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. THE DNA NUCLEAR BLAST STANDARD (1 KT)

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SJoseph E. Crepeau

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Final Report for Period 2 January 1980-30 January 1981 NCONTRACT No. DNA 001-80-C-6102

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Nuclear DetonationAirblastShock WaveBlast StandardBlast ScalingAOSTAAC? (COAnfte Ona Foviffe aid@ It n~foodiY 'A lMal titir OF 61066 Ain

A set of subroutines has been developed which provide completedefinition of the blast environment resulting from the free airdetonation of a one kiloton device in a sea-level atmosphere.The subroutines provide the pressure, density, and velocity a¢a fuuction of space and time (from I me to several minutes).The analytic fits are compared with results of hydrodynamiccalculat ons and with experimental data. Blast parameters Are

1D 1473 , ooN oP essoae UNCLASSIFIED

SECURITY C60 1 I4 0 1 I Ii

u,4CIAS I ý T ED

* TtV T CL A-%A10- A I'ON OF T I, I A•n(WkogaI Ne rldl

20. ABSTRACT (Continued)

as a function of radius at a given time. By su,,cossivecalls to the routines, time histories of the variousparameters may be generated.

A complete set of scaling routines is included to permitdefinition of blast waves resulting from arbitrary Violdand altitude combinations. A real gas equation of statefor air and a model of the US Standard atmosphere arealso included.

This report supercedes AFWL-TR-73-55 and AFWL-TR-73-55 (REV).

UNCLASSIFIEDIrCURITY CLASSIIICATION Of THIS PAO•ReM0I 4i* InlOW eiI)

TABLE OF CONTENTS

Section U1 .I N T R O D U C T IO N . . o . . . . . . . . . .... . . . . . . . . . . . 3

2. THE DATA BASE ....... . . . . .... . .. ............. 4

3. OBJECTIVES ...... ..................... .........

4. WAVEFORM DESCRIPTION ... .. ......... .... ... ..... .

5. SUBROUTINE DEFINITION ................... .....

6. USE OF THE ROUTINES .................. .. . .. ... . 21

7. RECENT DEVELOPMENTS AND CONCLUSXONS ,............ 24

REFERENCES .... ........................... 27

Appendi?

I. COMPARISON OF THE FIT WITH THE 0.50METER SAP CALCULATION ............. .* ........ , .... 29

II. COMPARISON OF I-KT STANDARD WITH OTHER FITS ...... 85

III. PEAK OVERPRESSURES AS A kUNCTION OF RADIUS ....... 109

IV. FORTRAN LISTING ................................. 111

V. PARAMETER VERSUS TIME PLOTS AT SELECTED RADII .... 131

NTIS ORA&KDtIC TAUtnannounoed

"A Juatitioation

Distribuation/.--Avll.billty Codel

'Avail and/orDi st jec

al

o0

1. INTRODUCTION

A roquirement for the descriptior of the blast environment

from a 1-kiloton, free-air detonation in a sea-level atmosphere

has been acknowledged for many years. This requirement has been

fulfilled by a variety of diverse calculations, curves and ex-

perimental data (Reference 1). in each case, only a partial

answer could be given, such as peak overpressure versus distance

or time of arrival versus distance.

One-dimensional calculations based on first principles

seemed to provide a solution. Probably the most famous of theme

was the IBM Problem "M" of the late 1940s (Reference 2). Con-

sideraole advances In the state-of-the-art of hydrodynamic cal-

culations have been made in the intervening years as more physics

was included in the codes. Even now, however, difference. occur

in the results of such calculations for a variety of reasons,

ranging from the basic differencing method used to the personalpreference of the person running the code.

A Nuclear Blast Standard ( KT.) was published by the Air

Force Weapons Laboratory (AMWL) in 1973 (Reference 3). Having

withstood the tests of time with only minor modifications, the

proposed standard has been accepted and is presented herein.

3

1 " r" ~~~~I " 1"."" r" 'r ' ~ ~ ' 1 •• r

2. THE DATA BASE

The set of subroutines presented in this report describethe airblast from a 1-kiloton, free-air detonation at sea level.

These subroutine, were developed as a fit to the resultsof one- and two-dimensional radiation hydrodynamic and pure

hydrodynamic calculations in Laqrangain and Eulerian coordinates

using first and second order differencing methods as well as

acoustic theory for the very late times (Reference 4).

A sufficient number of varied calculations have been madeso that effects of zone size, difference method, or other pecu-liarities of individual calculations have been eliminated fromthe fits. In addition to the first principle calculations, thefits have been checked with experimental data whure available(References I and 5). Several previously published curves foroverpressure versus distance have also been consulted (Refer-ences 1, 6, and 7).

Extrapolation has been used on the calculated peak over-pressures. This extrapolation has reduced the error due tonumerical smearing to less than 1 percent over a factor of tenin zone size. We are thus able to qive considerable confidenceto the calculated peak overpresaures and arrival times as a

function of distance. These parameters form the basic informa-

tion for the fits. The fit to the peak overpressure versus

distance curve wae presented in August .971 at the DASA Land-Naval Systems Lonq Range Planning meeting and is published inthe Proceedings (Reference 8). Since that time some minormodifications have been made, but the form of the equationremains unchanged. The maximum error between fit and extra-polated calculation is approximately 5 percent with the average

error less than 3 percent over the range from ten meters toseveral kilometers. The maximum error occurs in the early

time region where secondary shocks cause perturbations at theshock front.

