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LA-7833-MSInformal Report
C.3Cl C- l 4 REPORT COLLECTI ON
REPRODUCTIONCOPY
Fireball Shape as a Height-of-Burst Diagnostic
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LOSALAMOS SCIENTIFIC LABORATORYPostOf f i ceBox 1663 Los Al amos, New Mexi co87545
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An Affirmative ActIon/Equal Opportunity Employs
This report was not edited by the TechnicalInformation staff.
Work supported by the Defense NuclearAgency.
T h, s rewtt was p rw. rrd s a n a cc ou nt o f work s pwwu mdb y th e U ntt ed S ta te s G ov rm me nt. N cIt he r th e U mle d S ti le sn or th e U .il ed S U1e s De mri men t o f En . rg v. n or an y of th ei r
m pl oy ee s. n ot a ny of th em c .nt mc wws . s ub con tr.ct o: s. o rtheir mployers, makes any warrantY. x vrei s o r Imp li ed . o ra ss um es M -Y 1 ,s s1 h .b il my 0 , re=vo nx tb d, t v fo, t he d CC U CY.c omp le te neu , ? r u sef uln es s of an . mf on nau o?. ap pdr at us ,n roduct . o r DIC.CeUdswlowd. or raaresents that m usc wouldn ot i n ft ln sc p nv.t .l y o wn ed n sh ls .
UNITED STATICS
DEPARTMENT OF lcNcIRGV
CONTRACT W-740 B-ZNG. 36
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LA-7833- MSI nf ormalReport
Swcial DistributionIssued: June 1979
Fireball Shape as a Height-of-Burst Diagnostic
Eric M. JonesJeffrey D. Colvin*
EG&G, Inc., P.O. Box 809 Los Alamos, NM 87544.
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i
FI REBALL SHAPE AS A HEI GHT- OF-BURST DI AGNOSTI C
by
Er i c M J ones and J ef f rey D. Colvin
ABSTRACT
The shock wave produced by an atmospheri c nucl earf i rebal l ref l ects f rom the ground and st r i kes thebot t om of t he gl ow ng f i r ebal l at t he t i me when t he sumof the f i rebal l radi us and the shock radi us equal st w ce t he bur st hei ght . RADFLO cal cul ati ons have beenused t o def i ne the f unct i on R f i rebal l ) + R shock) =f Y, t) . Fi rebal l shape i nf ormat i on i s used todet er mne t he t i me when shock/ f i r ebal l i nt er act i onoccurs and to deri ve the hei ght- of- burst .
I . I NTRODUCTI ON
The evol ut i on of an atmospher i c nucl ear f i rebal l i s governed by the weapon
mass, yi el d and conf i gurat i on, the pressure and temperature of the atmosphere,
and the hei ght- of - burst. I n many ml i t ary appl i cat i ons hei ght s-of - bur st ar e l ow
enough t hat i nt eract i on between the gl ow ng f i r ebal l and t he shock wave
r ef l ect ed f r om t he gr ound sur f ace occur s l ong bef or e buoyancy f or ces become
i mport ant . I n many of these appl i cat i ons, the desi r ed ef f ect i s a sensi t i ve
f unct i on of bur st hei ght . Real - t i me hei ght -of - burst data may be of potent i al
val ue, part i cul arl y i f t he dat a can be determ ned f rom a si ngl e observi ng
stati on.
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Let us suppose t hat an at mospher i c nucl ear bur st of unspeci f i ed y-
occurs at an unknown range from a proper l y i nstrumented observi ng stat i on.
parameter s to be determned are yi el d, range, azi muth, and hei ght -of - burst .
pr opose t hat al l f our par amet er s can be det er m ned w t h t wo pr i mar y i nst r um
el d
The
We
nt s
and a smal l computer or processor. The two i nst ruments are a bhangmeter and a
fast read-out , real - t i me i magi ng ar ray. The bhangmeter i s used to determnem ni mum t i me and, hence, t he yi el d whi l e r eal - t i me f i r ebal l shape i nf or mat i on
provi des the three remai ni ng parameters.
