UNCLASSIFIED EIIIEEEEIII MAY LAMB FOR VARIOUS E ...AFWL-TR-79-20 AFWL-TR-79-200 LAMB MULTIBURST...
Transcript of UNCLASSIFIED EIIIEEEEIII MAY LAMB FOR VARIOUS E ...AFWL-TR-79-20 AFWL-TR-79-200 LAMB MULTIBURST...
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A.A09S 641 AIR FORCE WEAPONS LAB KIRYLAND AFB NM F/6 18/3
LAMB MULTIBURST CALCULATIONS FOR VARIOUS ATTACK SCENARIOS.MU)MAY 0 1 '. AUBREV, H J ABEYTA, E GIFFORD
UNCLASSIFIED AFWL-TR-79-200 NL... EIIIEEEEIIIIlllfllllllfl
IEEEEEEEEEIIIIIIIIIIEEEEIIEEEEEIIIIIImIIIEIIEIIE
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AFWL-TR-79-20AFWL-TR-
79-200
LAMB MULTIBURST CALCULATIONS FORVARIOUS ATTACK SCENARIOS
L00
H. J. AbeytaICapt W. E. Gifford, IIIJ.W. Aubrey
May 1980
Final Report
Approved for public release; distribution unlimited.
THIS RESEARCH WAS SPONSORED BY THE DEFENSE NUCLEARAGENCY UNDER SUBTASK Y99QAXSG677. WORK UNIT BZO, WORKUNIT TITLE: FREE-FIELD AIRBLAST ENVIRONMENT DEFINITION.
Prepared forV Director
DEFENSE NUCLEAR AGENCY4.> V Washington, DC 20305
AIR FORCE WEAPONS LABORATORY AAir Force Systems Command
Kirtland Air Force Base, NM 87117
81
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AFWL-TR-79-200 -
This final report was prea;ed by the Air Force Weapons Laboratory, KirtlandAir Force Base, New Mexico, under Job Order WDNB4405. Mr James W. Aubrey (NTESB)was the Laboratory Project Officer-in-Charge.
When US Government drawings, specifications, or other data are used for anypurpose other than a definitely related Government procurement operation, theGovernment thereby incurs no responsibility nor any obligation whatsoever, andthe fact that the Government may have formulated, furnished, or in any waysupplied the said drawings, specifications, or other data, is not to be regardedby implication or otherwise, as in any manner licensing the holder or any otherperson or corporation, or conveying any rights or persmission to manufacture, use,or sell any patented invention that may in any way be related thereto.
This report has been authored by an employee of the United States Government.The United States Government retains a nonexclusive, royalty-free license topublish or reproduce the material contained herein, or allow others to do so,for the United States Government purposes.
This report has been reviewed by the Public Affairs Office and is releasableto the National Technical Information Service (NTIS). At NTIS, it will be avail-able to the general public, including foreign nations.
This technical report has been reviewed and is approved for publication.
ES W. AUBREY Jroject Officer
FOR THE DIRECTOR
GARY P. GANONG STEWART W. JOHNSOLt Colonel, USAF Lt Colonel, USAFChief, Technology and Applications Br Chief, Civil Engineering Research Div
DO NOT RETURN THIS COPY. RETAIN OR DESTROY.
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STALCULATIONS FOR VR!" I / J -ATACKU SCENARIO .. FinalAQ A ' f oG NUMBER
7. AUT"OR('.) a. CONTRACT OR GRANT NUMBER(s)
a w./hubrey @p, . T ?d 11H. J. beyta!-r
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Air Force Weapons Laboratory (NTESB) WDNB4405Kirtland Air Force Base, NM 87117 62704H
It. CONTROLLING OFFICE NAME AND ADDRESS
DirectorDefense Nuclear AgencyWashington D C 20305 136
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Air Force Weapons Laboratory (NTESB) UNCLASSIFIEDKirtland Air Force Base, NM 87117
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18. SUPPLEMENTARY NOTES
This research was sponsored by the Defense Nuclear Agency under SubtaskY99QAXSG677, Work Unit BZ0, Work Unit Title: Free-Field Airblast EnvironmentDefinition.
