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ATM 1046
LSP EXPLOSIVE PACKAGES
FRAGMENTATION STUDY
Prepared by: ,11. 15. :n-~ G. B. Min
Approved: Don L. Dewhirst
Approved:
ABSTRACT
The purpose of this ATM is to estimate from theoretical considerations
the probability of fragments from an LSP explosive package striking
the ALSEP Central Station. For the assumptions listed, this probability
is calculated to be less than • 068<fo (. 00068).
ATM 1046
1.
TABLE OF CONTENTS
I. INTRODUCTION z
II .. ENERGY DISTRlBUTION 3
w. EQUATIONS OF MOTION 5
IV. FRAGMENT TRAJECTORY 8
v. PROBABILITY DISTRIBUTIONS 11
VI. SAMPLE NUMERlCAL CALCULATIONS 13
vu. CONCLUSIONS 17
vm. REFERENCES 18
TABLES
FIGURES
APPENDIX: COMPUTER PROGRAM LISTING
ATM 1046
2.
I. INTRODUCTION
The Lunar Seismic Profiling Experiment requires that Explosive Charges be detonated on the luoar surface early in the ALSEP lunar mission. Two factors of the lunar environment are its ultra-high vacuum (no air resistance or air drag) and its low gravitational field. Both of these factors contribute to an increased trajectory of fragments. Therefore there is legitimate concern that fragments and debris from detonating an Explosive Package might strike and cause damage to the ALSEP Central Station. _The purpose of this study is to determine the probability of fragmentation damage to the ALSEP Central Station.
One parameter of jreat importance in this study is the initial velocity of fragments ejected by the explosion. One method for obtaining the initial velocity is to assume that all of the explosive energy is converted into the kinetic energy of the fragments. Because much of the explosive energy goes into the blast wave and into the fracture energy of the case materials, this method establishes an upper boUDd to the initial velocity. Another method for obtaining the initial velocity is by reference to empirical data. Reference 1, the SRI report, presents test data that establishes a velocity range from 200 to 600 meterl/second. The probability calculations presented in this study are based on kinetic: energy considerations up to a limit of 600 .'meters/second.
The striking pl'obabUity is considered as a compound probability of two conditional eveats. 1'bese events are associated with the number of frag-ments and their probability of hitting the target. Due to the irregular package configuration, the number of fragments and their break-up pattern are difficult to predict. Therefore a distribution curve similar to the chi-square distribution is assumed for convenience of calculation. The second event involves the traj-ectory. Since the ALSEP Central Station has a honeycomb pane 1 on its top as a protective shield, the most probable damage would be from fragment penetration of the side curtains wb:i::h are made of soft materials, such as mylar, silk meah and Kapton. Therefore the damage criterion is based on the probability of striking the vertical sides of the Central Station, rather than on impacting ita top surface.
If the prototype model field tests provide information about fragment sizes. numbers and break-up pattern, the collected data can be used to modify the curve assumed in the study for the first probability event.
ATM 1046
3.
II ENERGY DISTRIBUTION
The purpose of this chapter is to determine how the explosive energy might be distributed between bla•t wave energy and the kinetic energy of the fragments. The equation• of this chapter are included for the sake of completeness. Because we will assume that the total energy of the explosive is converted into kinetic energy of fragments, the reader may omit a thorough understanding of this chapter.
The distribution of energy in a high explo•ive during explosion is highly complex. Three types of energy predominate:
1)
2)
3)
EF, KioeUc energy of the fragments.
E 2, Energy retained by the hot gases of the explosive
E 3, Energy contained within the region bounded by the blae't wave front.
. The sum of energiee £2+ 1:3 is tbe eneriY associated with the blaet wave
1tself. If we define E8
= 1:2
+ £ 3, then:
ET:; EF + EB (U-1)
where ET is the total energy released by the explosive. This expression separates the energy into two major categories: energy due to fragments and the kinetic and potential energy of the spherical blast wave. A wave of finite amplitude has tbe following relationship between pressure and velocity:
u = 2a { !_ ( ~ -1)/Zy_l 1 (U-2) y-1 ( p )
0
where p = standard pressures, usually atmospheric 0
"''= ratio of specific heats (=1. 405 on earth) p =pressure a =velocity of souad in undisturbed atmosphere u =velocity of wave in air
Then the kinetic energy per unit mass can be expressed as a function of the pressure change:
where y = p/po.
ATM 1046
4.
The potential energy per unit mass is 5 (p/po) d(l/p) which, in view of the adiabatic relationship, p/po = (p/po)Y, is
(II-4)
so that
E = P. E. + K. E. = 2{ 3y-l (y-1)/y
B a 2y y/(y-1)
+ 1 -1/y 4 (y -1 )/2y 2.:.L } (II-5) -y 2
y + 2 y (-y-1) (y-1)
The total energy of a complete spherical wave (per unit mass) is
(II- 6)
where r 0 and r 1 are the outer and inner limits of the wave.
Equation (II-6) provides a basis for calculating blast wave energies. However, in this study, we will set EB equal to zero. This assumption provides conservative estbnates of fragment velocities. That is, the velocities calculated in Chapter VI will neglect the blast wave component of energy and will therefore be upper bounds to the actual fragment velocities.
ATM 1046
s.
Ill. EQUATIONS OF MOTION
The purpose of this chapter is to determine from theoretical considera .. tions the most probable velocity vector for fragments of the case following detonation.
Except for the six-pound charge, the explosive charges are of cylindrical shape with roughly equal dimensions between diameter and height. The housing of EP is of rectangular shape. Eccofoam of 3 lbs/ft3 density is filled between the space of the rectangular wall and cylindrical charge. When the explosive is detonated at one end, the detonation wave moves down the case leaving the expanding case in its wake. The rectangular case is assumed to deform into a circular shape which is theoretically investigated by Reference 2. The gas pressure which acts on the foam and the case has both radial (expansion) and longitudinal (extrusion) components of velocity. The expanding gas gives kinetic energy to different parts of the case at different times.
\ \
\
z
I I
I
/ I
!
I
/ Detonation Front !_......--/
ATM 1046
Based on the derivation of Reference 2, the equations of motion are presented as follows:
The equation of motion of the case is
(Ill-1)
The equation of motion of the gas is
= (Ill-2)
And the equation of continuity is
where
2 - 2 upr - Up0
r0
(Ill-3)
U = the velocity of the detonation wave
M ::::: the mass of the case per unit length
r =expanding radius
p = gas pressure
z = distance measured along the axis
r 0 = the external radius of charge before explosion
P1 = density after detonating
p = density before detonating 0
u = the velocity of the gas
Equations (1), (2), (3), together with the adiabatic equation of state connecting p and p in the expanding gases, suffice to determine all the quantities concerned. By defining e as the angle between an axial section of the case and the axis at distance z from the detonation front, the relationship is established (Ref 2) by using Eqs. ( 1 ), (2) and ( 3)
where
tan 2 a = __L_ ( ..£. + u - u ) aU up
M a= -m
= weight of case weight of explosive
(ill-4)
(Ill-S)
and U is determined by numerical integration of (2) using the p, p relationship.
ATM 1046
6.
The caee is at rest until the detonation wave reaches it. Afterwards it moves with velocity whose components are U(l-cos e) forward in the direction of the detonation front and U sine perpendicular to the axis. Combining these two components gives the velocity of the case:
7.
v = uJ(I -cose)l + sin2 e = ZUsin ~ (III- 6)
If we equate the total explosive energy to the kinetic energy of the fragments as discussed in Chapter Z, we obtain from equation (ID 6) and the trigonometric identity, . z e 1 ( 1
sm z = z -cos e):
1 z z ET = EF = z Mv = MU (1-cos e) (III-7)
Equation (m-7) can be solved for 9, if the magnitude of the explosive charge is known.
