DNA 4702F

NUCLEAR WEAPON EFFECTS_" CALCULATIONS IN THE TACWAR CODE _

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Algorithms Nuclear Warfare TargetingComputer Aplications Nuclear Weapons War GamesMilitary Applications Operations Research Weapons Effects

iMilitary Operations SimulationNuclear Radiation Tactical Warfare

0 ABSTRACT -I(d,' I I .. II ll .I I hI- l-Ll h-l)

he study reviewed the accuracy of nuclear weapon effects data and algorithmsused by the IDA TACWAR theater warfare simulation computer model to makedamage evaluations. The report describes areas where improvements inspecifying the nuclear explosion-generated effects--nuclear radiation, thermalradiation, and air blast--could be made.

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PREFACE ]The authors wish to express their

gratitude for the active assistance and

cooperation of the following individuals,

without whom this investigation would have

been far less efficiently executed: Mr.

Edward P. Kerlin, Dr. Leo A. Schmidt and

Dr. Dale L. Moody of the Institute for Defense

Analyses, and Captain Randall B. Saylor (USAF)

of the Defense Communications Agency's Command

and Control Technical Center.

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TABLE OF CONTENTS

Section Page-_

PREFACE 1

CONVERSION FACTORS FOR MEASUREMENT UNITS 2

TABLE OF CONTENTS- - ----------- 3

LIST OF ILLUSTRATIONS- - ---------- 5

LIST OF TABLES- - ----------- 7

= I INTRODUCTION AND SUMMARY- - ------- 9

II DETAILED DISCUSSION OF SUBROUTINES 16

2-1 DAMEVL --------------- 16

2-2 DOSLIM --------------- 18

2-3 FN ----------------- 18

2-4 PREFN --------------- 19

2-5 QKINR --------------- 20

2-6 WRAD ---------- 35

2-7 WRADVN --------------- 37

2-8 OFFCOV --------------- 41

2-9 SIMCN --------------- 49

* 2-10 SIRCOV --------------- 53

2-11 CIRCOV --------------- 67

REFERENCES --------------- 73

Appendix

I A FUNCTIONAL DESCRIPTION OF ALGORITHMSEMPLOYED BY SUBROUTINE QKINR FORCALCULATING INITIAL RADIATION DOSES A-I

3-

TABLE OF CONTENTS (CONTINUED)

Appendix Page

B A NUMERICAL FIT TO AN ALGORITHM WHICH

COMPUTES PROMPT FISSION PRODUCT GAMMA

RADIATION DOSES ------------- B-I

C FORTRAN LISTING OF SUBROUTINE WRADVN - - - C-iI

D TABULATED COMPARISONS OF SUBROUTINE

OFFCOV WITH EXACT NUMERICAL INTEGRATION D--1

A

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! LIST OF ILLUSTRATIONS

Figure Page

2-1 Initial Radiation Dose vs Ground Range

for a I-KT Fission Air Burst (HOB = 53m). - 22

2-2 Initial Radiation Dose vs Ground Rangefor a l-KT Fission Surface Burst. ------ 23

2-3 Initial Radiation Dose vs Ground Rangefor a 10-KT Fission Air Burst (HOB = 114m). 24 °

2-4 Initial Radiation Dose vs Gound Rangefor a 10-KT Fission Surface Burst. 25

2-5 Initial Radiation Dose vs Gound Rangefor a 10-KT Thermonuclear Air Burst(HOB = 114m) ---------------- 26

2-6 Neutron Dose vs Ground Range for a 10-KTThermonuclear Air Burst (HOB = 114m) . 27 !

2-7 Air Secondary Gamma Dose vs GroundRange for a 10-KT Thermonuclear AirBurst (HOB = 114m). ------------- 28

2-8 Fission Product Gamma Dose vs GroundRange for a 10-KT Thermonuclear AirBurst (HOB = 114m). ------- ------- 29

2-9 Initial Radiation Dose vs Ground Rangefor a 10-KT Thermonuclear Surface Burst.- - 30

2-10 Initial Radiation Dose vs Ground Rangefor a 100-KT Fission Air Burst(HOB - 246m).- - - - - - - - 31

2-11 Initial Radiation Dose vs Ground Rangefor a 100-KT Fission Surface Burst. 32

2-12 Initial Radiation Dose vs Ground Rangefor a 100-KT Thermonuclear Air Burst(HOB = 246m). ---------------- 33

2-13 Initial Radiation Dose vs Ground Range- for a 100-KT Thermonuclear Surface Burst. - 34

>

,-,

A

I. *,... j

LIST OF ILLUSTRATIONS (CONTINUED)

Figure Page

2-14 Sample curve of weapon radius vs yield,for personnel. ---------------- 36

2-15 Increase in weapon radius by use ofOptimum Height of burst. ----------- 39

2-16 OFFCOV - Error in COV for TAR = 0.2. - - - - 43

2-17 OFFCOV - Error in CCV for TAR = 0.4. - - - - 44

2-18 OFFCOV - Error in COV for TAR = 0.6. - - - - 45

2-19 OFFCOV - Error in COV for TAR = 0.8. - - - - 46

2-20 OFFCOV - Error in COV for TAR = 1.0. - - - - 47

2-21 OFFCOV - Error in COV for TAR = 2.0. - - - 48

2-22 SIRCOV - Error in COV for SIGT = 0.1. - - 60

2-23 SIRCOV - Error in COV for SIGT = 0.2. 61

2-24 SIRCOV - Error in COV for SIGT = 0.3. 62

2-25 SIRCOV - Error in COV for SIGT = 0.4. 63

2-26 SIRCOV - Error in COV for SIGT = 0.5. - - - 64

2-27 The Circular Coverage Function CIRCOV 69

2-28 The Circular Coverage Function CIRCOV - - - 70

6Il

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LIST OF TABLES

Table Page

2-1 Comparison of weapon radii at optimumair burst altitude with those at the Astandard height used in TACWAR ------ 40

2-2 Comparison of SIMCN Algorithms ------ 51

2-3 Offset Circle ProbabilitiesDistance Damage Sigma (SIGT) 0.1. 55

2-4 Offset Circle ProbabilitiesDistance Damage Sigma (SIGT) 0.2. 56

2-5 Offset Circle ProbabilitiesFDistance Damage Sigma (SIGT) 0.3. 57

2-6 Offset Circle ProbabilitiesDistance Damage Sigma (SIGT) 0.4. 58

2-7 Offset Circle ProbabilitiesDistance Damage Sigma (SIGT) 0.5. 59

2-8 Offset Circle ProbabilitiesError Arising From Use of Constant0.213. SIGT = 0.4. ------------- 65

2-9 Offset Circle ProbabilitiesError Arising From Use of Constant0.213. SIGT = 0.5. ------------- 66

! 2-10 The Circular Coverage FunctionNumerical Intecration ----------- 71

A-I Values of Exponents and Coefficients Usedin Calculating Neutron and Air-Secondary ;

Gamma Ray Doses in Subroutine QKINR - - - - A-2

D-1 thru OFFCOV ------------------ D-2 thruD-33 D-34

7 '

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SECTION I

INTRODUCTION AND SUMMARY

This report documents the results of investigation

of the nuclear weapons effects module of TACWAR, a theater-

level computerized warfare simulation code*, with the pur-

pose of verifying the accuracy of its data. Periodic

checks of nuclear effects data in wargaming codes are

desirable to ensure that errors do not cause discrepancies

in the intercomparison of various models and to preclude

the propagation of erroneous results or the influencing of

decisions affecting force posture or ha-dware procurement

based on faulty nuclear effects data.

This report is not intended to stand apart from

the extensive body of TACWAR documentation. It assumes

reader familiarity with the capabilities and content of

the TACWAR code. A complete description of this code

and its subroutines is contained in the TACWAR documenta-

tion -7**

This study has investigated the accuracy of (1)

the nuclear weapon effects information contained in thedamage assessment subroutines, (2) selected algorithms tocalculate target coverage, and (3) logic in the subroutines.

The effort has rot addressed escalation criteria, priority

criteria in nuclcar targeting, or the logic of weapon

assignment algorithms.

* TACWAR was developed by the Institute for Defense

Analyses.r ** References are listed immediately following Section II.

9

' F

The following subroutines were scrutinizea in this

project:

NUC6. The master program for nuclea, damageassessment.

DtANIEVL. The main subroutine which performsdamage assessment calculations with the aidof nine called subroutines.

DOSLIM. Sets the limiting nuclear rauiationdoses to d f n "t)ools" into which personnelare p1laced, dependinu on the dose theyr-C Ce-iv'•

* FN. Calculates the range to given initialnuclear radiation doses, the boundaries ofthe pools established by DOSLIM.

* PREFN. A utility subroutine which acts asan interface between FN and QKINR, and callsQKINR to calculate the initial radiation doseat each of 23 slant ranges.

* QKINR. Calculates the dose due to neutrons,air-secondary gamma rays and fission-productgamma rays at each of the ranges specifiedby PREFN.

* WRAD. Calculates the weapon radius againstpersonnel in specified shelter postures,exposed to nuclear air bursts or surfacebursts of specified yields.

" WRADVN. Implements the Physical VulnerabilitySystem9 to calculate the weapon radius againstmaterial targets given the yield and burstheight of the weapon and the vulnerabilitynumber of the target.

* OFFCOV. Calculates the expected cuverage ofa circular target of uniform value by a wea-pon delivered at an offset aimpoint.

* SIMCN. Calculates the cumulative circularnormal distribution function.

10

|I

The following subroutines were scrutinized in this

project:

* NUC6. The master program for nuclear damageassessment.

* DAMEVL. The main subroutine which performsdamage assessment calculations with the aidof nine called subioutines.

0 DOSLIM. Sets the limiting nuclear radiationdoses to define "pools" into which personnelare placed, depending on the dose theyreceive.

* FN. Calculates the range to given initialnuclear radiation doses, the boundaries ofthe pools established by DOSLIM.

0 PREFN. A utility subroutine which acts asan interface between FN and QKINR, and callsQKINR to calculate the initial radiation doseat each of 23 slant ranges.

0 QKINR. Calculates the dose due to neutrons,air-secondary gamma rays and fission-productgamma rays at each of the ranges specifiedby PREFN.

* WRAD. Calculates the weapon radius againstpersonnel in specified shelter postures,exposed to nuclear air bursts or surfacebursts of specified yields.

* WRADVN. Implements the Physical VulnerabilitySysteme to calculate the weapon radius againstmaterial targets given the yield and burstheight of the weapon and the vulnerabilitynumber of the target.

* OFFCOV. Calculates the expected coverage ofa circular target of uniform value by a wea-pon delivered at an offset aimpoint.

* SIMCN. Calculates the cumulative circularnormal distribution function.

10

_ =- - _ .- 2 -'_ _ _ __-____ _ _ _ -

* SIRCOV. Calculates the expected coverage of acircular Gaussian-distributed target by a weapondelivered at an offset aimpoint.

0 CIRCOV. Calculates a Gaussian function integratedover an offset circle. It is eauivalent toeither the pzobability of an offset aimed wea-pon impacting a circular target, or that an off-set aimed weapon having a specified radius willhit a point target.

Detailed descriptions of the results of investiga-

tion of these subroutines are presented in sections 2-1 to

2-10 of this report. A summary of those results is presented

below*.

