that the MAGI calculations of the window contribution to the basement of

structure #4 may be low by a factor of 2.5.

0. Neutrons and Secondary Gamma Rays

Under a later subcontract with NBS (March 1981) MAGI also made Monte

Carlo calculations of reduction factors for neutrons incident on benchmark

structure #4. They tabulated reduction factors for both neutrons and for

gamma rays produced by neutron interaction in the structure. These calculations were reported in MAGI-7072 [12]. Table XII shows comparisons for source

neutrons entering through the roof and windows.

32
MAGI also distinguished between reflected and unreflected components.

Although there is some question of the MAGI's operational definition of the

two terms, unreflected is intended to mean the contribution from neutrons (or

gammas) which enter the room through the floor, ceiling or exterior walls and

reach the detector before being reflected from a room surface. All others are

reflected, including gammas which were generated in a surface by neutrons

entering the room.

For the roof source in Table XIII we find reasonable agreement for the

sum of reflected and unreflected and for individual components. The agreement

is also reasonable for basement detectors.

For the window source and first-story detector however, the NBS results

are generally higher by a factor of 2. In this case, we believe that the

unreflected neutron component may have been underestimated by MAGI. For

example, they calculated .034 and .048 for the air-secondary and fission

product source in structure #2 (See Table VIII). Since the neutrons are even

more isotropic than the FP gamma rays we would expect a greater contribution

from neutrons. Therefore the unreflected contribution of .0566 calculated by

NBS seems more reasonable than the contribution of .0266 calculated by MAGI.

Furthermore, the reflected contribution calculated by MAGI is almost three

times that of the unreflected — too high a ratio, in our opinion. We

therefore believe that the MAGI calculation of the unreflected contribution is

low by at least a factor of 2.

For the window source and basement detectors the same problem exists. In

this case, however, the problems is complicated by the attenuation in the

ceiling barrier. But the attenuation factor for neutrons is less sensitive to

the incident angle than for gamma rays. Therefore, even though the ceiling

barrier factor for neutrons and secondary gammas is treated by "folding" the

ceiling up against the outer wall and calculating the barrier factor for a

roof source, the approximation is expected to be a good one.

33
For the wall source and first-story detector the same comments apply as

for the window source. For the wall source and basement detector the NBS

unreflected neutron contribution is even more than a factor of 2 greater than

that calculated by MAGI, but the reflected contribution is lower. The result

is fortuitously close agreement for the sum of the two contributions both for

neutrons and secondary gammas.

The combined contributions of all three sources are also shown in

Table XIII. Since the contribution from the roof source dominates, the ratio

of NBS results for all sources are similar to those for the roof source alone.

Table XIII shows a similar comparison for Benchmark structure #5. For

the first story source and the first-story detector, we believe that the NBS

reflected neutron contribution may be somewhat high because the code does not

take into account the decreased reflection when the two walls adjacent to the

source wall are replaced by windows. It does, however, account for the

decreased reflection from windows in the wall opposite to the source wall. On

the other hand, just as for the other structures, we believe that the MAGI

calculation of the unreflected neutron component is too small. This can be

demonstrated for the detector on the first story, in which case the estimate

is particularly simple. The INR code gives a reasonably rigorous estimate for

the unreflected neutrons, namely:

R

f

= 0.58 GUJ

where G((ow

) is the geometry factor for the solid angle opening ^

of the

windows. This yields R^ = 0.196, almost a factor of 2 greater than the MAGI

value of .106.

34
For the basement, the MAGI values for the unreflected component are

probably again too low, but the MAGI values for the reflected component are

high, so that the sum of the contributions Is consistent with those of MBS.

The contributions from stories 2-9 are also shown in Table XIV. For the

first story detector the NBS values are consistently lower, probably because

contributions from the third and higher stories are neglected in the I NR code.

The MAGI values for the basement detector give an idea of the underestimate of

the NBS calculation.

Finally, the contribution from all sources are shown in Table XIV. The

"bottom line" is that the NBS values for the reduction factors for neutrons

and secondary gammas in a detector above grade are higher than the MAGI values

by a factor of about 1.5 but probably more correct. For detectors in the

basement the NBS value for the sum of the components is 0.8 times that of

MAGI, that is, in rough agreement because of compensating estimates of

reflected and unreflected contributions.

VI. CONCLUSIONS

In summary, the approximate procedures developed for calculating

protection from initial gamma radiation appear to be promising. Estimates of

protection with a single ceiling slab in place have been compared with those

from Monte Carlo calculations. Procedures for more complicated interior

structure such as interior walls are available, but have not yet been compared

with more accurate calculations.

The two areas in which the INR codes could be improved are the ceiling

attenuation for AS and FP gamma rays, and the calculation of the contribution

from windows in the story above the detector.

35
References

[1] L. V. Spencer, Structure Shielding Against Fallout Radiation from Nuclear

Weapons, NBS Monograph 42, U.S. Government Printing Office (June 1962).

[2] C. Eisenhauer, An Engineering Method for Calculating Protection Afforded

by Structures Against Fallout Radiation, NBS Monograph 76, U.S. Government

Printing Office (July 1964).

[3] L. V. Spencer, Structure Shielding Against Initial Radiation from Nuclear

Explosions, I. Attenuation of Air Secondary and Fission Product Gamma

Rays, Nucl . Sci . Eng. 57, 1 29-1 54 (June 1975).

[4] J. A. Auxier, Z. G. Burson, R. L. French, F. F. Haywood, L. G. Mooney,' and

E. A. Straker, Nuclear Weapons Free-Field Environment Recommended for

Initial Radiation Shielding Calculations, ORNL TM 3396, Oak Ridge National

Laboratory (Feb. 1972).

[5] L. G. Mooney and R. L. Swanson, Initial Nuclear Radiation Support Studies,

RRA T7411, Radiation Research Associates, Inc., Ft. Worth, Texas (1974).

[6] M.. 3eer and M. 0. Cohen, Effects of Ambient Field Specification on Initial Radiation Dose in Concrete Structures, Trans. Am. Nuc. Soc. 21_,

545 (1 975).

[7] G. L. Simmons, An Adjoint Gamma-Ray Moments Computer Code, ADJM/M I,

NBS Technical Note 748, National Bureau of Standards (Feb. 1973).

[8] L. V. Spencer, "PI ural -Seri es " Approximations of Functions, NBS J. Res.,

76B , 91 (1972).

[9]

G. L. Simmons and W. K. Hagan, Initial Nuclear Radiation Penetration

Study, SAI01381 052LJ , Science Applications, La Jolla, California (1981).

[10] C. Eisenhauer and A. B. Chilton, Angular Distribution of Scattered Gamma

Rays from a Fan Source, Trans. Am. Nuc. Soc. J_4, 1 (June 1971).

[11] M. Beer and M. 0. Cohen, Adjoint Monte Carlo Calculations of Initial

Gamma Radiation Doses in Structures, Trans. Am. Nuc. Soc. ]_8, 377 (1974).

(See also: M. Beer and M. 0. Cohen, Initial Gamma Radiation Dose in

Five Concrete Structures, Report Mr 7037, Mathematical Applications

Group, Inc., Elmsford, N.Y., Nov. 1973).

[12] M. Beer, Monte Carlo Studies of the Shielding of Blockhouse Structures

Against Initial Neutron Radiation, Mathematical Applications Group, Inc.

Report No. MAGI-7072, Elmsford, New York (March 1981).

36
Table

I.

Relative

Energy

and

Angle

Distribution

of

4nR

Secondary

Gamma

Fluence

1200 m

from a

Point

TN

Source

in

Infinite

Air.

(Reference

[4])

(gammas/group/angle

bin/incident

dose) oLO iD LO LO LO LO LO LO LO LO LO LO LO VO

cn cn o o o o o o o o o o o o o o o o o o

a; . U LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU I— o co o cn 3 3 o r— cn C\J o 3 CO CO CO CO LO LO O0 I o OO 3 cm 3 CO LO co LO cn r— CO LO LO LO LO CM co C II CO 3 CO LO CM LO LO r— o o o CO O 3 ‘O' co CO CM

<c 32; i CM CM 3 oo 3 LO LO LO LO LO < <—=

cn 1— 3 •

lor_ 3 lO LO LO LO LO lO LO LO LO LO LO LO LO CO CO

CM

<D • o o o o o o o o o o o o o o o o o o

LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU f— CD CO 3 LO r— LO LO CO *=3" r— LO VO CM i

coO cn i O'* cn cn CM r— 3 uO ao 3 3 LO 3 o LO rs. SZ II co LO LO 3 '

CO 3 LO 1— f— co CM 3 3 '

s cn « 1

*

3 CM 3 3 LO LO CNJ lO r*^ CO •

3 LO •— O

CO 3 LO LO LO LO LO LO LO LO LO LO LO LO LO lo o o o o o o o o o o o o o o o o o O

O) • LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU r— O <n LO LO co o 3 o CO o co CNJ 3 3 cn CO LO cn i o o co co LO vo LO o LO 3 cn lO r— 3 LO LO c a <C 13

LO r*^ LO 3 CNJ cn o o f— o o lo CO CO cn

OO

s: CO <— r— 1—

co

—

co CNJ •=3“ 3 CM CO •=3“ LO 1 co LO •—

cn

r^* *3“ LO LO LO LO LO LO 3 lO LO LO LO LO 1

r*» LO

vo <—

VO

a> • o o o o o o o o o o o o o o o o o o

LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU

— o 3 oo C0 3 co o LO lO CO 3“ CO r— LO CO 1— cn cn i r— co LO cn CNJ <3* ao cn LO o 3“ 3" cn cn uO cn o c ii co o lO co LO LO o co 3“ CM r— CO cn CM r— co i— OO

<c ddZ co CM 1— LO LO CM CM 1^ cn «— CNJ CO CNJ 3" * co LO cn oLO 3" LO LO LO LO LO lO CO 3° 3” UO LO LO LO r*^ LO LO LO o a o o o o o o o o o o o CD o o o O

aj • LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU r— O 3" 3* r^. CM LO cn co CM cn cn vO CO r— o LO cn cn i 3" r— cn cn 3* CM o LO cn CO o LO co 3- r— r—> r— LO C II < ZD

cn co CM CM LO LO vO 1 LO LO cn LO o CM LO z LO r— LO LO CM •— LO CM r— co • CM CM 3" I I

LO

LO 3“ LO LO LO LO lO LO 3" 3 co 3 LO LO VO LO LO co

<L) • o o o o o CD o o o o o O o O o O o o

LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU >— O co 3* co CM CM CM VO f— CO o LO o cn LO LO

oo i oo LO cn CO 3' o 3" r— o OO r— LO 3 LO LO r—> L

O o C ll (— o cn 3d o LO CO co 3 lO r— ao

co CO c r— CO

<=C z 3* •— CM 3* r—’

r— CO i— LO r— i

5 —1 r^. CM CO LO I

vO3 3 3 LO CO 3 3 3 3 LO 3 co CO LO LO LO VO

CO 3ao 0) • o o o o o o o CD o o o o o o o o a o

UJUuu

U

U

U

u

uUuU

U

UUU

UU

r—

O LO co LO 3 LO LO CO o r— LO -co r— to co LO LO cn i o CM 03 LO CM LO co CM 3 LO LO LO o o LO ao CO C II c o

lO oo

O 3 1 1—

r

— lO CM co O'* lO o CM o z r— r— CO CO CM co oo oo i

LO CM CO LO LO 1— CM co 3ao CO co 3 3 3 CO 3 3 lO 3 co 3 lO LO LO o LO LO CM cooo

a> • o o o o o o o o o o o o CD o o o o o u u U U U u u U u U U U u u u U u u r— O CM vO 33 vO r^* 3 LO ao o CM LO VO r^* r— LO LO 1

ao i co 3 n** CM CO vO VO r— ao CO LO lO ao o r— 3 C II <C ZD o LO CO 1— CM ao 3 o ' o CO CO 3 1— LO CO LO z CO LO LO ao LO CO 3 i— cd CO 3 co CM CM LO CO* «

I l I l II

r—> o o o o o o o o o o r— r— r— r—.

r_ , CM o o o o o o o o CD 3 o o 3 3 3 3 3 O u u U U U U U u u u u u u u u u u u o o o CD o o o o LO CO o 3 3 3 3 3 o 3 > o o LO CD o o LO o nO co o 3 3 3 3 3 3 3

>iS

r—,

co’ LO LO 3 co CM CM ,

,

f— CO LO 3 CO CM r—>LO

ao

s. 11 11 11 11 11 11 11 1 1 ii 11 11 11 11 1 11 11 11 a» a. 1 1 1 1 1 1 1 1 i 1 1 1 1 1 1 c a o o o o CD o o o CD o r— r— r— i— r—

r— CM CM

u o o o o o o o o o O o 3 3 3 3 3 3 3 3

CD

uuU

u

u

u

u

u

uuuuu

u

uuuu o o o o o o o LO CO o 3 3 O 3 o 3 o 3 o lo o o o LO o VO co o 3 3 3 3 3 3 3 3

CO LO LO 3 co CM CM r-

— co vd 3 CO CM r— LO CM

37
Table

I.

Continued 3- 1— O'1 x p^ p^ p^ p^ p*

x

X

X CO cOX NO NO 0^ p* NO r— CO

cr> a; • o o o o o o o o o o o o O o o o o o

LlJ LU LU UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ

— o p^.

X P- p^ 3" oo

CZD p^ oo CO

X CO 3- CM 3- ON NO NO

CD *=3" CM co p^ C\J CNJX r— 3* CM co

X 3-X CO o C II << o oo CM X X CO CM p^ co X CO ON 3- CM CM o 3- o

s: ' X CM CSJ '

'—

x ID CNJ CM 3* CM OO '—

»—1 CM

x

NO "NT NO NO p* p^ p* p*. p^ p* p^ NO

X NO NO NO p^ NO <— 3"

ON

CD • o o o o O o o o o o o O o o o o o o

UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ LU LU UJ LU r- C f— CO 3* 3" CM 3- NO p*. NO 1— 3“ 3“ O p» co NO r—

CO ON o o co p^ co 3- 3" p^ NO p* r— 3* NO 3* NO CO p^ C II < zc

NO NO CM ON co co 3- o o o 1— CM 1— o 'co CM NO s co co 3" <

CM «

<

I

1— i NO NO ON NO p*. CM CO 3-

x NO NO NO NO p^ cO p*» NO P* NO p* NO NO p^ NO ip p^

p <o <—

co

0) • o o o o o o o o o o o o o o o o o o

LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU

— o NO CO o NO 3“ NO ON co NO CM o CO CM 3* co *=3“ P *3“ ON NO 3" o ON NO NO p* CO C0 r— CO =3" ON co IP o r— C II <C ZD

NO p^ CM co NO o o o CM 3- NO CM CM o *=3* CO ON s »— co CM ON r— co 1— ON r— 1— C0 co’ i— rp '«

CO 3*

X o ^3- LD LO NO p NO NO NO NO NO NO NO NO r*^ NO s LOP o o o o o o o o o o o o o o o o o o

cd OJ • LU LU LU LU UJ LU LU LU LU LU LU LU LU LU LU LU LU LU

«j0

— o *3* *3“ oo o NO 3" <3- NO P^s co r— r— r— LO P^

O ON

r

r— NO NO NO *3* 3“ ON «3- sO

O r— co NO r— NO CM

T3 c ir CM P r— co o CM CM o «3* ,

ON o *3* NO CM co o ON < X U> s: oo' «— l CO NO 3“ NO NO co t— co r— r— co i— *3* NO co c

CD "O

•r- ON U CO P^ X) NO NO NO NO NO NO X) NO NO NO p^ p^ NO P** r^. P^ ' c P— r— o o o o o o o o o o o o o o o o o o r” NO

d) • LU LU LU CsL LU LU LU LU LU LU LU LU LU LU LU LU LU LU c .— o r— CO P^ NO co o NO NO CM CM NO r— CM CM r— *3“ o CO

•r— CN LO CM o ON P^ CO CM CM r— P^ NO «3" lO r*^ CO CO P^ NO JO C II ON o LO ON ON ON o CM 1— CO NO o NO CM <3* CO ON o

<c rc

a» s: •

i— CM r— co CO LO CO 1— i ON r— *3" NO '

cdc

03

O CM CO LO LO NO NO NO NO NO NO NO NO NO NO P>. NO P^ P^ P^ P>. CL

Z2 r— lO

*3* o o o o o o o o o o o o o o o o o o o D • LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU U r- O CM CO lO P"» o NO CM P"* r— CM o P^ ON P^ -X X r— ON ON ON CO X NO NO CM NO *3* co r— r— , o r— *3“ r— X CM X c u NO r— ON ON *3- i *3" CO CO NO *3“ CM P^ NO LO 1— NO r—

NO <c 10

ro s: CO CO LO <CM r— •— r— CM *3" LO ON ' ON LO P". « <=

03CD

X r— ,

lO nO CO

XX

XXXX

XXX p^

X P^ P*- P^ p^ r— COCM

<D • o o o o o o o o o o o o o o o o o o

LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU

— o ON CO

X ON p— «3"

X CM

X CM o CM *3* P>»X r—

X P^

CD P^ CM CO ON ON ONX

X CM o ON CO CO

X CO

X CO CO

C II c =o

CO

X

X CM p— CO o ON o X

X p".

