A11100 TflTSEl

NBSIR 80- A 1 1 1 OS 0A7543

Probabilistic Assessment of

Tornado-Borne Missile Speeds

Emil Simiu

Structures and Materials Division

Center for Building Technology

National Engineering Laboratory

National Bureau of Standards

U.S. Department of Commerce

Washington, D C. 20234

Martin R. Cordes

Mathematical Analysis Division

Center for Applied Mathematics

National Engineering Laboratory

National Bureau of Standards

U.S. Department of Commerce

Washington, D.C. 20234

September 1980

li

Prepared for: United States Nuclear Regulatory Commission

Washington, D.C. 20555

QO

100

. U56

80-2117

1980

L.

NBSIR 80-2117

PROBABILISTIC ASSESSMENT OF

TORNADO-BORNE MISSILE SPEEDS

National Bureau of Standards

Library. E-01 Admin. Bldg.

MAR 2 1981

A

(J

U6>£

fib'

Emil Simiu

Structures and Materials Division

Center for Building Technology

National Engineering Laboratory

National Bureau of Standards

U S. Department of Commerce

Washington, D.C. 20234

Martin R. Cordes

Mathematical Analysis Division

Center for Applied Mathematics

National Engineering Laboratory

National Bureau of Standards

U.S. Department of Commerce

Washington, D.C. 20234

September 1980

Prepared for: United States Nuclear Regulatory Commission

Washington, D.C. 20555

U.S. DEPARTMENT OF COMMERCE, Philip M. Klutznick, Secretary

Luther H. Hodges, Jr.. Deputy Secretary

Jordan J. Baruch, Assistant Secretary for Productivity. Technology, and Innovation

NATIONAL BUREAU OF STANDARDS. Ernest Ambler, Director

Table of Contents

Page

1. INTRODUCTION 1

2. APPROACHES TO THE PROBABILISTIC STUDY OF MISSILE SPEEDS 1

3. PROBABILITIES OF OCCURRENCE OF TORNADOES 2

4. PROBABILITIES OF OCCURRENCE OF MISSILg HIT SPEEDS 4

4.1 Simplified Analysis 4

4.2 Analysis in Which Variabilities of Additional Factors are Considered 5

3. NUMERICAL EXAMPLES, 6

3.1 Simplified Analysis 6 3.2 Comments on Results of Simplified Analyses 8

3.3 Comparison Between Values of hit Speeds for the Basic Case

and Values V^iax Obtained in Ref. 1 9

3.4 Analysis in Which Additional Variabilities are Taken into

Account 13

b. SUMMARY AND CONCLUSIONS 14

7. REFERENCES 15

APPENDIX A1 41

APPENDIX A2 46

iii
LIST OF FIGURES

Page

Figure 1. Schematic Representation of a Tornado Path 37

Figure 2. Notations 38

Figure 3. Plan View of Nuclear Power Plant (Courtesy of

Don Mehta, Bechtel Corp. , Gaithersburg) 39

Figure 4. Schematic Representation of Nuclear Power Plant 40

Figure A1 . Tornado Strike Probability within Five-Degree

Squares in the Contiguous United States (Ref. 2) 43

Figure A2. Calculated Tornado Wind Speed by Five-Degree

Squares for 10 Probability per Year (Ref, 2) 44

Figure A3. Estimated Probability Density Function of

Tornado Wind Speeds 43

iv
1 . INTRODUCTION

Estimates of tornado-borne missile speeds for nuclear power plant design

purposes were previously presented by the writers in Ref. 1. One of the

assumptions on which these estimates were based was that the missiles start

their motion from a point located on the tornado translation axis, at a distance upwind of the tornado center equal to the radius of maximum circumferential wind speeds. In addition, it was assumed in Ref. 1 that the speed

with which a missile hits a target is equal to the maximum speed, denoted

by VHmax

, that the same missile would attain if its trajectory were unobstructed by the presence of any obstacle.

Clearly, neither of these assumptions is realistic. The purpose of this

report is to attempt an approach to the missile speed problem that takes into

account the fact that the initial positions of the missiles with respect to

the tornado center are not necessarily those assumed in Ref. 1, and that the

speeds with which the missiles hit the targets are not necessarily equal to

v max

V H

2. APPROACHES TO THE PROBABILISTIC STUDY OF MISSILE SPEEDS

Estimates of tornado-borne missile speeds corresponding to a specified probability of occurrence must take into account a large number of factors,

including: rate of occurrence of tornadoes at the geographical location of

concern; tornado wind field; number, location, and physical characteristics

of potential missiles, including aerodynamic characteristics; nature and

magnitude of forces opposing or inducing missile take-off; and location

and configuration of potential targets.

One possible approach to a probabilistic study of tornado-borne missile

speeds is the use of Monte Carlo techniques in conjunction with probability

distributions of the various parameters characterizing the factors listed

above. Such an approach would involve a volume of computation that is likely

to be enormous indeed. Moreover, many of the pertinent probability distributions are not, or are still only poorly, known. The writers believe that an exhaustive Monte Carlo approach of the type outlined above might be warranted

for long-term research purposes, particularly if significant improvements are anticipated in the probabilistic modeling of the various factors involved.

However, for the present, it is the writers opinion that much of the probabilistic and physical modeling of tornadoes and tornado- borne missiles that

has evolved since the publication of Ref. i is not sufficiently well

established to be relied upon confidently in the study presented herein.

For these reasons, the objective of this investigation has been limited to

attempting a comparison between the speeds estimated in Ref. 1 on the one

hand, and hit speeds obtained on the basis of the assumptions listed below,

on the other hand:

1
1. The models used in Ref. 1 are correct with respect to (a) the

probabilistic behavior of the tornado wind speeds, (b) the tornado

wind field, and (c) the aerodynamic behavior of the tumbling

missiles

.

2. The number, geometry, and location of the potential targets is

specified

.

3. A specified number of missiles with specified properties and

locations are present at the nuclear power plant site at the time

of the tornado strikes, i.e., a "missile set-up" is specified.

Alternatively, several possible missile set-ups are specified, each

associated with a specified probability of occurrence, the sum of

these probabilities being unity.

4. A specified area over or near the nuclear power plant is swept by

tornadoes with specified wind speeds, to which there correspond

probabilities of occurrence consistent with the estimates of Ref. 2.

b. Each missile starts its motion when the tornado-induced aerodynamic

force, Fa

, acting upon the missile at rest is such that

3. PROBABILITIES OF OCCURRENCE OF TORNADOES

Consider some point A within a nuclear power plant site. Let the event, T,

that a tornado will hit point A, and the event, (T, ^ torn )> that the point A

will be hit by a tornado with maximum speeds larger than V torn be denoted by

Pa

(T) and P a

(T, V torn ), respectively.

Assume first, for the sake of simplicity, that the direction of the tornado axes of translation is fixed. Point A will be hit by a tornado only if the

distance, L, from point A to the tornado axis of translation is L < b/2, wnere b = tornado path width (Fig. 1). An additional condition is that the

distance, M, (along the axis of translation) between point A and the center,

O, of the tornado path area be M < d/2, where d = tornado path length

(Fig. i). The following relation holds:

( 1 )

where F = specified force. For convenience, the value of F is

specified via a coefficient, k, in the relation

F = kmg ( 2 )

where m = mass of missile, and g

= acceleration of gravity.

V

torn’ m, fc) d it dm (3)

2
where P a

(T, v

t orn’

dm dA = Probability of occurrence of a tornado such

that the center of its path is inside the elemental area di, dm.

The effect of a tornado upon the trajectory of a given missile that it is

going to pick up is clearly dependent upon the distance between that missile

and the tornado axis of translation. On the other hand, if Eq. 1 holds, the

effect of the distance betweem the missile and the center C is in most cases unimportant. Indeed, this 'effect is significant only if M * -d/2. The

tornado path length, d, being of the order of 10 km, the probability that

M a -d/2 is relatively small. Therefore, the influence of M upon the probabilistic estimates of missile hit speeds will generally be small.

I Denoting the marginal distribution of PA with respect to m by PA

, Eq . 3

is written as VT > V torn) ~J

b/2

PA(t - V tornd* (4)

where P.(T. V , j, ) dj, probability of occurrence of tornadoes that strike

point A and have axes of translation crossing the segment da, the midpoint of

which is at a distance a from A (Fig. 2a). In terms of discrete probabilities, Eq. 4 is written as

N

1 PA

<T > V torn ) = ^

, PA< T > V torn- Li 5 (5)

and

L. + AL/2

P

A< T > V torn. V “I PA< P > V torn> dl

- AL/2

N

1

b_

AL

( 6 )

(7)

P

a

(T, V tor , L^) is the probability of occurrence of tornadoes that strike

point A anct have axes of translation crossing the segment AL, the midpoint

of which is at a distance from A (Fig. 2b). Since it is reasonable to assume that the probability of occurrence of tornadoes across the distance

b is uniform,

pa(t, V

torn • L

i> P A

(T > V

torn> ( 8 )

Let now the probability that point A will be struck by tornadoes with maximum

wind speeds included in the interval (V. - AV. , V. + AV. ) be

, K torn tQrn’ , toyn _ tofn

denoted by p.(T, V. ; aV^ • Tails of probability density functions

. J f A , torn torn r

. . n . Pa(T, V. ) can be estimated from the results of Ref. 2, as shown in

Appendix°R¥

.

3
n additional assumption used in this work pertains to the choice of the

width b. The estimates of probabilities of occurrence Pa

(T) and Pa

(T, v torn) given in Ref. 2 are based, for any geographical location, upon the average

individual tornado area, a (or, equivalently, upon the product of the average

tornado path length, d, by the average individual tornado path width, b.

For consistency with the estimates of Ref. 2, it is assumed in this report

that if V torn is equal to the maximum wind speed of the Design Basis Tornado

[2], then to a probability PA

(T, V to ) = 10 _/year there corresponds in

Fig. 2 a value of the tornado path width b = b.

A final comment pertains to the case where the direction, a, of the tornado

axis of translation is a random variable. In that case

P

a

(T, torn) = 2 p a

(t. ^torn* ai^ (9)

where P^(T, V^ orn , a^) = probability that point A will be struck by a tornado with maximum wind speed larger than V tQrn , and with a translation axis

having a direction defined by a..