S- 1 DAMEVL

The portion of DAMEVL which assesses damage to per-

sonnel contains a call to WRADVN with a vulnerability number(VN) for personnel. No source for such a VN could be iden-

Ktified. An alternative method using subroutine WRAD would i

require classified input data and a rather subtle program

change to be operativc. This alternative method should be

added to the program.

In addition, weapon radii in radiation-dominatedportions of WRAD, which are based on a 450-rad lethality

criterion, when compared with the results of FN, are always

selected over those for higher radiation "states." As a

result, no targeted personnel would ever undergo transitions

to the higher states.

Finally, DAMEVL does not assess damage to military

personnel at surface to surface missile sites or at supply

depots.

1-2 PREFN

Opportunity for user input of weapon type, fission

fraction and air density has not been provided. These have

Note that not all subroutines listed in Section II are* mentioned in this summary.

!4

-M11

been fixed at fission, one-half and 1.1 x 10- gm-cm - f

respectively. Height of burst can be either 174 ft/kt' or

zero. Aside from contributing to unrealistic input data,

this inflexibility could result in errors of 20 to 50 percent

in dose at a given slant range. An error of a factor of 100

exists in the height of burst argument for calculating the

slant range, which will cause significant errors in some

ground ranges.

1-3 QKINR

Significant divergences occur between TACWAR cal-

culations and other newly calculated radiation levels at

given slant ranges. A neutron multicollision term (x 2)

has been introduced into the calculations but apparently

not into the shielding or biological response data. This

point is the subject of further investigation. The weapon

types, "fission," "intermediate" and thermonuclear" are not

sufficiently broad for force posture studies requiring the

capability to assess the possible impact of enhanced radi-

ation weapons.

1-4 WRAD

Only nuclear radiation and air blast effects are

now included in this subroutine. Thermal radiation is the

dominant lethal effect on unwarned, exposed personnel, over

a significant range of yields from nuclear sur ..-e bursts.

This effect could be incorporated in the subroutIne. Yieldinterval breakpoints, coefficients and exponents have notbeen verified.j

12

.= - - - . -I= __

1-5 WRADVNA

This subroutine now permits use of only two scaled

heights of burst, zero and 174 feet. Consequently, weapon

radii against soft targets (i.e., QVN < 10, PVN < 15) are

reduced up to 40 percent because optiumum height of burst

Acannot be utilized.

1-6 OFFCOV

The algorithm uses dimensions normalized in units

of the weapon radius. However, prior to this normalization

a lower limit to the calculation is established by setting

the coverage at zero if the weapon radius (WR) (unnormal-

ized--any units) is less than 0.001. WR should first be

normalized in units of target radius. f

In the target coverage interval between 10 and 90

percent, the accuracy of the algorithm frequently deviates

by as much as 20-30 percent from the true value. in one ex-

treme case, a numerically integrated value of 0.100 is calcu-

lated by i. algorithm as 0.186, an 86 percent error. Mot,

extreme values of coverage contain larger (percentage)

errors.

H 1-7 SIMCN

The algo-ithm used to replace the exact integra-

tion is sufficientL.y accurate in all relevant regimes of the

independent variab'. . However, another algorithm, somewhat

* simpler to implement and slightly more accurate, is

jsuggested for use. Numerous documentation errors have

*, been noted and tabulated.

13

!I

1-8 SIRCOV

This algorithm also normalizes the variables in

units of (adjusted) weapon radius. However, prior to nor-

malization, the coverage is set at zero for values of the

weapon radius (in any units) less than 0.1. A method of

normalizing this variable, making it dimensionless, is

suggested. Several documentation errors have been noted

and tabulated.

1-9 CIRCOV

The selected algorithm is accurately implemented

in the Fortran, but has discontinuities at two points in

variable-space, and other inaccuracies which produce 10-

percent errors in predicted coverage when the coverage is

in the range 5 percent to 95 percent. Outside this region

the errors rapidly increase to, for example, a factor of

two at 1 percent coverage.

1-10 RECOMMENDATIONS

Based upon analysis of the TACWAR nuclear

effects data and subroutines, the following changes or addi-

tions to the subroutines in NUC6 are reconmended:

a. Provide an algorithm for calculating dose

from enhanced radiation weapons.

b. Allow only one option, that employing sub-

routine WRAD, to calculate weapon radius for personnel

damage, and set WRAD = 0 over yield ranges where it is

radiation-dominated.

c. Update the dose calculation from initial

nuclear radiation to conform to more recent, more accurate

calculations.

14

d

d. Include a thermal option for unwarned person-

nel exposed to a surface burst.

e. Include personnel damage assessment in

surface to surface missile sites and supply depots.

f. Implement various normalizations (OFFCOV,

r. SIRCOV), an algorithm change (SIMCN), and correct the

numerical error (SIRCOV) in the several circular coverage

subroutiizas.

15 I

-- I

ii

.... I

• . *. -: I' ,

SECTION II

DETAILED DISCUSSION OF SUBROUTINES

2-1 DAMEVL

This is a multipurpose subroutine which has among

its functions the evaluation of damage to targets includ- -:

ing military and civilian personnel. As presently coded,

DAMEVL calculates personnel damage in the following

situations:

Military CivilianSituation Personnel Personnel

Battlefield x xAirbases x xSStl Sites* xSupply Depots* x

The assessment should be extended to include military

personnel at supply depots and at surface to surface

missile sites. Conversations with field-experienced army

officers as well as with members of the analytical com-

munity have confirmed our belief that trained military

personnel are important to successful operation of both

of these facilities.

Radii of effects against personnel from two dif-ferent calculations are compared: (1) calculations using

Part III of reference 8, and (2) subroutine FN. These two

calculations are referred to as methods (1) and (2) below.

* Comparison of WRAD with FN is not carried out in thecurrent version of TACWAR in assessing civilian per-sonnel damage at SSM sites and supply depots.

16

7."" t • " €

Method (1) involves calculation of weapon radiusas in reference 8 by use of a personnel vulnerability num-

ber (VN). No VN is provided, nor is any acceptable VN known

to exist. There is another option, which can be activated

by a change in coding. This option relies on power-law fits

to the curves of weapon radius against personnel in Part III

of reference 8. For a given shelter posture, weapon radius

against personnel depends on yield and height of burst.At low yields nuclear radiation is the dominant kill mecha-

nism and at higher yields air blast becomes dominant. Sub-

routine WRAD implements an algorithm which approximates

the weapon radius vs. yield curves and calculates weapon

radii against personnel in given shelter postures subject-

ed to weapons of specified yields. This will b discussed

in more detail in Section 2-6.

Method (2) uses the initial radiat aigorithmsto determine radii to the limiting dose levels of higher

radiation "states" or "pools" (see discussion under sub-

routine DOSLIM). Subroutines FN, PREFN and QKINR areexercised to determine the radii from surface ground zero

to given initial radiation doses at the boundaries of the jvarious "states." I

Weapon radii calculated by methods (1) and (2)

are compared. The larger radius is selected for calcula-

tion of target coverage. This means that transitions into

higher radiation states can never occur because for lowyield weapons the radius to 450 rad will be larger than

that for transitions to higher radiation states, and for

higher yield weapons blast or thermal radii will dominate.

It therefore seems appropriate to set weapon radius toI

17

. .. ---- _ . wl_---- " - -J_

zero in the yield intervals of WRAD when the weapon radius

is dominated by nuclear radiation.

2-2 DOSLIM

i This subroutine establishes upper and lower

boundaries of radiation states. For example, in the TACWAR

print-outs examined in this effort the following dose

levels were selected as defining radiation states.

State 1 2 3 4 5

Dose, rad 0 50 450 3000 8000 >20000

TACWAR logic allows for statistical fluctuations by placing

all personnel in the center of the dose range defining each

pool or state. Thus, exposure to 25 rad will result in

transition from state 1 to state 2, 200 rad w. L1 cause a

transition from state - to state 3, etc.

2-3 FN

This subroutine scans the array * doses calcu-

lated by QKINR as directed by PREFN, and findf the hori-

zontal range at which the dose is equal to the input value,

which is one of the boundaries of the radiation states

furnished by DOSLIM, o, i- the case of civilian personnel,

the casualty or fatality dose (250 or 450 rad, respective-

ly). Neutron and gamma transmission factors are first

applied, according to protection category date for the

personnel being considered.

FN is called only for military and civilian

targets at airbases and on the battlefield.

Iii

2-4 PREFN

This subroutine is used as a controlling sub-

routine between FN (where range to a given dose level is cal-

culated) and QKINR (where the dose level at a given range is

computed). PREFN receives input parameters from DAMEVL and

calls QKINR at each of 23 horizontal ranges and input burst 1heights for every weapon.

PREFN is uoed to provide to QKINR certain input data

which set the parameters for dose calculations. These para- it meters appear to be frozen at single values, without present-

ing any options to the user for inserting weapon-specific or

situation-specific values. Some inputs are in fact rather

unrealistic. For example, only fission weapons and 50-percent

fission fractions are presently used. Only two heights of

burst, zero or 174 ft/kti, are allowed. Atmospheric density

is set at 1.1 x i0 gm/cm. We recommend that weapon para-

meters be specified as part of the input data base and that

user options be added for air density as well.

PREFN also furnishes input on the neutron multi-

fcollision factor. This factor is presently set at 2. The

effect is that all free field neutron doses are doubled for

calculations of biological response. It appears that thefactor is inserted correctly in defining the in-body radia-tion environment, but that it must also be applied to bio-

logical response criteria which are, so far as can be, based

on free-field doses.

.4I

19

, -

One of the functions of PREFN is to calculate slant

range to the target and this appears to contain an error. As

described in the documentation IHOB is either 1 (airburst) or

0 (surface burst), and if 1, the height of burst is set at .11.74, in units of one hundred feet. Thus when calculatingslant range it appears that a factor of 100 should multiply -4

the term HBR in order to produce a correct value of slant

range to the target.

2-5 QKINR

This subroutine, which calculates the initial

radiation environment from nuclear air and surface bursts,9!was verified against the source material 9 on which it was

based, and was also compared with results of more recent

work" in the field of radiation transport models.

Calculation of dose from neutrons and air-secondary

gamma rays is a relatively straightforward process involving

spherical divergance and exponentials in slant range, normal-

ized to fit available empirical data. A rather simple height-

of-burst correction is also employed. Examples of expressions

used in the QKINR algorithm are contained in Appendix A.

The algorithms used in QKINR for the fission product

contribution were developed as a fast-running implementation

of the method of French and Mooney 9 . They are fully described

in a working paper provided by the Institute for Defense IAnalyses and reproduced as Appendix B. A functional descrip-

tion of the algorithms is also given in Appendix A.

Two routes were followed in verifying initial nu-

clear radiation environments of TA''*R:

0 Results of independeiit ("offline") use of thesimplified algorithms were compared with themodel on which they are based, and on morerecent calculations.