For small values of the angle e, equation (III-6) can be simplified to the following form:
(III-8)
ATM 1046
8.
IV. FRAGMENT TRAJECTORY
The motion of a particle in a uniform gravitational field is available in many testbooks. In order to fit this study, a modified set of the equations of the motion is derived.
The break-up pattern of the explosive package is more complex than predicted by the theory of Chapter 3. Much of the complication comes from the electronic instrument sitting on the top of the explosive. Although the fragment pattern during explosion is very complicated, two different approaches will be studied. The first approach is to consider a homogeneous fracturing such that all fragments are of equal size. Secondly nonuniform fragments will be assumed based on the package components. The fQllowing assumptions are made:
1. Since the air pressure and density on the lunar surface are lo-13 times that of the Earths surface, it is possible to neglect the air resistance.
z. When the explosion occurs, the fragments fly out radially from the explosion center, each with the same speed. For convenience, the trajectories in a plane bounded between e. to 90. (8 defined in previous section) are considered. The resulting flight trajectories are described in the following figure.
y
1\ j
X
Based on the above assumptions, the motion of fragments in a uniform gravitation field can be derived as follows. Let the x y plane be the plane of
ATM 1046
9.
motion withy axis directed vertically upward. Assume for convenience that the particle is located at the origin 0 at timet= 0 and is moving with velocity v0 at an angle <P with the horizontal. The initial velocity components are
v (0) = v cos <P X 0
v (0) = v sin <P y 0
with the acceleration components
a = o X
a = -g y·
where g is the lunar gravity
(IV -1)
(IV -2)
(IV -3)
(IV -4)
Since the motions in the x andy directions are independent, the velocity and displacement components are
v = v cos <P (IV -5) X 0
v = v sin <P - gt (IV -6) y 0
X = v t cos <P 0
(IV -7)
v t sin <f> -1/Z g t z
(IV -8) y = 0
Solving equation (IV -7) for t and substituting into equation (IV -8) gives:
y = x tan <1>
z gx
2 z Zv cos <f>
0
(IV -9)
which is the equation for a parabolic trajectory. It is desired to arrange Eqtn (IV -9) to express the initial flight path angle <1> in terms of any coordinates x, y through which a fragment may pass. Using the trigonometric identity
1 z
cos <I>
2 z = sec <f> = 1 + tan <f> (IV -10)
ATM 1046
and rearranging the terms of Eqtn (IV -9), we have:
z tan+ - gx tan+ +
zv2 0
z gx
+ 1 = 0 (IV-11)
1 o.
There are two rcots of this quadratic equation in tan <j>, corresponsing to the low and high flight angles <1>1 and <j>z. Complex roots result for the case where the point is out of range. The roots are expressed as
tan+ = v! "'{(v!) z gx gx
(IV -lZ)
Having known values of y (the height of the central station), x (the distance between the explosive package and the central station), and v 0 (the initial fragment velocity), Eqtn (IV -1 Z) provides the desired angles <j>, <I>'.
I I/ ' i
ALSEP c. s.
Eqtn (IV -ll) can be applied to soil dust particles as well as explosive fragments. The volwne of soil cratering can be estimated using Olsen's Formula:
V = 0. 4 QB/? (IV -13)
where V:::: volwne in cubic ft, and Q =weight of exploding charge in pounds. See Ref 6. However this formula is quite conservative. ' Much of the debris cratered from below the explosive charge falls vertically back into the crater partially refilling it as shown in Figure 1. For the purposes of this study, we neglect the effects of these soil dust particles relative to the explosive fragments.
ATM 1046
II.
V. PROBABILITY DISTRIBUTION
Based on the assumptions stated in chapter 1, there are two events (X1, Xz) influencing the determination of fragmentation probability. The first one deals with the probability associated with the number (X 1) of fragments produced. This probability curve can be determined through field test results. A probability curve using the chi-square distribution shown is assumed. The peak of the curve is based on consideration of mean value of non -uniform fragmentation, the tail of the curve on consideration of uniform fragmentation.
p (x)
-n X
Its density is in the form:
where
p (i) 1 -iii/z-1
X -i12 e (V-1)
-X : (xl: number of fragments; n: mean value of number of fragments)
iii = degree of freedom = 4 00
r< s) = garmna function = s 0
r<4/Z> = r<z> = 1 . r o > = o r = 1 • •• p (x) = 1/4 ie -x/2
ATM 1046
s-1 -z z e dz
(V -2)
12.
The second event considers the striking probability of a known fragment number with velocity and location of target as its independent variables. By using the results of the range of striking angles in the previous section, this probability event can be expressed as follows:
where X is the distance between the EP and the central station, and N is the number of fragments. The value of 3. 54 feet comes from the maximum exposure range of side curtains perpendicular to the fragment path shown below.
~5 I r- - ' ··- .. -aj
3. 54'
1 Path of Fragment
Now the compound probability can be calculated as follows:
(V -4)
or 00
P (xl, x2) = P (x2) s xl P (x) a.i (V -5)
ATM 1046
13.
VI. SAM?LE NUMERICAL CALCULATIONS
A detailed description for the 1/8 lb charge explosive package at 125 meters distance is presented, step by step, as follows:
1. Weight of charge = • 125#
2.
3.
Weight of Housing Assy = • 402# - • 125# = . 277#
Weight of E & S/A Assy* = 2. 286#
Wt. of case= wt. of Housing Assy + wt. of E&S/A Assy = 2. 286+. 277 = 2. 563#
6 Assume HNS charge energy E = 1. 5 x 10 ft-lb
:. ET = 1. 5 X 106
X • 125 = . 1875 X 106 ft-lb
al =
a2 =
= • 1875 X 106 ft-lb x • 30!8M x • 451~6Kg = • 0259234 x 106 meter-Kg
wt. of case 2.56/.125 20. 5 = = wt. of charge
wt. of housing • 277 2. 216 = = wt. of charge • 125
4. From Del Mar Engineering Laboratories
Gas front velocity, U = 7000 meters/ sec.
5. Upper Bound of blast angle e:
EF = ET. From Eqtn (111-7):
EF = aU 2 (1 - cos e)
* . Electronics and Safe/Arm Assembly
ATM 1046
For a1
:
. . .
. 02592 X 106 = 20. 5 X (7000)
2 ( 1 - COS 8)
= 1 - • 02592 = 1 cos 81 20. 5 x 49 . 0000258 = • 9999742
e1 = .41e = .41x 3.1~~16 = . 00715587 radian
. 02592 cos a2 = 1 - 2 . 216 x 49 = • 99976129
e = 1. 25 ° = 1. 2s · 2
3.1416 180
= . 02181667 radian
6. Theoretical fragment velocity, using eqtn (ID .. 8):
Vl ; U X 81 = 7000 X • 00715587 =50. 09 meter/sec
V2 = U X e 2 = 7000 X • 021816 : 152.72 m/ &.eC
7. Max. angle subtended by Central Station in plan view:
eH = 3. 54 X. 3048 = • 0013738 radians 2v x 125
8. Vertical extended striking range from flight trajectory
ev = (high striking angle) + (low striking angle)
= <<P -4> ') + (4> -4> ') 2 2 1 2
ATM 1046
14.
15.