X CM P-. CM

s: CM cO *3" <

CM ON ONX

X *— CO

X <

ON r—X p^. *

O o x

X

X

XXX

XXXXX

XXX P^ p^ p^

r— CD o o o o o o o o o o o o o o o o o o

Q) . LU LU LU LU LU LU LU LU LU LU LU LU UJ LU LU LU LU LU — o ON X o t— P". o CM CO 3“ X p— CM P^ P^ r— CO o ON

CD

XX CO "3* *3* <3- ON p—

X o ON p— ON

X r— coX

X

C II ON <3-

X CM

XX

X

X o CO f— CO

X

X r—

X CM

<C

X

s: '

*3* co r— r— P^ p^ •3* 3- p^ <

3* r—'

ON '—X p^ r—

r

o o o o o o o o O

O ,

r— r— r—> ! r— CM o o o o o o o a o o O o o o o o o o

LU LU LU LU LU LU LU LU LU LU LU LU LU UJ LU UJ LU LU -—«» o o o o o o O o X CO o o o o o a o o C> o o X o a o X o X co o o o o o o o o ,

x’

X

X 3- no CM CM , x’

X 3” CO CM , X CD'—' 11 11 11 11 11 ii 11 11 11 11 11 11 11 1 11 11 11 11 OJ CL 1 1 1 1 1 i 1 1 1 1 1 1 1 1 1 1 1 1 CZ C3 o o o o o o o o o o r— r— r— (— r— p— CM CM LU O o o o o o o o o o o o o o o o O o o

CJ LU LU LU LU LU LU LU UJ LU LU LU LU LU LU UJ LU LU LU o o o o o o o X CO o o a o o o o o o o X o o o X o X CO o o o o o o o o o X X X 3- co CM CM r- r— r- CO X 3* CO CM r- X CM

38
o

cuue3O

oo

CDo

4J

+-> u

CDQ.

l/> d) QC

+>s

(D p—

CD • E

=c l 1 o E 1—1

(13 r— <D o c_> o_ E

a> -a E E CD

ITS 4-

CD >> as CD •

E

CDE

LU 4 00 4— Q_ o o E CO O

CD UC E3 o

U_ oCO

(13

—

(/)

(13 Eo

CDN

CJ *f~* E E

<DO 3 nr r—U. CD .E

>> +J

ITS CC <D 1 > 2 O £ JO

(13 ITS o 0O 4-> CO

CJ3 00 TJ •! O X E C a.i E E O O -M

•r— CJ

LO CD 00 +->

•r— CD

Ll_

O

Ol JO

(13 I— (o• r-

"O

(13 E

CD -Muo

O)uc

O)3

>>

(13 QCI <13

ITS o

CD

<D T3

CD

OCDI

CTl E

<c

cd

r>-

CD

O) -a

CD

CDi CDE

<c

co

CO

CD

<u a

cjCDEc

00

loI C\J

D-. LO

CD CM

CD -a r-. — LO

CD i I— CO

CDE

ec

CO

cn CO

<D a

CDCDEc

CO

"d"I •51* LOCO

CD

QJ a

<dCDE

=t oCOI 'd-

==*• cxi

CD

CD -O

ajCDE

«=c

=d- <XI

=d- CO

CD •=d- aj X3 CO

CD

To CDE O

=c

CD

>0CDE

CDE O o <3* ^d“ 'dP CO CO CO co CVI CVI CVI o o o o o o o o o o o o o o o o

UJ LlJ UJ LU LU LU LU LU LU LU LU LU LU LU LU LU o r— 1^ CD o ^P LO I o LO LO LO I—- CO CO CVJ o CO o co LO LO <PP CVI o co r—

CVI LO CO l— LO CVI co LO r- CO o CVI o o r—

r— on r— r- CVI CVI co <D r— CO CO LO CVI r— o o «=d- 'SP CO CO CO CO CO CO CM CM CM o o o o o o o o o o o o o c o o

LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU f— 1 CM CO CO LO LO O O LO r— co I 1 p^ CVI CD CO co P^ CO p^ (XI CD CM CM CM o ( ' CO p^ O CM ^P r— o p^. CO o LO LO LO <—

C\J co CVJ CM CO p^ r— r- CM

O ^r LO r— CM r—

LO <^d“ ^P •^P CO CO CO CO CO CO CO CM CM CM o o o o o o o o O O o o o O O o

LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU

r^. co o LO CM CO CO LO r—•

LO o r^.

O CD CO

CO LO CD CO *3- o CO CD co CM ^P CO CM o CO O'. CM to co *=d" CO UO o CM LO «

LO LO 1—

r— LO ^p p^. CO r- CM CM ^P p^ r— (XI r—“

^d" ^p CO *=d- CO CO CO CO CO CO CO CO CO CM CM CM o o o o CD o o o o o o O o o o o

LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU

LO LO LO CO LO

O CM CO LO

O CO LO CO o <=d- LO I CM CO o LO LO CD CO CO CO LO ^p co CD o CO 1— LO LO LO CO CD CO o rv. p^ LO o

r- CO r— CTi r— r— CM •=3" CO LO CD LO p^ r— CM ,

*3“ "dp CO CO CO CO CO co CO CO CM CO CO CM CM CM o o o o o O o o O o O o o o O o

LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LO CD CO LO P^ CO | » co CM co LO co LO LO CO LO

LO CO LO LO CD o CM o CO I CO

CD <D o D-* LO CD 1— CD LO

O o o LO o

r— LO CM r~ CM CM LO LO r— LO 00 r— CM r—

CO CO CO CO CO CO CO CO co CM CO CO CM CM CO o o o o o o o o O o o o o O o o

LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU

CO CO CO CD LO CDO LO CO LO CD LO LO CO

O CD o LO r^. CD <DO CM CM CM <D CO co LO 1— LO CD LO LO CD LO CM 1— CM LO CM 1—

CO CO CM LO CD CD r- LO r— CM CD

*^d“ co CO CO CO CO CO CM CO CO CM CO CO CM CM CO o o o o o o o o o o o o o O o o

LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU

CO CO CD <D o LO CD oo ^d" i—=

CD 1^. CD CO LO CM LO f— r— CO O LO LO LO CO LO >— LO LO 1— LO co CO o ^d“ ^d“ CM P^ co CO CM LO LO <D r— CO CD r— LO LO r— LO

CO CO CM CO CM CO CM <XJ co CO CO CO CO cn CM co o o o o o o o O o o o o o o o O

LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU

CM i—-

co CO CO o CO D- d* CM CM P>« co CD

O CO P^ r-» CO CO CO r— <D r—O CM CM co o LO CO CM CM 1— CD 1— CO LO (XI CO CO CO o co

CM LO r— co r— as r— LO P^ CO CO p^ r— CO o o o LO O LO co o 00 LO ^d- CO CM rLOo

(XI o

LO CO CM CM r- r- f— o o o o’ o o o o I LO o o 1 o 1 LO o 1 LD CO 1 o 1 CO LO 1 CO 1

(XI 1 . 05-

lo lo *d- co cm cm .— .— <—0000000

39
Energy(MeV)

Angle(deg)

Angle(deg)

Angle(deg)

Angle(deg)

Angle(deg)

Angle(deg)

Angle(deg)

Angle(deg) o

COI

co

coi co

lO

CO

loi LO

cn^ri

'3- oo

'3- ooi oo

c\j

oo

CXI

<XJ

CcJI oooI o

CO LO LO LO LO LO LO LO LO CO oo CXI CXJ CXI o O o O o o o o o o o o o o o o

UJ LU LU LU LU LU LU UJ LU LU LU LU LU UJ LU LU oo O CO LO CXI o LO OO CO •=3* CTi o CXI OO LO

CO CO 1

LO CO oo co p^ OO o r— CO CO CO

CXI LD o CXI CO o LO o cO cn LO

CO CXI LO OO LO CO LO r— oo CO r— OO rCO LO LO LO LO LO LO LO LO ^d" oo oo CCJ ccj CCJ o o o o o o o o o o o o o o o o

LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU o <T> LO LO CTi CO CO OO r— o | OO CO o LO

CXI OO oo CO co p^ CXI cn co OO CTi CO o o 1— 1— CXI oo OO cn CXI CO O o CO p>* o ^J- CO CCJ LO oo CO LO CO CO r— ^p CXI CO oo

CO LO LO LO LO LO LO LD LO oo oo CCJ CCJ <XJ O o o O o o o o o o o o o o o o

LU LU LU UJ LU LU LU LU LU LU LU LU LU LU LU LU

oo co LO oo P— CCJ CCJ oo p^

O (XI cn r— CXJ cn cn cn Cn oo LO OO ccj r— i

O cO o o CO cn o 1— OO LO CCJ o oo oo CCJ CO LO CO co ccj LO CXI LO oo LO CO r-^ r— LO CXI LO r— CCJ r—

CO LO LO LO LO LO LO LO \P oo oo CXI CCJ CCJ o o o o o o o o o o o o o o o o

LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU o CO CO O p^ ccj LO CO OO oo OO cn cn CO LO p—

CO P^ CO o o P^ |— *3- o 1

CXI oo CCJ OO CO 1— 1— '

cn oi o oc co LO LO oo LO CO 1—

CO CXI LO oo LD ^p CO r- cn CO ccj LO r- CCJ r—

CO LO LO LO LO LO LO OO oo CM CM CM o O o o o o o o o o o o o o o O

LU LU LU LU LU LU LU LU LU LU LU LU LU UJ LU LU

CO cn r— CO CCJ o cn co CO OO ^d- CM ( CO

CCI LO 1oo p** CO cn p>* LO cn cn LO oo

co CO

O CCI 1— CM cn CO r— LO CM LO 1—

co ccj CO CO CO CO r— CM CO CM LO r— CM ,

CO LO LO LO LO LO *^T oo OO OO CM CvJ CM o o o o o o o O o o o o o o o o

UJ LU LU- LU LU LU LU LU LU LU LU LU LU LU LU LU 1— oo CO LO co LO CM OO cn LO O LO CM P^ o oo cn o CO J OO o co oo P>* cn cn CO , ^d" co co 1— CO CM CM CM CM CM CM CO oo LO p^ CM co LO CO ,

CM CM ^p CM LO ,CM ,

CO LO LO LO ^d” ^d- ^d- OO oo OO CM CM CM O o o o o o o o o o o o o o O o

LU LU LU UJ LU LU LU LU LU UJ LU LU UJ LU LU LU CM LO cn ^d- LO I <3- |— CO <n CO CO LO P^ OO CM

CM LO cn CO o OO CO o ^d* CM (— CO cn p— oo r—

LO

O 1— oo o 1— P^ CO CO CO co LO LO LO r—

CO OO co CO r- r- ,

oo OO CO ,CM LO , CM ,

lO LO LO ^d- oo oo OO oo CM CM CM o o o o o o o o o o o o o o o o

LU LU LU LU LU LU LU LU LU LU LU LU UJ UJ LU LU

cn o CO CM co

O oo OO CO i

co ^p co r— o oo P^ ^p CO o LO LO o cn o LO CO ^d* LO ,

o P^ o LO ^d- CO CO ^d- co CO 1— co LO LO 1—

r- oo CO ,

CM LO LO CM oo LO CM ,

o o o LO O CO oo O CO CO oo CM

LD »— o

CMo

LO =3- oo CM CM i— .

o o o o o o o o I I I I I I I I I I I I I I I LO o o o LO O CO OO O CO CO *=3” oo CM

LO r— O

CO LO OO CM CM .— .

r—

O o o o o o o

40
Table

III.

Relative

Energy

and

Angle

Distribution

of

4irR

Neutron

Fluence

1200 m

from

(Reference

[4])

S- < o 3 •=5* 3 lO LO LO LO LO LO LO LO LO

p

pp

p LO LO LO LO LO LO

<D 3 lo o o o o o o o o o o o o o o o o o o o o o o +-> 3a O UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ LU UJ UJ UJ UJ c 3 3 3 o 3 LO CM r— CM CD CO r— CM CO CM co ‘CO CO 3 LO O CM • r- 3)0 3 3 lO co 3 3 P o r— CO 00 CO co r— CO CM CM CO LO (— P CO

4- c i CM LOp

p CD LO LO lO •=3- 3 3 CM CD 3 *53* 3 CD CO CO P LO o c «C II • • c

MU CM LO 3 CM 3 LO vO LO CM ” CO cd co 3) P CD LO LO LO

0) CO co 3 3 O LO LO LO LO LO LO LO LO P p

pp LO LO LO LO LO LO

u CO r— o o o 3 o o o o o 3 o o o o o o o o o o o o u3

CO

aj cm UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ o r— c lO o f— LO P LO r— LO CM LO CD LO CM LO r— lO CM /— co CM CM r—

LO 013 lo o CO CD 3 *3"

p CM LO lO 3 CM LO

p 3 co CM LO CO r— co 3 C 1 co o 3 o o P co LO CD CM o CM p r— CO co CO CO P CO co P C il z :z>33locm33lolo.

.— co p co .— <— cn ^ co ^ m 't o

CL.

H3 o CO 3 3 LO LO LO LO LO LO LO P CO

LO o o o o o o o o o o

0) UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ LO co LO LO 3) LO an 3 P o

cno CM r— CD lO o CD CD r— P 3 C 1 CO CD CD LO CM 3 o LO LO o

eC II MU 3 CM 3 CO CO LO 3 1 1 '

LO LO P P P P LO LO LO LO LO LO o o o o o o o o o o o o

UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ 3 co co LO o LO o IP CM CO co CM

3) P co 3 r— o CO LO LO r—>

CM

O LO *— LD co CM CM 3 LO 3 1— CO co CM LO r- CM r— r- CO LO IP LO 3 •=3“ 3 CO 3 <3 LO LO LO LO LO LO LO LO LO P P P P LO LO LO LO LO LO

a> lO P o c o o o o o o o o o o o o o o o o o o o o

LO CD LO UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ a r— • CO LO co LO co r— CM 3 CM o LO CM 3 co LO 3 3 UD co f

LO LO

•o cno CO CO CM CM VO P OJ 3 3 r— 3 r— 3 3 •3 3 3 LO co LO co CO C 1 CO CM P r— 3 CM co P CM 3 r— i— CM 3 o o CM P CO 3 r— p 4-> C II c ZD co CM co r— CM CO 3 co r— co CM LO f— CM r— 1

P LO LO 3 <3- CO

a> 21 -o

•r-uc o co •^r «3“ LO LO LO LO *3* LO LO LO P P LO VO LO LO LO LO LO LO

•r— LO LO

lO

CD P o o o o o o o o o o o o o o o o o o o o o o

UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ

•t— p— . 3 ^3” LO CM r— CO r— CM CO co CO CM LO r— 3“ co CO 3 3- co 3"

JO CIO 3 co co co •3" LO o CM «3“ co 3 CO 3“ CO 3“ CO

p f— CO LO CM LO

C 1 CM co co CM CO LO LO o 3- LO LO o o 3 LO lO 3 p LO o 3° o

aj <=C II • r— ZD co r— CM CO r— CM co co 3 LO r— •3“ r— r— co ’C0 LO 3" LO 3" co O0 3 21 c

<T3 CL LO co 3" 3" 3“ LO LO LO LO 3 LO LO LO LO P LO LO LO LO LO LO LO LO 3O 3 LOLO o o o o o o a o o o o o o o o o o o o o o o u oj co UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ LU LU LU LU LU LU LU LU LU LU 3 r— • CO LO 3 3 CM co r— CM 3 o CO CO 3 co co CM co co P 3 CO CM CTO 3" VO co o r—» LO 3 3 CO 3 3 LO CM '30 CM CM 3 LO 3 LO 'CO r—

</> = i P CO o co co co LO CM P P CM 3 P 3 3 3 3 LO CM o LO CO C < ii ou

+J3

0)

MU CM LO CM CM LO 3 CM P lO lO 3 CO 3 co CM CM

C LO r— co 3* 3" 3* LO LO LO 3 lO LO LO LO lO LO LO LO <o LO lO LO LO '—’

CO 3“ o o o o o o o o o o o o o o o o o o o o o o

aj an UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ LU LU UJ LU LU LU LU LU LU LU r— • LO CM o 3“ CO p P CO 3 LO CM -O o LO P co CO CM CM 3 3 o OlO r— o LO P 3 p r—*> 3 o 3 r— CO LO o lO LO r— o LO P P o C 1 3* LO CM vO CM r— P 3 CM 3 3 co 3 LO r— r

3 CO P 3 LO LO

<C II • MU CM CO

r“" CO C0 * 1 3 CM P '— 3 3 3 3 CM CM CM '1— 3 CM co co 3 3 3 3 3 3 LO LO lO LO LO LO LO lO LO LO LO wO LO CM 3CO

CD 3 o o o o o o o o o o o o o o o o o o o o O o

LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU UJ LU »— • o LO co P P LO r— LO CM CO CM co LO co DJ co 3 co 3 lO co o cno P CM p CO P CO P 3 3 CO o o co LO o o LO co 3 co LO r— i 3 LO (— LO LO o 3 CM P CM 3 r—>

r— r— CO CO CM 3 r— LO CM lO

C II • • o co co LO * CO LO P LO |—3 r— co CO CM 3 i— -—

i

3 3 i—1 so P LO I o o

a; 3'*—’

CL) CL C 3

LU

O

s. CD

Olo

c\j CM o o

UJ UJ CM O CM

r— o o o o o o o O o , r— CO 3 3 LO LO LO LO P o o o o o o o o O o 3 o o o o 3 3 o o 3

LU LU UJ LU LU LU LU LU LU LU LU LU LU UJ LU UJ LU LU LU LU o 3 lO P P r— LO LO CO i— o r— lO CO r— 3 P LO CM 3 o CO 3 o o 3 CO co LO r— co oo 3 3 3 3 1 CO1 LO1 31 31 CO1 CM1 CM1 1 1 LO1 1 coi LO1 1 CM1 1 CO1 3l 1 o 1 o 1 o o o 1 o 1 O 1 o 1 o 1 1 1 co i 3 1 3 1 LO 1 LO 1 LO 1 LO 1 P : o o o o o o o o o o o 3 o o 3 3 3 3 3

LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU 3 LO P P r—»

LO LO CO r—> o r— LO CO r— 3 P LO CM 3 1— co 3 o o 3 CO oo r— lO CO co o 3 3 3 1— •— 3

oo LO 3 3 CO CM CM r— LO r— CO LO r— CM r— co r— 3 o

41
Table

III.