19. KEY WORDS (Continue on reverse side if necessary and identify by block number)
LAMB system Reentry VehiclesMultiburst ShockOverpressure NuclearOverpressure Impulse
20. ABSTRACT (Continue on reverse side Ift necessary and identify by block number)
-?This report contains the results of 33 Low Altitude Multiburst (LAMB) calcula-tions. These calculations provide overpressure and overpressure impulse timehistories, as well as shock front velocities for 12 multiburst attack scen-arios. Yields of 1, 3, and 5 Mt were used in these calculations, with shelterspacing of 1000, 1500, or 2000 m.
DD JAN 73 1473 UNCLASSIFIEDSECURITY CLASSIFICATION OF THIS PAGE (*hen Data nto40r
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UNCLASS IF IEDSECURtITY CLASSIFICATION OF THIS PAOKQWho Data Enteed)
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AFWL-TR-79-200
CONTENTS
INTRODUCTION 3
APPROACH 4
RESULTS 6
~ijAPPENDIX A 13
APPENDIX B 26
1, 1/2
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AFWL-TR-79-200
INTRODUCTION
This report consists of 33 LAMB calculations (Table 1) and a description of
the data. It was written to provide overpressure and overpressure impluse-time
histories as well as shock front velocities for various multiburst scenarios.
The Air Force Weapons Laboratory LAMB code was used because of its fast computa-
tion running time and economy.
TABLE 1. tIULTIBURST PROBLEM MATRIXPEAKS
RV/Shel ter PRES IMPProblem Attack W'eld HOB Spacing (MPa) (MPa.s)
1 33.1012 1/2(a) 3 Mt 0 M 1500 m 3.5 2.42 33.1122 1/2(b) 3 Mt 0 rr 1500 m 7.6 1.93 33.1232 1/2(c) 3 Mt 0 m 1500 m 3.6 2.54 33.1142 1/2(d) 3 fit 0 m 1500 m 7.6 1.85 33.8001 1/3 3 Mt 0 m 1000 m 18. 2.86 33.8002 1/3 3 Mt 0 m 1500 m 4.8 1.37 33.8003 1/3 3 Mt 0 m 2000 m 2.0 0.78 53.8001 1/3 5 Mt 0 m 1000 m 30. 4.79 53.8002 1/3 5 Mt 0 m 1500 m 7.8 2.1
10 53.8003 1/3 5 Mt 0 m 2000 m 3.2 1.211 33.8012 1/3(a) 3 Mt 0 m 1500 m 4.8 1.412 53.8012 1/3(a) 5 Mt 0 m 1500 m 7.8 2.213 33.8032 1/3(c) 3 Mt 0 m 1500 m 2.3 1.414 53.8032 1/3(c) 5 fit 0 m 1500 m 3.8 2.515 33.1201 1/3(e) 3 fit 0 m 1000 m 9.3 4.616 33.1202 1/3(e) 3 fit 0 m 1500 m 3.5 2.117 33.1203 1/3(e) 3 Mt 0 m 2000 m 1.7 1.118 53.1201 1/3(e) 5 fit 0 m 1000 m 15. 8.019 53.1202 1/3(e) 5 Mt 0 m 1500 m 5.6 3.520 53.1203 1/3(e) 5 Mt 0 m 2000 m 2.7 2.021 53.6001 1/4 5 Mt 0 m 1000 m 15. 2.522 53.6002 1/4 5 M-t 0 m 1500 M 4.1 1.223 53.6003 1/4 5 it 0 m 2000 m 1.8 0.6624 33.6011 1/4(a) 3 Mt 0 m 1000 m 9.0 1.425 33.6012 1/4(a) 3 Mt 0 m 1500 m 2.6 0.6826 33.6013 1/4(a) 3 Mt 0 m 2000 m 1.1 0.3427 53.6011 1/4(a) r Mt 0 m 1000 m 15. 2.228 53.6012 1/4(a) 5 Mt 0 m 1500 m 4.1 1.129 53.6013 1/4(a) 5 Mt 0 m 2000 m 1.8 0.6430 13.1211 2/3 1 Mt 0 m 1000 m 4.8 2.231 13.1212 2/3 1 fit 0 m 1500 m 2.0 1.132 13.1213 2/3 1 Mt 2000 m 1.0 0.6433 13.1012 2/3(a) 1 fit 0 m 1500 m 1.4 0.84
44 3
$q
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AFWL-TR-79-200
APPROACH
A uniform laydown of reentry vehicles (RV) over an evenly distributed system
of targets (shelters) was assumed. The ratio of RV to targets was used to des-
cribe the attack laydown pattern. Thus, attack scenario 1/2 refers to an attack
laydown such that there is one RV attacking each pair of shelters. The suffixes
on the various scenarios (e.g., 1/2 (a)) refer to the different laydown configura-
tions possible. Using this nomenclature, the 12 attack scenarios examined were
1/2(a), 1/2(b), 1/2(c), 1/2(d), 1/3, 1/3(a), 1/3(c), 1/3(e), 1/4, 1/4(a), 2/3 and
2/3(a) (figures are in Appendix A). Yields of 1, 3 and 5 Mt were used. Spacing
between shelters was 1000, 1500, or 2000 m. Bursts were numbered sequentially
as a function of increasing angle clockwise from 0* (top of page) and were
detonated simultaneously at ground level.