4. PROBABILITIES OF OCCURRENCE OF MISSILE HIT SPEEDS

4.1 SIMPLIFIED ANALYSIS

For the purposes of this report, a simplified analysis is defined as one that is based upon the following assumptions:

1. The number, geometry, and location of the potential targets is

specified.

2. A missile set-up (consisting of number and location of missiles, all

the missiles having the same aerodynamic coefficient, area, and mass) is

specified. The probability of occurrence of this set-up is assumed to be

unity.

3. The coefficient k in Eq. 2 is specified.

4. Tornadoes with a specified maximum wind speed, V torn > equal to the

maximum wind speed of the Design Basis Tornado will occur in such a way that

their axes of translation will cross, and be normal to, a specified segment

with length b. The seqment b is divided into subsegments. The probability of occurrence of a tornado, T^, whose axis of translation passes

through the center of such a subsegment is 10 /N^ per year.

The effect of tornqdo T^ is to sweep a number of missiles and cause some of

them to hit the targets with various horizontal speeds. Let the highest of

fflcLX these speeds be denoted by . The probability of occurrence of at least

one nit with speed VTMax is then 10 /Nj. If, of the tornadoes T^

4
(i = 2, 3, . . . Nj), a number q will be associated with hitting missile

speeds greater than VTMax

, the probability of occurrence of hits with speeds

equal to or greater than V|||ax will be 10 q/N^

4.2 ANALYSIS IN WHICH VARIABILITIES OF ADDITIONAL FACTORS ARE CONSIDERED

The procedure for estimating missile speeds developed in this report can also

take into account the variabilities of the following factors:

1.

Missile set-ups. As previously indicated, it is possible to specify

N^ missile set-ups, denoted by S^, (i = 1, 2, . . . N

2

), each set-up being

associated with a probability of occurrence P(S^). The sum of these

probabilities is unity.

2.

Tornado type. Each tornado type is characterized by a maximum tornado wind speed and by the corresponding wind field as defined in Ref. 1.

Let each tornado type be identified by the symbol Ty . (i = 1, 2, . . . N^).

Probabilities of occurrence of various tornado types, P(Ty^), can be estimated as suggested in Appendix Al or by using additional information given,

e.g., in Ref. 2. Note that

n

3

l P(T

y

.) = 10" 7 C (10)

i=l 1

In Eq. 10, C = 1 if the maximum wind speed in the least intense of the i

tornado types, min[V torn is equal to the maximum wind speed of the Design

basis Tornado at the geographical location of concern, . If “in ‘ Vtornll <»SSn. then 01.

3.

Direction of Tornado Axis of Translation. Let each translation axis

direction be denoted by To each a- (i = 1, 2, . . . N^) , there corresponds a probability of occurrence P(a

i ), the sum of these probabilities being

unity.

The probabilities of occurrence of missile hit speeds when the variabilities

of factors 1 through 3 above are taken into account are calculated in a manner similar to that indicated for the case of the simplified analysis,

except that the probability of occurrence of the largest hitting missile

associated with a given missile set-up SM , a given tornado nj speed, VTMax

,

type, Ty^, a given direction of the axis of translation,

portion of the axis of translation, L^, is

(v max

) = p( L .) P (sM ) P ( Tui ) P ( an )

and a given

i jk a m Vk

' (ID

5
where

P (L -j) = -2- (12a) 1 AL

(12b)

The total probability of occurrence of hitting missile speeds equal to or larger than V®ax is

N

1 NL

N

i N4

'

P(v£ax

) = Z Z E Z P(L

i )P(SM

)P(T

y,)P(aJl ) (13)

i=l j=l k=l £=1 3 x

5. NUMERICAL EXAMPLES

Figure 1 shows the plan of a BWR (Boiling Water Reator) nuclear power plant

in which the structures denoted by 1 ,2,4,8, and 12 (i.e., containment, aux- iliary building, control building, Diesel generator building, and standby

service water cooling tower and basin, respectively^ are considered to be

important to safety and, therefore must "be designed to withstand the effects

of natural phenomena such as tornadoes without loss of capability to perform

their safety functions" [3], These structures have been redrawn schematically

in figure 4 to conform to the computer program input format. In Figure 4 the

targets are numbered from 1 through 9, and the areas (or "lots") where the

potential missiles are located before the tornado landing are numbered from

I through IV. The missiles at rest are assumed to be at ground level

(elevation zero). Elevations of the top horizontal plane of the targets are also shown in Figure 4 (for example, for target 1 the elevation of the top

plane is + 40m). All dimensions of Figure 4 are in meters.

5.1 SIMPLIFIED ANALYSES

A set of basic cases was defined, corresponding to the following assumptions:

1. The target consists of any of the buildings denoted by 1 through 9

in figure 4.

2. The positions of the areas (lots) where the missiles are located

before the tornado landing are those shown in figure 4.

5. The number and locations of missiles within these areas are as follows

:

-Lot I:

-Lot II:

-Lot III:

One row of two missiles (distance between missiles in x direction: 15m)

Two rows of 15 missiles each (distance between rows in y

direction: 12m; distance between missiles in x direction:

3m.

One missile

6
-Lot IV: Twenty rows of 14 missiles each (distance between rows in

y direction: 3m; distance between missiles in x direction: 11m).

4. The tornado axes of translation cros_s, and are normal to, a segment

O'B = b = 15U m (see figure 4). The segment b is divided into 15 equal

subintervais.

o. The angle a between the tornado translation axis and the y axis

(figure 4) is 22°.

Calculations corresponding to the basic case were carried out for various

values of V. and of k, for five types of missiles:

I - automobile with properties assumed in Ref. 1 II - automobile with properties based on data suggested in Ref. 4

III - wood plank

IV - 12" pipe with properties assumed in Ref. 1 V - 12" pipe with properties based on data suggested in Ref. 5.

The drag coefficient, area, and mass of these missiles are given in Table 1.

In addition to calculations based on the assumptions just described and

corresponding to the basic case, calculations were carried out with one or two of these assumptions modified, all other assumptions being unchanged.

The modified assumptions were the following:

-The angle a is different from 22°

-The coordinates x

Q

.. , y .. of point 0" (defining the position of lot

IV) are different from those given in figure 4.

-The number of missiles in lot IV is different from that previously

given for the basic case. (The modified number of missiles is

devoted by n, while the number of missiles given for the basic

case is denoted by n ) “Tne target consists outbuilding 9 only, rather than of any of the

buildings 1 througii 9 of figure 4.

The results of the calculations are given in Table 1 for three probability

levels. Note that Table 1 is divided into subsections, each identified by

a group of three symbols. The first symbol is a Roman numeral indicating

the missile type (I through V); the second symbol is a lower case letter

indicating the maximum tornado wind speed (a, for 360 mph; b, for 300 mph;

c, for 240 mph; d, for 380 mph; and e, for 200 mph); the third symbol is an arabic numeral (1, for the basic case; 2, for the case in which lot IV

is displaced; 3, for the case in which the number of missiles is changed;

and 4, for the case where the target consists of building 9 only).

Note also that for certain parameter values, missile speeds corresponding

to the probability 10“ , and/or 0.5 x 10“ , and/or 0.06 x 10~ 7 are not

entered into Table 1 (see, for example, subsection Ia2 of Table 1 for k = 0.9, x

o

- = 60 m, yQ

« = -200m). This reflects the fact that at least one,

7
eight, or fourteen respectively of the = 15 tornadoes hitting the site

(each with probability 10 / /15) fail to hurl at least one missile onto the

target

5.2 COMMENTS ON RESULTS OF SIMPLIFIED ANALYSES

Effect of Parameter k. Note from subsection Ial of Table 1 that as k

increases, the speeds corresponding to a given probability level increase.

Indeed, if k were extremely small, the motion of the object would in general

begin at a time when the distance between the object and the tornado center

would still be relatively large, so that the object would in effect be swept

away from the zone of strong tornado winds. Conversely, if k is relatively

large, the object stays in its rest position until the tornado winds are sufficiently strong to hurl it with great force. The trend observed in subsections Ial is also evident in other subsections.

However, an increased k does not necessarily result in an increased hit speed

(at some given probability level): see, for example, subsection Illdl of

Table 1). One explanation is that to an increased k there may correspond

certain missile trajectories that do not result in a hit. Therefore, even though the speed of the missile at some point on its trajectory would

increase if k were increased, this is irrelevant from the standpoint of this

project as long as the missile with the higher speed would fail to hit a target. Another explanation for occasional decreases of the hit speed (for

any given probability) as k increases is that, in certain cases, to a smaller

value of k there could correspond more unfavorable initial conditions for

some missiles.

Direction of Tornado Axis of Translation. For each type of missile, subsections

of Table 1 identified by symbols ending in al and bl include in parentheses

and brackets speeds corresponding to the angles a =1° and a = 45°, respectively (as opposed to a = 22° , which constitutes the basic case). It can

be seen that, for the cases investigated, the tornado effects are generally

less severe in this example for a = 1° and a = 45° than for a = 22°.

Influence of Location of Lot IV . In this example, lot IV contains the bulk

of the missiles present on the nuclear power plant grounds. It is seen that

if the lot is at a relatively large distance from the targets (yo

„ = -500 m),

the hit speeds are, as expected, lower than those corresponding to y „ = 100 m in most, though not all cases.

Note that changing the position of lot IV from x

q

.. = 60 m, yQ.. = -100 m to x

Q

.. = 160 m, yQ

» = -200 m, does not always result in a reduction of the

hit speeds corresponding to a given probability. For example, such a reduction (from 43m/s to 13 m/s) does occur for hit speeds with 10~

of occurrence in the case of missile I with k = 0.9 and V

t = (subsection Ia2 of Table 1). However, in the case of missile I and V

t = 240 mph, there occurs an increase from 33m/s if x

q

..