Continued

LO lO LO LO LO LO lO LO LO LO LO LO LO y> yo LO yo LO LO LO LO LO

on o o o o o o o o o o o o o O o o o o o o o o r— CO

on LU UJ UJ LU LU LU LU UJ LU LU LU LU LU LU LU LU LU LU LU LU LU LU

a; • LO r— on CM r— CNJ r— LO r— LO 00 LO r— pp CO pp LO o LO r— o p^ p* o oo LO CO LO o LO p** pp co ON CO oo co LO pp

ON

II 10

lo CM CO CM lO 1 LO CNJ '

LO CO yo CO LO

r““ lO co

<c lo LO on r— r— oo’ LO r- pp r— r— CO LO CNJ CNJ r— r— r-

— ON co

LO LO LO lO LO LO LO LO LO LO LO LO LO pp lO LO LO lO lO LO LO LO

LO o o o o o o o o o o o o o o o o o o o o o o r—

ON UJ LU LU LU LU LU LU LU LU LU LU LU UJ uU LU UJ LU LU LU UJ LU UJ

a> • O LO r— p^ ON CNJ CM LO LO co r— lO o rp pp CO ON co LO pp r— a pp LO f— co r— CO pp r— CM LO 00 r— oo LO LO ^3“ CO o co Pp o or

II ID

LO LO co LO CM o pp '

'

ON LO o *3“ yc LO co o LO LO ' ON rp r— r- ON i— co" CM CM LO r- r- LO LO CO CO co CM CM nlo LO LO LO LO LO LO LO LO LO yo LO LO pp pp LO LO LO LO yo LO LO LO LO LO o o o o o o o o o o o o o o o o o o o o o o 1 LOCO LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU

<d • o ON co r— LO CM CO r—

ON CO 'CO CM pp CM r— ON CM CO LO CM o r— o p* CO r— r— LO co co LO LO r— «=r co pp o rp ON pp ON co CO

Ol

II ZD o CO co CM CM o Pp LO LO ON co

r“ LO oo Pp LO CO CM CO >5 co CO LO r- r- r- r— pp CM CO oo’ r- CM CO CO LO LO co CO CNJ o LO LO lO LO LO yo LO LO LO LO LO pp PP PP Pp p* •yo LO LO LO LO LO LO

LO o o o o o o o o o o o o o o o o o o o o o o

rp UJ LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU UJ LU LU LU LU

<D • pp r— CM C0 r— yo CO LO r— ON LO CM o o LO CM pp co OJ CO o r— o co co LO CM co C0 o CO rp ON LO r— r— CO ON Pp LO pp ON r— CM r—

ON

II :3

s:

CO ON OJ CM

— LO LO o co rp o o co ON

O CM rp

<5— CM CO ON »-

——

— LO CM—— CNJ——

rLO LO LO ^3" CO

ON LO lO LO LO LO LO LO LO lO LO LO p^ P^ p^ 1*^. yo LO vO LO LO LO co Pp 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 O 0 0 0 0 O

LO LU LU LU LU LU LU LU LU LU LU UJ LU LU UJ LU LU LU LU LU LU LU LU

oj • r— co ON CM yo Pp PpO ON LO CO 0 co ^3- LO ON CM LO LO LO r— LO r— o CM Pp LO r— CM LO lO Pp r— LO CM LO P^ LO ON r— CO LO LO ON

II ZD

21 '

pp co 0 0 0 CO CO *^r LO 0 O 1 CM CM PN. co CM CO ON CO < — — CM LO — — — — LO CM -- CM co — — 00 LO 00 LO <3- 0 LO LO LO lO LO LO lO LO LO LO P^ Ps» p^ p^ lO LO LO LO LO LO CM CO

LO 0 0 0 0 0 0 0 O 0 0 0 0 0 0 0 0 0 0 0 0 0 0

UJ LU LU LU UJ LU LU '-U LU UJ LU LU LU LU LU LU LU LU UJ uJ LU LU

a; • 0 LO P^ ON r— co CM ON ON LO P^ r— CM 1— LO CO 0 CO CO LO CO r— 0 CM O LO p>. CM co LO r— co *cr 0 co co 0 lO ON P^ CM ON

II ZD

51

p^ 1— 0 CM co p^ UD »— co CM LO 0 '— CO LO LO 0 *=T co <5 — CM LO co 00 ON — CM — CM co — — ON P*v ON LO LO

LO -o- LO LO lO LO LO LO lO LO LO LO P^. P** P^ P^ P- LO LO LO LO LO

r—r— 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 O

O 0 0 0 0 0 ’ ’ coCM LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU UJ LU LU LU LU LU LU

aj • LO ON ON CM LO LO CO vJD P^ ON P^ CM ON P^O ON t— O ~o r—

P^ ON 0 0 ON 0 uO CO CO LO JD LO r— CO r— CM lO CO ON

II ZD

P^ CM LO CM ON LO LO LO 0 CM ON 1— LO 0 ON LO 00 1—. 0

=c LO ON r— LO p>* ao ON CO CM ON CM CO r— r— P^ ON LO LO LO 0 uO LO -O LO lO LO LO LO LO LO P^ P P^H p^ vO LO LO LO lO 0 LO

ON

a 0 O 0 0 0 0 0 0 0 0 0 0 0 OO 0 0 0 O 0 0 0 LU LU LU uJ UJ LU LU LU LU LU LU LU LU UJ UJ LU LU LU LU LU UJ UJ

a> • CO uO CO P^ CO r— CO P^ 0 0 LO LO LO LO LO r— LO

O lO 0 r— 0 ON ~n O CM ON <^r 0 0 -T) LO LO P^ yO CM LO r— ON CM LO

ON

II ZD

21

ON CO 30 LO ON ON P- ON 1— 0 lO 0 0 LO CO CO 1—

<c CO p^»

— co lO LO P^ P^ CM

— CO ON CM co

—— CO ON yO LO lO

r— , , 0 0 0 0 0 0 0 0 0 r— r— CO

OO LO LO p^ 0 O O O 0 O 0 0 0 O 0 0 O 0 0 0 O 0 0 0 0 O

LU LU LU LU LU LU LU LU UJ LU LU -U LU UJ LU LU LU LU -U LU LU UJ 0 CM 0 ON LO P P-y X) LO CO f— 0 r— LO CO «— O LO CM

CD 21

LO CM 0 1— CO ON

O 0 'O' CO CO •

LO 1— CO oo 0 ON 0 0 1—

Cy r— , r— co" LO co CM CM LO CO LO , CM CO

ONU ’ " 1 1 11 1 11 11 11 1 11 11 11 11 1 11 11 11 11 11 11 1I 1 1 CJ Q- 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 C Z3 1— r— 0 0 0 0 O 0 O 0 0 r— r— co LO LO -0 LO P'y LU O 0 0 O 0 0 0 O 0 0 0 0 0 O 0 0 0 0 0 0 O 0

LU LU LU LU LU UJ LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU CM 0 ON LO P P-y r—

LO LO co r— 0 r— LO CO r—

0 P^ LO CM CM 0 *— co ON O O CO CO LO CO co O ON O 0 — 0

r— r— co LO CO CM CM , r— LO r- co LO r- CM ,CO ,

0

42
Table IV. Structural Details

Structure Thickness of

Number Basement Ceiling Wi ndo\

1 0 psf No

2 0 psf Yes

3 57 psf No

4 57 psf Yes

43
Table V

Comparison of Roof Barrier Factors

Z(psf) Ai r Secondaries FP Gammas

MAGI NBS RATIO MAGI NBS RATIO

0 1.00 1.00 1.00 1.00 1.00 1.00

10 .72 .80 .90 .58 .63 .92

28 .47 .53 .89 .31 .33 .94

57 .27 .28 .96 .153 .145 1.05

85 .156 .155 1.01 .076 .071 1.07

44
Table VI

.

Comparison of Reduction factors for combi ned Components

Structure #

4

First Story

High Low

Yield Yi el d

IRF IRF

AS FP N NG (eq. 4) (eq. 5

NBS .305 .208 .485 .096 .258 .451

MAGI .298 .173 .339 .060 .266 .334

Ratio

Basement

1.0 1.4

NBS .234 .128 .1127 .0343 .155 .161

MAGI .178 .085 .0314 .0351 .113 .122

Ratio

Structure #5

1.4 1.3

First Story

NBS .242 .260 .490 .082 .350 .444

MAGI .225 .190 .331 .047 .253 .310

Ratio

Basement

1.4

' 1.4

NBS .073 .0290 .063 .0122 .052 .066

MAGI .059 .0102 .069 .026 .045 .056

Ratio 1.2 1.2

45
Table VII Comparison of AS and FP Gamma-Ray Reduction Factors

Structure #1

(On first story at a height of 3 feet above the floor)

Air Secondaries FP Gammas

Roof Wal 1 s Total Roof Wal 1 s Total

NBS .232 .053 .285 .123 .043 .166

MAGI .228 .052 .280 .101 .034 .135

Ratio 1.02 1.02 1.02 1.22 1.26 1.23

(In basement at a depth of 9 feet below the basement cei ling)

NBS .184 .109 .293 .112 .038 .150

MAGI .156 .091 .247 .083 .026 .109

Ratio 1.18 1.20 1.19 1.35 1.46 1.38

46
Table VIII. Comparison as AS and FP Gamma-Ray Reduction Factors

Structure #2

(On first story at a height of 3 feet above the floor;)

Ai r Secondaries FP Gammas

Walls and Walls and

’dal 1 s Wi ndows Wi ndows Wal 1 s Wi ndows Wi ndows

N8S .042 .031 .073 .032 .053 .035

MAGI .0360 .0340 .070 .0244 .0480 .072

Ratio 1.17 0.91 1.04 1.31 1.10 1.18

(In basement at a depth of 9 feet below the basement ceiling)

NBS .068 .119 .187 .025 .088 .113

MAGI .0664 .0693 .136 .0209 .0409 .062

Ratio 1.02 1.72 1.38 1.20 2.15 1.32

47
Table IX. Comparison of AS and FP Gamma-Ray Reduction Factors

Structure #3

(In basement at a depth of 9 feet below the basement ceiling)

Air Secondaries FP Gammas

Roof Wall s Total Roof Wal 1 s Total

NBS .066 .029 .095 .0312 .0055 .037

MAGI .053 .015 .068 .025 .0017 .026

Ratio 1.35 1.93 1.40 1.25 3.2 1.42

48
Table X. Calculated Gamma-Ray Attenuation Factors for Basement Ceiling

Structure #3

Ai r Secondari es FP Gammas

Roof Wall s Roof Wal 1 s

NBS .36 .266 .28 .211

MAGI .34 .165 .29 .065

49
Table XI. Comparison of AS and FP Gamma-Ray Reduction Factors

Structure #4

(In basement at a depth of 9 feet below the basement ceiling)

Air Secondaries FP Gammas

Walls and Walls and

Wal 1 s Wi ndows Wi ndows Wal 1 s Wi ndows Wi ndows

NBS .018 .032 .050 .0036 .0128 .0164

MAGI .012 .0098 .022 .0014 .0010 .0024

Rati o 1.50 3.3 2.3 2.6 13. 6.8

50
Table XII. Comparison of AS and FP Gamma-Ray Reduction Factors.

Structure #5

(On first story at a height of 3 feet above the floor)

Air Secondaries FP Gammas

Stories All Stori es All

Wal 1 s

:

Story 1 Story 2 3-9 IJal 1 s Story 1 Story 2 3-9 Wal 1 s

NBS .165 .077 .0 .242 .233 .027 .0 .260

MAGI .165 .041 .019 .225 .179 .009 .002 .190

Ratio 1.00 1.88 0.0 1.08 1.30 3.0 0.0 1.37

( In basement at a depth of 9 feet below the basement ceil i ng)

NBS .073 .0 .0 .073 .0290 .0 .0 .0290

MAGI .039 .013 .007 .059 .0080 .0014 .0008 .0102

Ratio 1.87 .0 .0 1.24 3.62 .0 .0 2.84

51
Table XIII. Comparison of Neutron and Secondary-Gamma Reduction Factors

Calculated by MAGI and NBS for Benchmark Structure #4.

Roof Source

First Story Detector

Neutrons Secondary Gammas Sum

MAGI NBS MAGI NBS MAGI NBS Rati o

Refl ected .0990 .126 .0302 .0378 .1292 .164

Unrefl ected .1117 .124 .00820 .0108 .1199 .135

Sum .2107 .250 .0384 .0486 .2491 .299 1.2

Basement Detector

Refl ected .0377 .0322 .0122 .0097 .0499 .419

Unrefl ected .0172 .0313 .0076 .0114 .0248 .0432

Sum .0549 .0640 .0198 .0211 .0747 .0851 1.1

Window Source

First Story Detector

Refl ected .0657 .0852 .00795 .0255 .0737 .1203

Unreflected .0226 .0566 .0 .0 .0226 .0566

Sum .0883 .1418 .00795 .0255 .0963 .1975 2.0

Basement Detector

Refl ected .0119 .0175 .00273 .0060 .0146 .0235

Unrefl ected .00432 .0173 .00477 .00121 .00909 .0185

Sum .0162 .0348 .00750 .0072 .0237 .0420 1.8

52
Table XIII. (Continued)

Wall Source

First Story Detector

Neutr ons Secondary Gammas Sum

MAGI NBS MAGI NBS MAGI NBS Ratio

Refl ected .0246 .0524 .0113 .01574 .0359 .0681

Unreflected .0152 .0403 .00222 .00620 .0174 .0465

Sum .0398 .0927 .0135 .0219 .0533 .115 2.2

Basement Detector

Refl ected .00915 .00697 .00554 .00209 .0147 .00906

Unrefl ected .00112 .00688 .00225 .00392 .00337 .01080

Sum .01026 .01385 .00779 .00601 .0181 .0199 1.1

All Sources

First Story Detector

Refl ected .189 .264 .0494 .0790 .238 .343

Unrefl ected .150 .221 .0104 .0170 .160 .238

Sum .339 .485 .0598 .0960 .399 .581 1.5

Basement Detector

Refl ected .0588 .0567 .0205 .0178 .0793 .0745

Unreflected .0226 .0560 .0146 .0165 .0372 .0725

Sum .0814 .1127 .0351 .0343 .1165 .147 1.3

53
Table XIV. Comparison of Neutron and Secondary -Gamma Reduction Factors

Calculated by MAGI and NBS for Benchmark Structure #5.

First Story Source

Neutrons

MAGI NBS

Secondary Gammas

MAGI NBS

First Story

Total

MAGI NBS

Rati o

Refl ected .157 .248 .026 .074 .183 .334

Unrefl ected .106 .196 .0 .0 .106 .184

Sum .263 .444 .026 .074

Basement Detector

.289 .518 • 1.8

Refl ected .041 .032 .011 .0095 .052 .041

Unreflected .012 .031 .006 .0027 .013 .034

Sum .053 .063 .017 .0122

2-9 Story Source

First Story Detector

.070 .075 1.1

Refl ected .047 .017 .011 .006 .058 .023

Unrefl ected .021 .029 .010 .002 .031 .031

Sum .068 .046 .021 .008

Basement Detector

.089 .054 0.5

Refl ected .0106 0 .0038 0 .0144 0

Unrefl ected .0054 0 .0053 0 .0107 0

Sum .0160 0 .0091 0

All Sources

First Story Detector

.0251 0 0.0

Refl ected .204 .265 .037 .080 .241 .345 1.4

Unrefl ected .127 .225 .010 .002 .137 .227 1.7

Sum .331 .490 .047 .082

Basement Detector

.378 .572 1.5

Refl ected .0516 .032 .015 .0095 .067 .041 0.6

Unrefl ected .0174 .031 .011 .0027 .028 .034 1.2

Sum .0690 .063 .026 .0122 .095 .075 0.8

54
LIST OF FIGURES

Fig. 1. Angular coordinate systems: The angle 3 is the polar angle with

respect to the original source-detector line. The angular distribution from a point source is averaged over all azimuthal directions <j> to form a ring source. Angular distributions are rotated to ( e ,

)

polar and azimuthal angles for radiation incident on the roof, and

to (’p,<p) polar and azimuthal angles for radiation incident on the

wal 1 s

.