II. METHOD
We presume that burst s of i nterest w l l be l ow- mass ai r burst s. The
assumpt i on of l ow mass assur es t hat we w l l be deal i ng w t h weapons w t h hi gh
radi at i ng temperatures and t hat t he ear l y f i r ebal l growth w l l be vi r tual l y
spher i cal . U. S. at mospher i c t est s of weapons i n massi ve t ower s or suspendedfrom bal l oons show consi derabl e asymmetr i es and bri ghtness i r regul ar i t i es even
at very l at e t i mes. Ai r dr ops of l ow mass- t o- yi el d rat i os al l pr oduce ver y
spher i cal f i rebal l s.
The yi el d i s determ ned fr om ti me- of- mni mum measured w th a bhangmeter.
Duri ng the bl ast wave phase of expansi on t he radi us i s cl osel y
approxi mat ed by
R= 301 Y/ P) l / 5 t */ 5, 1)
where R i s the radi us i n meter s; Y the yi el d i n ki l otons; p the ambi ent
at mospher i c densi t y i n m l l i grams per cubi c cent i meter ; and t the t i me i n
seconds. Because the
acceptabl e to assume a
as yet t o be det er m ned
I magi ng data can
radi us i s so i nsensi t i ve t o densi t y i t w l l probabl y be
val ue f or t he densi t y. An i t er at i ve scheme based on t he
burst hei ght coul d be adopted i f deemed necessary.
be used t o der i ve t he t i me hi st or i es of t he ver ti cal and
hor i zontal angul ar di ameter s. Know edge of the yi el d and the hor i zontal angul ar
di amet er l eads di r ect l y t o t he r ange and, f r om t he posi t i on of t he i mage on t he
detector, azi muthal data i s obtai ned.
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The f i nal pi ece of data, the hei ght - of -burst , can be obtai ned f rom
compari son of the two angul ar di ameters.
The f i r ebal l expansi on w l l be t spher i cal unt i l t he r ef l ect ed shock wave
st ri kes t he gl ow ng f i r ebal l . Shor tl y af t er shock/ f i r ebal l i nt er act i on t he
bot tom sur f ace of t he f i r ebal l i s sever el y f l at tened. Before the i nteract i on,
t he r at i o of t he ver t i cal di amet er t o t he hor i z ont al di amet er i s appr oxi mat el y
equal one but as t he i nt er act i on pr oceeds t he r at i o dr ops shar pl y. Anal ysi s of
t he t i me hi st or y of t he di amet er r at i o pr ovi des a t i me- of - i nt er act i on whi ch can
then be used to deri ve the hei ght- of - burst.
III. HEI GHT- OF- BURST SCALI NG DATA
The LASL one-di mensi onal , spher i cal , radi ati on tr ansport / hydrodynam cs
pr ogr am RADFLO has been ver y successf ul i n cal cul at i ng at mospher i c nucl earf i r ebal l evol ut i on. Fi r ebal l and shock r adi i pr oduced by t he progr am ar e i n
good agreement w th data.
We assume w th some conf i dence that the shock/ f i r ebal l i nteract i on occurs
when
SH = 2H- RFB 2)
where RSH i s the shock radi us, RFB i s the f i rebal l radi us and H i s the burst
hei ght Fi gur e 1) . We r ecogni ze t hat t he r ef l ect ed shock t r aver ses sl i ght l y
heat ed ai r bef or e st r i ki ng t he f i r ebal l and t hat t he i nt er act i on act ual l y occur s
sl i ght l y bef or e t he t i me gi ven by equat i on 2) . However, we expect that the
ef f ect i s smal l compar ed t o l i kel y yi el d uncer t ai nt i es.
A ser i es of RADFLO cal cul at i ons have been made f or burst s of var i ous
yi el ds at sea- l evel densi t y 1. 2x10- 3 gcm 3) . The f i r ebal l r adi us was chosen as
the 0. 2 eV temperature contour whi l e the shock radi us was chosen as the l ocat i on
of maxi mum densi ty i n the computed shock prof i l e. Posi t i onal uncer tai nt i es are
about one cel l w dt h or about one per cent of t he r adi us. These data were used
to compute t i me hi stor i es of RSH + RFB. The r esul t s ar e pr esent ed i n f i gur e 2.
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UNCLASSI FI ED
Fig. 1Determnat i on of the t i me of f i rebal l / shocki nteract i on permts der i vat i on of burst hei ght .