Example (angle in radian)
Velocity (M/S) <1>2 cf>' <1>1 cf>' e 2 1 v
50 1.53025 1. 53024 .0466513 • 0405452 • 61165xl0- 2
200 1.56826 1.56826 .863626x1o- 2 • 253295x1o- 2 .61033x1o- 2
600 1. 57051 1. 57051 • 65917x1o- 2 • 24414x10 -3 .634756x1o- 2
9. Conditional (independent) probability of strike based on fragment size
f 9v p (x2) = p (x2 x 1) = N • -;-;2 . 'If 2
• eH
Example: For V = 200 M/S
N ev eH p (x2)
2563 .61033xlo- 2 • 0013738 .0136757
427 • 61033x1o- 2 • 0013738 • 0022793
122 .61033x10 -2 • 0013738 .0006512
Refer to Table U for more results.
10. Probability of number of fragments based on the following assumed curve:
p (xl) = loo xl
p (i:) dx
, (i:).
xl p (xl)
2563 • 05 \ • f65
427 • 30 I
122 • 95
I
i ' J,/ l ~------·-------~~----- ··----·---·-· ------
"· .......... -...
n
Refer to Table U for more results.
ATM 1046
16.
11. Resulting probability of striking ALSP Central Station
P (xl, x2) = P (xl) P (x2 J xl)
Example: V = 200 M/S
XI p(xl) p(x21·xl) p(xl, x2)
2563 .05 .0136757 • 683786xlo- 3
427 .30 • 0022793 • 683786x10- 3
122 .95 • 0006512 • 618664xlo- 3
Refer to computer plots and Table II for more results.
12. Kinetic energy: This item may provide criteria of damage level.
where mf is the mass of fragment. Use v = 200 M/S as sample.
Frag. wt. (lb) K. E. (M-Kg)
• 001 0.9251
.006 5. 5505
• 021 19.4268
Refer to computer plots for more results.
ATM 1046
VII. CONCLUSIONS
The conclusions of this study are summarized in Tables I and II and Figures Z through 16.
17.
Table I presents the calculated values of upper bound velocities and blast angles for the assumption that the total explosive energy is converted into fragment kinetic energy. Two values of the mass ratio a are used, because the definition of this term is somewhat ambiguous for this situation. The results thus prQvide for any possible interpretation of a • The values of V z for the 3# and 6# charges are calculated by the theory as being greater than 7000 meter/sec. However, because fragment velocity cannot be greater than the gas front velocity, it is obvious that the assumptions used are conservative, and V z is therefore listed as 7000 M/S. Except for the 1/8 lb charge, all of the calculated velocities are greater than those given in Ref 1. Therefore, the results of Table I affect only the velocity range for the 1/8 lb charge of Table II.
Table II presents in column 7 the probability results based on the input parameters listed in columns 1 through 4. Column 5 lists the probability that the number of fragments is equal to or greater than the numbtar listed in column 4. Column 6 lists the conditional probability p (xz J x 1) described in Chapter V. The values in column 7 are the products of the corresponding numbers in columns 5 and 6. Note that, for example, for the 1/8 lb charge, a probability of • 068o/o (i.e., • 00068) is almost independent of the assumption regarding the number of fragments over the range considered.
Three distinct figures are presented for each charge mass. Figures Z, 5, 8, 11, and 14 present four curves each for kinetic energy as a function of particle (earth) weight, and velocity. These curves are included for the convenience of the readers, in case that a damage theory based on kinetic energy is used. Figures 3, 6, 9, lZ and 15 present conditional (or "independent") probabilities as functions of fragment initial velocities up to a limit of 600 meters/sec. Note that these probabilities are nearly independent of the velocity over the range considered. Finally, Figures 4, 7, 10, 13 and 16 present the striking probabilities as functions of fragment weight and velocity. Because of the small differences in some of the calculated probabilities, a few of the curves are virtually coincident, e. g., the 550 M/S and 600 M/S curves of Figure 4.
No damage criterion is given by this study. Such a criterion would probably be related to thermal control deterioration due to damage of the protective curtains.
ATM 1046
18.
VIII. REFERENCES
1. "Fragment Hazards Associated With the Active Seismic Experiment," by T. J. Ahrens and C. F. Allen, SRI Project FGU-6011 Report, May, 1967.
2. "Analysis of the Explosion of a Long Cylindrical Bomb Detonated at One End," by G. I. Taylor, Scientific Papers of G. I. Taylor, Vol. III, No. 30, Cambridge University Press (1963).
3. "Blast Impulse and Fragment Velocities from Cased Charge," by G. I. Taylor, ~ientific Papers of G. I. Taylor, Vol. III, No. 40, Cambridge University Press ( 1963).
4. "The Dynamics of the Fragmentation Process for Spherical Shells Containing Explosives," by S. T. S. Al-Hassani and W. Johnson, Int. J. Mech. Sci., 1969, Vol. ll, pp. 811-823.
5. "Theoretical Blast-Wave Curves for Cast TNT," by John G. Kirkwood and S. R. Brinkley, Jr., OSRD Report No. 5481.
6. E x.p1osions: Their Anatomy and Destructiveness, by Clark S. Robinson, McGraw-Hill, 1946.
ATM 1046
•
TABU: I U~ BOUND VELOCITIES
UaiDI i:F ,. ET aa Upper B011nd ..:'.:!·
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) ....
Chara• Wt. Wt. of Wt. of Wt. of Case Total paeray •t ,gol, m • ~1· m • HCNsing E. S/A Col. f2)+Co1. (3) ·to 0. 2 0 • e1 ez V1 vz
Distalac:e (lb) (lb) (lb) fft-lb) (Radian) (R.adian) (m/s) (m/s)
> ., 1/81 • 277 2.286 2.563 .1875 20.5 2.216 ,007156 .o:U82 50 153
~ *@125m .....
0 ~ 1/41 0'
.275 2.286 2.561 .375 10.244 1.1 .03875 .11807 271.25 826.49
@250m
1/21 .410 Z.Z86 2.6_96 .75 5.392 0~82 • .o7s398 I • 20769 527.79 1453.8
@SOOm
. 11 .451 z. 286 2.737 1. $." z. 737 0.451 .14974 .3705 1048.2 2593,5
@ looom
31 • 525 2. 286 2. 811 4.5 0.937 0.175 .4465 1.0756 3125.5 7000
@3.5km
6# • 528 2.286 2.814 9.0 . 0,469 .088 .• 9168 1. 5708 6417.6 7000
@3.5km
(8), (9) = ei .. cos ·•0 -E T1 ) = cos •1(1 -~) (10), (11) ::vi = uei U :7000 m/i
aiU at U
* Actual planned minimum distance is 500 fee.t. 125 meters or 410 feet·ia used as minimum distance to assure conservative probability.