The radius versus time curve is accurate to 1 percentover the range from ten meters to several kilometers with themaximum error (1 rercent) occu, ring between 15 and 40 milli-

seconds (160 and 270 meters).

We xhnuld point out that this set of fits ignores secondaryshocks and is designed to give accurate answers in the rela-

tively ideal case of single shocks. The fits are designed toaccount for the added impulse due to secondary shocks without

giving a second peak. The calculations show that no oonsequen-tial secondary shocks occux beyond a time of 0.01 second.

Tha uson is warned that the use of any "standard" definitionoe a blast wave for pressure greater than about 100 MPa canlead to errors. For radii less than about 15 meters (-100 MPa)the specific weapon characteristics may dominate the blast

environment.

*

S. . . . . . .... . . .. .. . . . . . . . . lll I I I I i i

3. OBJECTIVES

The 1-KT Standard was designed to accomplish the following

objectives:

I. Determine a functional relation that describes the

waveforms as a function of radius for each of the variables,

overpressure, overdensity, and material velocity.

2. Provide functional relations tor peak values for each

of theme variables as a function r•f radius.

3. Provide a method for obtaining the time of arrival of

the shook front.

4. Determine functional relations for the positive phaselength as a function of time.

S. Whenever possible the%* relations are required to be

physically rmleaninqful and to reproduce the predicted asymptotic

behavior of the variables.

6

4. WAVEFORM DESCRIPTION

The following is a general statement which traces theevolution of the waveform from strong shock to a nearly acousticwave.

4.1 Overpressure Waveform

The first objective was to find a functional relationthat describes the overpressure wavefrrM, i.e., a relation betweenradius and overpressure at any given time. This relation mustnecessarily describe the following overall time history of thewaveform development.

a. At early times the entire wavefoesm consists ofpositive overpresaure values (positive phase) only. The over-pressure values that describe the waveform decay monotonicallyfrom the peak overpressure value at the shock radius to a smallar,but positive, overpressure value at zero radius. As time pro-greases, the waveform peak overpreusure value decreases an doesthe positive overpressure value at zero radius.

b. At a time t5 (- 0.13 second) the waveform decays

in such a manner that it assumes a zero overpressure value atzero radius.

o. For time greater than t2 the waveform is described

by both negative (negative phase) and positive (powitive phase)

overpressure values. For a brief period of time the waveform

decays monotonically from its positive peak overprossure valueto a zero overpressure value at some radius (Ra) and continuesmonotonicaily to a negative overpressure value at zero radius.

d., From some time (tl) on, tte strictly monotonic

decay ceases and the waveform begins to assume a waveform which

7

-a -. . . . . . . . . . . I I I I I I I . . .. .l -' • ". JS. . . , , , ,. , , p II III| -

will be referred to as a well defined negative phase waveform.

These waveforms can be described as follows: The waveformdecays monotonically from a peak overpressure (positive) value

through a zero overpressure value at some radius Rz, and

continues to a minimum neqative overpressure value at some

radius, RMIw: for radii less than RI, and continuing to zero

radius, the overpressuro remains negative but monotonicAllyreturns to zero overpressure value as the radius approaches zero.

The region defined in paragraph d abovo may be character-ized by five basic parameters:

1. The peak overpressure (OP p).

2. The radius of the peak (R p).

3. The radius of the point at which the overnressure iszero (Rz).

4. The minimum overpressure (OP Im).

5. The radius of the minimum overpressure )

Using essentially trial-and-error methods, we found :hatthe initial decreasing region immediately behind the shockcould be fit ve:y well by a hyperbola of the form.

R -rOP(r) - (-r) ÷O (i+)AlR p-r)+3• p

where A and 8 are functions of time. This form holds from

r a RP through r w Rz. It is then necessary to modify thefunction so it passes through the points RMI, and OPM.N andreturns to zero. This is accomplished by multiplying thehyperbola by the S shaped function (Reference 9)

G (r) - -b (2)

where b, c, and n are functions of the basic parameters above.

Unfortunately G(r) approaches I as r + a but may be significantlydifferent from 1 at r a R P G was modified to the form

H(r) - G(r) +(3)

for R. i r I Rp and H(r) a G(r) for r < Rz.

The expression for overpressure versus radius at any time

greater than 0.95 second for R. I r I Rp is given by

OP(r) R Rp -r + OP -ber + rRZ1 (4)

and for r 1- RZ is given by

OPit) R P-r + O (,p-bern)

In the time region described earlier in this secion (t 40.1 second) there is no point at which tI•e overpressure is zero.

RHIN is then taken to be zero and OPM1N is the overpressure at(or near) RM.- The overpressure waveform for t < 0.1 second

is of the form

OP(r) - Decr + OPM1N (6)

:,I

where c is a function of time, and B is determined by the peak

conditions. in the time interval 0.1 1 t 1 0.95 a smooth

switching function is used to transform the early-time function

to that of late time. The overpressure waveform for any time

was now defined in terms of the five basic parameters.

The peak overpressure versus radius curve is a slightly

modified version of the formula presented at the ONA Long-Range

Planning Meeting in 1971 (Reference 8).