Fig. 2. Initial gamma ray barrier factors.

Fig. 3. Initial neutron and wall secondary gamma barrier factors.

Fig. 4. Overhead geometry factor, air secondary gamma rays.

Fig. 5. Overhead geometry factor, fission product gamma rays.

Fig. 6. Overhead geometry factors, neutrons.

Fig. 7. Overhead geometry factors, wall capture gamma rays.

Fig. 8. Wall geometry factor G 1} air secondary gamma rays.

Fig. 9. Wall geometry factors G 1? fission product gamma rays.

Fig. 10. Wall geometry factor G

L

, neutrons.

Fig. 11. Wall geometry factor G 1S wall capture gamma rays.

Fig. 12(a). Detector on same story as radiating walls: geometry factors for

upper and lower solid angles are added.

12(b). Detector on story below radiation walls: geometry factors for

upper solid angles are subtracted. Solid angle fractions such as may be determined by exterior building.

55
Fig. 13

Fig. 14

Fig. 15

Fig. 16

Fig. 17

Fig. 18

Fig. 19

Fig. 20

Fig. 21

Fig. 22

Wall geometry factors G

2

, air secondary gamma rays.

Wall geometry factors G

2

, fission product gamma rays.

Wall geometry factor G

2

, neutrons.

Wall geometry factor G 2 , wall capture gamma rays.

Mutual shielding geometry factors MR for roof and M«. walls.

Si n 4> o •or

Neutron reflection factors p for sidewalls and p e for end walls.

Data for estimating attenuation factors in ceiling, air secondary

gamma rays.

Data for estimating attenuation factors in ceiling, fission product

gamma rays.

Plan and elevation views of benchmark structure with basement

ceiling and windows on two sides.

Views of benchmark structure 5. Figures a) and b) represent

elevation and plan views, respecti vely . Dots represent detector

points.

56
Fig. 1. Angular coordinate systems: The angle 3 is the polar angle with

respect to the original source-detector line. The angular distribution from a point source is averaged over all azimuthal directions <p to form a ring source. Angular distributions are rotated to (e,<j>)

polar and azimuthal angles for radiation incident on the roof, and

to (ip,<p) polar and azimuthal angles for radiation incident on the

wal 1 s.

57
1 2 3 4 5

X, Feet of Concrete

Fig. 2. Initiai gamma ray barrier factors.

58
0 1 2 3 4 5

X, Feet of Concrete

Fig. 3 Initial neutron and wall secondary gamma barrier factors
Fig. 4. Overhead geometry factor, air secondary gamma rays.

60
(x> co

r-:

to

in

<t.

to

in

oj

in

_ohds

to

in

mm

.0 2

.01 5

.0 I

.01 .02 .03 .05 .07 .09 1.5 .2 .3 SOLID ANGLE FRACTION

.5 -7 .9

Fig. 5. Overhead geometry factor, fission product gamma rays.

61
Solid Angle Fraction, co

Fig. 6. Overhead geometry factors, neutrons.

62
G (X, Cl)

F ‘d* 7. Overhead geometry factors, wall capture gamma rays.

63
Fig. 8. Wall geometry factor G

x

, air secondary gamma rays

64
Fig. 9. Wall geometry factors G 15 fission product gamma rays.

65
Fig. 10. Wall geometry factor G

1

, neutrons.

66
Fig. 11. Wall geometry factor Gj, wall capture gamma rays.

67
G(Wu)

+ G(OJ^)

(a)

Fig. 12(a). Detector on same story as radiating walls: geometry factors for

upper and lower solid angles are added.

G(Wu') - G(WU )

(b)

Fig. 12(b). Detector on story below radiation walls: geometry factors for

upper solid angles are subtracted. Solid angle fractions such as

ojy may be determined by exterior building.

68
.01 .015 .02.025 .04 .06 .08 .1 .15 .2.25.3 .4 .5 .6 7.8.91.

sin d>

rn

Fig. 13. Wall geometry factors G

2

, air secondary gamma rays.

69
Fig. 14. Wall geometry factors G

2

, fission product gamma rays.

70
G2 (sin <t> 0 )

Fig. 15. Wall geometry factor G

2

, Neutrons.

71
sin ct>0

Fig. 16. Wall geometry factor G

2

, wall capture gamma raus.

72
Fig. 17. Mutual shielding geometry factors M^ for roof and

walls. Data for mutual shielding estimates.

M

s

=

si n ,}>, for

73
Fig. 18. Neutron reflection factors p for sidewalls and pe for end walls.

74
AIR

SECONDARY

GAMMA

RAY

ATTENUATION

Fig. 19. Data for estimating attenuation factors in ceiling, air secondary

gamma rays.

75
FISSION

PRODUCT

GAMMA

RAY

ATTENUATION

Fig. 20. Data for estimating attenuation factors in ceiling, fission product

gamma rays.

76
(PLAN)

84’

64’

tzzrzD r 1 WINDOWS 0.6 OF LENGTH

(ELEVATION)

X0 = 57 psf

lr t u

Fig. 21. Plan and elevation views of benchmark structure with basement

ceiling and windows on two sides.

77

67

psf
* 10

’

4 10

’

t ~r

10

’ i

10

’ ~r~

10

’ _L_

4 10

’ _i

4 10

’ 4^

10

’

4

64’

(b)

Fiq. 22. Views of benchmark structure 5. Figures a) and b) represent

elevation and plan views, respectively. Dots represent detector

poi nts

78
APPENDIX A

Sources of Data for INR Computer Codes

INRG5

Barrier Factors L.V. Spencer NSE 57_, 129-154 (1975) Table X Geometry Factors L.V. Spencer op cit , Tables XIV, XV, XVI, XVII,

XVIII, and XX

INRN5

Barrier Factors L.V. Spencer (unpublished) 1 ft concrete = 146.6 pst

Geometry Factors L.V. Spencer (unpublished) Tables

Duct Reflection Factors L.V. Spencer (unpublished) Graphs

Mutual Shielding Factor L.V. Spencer (unpublished) Graphs M0 , m

K S

79
APPENDIX 8

TREATMENT OF MUTUAL SHIELDING FOR NEUTRONS

The present version of the code assumes that the mutual shielding factor

for a wall or roof is determined by the m and M^ curves generated by Spencer

(fig. 17). The solid angle subtended by open space in the upper hemisphere is

determined for the exterior walls and the roof. A table-lookup for each solid

angle is used to find some response for the walls (m ) or the response for the

roof (M ).

The following steps are included in the subroutine NMSHLD:

1. If the mutual shielding input index IMS < 0 the mutual shielding

factor for the walls is set equal to 0.5 and that for the roof is

0.58.

2. If IMS > 0, solid angle fractions are determined for each of the four

walls at a point at detector height on the outsi de wal 1 . The solid

angle fraction is calculated on the center line of a hypothetical

horizontal area twi ce the size of the actual open horizontal area

next to the side of the building. The field length is assumed to be

symmetrical about the vertical plane perpendi cul ar to the wall and

including the detector point. The mutual shielding factor is set

equal to 1/2 of the solid angle fraction.

3. To determine the mutual shielding factor for radiation incident on the roof, the maximum height HMAX of nearby buildings is first

determined. If the height on any side is less than the roof height,

the distance to the nearest building is arbitrarily set at 1000 ft.

Otherwise, the unobstructed solid angle is projected onto a horizontal plane at level of HMAX. In this plane the width X of the

clear field of view is determined by similar triangles, as shown in

figure 8.1.

30
X Y + WM

(HMAX-HR) = HM - HR

Fig. B.l

4. Solid angle fractions are then calculated for the four quadrants

around the detector point on the roof, as shown in figure 8.2.

€j = Xj/Xi + 1 Tj

j = (HMAX-HR)

5. Response functions m

s are then looked up ( INTRPR) for solid angles

subtended by detectors on each of the four sides of the building.

These are multiplied by 0.5. Response functions M

p are looked up for

each of the four quadrants surrounding the roof detectors. These four

responses are averaged and multiplied by 0.58 to obtain the mutual

shielding factor for the roof.

81
APPENDIX C

82
'

I NRG
SUBROUTINE SECTOR (IL,HU,HUR,HL,XL,W,Y)

DIMENSION Y ( 18# 2 ),QM< 4 ) , SPHI { 4

)

C EXPRESSION FOR SOLID ANGLE SUBTENDED 6Y A RECTANGLE

T AU-< A 1—2 1 * A T A N4-A /-S-/ SO~R T i A *-* 2-+--B * *2-*- J,«-GT ) / 3 . 1 41 >9

H*HU

CALL GEOM {H,XL, MUilr-5 P H 1

C SET UP Y---ARR AY- E-RO M V A L U-E-S—O-F—&NE-6HV- A NO—S I M- P HIO-G—2-0--J-* -l-,-4 J P = J +5

Y Lj y l ) ) 20 Y{ J P ,2 ) =SPHI ( J )

C EQUATE FIFTH Y VALUE TO SOLID ANGLE FRACTION SUBTENDED BY RQCF

EPS=W/XL

-TZR*-2 .*HUR—

ETA=TZP/XL

Y ( 5- >-14 = T-ALM E P-S-, E-T AO

G

C

C —C A-L CUt AT-E—5-O-L-IDAN-Ot-E—P-R-A-C-T- t&N—S 0- 3-T-E-N G E-C- aY--H_GGSr -(NGT-USEO ) TZP*2.*HL

£TA=TZP/XL

Y ( 14, 1 ) = TAO( EPS, El A

)

200 RETURN

A T€- Y-A R RA Y- F 0-R- PORTION OF WALL

L/TESTDETEC TOR PLANE < I L = 1 ) OR EXIT ( I L = 0 )

IF ( IL.EQ .0 ) GO TG 2C0

H=+i-L

CALL GEOM (H,XL,W,0M,SPHI)

C 0- 1^4—

J 1 = J +9

J 2 = J +14

Y ( J 1 , 1 ) = 0 M ( J ) 40 Y ( 02,2 ) *SPHI

(

J

)

1

84
o

o

o

c

6E0M

SUBROUTINE Gt ON (hi » X t\> to XU M > S P Hi > DIMENSION GM(4),SPHI(<t)

EXPRESSION FOP SOLID ANGLE SUBTENDED 6Y A RECTANGLE

TAUU*B)«2.*ATANU/8/SCRT(A**2 + e**2 + 1.0))/3.iA159

C CALCULATE PARAMETERS ETA AND EPS(ILON) FUR SOLID ANGLE FRACTION SUt;

C SUBTENDED- 3-Y- EACH WALL--

• DO 40 J = l,4

TZP = W IF ( J . ED . 2 • OR • J • E Q • A ) TZP^XL

X L P = XL

IF ( J. £0.2. OR. J.EC.4I XLP = to ETA=TZP/XLP

C CALCULATE AZIMUTHAL HALF-ANGLE PHI SUBTENDED BY EACH WALL

PHI*ATAN( XL/W)

IF (J.E0.2.GR.J»£G.R) PHI s AT A N { w / X L ) WP=2 .*HI

EPS=toP/XLP

REPLACE EACH WALL BY SECTION OF CYLIOER WITH VERTICAL AXIS THRU

CETECTOR POINT AND CALCULATE SOLID ANGLE FRACTION OMEGA SUBTEND

-ED BY EQUIVALENT CIRCULAR CEILING

DM ( J ) - *! .—± * 57 GB * T-A O fx P SrE T A > / a Hl

AO SPHI { J

) *S I N ( PHI ) 2 GO RETURNEND

85
*INPUTT

SUBROUTINE INPUTT ( IPR*QMTA8*5PTAB)

DIMENSION XTA8(ll),tJTA6<ll*A)*ZTAB(6)*aMTAB(ll},SPTAB{ll),GTA6l6,

1 11,6) rYTABMl-»2 ) - DIMENSION XL ABEL ( 16

)

COM MC-W-XRA-X,nTA a, G-lAB-*-! TAU-*Y-TA-3-*-G-T AB —

DATA XLABEL /4HG ( X** 4HGM ) R * 4HAS * 4 HG { X * , 4H0M ) R * 4HF P *4HG(X**

1 4 H0 MIW-AHAS — > 4 HG ( X * * 4 Hu M ) W * 4 H-PP * 4ttG-2 ( X * 4H*-S IN * 4R) w A 5 * 4FIG2 i X * 4H*

2SlN,4H)wFP/

C READ IN TABULATED BARRIER THICKNESSES

READ 1» X T A 3 DO 30 1=1,11

30 XTA6 ( I ) =&S.1*XTAS( I

)

C READ IN TABULATED BARRIER FACTORS

READ* 1, ((BTA3(I,J),J=i,4),I=l,ll)

1 - FORMAT-

(

8-E-10-.-34-

2 FORMAT ( I HO

)

3 FORMAT ( 1 H—

4

5 FORMAT (3X,»XTAB , ,6X*'6(X)RAS , *5X,'8(X)RFP*,5X,*B<X)«»AS , ,5X,*B(X)*

7 FORMAT (F1C.3*1P4E12.3) — I F

( I P R » £ 0 »

0

4—00 -It}—66-

PRINT 2 PRINT 5-

PRINT 2 -D-0—5

-0 W-,-1-1 —

PRINT 7 * XTA6(I)*(8TA8(I*J),J=1,4)

5C CONTINUE

C READ IN TABULATED BARRIES THICKNESSES, SOLID ANGLE FRACTIONS* AN

C AND VALUES OF SIN PHI FOR GEOMETRY FACTORS

60 READ 110* Z T A 8 READ 110* OMTAB

READ 110* SPTA3

OMTAB ( 1 ) =1 .GE-1C

S P T A B ( 1) 1.0E-10

110 FORM A T ( 1 2F 6^ A )

C — READ IN TABULATED GtCTME TRY- FACTGRS

DC 15 0 K * 1 * 4

IF ( K— 2 ) 130*120*130

12 C READ 1 1Q»—U-G-TA6 U-*-4 I-=n-<n*4-=2-*ni ) GO TO 1

A

C

130 READ 110* < (GTAS( I* J *-R ),I«1,6) *J=1*-11 ) 1 A 0 D 0 1 A 5 1 = 1*6

IF (K»LE .2) G-TABU-*1,K.1=1^0E-16

IF { K • G T • 2 ) GTAB( I, ll*K )=I .CE-10 —IF—-(-K-»-G44-2-»-AN-6-» K .-4-4- -G-TA3-<-I-*4 l*-K-h=4 ,-Ofc-l 0

1 A 5 CONTINUE

150 CONTINUEDO 15A K = 5 * 6

READ 110* ( <GT AB( I,BrK )rri*l*cl^4«l*0)-

DQ 1 5 A I*l,fc

0-0—b5-3—*H=-7-*-i-l 153 GTAB(I,J,K)*1.0E-10

1 5 A GTA8( I*i*K )=1.0E-1C

IF (IPR.EC.O) GO TO ACO 86

PRINT 2
PRINT 165

1 60 FORMAT (23X* 1 X ( P S F

) * • # b FlOvO ) 162 F CR MAT ( 5 0 X * 3 A H ) 165 f G R M A T { i 3 X * ’QMtGA^lCX* 'SIN PHI 1 » 15 X *

1 G T A 6 < X 1)

OC- 2 50 <*1*6

PRINT 2 K i=3*K-2

K 2 3 K 1 + 2

PRINT 162* ( XL ABE U I ) * I*K1*K2

)

PRINT 3

PRINT 1 o G t 1 i A 8—

PRINT 3 OC: 250 -j = i* 11

PRINT 17 3* QMTA3(J)*SPTA3(J)*(GTAe<I*J*K)»I 3 l*6>

170 FORMAT ( 2 F 15 . <t * 6F10 . 4 > 250 CONTINUE

H CO RETURN

END

OMEGA • )

i

87
INNER

SUBROUTINE INNER {IP>Xfc#XIjXUE*XUI*XXLE#XXLI*XW>Xl>*XXL)

DIMENSION XE(5),Xl{5),XUEm # XUI(5),XXlE(5),XXtI(5)>XW(9),XU{9),

1 XXL {9 }

c SgT--^^^^.I-eR-- THICKS S-S—EGUAL--T-0- xEI 5 )* CEILING- THICKNESS

C EQUAL TG XUI(5)» ANG FLOOR THICKNESS EQUAL TO XXLI(5)

XW( 5 ) = XE ( 5 ) XU{ 5 ) *XUI ( 5)

XXL(0)=XxLI(5)

IF ( IP-»GT *-G4- GO—TO—SC- — — - DO 20 L*l#4

X W ( L ) * X E { L ) XU(L)=XUE(L)