T*'BLEU STR.IKING PR.OBABlLITlES OF EXPLOSIVE PACKAGES
(l) (1) (3) (4) (5) (6) (7)
Charge Wt. Fra1. Cond. Prob.-.. Velocity aaa,e Slse No. ol p Cxt)
·'~··' P .. ~~) a p(:azl••, Di•tane• 'emeteri/MC) • (I) Fn1. Clwac:e ~)
'
l/81 50-600 .001 2563 .os 1.4 .068 @ .003 854 .IS .45 .068
-~ 427 .30 .23 .068 125m .oo; 285 .45 .15 .068"
,015 1?1 .7"5 .091 .068 .021 122 .95 .065 ,062
> 1/41 200"-600 ,001 2561 .05 .·343 ,0172 ~
@ .003 854 .IS .114 .0172 ~ .006 440 • 30 .OS? .0172
250m ,009 285 .45 .038 ,0171 - .015 171 .75 .023 .on 0 ~ .021 122 .95 .016 .015 0'
1/2# 200-600 .001 2696 .os .09 .0045 @ .003 895 .15 .03 .0045
.006 450 .30 ,Ol5 .0045 soom ,009 300 .45 .01 ,0045
,015 180 .75 .006 .0045 .021 us .95 .0043 .0041
11 200-600 .001 2737 • 065 .0228 .00148 @ ,003 912 .135 .0076 .00103
.009 304 .48 .0025 .0012 lOOOm
3# Z00-600 .001 2811 .10 .0019 • 000190 @ .003 938 .18 .0006 • 000108
.006 409 .32 .0003 .000090 3.5km ,009 313 .48 .0002 .00096 • 015 188 .77 .00013 .0001
61 200-600 .001 2814 .15 .0019 .00029 @ .003 938 .20 .• 0006 .00013
.006 469 .35 .0003 .00011 3.5km .009 313 • 50 .oooz .00011
.015 188 • 80 .00013 .0001
1. Explosive Before Firing
Explosive
'1=>7'>'"""'"'~-,.yty :~'"'1 '•' ''"""s :::::::: (<;:;;~P) 2. Explosion Starts
c;>Q'( c;;Jt.,)~ ~ ~ Earth Surface {Test) ~ a Moon Surface (ALSEP)
/ /.(:-..Y/ .-('Y/,(';>"/~5~)~~j:;~.~~~~;;<~?,Zo//~y%S>"//
Ground Under Compression
3. Crater Forms
. Ki j Debris Blown From Hole
Earth Surface (Test) --..!..~ .h. V. / Scouring Blast Moon Surface (ALSEP) , ' • 6 • ,., i. A 4 ./,.,
4. Final Form
/1!..-,.Y.- '/:o:y;;~:"·t::- .~ •. ~~.-; ~ 1ff///§?i.W7£w . \ .6 A u
' ~ A , '-.J" ~· .. "!" ~ •• ' 6. 'j/~
Apparent Diameter
Figure 1 Diagram of EP Explosion
ATM 1046
Olsen Formula for Cratering
v == o. 4 o817
BENDIX AER~SPACE SYSTEMS DIVISION-FRAGMENTATION STUDY
CHARGE WT. (•) =0. 125 CASE WT. (•) =2. 563 0 I STANCE CMETfASl = 125
~FRAGMENT WT. C•l•O.OOl ~FRAGMENT WT. C•l•0.003 ~FRAGMENT WT. (•)=0.006 +FRAGMENT WT. C•l•0.009
0 0 •
0 ::J' .....
0 0
• 0 C\.1 ......
0 0 . 0 0 .....
0 (...)CO -t-w zo _o ~0
::I'
0 0 . 0 C\.1
0 0 . 0 10.00
/ /
v /
/ v v ~
~ v ~ ~ ~ -""'---
~~ -20.00 30.00 ijO.OO 50.00 pO.OO
VELOCITY (METERS/SECOND) K10
~,uj:J&URE z FRAGMENT K. E. VS. VELCJC I TY ATM 1046
70.00
BENDIX AEROSPACE SYSTEMS DIVISION-FRAGMENTATION STUDY ' '
CHARGE WT. (•) =0. 125 SASE WT. C•l =2. 563 0 I STANCE CMETERSJ = 125
C!.J FRAGMENT HT. hal .. o. 001 (!)FRAGMENT WT. f•l •0. 003 ..tr. FRAGMENT WT. (•l •0. 006
+FRAGMENT WT. f•l•O.OOS
0 U)
• -. -
0 -• --~ >t-0 ......,.<»
--'o ........ co a: co E:lo a:::ra_c:)
• Q_
w Do ZU> ........ .
0
0 ('t') . 0
0 -. 0 10.00
- ... ... /\ (V - - -
~ ~ - - ,...... .., ...... ......
_&. _&. - ---.,..
20.00 30.00 ~0.00 50.00 pO.OO VEL~CITY CMETERS/SEC~NDJ wlO
·~&~fIGURE 3 I NOEPENDENT PR~BAB I L I TY VS. VELOCITY ATM 1046
70.00
BENDIX AEROSPACE SYSTEMS DIVISI~N-FRRGMENTRTION STUDY
£HAAG~ Hr. (•) =0. 125 CASE HT. (•) =2. 563 OisrqNCE (METEASl=125
4 VELOCITY (M/5)300 ~ VEL~CITY lM/5~~00
+ VEL~CITY ("/5J350
VELOCITY l"/5)500
"' I
0 -X
U') -• 0 -• r-
U') 0
• r-
0 0 • _,_
N -)-
1-&n -m ...Jai -co a: co Co a::m CL •
tD
&I) CD •
tD
0 CD •
ctt. 00
---
-
~VELOCITY lH/SJcSO X VELOCITY (H/5)ij00
. ~VELOCITY (H/5)550
-- ------
-- ------
~ VEL~CITY lH/5Jij50 z VEL~CITY CM/5)600
---s
'
r---. o.o2 o.oq o.os o.oa
1 0.10
FRAGMENT WT. (LBSl * 1 a-0.12
~·~1 I GU~E 4 PRCJBAB I L I fY OF 5 TRIKE VS. FRAGMENT SIZE ATM 1046
BENDIX AER~SPACE SYSTEMS DIVISI~N-FRAGMENTATI~N STUD!
CHARGE WT. (a) =0. 250 CASE WT. (#) =2. 561 0 I STANCE (METERS) =250
1!1 FRAGMENT WT. (a) =0. 001 (!) FRAGMENT HT. (•) =0. 003 & FRAGMENT HT. C•l =0. 006
+ FRAGMENT WT. (a) •0. 009
0 0 . 0 :::J' -0 0 . 0 N -0 0 . 0 0 -
0 (JCD ........ tw zo ......,.o Y:o
:::J'
0 0 . 0 N
0 0 . 0 10.00
/ /
v /
v /
~ ~
~ / ~ r----
~ -e--
~~ - -20.00 30.00 ij0.00 50.00 pO.OO VEL~C I Tl (METERS/SEC~ND) * 10
~ ~~fIGURE s FRAGMENT K. E. VS. VEL~C I Tl ATM 1046
70.00
BENDIX AER~SPACE SYSTEMS DIVISI~N-FRAGMENTATI~N STUDY
CHARGE WT. l•l =0. 250 CASE WT. (#) =2. 561 DISTANCE (METERSJ=250
l!l FRAGMENT HT. l•l •0.001 (!)FRAGMENT WT. (•l =0.003 lh FRAGMENT WT. l•l =0. 006
+FRAGMENT WT. (a)•0.009
OJ (T') . 0
(Tl (T') . 0
CD C\1 .
>t-(Tl
-C\1
-1o -co a: co Ceo a:-O...c:)
CD 0 . 0
(T') 0 . ~0.00
...
\/\) \ v -I .... ....
L;:J -~
.... ~ ~ - - -""
__.. ....----- ---t"' -
20.00 30.00 ijO.OO 50.00 pO.OO VEL~CITY (METERS/SEC~NDl *10
FIGURE 6 INDEPENDENT PR~BABILITY VS. VEL~CITY ATM 1046
70.00
BENDIX AER~SPACE SYSTEMS DIVISI~N-FRAGMENTRTI~N STUDY
·cHARGE W T • ( •) = 0 • 2 50 CASE W T • ( • l = 2 • 56 1
~VELOCITY fH/5)200 ~VELOCITY (M/5)250 +VELOCITY fM/5)350 X VELOCITY (M/5)ij00
~·· ·~ELOCITY (M/5) 500 X VELOCITY (M/5) 550
N
' 0 -X
. -0 CD . -co r-. ......
C\J ,_ .
>I-CD t-tCO _J...: 1-t
(l)
a: (l)
O.::r a: co o......:
0 co • ......
co lt) .
-- -
-... ... - -- -
-..
