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Prepared for the
U.S. Atomic Energy Commission
Division of Research
Under Contract No. AT(04-3)-34 P.A. 205 Mod 2
UCLA-ENG -7426
MARCH 1974
ESTIMATE OF THE HAZARDS TO A NUCLEAR
REACTOR FROM THE RANDOM IMPACT
OF METEORITES
HAZARD HOUSE COpy
1,\
llt
UCLA
•
SCHOOL OF ENGINEERING AND APPLIED SCIENCE
K.A . SOLOMON
R.C. ERDMANN
T.E . HICKS
D. OKRENT
LEGAL NOTICE
This report was prepared es an account of work sponsored by the United States Government. Neither the
United States nor the United States Atomic Energy Commission, nor any of their employees, nor any of
their contractors, subcontractors, or their employees, makes any warranty, express or implied or assumes
any legal liability or responsibility for the accuracy, complateness or usefulness of any information,
apparatus, product or process disclosed, or represents that its use would not Infringe privately owned rights.
published by
REPORTS GROUP
SCHOOL OF ENGINEERING AND APPLIED SCIENCE
UNIVERSITY OF CALIFORNIA, LOS ANGELES 90024
----
--~-
-
- - -------.~-~-------~-~-
....
UCLA-ENG-7426
MARCH 1974
.dI
ES TIMATE OF THE HAZARDS TO A NUCLEAR REACTOR
FROM THE RANDOM IMPACT OF ,METEORITES
"
VII/II
K.A. Solomon
R.C. Erdmann
T.E. Hicks
D. Okrent
'<iIIP
'"
Prepared for the
U.S. Atomic Energy Commission
Division of Research
Under Contract No. AT(04-3)-34 P.A. 205 Nod. 2
'>.f!ji
'viii
"'i!IIII
"""
i-.;
School of Engineering and Applied Science
University of California
Los Angeles, California
PREFACE
This report is one of a series of four prepared by UCLA (and a subcontractor, JRB Associates, where Prof. R.C. Erdmann of UCLA was spending a
leave of absence) and issued as UCLA Engineering Reports at the request of
and with the support of the U.S. Atomic Energy Commission (under Contract
No. AT(04-3)-34 P.A. 205 Mod. 2.
The titles and numbers 9f the four reports are as follows:
1.
"Estimates of the Risks Associated with Dam Failure," by P. Ayyaswamy,
B. Hauss, T. Hsieh, A. Moscati, T.E. Hicks and D. Okrent, UCLA-ENG-7423.
2.
"Airplane Crash Risk to Ground Population," by K.A. Solomon, T.E. Hicks
and D. Okrent, UCLA-ENG-7424.
3.
"The Risk of Catastrophic Spills of Toxic Chemicals," by J.A. Simmons,
R.C. Erdmann and B.N. Noft, UCLA-ENG-7425.
4.
"Estimate of the Hazards to a Nuclear Reactor from the Random Impact of
Meteorites," by K.A. Solomon, R.C. Erdmann, T.E. Hicks and D. Okrent,
UCLA-ENG-7426.
These reports represent an effort to evaluate the probabilities and
consequences associated with some unlikely, potential accidents, most of which
a certain degree of intuition regarding risk exists.
These estimates repre-
sent preliminary, early results that need to be continued, expanded and
refined over the next few years so as to better understand technological
risks.
The mortality and property damage estimates are made to provide some
perspective on the current risks of modern technologies.
For this purpose,
preliminary estimates of probabilities and consequences can be of value, even
if there exists considerable uncertainty in the results.
ii
Table of Contents
Page
List of Figures.
iv
List of Tables •
v
1.
Summary •
1
2.
Introduction.
2
3.
Probability of a Meteorite Crash on a Target.
3
4.
Probability of Serious Reactor Damage to a Reactor from
a Direct or Nearby Hit.
5.
9
Tidal Wave Induced by Offshore Crash of Meteorite •
12
Conclusions
18
References •
19
...
iii
List of Figures
Page
Figure 1.
Figure 2.
Frequency of Impacts of Meteorites whose Weight is
W or More Before Entry into Earth's Atmosphere ••
Comparison of Target Area and Affected Area for a
Meteorite Crash; Assume Meteorite can Only Crash
on Land • • . . . . • . . . . . . • . . • . . . •
Figure 3.
Figure
4.