•• = -100 m, to 43 m/s if x » = 160m, y .. = -200 m.

probability

360 mph

with k = 0.9

= 60 m,

y

b
Influence of Number of Missiles . The number of missiles in lot IV was reduced

in the ratios n/n

t =1/8 and n/n

t * 1/50. This was done by reducing the

number of rows of missiles, and of missiles in each row, from 20 to 5, and

14 to 7, respectively, for n/n. = 1/8, and from 20 to 2, and 14 to 3

respectively, for n/n

t

= 1/50. For the case n/n

t = 1/8 the effect of

the reduction upon the missile speeds corresponding^ to a given probability

of hit was generally small, although, in many instances, of the Nj = 15

tornadoes assumed to hit the plant site (each having a probability of occurrence 10“' /N^) at least one hurled no missile onto the targets when the

number of missiles was reduced. For the case n/n = 1/50 the effect of

the reduction was, as expected more significant inymost situations.

When the number of missiles in lot IV was increased by a factor of 4 (this was done in the case of the. plank and of the 12" pipe), the resulting missile

hit speeds were found not to differ, or not to differ significantly, from

those obtained in the basic case.

Influence of Target Area . If the only target considered was building 9, as opposed to ,any of the buildings 1 through 9, the missile speeds corresponding to a given probability level were generally reduced with respect to those

obtained for the basic case, although in a few cases the reductions were

small.

m, 5.3 COMPARISON BETWEEN VALUES OF HIT SPEEDS FOR THE BASIC CASE AND VALUES V.. OBTAINED IN REF. 1

It is recalled that the tornado paths assumed in Table 1 are defined by the

position of the segment O'B of figure 4. It may well be that a different set

of paths might in certain instances have resulted in more severe hits. It

speeds corresponding

v-7

appears therefore reasonable to use for design purposes

in Table 1 to the probability level 0.5 x 10” , say, rather than exactly 10

Missile I ("NBS" Automobile), V

t:orn

= 360 mph : V^ = 59 m/ s (Ref. 1). It

is seen from Table 1, subsections Ial through Ia4, that for k _< 0.9, Vm

< 47 m/s

in all cases investigated. While it may be argued that the restraining force

for an automobile would usually be of the order of magnitude of the friction

force, i.e., k = 0.3, say, it is conceivable that some automobiles might

experience some form of blockage that would raise k to higher values. However, if such blockage occurs, it might be expected that the number of automobiles affected by it would be small. Table Ia3 shows that if n/n * 1/50

(,i.e., if tnere are only about five automobiles in lot IV, then Vm

corres- ponding to the probability 0.5 x 10“ decreases both for k = 0.9 and k = 2.0

from 45 m/s and 64 m/s to 39 m/s and 17 m/s respectively.

Therefore, in view of the results of subsections Ial through Ia4 of Table 1,

and assuming that very few automobiles have restraining forces with k _> 1.3,

it is reasonable to assume for design purposes that the speed of missile

I is:

V^ k 50 m/s for V tQrn = 360 mph

9
This is a less severe design criterion than that suggested in Ref. 1.

maX

Missile I ("NBS" Automobile, V torn

= 300 mph : V

H

= 52 m/s (Ref. 1)

A comparison between subsections Ial and Ibl of Table 1 shows that the values

of the hit speeds corresponding to a probability of occurrence 0.5 x 10 are about the same for V torn = 300 mph as for V

t n

= 360 mph, except in the case k = 0.3, when they are considerably larger for V tQ ^n

= 300 mph. This

is a surprising result, which could be explained by noting that, for constant

k, the missile will begin its motion from a position that is closer to the

tornado zone of strongest winds when the oncoming tornado is weaker; such a position may in certain cases result in larger hit speeds.

A comparison between subsections Ibi and Iai suggests that design hit speeds

for missile I should be only marginally lower in the case V

t = 300 mph

than in the case V tQrn = 360 mph. It is therefore suggested that for design

purposes

= 48 m/s for V torn = 300 mph

This value is somewhat lower than that suggested in Ref. 1. max

Missile I ("NBS" Automobile), V torn

= 240 mph: = 41 m/s (Ref. 1)

A comparison between subsections Ial, Ibl and Icl of Table 1, for both the

0.5 x 10 and the 10 probability levels, suggests that for design purposes

it is reasonable to assume

V

ra " m/ s for v torn

= 2 ^° mph

This value is somewhat larger than that suggested in Ref. 1.

Subsections Idl and Iel show values of Vm

for

n

= 380 mph and V torn = 200 mph, respectively. The values for V tQrn = 380 mph differ little from the

corresponding values for V torn = 360 mph. Note also that, for k = 0.5 and

k = 0.9, values of Vm

for the probability level 10~" are, surprisingly, con- siderably higher for V = 200 mph than the corresponding values for V f = 240 mph.

uissi-Le II ( EPRI Automobile), V

torn

= 360 mph : VH = 46 m/s (Ref. 1)

From a comparison of subsections Hal and Ial it is seen that, for the same values of k, speeds V m

are higher for Missile II ("EPRI” automobile) than

for Missile I ("NBS" automobile). The explanation offered is similar to that

advanced in connection with Missile I, V tQrn = 300 mph. In this case Missile

II will begin its motion from a position that is closer to the tornado zone

of strongest winds than would Missile I (the coefficient k being the same),

with a consequent increase in the value of Vm

.

10
Therefore it appears reasonable to suggest for design purposes

V = 55 m/s for V. = 360 mph

m torn r

i.e., a larger value than that suggested in Ref. 1. max

Missile II ("EPRI" Automobile), v

t:orn

= 300 mph : Vjj =27 m/s (Ref. 1)

A comparison between subsections Ilbl and Hal of Table 1 suggests that, for

design purposes, the hit speed should be at least

Vm

= 50 m/s for V tQrn = 300 mph

This is considerably higher than the value suggested in Ref. 1.

I313.X aissile II ("EPRI" Automobile), V

t:or n

= 240 mph ; = 7 m/s (Ref. 1)

From subsections IIcl, Ilbl, and Hal, it would follow that, for design

purposes,

Vm

= 45 m/s for V tQrn = 240 mph

versus 7 m/s, as suggested in Ref. 1. max

Missile III (Plank), V

torn

= 360 mph : = 83 m/s (Ref. 1)

Subsections Illal through IIa4 of Table 1 suggest that, for design purposes,

missile speeds need not exceed

Vm

= 60 m/s for V tQrn = 360 mph

i.e, about 20 m/s less than the value of Ref. 1. Note that the restraining

force for a plank can be many times larger than the plank weight. This is a factor that was considered in selecting the speed suggested above.

niax

Missile III (Plank), V torn

= 300 mph : VR

= 70 m/s (Ref. 1)

Subsections Illbl and IIIb2 of Table 1 suggest that, for design purposes,

missile speeds need not exceed

V = 55 m/s for V.. = 300 mph m torn K

i.e., 15 m/s less than suggested in Ref. 1. m3.x aissile III (Plank), V tQrn

= 240 mph : = 58 m/s (Ref. 1)

Subsections IIIcl through Illc3 of Table 1 suggest that, for design purposes,

missile speeds need not exceed

= 50 m/s for V torn

= 240 mph

i.e., 8 m/ s less than suggested in Ref. 1.

11
Missile IV ("NBS 12” Pipe), V torn

= 360 mph: = 47 m/ s (Ref. 1)

Subsections IVal through IVa4 of Table 1 suggest that, for design purposes,

V = b5 m/s for V. „ = 360 mph

m torn r

i.e., considerably more than suggested in Ref. 1. As in the case of the

plank, the writers believe that, in the case of the pipe, the restraining

force can be larger than the missile weight.

max

Missile IV ("NBS” 12" Pipe), V

torn

= 300 mph : = 28 m/s (Ref. 1)

Subsections IVbl and IVb2 suggest that, for design purposes,

V =60 m/s for V . = 360 mph

m torn r

i.e., more than twice as high as suggested in Ref. 1. max

Missile IV ("NBS” 12" Pipe), V

^ = 240 mph ; = 7 m/s (Ref. 1)

Subsections IVcl through IVc3 of Table 1 suggest that for design purposes,

V = 50 m/s for V. = 240 m/s

m torn

i.e., more than seven times as high as suggeted in Ref. 1.

Missile V ("JFC-AES” 12" Pipe), V torn

= 360 mph : V®ax = 38 m/s (Ref. 1)

Subsection Val of Table 1 suggests that, for design purposes,

= 62 m/s for V tQrn = 360 mph

This is close to the value obtained for missile IV

Missile V ("JFC-AES*' 12” Pipe), V

tQrn

= 300 mph : V®ax = 15 m/s (Ref. 1)

Subsection Vbl of Table 1 suggests that, for design purposes:

Vm

= 52 m/s for V torn = 300 mph

This is somewhat less than the value = 60 m/s obtained for missile IV.

Missils V ("JFC-AES" 12" Pipe), V

torn

= 240 mph : v“ax = 7 m/s (Ref. 1)

Subsection Vcl of Table 1 suggests that for design purposes:

V = 45 m/s for V. = 240 mph

m x torn r

i.e., about 10% less than for missile IV.

12
5.4 ANALYSIS IN WHICH ADDITIONAL VARIABILITIES ARE TAKEN INTO ACCOUNT

Calculations were also carried out for missile II (compact automobile) and

k = 0.3, k = 0.5, and k = 0.9, using the assumptions 1 through 5 that define

the basic case in the preceding simplified analyses. However, unlike the cases previously dealt with, it was not assumed that the site is swept by

tornadoes with equal intensities v torn » Rather, it was assumed that in Eq.

13 the number of tornado types is k = 11, and that the probabilities of

occurrence at the site of tornado types T are as follows:

k 1 2 3 4 5 6 7 8 9 10 11

T

vk

^ mph) 200 240 300 310 320 330 340 350 360 370 380

10^ P(T ) per year

&

100 20 1.6 1.4 1.2 1.1 1.0 0.8 0.50 0.25 0.20

Note tnat £P(T

y ) for k 9 (i.e., the probability of occurrence of tornadoes

with maximum speeds equal to or larger than 360 mph) is approximately 10

The probabilities P(T ) were calculated from Appendix A1 for maximum tornado v k

speeds equal to a larger than 310 mph, as follows:

P(T .) Vk) = p(T, V torn

V

k+1

" V

k-1

torn = V,

For maximum tornado speeds less than 310 mph, the curve representing the

percent probability of exceeding the value of any given wind speed, included

in Ref. 2, was used as a guide.