Stations were not colocated with shelters (which tend to fall on symmetry
points) for the following reasons:
1. The LAMB code underpredicts peak overpressure at symmetry points.
2. Perfect symmetry will not occur in MX construction.
3. Zero CEP is highly improbable.
4. Assuming zero CEP, simultaneous detonation and perfect symmetryare not operationally obtainable environments.
Thus, measuring overpressure-time histories at nonsymmetry points provides more
realistic waveforms for physically plausable attack scenarios. Stations were
placed 100 m from the shelter and 200 off a direct line between the shelter and
the nearest burst (Fig. 1). Three stations were required to define overpressure
and overpressure impulse-time histories for the 1/3 and 1/3(a) scenarios. One
station sufficed for each of the other scenarios.
stationpoint (Not to Scale)
$200
shelter point nearestburst
Figure 1. Shelter-station relation.
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AFWL-TR-79-200
Test cases were run to determine the number of bursts to be used in each
calculation. These test cases represent the worst possible attacks (for the
scenarios examined) in terms of the number of bursts reaching the station point
at approximately the same time. The results of the test cases (Fig. 2 through
7) show that restrictions on the number of bursts in a calculation could be made
while preserving the siqnificant overpressure-time history at the station point.
All bursts which were within four closest burst-to-shelter radii of the shelter
were included in the calculations for the 1/3 and 1/4 scenarios. For economy,
the number of bursts was restricted to 12 for each of the other scenarios.
All the calculations were run to detonation time, plus 12 s. All of the
shock waves had passed over each station by this time. The shock front velocities
were computed in the following manner:
A shock velocity function subroutine, VSHCK, was called from
the LAMB code with height of burst, shock radius, height-of-
station point, and yield as input parameters. The analytic
expression used for shock velocity was obtained from the
Rankine-Hugoniot relation:
U c( 1 + I1 AP ) / 2
where
U = shock front velocity
c = ambient speed of sound
y = ratio of specific heats for air
AP = overpressure
P = ambient pressure
y = 1.4 was used for this case
The direction of the shock was determined by computing the angle between the
burst and the station in polar coordinates.
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AFWL-TR-79-200
RESULTS
Overpressure and overpressure impulse-time histories are presented in AppendixB. The number associated with each peak is the burst number. The shock arrivaltime (s), shock velocity (m/s), shock direction (0), burst number, and burst range(m) are presented in tabular form. The attack scenario is presented at each over-pressure plot where the number corresponds to a burst point and the letter sdepicts a station point (Appendix A). Shock direction is equivalent to thebearing from the burst. As it passes over the station, the shock is travellingparallel to the bearing from burst station. Burst range refers to the distancebetween the burst and station.
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I
TEST CASE
OVERPRESSUFE ". TIME
T R E+A!:; 2t, D00f-]E+02bfHcTF I .I LC, E+O2.j iEI dHT: O.
"13. 1 .2FBPC1BLEM - 13E. 101.
w1
I~I
9. 7.. 9. .I M T27
7I* :1
1_ 2t' ., XCDEL, '- -
I ,,* ,
Figure 2. Overpressure versus time-2/3(a) attack (with added bursts).
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i i I , '1
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TEST CASE
OP IMPULSE V. TIME
~ I AD IUS . Ci i: E 4 2 N
3d I THETR: - IHEIGHT: ij.5TRTIiIN NO.
i
T' "-,
.,-- ---.
E SE
aI /
PFA " RM -4DE ,' LUIP1C'0E/
/
.. r!l '
1 I
TIME v3EEI
Figure 3. Overpressure pulse versus time-2/3(a) attack (with added bursts).