20 X XL ( L4=4X4-E (L4 —

GO TO 200

• 5G IF —(IP « GT- « 1

)

—GO—TO—1GG

00 6 C L»l>4 — X W4L T—XE4 L 4*444 L ) XU(L)=XUt(L)+XUI(L)

o 0 X X tr {-fc~4®-X X L t I G 4X X L I I L ) —

GO TO 200

1-GO—X-1» -(14 = XEIil * X I41r4 —

X W < 3 ) « X W ( 1

)

X W424—X 64 2 ) Xw(4) = Xw(2)

XU( 1 ) = XUE ( 1 ) +XU44 1-4

X U ( 3 ) = X U ( 1

)

XUI24=-XU£<24

X U ( A ) = X U ( 2 ) XXL ( 1 ) = XX L H 14+-X4L 14 14—

XXL { 3 ) = XXL ( 1 ) XXL(2)=XXLE<2)

XXL ( 4 ) = X X L ( 2 ) 200—R-E4U-RN —

END

88
*INTRPS

SUBROUTINE INTRPB ( X T A B j X> 8 TAB * 2

DIMENSION XTAfl(ll)*8TA8<ll>4),B(5*2)>X(5)

C RELAXATION LENGTHS FOR EXTRAPOLATION

C RELATE K (TYPE-GF R A D I A T I ON) -AND L < INDEX OF WALL OR CVERHEAC

C TO PARAMETER J WHICH INDEXES BARRIER FACTOR TABLES

ICO DC 25C K=i,2

- OG 2 50 1 = 1, &

IF (K-*£Q. 1. A NO.L.EQ. 5) J = 1 IF (N.tw.l . AND. L.N6 .5 ) J = 3 IF (K.EQ.2.AND.L.EQ.5) J = 2 IF (K.EQ.2.AND.L.NE.5) J = A

2 CO 1=1

210 1 = 1+1

IF (I.EO.ll) GO TO 22C

IF (X{L).LT.XTAB(I>) GO TO 220

GO TO 210

C LINEAR INTERPOLATION ON x AND LOG OF BARRIER FACTOR

220 B(L#K)=EXP(AL0G(3TA3(I-I,J) )+ALOG(BTA0(I#J)/3TAB(I-l#J))*

1 (X<L > — XTABt I —1 ) )/{XTAB<I ) —X T A 3 { I -1) ) ) 25C CONTINUE

300 RETURN

END

89
o

INTPPG

SUBROUTINE INTRPG (X ,Y»G)

DIMENSION Z T A B ( 6)#YTA3(ll#2)#GTAS(c#ll#6)#Y(18#2)#Gl(ll#6)#X{9)#

1 G ( 9 * 2 ) # X T A B ( 1 1 ) * B T A 6 FI 1 *4 V COMMON XMAX,XTA3_»3TAB#ZTA6#YTAB#GTAS

C RELATE M (TYPE JF RADIATION) AND L (INDEX OF WALL OR OVERHEAD)

C T

-0- - P4FR-A M-E- T E R — K—WFFTCH— ItV-D-E-XES—G EDS MET R~Y~—f-AG TOR— T A6UrE"S—

00—450-4=1 r 2r —

DO 450 L = 1 # 9

IF DM . EOr-1-* A ‘VO , L *-€-£-« -3-)—K-=-l ir (M.cQ.2#AND.L»cQ»5 ) K = 2 IF <M«EQ*i»AN0.L»LT.5"l~R —3

IF (M.EC.2.AND.L.LT.5) K=4

Ir ( M * bO.l .AND»4.»GTi 5 ) ft — —-—

IF (M.EG.2.AN0.L.GT.5) K=b

C INDEX I FOR TWO NEAREST BARRIER THICKNESSES

I *1

11G 1*1+1

IF (I. EG. 6) GO TO 2CC

1 f—( XFtFnrFrTTrt-F-A B FT-)- ) —-o-S —T 3—2-0-C

GO TO 110

200 I X=

I

I N = I — 1

C DETERMINE IF VARIABLE IS OMEGA (K.LE.4) OR SIN PHI (K.GT.4)

IF (K-4) 320# 32C# 330

320 K I =

1

GO TO 3 5

C

330 Kl = 2

C -^I.VGGX--0--«R--^Vre-^E-AR-6^T-- &M-BOA £-R—S4-N —P-H I— V AtOE-S—

350 J=1

360 J-J + l IF (Y(L#KI ) .LT.YTAB( J>KI ) ) GO TO 3CC

GO TO 260

3 CO 02*4

Jl= J-l

C TWO-WAY INTERPOLATION ON GEOMETRY FACTORS

390 CO 400 J *J1# J2

LINEAR INTERPOLATION ON BARRIER THICKNESS X AND LOG OF

- GEOME TRY FAO-TQRSG 14 J,Kl=i X P F AU GG ( GT-A-B4 I M,-4 , R 5-14AL-GG ( G4 A B F I X t K WG T A-B T I4#V »-K ) 1 1* (X (L )-ZTAB ( IN ) ) / ( ZTAfl ( IX) -ZTAB ( IN) )

)

400--GGm-T-li4G€—

C LINEAR— IN-TERPOLA-T HON- ON—tOG—Y-ANO LOG- OF-GcOMtTR Y FACTORS

IF (K.EQ.3.GR.K.EQ.4) GO T G 4 2:> G(L#M)=EXP(AL0G(G1(J1#K))+AL0G(G1(J2»K)/G1(J1#K))4AL0G(Y(L#KI)/ — 1. Y-T- A B-F J-l-t-K- 1-)-) /-A L oG ( Y l-A-c^F J 2 yR t ) / Y-T A o ( J 1 fK-I ) ) ) GC TO 450

C FOR K = 3 AND K=4# INTERPOLATE ON LGG( 1 -OMEGA)

90
<t25 YI*1.-Y(L>KI)

IF ( YIvtTiliOE-aOt Y I = 1 • OE — 1C'

Yl— !• — YT^BC J 1,K I ) IF ( Yl.LT .1 .OE-1C) Yl«i,OE-luY2*I ,-YTAB ( J2,K I ) IF < Y2.ET.1«0£-10> Y2 = I GE — 1

GC L, M) =EXP ( ALQGtGl ( J1*K ) ) + ALQG{ G1 ( J2>K ) /G1 { J 1*K ) )*ALOG( YI/ Y1 } / ALQG

II Y2/Y1 )

4 5 0 CONTINUE

RETURN

END

91
PRQGRAfl TEST ( INPUT , QUTP UT * T AP E5 * INPUT, TAP E6*0UTPUT

DIMENSION XTAd( ll),0TA6( 11,4), YTA5(I1 ,2), X(9)

DIMENSION ZTAS(6),0MTA8(11),SPTA3{11),GTA8(6,11,6)

DIMENSION R F { 5-* 2 ) * X U ( 9 ) * X X L <-9-

)

DIMENSION XLM(4),WM(4),HM(4),XE(5),XI(5),XUE(5),XUI(5),XXLE(

-1--X44d4-D4*-Wl €4-2- Q-)

COMMON XMAX,XTA8,8TA8,ZTA3,YTAS,GTA6

T BUR MAT—( 8 E lC^r 8 ) — — —

2 FORMAT (IHC)

3 FORMAT ( 1H—

4 FORMAT ( 5 X, * X • ,7X, » 8 ( X ) AS ' *8X, * 8 ( X ) FP * ) 5 -FORM A4- - {-09^-»--X^Ag--A-*-o-X-^J -34-X-W<- A S « ^-5- X *

- •-& 0X4 R f-P- « ,->X , * 84 X ) * A S * 5 X *- • 6 ( X ) * 1FP ' ) 6 F-G k M AT ( I HI ) —-—

3 FORMAT (F1G.3, 1P2E12.4)

9 FORMAT—4 2 OA 4}

READ (5,9) TITLE

WR ITE—( 6 ,-64

WRITE (6,2)

WRITE (6,9) TITLE

READ (5, 1C) I W , ID, IPR, IMS,IP,HI,HS,HT,HD,HR,FW,HIU,HIL,XL,W

WRIT E —T 6 * 1 G V I- W-*- ID , 1 P R-*-T-H S

- *- I P ,H T rH S , i-»T ,h OrHR , FW*BIU,BIL,XL*W

1C FORMAT ( 5I5,5F10.2/5F10.2) —4-0

R £ AG 4-5-,—X-t-M PRINT 45, XLM

READ 45, WM - PRINT 45, WM

RE AG—43^- HM

PRINT 45, HM

4 5 -FORM AT- ( 4-FlC-»-3-)

CALL INPUTT ( IPP,CMTA8,SPTA9)

DO 5 0 J = l,ll - YTA8 ( J , 1 ) =GMTAB ( J ) 50 YTAB(J,2) *SPTA8U)

READ (5,1) (XE(L),L=1*5)

- WRIT E ( i->-4*€4 t)- *L-l r54

READ (5,1) (XI (L) ,L=1,5)

WRITE <6d> ( XI ( L1,L*1,5)

XMAX=681.

READ (3*1) < XUE(U , L = l,54

WRITE (6,1) (XUE(L),L=1,5) —R £ A D -(5 *44—4 X U4X-L4,L=a*41

WRITE (6,1) ( XUI IL ), L*l,5

)

READ (5,1) ( XXLE (L ) , L=l,5)

WRITE (6,1) ( XXL E ( L ) , L= 1, 5 ) READ (5,1) <XXLI(L),L=1,5)

WRITE (6,1) ( XXL I (L ) , L=l,5 ) CALL IjShN-E-R— ( 14 , X€-, X4, XJjc *-XU-I>44LE ,-X-XLI , X *-XU-*-X-X-U~

CALL RFSTOR ( I W , HI , HI U, hlL , HS , HT, XL* W, X * XU, XXL , F W,

1 ID, IPR, IMS,IP,wM,riM, BO , HR*XI,-XU4, X X L I ,R £ ) 1000 STOP
*RF STCR

SUBROUTINE ft F S f 0 ft ( 1 w # HI # Erl U> HTrt > H$ #HT#XL#W# X # XU#XXL#Fw#

1 1 D# I PR# IMS# IP # WM# Him# HD# HR, XI# XU I » XXL 1# RF ) 01.HEN SIGN- XTAB< il) # 3T A6< II# 4 ) # Y< IE* 2 ) # Y T A6< 11* 2 )# G ( 9 # 2 ) * X (9)

DIMENSION ZTAo(6), GTa8(o#11#6)#3(5#2)

Q INENSIGN GP < 7 , 16,-2 ) > XW (9)

DIMENSION XMSG(4#5#2)#RF{5#2}#F{4)#XU<9},XXL19),BU(5#2)#8L(5#2)

DIMENSION X I { 5 ) # X U

I

( 5 ) # X XL I ( 5 ) # XX ( 9 ) # 3 I LB# 2)#3Uf(8>2)#6LI(5#2I

COMMON XMAX#XTAB#8TAa#ZTA3#YTAB#GTA3

TAUU»a-1=2.* AT AN ( A/e / SORT! / 3 . 1415- 9-

1 FORMAT ( I H 1

)

2 FORMAT (-1H0) - 3 FORMAT (1H } A FORM AT (5X# * X * > 7 X# * BIX ) AS* # 6 X #

8 ( X )f

P

} ) 3 FORMAT (F1C.3#1P2E12 .4)

9 FORMAT { F 10. 0# 3 FIG * A

)

DC 50 M=l# 2 OQ -50 J=l#rHlDC 50 K = l#7

50 GP(K#J , M ) = 0.0

C CALCULATE BARRIER FACTORS FOR FOUR WALLS AND OVERHEAD

CALL I N T ft P B (XT A 6 # X- # ETA 6 # 6 ) CALL INTRPb ( XT43# XU# 6TA3# 6U)

CALL INTRPB ( XT A 8 # X X t # B T A 6 » 3 L ) IF ( I P . EG .0 ) GO TO bC

CALL INT-R-P-& < X T AB # X I # BT A8# 8 I

)

CALL INTRPB ( XTA8#XUi# 61 A 3 # 3 U 1 ) CAL L INTRPB {-XT A 3 rX XL I > B T A 8 # B L R

GO TO 7b

60 DO 70 K = 1 # 2 DO 70 L = l#5

B I ( L#ft.) = I*u

BUI ( L# K ) =1 • 0

70 611 <t-rK4 = i.O

75 CONTINUE

— PR I HT—

2

PRINT 2

P-R.LN4L. 4

PRINT 2 DC- 8-C- L s 1- #-5- 80 PRINT 8, X(L)#(B(L#K)#K=1#2)

PRINT 2 ^ 00 81 L = l#5

B1 PRINT 8#-- XU(L> #-(-8C(l# K ) #K*1#21

PRINT 2

DC -8Z-L =-M 5 82 PRINT 8 # XXL(L) > (8L(L#K ),K = 1#2)

PRINT 2

DO 83 L = 1 * 5 83 PRINT B# XI (L ) * ( 3 I M #^M*=-1 ,-2 ) PRINT 2 DQ

84

PRINT 8 > XUI (L) # ( BUI ( L#K)#ft=l#2

)

PRINT 2

DO 85 L = 1 » 5

85

PRINT 8 # XXLI ( L ) # ( 6L I ( L#K ) , K = l# 2

)

CC SET PARAMETERS F ( L

)

FOR FRACTION Or PtRIMcTER OCCUPIED o

Y

WINDOWS

C I

W

x 0 NO WINDOWS# I'W = 1 WINDOWS ON ALL FOUR SICES# Iw = 2 WINDOWS

93
o

r>

o

r*>

o

C ON TWC LCNG SICES

OC 30C L

3 1>A

IF (IW.EC.C) F(L> 3 C.GIF (Iw.GT.O F(L)=FW —tf—4-£¥*£T

IF ( IW.GT.I.AND.L.EO.A) F(L) 3 Q.C

-3C0---GQNTINGE

X W ( 5 ) 3 X ( 5 )

C LOGP ON K,

-C K, 3- !

3-&Q- F* w-AL t S- OF- S A* t—S TG R Y K = 2 WINDOW WALLS GF SAME STGRY —K = 3 WIN DG W"S—Of $ AHE S TORY ~ K = A WALLS GF UPPER STORY

- K-*-5— - *-I NQ-Gw-S- -Gf~-UP--P- E-R—

S

T Gft Y- - K 3 6 WALLS GF LOWER STGRY —K * 7 *4: NGG W~5—G F—LG W"6"fc —S T G ft Y

DO A 50 K »-l-r7-

C FGR NO WINDOWS* CALCULATE- ONLY FOR- K 3 i r 4 * ANDG —IhF—4-1 WG—GE-GrGiGrGGG

310 HU=HI-3.

Fl Lr* 3-« IF (K.NE.1.AND.K.NE.4.AND.K.NE.6) GC TG 4 50

GO- TO 330 -

C —GET- &S-T- EG TG ft—HE 4&H-T—

T

G—S4G L--HE-IGRT—UNI ESS- T HE-R-G AftG NO WINDOWS

C (Iw-0) t IN WHICH CASE SET IT EQUAL TO 3 FT

320 Hl=HT-HS

HL = HS

IF (K.EQ.l) hU 3 H I-HS

3 30 IF- < K «-£G • A «-GR-cK • EG-.-54—KG * H £ +-H I G”tt S IF (K.EQ.o.OR.N.EQ.7) hL=HS-*-HIL

IF { K.EQ.l) HUR*KR-hO—

I L*C

C CALCULATE GEOMETRY FACTOR FOR WALLS BELOW OETECTOR PLANE ON FIR:

C F IRS4 -g-A-SS -IK-U- -T-WJUj- 45GG*-UGGP

IF (K.tC-.l*QR.K.-EQ.6 *0R »K £ C +-7 )— I L = 1 DO 3 AO L 3 1 > 4

LP= L+5

X W ( L ) = X ( L ) — X-X (-L ) * XI4L ) X X ( LP ) *X I ( L

)

X ( L P ) 3 X { L ) 3 A 0 X W ( L P ) 3 X ( L ) IF (K-A) 34 5 * 3 4 1 >3 4-3 3 A 1 DO 3A2 L

3 1 * 4

i p^L ^5

X W ( L ) = XU ( L ) XX (L >*-XW(L4

X X ( L P ) 3 X U I ( L ) 3A2 XWLLP )=XU<L>-

GC TO 3A5

3-4-3

-

I

- F- iK-r-Nfe-^64—G€—RT -G4-5

DO 3 AA L 3 I f A —L P-*-G+5 —

XW ( L

)

3 XXL ( L ) XX (L ) *X XL I <L > 54
XX(LP)=XXLI(L>

3 44 XW~t LP ) =x XL < t ) 383 FORMAT (I5»7F10.3)

345 If M^e-J.C) GO TG 380

IF ( K — 3 ) 36 0 *346*346

34o IF ( K » Nti 3~» A N 0“« K • N E~ *5 -* A N-t) * K-# N c • 7- T GG— T Q 3oG

C RESET VALUE OF—X w TG ZERO FOk WALLS WITH WINDOWS'

IF (IW.GT.l) GO TO 360

DC 346 L*l*4

XW(LP)=XX(L)