1 ?
BLAST WAVE
~ REGIME
fa
102,:2 ,~-1 d
TI ME see)Fig. 2
The f i rebal l radi us RFB) and shock radi us RsH)are cal cul ated w th RADFLO. Know ng the yi el dand t i me of f i rebal l / shock i nteract i on gi ves2H = RFB+RSH f r om t he gr aph. See t he t ext f or afur ther di scussi on of thi s f i gure.
UNCLASSI FI ED
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The curves i n f i gure 2 are l abel ed w t h t he paramet er 301 Y/ P) l / 5. The
curves, i n ascendi ng order, correspond to sea- l evel burst s w t h yi el ds of 1,
3. 5, 12, 32, 75, 200, 800, and 1600 ki l ot ons.
The pl ane of f i gur e 2 i s di vi ded i nt o t hr ee phenomenol ogi cal r egi ons.
Dur i ng t he ear l y f i r ebal l expansi on t he ai r i mmedi at el y behi nd t he shock hasbeen heated t o great er than 0. 2 eV and the shock and f i rebal l radi i are
i denti cal . Dur i ng t hi s bl ast wave phase bot h r adi i ar e cl osel y appr oxi mat ed by
equati on 1. At a t i me gi ven by t he l ef t most dashed l i ne, t he weakened
no l onger capabl e of heat i ng ai r above 0. 2 eV and t he shock det aches
f i rebal l .
shock i s
f rom the
At very l ate t i me, f i r ebal l s whi ch have not yet under gone shock i nt er -
act i on are def ormed by buoyancy f orces. The ver t i cal def ormat i on i s
approxi matel y gi ven by
AR = gtz 3)
wher e g = 9. 8 m S- 2 i s t he gr avi t at i onal accel er at i on. Dur i ng t he l at e f i r ebal l
evol ut i on t he f i r ebal l r adi us r eaches a maxi mum and sl ow y decl i nes t her eaf t er
whi l e the shock wave vel oci ty approaches the sound speed. The upward curvature
of the RFB + RSH l i nes i s a resul t of thi s behavi or . ) The maxi mum f i rebal l
r adi us i s desi gnat ed as RM I f t he buoyant def or mat i on exceeds a f ew per cent ,
t he hei ght - of - bur st anal ysi s suddenl y becomes mor e compl ex. Thi s buoyancy
regi me has been del i neated by the AR = 0.02 RM l i ne at the r i ght of f i gure 2.
The graph
determned f rom
di ameters. The
the burst hei ght
Iv. TEST DATA
i s used as f ol l ows: t he t i me of shock/ f i r ebal l i nt er act i on i s
the hi story of t he rat i o of the ver t i cal to hor i zontal
known yi el d i s t hen used t o i nt er pol at e bet ween t he cur ves and
i s read as hal f t he sum of t he t wo radi i .
We have anal ysed photographi c
t est s conduct ed i n Nevada f or whi ch
dat a f or seven U. S. atmospher i c
uncl assi f i ed yi el ds ar e avai l abl e
nucl ear
and one
Paci f i c t est . Al l were l ow mass ai r drops. The rel evant data for t h e seven
events w t h t he uncl assi f i ed yi el ds are gi ven i n Tabl e I . Al l had p= 1.OX1O-3
5
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gcm 3. The hi st or i es of t he r at i o of t he ver ti cal and hor i zont al di amet er s ar e
gi ven i n f i gures 3 t hrough 9. For t he pur pose of t hi s paper we have m r el y
est i mat ed t he i nt er act i on t i me as t he t i me of a si gni f i cant , sust ai ned dr op of
t he di amet er rat i o. The range of t he est i mat ed i nt er act i on t i me t i ) f or each
event i s gi ven i n Tabl e 1,
The der i ved bur st hei ght s HD) ar e pl ot ted agai nst t he act ual hei ght s i n
f i gure 10. Cl ear l y, the error s are l ess t han 50 meters i n al l cases. The
rel at i ve error s are gi ven i n Tabl e I f or t he seven uncl assi f i ed events. Al 1
ei ght event s have er r or s l ess t han 20 per cent .