8
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TEST CASE
1, T-R
'Cl
I C.O r2CC
7~ C ID .FU,4 . .09 n 97TXMEf f-qj
PFLL M I,'l P I1PTCrl
Fiue4 vrrsuevru ie-/ tak(ihaddbrt)
II9
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TEST CASE
jP IMPULSE "v"3. TIME
.'Fs -LI: . UC, fDE'-'2THETR: 1 .OOOE+02EGHEI 67HT: O, MSTPTION t-4.:PROBLEM 1 3.I21.:8
-TIM
-t
1 E-
TIME i':E
-- P- LE LrP. TI . -9H I--_. Z-r': ,
Figure 5. Overpressure impulse versus time-213 attack (with added bursts).
10
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TEST CASE
O"ERPRE551IRE V5. TIME
T T= 7.O 000E+01DEC,-j] STRT I'N NIL
PR'SIL EM, z . 12 5:,2
7
II
II
I''
N:N
A-1
-\- ' -,
,, . (
" '., .. . .--
- ~ )1 ~ .IJ g.lJD 5.rn ., F.. 9.ZI ir'.:1 jI.'n3, Z2
R7JL LPMEB MCJEL LC;L[ LETLE3.
Figure 6. Overpressure versus time-1/2(c) attack (with added bursts).
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TEST CASE
OP TMPULSE VS. TIME ,
RH-D1Us -- 1. I00O0E+-,2MTIHETR: 7. bOCOE OiDEGHEiGHT:- 0.STPTION NO. -F'ROBLEIM 3 5-3.J2s
I /L /
; M1/
/
r.12
'I ,
L I /
S/
i /t" I I 1 I
TIME ISEC)RiFWL LRqMB ,MOOEL ICRLCULRTI ONS, P!,C8 ..,__.1 - ..,2 -.. ,..2-,2
Figure 7. Overpressure impulse versus time-1l2(c) attack (with added bursts).
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AFWL-TR-79-200
APPENDIX A
The following 12 figures illustrate the various attack scenarios used in this
multiburst study. Included in these figures are launch points, aim points, calcu-
lational burst points and station points. The various attack scenarios are
described as a ratio of RV to targets. For example, a 1/2 scenario refers to
one RV attacking each pair of targets.
1
13
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LEGEND:Launch PointAim PointCalculation Burst Point
0 Station Point
+ • + 4- • -
-4 • -t t . +
+ +-+ • 3 ED +
1/2(a) ATTACK
14
E8I
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LEGEND:* Launch Po int+ Aim Point
Calculation Burst Point Io Station Point
*E E1* * * 9 99 o +-
* * ~. w *9
*~~ ~ -4-.
1/2(b) ATTACK
15
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LEGEND:Launch Point
+ Aim PointO] Calculation Burst Point0 Station Point
+
. .. • - * , + •
-t " 8 l * ... . .
* - • B * • l - "
I * 4- *4
1/2(c) ATTACK
16
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|I
LEGEND:* Launch Point+ Aim Pointo Calculation Burst Point0 Station Point
M --h ±r ~ E I ---E ED + 0 ID Ir i --
1/2(d) ATTACK
17
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LEGEND:*Launch Point
+ Aim Pointo3 Calculation Burst PointO Station Point
+ E3 ± +
± 818
-PON
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LEGEND:* Launch Point9 Aim Pointo Calculation Burst Pointo Station Point
++
1/(a ATTAC
* 819
-
'1
LEGEND:Launch Point
+ Aim PointC Calculation Burst PointO Station Point
* -t •4 - • • +- • * +
4-
1/3(c) ATTACK
20
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LEGEND:Launch Puint
+ Aim Pointo Calculation Burst Pointo Station Point
+ + +* + 8R +
B8
ED EB
EB 93
* + •8 t-
1/3(e) ATTACK
21
*
-
15' -
LEGEND:* Launch Point+ Aim Point0 Calculation Burst Point0 Station Point
F. {-1
1/4 ATTACK
22
V V I
-
LEGEND:Launch Point
4- Aim PointEl Calculation Burst Point0 Station Point
F I
1/(a ATAC
234
-
LEGEND:Launch Point
+ Aim Point
o Calculation Burst Point0 Station Point
+ t- +~ ~ .+
+ - b
+ + []±[] + .
+-- • - ± t - -
* 4 4-°
2/3 ATTACK
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LEGEND:launch Point
+ Aim Point] Calculation Burst Point0 Station Point
* - . + + .