3
7
Schematic Drawing of the Maximum Wave Transformation
as it Propagates Towards the Shore. • • • • • • • • •
13
Area Affected by a Meteorite Crash; Assume Meteorite
May Crash in Land or Adjacent Ocean • • • • • • • • •
16
iv
•
List of Tables
Page
Table 1.
Meteor and Meteorite Data for Entire Earth
Table 2.
Probability of a Stone or Iron Meteorite Hitting
and Damaging a Nuclear Reactor in the United States.
v
4
10
1.
SUMMARy
A method and statistics given by V.E. Blake have been employed to estimate
the probability per year that a nuclear reactor could be seriously damaged by
a meteorite strike.
The probability per year that a target area of 10 4 sq. ft. will be
struck by a meteorite weighing more than a pound is estimated to be
4.3 x 10-9 per reactor year.
However, only a fraction of these meteorites,
corresponding to weights exceeding 100 pounds, are very likely to seriously
damage or destroy the reactor to the point of an uncontrolled release of fission products.
For a vulnerable target area of 10 4 sq. ft., this probability
is estimated to be 7 x 10
-10
per reactor year.
If the vulnerable target area
per reactor were as much as 10 6 sq. ft., the probability of serious damage is
estimated to be 6 x 10-8 per reactor year.
The probability that a coastal plant will suffer serious damage arising
from a tidal wave induced by a meteorite is estimated to be of the order
of 9 x 10
-10
per reactor year.
1
2.
INTRODUCTION
A meteor is a mass of stone or metal that enters the earth's atmosphere
from outer space; a meteorite is a meteor that falls to the earth's surface.
Meteorite masses are usually much smaller than those of meteors, due to the
loss of material by ablation in the fall through the atmosphere.
Meteors vary in size from dust-like particles to asteroids several hundred
mlles across.
Due to the effect of the earth's atmosphere all bodies having an
initial mass of less than about 100 pounds (about the size of a football) are
reduced to dust-like particles by the heat developed from passing through the
atmosphere. (1)
The number of fragments striking the earth each year weighing
over a pound at impact has been estimated to be about 3,500, with the majority
being small i.e., between one and two pounds. (2)
The entry velocity of meteors can vary from 37,000 feet/sec. (the escape
velocity from the earth) to 290,000 feet/sec. (the sum of the earth's orbital
velocity and the solar escape velocity). (1,2)
At 37,000 feet/sec., one ton
of meteoritic material possesses the kinetic energy of about 15 tons of
high explosive. (3)
At 240,000 feet/sec., this energy increases to the
equivalent of over 600 tons of high explosives. (3)
Meteorites of a large size can cause serious damage to a nuclear reactor
(or other structure) either by directly hitting a vulnerable part of the
reactor or, for a very large meteorite, by generating a huge heat flux
arising from a very near miss.
For coastal reactors, it is also conceivable
that a reactor damage might result from a large tidal wave initiated by an
offshore crash of a meteorite.
2
3.
PROBABILITY OF A METEORITE CRASH ON A TARGET
Blake(2) has examined the probability that meteorites of various sizes
will fall to the Earth.
His estimates of meteorite size vs. frequency of
impact are given in Figure 1, and estimates for larger meteorites (2.4 x 10+ 2
pounds on impact) are listed in Table 1.
The latter table also gives Blake's
estimates of the "lethal area" to be associated with meteorites of various
sizes.
Blake derived these estimates by considering the size of Meteor
Crater in Arizona, and then evaluating the probability of fall of a meteorite
of the same size and velocity.
Blake also estimated the probability that a person might be killed or
injured by a meteorite.
He calculated the probability of impact in a populated
area, Pi' as:
P. = 1 - (l_F)x
1.
where F is the fraction of the Earth's area inhabited by
number of meteorite impacts per year.
human~.
and x is the
An estimate of mortalities is then
derived from consideration of the "lethal area" for meteorites of various
sizes •
. Using Blake's general approach, one can calculate the probability of a
crash on the U.S. of a meteorite exceeding one pound in weight.
(1,2)
area of the Earth is 5.48 x 1015 square feet.
U.S. is 1.05 x 10
14
square feet.