The formula demonstrates our objective of finding physi-

cally meaningful relations. The formula is of the form

OF,(R -A C (7)

p RR Zn ~43 exp 3 )1

where A, S, C, and RO are constants, and R is the shock radius.

The first term reflects thu reduction in pressure at early

times due almost entirely to the increasing volume. We realize

that radiation losses reduce the pressure oven more rapidly

than l/R3 at very early times, however, comparison with radia-tion-hydrocodes substantiates the inverse R3 behavior in theregion of the fireball even prior to hydrodynamic shock formation.

The second term is the "normal" spherical divergence term,

the pressure falling inversely as the surface area.

The third term is a modification of the asymptotic form,the shock wave decaying toward thd behavior of a sound wave.

The asymptotic form before modification is

OP (R) - (a)(I

,n (8)

(RO)

This form is not defined for R < RO and rather than using

a switching function, the term was modified (see Equation (7))to retain definition for all R.

The radius versus time curve is a combination of two

regions. At times lose than 0.21 second, a function of theform

R(t) - at 0 ' 3 7 1 [l.(bt+c) . (l_-dto.79)] (9)

where a, b, c, and d are constants.

For times greater than 0.21 second, an iterative procedurewas used in the original I-KT Standard.

The zero-crossing point (Rz ) and the positive-phase dura-

tion (R÷) have well defined asymptotic forms. These are givenby

Rz * C0t + a (10)

and

where a and b are constants, C is ambient sound speed, and

RO is the same as in the overpressure versus distance expression.The same modification to the R• relation must be made to ensuredefinition for all R. The peak radius is defined as RZ + R+,thus retaining the asymptotic form for R p. However, Re isdefined in terms of R., thus, the necessity of the iteration.

The iterative procedure was time consuming and comparison withearly-time hydrodynamic calculations indicated that the asymptoticform was not really applicable to the early time (0.1 to 0.4second) behavior.

Ai*

. . •, I , I I I II -lll .

• • i rr .

To eliminate the necessity of an iteration, a function

was needed to define the positive phase length (R+) as a

function of time. The revised l-KT Standard included such a

futction, however it suffered from larger inaccuracies thandid the iterative scheme it replaced. The current Standardrecommends a new function for times greater than 0.21 second.

The accuracy has been checked from 0.21 to 200 seconds and

has a smaller greatest relative error than either of the two

previous fits. The fit is of the form

R+ - a + b Ln(t) + atd (12)

where a, b, c, and d are constants and t is time.

A smooth-switching function is used in the region 0.21 to

0.28 second. The point of zero overpressure is of the form

Rs(t) a (l-b c) ( 0 0 t+d) for times > 0.95 becond, where a0 is

the ambient sound speed, t is time, and b, c, d are constants.The radius at which the minimum occurs is given by

.I(t) - 1z(t) - atb (13)

for t > 0.21 second, where a and b are constants. The over-pressure minimuw is defined in terms of the peak overpressure

and time.

4.2 Velocity Waveform

The general description of the evolution of the

velocity waveform is similar to that givAn for the overpressure

waveform. However, significant timing and shape differences.uust be reflected in the fits.

The five basic parameters used to describe the .,%locity

waveform arei

12i _ _ _ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ _ _ _ _

I ___________I___________I_______I_____I________ - - ,

1. The peak velocity.

2. The radius of tho peak velocity.

3. The zero velocity point.

4. The minimum velocity.

S. The radius of the minimum velocity.

The peak velocity is obtained through the Rankine-Hugoniot

relations using a variable y equation of state for air.

The radius of the shook front (the peak velocity) is the

same as that for the overpressure and this value is used.

The equation for the radius of the zero crossing is

similar in form to that for the overpressure and differs only

in the constants.

The radius of the minimum and the minimum velocity also

have forms similar to those of the overpressure.

The radius of zero veaocity bocomas defined at an oarlier

time than that of the overpressure (about 85 meters). The

switch to the late-time form takes place at an earlier time

(0.7 second) and the form of the early time waveform is

V(r) = Vpk (rlR )• (14)

where Vpk and Rp are the peak velocity and radius, respeatively,

and a is a function of time.

This form, as in the overpressure fit, does not account

for secondary shocks. The neglect of velocity fit@ at early

times and small radii (r 4 R /2) can be Justified by comparinqp

the momentum from the fit and calculation. Although the veloc-

ities may be significant, the density is small, and therefore#

the momentum, energy and mass flux are also small (by two orders

of magnitude) and may be ignored.

13

I I .... . .A1'. . . . l I. ...

, - , i m l -4

A smooth switching function brings the velocity waveform

from the early to the late time form between 0.25 and 0.7 second.

4.3 Overdensity Waveform

The overdensity waveform differs from that of the

overpressure and velocity in that it has a zero crossing evenat very early times (due to conservation of mass). The over-density has the following evolution:

a. The Monotonic Decreasing Phase. Here the over-

density drops from some peak vaLue at the shock front to aminimum value (negative) and rerains nearly constant to the

center.

b. The areak-Away Phase. The shock begins to separate

from the hot underdense fireball. The overdensity decreases

from the peak, begins to lev"%l off, and then rapidly decreasesto a minimum value where it remains nearly conctant to thecenter. This nearly constant relion becomes well defined and

is reftrted to here as the density well.

c. The Late-Time Phase. The shock is separated from

the density well. The overdensity docreases from the peak to aa minimum value, increases to nearly zero and then decreasesrapidly into the density well. Zn one dimension, this wellpersists for many seconds. Zn two dimensions it beqins to till

in and distort at a time depending on the height of burst.

