Probabilistic assessment of tornado-borne missile speeds · 2019-04-10 · NBSIR80-2117 PROBABILISTICASSESSMENTOF TORNADO-BORNEMISSILESPEEDS NationalBureauofStandards Library.E-01Admin.Bldg

A11100 TflTSEl

NBSIR 80- A 1 1 1 OS 0A7543

Probabilistic Assessment ofTornado-Borne Missile Speeds

Emil Simiu

Structures and Materials Division

Center for Building Technology

National Engineering Laboratory

National Bureau of Standards

U.S. Department of CommerceWashington, D C. 20234

Martin R. Cordes

Mathematical Analysis Division

Center for Applied MathematicsNational Engineering Laboratory


U.S. Department of CommerceWashington, D.C. 20234

September 1980

li

Prepared for:

United States Nuclear Regulatory CommissionWashington, D.C. 20555

QO100

. U56

80-2117

1980

L.

NBSIR 80-2117

PROBABILISTIC ASSESSMENT OF

TORNADO-BORNE MISSILE SPEEDS


Library. E-01 Admin. Bldg.

MAR 2 1981A(J

U6>£

fib'

Emil Simiu

Structures and Materials Division

Center for Building Technology



U S. Department of CommerceWashington, D.C. 20234

Martin R. Cordes

Mathematical Analysis Division

Center for Applied Mathematics



U.S. Department of CommerceWashington, D.C. 20234

September 1980

Prepared for:

United States Nuclear Regulatory CommissionWashington, 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 Caseand Values V^

iaxObtained in Ref. 1 9

3.4 Analysis in Which Additional Variabilities are Taken intoAccount 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 ofDon Mehta, Bechtel Corp.

,Gaithersburg) 39

Figure 4. Schematic Representation of Nuclear Power Plant 40

Figure A1 . Tornado Strike Probability within Five-DegreeSquares in the Contiguous United States (Ref. 2) 43

Figure A2. Calculated Tornado Wind Speed by Five-DegreeSquares 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 dis-

tance upwind of the tornado center equal to the radius of maximum circumfer-

ential 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 maxVH

2. APPROACHES TO THE PROBABILISTIC STUDY OF MISSILE SPEEDS

Estimates of tornado-borne missile speeds corresponding to a specified prob-

ability 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 characteristicsof potential missiles, including aerodynamic characteristics; nature and

magnitude of forces opposing or inducing missile take-off; and locationand configuration of potential targets.

One possible approach to a probabilistic study of tornado-borne missilespeeds is the use of Monte Carlo techniques in conjunction with probabilitydistributions of the various parameters characterizing the factors listedabove. Such an approach would involve a volume of computation that is likelyto be enormous indeed. Moreover, many of the pertinent probability distribu-tions are not, or are still only poorly, known. The writers believe that anexhaustive Monte Carlo approach of the type outlined above might be warrantedfor long-term research purposes, particularly if significant improvements areanticipated in the probabilistic modeling of the various factors involved.However, for the present, it is the writers opinion that much of the proba-bilistic and physical modeling of tornadoes and tornado-borne missiles thathas evolved since the publication of Ref. i is not sufficiently wellestablished 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 onehand, 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 tumblingmissiles

.

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

specified

.

3. A specified number of missiles with specified properties andlocations 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, eachassociated 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 correspondprobabilities of occurrence consistent with the estimates of Ref. 2.

b. Each missile starts its motion when the tornado-induced aerodynamicforce, F

a , 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 Awill be hit by a tornado with maximum speeds larger than V

torn be denoted byPa(T) and Pa (T,

Vtorn ), respectively.