DISTANCE (METERSl=250
A VELOCITY lM/5)300 ~VELOCITY CM/5)ij50 z VELOCITY CM/5)600
--
'" ---
""b. 00 o.o2 o.Oij o.o6 o.oe 0.10 FRAGMENT WT. (LBSl * 10-1
0. 12
~~~FIGURE 1 PR~BABILITY ~F STRIKE VS. FRAGMENT SIZE ATM 1046
BENDIX AEReJSPACE SYSTEMS DIVISieJN-FRAGMENTRTieJN STUDY
'CHARGE WT. (a) =0. 500 CASE WT. (a) =2. 696 DISTANCE (METERSl=SOO
[!) FRAGMENT WT. C•J •0. 001 (!) FRAGMENT WT. C•l =0. 003 .t. FRAGMENT WT. C•l •0. 006
+ FRAGMENT WT. C•l •0. 009
0 0 . 0 .::r ......
0 0
• 0 N ......
0 0 . 0 0 ......
1-w zo ........ o :x:::ci
::!"
0 0 . 0 N
0 0 . 0 10.00
L v . / /
/ / v ~
~ ~ ~ ,...-
i~ ~ -------20.00 30.00 ijO.OO 50.00 SO.OO
VELeJC 1 T I (ME TERS/SECeJNDl * 10 1
FIGURE s FRAGMENT K.E. VS. VELeJCITI ATM 1046
70.00
BENDIX AER~SPACE SYSTEMS DIVISI~N-FRAGMENTATI~N STUDY
CHARGE WT. C•l =0. 500 CASE WT. C•l =2. 696 DISTANCE lMETEASl=SOO
[!)FRAGMENT WT. l•l=O.OOl (!)FRAGMENT WT. (•l=0.003 .& FRAGMENT WT. C•l=O.OOS
+FRAGMENT WT. (•1=0.009
. 0
C\1 -• 0
0 -• ,......C)
~
>t-<D _o --'o -
• a... w 0:::1' zo -. 0
C\1 0 . 0
0 0 . 0
10.00
m
- -- /\ ,,.-- ... .... ...
.... .... ..... A
~ _......_
20.00 30.00 ijO.OO 50.00 60.00 VELOCITY (METERS/SECCJNDl * 10 1
FIGURE 9 INDEPENDENT PRCJBABILITY VS. VELCJCITY ATM 1046
70.00
BENDIX AEROSPACE SYSTEMS DIVISION-FRAGMENTATION STUDY '
, CHARGE WT. (•) =0. 500 CASE WT. (•) =2. 696
~VELOCITY (M/5)200 ~VELOCITY (M/5)250 +VELOCITY lM/51350 X VELOCITY lM/5)ij00
VELOCITY (M/SJSOO ~VELOCITY (M/5)550
N I C) -X
•
N lJ') . 0
0 lJ')
• 0
CD :If
• ....... o N ->t-CD ,......:If
-1o ....... CD a: CD o::lf CI:::lf a.._ •
0
. 0
•
- -- ..,
-- -
-- -
DISTANCE CMETERSl=SOO & VELOCITY CM/5)300 ~VELOCITY CM/5)ij50 z VELOCITY CM/5)600
---
--
9J.oo 0.02 O.Oij 0.06 0.08 0.10 FRAGMENT WT. (LBSl K 10-1
o. 12
FIGURE 10 PA~BABILITI ~F STRIKE VS. FRAGMENT SIZE ATM 1046
BENDIX AER~SPACE SYSTEMS DIVISI~N-FRAGMENTATI~N STUDY '
, CHARGE HT. (•) =1. 000 CASE HT. (•) =2. 737 0 I STANCE (METERS) = 1000
~FRAGMENT HT. l•l•O.OOl m FRAGMENT HT. (•)•0.002 A FRAGMENT HT. C•l=0.003 + FRAGMENT HT. (•) •0. 006 X FRAGMENT HT. l•l =0. 009
t.:)
X:
0 0
• 0 ~--------~------~------~------~------~----~ -0 0 . 0 N+-------+-------+-------+-------+-------+-----~ -0 0
• 0 0+-------+-------+-------+-------+-------+-----~ -
* ~0 ""-Jo • 04-------+-------+-------+-------+-------+-----~
)-CD t.:)
a: w :zO wo
•
...... tw :zo ....,.o x:o~------+-------+-------+-~~--+-~----+-----~ ~
0 0 . 0~------+-------~--~~+-------+-~~--+-----~ N
FIGURE 11 FRAGMENT K. E .. ;VS. VEL~C IT:Y ATM 1046
BENDIX AEROSPACE SYSTEMS DIVISI~N-FRAGMENTATI~N STUDY '
. CHARGE HT. (•) =1. 000 CASE HT. l•l =2. 737 DISTANCE (METERSl=lOOO
~FRAGMENT WT. (el•O.OOl ~FRAGMENT NT. l•l•0.002 • FRAGMENT NT. C•l=0.003 +FRAGMENT WT. (el•0.006 X FRAGMENT NT. (•1•0.009
...
CD N
• 0
::1" N
• 0
•o ON ......... . :10
• >-0 1---_J -CDN -a: . (DO
0 cr: CL
::1' 0 . 0
0 0 . 0 10.00
-a..... - 1ft - - -
- -- - - -..... - .....
,
20.00 30.00 ijO.OO 50.00 pO.OO VELOCITY (METERS/SEC~NO) K10
FIGURE 1z INDEPENDENT PA~BABILITY VS. VEL~CITY ATM 1046
70.00
B'ENDIX AEROSPACE SYSTEMS DIVISION-FRAGMENTATION STUDY '
CHARGE WT. (a) =1. 000 CASE WT. (•) =2. 737 DISTANCE (METERS) = 1000
[!] VEU,CJTY
+ VELfJClTY "'
1ELfJCITY
.... I
::1' -• 0
N -• 0
0 -• 0
0 ...... X
CD 0
• -o :-.:
>t-CD t-tO
..Jc:) ...... ID a: ID E) ::I' a:o O...c:)
N 0 •
0
0 0 •
(H/5) 200
(H/5) 350
(H/5) 500
• .
9:1.00
(!) VELrJCITY U1/5l 250 A VELrJCITY (M/Sl 300
X VELfJCJTY (M/S) 1100 ~VELOCITY (M/Sl 1150
~ VELfJCITY (M/S) 550 z VELOCITY (M/Sl 600
--.... -
o.o2 o.oq o.os o.oe 1
o.1o FRAGMENT WT. (LBSl * 1 o-
0 .. 12
FIGURE 13 PROBABILITY OF STRIKE VS. FRAGMENT SIZE ATM 1046
BENDIX AEROSPACE SYSTEMS DIVISION-FRAGMENTATION STUDY '
tHARGE WT. C•l •6. 000 CASE WT. £•) •2. 811.J DISTANCE (METERSl=3500
~FRAGMENT WT. (a)•O.OOl ~FRAGMENT WT. (a)•0.003 6 FRAGMENT WT. C•l=0.006
+FRAGMENT WT. (•)•0.009
0 0
• 0 ::::1' -0 0 •
0 N -0 0 •
0 0 -
0 UlD
0 0 . 0 N
0 0 •
0 10.00
/ /
v /
/ /
/ ~
~ ~ ~ r---
.~ ~ ~ --sr- - --2o.oo 3o.oo ~o.oo so.oo po.oo
VELOCITY (METERS/SECOND) K10
FIGURE 14 FRAGMENT K. E. VS. VELOCITY ATM 1046
70.00
BENDIX AER~SPACE SYSTEMS DIVISI~N-FRAGMENTATION STUDY
CHARGE WT. £•) =6. 000 CASE WT. (•) =2. 81 ij DISTANCE CMETERSl=3500
~FRAGMENT WT. (a)•0.001 ~FRAGMENT WT. (•)•0.003 A FRAGMENT WT. (•)=0.006 ~· fRAGMENT WT. (a) •0.009
Cl) N . 0
:f' N . 0
N •o ON
• >-0 t-....... _J ....... Q)N -a: . Q)O
El a: a...