The peak overdensity is found from the peak overpressure

using the Rankine-Hugoniot conditions. The ideal Rankine-Hugoniot conditions specify the density as a function of shock

pressure and ambient conditions

03I (y41)P1 * (y-l)pO001 (Y-l)P I + (Y-U)Po (15)

I 0 IYU I + I.+~ 0

where subscripts 1 and 0 represent the shock and amubLent condi.tions, respectively, this relation is valid for variable Y

gases if an appropriate average Y is chosen. ?or a gas withspecific heat, a linear function of temperature, the appropriate

average is given by

where Ye is the average value, Y0 is the ambient, and YI in the

value immediately behind the shock point.

2 (yO-1) (l-l) 2(y 1 -l)" .... + 1 ( 17)

Ye (yo.1)+•(yl.1) 1+÷71."

Yo-I

For ambient sea level iAr y, 7/5 a 1.4, then

2(y 1 -1)

e 1+5/2(y 1i-) 1 (19)

This is the form used in finding shuck front conditions.

The value for yis found by an iterative procedure through areal air equation of state.

We recognize that tne combination of equations 15 and 18

to not the usual formulation of the Rankine-Hugoniot equations

for density, however, this form is in agreement with available

radiation hydrodynamic calculations.

rf the usual equation

15

Ai

* is used (19)

Y ~ To1-

the shock densities resulting are as much an 30 percent greater

than any current radiation hydrocode results for radii less

than 40 motors, Beyond 40 meters the two formulations are ingood agreement.

The dAscrepancy between radiation hydrodynamic calculational

results and the ideal Rankine-Hugoniot conditions above 6 MPahas not been resolved. Zt may be some physical process orprocesses or it may be the inability of hydrocodes to resolve

high pressure shock waves.

The radias of the peoo is given by the radius of the shockfront. The radius of th, Z4.LU crossing has the same late time

and asymptotic form as the ;verpressure. At early times the

zero crossinq has the form

RI(t) a atb (20)

This form is used for times less than 0.265 second after

which time the late time for is uod.

During the monotonic decreasing phases the overdensity

waveform is given by

OD(r) w A + Beor (21)

where A, B, and c are functions of time.

IG

The late time fit has the same form as the late timeoverpressure and velocity fits. This means that the long

lasting density well is not described for times qreater than

0.2 second. This in also true of two-dimensional calculations

where the duration of the density well in a function of the

height of burst. Therefore, this seems to be a sufficientdescription of the overdensity for blast environment based

on one dimensional behavior.

The switching from early time to late time form takes

place between 0.2 and I second.

d1

L 1

5. SUBROUTINE DEFINITION

Considerable care has been taken to ensure that the routines

will be compatible with a large variety of computers and compilers.

The routines are written in standard FORTRAII, Word length or

exponent *ise limits should not be of concern to any user.

SMBROUIZN PXAK calculates all the information needed for

the three waveform fits--overpressure (OP), overdensity (00),

and velocity (V)--by a continuous series of transfers to par-

ticular subroutlies and functions. The subroutine is called

with time and radius, and returns the peak radius, the peak and

minimum overpressure, overdensities, and velocities, the radii

of zero, and minimum OP0, CD, and V. The calculated values are

carried from one routine to another throuqh the labeled common

block, WFRT, or may be obtained through an argument list (see

Section 6).

FUNCTIONS WFZR ,(waveform overpressure zero radius), WFDZR(waveform density zero radius), and WFVZR (waveform val.o.ity

zero radius) calculate the waveform radii at zero overpressure,

overdensity, and velocity, respectively. This is the radius

which separates the negative-positive phase portions of the

waveform at the specified time t.

FUNCTION vFPR2 (waveform peak radius) calculates the

radius of the shock front at the specified time Wt). The radiusof the shock front must be calculated before the OP, O, or V

peaks can be determined. The overpressure zero point must be

calculated before WFPR is called.

FUNCTIONS WFPKOP (waveform peak overpressure), WFPKOD(waveform peak over density), and WrPKV (waveform peak velocity)are callable with the peak radius and they return the waveformpeak OP, OD, and V, respectively. The routines must be executed

is

S. . . . . .. p

in the above order, as the OP peaX is needed in the OD peak

calculation, and both are necessary to determine the V peak.

SUBROUTzNES wFPImT, WFDRMT, and WFVRMT are callable with

a specified time (t) and radius (r), and calculate the OP, OD,and V at r. These routines require peak radius, peak andminimum parameters, and zero crossings before being called.

SUBROUTINE AIR is the equation of state for air used at

the Air Fores Weapons Laboratory and is included as part ofthis package. it is used in evaluating the Rankine-Hugoniotrelations for variable Y. The calling sequence is

CALL AIR(E,RHOGMONE)

where E is the energy density in ergs/gm, RHO is the density

in gm/cc, and OMONZ is (y-l).

SUBROUTINE MATM62 is a model atmosphere. Specifically,

it is the 1962 U.S. Standard temperate atmosphere with extensionto 700 kilometers. The subroutine in called with an altitude(in metors) and it returns the atmospheric pressure, densityand temperature at that altitude.