3 A 8 X y ( L ) = X X { L ) GO TO 380

360 X w { 1 ) * X X { 1

)

X W ( 2 ) * X ( 2 ) XW< 3 ) -XX (3

h

XW(4)=X{4)

DC 370 L

a l*4

L P 3 L +5

370 Xw(LP)=XW(l)

C CALCULATE Y—ARRAY

380 CALL SrCTQR (IL*HU*HUR*hL»xL*W*Y)

361 FORMAT (2F10.3)

C CALCULATE GEOMETRY FACTORS A6QVE DETECTOR PLANE

CALL INTRPG (Xw*Y»G)

IF (K»GT«1»AN0« K-» L T • 64 GO —TO 365

C CALCULATE GEO MET R--Y- FACTORS 6 c L 0 W DETECTOR PLANE

GO 362 4*1*4

LP=*L +9

DO 382 M * i * 2

3 82 GP( K*LP*M)=1.-Y 1 1 P * 1 ) **

3

3 6 5 DC 390 1 = 1*9

DO 390 M = 1 * 2 - 390- GP ( K-rl *M ) IF (IPR.EQ.O) GO TO A 50

PRINT . 3. . — .——

DC 515 L= 1* 9

IF (L.E 0 .4 1 PRINT 520

IF (L.EQ.6) PRINT 521

1 f. -44-*4 E > 5 ) J a-1- IF (L.GT.5) J =2

515 PRINT -4W{LT^Y44^44^LG^L^M4^M = ir2)”

PRINT 410* GP

410 FORMAT 4?-Fl-0*-4)

450 CGNTINUE

-520- F 04M A-T- fi x- G M-tHGA- G4 X rG M ) -AS G ( X , Ort > F P * ) 521 FORMAT (* X SIN PHI G 2 ( X , S I N ) AS G2(X*SIN)FP'

IF (IMS) 5 1 60 r 6 1 50* 5 1

6

5150 DO 517 M = l,2

DO 517 J * 1 * 4

DO 516 L = 1 > 4 516 XMSG( J* L* M >=G,

5

517 XMSG( J ,5*M ) =C . 85

GO TC 500

518 CALL GMSHLD { W M , HM * X L * W * HD * H I * H I U * HS * HT * HU R » X > Y * G P * I W

1XMSG)

95
5 CO DO 551 M=l,2

C CALCULATE REDUCTION FACTOR FOR ROOF

530 RF( 5,M)=5(5,M)*GP(1,5,M)

R F ( 5^ML=<-F4 = 3-G-(-l-,--5-,-M-)

I F (ID.EQ.C) GO TO 551

C CALCULATE REDUCTION FACTOR FOR WALLS

5 AO DO 550 L = 1 ,

4

LPP =L +9

C StFl* 6-f L y f0< & 5^G iHl ,L,M)A6P(1,LP,M) >

1

* XM S G ( 1 , L , M >

1 +.85*F(L)*<3nL,M)*GP(3,L,M)*GP{3,LP,M)-6(L,M)*GP<2,L,M)*GP(2,LP,

2 M l ) *-XHSG<-£rt-r*U

C SU = C SU1 +C S U2

IF —( I0.LT-r21 -€-Sl>s 0»0

CSL a 3(L,M)*(C.15*GP(i,LPP,M)*GP(l,LP,M}}

CSL a C.5*CSL

IF (ID.LT.3) C S L = C • 0

CS = C-SU+C$-LC U1 a

2 +. 85*8U(L,M)*(GP( 4,L,M>*GP<4,LP,M)-GP{1,L,M) *GPf 1 1 L P~,M ) ) 1*XMSG(3,L,M)

CU2*0. 85*F ( L )

3 (3UI(L,M)*(GP( 5,L,M)*GP(5,LP,M)-GP 13,L,M) *GP(3,LP,M))

A -84H L ,-M !*(-£ P4 A-> L r M ) *G P ( 4> L P , G~P-( IrLrT. >*&P< 1, LP,M > > h

5*XMSG( A, L,M ) CU=CUlr*CU2

IF (ID.GE.5) CU a O.O

5 +«15*8l(L,M)*(GP(6,LPP,M)*GP(6,LP,M)-GP(l,LPP,M)*GP(l,LP,M))

6- + ,-15*F< L

)

* ( B L I ( Lrft Y± GCrP-(-7 y L PP , WftTt L F, M- T-GP i 1 , Lf P rfU*GNlHF»«

7 ))-BL(L,M)*(GP(c,LPP,M)*GP(6,LP, M >-&P (i,LPP,M)*GP(l,LP,M)))

C L=0 • 5*CL

I F ( ID.LT .A. OR. ID.GT .5) CL=0.G

C PRINT 1050, C$U1,CSU2,C5L,C41,CU2,CL,3U<5,M),&L15,M),XMSG(2*L*M)

1050 FORMAT (1P9E10.2)

Rf l-L^-ni-^-S^aU ( 5 y M ) * C U * &14 -5+# 1*-CL —

550 CONTINUE

5 51 CGNTINUEGO TO 900

600 00 650 M-1,2

DO 650 L

a 1 ,

5

6-50- -£F ( L^M4-=aU) — 900 PRINT 1 PRINT 2 PRINT 920

00 915 L = 1 ,

5

PRINT 910, X ( L ) , ( RF ( L,M ) ,M =1,2 ) 910 FORMAT (FIG. 0^1 0 X^iR2 £ 10-»-2 T- 915 CONTINUE

920 FOR MAT—(-•— -X— RF—AS- «F-FP')-

RETURN

END

96
0

0

0

0

0

0

0

*G,1SH|_D

Subroutine g m s h l o t w m t h m> x l t w t ~h o » h i > h i

u

* h

l

> h

t

» h u

r

» x w

y > g p

i w » i x m s w

)

D IM ENS I ON- X W ( 9 ) j GP i 7 >1 c j 2 T / XfMSirt M > 5- / 2 ) > HM( A ) > Y ( 1 8 .# 2 ) > GM ( 9 » 2 ) > YM ( A ) 1 , X ( 4 ) ,TAUMRF (A ) *G( 9,2 » * WM ( A)

C GM MON —-X M A X, X T A 6 , BT A 6 , L fAB*YTA6,GT A B

TAU( Ar8)=2.*ATAN< A/B/SGRTI a**2+6**2+1.0) T/ 2.1 A 15

9

C XMSw(l,L,M> IS Trie MUTuAL SHIELDING FOR THE SOLID wALL

C CONTRIBUTION TO CSU i IN RFSTCR)

X M S W ( 2 , L * M ) IS Trie MuluAL SHIELDING FOR THE w I NDQ W CONTRIBUTION

TO CSU

XMSW(3,L,M) IS T H t MUTUAL SHIELDING FOR Th£ SOLID WALL

CONTRIBUTION TO C

U

XMSw(4,L,M) IS Trifc MUTUAL SHIELDING FUR THE WINDOW CONTRIBUTION

TO CU

XMSW (1,5,M) IS THE MUTUAL SHIELDING FOR THE ROOF

IL*C

YM(1)*C.5*W

YM< 2

) *0. 5* XL

Y M { 3 ) = Y M ( 1 } Y M < H ) * Y M U20

DO ICO L*l#4

I F { HM ( L ) —HD ) lG,l€- r 30-

lC CO 15 M = l,2

DO 15 J = 1,M

15 XMSW( J , L, M) =0.5

-GO T G 1 GO—

30 H T E S T = ( HM ( L )-HD ) *YM ( L ) / ( WM ( L ) +YM ( L ) ) HU= HT-H-L - IF (HTEST-HU) 35,25,cC

35 CALL S E C T OR- - ( I L t r* T c S T , H UR ,-HL , X L v* , Y ) CALL INTRPG (XW,Y,GM)

DO - XMS W ( i,L, M ) = ( GP ( 1>L ,M } -GM ( L,M))/GP(l,L,M)/2.

IF (lw.GT.-0)

iXMSW(2,L,M)=(GP (3,L,M)-GM( L > M ) ) / GP ( 3 , L , M ) / 2

.

X MS * ( 3 *L , M ) = 0 * 5

50 XMSW{*»,L,M)=0.5

-GO TO ICO60 HU=Hi-HL

If (HT-EST^HU-) -65*65 ^&0-

65 CALL SECTOR ( IL»HTEST,HUP,hL,XL,W,Y)

CAUL INTRPG ( X*, Y*GM)

C REDUNDANT *ITH PREVIOUS LOOP, BUT INCLUCED FOR POSSIBLE

C f-UIU-R-E—CHAN-GE-S

DO 70 M = l,2

X MS W ( 1 *L * M > = ( GfM-i * L , M T-GM LL *-M-> ) / G P { 1 * L , M ) / 2 . IF ( I W . G T . G ) 1XNSW(2,L,M)-(G? L 3 , L , M ) -GM< l,M ) ) / GP ( 3, L* M } / 2

.

PRINT 1050# GP ( 3, L,M J ,G«(L, M ) , XMSWt

2

j L,M

)

1050 FORMAT UP4E10.2)

XMSto(3,L,M)=Q«5

70 XMSw<4,L,M)=0.5

GO TO 10G

80 HU*h I h H I

U

— HL

IF (HTE5T-HU) 85,85,95

85 CALL SECTOR ( I L , HT E S T-, HUR , HL , XL , w , Y > CALL INTRPG (XW,Y,GM)

DO 9 C M = 1 ,

2
XMSrf{3>L>M)*(GP(4>L*M)-GM(l*M))/(GP{4jL#fl)-GP(l>L>M))/2.

IF (IW.GT.C)

1XMS W(4*L, M ) = { GP ( 5>L>t* >-GM( L rM ) ) / { G? ( 5, L,H ) — GP ( 3> L*M ) ) IZ . 9G CONTINUE

GO TG 10G

95 OG 96 •.1=1*2

XMSW(1>L*M)=C.G

XHSwf2>LjM)^G.£-

XflSW (3>L>M)=0.0

9e- XKSWT 4^L^MO-rO—

100 CONTINUE

DE GH-kUR

DC 300 1*1,4

j-j-^ g~s T H nttft )~*“Tr&- I^YM! LT- / Gwtt { L ) + Yfl { l } > IF ( H T EST-DELH ) 220,220,240

2 20 X TO

GC TO 300

240 -X (L }—D£LH*-{ w-M ft H-YftfL h) / (HM<L )-nO)

300 CONTINUE —E-P-S^-X4 1 ) / X ( 2 ) ETA = OELH/X (2 ) T A-Un R-F Ti l—T AU( EP S r E T A > EPS = X ( 2 ) / X (

3

) tT-A *0 E L H /-XG30

TAUMRF (2 ) =TAU( E PS, ETA ) EPS = X(3) / X { 4 )

- ETA =DELh/ X ( 4 ) TAUMRF<3)=TAU<EPS,ETA)

EPS“X(4)/X(1)

ETA=D6LH/XU ) TAUNRF ( 4 ) = T A U ( E P S , t T A ) DO 400 L = 1 ,

4

Y (5# 1

)

3 T A UMR F (L ) CALL INTRPG ( X * » Y » G ) DO <*CG M = l,2

400 GM4L-*H>-*64-5-**l

DO 500 N=l,2

5 00 XMSW(1,5,M) —G »25YO»65^( GttI 1 rH ) +GN ( 2 , M > +GM< 3? M >+GM ( 4, M ) ) / GP ( 1, 5 , M > RETURN

END

98
I NR N

.

QQ
* ScC TOR

SUBROUTINE SECTOR lIL*HU.»rtUR.»rL.»XL.»*»Y)

DIMENSION Y(18*2>>aMlA)*SPHI(4)

C EXPRESSION FOR SOLID ANGLE SUBTENDED E Y A RECTANGLE

TAU(A#B)*2.*ATAN(A/a/SuRT(A**2-»-a**Z + 1.0))/3. 14159

CALL GEOM (H#XLjWjOMjSPHI)

C SET UR Y ARRAY FROM VALUES OF OMEGA AND SIN PHI

DO 20 J = 1 j A

J P = J +5~

Y ( J , 1

) =0M ( J ) 20 Y < 0 P +2 1 —S PH 1 1 JO

C tOU-ATE FIFTH Y- VALUEr TO —SO L I G~ AN G L t~F R-A £ T ION SUBTENDED BY ROOF

-E-P-S-WVXL

TZP=2.*HUR

ETA=TZP/XL

Y(5, 1 ) = T A U ( t P S > E T A )

C TEST TO SEE WHETHER TO CALCULATE Y ARRAY FOR PORTION OF *ALL

C — BELG*- OET EC TOR P L AN £ { 1 L = i ) u®- cAlT L I L = 0 )

IF ( IL.tQ.CI GO TO 2CC

H = H L CALL G E QM ( H t X- L-»-W-»GMTj-S-F-H-I-) DC AO J = i,A

0 1 = J +-9

J 2 = J + 1

A

Y(J1»1)=QM(J

)

AO Y(J2»2)=SPHI(J

)

C CALCULATE SOLID ANGLE FRACTION SUBTENDED BY FLOOR (NOT USED)

TZP*2.*HL

E T A = TZP / XL

Y(1A,1)=TAU(EPS,ETA)

200 RETURNEND
o

o

r>

* G £ 0 M SUB RiCLST TNE G E Q M

_ (• H I' » X t > w »GM>

DIMENSION GMm*SPHim

C EXPRESSION FOR SOLID ANGLE SUBTENDED BY A RECTANGLE

TAU{A,3)=2.*ATANU/B/SGRTU**2+6**2-H.0)}/3.iMlB9

C CALCULATE PARAMETERS ETA AND EPS(lLON) FOR SOLID ANGLE FRACTION S,U c C SUB-TENDtD BY cACH- WALL -

CO 40 J = l,4 - TZP * W IF U .EG.2.GR.J .tC.A ) TZP = XL

X L P = XL

IF ( J .EG. 2. OR. J .EC.V) X L ? = W ETA=TZP/XLP

C CALCULATE AZIMUTHAL HALF-ANGLE PHI SUBTENDED BY EACH WALL

Phi *ATAN ( XL / W

)

IF (J.EQ.2.QR.J. cQ» A I PH I - AT AN Or / X L ) WP*2 .*HI

£PS=WP/XLPREPLACE EACH- WALL BY SECTION OF CYLIDBR WITH VERTICAL AXIS THRU

DETECTOR POINT AND CALCULATE SOLID ANGLE FRACTION OMEGA SUBTEND

-ED BY EQUIVALENT CIRCULAR CEILING

QM { J-} ~ *1* —i-*-> 7 C-8 *T A Uf£ R- S r E- T-A-L/PH4I

AO SPHI ( J

)

S I N ( PHI ) 2 GO -R tT-LIRN

E ND
INPUTT

SUBROUTINE INPUTT ( I P R * OMT A B * SP T A0 } DIMENSION XTA3 ( 11 ) * 8TA8 ( 11* 4 ) * ZTAB (6 ) * 0MTA8 ( 11 ) * SPTAB < 11) * GTAB < 6*

i 11*6) * YTAB < 11* 2 ) DIMENSION XLA8EU18)

1

*OMRTA 844-7-)-* R T A B < 17 *4 ) DIMENSION CMSTA3(17) »XMSTAB117*2)

CGMM ON XMA XrXTA-B *B-T AM. T A 3 * Y T A»,GTAB

COMMON GMRTA6* RTA6 ,GMSTAB,XM STAS —C AT Ar -XLA84L / 4HG< X**4H&M> R* 4- HN *4HG4X *-*-4H&M )ft *4HG *A~H G ( X-*-* 14H0M) W*4HN * A HG ( X* > 4HGM ) w * 4HG * 4HG2 ( X* AH* S IN# 4H ) WN *4HG2(X*4H

C RcAO IfH T A-6-UtATE-&—BARR-f ER-THICKYit-SSES

READ 1* ( X TAB ( I 1*1 =1*6)

DO 30 1=1*6

30 XTA6-H ) *14-&.6<X4A£m

C READ 4Y- TA3UL ATEtM-BARR-I4R -f AG-TGRSREA 0 4 *44FT A4(-4*l )*4 =1 * 60 *-0 — 1*4 ) A FORMAT (6E1C.3)

B44fl- ( 1 * 2 ) * 1- .-04—40

6 T A B ( 1*4 ) sl.OE-10

4 -FG ^44-4344Cr, 30

2 FORMAT ( 1 HO

)

3 FORMAT UH--4-

5 FORMAT (3X,'XTAa , *bX* , fa(X)RM'*bX»'b(X)KG , ,6X**S{X)»<N'*6X,»B(X)^G ,

) -7 -FORMAT {FIG. 3, 1P4E12.3)

IF { IPR.EO.O) GO TO 60

PR I NT 2

PRINT 5 PRINT 2

DC 50 1*1*6

PR I NT 7*

X-TA34 I )*4B-4A 8 ( I » vl ) * J ~ 1 * 4 ) 50 CONTINUE

C READ IN TABULATED BARRIER THICKNESSES* SOLID ANGLE FRACTIONS* AM

C AND VALUES OF SIN PHI FOR GE GME TR Y -FAC TORS

60 READ 110* ZTA6

READ 110* (0MTA6(I)#I=1*11)