* ~ ~ ~ - 4- * - 1-4
* -r • l +:: - t•
+ *f 4-. . . .m EGF • *- .
2/3(a) ATTACK
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AFWL-TR-79-58
APPENDIX B
The following figures are overpressure and overpressure inpulse-time histories
of the various attacks described in Appendix A. The burst number associated with
the overpressure peaks corresponds to the attack scenario burst number inset on
each plot. In addition, the shock arrival time, shock velocity, shock direction,
burst number and burst range are presented on the overpressure plots.
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YIELD= alltSPACING=~ KUMc
cjVH~E d];~VS. TI MF
I N
4, 2 2c, j7:.T
3, 10 . 2
7! 8 s4
8 6
1/(a AT6. CK
__
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1.(U ~ ~ ~ ~ ~ ~ ~ ~ ~ ' 1.9 .3 VI 4 " U U u Q .[l rT~ ~ ~ IM I~
PFW1 ,l-4- i -jj jIL J fl/7 --/2
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JA-i I tl- / I l-JLU I [JFG
c 2. lL1 '? -3 4.0 22
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4~~~T.?l .IP. 3[ ____9
1 t AT
2. lT r ur fT 6.m. i. In
RFW1~~~~ I IM E (E(> C 3(T
MO EDEL CR1LULflTINw PROBi-M 3 3. 1.12 2
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c.. /
L . / /:
/
T lfiC tiC;;Iff, ,l~ L R ~i5I t.Lt -, LV I LiiL I... P[,ijf[ ,[r' .-: 112
30
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~HOD= e
YIELI= 31t{ V[_FI~fE°'_'.jI.qIC %. 1] MFSPACING= SOc1
BRDI I tIS7 c; cfiI1 Hl- H.. 7. 000fltri k) _ nGHH1R 1 !;4f0. MS I H I .,1 - :33. 1232
8___-~r BURSTSI -C KtT[S! V4 - tLtit/I 1 li -: I i (DE, - L (r
0.5946 1e27.3 271.4 4 1436."0.6569 977.7 176.3 1 1469.
p.7288 929.3 3.5 7 1537.0.7923 892.9 ,?. 1P 1594.3.4813 496.9 243.2 3 326S.3.5354 494.6 20=.4 2 3282.3.543? 494.3 2?7.8 5 3286..6,2 48. ,6 335.1 6 3344.3.70!40 487.9 151.7 12 3367.
1 3.8177 483.7 135.4 11 3424.3. 4 483.4 27.7 8 342 7.. 8 SO 481.6 63.6 9 346.
'-8
L8
~12 •2•
11 • I • 3
10 S 4
8 5
Iii 1/2(c) ATTACK
Lm1,O 2. ou .Co V. rv 5 t n ?A .El 0 1.0 1.
8.. iO 2l
TIM1EOSEM
RFNL LRMB MUOUL CFAL(UlRT]ONS PROFBLEM 33. 1232
31
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YAPI 1 9.'IjI~ D71 ~ Mil FJ) . S.I~ *in1 to.t Do .D) 12. W)
RLI MOUC IL r"N U. fl'i I OS PRBULEM 3 1 ~3
32
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HOE= emYIELD= 3Mt
OVEBPFE55UflE VS. TIME SPACING= LO0n
RADI US: 1. OOOOE+02MTHErAn 2. OUOE+02DEGHEIGHT: 0. I
" STATION NO. IPBUBLEM : 33.1 [2
SHOCK BURSTAT(S) VEL (I/S) BIR(t(EG) NO. RAN GE t 1)
8.0955 2763.8 357.0 7 657.0.8658 886.0 65.9 8 1606.8.87?8 850.6 293.2 5 1669.1.8394 619.8 180.8 1 2344.
8 2.5508 548.8 148.0 11 2765.2.6182 544.6 213.2 2 2601.3.X682 517.0 77.6 9 3038.3.1834 51.3 232.2 4 3104.K 4.2950 468.3 3S9.5 6 36S6.
-7 4.5569 461.2 128.3 18 3788.4.6725 458.4 232.3 3 3834.