The resulting missile speed hits Vm

, and their calculated probabilities of

occurrence, are given below:

Missile II ("EPRI" automobile)

k = 0.3

k = 0.5

k = 0.9

fm

= 47 m/

P(47) = 2.47 X 10 ^/year

r in = 48 m/

P(48) = 0.73 X 10 '/year

r m

= 49 m/

P(49) = 0

m

= 58 m/

P(58) =s 1.44 X 10 ^/year

r

1 m

- 59 m/s P(59) = 0.65 X 10 /year

rm

— 60 m/

P ( 6 0

= 0

m

b6 m / s P(66) 1.12 X 10 ^/year

r m

= 67 m/

P(67

= 0.68 X 10 /year

m

— 70 m/

P(70) = 0

13

i
It can be seen that the results differ relatively little for those corres- ponding to the probability level 0.5 x 10” in subsection Hal of Table 1 (V = 360 mph) , i.e., 48 m/s versus 44 m/s (k = 0.3), 59 m/s versus

58 m?s (k = 0.5), and 67 m/ s versus 64 m/s (k = 0.9).

6. SUMMARY AND CONCLUSIONS

A procedure was developed for estimating speeds with which postulated

missiles hit any given set of targets in a nuclear power plant or similar

installation. H^t speeds corresponding to probabilities of occurrence of

the order of 10 were calculated for a given nuclear power plant, under

various assumptions concerning the magnitude of the force opposing missile

take-off, direction of tornado axis of translation, number and initial

location of missiles, and size of target area. One feature of the calculations that distinguishes them from those of Ref. 1 is that the missile

motion does not start from an initial position postulated a priori. Rather,

the initial position of the missile is determined by the condition that the

aerodynamic force induced by the tornado wind field exceed a specified

restraining force specified via a nondimensional parameter k. As explained

in some detail in Section 4.2, the results no longer depend on the parameter

CjjA/m alone, but on that parameter and on the parameter k.

The results of the calculations suggest that it is reasonable to use the

following hit speeds, V , for design purposes, in lieu of the speeds given

in Ref . 1

Missile I ("NBS" automobile)

Region I (see Ref. 2):

Region II:

Region III:

Missile II ("EPRI" automobile)

Vm

"

Vm

"

Vm

"

Region I: Region II:

Region III:

Missile III (plank)

Region I: Region II:

Region III:

Vm

=

Vm

"

Vm

"

Vm

=

Vm

=

Vm

=

= 50 m/s in lieu of 59 m/ s = 48 m/s in lieu of 52 m/

= 45 m/s in lieu of 41 m/

t lieu of 59 m/s

l lieu of 52 m/s

t lieu of 41 m/

l lieu of 83 m/

l lieu of 70 m/

i lieu of 58 m/

Missile IV ("NBS" 12" pipe)

Region I: Region II:

Region III:

Vm

"

Vm

"

Vm

"

65 m/s in lieu of 47 m/s

60 m/s in lieu of 28 m/s

50 m/s in lieu of 7 m/s

14
Missile V ("JFC-AES" 12" Pipe)

Region I: Vm

= 62 ra/s in lieu of 38 m/s

Region II: = 52 m/s in lieu of 15 m/s

Region III: = 45 m/s in lieu of 6 m/s

The design values suggested above are tentative and subject to three major

qualifications. First, they are based upon climatological, meteorological and

aerodynamic models that are uncertain. In the writers' opinion these uncertainties are extremely difficult, if not impossible, to quantify in the present state of the art. Second, the suggested values are based upon a single

nuclear power plant basic set-up. Calculations carried out for a different

set-up might yield somewhat different results. Third, although calculations

were carried out assuming thousands of tornado hits sweeping hundreds of

missiles each, these calculations have not been exhaustive even for the

single basic plant set-up dealt with herein. This was due to the limited

resources (approximately one half man year, including computer program development) available for this project,

In spite of these limitations, the writers believe that useful new insights

into the tornado-borne missile speed problems have been obtained, and that an

I efficient and practical computational tool has been developed, that can be

used for the purpose of further investigating individual power plants and

of refining the design criteria suggested herein,

7 . REFERENCES

1. Simiu, E. , and Cordes, M t , Tornado-borne Missile Speeds , NBSIR 76-1050,

National Bureau of Standards, Washington, D.C. 1976.

2. Technical Basis for Interim Regional Tornado Criteria , Wash-1300 (UC-11)

U.S. Atomic Energy Commission, Office of Regulation, Washington, D.C.,

197b.

3. Code of Federal Regulations , Title 10, Part 50, Appendix A, Criterion 2 (Design Bases for Protection Against Natural Phenomena), Office of

Federal Register, General Series Administration, Washington, D.C., 1976.

4. Wind Field and Trajectory Models for Tornado-Propelled Objects , EPRI NP748, Electrical Power Research Institute, Palo Alto, Calif., May 1978.

5. Costello, J. F., and Stephenson, A. E., "Free Fall of Large Pipes”,

Journal of the Engineering Mechanics Div . , ASCE, April 1978, pp. 477-480.

15
Table 1. Values of Horizontal Missile Speeds at Time of Hit, Vm> in

Meters Per Second, Corresponding to Various Probabilities

of Occurrence

Automobile with = 2.0, A = 6. 3m , m = 1810 1

Vtorn

=

, max

360 mph (V^ per NBSIR 76-1050: 59 m

la 1

.

Basic Casea

10 7 x Probability

k 1.0 0.5 0.06

0.3 20 (20) 22 (23) 24 (24)

0.5 27 37 43

0.9 43 45 47

1.3 53 (45) [39] 54 (54) [55] 55 (56) [56]

2.0 62 64 65

a Numbers between parentheses correspond to tornado direction a = 1°

Numbers between brackets correspond to tornado direction a = 45°

Ia2. Influence of Location of Lot IV

10 7 x Probability

k v> v

a 1.0 0.5 0.06

60, - 100 43 45 47

0.9 60, - 200 - 39 47

160, - 200 13 47 47

60 } - 500 - 39 43

60, - 100 62 64 65

2.0 60, - 200 - 40 65

160, - 200 63 64 65

ameters

16
Ia3. Influence of Number of Missiles

10 7 x Probability

n/ntyp v> v

a 1.0 0.5 0.06

1 43 45 47

1/8 60 , - 100 - 43 47

1/50 - 39 46

1 _

.

39 47

1/8 60 , - 200 - 39 47

1 13 47 47

1/8 160 , - 200 - 47 47

1 62 64 65

1/8 60 , - 100 - 63 64

1/50 - 17 64

1 40 65

1/8 60 , - 200 - 39 64

1 63 64 65

1/8 160 , - 200 16 62 64

ameters

Ia4. Influence of Target Areaa

10 7 x Probability

k 1.0 0.5 0.06

0.5 27 (27) 36 (37) 41 (43)

0.9 - (43) 41 (45) 45 (47)

1.3 - (53) 49 (54) 54 (54)

2.0 - (62) 58 (64) 64 (65)

aNumbers not between parentheses represent speeds of hits on building 9 only.

Numbers between parentheses represent speeds of hits on any of the buildings

1 through 9.

17
Ib * V

t 0 m

= 300 mph ^ V

H per NBSIR 76-1050: 52 m/s)

Ibl. Basic Case, and Influence of Target Area3

10 7 x Probability

k 1 .0 01.5 0..06

0.3 22 31 35

0.5 22 (22) 33 (33) 37 (37)

0.9 38 (38) 46 (41) 48 (47)

1.3 52 (-) 53 (47) 54 (54)

2.0 59 (-) 60 (55) 60 (60)

a Numbers not between parentheses represent speeds of hits on any of buildings

1 through 9.

Numbers between parentheses represent speeds of hits on building 9 only.

Ib2. Influence of Location of Lot IV

10 7 x Probability

x

o"> V

,a 1,0 0,5 °* 06

60, - 100 38 46 48

60, - 200 38 39 40

ameters

k

0.9

18
Ic. Vtorn

= 240 mph (VH per NBSIR 76-1050: 41 m/s)

Icl. Basic Casea

10 7 x Probability

k 1.0 0.5 0.06

0.3 22 26 31

0.5 16 33 34

0.9 33 44 46

1.3 47 ( 35 ) [-] 50 ( 50 ) [ 50 ] 41 ( 51 ) [ 52 ] 2.0 53 53 54

a Numbers between parentheses correspond to tornado direction a = 1°

Numbers between bracktes correspond to tornado direction a = 45°

Ic2. Influence of Location of Lot IV

10 7 x Probability

k V’ v

a 1.0 0.5 0.06

60 , - 100 33 44 46

60 , - 200 32 33 45

0.9 160 , - 200 43 44 45

60 , - 200 32 33 33

60 , - 100 53 50 54

2.0 60 , - 200 - 33 49

160 , - 200 - 21 35

ameters

Ic3. Influence of Number of Missiles

10 7 x Probability

n/ntyp 1.0 0.5 0.06

1 33 44 46

1/8 33 44 46

1/50 33 38 45

1 53 53 54

1/8 47 55 54

1/50 - 21 54

19
Idl * V torn

= 380 mph

Idl. Basic Case

10 7 x Probability

k 1.0 0.5 0.06

0.9 42 44 47

2.0 64 65 66

Iel. V = torn 200 mph

Iel . Basic Case

10 7 x Probability

k 1.0 0.5 0.06

0.5 34 35 35

0.9 40 42 43

1.3 44 45 46

2.0 - - 45

20
II Automobile with = 1.5, A = 3.8 m^, m = 1810 kg

„ max . , . Ila. ^torn

= ^60 mph P er ^BSIR 76-1050: 46 m/s)

Hal. Basic Casea

10 7 x Probability

k 1.0 0.5 0.06

0.3 44 48

0.5 27 58 60

0.9 55 64 69

1.3 62 (38) [39] 68 (63) [55] 71 (70) [56]

2.0 67 71 74

a Numbers between parentheses correspond to tornado direction a = 1°

Numbers between brackets correspond to tornado direction a = 45°

IIa2. Influence of Location of Lot IV

10

7 x Probability

k x

o" » v

a 1.0 0.5 0.06

60, - 100 55 64 69

60, - 100 - 64 68

0.9 160, - 200 64 65 68

60, - 500 - 1 32

60, - 100 67 71 74

2.0 60, - 200 - 74 75

160, - 200 66 70 74

ameters

21
IIa3. Influence of Number of Missiles

10 7 x Probability

l / n tyP V» V* 1.0 0.5 0.06

1 55 64 69

1/8 60 ,

•- 100 54 63 66

1/50 - 55 66

1 60 , - 200

• i -- 64 68

1/8 49 68

1 160 ,

•- 200 64 66 68

1/8 63 66 66

1 1/8

60 , - 500

- - 32

32

1 67 71 74

1/8 60 , - 100 57 71 74

1/50 - 51 70

1 60 ,

•- 200

- 74 75

1/8 — 64 75

1 160 ,

-- 200 66 70 74

1/8 63 70 74

ameters

IIa4. Influence of Target Area3

10 7 x Probability

k 1.0 0 ..5 0,.06

0.5 27 (27) 44 (58) 54 (60)

0.9 41 (55) 54 (64) 68 (69)

1.3 40 (62) 63 (68) 71 (71)

2.0 - (67) 67 (71) 74 (74)

a Numbers not between parentheses represent speeds of hits on building 9 only.