SUBROUTINE SCALKT calculates the modified SACfl's scaling

coefficients using the model atmosphere MATM62. The routineis called with the height of the point of interest in m andthe yield of the burst in KT. The routine then calculates

scaling factors for velocity, density, time, distance andpressure.

SUBROUTINE WELL defines the fireball density well to a

time of I second. The fireball is filled between I and 1.2seconds because, in the real case, a fireball would have risen

from the point of detonation. For a more realistic model ofthe fireball a three-dimensional model must be used.

19

r~4

S .. . . .. . . . . . U- . . . . . . . . . . . . . . . .III . . I- -I I I I . .

/

SUBROUTINE SHOCK is called with an arbitrary yield andaltitude. Scaling in done interior to the routine and theoverpressure, overdensity and velocity for the given yield,altitude, time, and radius are returned.

20

Z 4

..*• .. ,,• t I

6. USE OF THZ ROUTINES

For a I-kiloton, sea-level, tree-air burst PEAK will bethe only routine called. Given a time and a radius, subroutine

PEAK returns tho shock radiua, the overprelsure, overdensity,

and velocity at the shock front and at the given radius.

The routines are much faster if several radii are calledfor a given time rather than severql times at a given radius.

The first evaluation a a nef time iequires approximately

four times as much computation at subsequent radii at the same

time.

The calling sequence is CALL PEAK (T, Ro SR, 0PK, ODK, OPR,ODR, VPK, VR) where

T is timq in seconds

R is radius in mSR is the shock radius at T in mOPK is the overpressure at SR in Pascals

ODK is the overdensity at SR in kg/mrOPR is the overpressure at R in Pascals

ODR is the overdensity at R in kg/mi3

VPK is the velocity at SR in m/s

VR is the velocity at R in m/s

The results are for a standard nuclear 1-kiloton detonation in

a free-air, sea-level environment.

For arbitrary yields and altitudes, subroutine SHOCK may

be used.

The calling sequence is CALL SHOCK (YIELD, ALT, T, R, OPR,ODR, VR) where the input parameters aroe

21

YIELD - the yield in kilotons

ALT - the altitude of the point of interestin meters

T - the time in seconds

R - the radius from burst po.nt to thepoint of interest in meters

The calculated parameters are:

OPR - overpressure in pascals at the point

ODR - overdensity in kg/mr3 at the pointVR - velocity in m/s at the point

SUBROUTINE MATM62 provides ambient atmospheric conditions

as a function of altitude. It is based on the 1962 U.S. Standard

tomperate atmosphere. The routine hat five arguments, the firstis the altitude of interest (in ineters). The routine returnsin order, the pressure, sound speed, density and temperature.Caution should be used when asking for atmospheric parametersabove 100-km altitude. MXATM62 assumes the constituency of theatmosphere tc be that of sea level, and does not account for

the molecular dissociation in the ionosphere.

CALL MATM62 (ALT,WSP,CS,WSR,WST)WSP - Pressure (pascals)

CS - Sound Speed (m/s)WSR - Density (kg/mr3 )

WST - Temperature (OK)

SUBROUTINE AIR is the Doan Nickel equation of state forair (Reference 10). The units for this routine are cgs.Ther7e are three arguments for SUBROUTINE AIR. The specific

energy and density are the first two arguments, and the valu&of Y-1 (wh.rre Y is the ratio of specific heats) is returnedas the third argument. This routine is valid for densitiesfrom 10 times ambient to 10-7 of ambient and for energies up

to 2 x 1012 ergs/gm above which it degrades gracefully.

22

- j... .. ...... . .- III - - - --.

EEE Specific Energy (ergs/gm)

RER - Density (gm/cc)

GMONE - (Y-l), where Y is the ratio of specificheats

Occasionally it may be desirable to determine the shock-

front pressure at some distance from the burst. Function WFPKOP

(waveform peak overpressure) may be used, however, the units

are c.g.s.. WFPKOP returns the shook-front overpressure in

dynes per square centimeter for a range R in cm.

The WFPR 2 function returns the shock radius in cm at a

time (t) in seconds.

SUBROUTINE SKALKT calculates the various scaling coeffi-

cients for arbitrary yield and altitude. The routine is calledwith the height of the field point and the yield of the burst.

HFPT - Height of the field point (m)

WB - Yield of the burst (kt)

The output parameters are the velocity, density, time, distance,

and pressure scaling factors. CAUTION. the time scaling factoris the inverse.

VSCALE - Scales 1-kiloton, sea-level velocity toWE, HFPT

DSCALE - Scales 1-kiloton, sea-level density toWE, HFPT

TSCALE - Scales HB, HFPT time to 1-kiloton sea levelCSCALE - Scales 1-kiloton, sea-level distance

to WB, HFPTPSCALE - Scales 1-kiloton, sea-level pressure to

WB, HFPT

For implementation and proper use of the scaling factors, refer

to subroutine SHOCK. It is not recommended that other routinesor functions be used independently.