READ 110* SPTA8--

OMTABll ) =1 . 0 E-l

0

SPTAB(i) =1.06-10

110 FORMAT ( 12F6 .A )

C READ IN TABULATED GEGMETRY FACTORS

DO 150 K = 1 * A 130 READ 110*- ( ( GT AB ( I *G*« ) *1=4 *64*0 =4*41- )-

1 AO DO 1A5 1*1*6

IF { K • L E * 2 ) G7A4 < I *4 * K )=1 »-G4- 1-0 IF (K.GT.2) GTAB( I, 11,K ) =i .0E-10

IF { K * GT • 2 • AND • K • L E • 4-)- GT A B { I * 1 1 *K ) = 1 » 0 t—1 0

1 A 5 CCNTINUE

1 50 CONTINUEDO 1 5 A K = 5 * 6

READ —140*-- UGTAo(-I*J*K)*4=l*6)*-J=-l*6)

DC 1 5 A 1*1*6

DC 153 4*7*44

153 GTAB( I*J*K )=1.0E-1C

1 5 A GT AB { I*1*K ) =1 *CE-1C-—

102
IF (IPR.EQ.O) GO TO 260

PRINT 2 PRINT 1 o 5 160 FORMAT { 2 3 X ,

» x ( PS F 5 = * , 6F 10-.-C-

)

162 FORMAT { 5 0 X > 3 A ^ > 16 6 FOR M A T (1 0 X ,

1 0M t G A *-r 10 X- y-J

S I N -- P t4 1

1 -t 1 6 X ,

* G T A B (- X , G M t G A )

J ) I )DO 2 50 N = 1 , 6~

PRINT 2

K 2 = K 1 + 2 PRINT 1 c 2 t ( X L A 8 EL M ), I = N 1 , R ? 5 PRINT 3 P H IN T 16 0 , Z T A 8

PRINT 3

DC 230 J = It 1

1

PRINT 170# GMTA8 ( J } , SPTA3( J ) ,(GTAB ( I# J,K ) , 1 = 1, 6)

170 FORMAT ( 2 F 1 3 . A , 6 F 1 0 . 4 )-

250 CONTINUE

C READ IN DUCT REFLECTION FACTORS

2 c 0 READ 110, ( GM R T A0 ( J ) , J - 1 > 1 7 ) OMR TAB i n = i i0E-10 - READ 110, ( ( R T A 8 ( J , I ) , J = 1 , 1 7 ) , 1=1,2)

R T A 8 ( 1,2 ) * 1 • G t ~ 1 0

IF (IPR.EQ.O) GO TO ACO

PRINT 265

265 FORMAT ( 5 X ,

' QM E G

A

» , o X

,

R HQ • , A X ,

RHC- SUB-E »

) DO 3 5 0 J = 1 , 1

7

PRINT 270 , OMR T A6( J ) , ( RTAS ( J, I ) , 1 = 1, 2 ) 270 FORMAT ( F 1 5 . 4, 2 F 10 . A

350 CONTINUE

C READ IN MUTUAL SHIELDING FACTORS

A 00 READ 110, (OMSTABIJ ) , J = 1 , 1 7 ) QMS T A 8 ( 1 ) » 1 • GE— 1

0

00 420 1=1,2

A 20 READ- - 1-lOy ( X M-S TAB44*4)-,^:U 17)

XMSTA8(l,l)=i.GE-10

- XMSTA3 (1

24 = 1*0 E— 1 0

IF (IPR.EQ.O) GO TO 500

P£IN-IL^30

A 30 FGSMAT ( 5 X

,

• DM E GA ' , 9 X

, • M

S

' , 6X ,

• M R »

)

OG A5C 4*1,17

PRINT 270, OMST A8 ( J ) , ( XMSTABt J, I ) , 1=1,2 ) A 50 CONTINUE

500 CONTINUE

RETURN - END

103
* I N T R P RSUBROUTINE INTRPR (Qi1RTA8*RTA6*TAUR>RHG)

DIMENSION GHRTA3<17>*RTA3(17*2)*TAUfi(5)*RH 0(5*2)

DO AGO 1=1*5

J = 1 - 260 0=0 ±-t- J IF (TAUR(I).LT.QKRTAB(J)) GO TO 3 DC

- I F—fd-rlrWr? ) -SQ- TQ~2bO~

300 J 2 = J 01 = 0-1 —

DO 350 K = l*2

3 >0- RHG (-£**- >-=E XP { At-CG ( R-£AS+04^K44-*MrQ4-( T Aof* ( 1 1/uM &T A-eM-01

A

LOG (

R

T Afc ( Oi

12*K)/RTA3(0l*K) )/AL0G(0MRTAB(J2)/CMRTA8(Jl))

)

A 00 €6tfT-TNtf€—

RETURN

END

I-

-i
INTRPB

S UB S' GUT i N £

TMTS P s - {-XT A 3> X > BT'AfiyB')

DIMENSION XTA8(11>,STAB{11,A),8(5,2),X(5)

C RELAXATION LENGTHS FOR EXTRAPOLATION

CC RELATE K ( T Y P E~ 0 F ft a D

I

A T I £ NT Af+OL {INDEX C F

_ W A L t— OR OVERHEAD

to parameter j *hich indexes barrier factor tables

ICO CC 250 K = l,2

DO 2 50 L = I > 5 IF (K.EC.l.AND.L.EG.s) J =

I

IF ( K • lr « • I • A N D « L » N E » > ) J = A

I r {K*cO»2«AND«L»i:«t3 3 J = ^. Ir (K.EG.2«AND»£ • N £ • 5 ) J = A 200 1=1

210 1 = 1+1

IF ( I . EQ .6 ) GO TO 2 20

IF (X(L).LT.XTAS(I)} GO TO 220

GO TO 210

C LliNEAR INTERPOLATION ON X AND LOG OF BARRIER FACTOR

220 0(LjK)=EXPlALOG(3TA3( I-ljJ ) )+ALGG(3TA3(I>J ) / 3 T A B ( I - 1 > J ) ) *

1 ( X { L ) —X TAB! £ — 1) W { XT A8 ( I }— XT AB ( I-i ) > ) 250 CONTINUE

300 RETURN

END

105
* IN TRP G

SUBROUTINE INTRPG (X ,Y,G)

DIMENSION Z T A 3 { o),YTA3(ll,2),GTAB(6,ll,6),Y(ia,2),Gllll,6),X(9),

1 G( 9,2 ), XTA3 (11 ),3TA6(li,4-)

COMMON XM A X, XTA8,BTA8,ZTAB,YTAB,GTAB

C RELATE M (TYPE OF RADIATION) AND L (INDEX OF wALL OR OVERHEAD)

C T Q-- P-A R AM E-T 6 ft— K—w- Hi€++—I HD & X ES—G E 0 M € T ft -Y-f-ACT 0 ft -T A 6 L E S DO—4-5T3 M = l,- 2

DO 450 L = 1 ,

9

IF (M.EO rUrAN D-^4 *-€~G-*-S4—K-=t

IF ( M. EG. 2. AND .1 .EG, 5 ) K*2

I F" FK • 6Q • 1 • AN€r» L • t T"» 5 ) — tF*S

IF ( M . EQ . 2 . AND . L .1 T . 5 ) K=4

I F -4 M-, &G-. I. AND .0 . GT » 54- K-^5

IF ( M. E0.2 .AND .L .GT. 5 ) K*o

C INDEX I FOR TWO NEAREST BARRIER THICKNESSES

1 = 1 110 1*1+1

IF ( I.E0.6) GO TO 20C

I F— < X-FF4 . L T . ZT A 8- FI H GO -TO—2GO

GO TO 110

200" IX*-I—

IN* I—

1

C DETERMINE IF VARIABLE IS OMEGA (K.LE.4) OR SIN PHI (K.GT.4)

IF (K-4) 320, 320,330

3 20 K I* 1 GO TO 350

330 KI=2

C — I NOE X— -J—F-Gft— I WO—N-E-ARE ST—&ME-&-A- OR SIN PHI VALUES—

350 J*1

360 J*J+1

IF (Y(L,KI ).LT.YTAB( J,KI )4- GO TO 300-

GG TO 360

3 00 J 2 = G —

Jl= J-l

C TWO-WAY INTERPOLATION GN GEOMETRY FACTORS

390 DO ACC J = J 1 , J 2

C LINEAR INTERPOLATION ON BARRIER THICKNESS X AND LOG OF

C GEGMETRY FACTORS

G1(J,44 = EXP< ALQG( GTAB < IN^J rK M + AL 0&( GT A & U X, J ,-K4 /-GT A & FI N , J , K ) 1 1*(X(L)—ZTAB(IN) )/(ZTAB(IX) — ZTAB(IN) ) ) 4 00—C- QN-T tNU £-

C LINEAR- IN-TERPGLAT IQ* -ON- LGG-Y- AND-LOG OF GEOMETRY FACTORS

IF ( K-«rE 0 . G-* GR-*Kr*-F Q *-4G- GO- T 9- 4-2 5- G(L,M)*£XP(AL0G(G1(J1,K) > + ALCG(Gl(J2,K )/Gl(Jl,K) )*ALQG(Y(L,KI) / 1YTAB(01,K I ) T7AL0GFYTA6 ( J2^K-I l-AY TA&-FJ 1H4-I ) 1

)

GO TO 450

C FOR K = 3 AND K=4, INTERPOLATE ON LOG ( 1-0 MEGA

)
4 2 5 YI=I.-Y(L>KI)

IF ( Y I . L T ; 1 « 0 £ - 1 0 ) Y1 = i .Ct- i t/~

Yl=l.-YTAB( jl,KI )

I F { Y 1 .t T * 1 .Or-i€- )—Y 1 = 1.0 1- 1 6-

Y2=l .-YT45{ J2,K I

)

— - I f { Y 2 « L T .1.0 c “ 1

0

F -Y2 = i.GE — 1 C~ G{L,M}=EXP(AL0G<Gl(Jl,K)) + ALQG{GiU2>*)/GlUl>K))*ALQG(YI/Yl)/AlCG

I ( Y2 / Y1 ) ) A 5 C CONTINUE

R E T U R-N

END

107
INNER

SUBROUTINE INNER (iP>XE>Xl,Xot>XUljXXLE>XXLI>XWiXU*XXL)

DIMENSION XE<5)>XI{5)*XU£(5)*XUI<5)*XXLE(5)>XXLI(5)*XW(9>>XU(9),

1 X X L { 9 >

c —S E-I—R Q-QF— &A-R R i-S k T H-IC

NE-S-S-- E-GU- At—I G--X-E t 5 t*—C £ I L IN G ?

H

ICKNESS

C EQUAL TO XUI ( 5 ) > AND FLGCR THICKNESS EQUAL TO XXLH5)

X W { 5

)

3 Xt < 5 ) XU4-5 l^UT(^)

XXL (5 ) = X X L I ( 5 )

C FOLD CEILING INTO UPPER STORY * A L L S AND

C F LOOP—IN TQ- t'Oir€R‘“S"TQft'Y_ WALLS “POP NEUTRONS AND N — G A ME A

S

IF I IP.rGT,G4-GG- TQ- >0

DC 20 L=l, A — <44->4(4 <44—- — —

XU(L ) = XU E (L ) + XUI <5)

_ A>V| [1 )rvy| P(| 1 + * X 1 T X l - - A w t t. r AAuL\tl T AALity/

XUI(L)=XUI(L ) + X U I l 5 ) s C\ **11 / LI-**! I/I l V i_ I l

S'. V t. v A A L i i L / AALi\L/ T rtAti\>/

GO TO 200

50

If- HR.GT.14- GG TO 10GCO 60 L 3 1 > A

X W ( L T* X6 ( L ) + X[(LI

XU(L)=XU£(L)+XUI(L)*XUI(5)

XXL ( L ) 3 XXLE<LH-XXLI<LH4<XL 1(5 ) XUI (L ) = XUI (L )+XUI( 5)

60 X XL I ( L > = XXL I ( L ) + Xx L I <-54-

GO TO 200

100 X W ( 1 1 = X E <14 ^X44-1- )

X W ( 3 ) = X W ( 1 ) X W ( 2 ) = X£ 124—

X W < A ) 3 X W ( 2 ) XU( 1 ) = XUE ( 14 + XUI ( D + XUK4}

XU( 3

) = X U ( 1)

X-Uf24*-XU 6 ( 2 ) + X U 1454

XU( A ) * XU ( 2)

xuim«xuim*xui<5>

XUI ( 3 ) = X U I ( 1)

XUI t24*XU-I t2 1*XUI ( 5 ) —

XUI ( A

)

3 X U I (2

)

XXL ( 1) = XXL£C1 ) +XXLI l 14* XXL 14 5 ) XXL(3)*XXL<1)

XXL(2)*XXLE(2)+XXLI454

XXL ( A) »XXL 12

)

XXL 1414= X_X L III 1*XX Lit 54

XXL I ( 3 ) = XXL I ( 1

)

X XL I ( 2 ) 3 XXL I < 2 ) * XXI It 54

XXL I ( A ) = XXL I (2 ) 200 RETURNEND

108
o

o

*RF S TOR

5 UB ROUT I N E R F S TOR- i I to >~FFI , Hi U HS > Pi T , HUR , XL , W , X , XU, XXL,Fw,XMS

1 ID, IPR, IP, HR, HD,XI, XUI, XXL I,RF

)

OIMENS ION XTA3I ii),8T-AallIr4i,Yi 18, 2},rTAB<ll,2>,G<9,2),X{9)

DIMENSION Z T A3 ( 6 ) , G T Ad ( 6 , 1 i , 5 ) , b ( 5 , 2 ) -OIMENS I QN--DP { 7,-18,- 2 ) , X to < 9 > ,C 3 R ( 49 , C UR ( 4 ) ,CLR ( 4 ) DIMENSION RF(5,2),XMS(5,2),F{4),XU{9),XXL{9),8U{5,2),dL(5,2)

1 , GMR-T A B { 171 ,RTA3(17,2)»TAUR{~),RHC{5,2)

DIMENSION XI ( 3 ) , XUI (5 ) > XXL I (5 ), XX (9 ) , 3 I ( 5,2 5 , BUI ( 5,2) , BLI ( 5,2

)

C GMM-GN—X-w A X-rX-T-A 3r8TA3,-ZTA»,YTAB,GTAtf

COMMON QMRTAB, RTAB, OM STAB, XM STAB

TAU{A,3> = 2.*ATAN<A/3/SGRT{ A**-2 + 3**2 + i , 0 ) ) / 3 *14159- -

1 FORMAT ( 1 H 1

)

2 FORMAT (1HC)

3 FORMAT ( iH ) 4 FORMAT <5X, I X'»7X, , 8(X) N‘,8X,‘5{X> G»)

8 FORMAT ( f 10.3, 1P2E12.4)

9 FORMAT (F10.0, 3F1C.4)

DO 50 M 3 1 ,

2

DO 50 3*1,18

DO 50 K = 1 ,

7

50 G P ( K , J , M ) = C.D

C~ — CALCULATE 3 A R k I € R -FAC TOR 5 ~FCk~ r 00 R WALLS AND OVERHEAD

CALL INTRRB I X T A B, X, BT AS , 8 ) CALL INTRP& { xTAS,XU,6TA3,&U)

CALL INT R ? 3 ( XTAB, XXL>BTA3,8L)

CALL INTRPB ( X T A B , X I , B T A B, B I ) CALL I N T R 9- 6—(- X T- A B y- X U I , & T A 8 , B U~£-

^ C PRINT 999, XUI, BUI

C 9 99 FORM AT { 1 0 F 10 . 5

)

CALL INTRPB {'X T A 6 , X X L I , 3 T A E , B L I ) GO TO 75

b 0 00 70 K 3 1 ,

2

DO- 70t«T,5

BI(L,K)=1.0

BUI ( L , K > * t •

D

70 BLI ( L,K ) =1 .0

75 CONTI HUE

PRINT 2

PR INT- 2- — —

PRINT 4

PRINT- 2

DG 80 L 3 1 ,

5

80 PR INT—

3

, X ( L-4-,4 t(L>.< rZ-V

PRINT 2

0-0- ai-L = 1^5-

81 PRINT 8, XU(L),(3U(L,K),K=1,2)

P R-INT-2

DG 82 L = 1 ,

5

82 PRINT Zr- XXUL )r (-B-L PRINT 2 - DO 83 L = 1 ,

5

83 PRINT 3, Xl<L)r<84(L,K),K 3 l,2)

PRINT 2 00 84 L=1 ,

5

64 PRINT 8, XUI ( L ) , ( BUI ( L,K ) ,K=1,2

)

- -PR -IN- 1-2

DO 85 1=1,5

85 PRINT 8 , XXL I ( L ) , ( 3L I ( L,K I , K-i ^2

)