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

Vtorn’

m, fc) d it dm (3)

2

where Pa (T,

vt 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 prob-

abilistic 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

V T >Vtorn ) ~J

b/2PA(t -

Vtorn-

d* (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 probabil-

ities, Eq. 4 is written as

N1

PA<T >Vtorn ) =

^,

PA< T >Vtorn- Li 5 (5)

and

L. + AL/2

PA<

T >Vtorn. V “I P

AVtorn> dl

- AL/2

N1

b_

AL

( 6 )

(7)

Pa(T, Vtor ,

L^) is the probability of occurrence of tornadoes that strikepoint A anct have axes of translation crossing the segment AL, the midpointof 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 •Li>

PA(T >Vtorn> ( 8 )

Let now the probability that point A will be struck by tornadoes with maximumwind 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 fA , 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 Vtorn

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

Pa(T, torn ) = 2 pa (t. ^torn* ai^ (9)

where P^(T, Vôrn ,a^) = probability that point A will be struck by a tor-

nado with maximum wind speed larger than V tQrn , and with a translation axishaving 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, allthe 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 thattheir axes of translation will cross, and be normal to, a specified segmentwith length b. The seqment b is divided into subsegments. The prob-ability of occurrence of a tornado, T^, whose axis of translation passesthrough 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 offflcLX

these speeds be denoted by . The probability of occurrence of at leastone nit with speed V™ax is then 10 /Nj. If, of the tornadoes T^

4

(i = 2, 3, . . . Nj), a number q will be associated with hitting missilespeeds greater than V™ax

,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 alsotake into account the variabilities of the following factors:

1.

Missile set-ups. As previously indicated, it is possible to specifyN^ missile set-ups, denoted by S^, (i = 1, 2, . . . N

2 ), each set-up beingassociated 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 tor-

nado 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 esti-

mated as suggested in Appendix Al or by using additional information given,

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

n3

l P(Ty .) = 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 Designbasis Tornado at the geographical location of concern, . If

“in ‘Vtornll <»SSn. then 01 .

3.

Direction of Tornado Axis of Translation. Let each translation axisdirection be denoted by To each a- (i = 1, 2, . . . N^)

,there corres-

ponds a probability of occurrence P(ai ),

the sum of these probabilities beingunity.

The probabilities of occurrence of missile hit speeds when the variabilitiesof 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 tornadonjspeed, V™ax

,

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

portion of the axis of translation, L^, is

(vmax

)= p(L .) P (sM )

P (Tui )P ( an )

and a given

i jk a m Vk' (ID

5

where

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

1AL

(12b)

The total probability of occurrence of hitting missile speeds equal to or

larger than V®ax is

N1 NL N

iN4

'

P(v£ax ) = Z Z E Z P(Li)P(SM )P(T

y,)P(a

Jl) (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 standbyservice water cooling tower and basin, respectively^ are considered to be

important to safety and, therefore must "be designed to withstand the effectsof natural phenomena such as tornadoes without loss of capability to performtheir safety functions" [3], These structures have been redrawn schematicallyin 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 thepotential missiles are located before the tornado landing are numbered fromI 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 topplane 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 locatedbefore the tornado landing are those shown in figure 4.

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

:

-Lot I:

-Lot II:

-Lot III:

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

Two rows of 15 missiles each (distance between rows in ydirection: 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 direc-tion: 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 equalsubintervais.

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 variousvalues 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 andcorresponding 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 xQ

.., 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 previouslygiven for the basic case. (The modified number of missiles isdevoted by n, while the number of missiles given for the basiccase is denoted by n )

“Tne target consists outbuilding 9 only, rather than of any of thebuildings 1 througii 9 of figure 4.

The results of the calculations are given in Table 1 for three probabilitylevels. Note that Table 1 is divided into subsections, each identified bya group of three symbols. The first symbol is a Roman numeral indicatingthe missile type (I through V); the second symbol is a lower case letterindicating 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 anarabic 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 correspondingto 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, xo

- = 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 aresufficiently strong to hurl it with great force. The trend observed in sub-

sections 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 correspondcertain missile trajectories that do not result in a hit. Therefore, eventhough the speed of the missile at some point on its trajectory wouldincrease if k were increased, this is irrelevant from the standpoint of thisproject as long as the missile with the higher speed would fail to hit a

target. Another explanation for occasional decreases of the hit speed (forany given probability) as k increases is that, in certain cases, to a smallervalue of k there could correspond more unfavorable initial conditions for

some missiles.