23

____.________________lI____-- .______... ...... .. ______

* -... m

7. RECENT DEVELOPMENTS AND CONCLUSIONS

As work on this model progressed, two deficiencies became

apparent. Several potential users have expressed the desire

to have the density of the fireball more well defined at late

times. This becomes a two-dimensional problem because the

fireball rises in time while the shock remains approximately

spherical. The structure within the fireball becomes even more

complex if we include the effects of reflected shocks and shock

torusing. Although these effects are not included in this model,

a fully three-dimensional model (LAMB) is presently available

to DNA users through Kaman TEMPO, Albuquerque.

Four changes have been made to the l-KT Standard routines.

of References 3 and 11. The first is in the function WFPKOP,which calculates the peak overpressure as a function of radius.

The constants in the data statement have been changed back to

those of Reference 3. The -nstants are as follows:

Parameters From To

AC 3.18E18 3.04E18AQ 1.00E14 1.13E14

ASTAR 9.0E9 7.9E9RSTAR 4.454E4 Unchanged

The major effect is in the region of peak pressures below5 psi (30 KPa). The new constants yield a lower overpreasurein this region- rhe higher pressure region is affected very

little.

The radius of ýhe shock front as a function of time is

calculated in the function WFPR2. The changes in this routine

affect answers for times greater than 0.1 seconds. Two separate

equations are dsed for times less than 0.21 seconds or greater

than 0.28 seconds. A linear interpolation of the two equations

24

-- -•.-

is used between these two times. Agreement with the 0.5-m SAP

calculation is very good for all times as shown in Appendix I.

A third change was made in the function routine WELL. A

constant in the equation for DEPTH was changed from -1.175E-3

to -1.21E-3. This allows the overdensitt inside the fireball

to fall to a minimum value of -1.21 kg/l , Examination of

results of the one-dimensional FAB calculation made by Kaman

AviDyne and of the Los Alamos National Laboratory (LANL) fire-

ball calculation reveal that the overdensity may fall as low3

as -1.22 kg/m . A reasonable average was taken to be -1.213kg/m . Comparison with the 0.5 meter one-dimensional SAP

calculation are also in good agreement.

The finaJ change was made to the internal units conversion.

The routines are now programmed for input and output in MKS

units. The routines internally convert to cgs units before

calculations are made and then back to MKS units before answers

are output.

25

REFERENCES

I. Moulton, J., "Blast Phenomena from Explosions in Air,"unpublished.

2. Galentine, P.G., "A Note Concerning Free AirblastInformation from the "M" Problem", LA-1367, February1952.

3. Needham, C.E., et.al., "Nuclear Blast Standard (1 KT)",AFWL-TR-73-55, April 1973.

4. Whitaker, W.A., "Theoretical Calculations of thePhenomenoloqy of HE Detonations*, AFWL-TR-66-141,November 1966.

S. Glastone, S., "The Effects of Nuclear Weapons",Atomic Energy Commission, 1962.

6. Brode, H.L., "Height of Burst Effects at High over-pressure", DASA-R.4-6301, July 1970.

7. Lehto, D.L., Larson, R.A., "Long-Range Propagationo! Spherical Shockwaves from Explosions in Air",NiOLTR-69-88, July 1969.

S. "Proceedings of the DASA Shock Physics Land-NavalSystems Long-Range Planning Meeting", August 1971,

9. Davis, Dale S., "Nomography and Empirical Equations",Reinhold Publishing Corporation, New York, 1955.

10. Doan, L.R., Nickel, G.H., "A Subroutine for theEquation of State of Air", RTD(WLR) TN-63-2, May 1963.

11. Needham, C.E., at.al., "Nuclear Blast Standard(I KT)", AFWL-TR-73-55, April 1975, (Revised).

12. Smiley, R.F., Ruetenik, J.R., Tomayko, M.A., "FADCode Computations of a 1-KT Nuclear Free-AirblastWave to Low Shock Overpressures", DNA-4825-F,January 1979.

27 pas N-- A w sum44•

APPENDIX I

COMPARISON OF THE FIT WITH THE 0.50 METER SAP CALCMATION

This appendix contains plots of hydrodynamic variables as

a function of radius at qiven times. Also on each plot are theresults of the AFWL SAP hydrodynamic code calculation which had

0.5 meter Zones in the atmosphere. The I-KT Standard is a fit

to many calculations, the 0.5 meter SAP calculation is repro-

sentative of those calculations, but does not constitute a"best fit*. The SAP data are represented by the Symbol X# the

continuous curve is the fit.

Thm radius of the shock front plotted here was calculatedby the non-iterative procedure described as optional in the

main text.

2

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~I .

APPENDIX 11

COIMPARSON OF l-1.T STANDARD WITS OTHEt FXTS

This Appendix contains comparisons of several parameters

generated from the I-KT Standard vith those from References 1,

5, 6, and 12. when parameters were not available from those

reforencess the 1-KT Standard is plotted alone.

b.

K __

10

100Radut...

yIi 0yARVLVESSRD

10-3

102

10

10

10

100 3.000 10,000Radius (m)

TXk4Z Or ARRIVAL VERSUS RADIUS

17

10 L

I I00 1 wO T I

10-iu 2aIZM OF IMVA IESSDU

P-4

-44

100 200 00

10-,

100 IV 1001,0A~ls M

10

90 I0 Iz II F A.

__ _ __ _ _ __ _ _ __ _ _ __ _ _ __ __4_ _ _ f I. I. F I

T II

*~ T1 K - tadx -

101

4.*X Standard.