Numbers between parentheses represent speeds of hits on any of the buildings

1 through 9.

22
max

lib. ^torn = 300 mph (Vpj per NBSIR 76-T050: 27 m/s)

Ilbl. Basic Case, and Influence of Target Areaa

10 7 x Probability

U0_ 0.5 0.06

0 ,>3 42 46 48

0,.5 44 ( -) 53 (45) 56 (54)

0 ,,9 52 (30) 57 (57) 61 (61)

1,,3 56 ( -) 60 (60) 62 (62)

2,,0 53 (-) 54 (55) 1 T 1 55 (56) —i—n—

a Number not between parentheses represent speeds of hits on any of buildings

1 through 9.

Number between parentheses represent speeds of hits on buildings 9 only.

IIb2. Influence of Location of Lot IV

10

7 x Probability

v- > v

a 1.0 0.5 0.06

60, - 100 52 57 61

60, - 500 30 30 30

ameters

23
lie. V. = 240 mph (Vm per NBSIR 76-1050: 7 m/s) torn ^ m r '

IIcl. Basic Case3

10 7 x Probability

k 1.0 0.5 0.06

0.3 35 42 46

0.5 40 46 49

0.9 46 47 51

1.3 45 ( 39 ) [ 30 ] 45 ( 55 ) [ 45 ] 45 ( 56 ) [ 46 ] 2.0 - - -

a Numbers between parentheses correspond to tornado direction a = 1°

Numbers between brackets correspond to tornado direction a ~ 45°

IIc2. Influence of Location of Lot IV

10 7 x Probability

x

o

"> v

a 1.0 0.5 0.06

60 , - 100 46 47 52

60 , - 200 26 51 52

160 , - 200 26 51 52

60 , - 500 26 28 31

60 , - 100 — — — 60 , - 200 - - - 160 , - 200 - - -

ameters

IIc3. Influence of Number of Missiles

10 7 x Probability

k n/n typ 1.0 0.5 0.06

1 46 47 51

0.9 1/8 40 47 49

1/50 26 40 48

1 — _ — 2.0 1/8 - 9

1 1/50 - - -

24
lid. Vtorn = 380 mph

Ildl. Basic Case

10 7 x Probability

k 1.0 0.5 0.06

0.9 62 65 70

2.0 71 74 77

He.

k

v torn

= 200 ”Ph

Ilda. Basic Case

10 7 x Probability

1.0 0.5 0.06

0.5 37 40 41

0.9 19 35 38

1.3 - 37 42

2.0 - - -

25
Ill Plank with C R

= 2.0, A = 0.7 m^, in = 51.9 kg

, max

Ilia. Vtorn = 360 mph (VR per NBSIR 76-1050: 83 m/s)

Illal. Basic Casea

10 7 x Probability

k 1.0 0.5 0.06

0.3 26 27 29

0.5 40 54 63

0.9 40 55 62

1.3 40 (-) [28] 55 (50) [53] 62 (58) [60]

2.0 31 55 62

5.0 34 (-) [28] 55 (-) [53] 62 (58) [60]

a Numbers between parentheses correspond to tornado direction a = 1°

Numbers between bracket correspond to tornado direction a 45°

IIIa2. Influence of Location of Lot IV

10

7 x Probability

k x

o" » y - a

J o 1.0 0.5 0.06

60, - 100 40 55 62

0.9 60, - 200 38 55 62

160, - 200 40 53 61

60, - 500 21 55 61

60, - 100 31 55 62

2.0 60, - 200 40 61 62

160, - 200 32 55 62

60, - 100 34 55 62

5.0 60, - 200 33 55 62

160, - 200 34 55 62

ameters

26
IIIa3. Influence of Number^ of Missiles

k

0.9

2.0

5,0

ameters

l/n typ

1 V* v

a

4

1/8

1/50

60, - 100

1 1/8

60, - 200

1 1/8

1

160, - 200

41/8

1/50

60, - 100

1 1/8

60, - 200

1 1/8

1

160, - 200

4

1/8

1/50

60, - 100

1 1/8

60, - 200

1 1/8

160, - 200

10^ x Probability

1.0 0.5 0.06

40 55 62

40 55 63

40 55 61

40 55 61

38 55 62

38 55 62

40 53 61

37 53 61

31 55 62

31 55 62

31 53 62

31 53 62

40 61 62

40 60 62

32 55 62

32 55 62

34 55 62

34 55 61

34 54 61

34 53 61

33 55 62

33 55 62

34 55 62

34 55 62

27
IIIa4. Influence of Target Area3

10 7 x Probability

k 1.0 0'.5 0..06

0.9 - (40) 50 (55) 58 (62)

2.0 30 (31) 50 (55) 57 (62)

5.0 - (34) 49 (55) 57 (62)

a Numbers not between parentheses represent speeds of hits on building 9 only.

Numbers between parentheses represent speeds of hits on any of the buildings

1 through 9.

maX nib. Vtorn = 300 mph (V

R per NBSIR 76-1050: 70 m/s)

Illba. Basic Case, and Influences of Target Area3

10 7 x Probability

k 1 .0 0 .5 0 .06

0.3 22 23 25

0.5 35 50 58

0.9 20 (-) 52 (50) 58 (58)

1.3 25 52 58

2.0 38 (33) 52 (50) 58 (57)

5.0 - (-) 52 (49) 58 (57)

a Numbers not between parentheses represent speeds of hits on any of buildings

1 through 9.

Numbers between parentheses represent speeds of hits a building 9 only.

IIIb2. Influence of Location of Lot IV

10

7 x Probability

x

o" v .. 3

» yo 1.0 0.5 0.06

60, - 100 20 52 58

60, - 500 20 52 57

ameters

28
IIIc. ^torn

= ^40 mP^ (Vr per NBSIR 76-1050: 58 m/s)

IIIcl. Ba$ic Case3

10 7 x Probability

k 1.0 0.5 0.06

0.3 19 30 21

0.5 16 45 50

0.9 30 46 50

1.3 32 (33) [33] 47 (38) [49] 50 (50) [51]

2.0 35 47 50

5.0 - (-) [45] 47 (-) [49] 50 (49) [53]

a Numbers between parentheses correspond to tornado direction a = 1°

Numbers between brackets correspond to tornado direction a = 45°

IIIc2. Influence of Location of Lot IV

10 7 x Probability

k V’ y .. a 1.0 0.5 0.06

60, - 100 30 46 50

0.9 60, - 200 29 46 50

160, - 200 31 46 50

60, - 500 38 47 50

60, - 100 35 47 50

2.0 60, - 200 - 47 50

160, - 200 - 47 50

60, - 100 — 47 50

5.0 60, - 200 - 47 50

160, - 200 - 47 51

ameters

29
IIIc3. Influence of Number of Missiles

10 7 x Probability

k n/ntyp 1.0 0.5 0.06

1 30 46 50

1.9 ^ 32 47 51

1/8 30 46 50

1/50 — 46 50

1 35 47 50

1 0

^ 35 47 50

* 1/8 - 46 50

1/50 46 50

1 — 47 50

. 0

^ - 47 50

1/8 - 46 50

1/50 - 46 50

HidVtorn 380 mph

Illdl. Basic Case

107 x Probability

k 1.0 0.5 0.06

0.9 43 53 62

2.0 37 54 63

5.0 30 54 63

IlleVtorn 380 mph

Illel. Basic Case

10 7 x Probability

k 1.0 0.5 0.06

0.5 28 38 45

0.9 27 39 45

1.3 28 39 45

2.0 32 42 45

5.0 - 42 45

30
IV 12" Pipe with = 0.7, A = 1.6 m^, m = 341 kg

TO3.X IVa . = 360 mph (V„ per NBSIR 76-1050: 47 m/s) torn r

IVal. Basic Casea

10 7 x Probability

k 1.0 0.5 0.06

0.3 , 36 45

0.5 29 57 59

0.9 55 64 68

1.3 61 (40) [36] 68 (63) [70] 71 (71) [71]

2.0 70 73 75

a Number between parentheses correspond to tornado direction a = 1°

Number between brackets correspond to tornado direction a = 45°

Influence of Location of Lot IV

10 7 x Probability

v> v

a

1.0 0.5 0.06

60, - 100 55 64 68

60, - 200 65 67

160, - 200 - 66 67

60, - 500 - - 30

60, - 100 — 68 71

60, - 200 - 71 73

160, - 200 - - 73

ameters

31
IVa3 Influence of Number of Missiles

10 7 x Probability

l/ntyp x

o"

y » aJ o 1.0 0.5 0.06

1 55 64 68

4

60, - 100 58 66 68

1/4 61 67

1/16 — 52 67

1 60, - 200

' - 65 67

1/4 ~~ 41 66

1 160, - 200

- 66 67

1/4 — 65 67

1 70 73 75

4 60, - 100 70 73 75

1/4 56 69 74

1/16 — 62 69

1 60, - 200 - 71 73

1/4 71 71

1 160, - 200

- - 73

1/4 70 71 72

ameters

IVa4. Influence of Target Area3

107 x Probability

k 1.0 0.5 0.06

0.9 - (55) 54 (64) 61 (68)

2.0 61 (70) 62 (73) 62 (75)

a Numbers not between parentheses represent speeds of hits on building 9 only.