20

0 QKINR as received from CCTC was exercised("online") to determine nuclear environmentsdirectly.

Figures 2-1 through 2-13 contain results of off-

line calculation of the algorithms described in Appendix B

and the CCTC listing. These calculations were programmed and

executed on a microcomputer. The results have been plotted

as total initial radiation dose as a function of ground

(horizontal) range for two types of warhead design, fission

and thermonuclear. Calculations were performed for surface

bursts and air bursts at yields of 1*, 10 and 100 KT. Com-

parison standards were selected as follows. At all three

yields, data from reference 9 labeled "French and Mooney"[on the figures are shown. For 10 and 100 KT, more recent

calculations" were obtained and added to the comparison

base, labeled "Gritzner et al." In addition, the 10-KT

thermonuclear air burst was singled out for more detailed

checks of the initial radiation components, i.e., neutrons,

air-secondary gamma rays, and fission-product gamma rays,

against available references. Data were also obtained, for

Vgeneral interest, from reference 11.

The degree to which TACWAR calculations agree with

comparison standards may be observed by examining Figures2-1 through 2-13. In general, TACWAR calculations of totaldose are in fairly good agreement with the data of French

and Mooney on which they were based. This seems to be due

to balancing errors of the dose components. TACWAR is high

by a factor of two in neutron dose, but low wiCh respect to

the fission-product gamma dose. The total dose has been

* In the interest of realism, only the fission case wasrun at 1 KT.

21

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I French Moe

Ln$ ]

0 1001

I tI I

10 A

5

0 500 1000 1500 2000

0Ground Range, m

Figure 2-2 Initial Radiation Dose vs Ground Rangefor a 1-KT Fission Surface Burst.

, ,23

- v-,

1 0

- 4

L 10- rrxtzncr ItI3&

loOK

L1 F A L I- -J 2-J - -L

0 500 1000 1500 2000

,round Pan(;(,, m

iuure 2 Initial Pa iat ion Dos(, vs (;round I Rancfor a 10-MT Fission Air Burst (M1OB :114m).

24

4i. . ... r 1

i0-

lo TACWAR

110B0 114m-

A

10 -

tol

Q-

U

0 10

.4J

100

French4 Mooney

10

i0--

2,

1 . , . J __ , L, . , , l ., I

0 500 1000 1500 2000Ground Range, m

Figure 2-4. Initial Radiation Dose vs Ground Rangefor a 10-KT Fission Air Burst (HOB114m).

24

S '1S. . . .. . . . . . .. .p

, --

Gritzner et al.

TACWAR\i 0

French & Mooney

1 00

K A

I

~10

- 5 -

- 2 -

0500 1000 1500 2000

i Ground Range, m:

Figure 2-4 Initial Padiation Dose vs Ground

" Range for a 10-KT Fission SurfaceBurst.

~25

' i i0o,

* -t H

ii]

TAC WARIOB = 114m)

1 6.

II

- Gritzner et a1"

(11 = 129m) I- IS I I.6- IIN

o

100--

I French & Mooney-

L- "S I

2{.

0 500 1000 1500 2000

Ground Range, m I

Figure 2-5 Initial Radiation Dose vs GroundRange for a 10-KT Thermonuclear

Air Burst (MlOB = 114m).

26

a g

6*

. ° ..

TACWAR

10, -1= 1_

10k.

Gritzner et al.(11OB = 12m)

0

10

C

ENW

, i100 -A

i 0

A

j I

10 -

French &Mooney

2-A

S , , , , , .. , , I A A A 10 500 1000 1500 2000

Ground Range, m

Figure 2-6 Neutron Dose vs Ground Range fcr a 10-KTThermonuclear Air Burst ([1OB = 114m).

27

4A.

; I

'iACOAR and

-10

0 French & Mooney

GritznerOI

0

I~LI

10

o -

2

0 00 --

fI0*Figure 2-7 Ai-eodr 2am Dsev Ground.4

10 fo ae

2-8

0.-=

A

io'

* •

S| -

~~Gritzner

S1 0 r-n- & Mooney *

o -

U,!

10

i 2-

0 500 1000 1500 2000! Ground Range, m

, S

SFigure 2-8 Fi'ssion Product Gamma Dose vs Ground

Range for a 10-KT Thermonuclear Air-;" :";.... .Burst (tlOB = 114m).

29I

\TACWAR

101

Gritzner et al.

C010

0

100 French Mone

10-

5-I

2-

1. T

050 0~ 0 2500 2000

Ground Range, m

Figure 2-9 Initial Radiation Dose vs Ground4R~ange for a 10-KT ThermonuclearSurface Burst.

d 301

fI

10

FI

TACWAR=I'i = 246m)

'I I

P Gritzner et al."o (II = 278m)

' I

010 3

Frnc &o Mone

10

i "I

[15F 5

2r

500 1000 1500 2000 2500 3000

Grofmnd Range, m

Figure 2-10 Initial Radiation Dose vs Ground Rangefor a 100-KT Fission Air Burst (IOB =

246m).

3114 :

I'I

i-

l05Gritzner et al.

lot

10 -

TACWAR

rench & Mooney

'10

0

100

10

2

500 1000 1500 2000 2500

Ground Range, m

Figure 2-11 Initial Radiation Dose vs Ground Rangefor a 100-FT Fission Surface Burst.

32

-ad

'77

105 TACIJARCH =246m)A

10 Gritzner et al. f

(11 278m)

in French &Mooney

(!=246m)

0

100 q

10

5 A2

500 1000 1500 2000 2500

Ground Range, mn

Figure 2-1-. Initial Radiation Dose vs Ground13an(i for a 100-KT ThermonuclearAil- urst (HOB =246mn).

331

TACWAR

10 1

Gritzner et al.

French &Mooney

101

0I14

-i0 i

0J

E40

100

10

5

2

500 1000 1500 2000 2500

Ground Range, m

Figure 2-13 Initial Radiation Dose vs Ground Range

for a 100-KT Thermonuclear SurfaceBurst.

34

' I• , -. .- , .%. A .

Vresolved into its component parts (i.e., neutrons, air-

secondary gammas and fission-product gammas) for illustrative

purposes in Figures 2-6 to 2-8.

Online calculations of these cases were performed

using QKINR on the S3 Univac 1108, and were found to be iden-

tical with the offline calculations.

None of the existing weapon types in QKINR addresses

the enhanced radiation (ER) warhead. The neutron spectrum of

the ER is sufficiently different from that of fission or

thermonuclear weapons that a separate weapon type should be

included in QKINR. Use or ER warheads is being studied at

many levels in the DOD, and it would appear to be prudent to

include an ER weapon in the calculations to allow inclusion a

of the ER within the scope of TACWAR studies.

2-6 WRAD t

This subroutine calculates the weapon radius due to

blast (or radiation) against personnel located in one of eightprotection categories. Input parameters consist of coeffi-

cients and exponents C and A in the expressionC WAWRP = wA

3.281

Where WRP is the weapon radius in meters and W the yield

input. C (in feet) and A are directly obtainable for various

protection categories as defined in reference 8. They are

not currently available in unclassified form, hence the data

array for these inputs is set to all zeros. The curves of

weapon radius vs. yield in reference 8 are divided into por-

tions of nuclear radiation-dominance and blast-dominance, each

approximated by a straight line segment, with changes in slope

occuring at yields where radiation becomes dominant over blast.

The yield at which this occurs is called the "breakpoint."

Thus WRAD uses an algorithm which specifies the broken curve

illustrated in Figure 2-14 by the constants C and A for each

region and the yield breakpoint separating the regions of

validity. 354

I35

0

a.'

-4 m

4-

4 0"-4

Q~ Q

>4

0 0

-4 4J

4..)

al )

CL4

'-44

;g 'sfl~prH uodraM

36

There is no allowance for thermal effects upon

unwarned personnel in the open. Comparison of weapon radii

due to thermal effects of both "fatal" and "incapacitating"

intensity shows that thermal fatality radii dominate blast

fatality radii for nuclear surface bursts at the higher end

of the abscissa. This can be accounted for, if desired, by

adding or adjusting the exponents and coefficients for theprotection category for exposed personnel.

Preliminary investigation indicates that one break-

point with two coefficients and exponents can adequately fit

the curves in reference 8. However, the actual values used

remain to be fully verified. TACWAR has the capability of

implementing a curve-fitting procedure using multiple break-

points.

2-7 WRADVN

This subroutine is used to calculate the weapon -

radius due to nuclear airblast. Methodology of the Physical

Vulnerability System8 is employed. Input quantities are

the yield, height of burst and vulnerability number. Output

quantities are the weapon radius and damage "sigma" as de-

fined in reference 12. Detailed investigation of the

Fortran listing for WRADVN reveals that methodology of refer-

ence 8 was accurately followed. Appendix C contains the

Fortran listing as it appears in TACWAR, with explanatory

comments.

TACWAR allows only two values for the scaled height

of burst, zero and 174 feet. In the case of a surface burst

the table of weapon radii, TABWR, contains entries from

j ITable 1-16 of reference 8 for P-type targets and from Table

1-18 for Q-type targets. For air bursts the height of burst

(HOB) inferred by interpolating weapon radii was 174 feet,

in agreement with subroutine DAMEVL which sets HOB at 174

feet for all air bursts.37

4d1

The vulnerability number IVN is unpacked by the

usual methods. Thus a VN of 14Q7 (which appears as 1427 in

TACWAR) is resolved into its component parts: VN, the hard-

ness; IPQ, the target type (1 = P, 2 = Q) and the yield-

adjustment factor XK (or K in the usual nomenclature of

reference 8). The "damage sigma" (WSIG) is set at 0.2 for

P-targets and at 0.3 for Q-targets. Next the VN is adjusted

for yield in accord with the methodology of reference 8.

The resulting VN is used as the entering argument for looking

up the scaled weapon radius in array TABWR. Logarithmic

interpolation is employed to correct for fractional values

of the adjusted VN. Finally, the weapon radius is scaled

up (or down) to the input value of weapon yield.

Restricting all nuclear airbursts to a fixed

scaled altitude of 174 ft/kt' has the effect of reducing the

effectiveness of weapons against soft targets. Increases

of up to 40 percent in WR compared to the value of WR at

174 ft/kt* can be achieved against soft targets by increasing

the HOB to its optimum value. Figure 2-15 shows, for P

type and Q type targets, respectively, the ratio of weapon

radius at optimum HOB to that at 174 ft/kt (WRoWR74 ) as

a function of the vulnerability number (VN). Significant

penalities in WR at 174 ft/kt3 are encountered only for soft

targets. Table 2-1 illustrates this for VNs represent-

ing soft targets. Thus, for P VNs of about 15 or

less, or Q VNs of 20 or less, the use of optimum HOB becomes

important from the standpoint of increased WR. This situation

can be corrected by adding 3 additional scaled heights of

burst, i.e., six additinal tables in array TABWR, and suit-

able programming to allow matching of weapon HOB to target

hardness. Moreover, direct consultation with members of the

IDA staff indicates that memory limitations do not preclude

a more detailed listing of WR as a function of HOB. A

38

! . . . . . . ..o

4

IN.1.41

1.2-

5 101

VN.

Fiue21 nraeinWao aisb sof Opiu HOB

H3

1.1F

$4 0

004

o4--

C) *d 0 C

4J.)