"- .- o-

.10

0000

I-I I-

I,,'.X ' I

106

1tadLuas (in)

OWIRflhSSOR VLSUS PADZWO

03

10

-~~7 - -,ME-- - .

vliz .......

I I -ST Standar r-..mu- Canister Pi

ISO100 6000

OV,"RPRESSURE VERSUS RADIUS

94

-r-f t Polynomial-

10000Ra14 m

LT..

10

*.porobie Polymmit ofCmie- Plnm

100

IVRKSP VERUSRAI.

I-RT tand~d 94

977

10~

eleaogFAN Calculation*--

100

Radius Wm

OVERPRESSUTRE VERSUS RADIUS

____________________98

10

I -e ias -- I I I

I- T Standard____

-a-.'- ri

lo 2 ...o-.

1~ 10 100Rais m

OVRRSUEIPLS6ESSRDU

W9

100

I I

100

04

100

10~

4.0

2..10 -

10 10 10

Radius (m)

DYNAmic PREssuRz rmpuLsE VERSUS RADTUS

103

100 100 110,0001

DYNAMICv PRSSR I~PS ISU RAIU

100

-10 M

tta

~V

-, 71h

105

Los-

4

1.0

>10

102

10

100

10 .. a --

10~00 2000X II

Radium (in

SHOCK VELOCITY VERSUS RADIUS

108

ot PE~:AK OVERPRESSURES AS A FUCTO OFnAtIon

'I J109

PEAK OVERPRESSURE AS A FUMCTXON OF RADIUS

R(W) OP (PASCALS) OP (PASCALS) R04)

10 3.1638 1.39 6.78

20 4.12V7 2.38 11.67

s0 3.04E6 I.E8 14.75100 4.9535 2.37 25.66200 1.05ES 1.37 32.6S

500 2.13E4 2.Z6 58.301000 8,10E3 I.36 75.732000 3.28E3 2.E5 147.35000 1.05E3 1.35 204.8

10000 4.58E2 2,E4 525.520000 2.05Z2 1.E4 856.3

50000 7.321I 2.33 2955.0

100000 3.4121 1.33 5190.0

2.E2 20450.0

1.32 37770.0

1.10

APPENDIX IV

roRTRAN LISTING

This Appendix conrtainh a FORTRAN l.isting of the not ofsubroutines described ina this reprt.

. M ,I '; "

,.I.-L4LA7'L•, ,,(.~ ' F~L Z

- 14.'. 1

.V **, -, ,*•. .. . . , i~t .*

A'Fo

1*44, : FA:. ",

f. "

11

P'. 71 %;

IVL'Tig

IN ~ ~ ~ h .4AM E L

ue" M.9* A I* M6

7?-I ACI.S 1;FAT CfrmlDNA1-ý VAýA;w 3 -N"'L~rlr 4.4! ýe

113

vtf .J7 -s ';r F- . Z~~

I r

,g?1~ ~ 1 ~M~ 114

IXiý 7P SL~-; TiCUN~ I RUTI

I ~FOý1AT A. T i .ii E.NhI~ C7

11

NR1 %,4 OLTX PART rCF THE CN I'vý7 STANOW BY 4U I E-, A.L,.

.11

c

II

117

'r'STS TOrIi4 :F Tii StU Ff17 AL.

44 oui 10 ell

CMMWN t'6rFRT/ 3

'41 O4N~

2MINiol4, 4AMAiOARAPI 6Z*ýWA AT i 'lW #

NE II Z r.2.

vp* ~&J~' vi

THI pWI I 4' F K wAH IW Vq-k L

IS 1

120

* ': .TC Z) 0 TO Z6

12-3t~ol. I.ddi

,.p,~ v p tn vM.

-MN

i) TO 5

:; IF (7iMU.T700. 00 TO 4

MLH

k 121

-'..,Ubij'E 7; OA F TKEZA1~ SiikARD VY :- k

E2..

122

%3 ;-*6T!NE 1S P'RT OF TKE :N 1-KT 174OWD 31 ýEwým V AL. F;ý

COMO/WrfTi '~ ~ ~ RfZV ~~~,~

DATA 700/0.I0./

lF~ GO TO 3

70Z 0TO Z

vA~ D

*~54t

10.~ !, ,.

Q. 6.6( - A l-5

C: 4

SI.,, '123M

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:AT

VI 1

12

12Z4

MKRIjTIE WVFAT (TO) v'7TWI AQGUT14E iS PMT OF Nh DA H!? ST"10 SV NOI~it ET AL..v

4 /~~~WF'%T/ ~,P1,~,

LATA 7=10I.01

MTO I

IV6

a.m

I * . .Mun .

102%_ 4V

125

4Z6

N M. rl k . W

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126~

OJN ..44

I F

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ala,.N;a.. .~ 4 00

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OA t

ta T " "E ' * 41114 R ý U . % : N E 1 .F : N-U,-b . Z 4 %

a ~ , I ,r , A, is . :-., -' 'mi I6 ~iV' t

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* .~::'Aa~ 4All

AtN

j 129

APPENDZX V

PARAMETER VERSUS TIM? PLOTS AT SELECTED RADII

This Appendix contains parameter versus time plots at

selected radii. The parameters include overpressure, oves.pressure impulse, velocity, dynamic pressure, and dynamicpressure impulse. The radii were chosen as those oorresponding

pressure levels of 10,000, 1000, 100, 10, 1, and 0.5 psi.