.m a...~ we Cl :z .......
:f' 0 . 0
0 0 . 0 10.00
A
li:L - '--'\ / v - -...
~ - -- ,., -
.... ..... -. "T
20.00 30.00 ~0.00 50.00 pO.OO VEL~C I TY (METERS/SECOND) M 10
FIGURE 1s I NOEPENOENT PR~BAB I L I TY VS. VELCJC I TY
70.00
BENDIX AEROSPACE SYSTEMS DIVISI~N-FRAGMENTATI~N STUDY
CHARGE WT. (a) •6. 000 . CASE WT. (a) •2. 81 ij DISTANCE CHETERSl=3500
A VELOCITY (H/5)300 ~VELOCITY lM/5Jij50
m VELeCITY fM/5J200 .·· ·YELeCITY (M/5J 350
EU,CITY lM/5) 500
.., I
CD (Y')
• 0
N (I')
• 0
CD N
• 0
o -X ::Jt N .
>t-o -N
-'o -(D
a: (D
Ceo a:-O...c::)
N -. 0
CD 0 •
~
I I
~
~VELOCITY (M/5)250 X VELOCITY lM/5Jij00 ~VELOCITY (M/5)550
t;;: ~ ~
z VELOCITY (M/5)600
.... --.,.
9>.00 o.o2 o.oq o.os o.oe o.to FRAGMENT WT. (LBSl "1 o-'
0.12
FIGURE 16 PROBABILITY OF STRIKE VS. FRAGMENT SIZE
APPENDIX
ATM 1046
> ~ t: ..... 0 If>. 0'
FU1<fi<AN IV G ltVU 1"' fo'AIN LAfl • 71209 13/58/07
0\JO 1 ut.O£ OCIJJ OC04 ovJ) CCC<> occ. 7 OCCd
OC09 0010 0011 0012 0013 OCllo OC1!J OClt> 01;11 1.1"11 0019
oczo 0021 OOlZ OCZJ OC24 ocz~ ooze 0027 0028 OCZ9 CC30 0031 00~2 0033 0031t OCH 0016 OCH OOJ!I 0039 OC40 0041 C01t2 0Cit3 0041t 004!) 004<> OC47 0048
0Cit9 ocso OC!ll 0.0~2 c c '.)3
OC54 OC55
UIIAEr-.StUN VtiZOioENG~IZOI 1 FIIBIO!OI,PkllU J:C
1 REAO lCoXoVolllltllf-oPRh 10 FOkMAT ltlflO,OI
1~ t~.Lr.c.J ~u 10 200 J :J+l PI<INT ~
J.fuRMATC'l X Y 1 Pit l.N N 1 1 PRINT £0oXtYt~ltWftPRh
20 FORMAT I!>F1~o6l Nf"'lolHF t-1\•Nt-f MASS• .. F •• 4536/9.10665 .... 1.t:2 ltG•x•G P~H•3.~~t•.304S/12.•l.14l6•,1 V•l7S. PRltil l'i
29 FORMAT I 1 0 lll:lCCilY PHil lHIG11 PHJl PH.IZ vA• z.s•.lo~oe 0\l ICC l•ltl7 V•V+25. II Elii:V V SQ•II•II Y•O. B•"SQ/liG bSQ•II•S c •1. 0 =SUR Tl IISU-C I PHll•ATAMII+DI P 11J 1=A TAM 8-0; Y=VA Cs1.+2.•11•V/ll
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0 =S'-iR 1 Ill SU-CI Ptti2•ATAMIHO) 1'11J2=ATAMil-OI AI•AIISIPHI2-PHI11 AJsAbSIPHJZ-PHJ11 PRA:IAI+AJI*l•/1.1416 P~INT 30oV•PHiloPHI2 0 AioPHJltPHJ2 0 AJtPRA
30 1- ORMAl I iii: I ~.61 PRtllll=f~H*PRA•Fti PRIJoii~PR81li•PRI\•10C. PKSIII•Pkdlli•100~ ~~GKIII=C.5*FHASS*VSQ
1CC CONTINI.f 110 PRINT 140
.. ,
PHil AhGU LQI
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140 fCRMAT 1'0 VELOCIJY KINETIC t:NEIHiY INOE.P PRO&. PRO_ 1BABILITV 1 1 PI.NCH· l45oJ PUNCH 146 olif. 00 120 1'"1t11 P IJNCH ,160,VEIII oEI\Gklli,.PRB Clio PR I Jtll
120 PRINT 130,VI::II1 0E~GKCII 0 PR6CIIoPRIJtll 1~5 FOR~AT I 151 14<> 1-pRMAT, CHC.41
APPENDIX~· TRAJECTORY AND PROBABil·ITY PROGRAM l.·ISTING AND PLOT ROUTINE
l>A~t: 0001
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V __ -000 1 _______ • ___ u I 'lENS ION BUFFI1024l.r_WORDA 120),WORC61-0002 D I HENSION ENGKI20,_101 ,PRBI20,101 ,PRII OC03 -- ------- M: 1 - . .
..,.,., lo - I I.C.I.V
'0RDCI201,VEI20l,EVl201 .ARRAYE(4t,WfUQL--_-- -------
OCC4 READ 5,kORDi ------------ -·---- --------- ---------------0005 READ S,WOROB 0006 =--=-=--= READ S, .. .JROC --====--=-=~==-~-=~_:_-~~=_:_-=-:_ _______ _
_P.AG E_ 0001
0007 5 FORMAl C20A41 ceca-=~-==--=-- READ a, .. cR,wCS~D_i~T-~-=-=---=--=--~=----=~-=--------·--:::_-:::_::::-_·-:::_-:::_-=.-_-_-_-_-____________________________ _ OC09 8 FCRMAT DElO.CI -0010------2 RfAO lC,.J - ------- ------
0011 -lO FORMAT C 151 OC12 ------ IF IJ.EQ.-11 GO-T0-)0--0013 --------- READ 7olofi.JI- - --- ------ ----- -----·----OCH 7 FOR~Al lElO.OJ ----·------------------0015 ·-------· DO 20 -1•1,17 -- --------------- --- . --- ----------------------
0016- ______ 20 REAl> 15o11EII I oEh~Kll~.jl ;~RBII ;.JJ,PA(.I,It_:'_ ~~ ·::--::-_-::_-_:_::_:.:_ ____ _ --------------0017 15 FORMAT t4E15.61 ocu·-- · ·· J.J&J · 0019·-------GO TO 2
--- 0020-----------lC ARRA"JECllcENGKilell.,. ---- "0021 --------- ARRA"YEI21•Ef'4GKUell-·--·- ---0022-- DO 4C J•l.JJ
·----·------ -·-·--------.,------t --0021 -------DO 40 a-..1,17 ' ---0024-------- IF I ARRAYEI U .LT .UGKCioJl J ARRAYE CU•E~GKC I;Jt ---·-----··-----:---
0025 --·------1.0 If IARRA"JEI ZI.GT .Ef\GKII oJI I ARRAYEC2J•ENGKC ltJJ --· ---------------------- ·-·---------------- --------0026 . --CALL FLCTS I BUFF ol021tolll - ----· ----;· -- --~------
0027---------CALL FLOT 120.,-30.5,-31 ----0028 ---------CALL AXIS I 1.5,1. 5,/IIELUCITY UIETERS/SECOhOI' e-21tt6ot0ot l~Q~;)90; J _____ _ 0029 .. CALL SYMBOl (0.6,C.5,.llt,'ffGURE 1 eO.-Oe6» ------------------------------0030-----·-· CALL SYMBOL ( 2.0 ,o. 5e .14,WORDAo0oOo80) . ----------- ·---0031------- CALL SCALE (ARRAYEo7o0,2tll > ==:_oo32 ___ . ___ ~:~~y:~~~l l l.5,1.5o'KINEHC E~RGv_:_i.t•KGf•:,~)~?~:;9cf_;;_~~!'~-_Hfi, _________________________ _..:
1-:3 ---0033 --------- VEl 18t.,lOO.O. ~ =:::::_oc34~: ______ VEI19)zlOO.O ... ---- --- ... --------- ------- ------------------------....,. ___ 0035 EVI181=Ai<RAYEI31 0 ___ 0036. EIICl'ilzARRA'fEC~t .. _________ _ ~ __ OC3~_ PRINT 6,WOROA . _____ _ 0' 0038 6 FORMAT ( 1 1 1 o20Aitl
---0039 35 CALL GRID ll.5,1.5oi.o,i~0,6,71 ---0040 --CALL SYMBOL (0.7,1C.5,0.14o 1 BENDIX AEROSPACfSYSTEMS-DfillSION-FRAG.__ ___ _
1M ENTATION Sil.DY' ,o.o ,53) -- --- -- - ----- -;---OCitl-- ----CAll SYMBOL (0.5,1C.lO,O.l2,'CHARGE WT.Ul••,o.O,lll•l--------·-- ----- . 00"2-------- CAll t-.U~BER 1999. ,9'l9.,0.l2,wCR,0.0,31 . ---------- -----::~::--_-_·---==--·--------0043·------- CALL SYMHCL 13.0,10.10,0.12, 1 CASE H.IU.;•,o.o;izt· 0044- CALL NuH6ER l'i'i9.,9'l9.,0.12,WCS,0.0,3l ---0045·.:.:._:::._:__ ____ CALL SY~IlOl- I 5.5 1 10.10,0.12 0 'DISTANCE. I METERS)•• ,O~O,l8f_·-------
--------------------·------------
-------------------·---
0Cito __________ CALL NUI-!IIER ~999. 1999. 1 0. U 1 DIST_,O_o0t-:::U. ______ _ ___ OO'o1___ _ __ CALl PLOT 11.5,1.5,-31 ____ ---------------------------------
0048__ .PO. _90 J•l,.,IJ __________________ -----·-----------0049 I NTEQaJ-1
=--=OC50 _DO lt1. l"l~fc=-~--: -------·--------------
___ 00~ l I f_J M.EQ.l)_j:\11 II•ENGKI I 1 JI' ___ 00!:2 _ .If' (M .EQ".2)_EVUt"'PR8( ltJI. _ ·----- __ ··----. --·---__ 0.053 47_CONTINUE ____________ --------- _________ _ _________________ o __ _
___ 0054 _G_Q .TO ... I lO._]J.._Iz_, 73 o.Ho 75,7 6 1 77.,78,79,80o8lo82o83) ,.,J_ ------------:-·
___ 07-0.~5 70 !:.A!.!._~_fl!!il)j._j_~l_~t-!l•.JO,Q.lO,_Oo_,O.o.c.lL -----------------------------------0056 Gp TO E"
,,
i I i :
~v ...... -
fOKTkAN IV G LEVEL 1'> MAIN CAT£ = 71210 1112.8107 PAGE 0002
·7 ···------- _71 CALL SYMBOL Jl.50,8.JO,O.lO,Ol,0.0,-11 ·-·---8 ...... ____ _ __ G 0 TO c4
72 CALL SYI'IBGL (4,QQ,8.30,0.t0,02tO•Ot-ll ... .. _. --·· __ ___ ----------OC&O --------····-- GCJ TO E4 ... . '---------·-------------·-·-----------·--·-· OC6l ________ J3 CALL S'I'I'BOL 1-l.Oo8.05,0.L0,03,0.0,-ll . __ __ ........ ______________ _ OC62 __ .____ GIJ TO e4 ... ····-------- ___ -----------0Cc3 _________ 74 CALL S~MBOL tl.50t8.05,0.10,Q4,0.0,-l). ----------------------00t4_ _GO TO E4 -··-. .. 0Cb5. ·- _____ 75 CALL S'I'MIIOL.14.00t8o05,0.l0t05,0.0,-lJ ___ -----------------------OC66 _ -------· GO TO c4 . .. -·--·-· OC&l _________ 76 CALL nHSOl l-l.0,7.80,0.lCr06,0,0,-U -·--------OC68 .. ------- GO TO E4 .. ____ -----------------·-----------· -------------· OC69 ------ _77 CALl S'I'MIIOl ( l.5o,7,80,0,1C,07,0,0,-l) . -------- -------------· OC70 --·- _______ GO TO Elo -----------OC 71 ___________ :78 CAll HH80l I It, 00 t 7. 80 ,0.1 0,08 rO .0 ,-U OC72____________ GC TO Elo . -·--------------·---OC73 .... --·· ___ 79 CALL SYMSOL C-l.O,l.55,0.1C,09,0,0,-U --------------OOH ------- GO TO @4 . . -------OC75 ·-------·· 80 CALL SYMBOL Clo50,7.55,0.10,10tO•Ot-U _____ _
-~-------- ----
> t-:1
OC76 ------··· GO TO E4 _ ·--~----OC77 Sl CAll S~M80L (4.00,7.55,0.10tllrOoO,-ll
=-=--~=-- 0078 -=--==~ GO TO E4 . _-_··=--=~=-~=~-~~:._-· OC79 ______ 1!2 CALL S'I',.BOL l-l.Oo7.30,0.lC,l2tOoOt-lJ ........ ····-···----···--·-----------OC80 .. ------· GO TO E4 .. ------···· ···-----------· OC81_ . 83 CALL. S~MilOL (1.50 1 7,30 1 0.1C,l3,0.0,-1) ... ·············----· OCII2__ 8_4 CALL SYMBOL C<;99.,999.,0.lo'FRAGMENT WT.UI•1 .t0 .• _0tl6L __ 0Cd3 CALL ~uHIIER (999,,999.,0.1,•FCJI,0,0,31 == OC84 __ ====:-~-- CALL lilliE IVE,EVol7rlo3tlfii1EQI aces 90 coNTll'-luE ···-- ~--------------------0086 H:H+l
--- OC87 ______ CALL PLOl (15.,-30.5,-31
ocas-==..==::-- ·_IF cM-31 91,93,tsc· ____ --------··-------·-·· _ OC89 ______ 9J .. CALL AXIS I 1. 5 ,1. 5 1
1 VELOCITY CMETERS/SECOIIOI ~.o.::-21er6ot_C., 10Q~.r lOQ .•. L ________________ : __ _ -----------
·------·--·---------------------
OC90 ____________ CALL 5YMBCL (C.6,C.5,.lle, 1 FlGURE 1 tO•Ot6J ____ ···----·-----------a:: OC9l .. • CALL SYMBOL (2.0,0.5,.14,WCRDBrOoOr80J ...,. ___ OC92 ···------· ARRAYEili:PRBll 1 ll___ ·-----·-- ____ --~-=~-~~- --------O ____ OC93 _ARRAYE(21:PRB(l 1 lJ .... ---········-- ··------~!:>- ___ OC91t _________ DO 92 J•l,JJ .. .. . .... ____ ___ ······--------------'----------------------------0' OC<;5 DO 92 1•1,17
~=:~~ OC96:-----:-~~ IF CARRA VEl lJ .LT~ PRBli 1 J) I ARRAYEIU=PRBCI,JJ":==-.:.-·· ----------------· OC97 .. . 92_ IF (ARRAYEI 2) .GT. _I'_KBli ,JI 1. A·RkAYE 12J•PReCI ,JL ______________ -------------CC98 ___ ··--···-···- CALL SCALE (A-RRAYEo7oOt2r1 f CC99 EVI1EI=ARRAYE(3) 0100 ---------E\11 191•ARRAYEI41. ---·· ·---··--· ...... ------·-----------