TABLE I
THE SEVEN NTS AIR DROP EVENTS EXAM NED I N THI S STUDY
NAME
GRABLE
FI ZEAU
CLI MAX
TS-DOG
BJ-EASY
BJ-CHARLIE
WASP-PRIME
T&-15
11.4
62.8
19
31
14
3
7160
152
407
317
401
345
222
65
68
102
119
128
143
157
s
. 075- . 1
. 08- . 1
. 3- . 45
. 4- . 5
. 3- . 5
. 45- . 5
. 4- . 5
518
490
689
543
599
511
375
180
180
415
350
368
328
224
HD- H
T
. 13
. 18
. 02
.10
-.08
-.05
-.01
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v. REFI NEMENTS
Thi s si mpl i st i c di scussi on of shock/ f i r ebal l i nteract i ons has l ed t o
f ai r l y accurate burst hei ght esti mati on f or ei ght nucl ear t est s. Some f i ne
t uni ng of the model may i mprove the resul t s and/ or i ndi cat e present l y
uni dent i f i ed l i mtat i ons.
1 For bur st s whi ch suf f er gr ound i nt er act i on bef or e m ni mum t i me, ~l N i s
a f unct i on of burst hei ght . Cal cul at i onal wor k has been done t o def i ne t he
var i at i on w th hei ght f or a ser i es of burst s w th the I VY- KI NG yi el d 540 kt ).
These r esul t s ar e pl ot ted i n Fi gur e 11. The anal ysi s r out i nes f or det er m ni ng
bur st hei ght shoul d i ncl ude an i t er at i ve scheme t o account f or modi f i ed yi el d
est i mates at l ow burst hei ghts.
2) Numer i cal test s of exi st i ng photographi c data must be made to determne
t he ef f ect s of f i ni t e resol ut i on el ement s and t hreshol d sensi t i vi t i es on t he
resul ts. We i magi ne t hat there i s a t radeof f between f i ne resol ut i on and
accur at e di amet er r at i o measur ement s on t he one hand and r educed i nt egr at i on
t i mes w t h coar se gr i ds on t he ot her . We i ntend to perf orm computer si mul ati ons
of sel ected data f rames to quant i f y these ef f ect s, and to determ ne the
l i m t at i ons i mposed by t he f r ame t i me r esol ut i on of t ypi cal i magi ng devi ces RJ
1/ 30 s) .
3) Si m l ar l y, at mospher i c at tenuat i on and decr easi ng i nt ensi t i es w t h
i ncreasi ng range may i ntroduce errors. Fi r ebal l s whi ch suf f er i nt er act i on af t er
a few t i mes second-maxi mum do not have par t i cul ar l y wel l def i ned edges. Unl ess
properl y tr eated, range and hei ght -of - burst er ror s may be i nt roduced whi ch are,
themsel ves, f uncti ons of range.
4) The speed of def or mat i on dur i ng t he ear l y st ages of t he i nt er act i on i s
a f unct i on of yi el d and hei ght - of - bur st . Anal ysi s of t hi s mot i on may pr ovi de an
i ndependent bur st hei ght i ndi cat or al t hough we ant i ci pat e t hat i t w l l not be
par t i cul ar l y sensi t i ve. Def i ni t i on of scal i ng l aws w l l requi r e anal ysi s of
t wo- di mensi onal cal cul at i ons.
Fi gur e 12 r epr esent s t he anal ysi s f l ow i n a hypot het i cal syst em i ncl udi ng
an i t erat i ve consi derat i on of t he ef f ect s of hei ght - of - burst on ~l N. We are
cur rent l y i mpl ement i ng such an anal ysi s scheme t o t est t he val i di t y of t hi s
hei ght- of - burst determnati on techni que.
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141 1I I 1 8 1 I I 1 I 1 1 I I I I 1 I I II .3
1.2
11
uPSHOT-KNOTHOLE /GRABLERecord 1798 I (Original)
1.1
1.0
0. 9 :
0. 8 ~A 0. 7 .