.'- 041> )0 0> 0l 0 0 0 C0

444 41 s 4)f N N OD ~ r- ON 00 > n o L1 L~0

0a 0Ln 0) 0)

0-40 0 0)

w -4 V-

4-4- E-4 -f M- -

E 4 4.) (N4 0r F0 (N -a0 'L

01- (N 44 (') 02 OD cmO

N t C1 (N -4 '. (N ,-

(n-41-

-4>

C) 41. 0 0 0 ) 0 0 0 C0

E- 0a ro C) m 14 r-4 OD N .

r- N -4 fl) 02 0 C m l

0)"C (4 .-4 'a ( -4

LI) 0 ifI U1- -4

40

'-It

For targets harder than 15P and 10Q, the relative

gain in weapon radius at the optimum HOB, compared to that

at 174 ft/kt', is diminishing rapidly. Accordingly, a con-

stant value of WR for 0 < SHOB < 400 and VN >lOQ (or 15P)

would be satisfactory.

There is another aspect of the height-of-burst

problem which should be considered. In some wargaming

studies, it may become necessary to depart from unclassified

representative yields of tactical and theater weapons and to I

assess the impact of the use of real, operational weaponry 4for both sides. To accommodate such a need it will be nec-essary to extend the height-of-burst argument to the entire jrange from zero to 900 ft/kt', and to add appropriate programsteps. For example a given yield and height of burst might

result in a scaled height of burst (SHOB) of 650 ft/kt'. In

this case linear interpolation would be required. For a

SHIOB of 400 ft/kt', a weapon radius between those for 174and 600 ft/kt' will be calculated by interpolation.

2-8 OFFCOV

This subroutine calculates the expected coverage

(that is, one having a distance-damage sigma of zero) aimed

with Gaussian aiming arrors at an offset aiming point. Thus,

the independent parameters are the CEP of the weapon, the

target radius, the offset distance, and the weapon radius.Any self-consistent set of units may be used, but in fact

the calculations are made in units of weapon radius.

4141

haentThe Fortran listings as provided by IDA have been

examined for consistency and logic flow (to confirm that all

areas of input variable phase-space have been covered), but

have not been verified against any original documentation. jThe only possible problem identified is at the beginning of

the subroutine in which, prior to normalizing all dimensions _ -

into units of weapon radius, the coverage is taken to be zero

for values of the weapon radius WAN < .001. This will lead

to a gross error if the units of dimensions are large, and

1 will lead to unnecessary calculations through the main algor-ithm if the units are small, such as meters. Normalizationin units of the target radius (TER) would be appropriate:

if WAN/TER < .001, set coverage equal to zero.

A complete flowchart complementing that shown in

figure 82 of the CCTC documentation1 3 was developed and pro-

gramnmed on a TI-59, with the exception of the called sub-

routine CIRCOV used for normalized values of the target

radius less than 0.2. The results of these calculations

using the OFFCOV algorithms are compared to the results ob-

tained by direct numerical integration (kindly provided by

L. Schmidt of IDA) in Appendix D, Tables D-1 to D-33. Illus-

trative samples of these data are shown in Figures 2-16

through 2-21 for values of the normalized target radius in

the range 0.2 < TAR < 2, in which the error in the coverage

function COV is plotted against the normalized aimpoint off-

set for parametric values of the CEP. Errors do not exceed

30 percent for values of the independent variables which

lead to target coverages in the range 0.1 < COV < 0.9.

Users of the TACWAR model should be aware, however, that if

extreme targeting regimes are being used (such as preclusionoriented targeting in which a collateral damage "target"

A

42

r c

-E

In °

(N

4a-

u oo

SO R

4 U

43

--.

4. 43L~

.... ...... ~

C4

0

co 0

C)C

-4

a)

C) a% 0 o -0 V N 0-00 4 0 0

AOD Ul 1013I

44

_______

I0-

INI

AOD Ul 10-1-1

45

ODc

E-

00

II

,o

* U

t4 -

0 u

,-.-4

00

o

00 V'

CDN

r 44

I" I

II

C a~~ r- '.0 LI C*~ N - Q,4 0 0 0. CD 0 CD 0 0 C) ~ 0

AOZ) UT aOJ113

46

-, , .- .. ,..- . . ., , :. ,.. • . ..,, -

i ' ':.-

.. . >. ._ _ , -.... .- ' . WWj!. * --2.. .. , , _ -.... ,r

CID

0

C-4

aA OD r-LM V

AOD U 101-

47N

r%4 N

* 01

U

C)

C L CC

AOD~U UTJ01

480

coverage <0.1 might be required, or in which there are very high

coverage requirements of >0.9) that the use of OFFCOV can lead

to large errors. The largest absolute error identified is for

TAR = 0.2, CEP = .04, OFFSET = 0.75, for which the OFFCOVi algorithm calculates COV = 0.848, whereas the numerical

integration gives the value of COV = 0.688.

The documentation r f was not specifically

reviewed for errors, but, where errors were noted, they have

been included here. Since these errors have in general not

been carried over into the Fortran statement, they will not

lead to any error through use of the TACWAR model itself,

but could lead to some confusion. I

1. Reference 2, page C-4 the constant 1.1744 i

was used rather than 1.1774. A2. Reference 6, page 490, the lower left box of

the flowchart contains the expression:

=PNO exp which should be

I 2 2COV= PNO exp -(OFFSET)

2

S 2(0')22i

2-9 SIMCN

This subroutine calculates the cumulative normal Idistribution function: .1

ARG 2

P(ARG) f-- e dt

- ARG t 2

e 2 dt

By defining x =I ARG/ /--, the integral can be put in the) form of the error function:

49 *1-. i

e.I

P(ARG) = [1 + erf x] if ARG > 0

= [i - erf x] if ARG < 0

in which erf x 2 e -t dt A

of0

An approximation'" is used to evaluate erf x (defined as the

variable CUP (x) in SIMCN):

erf x = 1 - (1 + a x + a x2 + a x 3 + a x4 )-4 ,1 2 34

where a = 0.278393 a = 0.230389 a 0.000972 a = 0.0781081 2 3 4

and having a stated error c, such thatlcl< 5 X 10 - . Thus,

P (ARG) [ + CUP (x)], (1)

defined as the variable COV. The Fortran listing for SIMCN as

supplied by IDA correctly implements this algorithm.

An alternative approximation' s can be used for P(x),

without converting to the error function first:

P(X) =1 + c x + c x + cx 3 + c x) (2)2 23 4

where c = 0.196854, c = 0.115194, c = 0.000344, c = 0.019527,1 2 3 4

and having a stated error F-, such thatlel< 2.5 X 10 - . Table 2-2

compares the tabulated data 1 6 with the results obtained from

algorithms (1) and (2) over a range of values of ARG. Nega-

tive values of ARG are not included since they will have

the same accuracies. Note that algorithms (1) and (2) areessentially identical for the trial values tabulated, dif- Ifering by about one in the seventh decimal place. Neither

of these algorithms differs from the exact tabulated data in

the NBS handbook by more than about two in the fourth decimal

place. Thus, either is totally adequate for the purposes of

TACWAR.

50

_:

C 6 : ": ".. : -,, . .

O's ~ 0 N. qT i-I1(10 N 0' n r - qgD N~ UT 0) c

In o C 00% 0 M ON rnIn 0

r- r'

C1 3% LM C* m ) C) - 4 co r

N 0% n eLA r~ - )I f -4 In 0) -4 wO m

-~ ~ C)D -M Lo r 0 N CP) I) C)

m~~ ~ ~ n nc o r 4 -

MN L

44 ~ ~ co CC T M r t co rn r, (1

0 N-4 -4 n N V)) (N '.0 0 ~ (NN o

I LI-I CO ) Ln .o N- co oo m% N

%.o C% 0% -I cJ i 0 -t %D In IH ) ( f -i coI ' ON %D M .4 -4

cJ ) C L n % 42 LM rn C) Cr 4 e1

o -r -4 Cf) -4 N- %D N (N LA NC%. - I D C) an '0) N CD C) IN I%

C14 w No 0 N 0 rn r4 0%j %D 0o- C14 Nl '0 N% Cn 0 q (N %D a%N N -4 N) If) 0% '0 0% (7 .ON

E-4 % 0% I 6 4 (

*~ ~ ~~C L N N ( '0 0 0 n (CN C)~ N 4 ' V 0 w %.D I 0 0 V) (

'4-4~~~- (N NnH ( N 0 ~ ~ '0 0

Xl 0 0 -4 N ' .0 W o 0 I

51

4A___________________

Numerous errors exist in the documentation we

have available. The CCTC description of SIMCN is in

error in its last two expressions on page 181. They

should read:

COV : P(ARG) = ( )*( + CUP (ARG/ 4)

if ARG > 0

COV = P(ARG) =-( )*(1 - CUP (ARG/ V)

if ARG < 0

The IDA documentation 8 has errors in five expressions

under the algorithm implementation. The correct expressions

are:

x4(x) 2 fe _t2 dt

0

A = 0.078108

(x) te /2 dt

(x) = 1 (x)]" if ARG < 0

w(x) = [1 + (x)] if ARG > 0

The Fortran listing itself contains none of these

errors, so they are not carried forward in the model.

52

___

2-10 SIRCOV

This subroutine calculates the expected coverage of

a Gaussian circular target with offset aimpoint by a weapon

CL having Gaussian aiming errors and a cumulative log-normal

distance-damage function. Thus, the variables used are the

aimpoint offset, the weapon radius, the CEP, the target

radius (containing 95 percent of the target area), and thedistance-damage sigma (in units of the weapon radius). The

algorithm implemented is that developed by Mason".I I

The Fortran listings as provided by IDA have been

compared to the referenced document and reviewed for obvious

errors. At tne beginning of the subroutine, prior to nor-

malizing all dimensions into units of (adjusted) weapon Iradius, the coverage is set to zero for values of weapon

radius WPN < 0.1. Since it is stated that the variables may

be expressed in any consistent units, a large error may

result if the units are large, while unnecessary calcula-

tions will be made through the main algorithm if the units

are small. Use of the variable R (R = WPN/SIG), defined

later in the statement, might be appropriate.

There is also a Fortran statement error in defining

the adjusted CEP, taken to be:

CEPP = SQRT (C*C+0.213*T*T).

The coefficient of T2 is, in fact, the ratio in2/1n20,which is:

in2/in20 = 0.231378.

This digit inversion also appears in reference 19. It will

cause an error of % 4 percent at most in the adjusted radius

(for those cases in which the CEP is small compared to the

53d

~i

target radius), and is used only in those parts of the sub-

routine in which the weapon distance-damage sigma is either

0.4 or 0.5. The minor impact which results over a range of

variables will be discussed later.

An exact (to the fourth decimal place) numerical

integration of this coverage function is available?' .

Normalization is in units of the weapon radius divided by

the adjusted CEP (WR/CEP a ) , and the offset distance divided

by the weapon radius (D/WR). Tabular data are presented for

distance-damage sigma of 0.1 to 0.5 in steps of 0.1.

Selected data from this report are shown in the first row

of each double row in Tables 2-4 through 2-8.

A detailed flow chart was made of the SIRCOV algo-

rithm and programmed on a TI-59. The results sampled over

* those regions of variable space which produce a target cover-

age generally in the range 0.1 - 0.9 are shown in the second

row of each set in Tables 2-3 through 2-7. It can be seen

that errors in the coverage are generally less than 15 per-

cent, and become this large only when the coverage drops to

the 0.1 extreme. As an alternative to the tabulation of

the fractional error of the fractional coverage, Figures

2-22 through 2-2t, show curves of the error in'cOveraqe for

the parameters WR/CEPat D/WR, and sigma They generally

fall in the range +0.07 , A COV > -0.14, with the algorithms

for SIGT = 0.3 and 0.5 being the least accurate.