Numbers between parentheses represent speeds of hits on any of the buildings

] through 9.

32
IVb. V torn

= 300 mph ^ V

II per NBSIR 76-1050: 28 m/s)

IVbl. Basic Case, and Influence of Target Area3

10 7 x Probability

k 1.0 0 .5 0 .06

0,3 45 47

0.5 27 53 56

0.9 52 (-) 57 (54) 59 (61)

1,3 58 60 62

2.0 62 (61) 62 (62) 62 (62)

a Numbers not between parentheses represent speeds of hits on any of buildings

1 through 9.

Numbers in parentheses represent speeds of hits on building 9 only.

IVb2, Influence of Location of Lot IV

10 7 x Probability

x

o"

V

3

* yo" 1.0 0.5 0.06

60, - 100 52 57 59

60, - 500 - - 30

ameters

IVc. Vtorn = 240 mph (Vj| per NBSIR 76-1050: 7 m/s)

IVcl. Basic Case3

10 7 x Probability

k 1.0 0.5 0.06

0.3 23 26 31

0.5 39 45 49

0.9 45 47 52

1.3 52 (26) [50] 52 (52) [52] 53 (52) [53]

2.0 | Q - -

a Numbers between parentheses correspond tu tornado direction a = 1°.

Numbers between brackets correspond to tornado direction ot = 45°.

33
IVc2. Influence of Location of Lot IV

10 7 x Probability

k x

o" » y » a•^o 1.0 0.5 0.06

60, - 100 45 47 52

0.9 60, - 200 26 47 51

160, - 200 26 47 51

60, - 500 26 28 30

60, - 100 52 52 53

2.0 60, - 200 - - - 160, - 200 - - -

ameters

IVc3. Influence of Number of Missiles

10 7 x Probability

k n^ ntyp 1.0 0.5 0.06

1 45 47 52

0 9 4 46 50 52

1/8 39 47 51

1/50 26 40 47

2.0

14

-

1/8 - - - 1/50 - - -

IVdl. Vtorn = 380 mph

Idl. Basic Case

10 7 x Probability

k 1.0 0-5 0.06

0.9 - 65 69

2.0 - 74 77

34
IVel. Vtorn

= 200 mph

Ie 1 . Basic Case

10 7 x Probability

k 1.0 0.5 0.06

0.5 34 35 35

0.9 40 42 43

1.3 44 45 46

2.0 - - 45

V. 12" Pipe with = 0 . 7, A

2 = 1 . 16 m , m = 341 kg

Va. Vtorn = 360 mph (Vmax

H per NBSIR 76-050: 38 m/s)

Val • Basic Case3

10 7 x Probability

k 1.0 0.5 0.06

0.3 - 53 57

0.9 5 5

( — ) 62 (55) 67 (64)

2.0 - 65 67

Numbers in parentheses represent speeds corresponding to

n/ntyp

= 1/50

35
Vb. Vtorn

= 300 mph ( v

h

3X

per NBSIR 76-1050 = 15 m/s)

Vbl. Basic Casea

107 x Probability

k 1.0 0.5 0.06

0.3 37 47 51

0.9 -(-) 52 (— ) 57(57)

2.0 43

a Numbers in parentheses represent speeds corresponding

t0 n/ntyp

= 1/50

Vc. Vtorn

= 240 mph ( v

h

3X

per NBSIR 76-1050 = 6 m/s

Vcl

.

Basic Casea

10 7 x Probability

k 1.0 0.5 0.06

0.3

0.9

2.0

34

20(-)

41

45(34)

44

46(46)

36
b/2 rr b/2

Figure 1

Schematic Representation of

a Tornado Path

37
MBi

U.

38

Notations
El

1,000.00

39

Figure

3

Plan

View

of

Nuclear

Power

Plant

(Courtesy

of

Don

Mehta,

Bechtel

Corporation,

Gaithersburg)
82.5

22.5

00 

0?l

MModo u

•h

d

U

d

d rH

Ml CM d

<}• <D

U

CO 0)

OJ (1) 3 M M O d a cm

bo a)

•rl Qj

H

Pm

d

40

Schematic
APPENDIX A1

PROBABILITY DENSITY FUNCTIONS OF

MAXIMUM TORNADO WIND SPEED

In this Appendix an approximate representation, consistent with the

assumptions implicit in Ref. 2, will be given for the probability density

function of the maximum tornado wind speed Vtorn at a location where the

probability, P(T, V torn ), that a tornado with speed Vtorn > 360 mph will

occur is 10

-7 /year. Let P(T) and p (V torn ) denote the probability that a tornado will hit the location in question, and the probability that the

maximum wind in a tornado is higher than Vtorn , respectively. Then

P < T > Vtorn> “ p ( T ) p< v torn> (A1 >

From Figs. A1 and A2 if follows that, in the regions where, nominally,

P(T, V torn ) = 10” 7 /year, the following approximate probabilities P(T) and

P(Vt0 rn^ are assume d Ref. 2:

torn <”>P h > P < T > P< Vtorn> = 10 7/P < T >

380 190 X 10“ 5 1/(190 x 102

) 370 130 X

10“ 5 1/(130 x 102

) 360 105 X 10“ 5 1/(105 x 102

) 350 70 X 10“ 5 1/(70 x 102

) 340 45 X

10“ 5 1(45 x 102

) 330 33 X 10“ 5 1(33 x 102

) 320 23 X 10“ 5 1(23 x 102

) 310 16 X 10“ 5 1/(16 x 102

)

Since, in Ref. 2, P(Vtorn ) is assumed to be independent of geographical

location, it follows from Eq. A1 that, at a location where P(T, 360) = 10" 7

, P(T, V torn ) = 105 x 10~ 5 P(VQ

). For various values of V

Q , P(T, Vtorn ) will than have the values tabulated below

v torn < mPh ) P < T > vtorn>

380 (105/190) 10“7 ~ 0.55 x 10“ 7 370 (105/130) 10“ 7 ~ 0.80 x 10“7 360 10“7 = 1.00 x 10“ 7 350 (105/70) 10"7 ~ 1.50 x 10“ 7 340 (105/45) 10

-7 ~ 2.33 x 10“ 7 330 (105/33) 10" 7 ~ 3.30 x 10“ 7 320 (105/23) 10“ 7 " 4.50 x 10“ 7 310 (105/16) 10“ 7 " 6.00 x 10" 7

Remembering that P(T, Vtorn ) = 1 - P

cu|n (T, V0

), where Pcum (T, Vtorn ) = cumulative distribution function of hit with speed Vtorn (i.e., probability

41
that a hit with maximum less than speed Vtorn will occur), it follows that

the tail of the probability density function p(T, V torn ) corresponding to

P cum ( T > V torn) be rePresented approximately as in Fig. A3.

Similar calculations can be made for regions where P(T, V tQrn ) = 10

-

^ for

v torn = 300 m? h and Vtorn = 240 mPh *

Note that the calculations presented in this Appendix are merely illustrative. Indeed, values of P(T) and P(Vtorn ) somewhat different from those of

Ref. 2 may be assumed, as indicated, e.g., in Ref. A1

.

REFERENCE

Al. Abbey, R. F., "Risk Probabilities Associated With Tornado Windspeeds”,

in Proceedings , Symposium on Tornadoes, Texas Tech. University,

Lubbock, TX, June 1976.

42
O i/» o * + n n CN < ea { **• s— I t d ^~s •H CNI 43

4-1 • •H 0) M-4 4d ai

4-J pd

tx

4-J

d

•H •d co rH cu •H CO 4-J ' 1 a) d

<3

d !-< 4-J 43 d CO

CUO

d

i-i cr -d d Ph CO <u 00 4-J *H 0) cu •H

Ph 4*1 a)

d

•H

u d> 00

4J a) CO CO n d i o O a) d

T3 > 00 d •H •H d pH 4-J d d o o H o

43
125

120

115

110

105

100

mo mo m

r-»

CM

<3

<U

V-t d

bO

•H

44

Calculated

Tornado

Wind

Speed

by

Five-Degree

Squares

for

10“

Probability

per

Year

(Ref.

2)
|jf#A j«4) |<u*»A ‘1)4 x

8

. 0i

Estimated

Probability

Density

'unction

of

Tornado

Wind

Speeds
APPENDIX A2

COMPUTER PROGRAM: PARTIAL LISTING, AND SAMPLE INPUT AND OUTPUT

NOTE: Computer program is available on tape from the National

Technical Information Service, Springfield, Virginia, 22151

46
Description of Input Data for Stage 1 Program

0 roup Module

1 MAIN

2 PRBDEF

3 SITE

Type

Integer

Integer

Real

Real

Variable Name(s) Format Description

PLEVEL 12 Determines the amount of output to the printer. Note : Each group of output starts with a preface of the form

(P<Level> - <Module>)

Here, <Level> is the minimum value that PLEVEL must have in order

for that particular output to occur.

<Module> is the name of the module

where the printing is done.

-2 _< No output (except for warnings and fatal errors)

.

-1 = Tornado landing distances and widths, number of hits, and hit counts by surface and face.

0 = (more than -1) Good level of descriptive

output about the input.

1 = (more than 0) Short summary of each basis

trajectory, summary of each hit.

2 = (more than 1) Summary of each event.

3 = (more than 2) Long summary of each basis

trajectory.

4 (more than 3) Full output of each basis

trajectory.

JPN, JSA, JHS

,

913 Problem definition indices.

JUT, HAM,, ITT, Note

:

These values do not affect the operation

I AD, ITD, IBM of the program. They may be used for documentation purposes.

JPN = Problem number. JSA = Site number. JHS = Hit surface distribution number. JMT = Missile type number. IIAM = Distribution number of missile sets. ITT = Tornado type distribution number.

IAD = Angle of tornado direction distribution

number.

ITD = Translation axes distribution number.

IBM = Basis distribution number.