A. - '.....131

T

OVERPRESSURE VS. TIME-

B,.

PROWES. 1.8770E401 M

'.•1

0.1\

TIME(SEC) (XIO -)

1-.%T STANDARD

2132

. . . .. ... .

OP IMPULSE VS. TIME

RAODUS : 1.677MtEO1 M

I-TANDARD

L3 3

_ _ _ *. -1I i i _

VELOCITY V33. TIME

AOUS : 1.877&O.I M

,i-l

3134

,I

J ,

U________II , I I I • iT"..'oaI m• Q•'DI .'Qo . i . I I. l.

TrME(SEc) ( XLO "•1

1-KT STANDARD

S... . I III lll ll3 4 ii -

E'YNPMIO"', PRESSURE VS. TIMIE

135

IMim

DP IMPULSE VS. TIME

RIFIUS = 1.V 001 M

~I

L n

:13

I ,

S',

iii

1-KT STANDARD

j 136

OVERPRESSURE VS. TIME

sAorus z 3.73 +0~1 M

I-T TOM

:13

OP IMPULSE 'VS. TTMC

RAMtS :3.7YM7oE l m

'..00 3.00 10.00 12.00 II.0 1.TI&ME (SEC) CXtO -2)

t-RT STAZ4DAND

138

i-

• VELOCITY VS. TIME

II"

Si

rI"ME(SEC .A1.0 -"I

2-KT ITAk4UMW

139

DTNRMECO PRESSURE VS. TIME

RADIUS :3. 7370E Io M

rrmE(sEc) mXo-2)

f 1I-K? STAMDAP.D

140

OP IMPULSE VS. TIME

RADIUS = 3.7370E.O1 M

S I

oI

i' •I I "I "I i ... .

-o.DO t.O'O Gi. O 1.00 t0.00 12.00 11L 00 W. 03TIME(SEC) CX!.O -2)

1-K? STAMMAR

141

OVERPRESSURE VS. TIME

~RD1US a. .79GOE+1 M

1*. I I0 Im 100 s

1-KT TNM

142

S

OP IMPULSE VS. TIME

RADUS /Smo

6.wI // •

/1

•. /

I';MESEC) (XIO -2)

I,.IT SITANDARJDmS143

III

i i -i i - - i | I i

VELOCITY VS. TIME

8.

RADIUS a. +05~E.1 M

ii- !

114

TrIMCCSEC) tX10-2)

1.-KT lTANHDARD

S....... j144

j _ _II -" . .. . • ....... *. • ,•

DYNRMIC, PRESSURE VS. TIME{ RADIUS a. 8+0E.1

'4"

206 L 040IO

SrESC (I 2

OP IMPULSE VS. TIME

I ~~RADIUS +0.~3~'1 M

L .c 0 1.04g LQ I.c

UEESC)(I

SIT TNDR

S.4

OVERPRESSURE VS. TIME

RADOIUS = ;&.8ON02 M

ja

147

S=,,• •-Fq .. .~~~~. r IIIi" ._.

*21 • ' , , n , i I I I I I I I --

OP IMPULSE VS. TIJME

'1RARDIUS = 2.IOWEi.O2M

TN (SC -XI -21)

11'

VELOCITY V'.. TIME

SRRDI•II 2.048E+02 M

B"'

I N'

W

""1 " _"_ _ _ __'III . .rIMECEC) (X. O -2)

1-KT STANDARD

S•149

DYNRME[ PRESSURE VS. TIME

I ~ADItUS :2.tJI48E+NJ M

o4

.~j

ITIME(SEC) X0-.

3.-KT STAN4DARD

ISO

DP IMPULSE VS. TTME

RA~rU = 2WBLW+CP

37. so a. LM 1. o 4. 0 4. 0c

/'.M (E ) CI 2

//TSTNA

LiI

OV\ERPRESSURE VS. T1IME

mprDus: 1. 1286E. M

115

OP IMPULSE VS. TIME

RAlDIUS 1. 12W M

~15

VELOCITY VS. TIME

PROWUS :1. 1286E.I M

JIK ITNA

'No

DTNRMIC' PRESSUME VS. TIME

RAO IUS :1. 128SE. M

MX 2100 2W.00 291.100 20S0 =.'go 31C.U 35TIMEISEC) (XIC 2

1-K? SANUMR

OP IMPULSE VS. TIME

RADIUS :1.12ME.03 M

TIE(EC --7 2

/ -TIAO

OVERPRESSUREV. TIME M

11<5

OP IMPULSE VS. TIME

RI ODUS : .9216E103 M

i,• //

/ /

TIME(SEC) XLO -2)

I-KT STA•DARD

250

VELOCITY VS. TIME

1 RADIUS' : 1.9218E0 M

1

£10.0N USAO MC £2.0 3300 0 UMa0 cc~TIMECSEC) CXLO -21

PI IKT STANDARD

[

DYNRMI:MC PRESSURE VS. TIME

RADIUS : 1.921E03 M

ISO

IK

16

OP IMPULSE VS. TTME

AROZUS :1.921W*WO M

riusc Iic2

U-TIJW

DISTRIBUTION LIST

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