(3)
The surface
The surface area of the
Assuming that impacts of meteorites are
evenly distributed over the Earth's surface, the number of meteorites striking
the U.S. (weighing more than one pound) every year is:
(3,500)
1.05 x 10 14
54.8 x 10 14
= 65
3
1012
,
109 ~ ,
*BEFORE ENTRY INTO EARTH'S ATMOSPHERE
,,
*
CI)
2:
0
,,
,,
l-
I
....J:
106
"
~
C!)
w
3:
,,
a:
0
w
....
w
103
~
III
5:
,,
,,
,
,
,,
STONE
10
,,
,,
,,
,,
10- 3
10-8
10- 5
10- 2
10
104
IMPACTS PER YEAR
Figure 1.
Frequency of Impacts of Meteorites Whose Weight is W or More
Before Entry Into Earth's Atmosphere.
4
Table 1
METEOR AND METEORITE DATA FOR ENTIRE EARTH(l)
Relative
Number of
Meteors
This Size
Or Larger
Per Year (1)
Meteor
Radius
Before
Entry (2)
(Ft)
Meteorite
Impact
Weight (3)
(Lbs)
Meteorite
Impact
Velocity (4)
(Ft/Sec)
10 0
10 1
1.0 + 1
9.9 - 1
2.4 + 2
4.5 + 3
2.7 - 2
9.9 - 1
1.8 - 6
2.0 + 0
2.1 + 0
9.0 + 3
1.8 + 4
1.6 + 1
8.3 + 0
1.3-4
10 2
10 3
5.0 - 1
4.6 + 0
1.4 + 5
2.8 + 4
6.1 + 2
2.8 + 1
1.4-3
9.0 - 2
9.9 + 0
1. 7 + 6
3.8 + 4
1.4 + 4
7.8:+- 1
1.1-2
10 4
1.8 - 2
2.1 + 1
1.9 + 7
4.4 + 4
2.0 + 5
1.9 + 2
6.7 - 2
105
4.0 - 3
4.6 + 1
1.9 + 8
4.7 + 4
2.4 + 6
4.4 + 2
3.5 - 1
10 6
7
10
10 8
8.0 - 4
9.9 + 1
2.0 + 9
4.9 + 4
2.6 + 7
9.8 + 2
1.7 + 0
1.6-4
2.1 + 2
2.0 + 10
5.0 + 4
2.6 + 8
2.1 + 3
8.1 + 0
3.0 - 5
4.6 + 2
2.0 + 11
5.0 + 4
2.7 + 9
4.6 + 3
3.9 + 1
10 9
7.0 - 6
9.9 + 2
2.0 + 12
5.0 + 4
2.7 + 10
1.0 + 4
1.8 + 2
10 10
1.4 - 7
2.1 + 3
2.0 + 13
5.0 + 4
2.7 + 11
2.3 + 4
8.3 + 2
1011
2.8 - 7
4.6 + 3
2.0 + 14
5.0 + 4
2.7 + 12
4.6 + 4
3.9 + 3
1012
1013
6.0 - 8
9.9 + 3
2.0 + 15
5.0 + 4
2.7 + 13
1.0 + 5
1.8 + 4
9.0 - 9
2.1 + 4
2.0 + 16
5.0 + 4
2.7 + 14
2.2 + 5
8.3 + 4
1.0 + 2
1.3 + 0
4.5 + 2
1.0 + 3
2.5 - 3
4.5 - 1
3.6 - 7
10
1.0 + 1
2.7+ 0
1.1 + 3
6.0 + 3
2.1 - 1
2.0 + 0
7.0 - 6
J10 2
3
10
104
1.0 + 0
5.8 + 0
1.5 + 4
2.1 + 4
3.7 + 1
1.1 + 1
2.2 - 4
1.0 - 1
1.3 + 1
1.8 + 5
3.4 + 4
1.2 + 3
3.5 + 1
.2 - 3
1.0 - 2
2.7 + 1
1.9 + 6
4.1 + 4
1.8 + 4
8.6 + 1
1.3-2
105
1.0 - 3
5.8 + 1
2.0 + 7
4.7 + 4
2.3
Meteor
Weight
(Tons)
Iron
V1
1
~oO1
Stone
Kinetic
Energy
Yield (5)
(Tons of high
Explosives)
+
5
Crater
Radius (6)
(Ft)
2.0
Notes: Numbers in patentheses refer to the notes following this table.
. 1
Second number in column refers to exponent; for example 1.0 + 1 means 1.0 x 10 •
+
2
Lethal
Area (7)
(Sq .Mf.)
7.5 - 2
Notes for Table 1
1.