Tables 2-8 and 2-9, u iing tho same normalization of

variables as above, show the error caused in the fractional

coverage arising from using the incorrect constant 0.213 in

calculating the adjusted CEP, as discussed above. The first

row of each group uses the correct constant 0.231 in the

54

49 cor- Iq D fn -4 qw -4o 6O % 0 f % C.0C' 0 .ON

rre en 6n'C%-4 (1N

o0 ma~ Wa' m %DN 0 va'.om r- 1 ~Lf CNCN

Lo f %DO ON .ON AJZ 00'3CN14 '-N '1-4 r-. M 'j W4\OC)

in a% ON (N L LAn' &I " C"m'. 0 010O O'.O .. T ' W 0N 0

Sen (IN~~ O'0% N N a%"0 % 0 r 4- ~

0%I ON a % r C )L) V TI

(N11C" - ('e .tLn '-r4 r.- -I rI

4

,) u L

In -T U'f a%2 N"' IDa %v

,4 r- 0 V)V)- -4" 0 ) 00

00 0

N6f r,- flA - 4 D0(n 0o0 )0 00 w...I 4

v n I"- .-n -4- -tD i4~~~~ A.)- 'I SS f

U)L/o 0np o /u;t s;

-4-

EV

0% CA -4 O14 0 D4cr 0 %?~

0D en -H N %0 (%1 Lm% HO1.

am ODq N NC o%aCD LA4f ON f -4 C4 % OD 40%

iir- %D cN 1 -0% a%~ CO O 4c o

OO ON HCN ir, 010 0 0 co4 ~LI(14 r-~ CO J (en en -4c CO , D DWL(( (

%oN CW OD VL f -(4f u1lf V ~0 0

f-i-o-0 r-9 r '1 t") rLn 00 00

o

11( 0%f N JC W0 ( VLH r- O O

,q en r4- a)W (- 000 oDr-A(nr 4

a - CD S

I- r0 CI

'N U Im~ OD %0 ItLo 4r- U%' 0

~ H r- -4 0

L I)0 0 0 AH)

gg 0 00000C

( S/J n~pr-S uodvom/8DUvlS~a 108;;0

~T. 56

o r- 0 D C4C Ln tfrn .-4t- %00ow0 0 0 loo 00N 00a% N m

0 r- N ON 0 .1 co CDV - 4 0 CN

0n -1-40 r -0 m~ %De CO -

VI~ 4 wn ON 1 - C c nrm a el ' Ln LA '0 r CNA 0 0

rq46 q% n ot 4 n CD v r ac Nf0' r" CO " %ri 0q O N 00L e

a% w O 0'. f- VIU v Nm 04 0 1J

m- m o14* l o% -

IIu

m 0% fo l r-~ u -. 01-.?* 00 0 00 % AL coC - N 01

w O r t LnL Qo ITV r n4-4 C)0

ing ODr 04% Ln- Mk vr 7a r D r.. 4 21 00I 00c O -f ( D 0 %rD(

Ln~~0 004 00n 4 0 nL N C

n -4 as r- -4 -4 en

54 4-4 -44 -4 0 I0

1 57

fn HO r- 0 D 0% 0) rH 0 UnOD N r-a ON IVq 0 - 0 C MN

o co' m D %D MM r.) m n Z 7CDO

CI c %~DD r v M en J N 00

L(,Q IW -4 m 0 WD Om r- 0 VrON a% IA(N (N C AD LnI Hr- C DCC

H % ODc '.o~ q MM m ( 0 0

r-OD HuVD -4 r-H O ' OD Mt" -4% 0 -4 -4OOD CI nN I*% M N -1r -L 0 N

Cm O D % o I V m~ en CNN 0 0 0 0

onr- %0- Lint LA 0 ON OH -4'..4 r

ON as r- r- n LAU v qw MM en M N ~ 0014

0 %Dr rv 0 0 - r- - D - C-1 %D Mrn VC4~ co~ ODr LnL n 4 nnC IM

MM R as LI r0 0N Ln r

1 0jro~~W~ coON0-OD%

) WH U4) % N M0

c N N00 0

4- IIO D -qHD Ifl f- 0 4 4 (n

(~t4/G m~P~ uovjrau~~ r, CD C

58 % 0%. nL

I. 00 00 90

aN (N L 00 r- Ic mt- DO enN

a ~~r- r LA LA w el r ON OI (n rnu N Im dN r-r- In L n 1 (N N 00 0 0

m~ v? %D~ 10 CD0 0O 0 V0 rN 'ON L ' v ID %DO Nr

-q O 0 r- r- U)Ln rel N AC 00 00

~~- r- L 4r M %D or fn L4 L

A40 C'D L AJ m v r-' LAIVen0 ra% LflC'ma *-r- LA) (1E(n Ne' - 0 C)0

r* %. L) r- OD ODODlr- -4 0-% (J*'T .-I a 0 I ) 0 r- NA Lr CODj'

m~ r- r-~i r, cl r, C-' LAO -- CD N a(OD ODwD Ij£ V M Arj r 1 0 0 0

U ko N ODL n r- -4 in

r(I LA Ln V(I e C' (N -4 '- 0 0

CLI

im Isel M0) 00ON ~4 7 NN N IkW 1 - OD 001 CO~ C~ O CLA -11 :)r 1U

14 Ln (-n W? (NO V Vr r-) CN 4 C

00

-4 4 0 m co ~0foo

03-4 ~E-4

-

r-ir 14 - -

IA o- N N r- 0C-i aqm

OD O - c 00r4 -4C- 0 0 0 0

V4

(xJ./cJ) sfltprH uodvat/aoujsTa las;oj

& ____59

-4 i l

-.4

o 0

CDC

V) N

* 0 a)

00 rn1-4 -40 0

600

0

-4

U)>C' 4 C'N

4 14Fo 0-

rn

M~ N r.C, C C C

AOD~~.. U I 1.

61,

WON&) 3

-4-

o0

r-~( CnC4 r

Clr~ c C

AOD U JOJ1

624 I

rr

44

II

AOD UT l 04

63I

In

r U-4

0 0

4JJ

C.-4

AOD UT a01

N 64

N\C 00

co( co~ %DN %Q VN q ( (4 0

'T o n fn' rn kor nr %O0~ ON- OC V11 r - O Dm0

p4 ONO atO a% I mmne n( Ln LA - -(IN O O OD %.Dt %. - m r CN 00

04 LA'-4

v-4 co a% 4 0~' iA D k Lnu

in 00' m %D u--r -4 -4-4N r q, %D ri - occo0 1 q 'D rqN rn~ U) i c 00 001-

* -)NO ' r-c'N LAO a a % aD .- n V'OD2~ cm L OD co0 r- OD 'DrN - -4 LA T NC14'

(-4C'J " co 0% tr 0 0 - 'CNt- a%6 C% r- LoiLA qr V m rm en n f 41-4 0 0

E 0

Im ) - I) v -4 r-v C4 D o D c 40 - 0 ' A 0 1 - - r D CI n .

L0Z40 3 DO )L - 1 - r n 0 nf

C) 0r)C 1* O 0 or. 0 -4 r 0 -4 r- c

14 0 t o Vu n Iq IT m M -4 -4 0 0

M 1-4 . . .. ..

I 40

-4- 1. 0t

00 00

00 00 0

00 0 0 0 0

co co - CD O

-4 f-4 )* '*nl

65i

C% -7 -r L n r

.Dli Oii v- -r 0 - 0 0

r- r N nm( N (N 0 0 0 0

r-4 OD n r-~ v~t ermv'C 00 M 00LnL

o-4 Lfl D v L l % 0 0 Ln ul "'4N

6d' r-, LfUlA M N N 00 0

* co a) -4 o 0 r- -4 C, L

ODf~ OD D TN q 0 0 0 0

0 LoW 0: - oc %0 04~ N - r- L r-r- N

00 00

0 i

LA .4 DO C D 00 -4 LA

00L N - 4C 0 0

0 0

I.OI. SOnf LALA* I 0 oc

-4 -4 .-4 I-.-

I -4 -4 p4 0 0

(am/a3) sflTpe- UOdM/aU'PSTG3 -4aS;;

66 -

SIRCOV algorithm, the second the incorrect one. The largest

error found was ACOV = 0.01.

Although the documentation was not specifically

examined for errors, the following were noted. They have

not in general been carried over into the Fortran statements.

The correct expressions in reference 2 should

read:

2[11. Page C-8, last line: CEP' = [C + 0.231 (T)

2. Page C-8, last line: If SIGT < 0.301...

: - 3. Page C-9, line 11: P(,O' = CUMN

L WPN (l-SIGT) .ec~n- . etc.

CEP'

4. Page C-9, last line: ...and r > 1.5,

5. Page C-10, line 3: PD = P(O) exp - P(O)r2/R2

On page 492, reference 6, the flow chart reflects

the unit normalization problem discussed above in connection

with the Fortran statement in which WPN > 0.1 is used rather

than the suggested R > 0.1.

2-11 CIRCOV

This subroutine calculates the circular coverage

function, which is a Gaussian function integrated over anoffset circle. It is equivalent to either:

a. Probability that an impact point will fall

within a circle of radius R aimed with an offset r if the

impact has a Gaussian probability of unit standard deviation.

b. Probability that a point target will be co'z.re-

by a weapon having an effects radius R (and a distance-I damage a = 0, i.e., a "cookie cutter" weapon) when aimed

67

with an offset r with an aiming error having a Gaussian

probability of unit standard deviation.

The integral to be evaluated is:

P(Rr) eX + y)/2 dx dy,

in which the integration is carried out over the circle

(x-a)V + (y-b)2 =R

where a2 + b 2 r z

In practice, when the distances (including the CEP

aiming errors, which are generally not unity) are given in

any consistent set of units, they are normalized by dividing

by (CEP/I.1774).

In TACWAR, this integral is evaluated by an algor-

rithm using an approximation in the reference 14 equations

26.3.25, 26.3.26 and 26.3.27. The Fortran statement has been

carefully checked and found to correctly implement the algo-

rithm. It was programmed on a TI-59 to generate the data

shown in Figures 2-27 and 2-28, in which discontinuities at

R = 1, 5 can be noted. To check the accuracy of the algo-

rithm, a numerical integration of P(R,r) was made for a

series of parametric values of the independent variables.*

These (having an accuracy of several in the fifth digit) are

shown in Table 2-10, along with the corresponding values

from CIRCOV, and are also shown as points on Figures 2-27

and 2-28. It can be seen that for probabilities in the

range 0.05 -0.95 the CIRCOV algorithm is generally accurate

within 10 percent. It should be kept in mind, however, that

* These data cover a broad spread of parameter space. Insome regions they have been confirm i by comparison tomore detailed tabulations such as icference 23.

4 68

4A

0 NumericalIntegration

S ..... /8

.7 r~.