0 101 --------.CALL AXIs C 1. 5 11. s·,,J IIOEP •. -PROBABILITY -,~)' ;zi;J-:o,9o:o;~ARR~_Y_EHl_r___ __ _ lA RRA'I'E lit J I
0102 ----------- PRII';T 6,wOROB -0103 -----·--GO TO 35 - --·-. ----
==~- ~~g~ ------~! ~~. ~i .. ~:~ ,zc .:~ ·-: . - .. . :~.=-:_---~- ·::_ ·-----~~=:::
---- --···---------------------------------
0106 CALL AXIS I 1.5,1,5,°FRAGHEH wT. (l8SI 1 r~18r6 .• Qr0•.o_Q_..._.Q_O~J. _0107 _CALL S'rHIIOL IOob 10.5tol4r'flGURE't0•0t61. _OlC8 ___ _CALl. SYMBOL (2._0r9• .. h_.lle_.r111CROC 1 0o0r80_1 _____________________________________ ~---
0109_ ARRAYEUizPR( li1L_·--------······----------___ OUO.__ ARRA'ri:l2J=PRI l ,_l) _________________________________ ~------ ---------· ___ 0111. _00 __ 100 _1=1,17 ____ --·----···-······-··· ·-··
__ 0112 ~-lQQ_,J·l~J ----------------------------------------------------~ ___ ...Q1!3 IF ~~-~B._AYEU.I.LT ,PR lh.LU __ !ARA'(I;_ll t .. PRI,Jt.H
..._
t I i ~ =
I •
V~JJ~TRiN IV G LEVEL 19 'lAIN DATE = 71210 11128101 __ _PAGE 000~ ____________ _ j
f ~ 100 IF IARRAYEIZI.GT.PRIJolll ARRAYEl2l,.PRIJ,U --~:, .5 --------- CAll SCALE lARRAYE,7.0,2,ll
";v.llb . ------------- E \IIJJ+ll =AR~A\'Et3J 0117 --------·--- E\IIJJ+2l=ARRAYE14l 0118 --·---- --- CALL' AXI!:> I l.5,1.5o 1 PROBABILITY IIP,lS,7.0,90~,ARRAVEUJ;
....... -- ----1Ail.RAYEI'oll 0119 ____ ----- wFI JJ+ 1)=0.0 0120------------ WF(JJ+2l"'0.002 0121------- PRINT t:,r..ORDC
--------------------- ------ ----------------
---·0122 .CALL GIUO llo5olo5alo0ol•Oobo71 -----0123--------- CALL SYMBOl ICo7olC.5,0.14o 1 BENOIX AERCSPACE SYSTEMS-OIVISION-FRAG,__ _________ _
- --------- .lHENTATION STUDY' ,C.0,53l -·-----------· OlH ------CALL SYMBOL 10.5o10.10o0ol2o 1 CHARGE wT.UI••,o.O,liof 0125 ------------CALL lliLM6ER 1999ot999.,0.l2,WCR,0.0,3t - ----------- ------------------------------0121:----- ----- CALL SYMBOL 13.0,10.10t0•12,•CAS£: wT.IIl•'oOeOol21 ----0127 ------------ CALL hUMBER 1999. ,999.,0.l2eWCS,0.0,31 _ ------0128 --------- CALL SYMDOL UeSolO.lOoOol2t'OIUANCE CMEJ£RU~ 0 t0eO~iej-0129 ------------ CALL 1\LMSER l999oo999.,0.12o01ST,O.O,-U ... -. ------------ -----·------------- ---------0130---------- CALL PLOT llo5tlo5o-3l ·- . ---------0131·----·- l1i. 00 1CiC l-=lollo2 ----.------------------------------------ ... 0132 -- ---- 00 l6C Ja1oJJ . --. -----· .. ----- ... 0133 --------16() E VI J l~PRlJt II . .. ---------------Oll'o --------- 11•1 0135. IF II.I\E.1i lial/2+1 --------------------0136. GO TO I 50o5lt52o53o!»ioo55,56,57,58,59o&0,6l,6i;6·31,JI-0137 ________ 50 CALL SYMBOL l-l.0,8.30,0.lCtOOoO•Oo-ll . . ... ------0138---- - GO TO t4 .. 0139 . ------51 CALL S~I'II!OL .. Cl.50,1!.30o0 •. 10,0lo0o0o-U -----------------
--------------
0140 ------ GO TO E4 o11t1 5z cALL sYMBoL·c~e;oo,e.3o~o.lc,oz,o.o~..:a:, ------=-=----_-_-_-_-_______________ _ > ___ 014;C . GO TO tit ___ -~- ~------ ___ _ __ :_--------------
1-:] _____ 0143 -------~3 CALL SYMBOL .1~1·0,8.05,0.10,03,0.0,-H ----------------------0144 GO TO t4 .
~ ----0 l4S 54 CALL Sli'BOCtl~SO~ii.os,0.10,04,o.o,-u -----Ol<t6 ---------- .. GO TO t4 .. . . . . -------.....
0 ~ 0'
0147 ---------·ss CALL s-rMsoL c4:oc,8.os,o.io,os,o.o,-u---_-___ -_-_-~--------------------0148- - GO TO E4 - . --------------.
0149 . 5b CALL SYMBOC(::'f~Oel~B0,0.1C,06,o.O,-l)·------0150- GO TU t4 -·
----- 0151 - -_57 CALL SYMBOL .. il.5o,7~80oO.l0,07,0.0o-ll ___ _ --.-0152--------- GO TO t<t --- . .. . -
Ol~l --------58 CALL SYMBOCl4~00,7.80~0.lOoOB,o.o,..:fjOl5<t ----,-- ----- GO TO t4 - . 0 15!: :=-----=--::=59 CALL SYHEHii._:(-i.~O, 7.55,0.1C,09,0.0 ,~U ---------0156 GO TO f4 0157 -------60 CALL nMBOL (1.50,7.55,0.10olO,O.Oo-U--------------Ol58 ------- GO TO tit .. .. ------·------
0159- --===--~61 CALL S'ri'BOL)It.00,7.55,0~10,ll,O.O,-U ---=- _ -------OHiO GO TO E4
--------------
0161 -----&2 CALL ·5'YM80Lj_::_l-;o,i.lO,O.lC,l2tO•Ot-U -=~-----------_-_________________________ ..:_ ___ _ 0162 GO TO tit .
____ Olb3 _l:3 CALL SYI180L=_ii":so,l.30,0.1Ctl3oO•Oo-U __ _ _______ ---------------- 0164 ______ l:4 CALL nMBOI,. _ _(Q99. ,999.,0.le'VELOCIJV _(M,t_SI...!.tO.~O...L.lltL ____________ _
0165_ _ __ CALL NlJMBER .. J9_99.,999.,o.l,VEtU,O_u-:-.. U__ ----0166 I"'TEQ=II-1 _ __ _ ' ·o lo 1 __ -_-CA!.L .. L INE_Iiit:;..lli~:.f;:i~--i:-;:i,..r_eQ"f_::-_~~ -- ------------------------------------
-- 9__168 l90_C_OitUNLE ____ ....Q_U~ 150 CAI..l......f.U.U .. l.il.tJ.":1..C...~C!9~L
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