Taken directly from Reference 2.
2.
The meteor radius was calculated assuming a spherical geometry with a
density of 490 pounds per ft 3 for the iron meteor and 245 pounds per ft 3
for the stone meteor.
3.
The impact weight was calculated based on the uniform removal of 1/2 foot
from the radius of each meteor during entry into the earth's atmosphere due
to the total calculated integrated heating of about loo,ood Btu per ft2.
4.
The impact velocity was calculated based on an initial velocity of 50,000
ft/sec., an entry angle of 45°, and a ballistic parameter based on the
meteorite dimensions as determined from the impact weight of Column 4.
5.
The kinetic energy yield was based on the relation that a I-ton meteorite
at 37,000 ft/sec. has the equivalent energy of 15 tons of high explosives.
Yield was assumed to be directly proportional to the impact weight times
the impact velocity squared •
. 6.
From the Nuclear Weapons Handbook, (3) the radius in feet of a crater from
a·surface burst in sandstone can be calculated from the formula r
where Y is the yield in tons of high explosive.
=
5.l2y l / 3
Using this relation it
can be determined that the Arizona crater could have been made by the
surface burst of a 59.5-megaton weapon.
The equivalent yield of an 8 x 10 6
ton meteorite (the largest estimate), at 50,000 ft/sec calculates to be
219 megatons; therefore one may assume a 59.5/219 x (100)
efficiency.
rl
27 percent
This allows the derivation of a new equation,
= 5.12. (0.27Y l )1/3
where r l is the radius of a crater in feet caused
by a meteorite of equivalent yield Yl in tons.
calculating crater radius in Column
7.
=
This relation was used for
7~
Lethal area was calculated assuming a lethal radius equal to four times
the radius of Column 7.
6
Assume that the "lethal area" for impact by a meteorite, for a structure
the size of a nuclear reactor, is Ai.
The probability (per year) that the
reactor will be struck by a meteorite weighing more than one pound is:
(2/3) (n) (Ai) } 65
P (K) = 1 - { 1 - -----=-:~
(1)
1.05 x 10 14
The factor 2/3 in (1) is due to the ratio of the projected area to the curved
surface area of the earth.
Formula (1) applies for meteorites with lethal
areas small compared to target areas.
For the case of meteorites with a lethal
area large compared to the target area, then formula (1) can be modified to:
_ (n) ~----l~aTT(- =!.JR~ 2 TT} 65
_(2/3)
(2)
where a(R) is the lethal crash area of the meteorite of weight range R •
. fA:
The term\l~ represents the radius in feet of a circular target area.
term yia(R)
TT
The
is the radius in feet of the lethal crash area of a meteorite of
weight range R.
The
sum~+~a;R)
is the effective target radius when a
meteorite crashes in or immediately adjacent to target area A .•
l.
Figure 2
compares. the target area with the affected area (Le., the reaction area).
The probability that a meteorite of a given weight range will crash into
a nuclear reactor is
P(K)R = 1
-11 -
(2/3)(n)
:i
f
2
+
(1. 05 x 1014 )
Ja;R)l
(3)
where R is the number of meteorites in the given weight range that is expected
to fall per year.
As a(R) increases the value R decreases.
7
,. ."",..------"""" .......
, \.
I
_-\.---_
".
-..
" \
.....
I
"
,,/'
" ',POSSIBLE LETHAL
I
/
/.<..
\
,.--}-.. . ~_~--::::..-:£.. A"-'--.. . "
,AREAS THAT COULD
// \"f \. // 1,~"'" I
,
\
EFFECT TARGET AREA
/
~~4 ~\
/ /
)-1-'
\ ,FROM CRASH OF METEORITE
, /( , \'" , \( 1/~~/ a(R)' \ 1 OF WEIGHT R
"
II
\
'~~1..
/1
I '
'V \
'
I "/'<-::"":::....:-;1'
I/
- ~\
AREA AFFECTED BY
~
2
)
(
= 2/ a(R)/1T +JA;/rr
METEORITE CRASH
r
1T
\\..
\
r
//'h A %
~fl j
I
"
,.//\
,,.......
'"
+J
Figure 2.