.6 2

/I

r 3

/ //r 7

.2 1

r-- I0

1 2 3 468

Figure 2-,Z/. Thei Ctrculj, ':v zq Function

SI RCA

69II

II

S. . .. .. --

TT

00

Eip~~~ 10- -- -

1 0 -- I ... . i .l

0268 10R

Figure 2-28. The Circular Coverage Function

CIRCOV

70

F _,~ --.- ~-71

V ~4a -4 -4 O a)o 0, m Nr

N N in N 4~W c -4 -4 'Dv N-4 'A N m -I ' -4.1 1 1 . .i .i .i . . . . . . i

rq -4 N 0o 4 -4 4 % 1-4 a', CC - .fq? --I

- j -4 4 ' , D 0 -

n- -VI-4 inO f 'r -T~N a'n in D( 0

ggg +

U4o i~JN'- 'n 0 C,

mlN (N -% -4 r-i (M NN i -4 ( -

cn-N N 144 C..N4r-4 N-r4

A g~ I + I I I+

m 0 N4 (N C% -4 DrIN

IN q0000 CI 0 % C

-4 v -4 -1 v- -- CN 4 4a C

0- -4 --4 -4 r-4 -44a -C!4

4 4 -- 4.-

I I I I + ++j- , I 0'o(N 0 Krl0 '4 O0

C) I'r 10 ID 0) 0

mC IT 'T, co ID U -1 0 a 'c -7, a , 0 , a , C )

4. 4.1

C:i -1-- -4 0> !11+ + + ++

_4 r,4 (N "-4- r4 . CF, M 0' -4 a' -

.4 )1. . . .

I W-.4

*Nr .N m ~ r- kD CC( l7 %r4. %r %C

u . .

-~~~~~~~~~~~ +-~--=----=-~* Z =--

for extreme probabilities these approximation errors increase

to about a factor of two at P = 102 and a factor of five at

P= 10 - .

There are several minor documentation errors, not

r carried over into the Fortran and hence having no impact on

the proper operation of the subroutine. References 2 and

5 fail to note that for R > 5 and RLS < 1, then ARG (for the

called subroutine SIMCN) is set equal to R, although this

branch is correctly noted on Figure 85, reference 6. Other

small errors are:

1. Figure 85, reference 6, the expression

T2 = g (2+2RL2)

is incorrectly written.

2. Page 185, reference 5 has the inequalitiesR > 1

and

1 < R < 5 incorrectly written.

72

d _ _ _ _ !

~4.. !

II** ~ .- . -

h~ u.., -~ i...............................

REFERENCES

1. Kerlin, E. P., and H. E. Strickland, IDA TACNUC Model: I

Theater-Level Asse'sment of Conventional and Nuclear -

Combat, WSEG Report 275, vol. I, Executive Summary,October 1975, Institute for Defense Analyses, 400 Army-Navy Drive, Arlington, Va. 22202, ADB009691L.

2. Ibid., vol. II, Detailed Description. I3. Ibid., vol. III, Part I, The Chemical Model and Other i

Modifications, November 1977.

4. Ibid., vol. III, Part II, Program Description, November1977. |

5. Defense Communications Agency (DCA) Command & Control ITechnical Center, Institute for Defense Analysis TacticalWarfare (TACWAR) Model, CSM MM 237-77, Program Maintenance jManual, Part I, 6 September 1977. 1

6. Ibid., Part II.

7. Ibid., Part III. wB. Defense Intelligence Agency, Physical Vulnerability

Handbook-Nuclear Weapons (U), AP-550-1-2-69-INT,

1 June 1969, Confidential. j

9. French, R. L., and L. G. Mooney, Initial RadiationExposure from Nuclear Weapons, RRA-T7201, 14 July 1972,Radiation Research Associates, Fort Worth, Tex.,AD 745906.

10. Gritzner, M. L., E. A. Straker, T. E. Albert, and H. T.Smith, Radiation Environments from Tactical NuclearWeapons, DNA Report 4267F, July 1976, Science Applica-tions, Incorporated, 2109 W. Clinton Ave., Huntsville,Ala. 35085, AD*047389.

11. Glasstone, S., and P. J. Dolan, The Effects of NuclearWeapons 3rd ed., U. S. Departments of Energy andDefense, 1977.

73

#A_ _ _ _ _ _ _ _ _ _

12, Defense Intelligence Agency, Mathematical Background andProgramming Aids for the Physical Vulnerability Systemfor Nuclear Weapons, DI-550-27-74, 1 November 1974.

13. DCA, Part II, p. 490.

14. Abramowitz, M., and J. A. Stegun, eds., Handbook ofMathematical Functions, with Formulas, Graphs andMathematical Tables, National Bureau of Standards,December 1972, equation 7.1.27, p. 299.

15. Ibid., equation 26.2.18, p. 932.

16. Ibid., p. 310 ff.

17. DCA, Part I, para. 2.2.6.33.2.

18. Kerlin, vol. II, p. C-7.

19. Mason, R. B., Computer Approximations of the CircularLog-Normal Damage Function, National Military CommandSystem Support Center Technical Memorandum TM 78-72,7 August 1972.

20. Farschon, J. W., and L. N. Matteson, Tables of Prob-ability of Damage Calculations for Point and circularNormal Area Targets, DNA 4051T, 19 July 1976, ScienceApplications, Inc., 1200 Prospect Street, LaJolla, Ca.92037, AD A038675.

21. Genrmond, Ii. H., The Circular Coverage Function,Memorandum RM-330, January 1950, the Rand Corporation,1700 Main Street, Santa Monica, Ca. 90406.

ii

.74

...... ~-f ZP I

IAA

APPENDIX A

FUNCTIONAL DESCRIPTION OF ALGORITHMSEMPLOYED BY SUBROUTINE QKINR

FOR CALCULATING INITIAL RADIATION DOSES

The following algorithms are used in the QKINR

subroutine to calculate components of total dose from

initial nuclear radiation. This information has been

taken from program listings and from the IDA paper re-

printed in Appendix B.

Neutron Dose

W TF CF• RBE rCDB + ADB• R 2 + BDB R]D =e 0n R 2

0

where R is the slant range from the detonation to the target,TF is a height-of-burst correction (1.0 for surface burst and

a fixed value for an air burst. The value of TF is dependent

only on the weapon type.), CF the neutron multicollision fac-

tor, RBE the neutron relative biological effectiveness, and

W is the total yield in kt. Parameters CDB, ADB, etc., and-TF are defined in Table A-1.

Air-Secondary Gamma Dose

w +cA ADA Ro2 + BDA R0 ]Va i b D - TF e o

R0

Variable definitions are similar to those given above.

I

"II; A-l

: ' _4 _ ........................................................

Table A-I. Values of Exponents andCoefficients Used in Calculating Neutron and

Air-Secondary Gamma Ray Doses in Subroutine QKINR

Parameter Weapon TypeFission Intermediate Thermonuclear

ADA 3.67E-8* i.OOE-7 1.28E-7ADB 3.48E-8 9.26E-8 9.36E-8BDA -4.42E-3 -5.09E-3 -5.15E-3BDB -3.22E-3 -3.81E-3 -3.70E-3CDA 22.46 22.91 21.95CDB 20.67 20.62 19.73TF 2.16 2.20 2.19* Read as 3.67 x 10-8

Fission-Product Gamma Ray Dose

Calculation of the prompt dose from gamma rays

emitted by mixed fission products is complicated by the

temporal and spatial dependence of the source spectrum,

medium absorption properties and source geometry. The jfollowing expressions were used in the calculation of

fission-product gamma ray dose from 1 kt, 10 kt and 100

kt surface burst and air burst weapons. They were derived

from Appendix B, which contains complete instructions and

algorithms for use with any set of parameters of interest.

R0 55.2

1 kt surface burst: DFP FF 108.845 660 RFP 2 0

HOB=lm, R > 362m** 0O0-

** If the range decreases below a minimum range parameter(defined in Appendix B) additional terms are introducedin the algorithm. Representative values of minimumrange are 362m, 415m, and 563m for 1, 10, and 100 kt,respectively. Ranges less than these are generally notof great interest because of (a) extremely high doselevels and (b) very high neutron dose relative to gammaray doses.

;" A-2

i

. .. .. .. ... .. ... .. .. .. ... . * .. ... -- • "j-. .. .. . _ .. . .. . .. . .. .. . .. -± . .. - . .. : I

R_ 0 64.21 kt air burst: _FF 108 837 66

R 0HOB=53m, R > 362m o

R20FF 109.118 o 10710 kt surface burst: D 660 R2... .FP R 0HOB=lm, R > 415m

0 0

R20FF 9 95- o 12610 kt air burst: D - 660O R-0 0

HOB=114m, R > 415m R 2 00

2F_ 9.765 O 385100 kt surface burst: D - 10" 660 R> FPm 2 0HOB=lm, R > 563m 0

00R

39200FF 09.686 - 39 I100 kt air burst: D 2F 86 -60 RFP 2 o 6 R0HOB=246mn, R> 563mn 0

Lam --

* I

A- 3

•II.

Best Available Copy

APPENDIX B I 11cLi Lu e 0for Do Afnn At I y',csT AC N I CWork inq er WP -4December '1975

A NUMERICAL FIT TO AN ALGORITHM WHICHCON1PUTES PROMPT FISSION PRODUCT GAMMA RADIATION DOSES

Leo A. Schmidt

Dlecember 19/5

B-I

, TZ _ " .. . I I I L_1I

A. INTRODUCTION

A 'mpt. 'subl"ot IW I O 1.e110th calcu [at. Lon of thle 'I III t.I 1.Nucl ear Had tat io01 Dose has, been d"ve10oped by C. E : Senhauer and

LSpence of' the Nationail Bureaju of Standards. This subroutine

computes the dose f'romT fisISionl Product. gama radiation, secondarygamma radiation, and neutrons. TPhe calculations are base(] upon

a1 paper by French and Mooney . T'he ca ilcu llatlo ns Vol- sec ondary

gamtma rays and neutron-, are made from equati orns of' the formn

D =a exp [b exp ((ci 0 )2) + d exp (el" 0)]

where RCH is the slanit v'a nge fm'oil weapon t~o 1mon I tor poi nt;. 1h

Canl be I [II I emne nted For re 1atI ye.1y ruid Cial c ul.ation . TPhe cal cu-

l at ions; for the fis sion product, garmma dose , oni the other hand,

are much more lengthy. They require more complex expressions

for dose as a funct ion of time. TFhese expresisions must be

Integrated as a function of time to obtain the tota1 do(se . 2 As

a result the comniuter rou tine which I tsplemnent~s these equat ions

a relatively slow calcu lat ion. For analys-is- wihere the doses

inust, be calculated a large num1rber o!f tIines, in pai'ticu i ar !I

damage assessment calculations* involving, many weapons arnd monitor

points, such long running calculations can adid most substantially

to computer requirements.

Anl algori thin for a more rapid cal cul1at ion of' the f issi on

product gamma dose is described below. 'Phi s alrorithm is a strictly

numerical fit to the resultsi of' calculations of' fission product

gamma dloses over a range of parametric values. TFhe fit is gener-

ally within 10 to 20 percent over the range 01f interes~t. TPhis

range Is, for yields, W, ranging from 0.1 to 10,000 KT, scaled

helrqhtls of burst (the height of bursL/W 1 / 3 ) from 0 to 1,300 feet,

1R. L. French and L. G. Mooney, "Initial Radiation Exposure from NuclearWeapons," Radiation Research Associates, Inc., Interim Report on OCD ContractNo. DAHC2O-72-C0123, RRA-T7201, 15 July 1972.