DELYTN F8.0 DELYTN = Distance between y translation lines

in meters . XC, YC, ZC, 6F8.0 ( Note : y translation lines are

LX, LY, LZ parallel to the O^Xp axis of the C^x^y^zj, coordinate system defined

below. They are used internally to locate efficiently regions where missile trajectories may intersect

targets.

)

XC,YC,LC = Coordinates of the point 0^ (in meters ) respect to the origin 0 of the reference Oxyz coordinate system.

0^ is the center of the rectangular

region that includes all the potential missiles at their initial positions. The system Oxyz is chosen arbitrarily for convenience.

LX,LY,LZ = Length of the sides parallel to the °MX1> °Myl» °MZ

1 axes meters ) respectively of the parallelepiped

containing all the potential

missiles at their initial positions. 0M

Xj, 0^, C^Zj are parallel to Ox, Oy, Oz, respectively.

47
Description of Inpat Data for Stage 1 Program

uroup Module

4 H1TSRF

Type Variable Name(s) Format Description

Integer NHR 13 NHR = number of hit regions [for example.

Figure 4 of the report contains 9 hit regions numbered 1 through 9], For each

hit region: NHR

Real [XCR, YCR, ZCR, [7F8.0]* XCR, YCR, ZCR = coordinates with respect to

^ THETDX, LX, LY, point 0 (in meters ) of one of the 4 LZ] corners of the rectangular base of the hit region. It is always assumed that this base is in a horizontal plane.

The 3 lines that form the corner are denoted by 0^2

, 0_y2

> ®

c

z2‘ °cz2 is parallel to the axis 0

z of the refer- ence system Oxyz. The coordinate

system 0

cX2y2

z

2 must be tight handed .

THETDX = Counterclockwise angle (in degrees ) by

which the vector 0X must be rotated in order to be parallel to and have the same direction as the vector 0„xo

c L LX,LY,LZ = Lengths (in meters ) of the sides of the hit region (hit regions are always assumed to be parallelepipeds).

6

7

* I.

MSLTYP

AMDDEF

TTDEF

Real CDRAG, AREA, 4F8.0 Missile description.

MASS, RFC CDRAG = Drag coefficient (nondimensional)

AREA = Effective area (in meters^).

MASS = Mass (in kilograms).

RFC = Horizontal restraining force factor (nondimensional) [RFC is denoted by k in the text, see Eq. 2 of the report]

Integer NIAM 13 NIAM = the number of missile set-ups

[denoted by Nj in the report]. NIAM Note: The I-th missile set-up is a union

Integer I, NC(I

13,16 of NC(I) component lattices. Each com- ponent lattice has NX*NY*NZ missiles

NC(I) where NX, NY, and NZ may be different

Integer [NX, NY, NZ] [313] for each lattice [for example, in

L 1 Figure 4 of the report there are

1

NTT

NC(I) = 4 component lattices, denoted

by I, II, III, IV].

Real [ PTT ( I ) ] [5E12.5] PAM(I) “ The probability of occurrence of the

1 I-th missile set-up [denoted by P(SM ) in the report].

Real, LUSER, RMXRTS, 2F8.0, 13 LUSER - Distance (in meters) between tornado Integer NTT touchdown point and first line of

Real

Real

NTT

1

NTT

[SOEV(I)]

[ PTT ( I )

[10F8.0]

[5E12.5]

1

potential missiles. This is used in the program only if RFC is so small that potential missiles would be swept off

the ground even if tornado were at a very

large distance from the site. (Recall

that the theoretical wind speed at the site is equal to the tornado translation

velocity, even if the tornado is at an infinite distance from the site.)

RMXRTS “ Radius of maximum wind velocity (in meters )

NTT = Number of tornado types [Denoted by Nj in the report].

SOEV(I) = Maximum wind velocity for the I-th tornado type (in miles/hour ) [Denoted

by V torni

in the re P° rt J-

“ means that this format is used repeatedly.
Description of Input Data for Stage 1 Program

Group

7

b

9

10

* [• •

Module

TTDEF

Al'DEF

i'UDEF

BMDEF

Type

Integer

Real

Real

Variable Name(s) Format Description

PTT(I) = Probability of occurrence of the I-th tornado type, divided by 10~' [denoted

in the report by P(TV )/10-7

].

NAD

NAD

13 NAD - Number of directions of tornado axis of translation [denoted in the report by N^]

[AD(I)[10F8.0]* AD(I

= The angle (in degrees) defining the

1

NAD

I-th direction of the tornado axis of translation [this angle is denoted in the report by a^]. AD(I) are the counter—

[PAD(I )

1 [5E12.5] clockwise angles [denoted in report by

ou] by which the vector Oy must be rotated in order to be parallel to and

have the same direction as the tornado translation velocity vector.

PAD(I) = Probability of occurrence of the I-th

angle [denoted in the report by PL(ou)].

Real USXORG, USYORG 2F8.0 (USXORG, USYORG) = Coordinates x,y (in system

Oxyz) of point 0 (in meters ) of segment Real LPTTD, DELTD 2F8.0, 13 O'B. O'B is normal to and intersects

Integer NTD the tornado axes of translation. The direction of O'B is such that the tornado translation velocity vector must be rotated counterclockwise by 90° in order

to be parallel to and have the same direction as O'B.

NTD Real [PTD(I ) ] [5E12.5]

1

Real HWUSER F8.0

Integer, TYPXBM, 13, F8.0

Real DELXBM

Integer, TYPLBM, 13, F8.0 Real DELLBM

Real T0, TDEL 2F8.0

LPTTD = Length (in meters ) of segment O'B

[denoted in the report by b]

DELTD = Distance (in meters ) equal to LPTTD/

(NTD-1), where NDT is defined below

[denoted in the report by AL].

NTD = The number of translation axes [denoted in the report by N^]. Note : NDT is same for all angles AD(I).

PTD(I) = Probability of occurrence of the I-th tornado translation axis [denoted in

the report by P(L^)].

HWUSER = The user specified tornado left or right width (in meters ). It is used in the program only if no (finite) left or right width distances can be computed

internally (see comment for variable

LUSER, Group 7). Note : The left (right) widths is the

the maximum orthogonal distance (in meters ) to the left (right) of the tor- nado translation axis such that a sta- tionary missile could still be moved

(horizontally or vertically) by the tornado wind field.

TYPXBM = 1 (Variable used internally in the program, indicating a set of basis missiles

equally spaced on a straight line normal

to tornado direction).

DELXBM = Horizontal distance (in meters ) between

basis missiles.

TYPZBM = 1 (Variable used internally in the program, indicating a set of basis missiles

equally spaced on a vertical line).

DELLBM = Vertical distance (In meters ) between

basis missiles.

.] = means that this format Is used repeatedly.

49
Description of Input Data for Stage 1 Program

Group Module Type Variable Name(s) Format

10 BMDEF

11 AMD Integer

Real

Integer

NIAM

' I, NC(I)

NC(I)

(XCT, YCT, ZCT

1 THETDX, DELX,

DELY, DELZ

NX, NY, NZ]

1

I 3 , 16

7F8.0,

313

Description

T0 « Initial time (in seconds ) to start a tra- jectory integration (suggested value T<b - 0 . 0 ).

TDEL “ Time interval (in seconds ) between stored trajectory points (suggested value TDEL =

0.1 sec).

Note : Thi6 essentially repeats group 6 but with complete information about the lattices. There are NIAM sets of data. The I-th

set of data has NC(I) descriptors. Each descriptor describes a component lattice

of NX*NY*NZ missiles.

XCT, YCT, ZCT = Coordinates in Oxyz system (in meters ) of one of the 4 corners of bottom horizontal plane of the lattice

THETDX “ A system of coordinates °lx

3^3^3 is defined for each lattice, analogous to the system O

cx2Y2 z 2

^ or each hit region THETDX is the counterclockwise angle (in degrees ) for which the vector Ox must

be rotated in order to be parallel and

have the same direction as the vector

°LX3

*

DELX, DELY, DELZ = Missile separations in the lattice (in the x

3

, y3

, z

3 directions,

respectively).
Descripti on o f Input Data for Stage 2 Program

C rou p Module Type Variable Name(s) Format Description

i MAIN Integer, PLEVEL, 12, PLEVEL ° Determines the amount of output to the Heal

,

VCUT, E12.5, printer.

Integer, HXI1VD, 112,

Keal, DELHV

,

E12.5, Note: Each group of output starts with a pre- Integer NHVI 112 face of the form (P Level - Module ).

Here

,

<Level> is the minimum value tliat PLEVEL must have in order

for that particular output

to occur. If <Level> is null the output will always

occur

<Module> is the natae of the module where the printing is done.

-1 Summary of all results

0 = (more output than -l) Input probabilities are listed.

1 j> (more output than 0) Hit velocities

by distribution are listed.

VCUT = Smallest value (in meters sec ^ consider^

in histograms of hit velocities.

MXNHVD = Maximum number of velocities of hitting

missiles being listed (starting from

largest velocity).

DELHV = Interval (in meters/sec ) in the velocity

histogram.