"
_~'
\
\
\
~,\
I
I
'
\ /
¥1/
" ~
......,
V a(R)/1T
Aj/1T
EFFECTIVE TARGET
RADIUS
- -
'I
,,//1
,,--"'-_..... I
", I
..... _ ....,tt'--"I
/
\
/:,"il-"\""/' ...... J I
,,\
/'-;::~:::,..., " , / ,
1/
"1
/
\\
,,-t \
TARGET
AREA"
,Rj/~
,
00
''--,-_1
I
1'"
'lYJ!/
~~l
I'
---7~I
r = LETHAL RADIUS =Va(R)/1T
1,/
I
...... --~~::::. .... ."",
.... ""
R j = TARGET RADIUS
Comparison of Target Area and Affected Area for a Meteorite Crash;
Assume Meteorite can Only Crash on Land,
=J Aj/1T
The value of P(K)R can be approximated by: (4)
~
P (K)
R
(R)(n)(2/3)
(1.05 x
[fA; + Va(Rl ]
10 14 )"~
27T
(4)
7T
0 < P(K)R « 1
when
4.
PROBABILITY OF SERIOUS REACTOR DAMAGE TO A REACTOR
FROM A
DIRECT
OR NEARBY HIT
To find the total hazard of meteorite damage to nuclear reactors in any
given year, it is necessary to account for the contribution from all size
ranges of meteorites.
A meteorite could completely destroy a nuclear reactor;
however, the probability of this is small both because of the infrequent
arrival of large meteorites and because of the smallness of the target area
compared to the entire surface area of the United States.
On the other hand,
a small meteorite striking a nuclear reactor may not cause any damage.
If by serious reactor damage, one means the potential uncontrolled
release of radioactivity at levels exceeding 10 CFR Part 100 of the AEC Rules
and Regulations, the exact target area becomes difficult to quantify, since
the destruction of a safety system such as the diesel generators or rupture of
the containment will not, of itself, lead to such a release.
A target area of
104 square feet may represent a reasonable lower limit for such a vulnerable
target area.
A value of 10
6
square feet should exceed the vulnerable area by
a considerable factor.
If all 65 meteorites hitting the U.S. per year are considered as small
missiles, and a target area of 10 4 sq. ft. is employed, Equation (4) gives a
value of
P(K) ~ 4.3 x 10-9 per reactor year.
9
However, since small meteorites, ranging in size between 1 and 100 pounds
make up a considerable fraction of the total, the value above tends to be
on the high side for the given target area.
On the other hand, some meteorites
have a large "lethal" a!ea, and are potentially more probable of "hitting" the
target area than a small meteorite.
Table (2) gives estimates of the range of meteorite weights and the
number of meteorites in each weight interval per year for the U.S.
The lethal
area of an average meteorite in the weight interval is calculated from Blake's
study. (2)
The lethal area is calculated assuming that the average meteorite
in a range is one half the weight of the upper limit of the weight range considered.
It is estimated that meteorites of between 10
-2 and 10 -1 tons could very
possibly cause damage to a reactor if they made a direct hit on the reactor.
Most certainly, meteorites of weight greater than 10-1 tons will cause serious
damage to a reactor if they hit.
Meteorites of weight greater than 10 2 tons
will cause extensive damage to a reactor if they hit the reactor.
Histories
of large meteorites crashing into the earth(l) show that for very large
meteorites (greater than 10 3 tons) the heat flux associated with the meteorite
is large enough to cause extensive damage to objects that are near but have not
been hit directly by the meteorite.
The probability of an iron or stone meteorite damaging or destroying a
nuclear reactor per year is calculated by summing the third through the sixteenth terms of the fourth column of Table 2.
This probability is about 7 x 10
2
target area 10 4 ft.
-10
per reactor year for a reactor of
This probability increases to about 6 x 10-8 per reactor
year, if one assumes a vulnerable target area of 10 6 ft2.
Even though the
target area increases by a factor of 100, (10 4 ft 2 to 106 ft 2), the
10
Table 2
Probability of a Stone or Iron Meteorite Hitting and Damaging a Nuclear Reactor in the United States
Range of
Meteorite
Weight Hiting Earth
(Tons)
Number of
Meteorites In
Weight Interval
Per Year in
United States
1/2 x 10- 3 - 10- 3
10- 3 _ 10- 2
10- 2 - 10- 1
10-1 - 10-0
100 _ 101
.....
.....