?1lie essential reanon for the inI.(egm'at ion Is, due toe time hydrcxiynarnic buoyancyof the fire-ball which not only changes the dist.,aice bwensource and receiver,but due to changes in air, density with heighit changes the radiation-,Visorptionin a comp~lex manner.

B- 2

ani slan t ranges ranIIng from (,, I, her t Ie vi I nmum slant range

at ground zero, or the mInimum ,;lant range where the fission

product gamma dose is less than 1/20 the neutron dose, to a

m,iximum slant range wnere the fission product gamma dose is

about IOR. The algorithm will be de,;crtbed directly first,

followed by a few comments corncerning ILs development.

B. ALGORITHM FOR FISSION PRODUCT GAMMA DOSES

A maximum slant range, SEM, is computed by

SR[4 = l,8q8 + 814.S.25-L + 111.241-L2

where 1, = lo 1 0 ( .J) If R 0 > 2 ,r th Dose, 1., is 0; otherwise,

the f'llowing procedure Is followed.

An "asymptotic logarithmIc" dose, Dasy, is compited as

follows. Let

R = 1,188.13 + 84.325)) L + 71. UO3L' + 12.140,811 3 - ..7729L 4

+ 2.837hlL5

asy 7 zIf B > 0.2, set D asy Dasy + RA )

where HB = scaled height of burst ((ft/(KT) 1/3)/l0O),2

R A -b'llB + c.H11

with b = 1.24151'10- 2 + 6.0937-10-

3L + 3.4654510- 3L 2

+1.534.10- L 5.933710- 5L

c = 9.9037 -0 Q.14710-51, + 1.96310-4I 2

-4 3 4 54+ 1.836161U- 4L3 -1. 09.10- L + 1.816210-5 L5

Comp'ute n difference lose, DF, by the f'oLluwtng procedure.

SB =362 + 74.3.L - 55.99L + 34.59L 3

B- 3

' I= 1 00/j

DJO -0.015 - 0.005611

X = 0.055 - 0.0013511B

m 0° + n SII

anri for L I

Mo = 0.552 + 0.3981, + 0.251,2

S = 0.0518 + 0.02985L + 0.01685L;

and for I, " 1

1 -1.71 + 2.78L;

Mf= 0.1690 0.0615L

For R let

D 0 + m(x-xo) + c(x-lOO/SB)

where Do, xo, ar d m are computed as before and

C =0.22 + [0.575(L+I)] L < 1.602)0.22 + [1.1144(L-0.61)]"

, L > 1.602Now if L > 2.4, we have: iIC R > S

DV = r ( - oF rn(x-x)

where x 100/R;

m -- -711.8819 + 95.3347,- 40.2997L 2 + 6.062118L;u 0-0217(I.-6-L,)

But if R < SB , compute

D 0. -R o ,when R>. 200

D 0 B-Ro + (200- , when n < 200

B-4

0 I ' i2 3 - 000 40311, 1, ,

LO0.00N8 - o).0001 8( L-jI) , , >

I !I . - -I. ) o-o + I.9 L0-.1O - l,"

Now let

It 130)o ") t!! 0+ ,

wher D 00 3") 001 -,

And lot D0

)F 10

Finally, let

D D -1r" a sy ' F

and D U ---

D =D•

where F is the weapon fission fraction.

C. COMMENT

"lie underlying motIvat.on of the above chia was obtained

by observing that the dose as a function of' Ro asymptotically

approaches an expression of the form

A.Wexp(-R0 ),DI 2 0 .

'_, 0

which would be obtained from a point source with no fireball rise

and constant absorbing cross section. The dose becomes close to.1 B-5

- !,. :' .' .. ' ,; %$,Am ; :" . .. " ,

Thu.- tit Ci7 tt. (,H I, t I o tliII 7 h a' 1. a 'i 'n i fr

'Pi as d neIsm n tg Ihe -,I11 0 1) tIe 1'0 1' all a'13Y'lltt t ,I Ck, I IV 0s . 1The t, b wt W, In f It male w I flu I 1 () a Ctiv c.-o "l

he g0ht- of b tIrs t was i tlien added . 1,11e hjelglib o ,I: buscorriect.1. of

0'ltik 11ZIi abou t, !30u p o ICe nt (a :IL ImIx I u flit I I jit. F b rt

0. 1 KT yieids t~o rsomewhiat, ove' "I at, large yjelds.

that haS I 1gb 1 va iue:; for tow ,;Ianit. v's uges and uI',tsoe:;- to .,,tro(a :,- the two, dose,; auppr'oach each other'. ) Pa :; a I'u I ( t I C.n1 of' IL/ R Isa I e IT.")r t. li near n.IIear 7; heIt or I .1 1 n 11 , fCo Ii owf-d( by a ;1 em ' wh ich , for

nIfo.;1. y ieis *was" app'o x ima te~. Ivy a pa ra:bok IJ huIU I"., tang11ent tohelt Itnear' p)tecr' at, their Thuesc .1o) ile intr:tA'ec tion occurs'.

wheret 1. 111 slan 11t. ran)re has a v.'m I Ii" , ";H , tha t v';a - it et'rm lfe( byinnspvct on Irvon) (it': o the f'uruet.10Len. At, ) pa ti en clar heiglht.01' vU1 ra;t. , t.1e .l1ne at' semnt or Z111. vtel.- .' low 2150 KT couldbe# taken, without too mruch foi'c lg, to have one comimon Inte~rsection,for' larger' yield: to have 'another di fferent, comnmon internectiOn.'This naturall11y eatd the caiculntlo ns- into two z'aniges kit y~eids,be low TO0 NT and ablove 150 KTl'. These I tre irswere height of'bun's I'. depjendent r'P lOW y i lUS, bunt, coulAd be lakeri as constant f'orhifgh yi t.ldg .. (The ot'd inate of' the 1ttbr'Oct.11 Ion MTs neatve , whiLch

renIsfrom errors In esnt-Imat trig the( asymptotes. .in erffc. t , theestimatton of' D1 . also partially eoimpen.-a to:-.; ?'oi erioi's in the1.aM' symp1 otc es t: I.ma te , a rnd g;ives a two -n;t. ep ro v'rectI. I or.

The s lope of' the. linear :;,,c tlon:; was z'epr'eserrted by a 1 inearl'unction of height of'hrs f'or low y.it 01(15, wt itl the coefl'F t, i nt.;

for the linear funct ion yield dependecnt. For the high yields, nohie Ight of' bursmt Ss,- t.1 vity wa, needed

F~or small r'anges, large vatues of 1/H, a parabollc !segmnentwas added to the linear variation whose coefficient was yieldI B-6

dependent In the .low yljel(i PflflgL, For the large yield range,

this procedure gave an inadequaIte fit, So for lo LWvAluesO Hf

an alternative procedure wan used, namely estimating logl,(D~)UfunIction Of' R0 A linear function was adequate, except for valuesof Dr under 200 feet, where a parabolic segment was added.

The algorithm used may seem a rather jerry-built assemblageof' curve fitting procedures, as in one sense It is. The numericalvalues were obtained either from graph paper or simple leastsquares polynomial fits. The rationale for this approach Is thata function of three variables Is to be fit, and there is no a

priori way of determining the runct:.ional rorms needed for efficientfitting. The variation of dose as a function of slant r'ange was,in fact, well approximated as a ratio of two polynomials. Unfor-tunately the coefficients of these polynomials did not systematically

vary as a function of yield, or height of burst, rendering the

development of an approximation valid for any yield or height ofburst difficult. A simultaneous vstimation technique with allthree independent variables included seemed require(]. Although1this was not, attempted, It appeared l ikely thai; rahe hih o.de

terms would be needed for any adequate polynomial approximation.Thus the method of "cut and fit" seemed more appropriate.

The original alfrorithm and the approximation were implementedon a Control Data 61100 computer, and compared over a range ofyields, heights of burst, and slant range _s. The average time percalculation of all three tynes of doses for the original alGo-

-ithm was 0.6110 seconds, and ror the approximation 0.00176 second.

A display of the accuracy of tho approximaltlon A1s presentedIn Table I where the minimumn and maximumn values; of' the ratio Of'

fission product of doses computed bY the aPpWoxIL1tio to tha co-puted by the numeri cal I ntegr'n 1. !ot i s presenLtt f'or vi iiou s yieldaarid scaied hal ghts of burut over' sant ra, e, of intxces .S Theslant range of interest for this table is defined as any slantrange where the fision product gamma dose Is over l011, and where20 timer, the manximum of ,-Ither the estimated or actual rission,

product gamma dose Is less than the neutron dose. As can be seen,

B-7

Table 1. IIINIMUM AND MAXIMUM RATIOS OF ESTIMATEDTARGET DOSES

Scaled 1Height of Burst (ft/(KT)1 / 3)

Yield(KT) 0 100 180 400 750 1250

0.1 0.99 0.99 0.99 1.00 1.00 1.000.99 0.99 0.99 1.00 1.00 1.00

1 0.98 0.98 0.99 0.99 0.99 0.990.99 1.00 1.00 1.00 1.00 1.00

10 0.98 0.98 0.98 0.98 0.97 0.941.03 1.03 1.02 1.01 0.99 0.96

100 0.92 0.96 0.98 0.99 .0.99 1.021.17 1.08 1.07 1.04 1.02 1.03

300 0.97 0.97 0.97 0.97 0.95 --1.05 1.04 1.04 1.03 1.02 --

1,000 0.94 0.95 0.95 0.89 0.94 --1.11 1.07 1.08 1.12 1.10 --

10,000 0.50 0.50 0.49 0.51 0.79 --0.99 1.12 1.10 1.10 1 .30 --

30,000 1.06 1.57 0.76 0.69 -- .0.66 0.71 1.24 0.95 ..

the difference is generally within 10 percent of the fission

product gamma dose except for the yields of 1OMT and 30MT. For

these larger weapons, however, the overpressures at the dose

ranges of interest are generally well over 30 psi. As can be seen

in Table 1, and as is even more evident from 1istings as a function

of slant range, the errors are quite :*y.,t.aematic. Thtus, If desired,

further corrections cou]d be readily developed to make the cstimated

error still closer to the actual error. Such corrections would

require possibly a 20 percent to 50 percent increase in calculation

time for each subroutine call. Use of this multiple approximation

technique is not untypical of this approach, where the error bounds

achieved are often dependent primarily on the effort expended in

developing the approximations.

B-8

APPENDIX C

FORTRAN LISTING OF SUBROUTINE WRADVN

This appendix consists of the entire listing of

subroutine WRADVN of the DAMEVL routine of the TACWAR code.

Comment cards have been omitted, and more detailed explana-tions added to the right of the Fortran statements to which

they apply.