SET PARAMETERS F(L) FOR FRACTION OF PERIMETER OCCUPIED BY

WINDOWS

109
O

o

cc

c

c

c

c —€

c

c

c

c

c

IW*0 NO WINDOWS# I W = 1 WINDOWS ON ALL FOUR SIDES# IW = 2 WINDOWS

ON TWO LONG SIDES

CO SCO L = l#-4 -

I F ( I W • E G • 0 ) F ( L

) =0 •

0

IF—LI W —F-L-t )~*F"W —

IF ( I W • G T »l.AND.L»cO.^) F(L) = C«C

I- F— <-IW-« G T .l t A-M Q-»4-r-i-0-*-44—F-4~L )-=0-r-G

3 C 0 CONTINUE

.. XW-I5 > = XL5 >

IrGfrP—SN--K-#

K = 1 ROOF, WALLS GF SANE STORY

K-*2 —W-I-N-DGW- W-ALL5 OF SANE STORY

K. = 3 WINDOWS OF SAME STORY

K

- *4- - wA Lt S- OF OF FFft - S TOR-TK = 5 WINDOWS OF UPPER STORY —K-*-6-—W A L L-5—OF—L-Q W-fcR --STQFY--

K = 7 WINDOWS GF LOwER STORY

DG 4 50 K * 1 ,

7

FOR NO WINDOWS# CALCULATE ONLY FOR <=1,4# AND6

IF (IW) 32C# 31C# 320

310 HU=HI-3.

HL = 3 • IF (K.NE . 1.AN0.K.NE .4 . AND.K.Nfc-,-64 GO IQ—4-50

GO TO 330

SET DETECTOR HEIGHT TG SILL HEIGHT UNLESS THtRE ARE NO WINDOWS

( IW-=-0 )—#—1.N-- W-RI CF4 -C-A-SE— SE T IT—FCOAl TO 3 FT

320 HU*H T-H-SHL=HS

IF ( K 1)—HU* H I “Ft'S 3 30 IF ( K . EQ .4. OP .K . EC . 5 ) HU=HI+HIU-HS

—I-F IK—E-Q-6-^-OR . ft » E Q .7) HL»HL+ H 14

IF (K.EQ.l) HUR =HP-HD

CALCULATE GEOMETRY FACTOR FOR WALLS BELOW DET EC TOR - P L ANE ON FIRS

FIRST PASS ( ft = 1 ) THRU 'DO 45C LOOP

IF (K»EQ»l»bR

L P 3 L +5

-X WIL4*X (L ) XX ( L ) = XI ( L ) XX ( lP4*XKL->—

X ( L P ) = X ( L ) 340 X W ( L P ) * X ( L )- IF (K-4) 345,341,343

341 DO 3 42 L = l#-4

LP= L + 5 X V ( L 1*XU LL )

X X ( L ) * X U I C L ) XML?>*XUI < L > 342 X W ( L P ) = X U ( L

)

GO TO 345

343 IF (K.NE.6) GO TO 345

0D44^I-1#4

ft*E0.6#GR.K.EQ.7) I L

= 1

110
C IF (L.EQ.l.ANO. M.EQ.l)

C imI NT~ 9 8 &r hrtrrtrU IF (ID.GE.5) CU=O.Q

5 +.R2*BL ( L>M)* { GP

(

btLPP ,M) *GP (6*LP>M }-GP <1>LPP*M) *GP

(

l, L?>M ) ) 6 +. 42*f < L )*( 3LI (L>M ) *-{G-P f ? * L P P> M ) *GP < 7 » L P , iT) —GP { 1 y L P ? »M ) * GP ( 1 1 IP t M

7 ) )-6l (UM )* (GP lb, LPP> M)*GP ( o, LP,M )-GP ( 1,LPP,M) GP ( 1, L?>M ) ) ) IF ( rD.LT.A.OR. ID.GT.5) CL=G.C

C TEMPORARY CHANGE 7-9-86

- IF C-rtrEG-rl . ARD^-ID.LT r2 F €S ft ( l ) =GS- ( * HO { L , I )+RHG< L, 2 )

)

IF { M .EQ .1 . AND. ID.GE .2) CS R ( U =C S* ( R HQ < L , 1 ) + RHO (

L

, 2 )

( 1

. -r W )

)

C— I-F—4-t-*-£ Q-»-Lt AN0-. M-tEQ .-T-)—P R T4FT—9-8-8- *-L--*~M-*-R H-GN L *-l) *-R HG ( l r 2 ) >CSaCSR < L } IF (M.EQ.l) CS=CS+CSR(L)

C PRINT 9998, C S U > C S L , C 5 R ( t ) > R H C ( L > i > , R H 0 ( L , 2 ) C 99 9 8 FORMAT l* C S U > C S L / C S ft * R HCi > R HO

2

, = ’ , 1

?

5 E 1 2 . 9 ) IF ( M.EQ. 2 )—G S *C S+O

.

3*C S R ( L ) C ADD REFLECTION TO CON TR 8 FROM OTHER STORIES

C TEMPORARY CHANGE 7-9-86

IF (M.EQ.l. AND. ID.LT.Z) CU R ( L ) =C U* ( R HO { 5 > i ) + R HO ( 8 > 2 ) ) IF (M.EQ.l.AND. ID.GE. 2) CUR-(L ) *CU*< RH0< 5 > 1 ) * ( 1 .-F W >+RH0< 5# 2 > ) C TEMPORARY CHANGE 7-9-86

C IF (M.EQ.l) CL R (L) =Ct*-(FHO (5 , 1 I+RHO { 2 )

)

IF (M.EQ.l) CLR<L)*CL*(RHQ(5*l)*(l.-Fw)+RHO(5>2>)

IF ( M. Ew-rt)-- CU»C LH-C UR-tt > IF (M.EQ.l) CL=CL+CLR(L)

I F ( M « EQ • 2 ) C U * 0 U+G. UR Tt

)

IF (M.EQ.2) CL*CL+G. 3*CLR( L

)

C ATTENUATION IN- -CE

I

LING IS NG * INCLUDED IN WALL BARRIER

R F ( L > M ) =C S +C U + C L RF(L>M>=QF(L>M)*XMS(L>M)

C PRINT 9999 > C

S

, C 0, C L > XMS ( L » M

)

C 9999 FORMAT (

» CS*CU*CL> XMS* 1 *1 P4E 1 2 .4 ) 550 CONTINUE

551 CONTINUE

900 PRINT 1 -P RINT 2

PRINT 920

DO 915 L*l*5

PRINT 910, X(L)>(RF(L,M)#M=1,2)

9 1 C -F OR MAT { FIG .-G>4 0**-1R 2£1U. 2 )- 915 CONTINUE

92C- FORMAT (-• X , - RF-= N PF--

1000 RETURN
TEST

PROGRAM TEST { I NPUT , OUT P UT , T A P£ 5= I NPU

T

, T A

P

E6 = OU T POT

>

DIMENSION XTA3(11),8TA6(11,4), YTAB(11,2),

DIMENSION ZTAB ( 6) ,GMTAtt( lllrSPTABMl },GTA3 (6,11,6)

DIMENSION PF(5,2),XMS(5,2),XU(9),XXL(9)

DIMENSION DM S T A 8 ( 1 7 1 r X M S T A 84 17 ,2 ) —

X( 9)

DIMENSION XLM(4),WM(4),HM(4),XE(5),XI(5),XUE(5),XUI(5),XXLE(5),

1 XXLI(5),TITLfc( 20)

1

,QMRTA8(17),RTAB(17,2)

C OHM GN—

X

M A-Xr X T A B-r£4A-8-rl T A6-»-Y4A-BrG4A-B —

COMMON GMRTA8,RTA3,QMST A 8 , XMSTAB

-1 FGR.M A T- -1-8-8 10 *-3 I 2 FORMAT (1HC)

3 PGR M A T—f l Ff—

)

A FORMAT ( 5 X, ' X

» , 7X, » 3 ( X ) AS ' , 8X, 1 6 ( X ) FP •) 5 FORM A4—( 3 X , • X T A 3 • *-8 4X IF AS-*r-5- XrL&fx)fiF P- 5 X-, *-D (X )WAS»r5Xr'B(X)

1 F P * )

• 6 FGRMAT ( 1H41

8 FGRMAT (F10.3,1P2E12.4)

9 F G R M-AT - 1

F

1

0

• 0 r-3 F I 0 • 3- > 11 FORMAT (20 A4)

READ (5,11) TITLE

WRITE ( fc > 6

)

W -R- HE—

(

©-r 2 ) —

WRITE (6,11) TITLE

REA D ( >r 10) I R , I Dr I P R r I M SrI ~P~rH-4, H S , HT rHD r HR , F W , K I U >4+ 1

L

, X L , W WRITE ( 6 , 1 C ) Iw, ID, IPR, IMS, IP, HI, HS,HT, HD, HR, FW,HlU,hIL, XL,

W

10 FGRMAT ( >I-Dr 5PlG c-2-ASF10 . 21

hUR =HP

40 READ 4-5-r—XLW~

PRINT 45, XLM

READ 45, WM

PRINT 45, WM

READ 4 5 , H 4

PRINT 45, HM

45 FORMAT (4F10.3)

CALL INPUTT ( IPR ,QMTAB, SPTAB

)

DO 310 4=4,11

YTAB ( J ,1 ) = C M T A 8 ( J

)

3 10 YTAB (4,2 ) *SPTABU ) READ (5,1) ( XE (L ) , L = l, 5 ) WRITE 46^ IT ( XETL l^L-=lr^)

READ (5,1) (XI(L),L=1,5)

WR ITE ( 6> 1 ) —4XT4 L4 r-Lr* 1,-54

REA 0 (5,1) (XUE(L),L»1,5)

WRITE ( 6 rl ) —4 XUE(L)rL*1^54

READ (5,1) (XUI(L) , L = 1 , 5

)

WRIT E- Xb+14 - TXU I (- L lr L • i rl 1

READ (5,1) (XXLE (L ) ,L=1,5)

W R IT E ( br ll 4 X-X1E (4 IrL—4rP-)-

READ (5,1) (XXLI(L) ,L=1,5)

W RIT E < 6,1 4 ( X XL I ( L 1 r L -*-1,-5-)

CALL INNER (IP,XE,XI,XUE*XUI,XXLE,XXLI,X , XU, XXL)

X M A-X =6-64.

IF (IMS) 60,60,80

60 DO 7 C I«l r2 - DO 65 J * 1 ,

4

6S XMSTJrl

70 XMS(5,I)=0.58

GO TO 60D

80 CALL NMSHLD ( X L M , w M, H M , X L , W , PC , HR , X M S

)

600 CONTINUE

CALL RFSTOR ( I W , H I , H I U , H I L , HS , HT , HUR , X L , W , X , X U, X X L , F W , X M S

,

1 I D r I P- P r4P-rH«-rH-D, X WX DlrX X L 4, R F L1 1 /i
1000 STOP

END

115
NMSHLD

SUBROUTINE NMSHLO ( X LM / WM/ HM / XL / « / HD / HR / XM S ) DIMENSION XTAB(ll)/6TA8(ll/A)/ZTAB(t)/6TA3(6/ll/6)/YTAB(ll/2)

DIMENSION XLM ( 4 ) / WM ( A ) ,HM( 4) / T AUM (

5

) / X ( A ) / Y ( 4

)

DIMENSION TAUMRF{5)/XMS(5/2)/XMSP(5/2)/0MSTA8(17)/XMSTAa(17/2)

DIMENSION- CM R T A BU7 4/ R-T A 644 7 /2> T COMMON XMAX/XTA6/STA6/ZTAB/YTA6/GTA6

COMMON 0 MR T A 6 /-R4 A t3 / QMS T A-fr/

X

M S T A S — -— TAUU/B)=2.*ATAN{A/8/SGRT(A**2 + B**2+i.O))/3.1A159

C PRINT Alz XLM

C 41 FORMAT ( 1QE10*-A4

AO CO 50 J-l/A

DEL H=HM

{

j T- HD

I F (CELH) A2/A2/AA

44TAUM(44^1-,v

GO TO 50

-44—E-P5 »-2-«*WM (

- 4 H4X4M4 J-)

ETA=2**(HM ( J )-HD ) /XLM ( J } T AUM 4*4 4=4AU( EP-S/-E-T A-) 50 CONTINUE

HN-AX=-HM444

IF ( HM ( 2 ) • GT • HM A X ) HM AX=HM ( 2

)

IF (HM(A) .GT.HMAX) HM A X * HM ( A

)

YU >*€••. 5**

Y (2 ) =0 • 5 * X L vm= m

)

Y ( A ) =Y (2 ) 0£LH=-HMAX--+iR

DC 70 J = 1 » A

I F - ( HM U 4- HR 1—5 2/5 2-^-5-A- 52 X(J)=1GG0.

60- TG--70

5 A X ( J ) = DELH* ( WM( J ) +Y( J ) ) / ( HM ( J )-HR

)

70 CONTINUE

IF (DELH) AG0/ACG/10C

ICO EPS*X(1)/X(2)

ETA=DELH/X ( 2

)

TAUMRF(1)=TAU( EPS/ETA4

EPS = X ( 2 ) / X ( 3 ) ETA*DELH/-X<3-)-

TAUMRF(2)=TAU(EPS/ETA)

EPS=X( 3> /X ( A

)

ETA=DELH/X( A)

TAUMRF (3 4* T A U { E P S * £ T A ) EPS=X( A) /X( 1)

E TA-=D-ELh/ X 1 1

)

TAUMRF { A ) *TAU( E P S/ E T A —

)

A 00 TAUM(5) = 1.0

TAUMRF (5) =1 .0

CALL INTRPR- ( QM ST AB , X M S-T AB /T AUN

/

X M S ? I C PRINT Alz T A U M / X M. S

P

DO 5 00—4*4 /2-

DO ABO J = 1 / A A 60 XMS(J/I)=0»5*XMSPfJ/2)

500 CGNTINUE

IF (OELHF 520/-5-20/-&3G

520 CO 525 1=1/2 —5 2 5—X MS4 5-ri )

• =0 »-56

GO TO 20C

5 30 CALL INTRPR - ( OM S T A6 /X MST-AB-/ T AU-MRR/X MSP ) DO 550 1=1/2

5 50 XMS45/44=0*25*4 XM-S-P <4^-1 4-H4MSP4 2/ I J+XHSPI 3/4) X MS P < A^-l

)

)*0.56

116
200 RETURN

—E nO

—

117

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1 . 1 . 1 . 1 . 3.897 C.923 0.953 0.976 0.993 0.999 0- 3.C68 0.721 0.763 0.815 0.679 0.942 0

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4 5 3 646 - 337

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1 • 0 .998

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0.542

0.217

. 0500

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.952

.994

1 . 0.999

0 » 6 9 G- 0.578

0.232

. 0526

.602

. 696

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.998

1 . 0 .999

0 • 4 i 0

0.631

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723 .852

962 .993

996 1 .

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• 1 *

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.708 0.31C

.297 0.370

0663 .0862

L. 1. 1. 1. 1. i. 0.9C2 C • 9 9 4 0.996 0.998 0.999 1.0

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1

0.911

). 375 0.464 0.51

6

0.597 0.705 0.823 .2817 C . 354 0.401 0.470 0 • 5 7i 0.692

.1862 0.238 0.272 0.326 0.405 0.508 .0919 .1175 .1354 .1641 0.209 0.266

). 0 0.0 0.0 0.0 0 u -0-* 0

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) • 265 0.399- 0,449 0,529 O. 64 6—0 .-709—0 ,4-1 5 O.c 09 0.668 0.761 0.670- 0.947

) . 600 0.835 0.371 0.925 0.960 i.C l.C 1 .

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119
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NBS-114A (REV. 2«8C ) U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

4. TITLE AND SUBTITLE

1. PUBLICATION OR

REPORT NO.

NBSIR 87-3507

2. Performing Organ. Report No. 3. Publication Date

FEBRUARY 1987

APPROXIMATE PROCEDURES FOR CALCULATING PROTECTION

FROM INITIAL NUCLEAR RADIATION FROM WEAPONS

5. AUTHOR(S)

6. PERFORMING ORGANIZATION (If joint or other than NBS. see in struction s) 7. Contract/Grant No. NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE 8. Type of Report & Period Covered

WASHINGTON, D.C. 20234

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State. ZIP)

10.

SUPPLEMENTARY NOTES

[ | Document describes a computer program; SF-185, FlPS Software Summary, is attached.

11.

ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here)

In this report we discuss procedures for routine evaluation of the

protection of complex structures against the initial radiations from nuclear

detonations. We describe procedures for evaluating and combining dose

reduction factors for four radiation components: early fission product gamma

rays, air secondary gamma rays generated by neutron interactions in the air,

neutrons, and wall capture gamma rays generated by neutrons through

interactions with nuclei in structural materials. We describe computer codes

developed to evaluate reduction factors for each of these components. The

radiation field in the vicinity of the structure was generated for a 30°

elevation angle for the detonation, as well as a "ring source" averaging over

the points of the compass. Comparisons are made with Monte Carlo calculations

for a series of five benchmark structures.

12.

KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

initial nuclear radiation; neutron transport; photon transport; protection

factor; reduction factor; shielding

13. AVAILABILITY 14. NO. OF

Uni imited PRINTED PAGES

| | For Official Distribution. Do Not Release to NTIS

i

i Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 130

' 15. Price 20402.

,y~| Order From National Technical Information Service (NTIS), Springfield, VA. 22161 $18.95

USCOMM-DC 6043-P80
'

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