101 _ 10 2
10 2 _ 10 3
10 3 _ 104
104 _ 105
45
Lethal Area
Of Average
Meteorite
(Sq. Miles)
Ai
9.0 x 10
7.6
12
6
6.3
2
4.1
-9
-8
x 10
x 10- 7
-6
x 10
-5
x 10
Probability of
Hitting One
Nuclear Reactor
In United States 2
A.=10 4 ft 2 A.=10 6ft
~
Will Meteorite Cause
Damage to Containment
of a Nuclear Reactor
(Assume A Direct Hit)
~
3 x 10- 9
8 x 10-10
3 x 10- 7
8 x 10- 8
very doubtful
4 x 10-10
2 x 10-10
5 x 10-12
10-8
very possible
2 x 10-8
certain rupture of containment
5 x 10- 10
certain rupture of containment
5 x 10- 12
4 x 10-10
serious damage
4
x
no
14 x 10- 2
2 x 10- 2
6 x 10- 3
3.5
6.8 x 10- 4
5.8 x 10- 3
1 x 10- 11
8 x 10-10
destroy nuclear reactor
13 x 10- 4
3.8 x 10 -2
5 x 10-12
4 x 10-12
1 x 10-11
5 x 10-12
destroy nuclear reactor
2.1 x 10-4
2.1 x 10
105 _ 10 6
5.9 x 10 -5
2.1 x
10 o
2 x 10-12
2 x 10-12
destroy nuclear reactor and
nearby area
10 6 _ 10 7
12 x 10- 6
5.0 x 10 0
1 x 10-11
1 x 10-11
destroy nuclear reactor and
surrounding areas
10 7 _ 108
2.6 x 10- 6
2.4 x 10
1
1 x 15 11
1 x 10-11
destroy nuclear reactor and
large surrounding area
10 8 _ 10 9
4.6
10- 7
1.1 x 10
2
8 x 10- 12
destroy a city
7 x 10- 12
8 x 10-12
7 x 10-12
1 x 10-11
1 x 10-11
1 x 10-11
1 x 10-11
x
-1
1010 - lOll
2.2 x 10- 8
2.4 x 10
3
lOll _ 1012
4.4 x 10-9
1.1 x 10
4
10 12 _ 1013
1.0 x 10- 9
5.2 x 104
*Sum
destroy nuclear reactor
destroy a large city plus
adjacent areas
destroy many counties
destroy about half of a state
of third through sixteenth term is equal to the probability of either a stone or iron meteorite
damaging or destroying a reactor per reactor year.
600
corresponding probabilities only increases by a factor of --7-85.
This is
because large meteorites have larger lethal areas than smaller meteorites.
The larger lethal area would be more significant in assessing damage to a
smaller target than to a larger target.
The probability of a very large meteorite (10
11
13
to 10
tons) hitting a
nuclear reactor is about the same order of magnitude as a meteorite of about
10 6 tons hitting a reactor; although the number of large meteorites is smaller
(about one thousandth as small), the lethal area of the very large meteorites
is about 1000 times larger than the lethal area of a meteorite of 10 6 tons.
For meteorites of lethal area greater than 1 square mile, the probability
I
that the meteorite will hit a target area of 10
4
ft
2
is about the same as the
probability that it will hit a target area of 10 6 ft2.
5.
TIDAL WAVE INDUCED BY OFFSHORE CRASH OF METEORITE
It is interesting to extend the analysis to a meteorite that could crash
into the ocean, induce a tidal wave, and damage a coastal nuclear reactor. (5,7)
Tidal waves only pose a threat to islands, coastlines, or any island structure
that is completely attached to the sea bottom. (5-8)
There have been numerous studies of tidal waves that are induced by
explosions. (5-8)
Van Dorn(5) has developed a formula that relates maximum
wave amplitude, nmax ; distance from the explosion, r; and size of explosion,
Y.
Both nand r are measured in feet and (Y) is measured in equivalent
max
pounds of TNT.
Van Dorn's formula is
(5)
12
The meteorite is assumed to detonate.the tidal wave at the upper critical
depth.
The upper critical depth is the specific depth of the water that will
produce the largest possible tidal wave for any given meteorite size and
velocity. (3,5)
When the meteorite hits the water, the associated tidal wave is
dependent on the meteorite size, velocity, and depth of water.
The wave period,
T, of the maximum wave is(3,5)
T
= l. 63yO.l5
sec, (y)
= equivalent
pounds of TNT
(6)
As the maximum wave propagates towards the continental shelf, its amplitude decreases as a result of radial spreading, until shoaling and refraction
effects become important.