NHVI = The number of intervals in the velocity

histograms starting from U.U.

i»ote : One extra interval is added at the higii end to handle any velocities exceeding

the velocity interval of the last bar.
Ill X

o 1 K a X < 1 3 in UJ u z 1 O Q u. M a 1 X J IL • X o o 3 in 1 * H 1 z X ID > 1 1 -> u a 3 M < 1 a

2 u. 1 1 a 01 K a > X _l a UJ < o 1 1 K X Z h X X UJ a 3 Q X 3 a z u

cr 1 1

ta- 1- »-4 z X z Q > Z X a < >-• u. o H 1 z z X •— < X K h m »- *- H <• 3

o Z 1 at « 44 j z 1- K i- X < - 3 in z CD a UJ 1 < X O

a Z 1 x a u z

«- i

</> 1 19 X u. UJ ta4 e> i z W 1 o o x X X X a u.

t- i < IU 1 x z a X X IL o X o IL u.

i/> i a to 1 a 19 0) UJ 1- Ul 01 X X X 0) * UJ UJ UJ

i i K in 1 - - X a IL O o X X X o a I X O N

- i a « 1 01 ta- 44 z z o a UJ X o < Q X X o >- ta- C 1 o 1 Z X X I ta- *— 1- »- K >- 1- H V- H - in 2 1 U. u 1 o z

a i M 1 »-• H

i < W 1 w <

—

t- i in 1 < in n o 3 I z X a X

<\J a i IL — 1 u • X I X li. X Q Q o X X V X • O -i 1 mt o a 0) X a »- z Z X X X z 0) *- Q Q X

** 1 J UJ u 3 r > z 3 3 < H o M X -i CD 0) UJ 3

o dJ CD 1 a a: in J > > UJ O O UJ i— 1- M 01 X X Q Z ml

CD -J < 1 a M o IL U. u. 19 X X 0) 0) 0) o I z a X J- M <

in 3 CC 1 < 3 • z u. >

UJ O o 1 O z M UJ o O a 1 i UJ o X o t- a z a • 1 i X tmt 0) UJ X a I < ”> z

3 in 1 i h- u. I V UJ UJ o > u X X X X UJ X

U z < UJ 1 (A < UJ a IL h* 19 n L- (M X < a: 0. X 19 X X K N X o

s —

N*

j UJ U o - ml in < CD Z > 0) t- z o UJ a < X > z H* X o

— < u_ K 1 z *-» z a Hi ta- X X X X X a 4 in H < X > > X ** in 3 in o z n 1 • M J CD u o Q a a X a X X X in in O X X o X u CVJ H U 1 Ul ta a 01 z

in Uj UJ o 1 (0 3 a z UJ II II

i X -J 1 3 Q < a J

*- < UJ 1 X U. > X X X M in cn a UJ

•-* H > 1 J <n IL UJ X > > 3 o a u K 1- X X X o X N

< W in 1 < J ta- UJ Q < X J" CD CVJ < X a < a K < X X a a t- in z L- 1 x < X O Q O z > J H > X • X K z UJ O X Q a Q h* a X u. • K u 1 UJ Z H O o Z z M o 0) 3 M * in X Z a o « Q o z z a z 3

in in < 1 z a < < < < CD z z O a a -J o M o X • -I < < < ID u z < CD — *-• a: a 1 aJ H a o z o D X W I •-* z 1 U 1- o o o X Z < u k u f M u. K z n a #

-/ 1 a o z X o 1 o n <

1 1 IL < u z

a.Q

1

1 * U u u u u u u u (J u u u c c <J u u u u o u u o u u u u o c c c c u u u u u CJ U c c c U o u V c c u u o o c c u u U

a

#e

- o it iiN«»o-Nr)<»ifi«MiiO'o - Nn<n/iiosor, ffenMn^Biesir^o - eg "i <t it u> r-- 3 -.-----«-^^(MN(\i(M('jMNMWNrinnr)nr)n'nr^n<»4^«^^<f<f<t*jiiflifiiniflininin

2

10 52
-J<u

<

>

z< a Z • • (/) mm z z z a i o o o

• i (0 MM « MM «— •

a: tO i i UJ K* <0 i »- 15 </> i > i J 3 > D UJ > i -j < i z > MM CD < i x z QD a < i 3 a o > IL V) m- a < < IL u_ fc-t a

O cr z 5! IL K- to or cr z < K M a i- or z

Z < mm a X K iL MM K < mm z X T 2- 5 z >- M <

< < < O a O ? <0 < a a. < < < < < co X «r <o S a u < < mm <0 z a a X >- N X >- MM 10 z

IL H IL Q i— Q u. H

o U z z O u z o U z

UJ MM UJ UJ *-M UJ UJ M

a: IL a -J u. J a U.

UJ IL UJ •-* IL M UJ IL T LU CD (0 UJ 10 m UJ ? S <0 (0 X

D mm MM D

Z Z 2 z Z

h- U) w

z -> X X uioii/ii

u. m t- _j a

UJa

t/> u. x J * - -J

U. IL Z IL U. V) M *- O t- - X aaaaaarwwwi/iwu- IIXIIXIIIXIUJ _ <JUU<JUOU.U.U.U.U.OU. X>NX>U<n3 U<C0 UX

U. IL H K

(/)(/)</!</></> I I I I I

U. U- U. U-

>- N X >

UJ

_J

(ft

If) b*X •

(0 1 J >• 1 < <r 1 D • a

t- CO cc z

UJ z < t-H X 3T < o < < <

MM to X z a

u. h- H- o O U z

CD UJ b- a MM u. UJ a u.

CD UJ X (0 D MM Z o

UOUOO<JUUUUVJLIUOOUUUUUUUUO(JUUU(JIJOUOUUOIJUUU'JUUOU<-)UUUUOOUUUOUU

T O' c - N n <f K1 ii»lD ^ o o o o •ONJJOO-'\l*)tfiO'CStOOO-N^<fifl'OSitlO vd'O^vONNNNNNNr^f'N'OXiOTlBOOCOOCOOOOeC C — ni P; « 10 <3 N

O'O'O'O'O'O'O'O1 IT O'

O' O' 0-«njf)<t,1£STC oooooooooo O - « n If

53
EFFECTS

APR

AYS

IN

MAIN CAM

LCBM

X

in

in<

CP

L-oN

z

z in D -

Z X

X

a a -j h I I *) z x x a

a z x k

j x z y

•

in

UJu

z

<

y

V)M

o

zo

<

_J

inz<

a

i

L

o

(XUJo

XD

Z

>z

<

UJIo

zo

J<

y • in O cr in UJ a o UJ -J y a FF y u y in

1 (X Ul y 1 in

• 1 o • • 1 FF •

in i 1 y < in R| o in i 1 z in i y i u a y i o y t y i < i Z UJ y < i < < i r i a F Z in < i a a > a z a t- f y > o FH cr J

a z z IL < UJ a z a a z a o in F z > in a z z z

< M o z y a -1 < M o < H * B z Z z UJ « < M m CD < y o Q H *-* < cr y < y j a z Z o o m < u U

in z a u f in in z f in z a F F F F U W in z

y IL in F U. F u. F

u z z Q u z o <J z Z o U Z

UJ FF FM z UJ •- UJ FF M UJ FF

u. a U. a U. a IL

u. UJ in IL UJ IL UJ • IL UJ cr *— UJ m UJ m in UJ z in z z F* D < 3 3 X

Z CD Z Z <

o o

(\J

o

o

in o

o

o

ii it il H il y

CD

-1zX

X

oy

z

X

X

crK

Z

XX

K

K

z

Xz

X

CDXz

X

z

* * * UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUIJUUUU

54

MXNYTN

=

100

NUMBER

OF

Y

TRANSLATION

INTERVALS
k k

UJ 44 UJ Z to k k tr X at a • o -v 44 UJ < o UJ J

i

• < tr X o Ul a k <

t~ o UJ a 4-4 I k z >

z UJ a k i X tO k UJ k UJ a.

uj 15 to o u z X (0 UJ 2 z — z M < k o u. k a k k

UJ < tu o (0 X UJ (/) u o *4 < z k X N 44 10 33 a k u. X M

< u 33 k « u. *-< o X CL k

h* in < x V) a b. k u UJ Ul z © UJ X y- < u • X k o

X 2 w a o «4 UJ UJ y- UJ X to k a k_4 < < UJ e o k X u X z UJ Ul o k

k J j u. < k M I u u. k <

< © o 5 z Z u. u. o k 44 M U J

Q UJ o i i— UJ • o U. a 44 * a UJ (0 D a k CM X o * w z to 3 z

Z J a. k k a (J > 3 -* UJ «I <

K-* < M UJ UJ < X tr k tr u tr a

> 2 I a e> <n UJ • UJ M • k k M k k

k D » < x UJ o k X 10 IL to o

UJ k y o k 3 X u z U z 44 <* z UJ >

in Z M UJ uj in Z u < 44 UJ < o J l—J X

UJ X k ID 3 u. 3 44 UJ k X

u X < cr a Ul a: tr UJ < cr t3 3T UJ UJ u

a a 5 o O o I I— 3 X a O UJ ta4 X X u. <

< 10 k IL y- (0 to h» i- u. tr -1 k k o UJ u O

in k

cr UJ

U.I X k

k k in

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81
NBS-114A IREV. 9-7B)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO.

NBS 80-2117

2.Gov*t. Accession No. 1 Recipient's Accession No. V' 'i.

" 'An-. — 4. TITLE AND SUBTITLE

Probabilistic Assessment of Tornado-Borne Missile Speeds

5. Publication Date September 1980

$ Performing Organization Code

%

‘

' '

'

7. AUTHOR(S)

Emil Simiu and Martin R. Cordes

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, DC 20234

11. Contract/Grant No.

12. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS fSn-eer, City, State, ZIP)

U.S. Nuclear Regulatory Commission

1717 H Street, NW

Washington, DC 20555

13. Type of Report & Period Covered Final

15. SUPPLEMENTARY NOTES

| | Document describes a computer program; SF-185, FIPS Software Summary, is attached.

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant bibliography or

literature survey, mention it here.) A procedure was developed for estimating speeds with which postulated missiles hit

any given set of targets in a nuclear power plant or similar installation. Hit speeds

corresponding to probabilities of occurrence of 10“? were calculated for a given

nuclear power plant under various assumptions concerning the magnitude of the force

opposing missile take-off, direction of tornado axis of translation, number and

location of missiles, and size of target area. The results of the calculations are shown to depend upon the parameters : CpA/m, where CD

= drag coefficient,

A = projected area, m = mass of missiles, and the ratio, k, between the minimum aero- dynamic force required to cause missile take-off, and the weight of the missile.

17. KEY WORDS ( six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name

separated by semicolons)

Missiles; engineering; structural engineering; tornadoes; wind.

18. AVAILABILITY J^X^Unlimited

[ j

For Official Distribution. Do Not Release to NTIS

Order From Sup. of Doc., U.S. Government Printing Office, Washington, DC

20402, SD Stock No. SN003-003-

iX Order From National Technical Information Service (NTIS), Springfield, VA. 22161

19. SECURITY CLASS

(THIS REPORT)

UNCLASSIFIED

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

21. NO. OF

PRINTED PAGES

85

22 . Price

$ 8.00

USCOMM-DC