~This appendix serves three purposes. First, it

provides an example of the degree of detail required for a

thorough review of nuclear effects calculations. Second,

it shows the implementation of reference C-1 on a modern

v digital computer and eixplains the program in terms under-

standable to readers who are not experts in Fortran program-

ming (although some knowledge of Fortran is necessary to

follow the program). Third, it shows the implementation of

AP550 targeting methodology (calculation of weapon radiusU

only) in a more advanced programming language (Fortran V)

than that given in reference C-2.K

1-

I

I. V

**, ..

Uo o 4*u 4

1 4 c"r

4* 4* CC 96

c4 I Ia, 4.A * t*4 0 V

-~~~~~ 14 - 94-C± 4 .V

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oa 44o >- C

z Z> C W C 3. ±4

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Cr £30 .4N, 3-'-. .~u-. a- - -

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3~3 0- 4, A 41

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P. ON. - OS. -,0& AN 3 -- N 4,IN~.JS N IC ~J

cC -'3C~. .4 40 - .-- A0m - C- C 4 ~'VA C- N - - 4'

U r4. 3. .~C J'

I) 4C N 4 @4 3

I -444'U S. nB -~ K

U0~

44'

C ... E" 444 4-

~ .? 0~

r 4' 30 -c-I

- a 04

c 4444CC 0 >.-i '4'

444.36 0 2-2:.-' -4 4N. 44 .4r~

- 4-. - - - 3 - 4' -

-- 3, .4' I.2~44 4 ~x- 4 I

.J.3 13 43 II I

4 4

2 14 -4I

'-4

4 4'

z aU

4 12

.4,a

t4 I3- 3 0

0 ~ -:z 2' j 2' I4Z j I

SN *N -

-J 30 31-- 3 C~ -

.4 *0 p. *0 .4

A' O~ 10 ~ *N30 3 3- I

i1j

C -. C -34' N -d N 'N N

A I I4=- U -n I..! ~.D f4.P4N4414 I 23030 222 ''232' fl~ *~ 'O'-C-3

I _ __ _ Ii_ __ __ ___ I

- ~4-. - -= -=4---,-. -~.-- ____ p

ci cvi w

5- >

0 0 0

0 0

A . " a 4)

S4

~m

C. ,

-. I -O

I. I c-4

2 1

REFERENCES

C-1. Defense Intelligence Agency, Physical Vulnerability vz

Handbook-Nuclear Weapons(U), AP-550-1-2-69-INT,1 June 1969, with changes, Confidential.

C-2. Defense Intelligence Agency Directorate for Intelligence,Mathematical Background and Programming Aids for thePhysical Vulnerability System for Nuclear Weapons,DI-550-27-74, 1 November 1974, with Change 1.

C-3. Hodgman, Charles D., et al, editors., Handbook ofChemistry and Physics, Forty-first ed., 1959-60,Cleveland: Chemical Rubber Publishing Company, 1959.

c -

* I

IC-

I-.'-

APPENDIX D

TABULATED COMPARISONS OFSUBROUTINE OFFCOV WITH EXACT

NUMERICAL INTEGRATION

This appendix contains the results of comparing the .

output of TACW\R subroutine OFFCOV with numerical integrations

of the coverage function. Arguments are identified as follows:

TAR (target radius/weapon radius), CEP (circular error probable/

* weapon radius), OFFSET (aimpoint offset/weapon radius). The

ratio of the coverages (OFFCOV algorithm/numerical integration)

is also tabulated.

I

I

II

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0C)0 0 -01 -4N (N U M~ M' M V W - ~N0 00000o 00 0 0N 4M l D

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0. 0 C) 0 ID 0 0 00In0o

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ac 0 00 0 o 000 00 0 0 L 0 00 M - 0 000 0004 r oo o oo o o 0I C,00 O 1 00r r-'4.10000000

u O O N O O O U 0ooamwoo0o0-004-M000000000 (NJ 0-00000000000

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C C C ; ;C 0 ; *0 0 'D-02C C

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D-34

DISTRIBUTION LIST

DEPARTMENT OF DEFENSE DEPARTMENT OF DEFENSE (Continued)_

Armed Forces Radiobiology Research Institute - Interservice Nuclear Weapons SchoolDefense Nuclear Agency ATTN: TTVNational Naval Medical Center

ATTN: Dirctor Joint Chiefs of StaffATTN: J-5, Strategy Division

Assistant to the Secretary of Detense AITH: SAGA/SFDAtomic Energy ATTN: J-3, Strategic Operations Div. -

ATTN: Executive Assistant ATTN: SAGA/SSO -ATTN: J-3

Command & Control Technical Center ATTN: J-5. Nuclear DivisionDepartment of Defense P n S

ATTN: C-31S Joint Strat. Tgt. Planning StaffATTN: C-343 ATTN- JLASATTN: C-312 2 Cy ATTN: JL/JPATTN: C-332 2 cy ATTN: JLTW-2 I

U.S. European Commnand National Defense universityATTN: J-3 ATTN: ICAF. Technical LibraryATTN: J-2 ATTN: NWCLB-CR IATTN: J-6ATTN: J-SNPG Net Assessment jATTN: J-LW Office of the Secretary of Defense

L ATTN: J-ZT ATTN: Military Assistant

Commander in Chief, Atlantic U.S. National Military RepresentativeATTN: N-22 SHAPE

ATTN: U.S. Docunents Officer

Lonweande, in Chief. PacifitcATTN: J-634 Under Secy. of Def. for Rsch. & Engrg,

i ATTN: J-32 ATTN: Strategic & Space Systems (OS)ATTN: J-54~DEPARTMENT OF THE ARMY

Defense Advanced Rsch. Proj. Agency DepAtM f TH aRM fPkITN: TIC Deputy Chiet of Staff for Ops. & Plans IL

Departnent of the ArmyDefense Civil Preparedness Agency ATTN: DAF.-ZXA

ATTN: Hazard Eval. A Vul. Red. DiO.. G. Sisson ATTN: DAMV-NC, V. Falter 5ATTN: Deputy Director C.McLain ATTN: DAIU-NCN, G. Hipp

Defense Documentation Center Harry Diamond Laboratories I :12 cy ATTN: DD Department of the Army

ATTN: DELHD-N-PDefense Intelligence Aqency 4

5 cy ATTN: 06-4 U.S. Army dallistic Research LabsATTN: Technical Library

Defense Nuclear Agency ATTN: DRDAR-OLTATTN: STVLATTN: DUST U.S. ArT.v Cond. & General Staff CollegeATTN: RATN ATTN: ACO Library Division

ATTN: STNA4 cy ATTN: TITL U.S. Army Concepts Analysis Agency2 cy ATTN: VLWS ATTN: !VCA-WGP

Field Comnnand U.S. Army Europe and Seventh ArmyDefense Nuclear Agency ATTN: DSOPS-AEAGE

ATTN: FCPR ATTN: DCSOPS-AEAGC

Field Conmand U.S. Army Nuclear & Chemical Agency

Defense Nuclear Agency ATTN: LibraryU.S. Army TRADOC Systems Analysis Activity

Intelligence Center, Pacific ATTN: ATAA-TACDepartment of Defense

ATTN: COMIPAC U.S. Army War CollegeATTN- Library

Dist-1

... q'". - ', C "~ " 'I

DEPARTMENT OF TIHE ARMY (Continued). DEPARTMENT OF TIlE AIR FORCE (Contirnued)

U.S. Military Academy U.S. Air Force, Pacific* ATTN- Document Library ATTN: XP

DEPARTMENT OF THE NAVY U.S. Air Forces in Europe!ATTN: XPX

Naval Postgraduate School ATTN: DEPATN: Code 0142 ATTN: DOT

ATTN: INTNaval Research Laboratory ATTN: INN

ATTN: Code 1240DEPARTMENT OF ENERG,

Naval Sea Systems CommandATTN: SEA-09G53 Department of EnergyAITN: SEA-06J11 Albuquerque Operations Office

IATTN: CTIONaval Surface Weapons Center

ATTU: Code F31 DEPARTMENT OF ENERGY CONTRACTORS

Naval War College Lawrence livermore Laboratory iATTN: Docunwrt Control ATTN: Technical Information Dept. Library

Nuclear Weapons Tng. Group. Pacific Los Alamos Scientific laboratoryDepartment of the Navy ATTN: MS 364

ATTN: Document Control ATTN: T. Dowler

Nuclear Weapons Tnq. Group, Atlantic DEPARTMENT OF DEFNSE CONTRACTORSDepartment of the Navy

ATTN- Document Control Advanced Research A Applications Corp.ATTN: Document Control

Office of Naval Research

ATTN: Tecinical Inforntion Services Aerospace Corp.AITN: Library

DEPARTMENT OF THE AIR FORCEBM Corp.

Air Force School of Aerospace Medicine ATTN: J. BraddockATTN: Radiobloloqy Division

General Electric Cu.Ai- Force Systems Conunand Aerospace Grp. btrat. Planning A Prgms. Ops.

ATTN: SD ATTN: R. MircklerATTN: XRATTN: Ill General Electric Cc.-TEMPO

ATTN: DASIACAir Force Weapons Laboratory. ArsC

ATTN: SU( General Research Corp.ATTN: DYT ATTN: Tactical Warfare OperationsATTN: NSB

Historical Evaluation & Rsch. Org.Assistant Chief of Staff ATTN: T. DupuyIntelligenceDepartment of the Air Force ludson Institute. Inc.

ATTN: INA ATN: . Kahn

Deputy Chief of Staff lit Research InstituteResearch. Development A Acq. ATTN: Documents LibraryDepartme~nt of the Air Force

ATTN: AFRDQSM Institute for Defense Analyses

ATTN: Classified LibraryForeign Technology Division, AFSC ATTN: J. Grutc

ATTN: TORATTN: SON JaycorATTN: CCN ATTN: R. Sullivan

Strategic Air Command Kaman Sciences Corp.Department of the Air Force ATIN: F. Shelton

ATTN: DOATTN: NR Lovelace Biomedical & Environmental ResearchATTN: NRI-STINFO Library Institute. Inc.ATTN: ADINDS ATIN: 0. RichncondATTN: XP

A .Dist-2

I

,A

DEPARTMENT OF DEFENSE CONTRACTORS (Continued) DEPARTMENT OF DEFENSE CONTRACTORS Continued)

Martin Marietta Corp. Science Applications, Inc.ATTN: F. Marion ATTN: D. Kaul

Mathematical Applications Group, Inc. Ship Systems, Inc.ATTN: M. Cohen ATTN: B. Dunne

Pacific-Sierra Research Corp. SRI International 1 -ATTN: G. Lang ATTN: M. Earle

R & 0 Associates System Planning Corp.ATTN: C. MacDonald ATTN: J. DouglasATTN: H. Brode S e Se Ao .I

2 cy ATTN: L. Hanneman Systems. Science A Software. Inc.2 cy ATTN: Document Control ATTN: J. Cane

ATTN: J. NorthropR & D Associates

L ATTN: J. Thompson Tetra Tech, Inc.ATTN: F. Bothwell

Rand CorpATTN: L. Smallwood TAW Defense & Space S)s. GroupATTN: M. Weiner ATTN: P. Dai

Santa Fe Corp. Science Applications, Inc.

ATTN: D. Paolucci ATTN: Document Control~ATTN: W. Layson

Science Applications. Inc.

ATTN: J. WarnerATTN: Document ControlATTN: C. WhittenburyATTN; M. Drake

ta

II

Dist-3

.1 e.T' , " p '1_.,' ' "1 . .. .. . . . --- F. . . .. - :

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