The calculation of wave amplitude including these
effects is rather complicated as discussed in Van Dorn.
Here, for simplicity,
it is assumed that the explosion is rather far away from shallow water so that
the waves are almost two-dimensional when they arrive.
Thus we may calculate
the maximum wave amplitude nmax by use of equation (5), until the water depth,
D, is equal to one quarter of the wave length, l/4L
•
max
shoaling becomes important when D = l/4L
•
max
It is assumed that
From there on, the maximum wave
height may be calculated by simply multiplying by the shoaling coefficient, S ,
c
as seen in Figure 3.
Refraction must be accounted for, and may be determined
from linear theory to a good approximation.
As the wave increases its amplitude by shoaling to the point that the
water depth is insufficient to transmit the wave energy, the wave will break;
this occurs at the intersections of the curve of wave height and the line of
breaking index as shown in Figure 3.
After the wave breaks, it propagates
towards the shore, as described by the non-saturated breaker region.
However,
previous calculations(lO) indicate that it is typically approximately equal to
twice the distance between the shore and the point of breaking inception.
13
..
-1--
RADIAL SPREADING
SHOALING
~
t
BREAKING WAVE REGION---
~ INCEPTION
.... -r--- ~
--"-.
0.78h
........ INDEX
BREAKING
-
~
--
30'WAVE7ALL
BREAKING
h
I-'
.po.
~
EXPLOSION LOCATION AT
DEEPWATER
CONTINENTA
L SLOPE
/1:::::::':::~.:".'"
,::",......... "-...
.:.::.:.:.:..
1/10 MILE
CONTINENTAL S
HELF
L_"'.'
..;.;:/:.:::..
.......,..... -:' -:':::::: \:':~F~::/.i-/}'
Figure 3.
Schematic Drawing of the Maximum Wave Transformation as it Propagates Towards the Shore.
.-.
An estimation of wave geometry can be extremely difficult in the case
of complicated shore geometry.
this analysis.
The methods of Van Dom(S) have been used in
To calculate the probability that a coastal reactor is damaged
by the wave resulting from an offshore meteorite crash, the following assumptions are made:
(a). (1) the nuclear reactor is located within 1/10 mile of the shore;
(2) the shore is locally straight; and
(3) the offshore beach has a shallow slope.
(b). The reactor break wall is assumed to be 30 feet high and can resist a
tidal wave of at least 20 feet in height.
(c)
A 20-foot wave is needed to topple the reactor building and,
(d)
The reactor is built on land at an elevation of 30 feet above sea level.
The calculation.of damage to a coastal reactor by an offshore meteorite
crash is performed using the same methodology to that used in calculating
reactor damage in a crash on land.
For each size meteorite that crashes into
the water, an equivalent Y(R) (size of explosion in equivalent pounds of TNT
caused by a water crash of a meteorite of weight R) is calculated.
The value
of r(R) (distance from the crash point to the position where shoaling effects
are significant) is calculated using the condition that the maximum Wave height
at the sea wall is 20 feet or more.
A wave of 20 feet or greater (height) is
assumed to be the minimum required to damage a reactor wall and cause significant damage to the reactor.
The distance r(R) plus the shoaling distance
represents the distance that a wave can travel in deep water, through shallow
water, and reach the sea wall at a height of 20 or more feet as a function
I
of the size of the meteorite crash in the water.
wave travels is called d(R) , (See Figure 4).
15
This total distance that the
The probability that a meteorite of weight R will crash in the water and
induce a tidal wave of significant size to damage the reactor is:
(1/2) (2/3) (n)
(1. 05 x 1014 )
(7)
1
where the factor (2) indicates that the tidal wave increases the effective
crash area on only the half of the reactor that faces the ocean,
The prob-
ability that a meteorite will crash in the target area or adjacent to the
target area is defined in equation (3) by P(K)R'
The probability that a
meteorite will damage a reactor either by crashing into the target area or
immediately adjacent to the target area or by inducing a tidal wave to damage
the reactor is equal to
(8)
The probe that a meteorite will damage a nuclear reactor
either by (1) crashing directly into the target area
~
near (immediately adjacent) to the target area OR (2)
induce a tidal wave to damage the reactor.
P(l) 1
The probe that a meteorite will damage a nuclear reactor
R
either by crashing directly into the target area or near
(immediately adjacent) to the target area.