, ,**9
0. 6 b. ~0. 5
tt
0. 4 , t 18/ 22m0a
0. 3 tB/ 5
0. 20.1
t0.0 I 1 I 1 1 I 1 1 1 1 I 1 1
1 1 1 1 1 1 0. 2 0. 4 Of i 0. 8 1.0 1. 2 1. 4 1. 6 1. 8 2. o
TIME (StlC)
Fi g. 3
Rat i o of t he ver t i cal t o t he hor i z ont al di amet eras a f unct i on of t i me f or GRABLE. GRABLE was a 15 ktexpl osi on 160 m above the ground surface at the NevadaTest Si t e NTS). t2~X i s the cal cul ated t i me ofsecond thermal maxi mumwhi l e tB, the buoyancy t i me, i sgiven by R t2AX) = g t?.
RExamnati on of the GRABLE
phot ogr aphs s ows i ni t i al i nt er act i on at about 0. 07 sal though no substanti al deformati on occurs unti l about0. 1 s.
: v~q
1.0 *:.
.0.9 :
0.8 :
A 0.7 ttR
0.6
0.5
0.4
0.3
0.2I
. . .
.. .
9
?
tfj/2
0.1
0.0 1 I I I I I 1 1 1 1 t I 1 1 1 1 1 I I 1 0.2 04 06 O. I .0 1.2 1.4 16 1.8 20
TI ME (see)
Fi g. 4
FI ZEAU was a 11. 4 kt expl osi on at 152 meter s. tRi s t he t i me of i ni t i al i nt er act i on det er m ned f r omvi sual i nspecti on of the photographi c records.
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1.4 I I 1 I 1 1 I I I I I I I I I I f I I1.3
J1.2
t
UPSHOT-KNOTHOLE/CLIMAX1.1 Record 171081 (Originol)
1.0 &*.~
0.91 , .. -10.8
I
t= .A 0.7 .. .
0.6.
.* .*
0.5.**.
.
04 10.3
0.2
[
ft~/5
o. I
ttB/2
0.01 I I I t I I I I I I I I I I I I I I 10.0 04 0s
I1.2 1.6 2.0 2.4 2B 3.2 3.6 40
TIME see
Fig. 5
CLIMAXwas a 63 kt explosion at 407 m burst height.
14 I I I I I t 1 I 1 I r I r I I I I I I1.3
-1
A
I .2 -
1.1-
1.0-
0.9 -
0.8 -
0.7 -
0.6 -
0.5 -
04 -
0.3t
0.2t
TUMBLER-SNAPPER /OOG
Record 13382 (Pr int)..
.
.
I
. . .
c J 1 1 1 I2.4 2B
J3.2 3.6 4.0
TIME (WC)
Fi g. 6
TS- DOG was 19 kt expl osi on at 317 m burst height.
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1.4 I 1 I I I I 1 I I I i 1 I I 1 1 I I 11.3 -
1.2- TEAPOT/ WASP-PRIME
1.I - Record 29339 (Print)
1.0 - .0.9 -
**
0.8 - . 9 .9 . .A 0.7 - . **.* . . .
**06 - 9.
0.5 -
0.4 -
0.3 -
0.2-
0.1-
0.0 1 t 1 1 1 1 1 1 1 I I 1 1 1 I I I to 0.4 0.8 I .2 1.6 2.0 2.4 2B 3.2 36 40
TIME (StiC)
Fi g. 9
WASP PRI ME was a 3 kt expl osi on at 222 m burst hei ght .
DERIVEOHEIGHT
900. I I I I
800 -
700 -
600 -
500 -
400 -
1300 -
200 -=
100 -
00 100200300400500600700 60090JJ
BURST HEI GHT
Fi g. 10For each of the seven Nevada test studi ed and onePaci f i c Test DOM NI C AZTEC) the deri ved hei ghtsagr ee wel l w t h t he act ual hei ght s. The r ange f oreach test i ndi cated the hei ght uncertai nty producedby t he uncer t ai nt y i n t he t i me of i nt er act i on.
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.
[
ed 12 A3900- woo ABdll k1600-5600~9d 10 A5600- 6800 ~Bd9 A8800-a240a9d 8 A8240- I oooo~
Bd 12
II
10
9
8
I 200 m 400 500
Burst Hei ght m
Fi g. 11
Ti me of thermal mni mum tM N) i n Vi3riOUSwavel ength bands cal cul ated for 540 ki l otonexpl osi ons at vari ous al t i tudes.
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