0c10 11 1 2 3
$ 9 8 7 5 4
-56
,-c m 2.,m 3.6 -4.1m -S0 r.,m r.E L011 ,11
TIME (SEC)
RFWL LRMB MODEL CRLIULRTIONS PROBLEM 33. 1142
33
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Li I t~ 1 )
J~ I-.34
-
HOP= O'iYIELD= 3M'
1 SPACING= 103i0
f1 I rl 1 1 I -
S1 HOCKBu 5,I
A T(S) VILU' D1I (EG) NO. pfl!"cE r,0.0441 4264.5 116.0 1 48S.A.3923 1272.9 244.8 3 1176.0.43CI 1201.2 37O 1233.1.3112 711.1 0C4.S 7 1999.
_____11.4448 682.8 43.4 6 2091..019 6 .0 314.2 4 2101.
.6642 644.8 181.6 2 2234.1 .9S16 6es.0 143.6 8 2417.
I 8 2
S37 1 3
S . 2 SI.-
6 4
17 1/3 ATTACKF 4 ,
-. " I J-- - 11 - UU- 11.--
35
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d3
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HOE= OmYIELD= 3tit
." ' "SPACING= M0Om
'i
2 1 1- , -* 1ds!
il,'-l ",M
I! HOCK BURST
.T(S) EL f!S) IJI R(DEG) NO. PANGEM I8.0441 4254.5, 236.0 1 48S.0.4381 1201.2 117.0 7 1233.
0.6678 970.4 322.4 5 1479.0.7743 9C09.6 22.3 6 1579.-.-I1 3 716.9 253.6 3 1982.
- 1.4449 682.C 163.4 8 2091..0262 596.3 201.5 2 2463.
2.6355 542.8 301.3 4 2811.
8 2
.•S3
S12 SI
6 4
1/3 ATTICK
L-," I ll |1t in .r; 5.1 ;.,F l'.n1 [II 5 [.L tLI. t LI.t'I t2.'i
.{1, ;~'r.2, iii',r I 11 I' " ff1 11 F'Ifl[ FM - . E rlfi
37F
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N
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338
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HOB= on
YIELD= 3Mtr'F -F 1SPAiCIlC= 1000M
-. , .' . ........ . , .,. ' , ", " ] ' P C I = l O
Ll
C.P, B U R"S,rr
-". T
I, T -k : V E L C I;, I I F f C N C . P fiG E (M )
s 0.0441 42C4.5 35I. 48S.-I 0.6,70 97C.4 82.4 7 1479.
0.7'90 923.1 277.2 3 I547..7,3 932.6 142.3 8 1579.
(J. 8290 873.3 199.2 2 1 E.28.1.3112 711.1 344.5 5 1999.
60S. 23.6 6 2417.3 0334 52 .0 317.4 4 3088.
8 2
S3
7 3,
1:;
* S2 Si
6 4
7
[38 1/3 ATTACK-2
Lj I__
TI::'. '"a.
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N.
if
[ N.
/'I
,1
2
F'
ri I
-------
rir;;. c
40
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HOD= emYIELD= 3Mt
Ij ,'::'! i! '.:i!iL V~i. I l'ilSPACIUG= 1500=
H>0 C ' B UJ " R Tj ,
I F7II1 '.
3.( 53 .16.7 10-.> 0 0b
| T i-f !: ].* / h, -- I IY:
346 49.6' 4 3222.I-I SHOCK BUI,I4 -- 'T S) 'VEL (iI/f Lir:(LEC) NO. RRNGE (Ii
.1430 227. 117.5 1 773.0.9795 808.6 243.2 3 1752.,1.0529 782.6 353.0 5 1810.S3.{:653 516.7 105.0 7 304g.
,,3.2397 507.8 44.3 6 3131.' I 3.4168 499.6 314.1 4 3222.
I3.7462 486.3 181.1 2 3388.4.334S 467.2 143.5 8 367S.
. S3,: 7 1 3/'
44
1/3 ATTACK
II
I .'-'--- --. "'--+" ------.-I! J ,II] 2,11J :,1 yII t.. :I] 7 :I UU ~ ~ 'l I+l. fO 21
T i-- 'I "l:Cl
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02 1 12
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HOB= OmYIELD= 3Mt
"' i t , ' " , V. SP CING= ISOO m
f'. 1
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99
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2~E5 5L! ?E I5 j I T M E
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TEST CASE
LIP L!MPULSE V.S. TIME
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1/2(c) ATTACK (WITH ADDED BURSTS)
129
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IT 9.11 .T -
1/2(c) ATTACK (WITH ADDED BURSTS)
130
-
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DAT
F LM
L