P(K) 11 -
The probe that a meteorite will damage a nuclear reactor ~
R
inducing a tidal wave to damage the coastal reactor.
plp(I)R/P(K)Rlll " The prob. that event P(l) 1 will happen given that P(K) 11
R
has happened.
16
R
.J;
BREAKING "
INDEX
./
'<
,
Y
NON-SATURATED
BREAKER REGION TIDAL
WAVE PROPAGATION ON
. / LAND A DISTANCE d(R)
FROM CRASH POINT
\~
\
L---
LETHAL AREA OF CRASH
OF METEORITE ON LAND
OF WEIGHT R
\
I
I--
r
I
,I t-~-- I /
/
I-'
'-l
I
I
,
,
I
\ '<-X' "
\
EFECTIVE TARGET RADIUS
FOR LAND CRASH OF
METEORITE OF WEIGHT R
= 'II a(R)/?r
..... _""
\
,"
SHALLOW
WATER
/
'- - - - - "
+.j A/rr
~I
,/
" - - SEA WALL
AREA AFFECTED BY LAND
CRASH OF METEORITE
=
LAND
Figure 4. Area Affected by a Meteorite Crash; Assume Meteorite May
Crash in Land or Adjacent Ocean.
(2/ a(R)hr +jA jill12) 1T
1
The size of a meteorite that will cause damage if it crashes on land is R
and the size of the meteorite needed to cause damage if it crashes in the
water and induces a tidal wave is Rll.
Figure 4 illustrates the area
affected by a meteorite crash.
Using the same methodology that was used in developing Table 2 and
assuming that a wave of at least 20 feet is needed to penetrate the sea wall,
then it can be estimated that the probability of a meteorite damaging or
destroying a reactor either by a direct hit or by inducing a tidal wave is
9 x 10-10 per reactor year for a target area of 104 square feet when the
reactor sea wall is 1/10 mile from shoreline.
Conclusions
There are 3500 meteorites of mass greater than one pound that hit the
earth per year.
Assuming that the hits are evenly distributed throughout the
earth, there are 65 meteorites of mass greater than one pound that hit the surface area of the United States per year.
The probability that a nuclear reactor
is hit per year by a meteorite of one pound or more is 4.3 x 10- 9 assuming that
the target area of the reactor is 10 4 ft2.
The probability that a nuclear reactor will be damaged or destroyed
(due to meteorites weighting more than 100 pounds) is about 7 x 10-10 per
reactor year for a target area of Ai
= 104
ft2.
This probability increases
2
to 6 x 10-8 per reactor year for a target area of 10 6 ft.
The probability that a coastal nuclear reactor will be
damage~
or destroyed
directly by being hit by a meteorite or indirectly by a tidal wave that was
induced by a meteorites is 9 x 10-10 assuming that a 20 foot wave is needed to
destroy sea wall and that the reactor has a target area of 104 ft2.
18
References
1.
Hawkins, Gera1d,The Physics and Astronomy of Meteors, Comets and
Meteorites, McGraw Hill, New York 1969.
2.
Blake, V.E., "A Prediction of the Hazards from the Random Impact of
Meteorites in the Earth's Surface," Sandia Labs, Aerospace Nuclear Safety,
December 1968, SC-RR-68-838.
3.
G1asstone, Samuel, The Effect of Nuclear Weapons - 1962, published by the
Department of Defense and The Atomic Energy Commision, pp. 292-293, 1964.
4.
CRC Handbook-Chemical Rubber Company, 15th edition, Cleveland, Ohio.
5.
Van Dorn, W. G., et al., "Handbook of Explosion Generated Water Waves,"
Vol. 1, State of the Art, Tetro Tech Report No. TC-130.
6.
Hwang, Li-San, "On the Oscillation of Harbours of Arbitrary Shape,"
J. Fluid Mech., Vol. 42, part 3, pp. 447-464, (1970).
7.
Hwang, Li-San, "A Numerical Model of the Major to Tsunami," The Great
Alaskan Earthquake of 1964:
8.
Oceanography and Coastal Engineering;
Hwang, Li-San, "Tsunami Generation,"
J. of Geophysical Research, Vol. 75,
No. 33, pp. 6802-6817, (1970).
9.
/
/
Le Mehaute, B. et al., "Explosion Generated Wave Environment in Shallow
Water," Defense Atomic Support Agency, Report No. DASA 1963, 1967.
19