Direction of Tornado Axis of Translation. For each type of missile, subsectionsof Table 1 identified by symbols ending in al and bl include in parenthesesand brackets speeds corresponding to the angles a =1° and a = 45°, respec-tively (as opposed to a = 22°

,which constitutes the basic case). It can

be seen that, for the cases investigated, the tornado effects are generallyless 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 bulkof 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 xq

.. = 60 m, yQ..

= -100 m to

xQ

.. = 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 reduc-tion (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 Vt

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

and Vt

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

..

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

= -200 m.

probability360 mphwith 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/nt

=1/8 and n/nt

* 1/50. This was done by reducing the

number of rows of missiles, and of missiles in each row, from 20 to 5, and14 to 7, respectively, for n/n. = 1/8, and from 20 to 2, and 14 to 3

respectively, for n/nt = 1/50. For the case n/n

t= 1/8 the effect of

the reduction upon the missile speeds corresponding^ to a given probabilityof hit was generally small, although, in many instances, of the Nj = 15

tornadoes assumed to hit the plant site (each having a probability of occur-rence 10“' /N^) at least one hurled no missile onto the targets when thenumber 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 missilehit speeds were found not to differ, or not to differ significantly, fromthose obtained in the basic case.

Influence of Target Area . If the only target considered was building 9, asopposed to ,any of the buildings 1 through 9, the missile speeds correspond-ing to a given probability level were generally reduced with respect to thoseobtained for the basic case, although in a few cases the reductions weresmall.

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 correspondingv-7

appears therefore reasonable to use for design purposesin Table 1 to the probability level 0.5 x 10”

,say, rarather than exactly 10

Missile I ("NBS" Automobile), Vt: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 forcefor an automobile would usually be of the order of magnitude of the frictionforce, i.e., k = 0.3, say, it is conceivable that some automobiles mightexperience some form of blockage that would raise k to higher values. How-ever, if such blockage occurs, it might be expected that the number of auto-mobiles 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 = 2.0from 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 missileI 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.

maXMissile 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 Vt n = 360 mph, except in the

case k = 0.3, when they are considerably larger for VtQ ^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 Vt

= 300 mphthan in the case V

tQrn = 360 mph. It is therefore suggested that for designpurposes

,

= 48 m/s for V torn = 300 mph

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

maxMissile 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 purposesit is reasonable to assume

Vra

" 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 thecorresponding values for V torn = 360 mph. Note also that, for k = 0.5 andk = 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), Vtorn = 360 mph : V

H = 46 m/s (Ref. 1)

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

m are higher for Missile II ("EPRI” automobile) thanfor Missile I ("NBS" automobile). The explanation offered is similar to thatadvanced in connection with Missile I, V tQrn = 300 mph. In this case MissileII will begin its motion from a position that is closer to the tornado zoneof 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 mphm torn r

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

maxMissile 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), Vt:orn

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

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

Vm = 45 m/s for V tQrn = 240 mph

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

maxMissile 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 VtQrn = 360 mph

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

niaxMissile 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 mphm torn K

i.e., 15 m/s less than suggested in Ref. 1.

m3.xaissile 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 Vtorn= 240 mph

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

11

Missile IV ("NBS 12” Pipe), Vtorn

= 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 mphm 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.

maxMissile 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 mphm torn r

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

maxMissile 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/sm torn

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

Missile V ("JFC-AES” 12" Pipe), Vtorn = 360 mph : V®ax = 38 m/s (Ref. 1)

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

= 62 m/s for VtQrn = 360 mph

This is close to the value obtained for missile IV

Missile V ("JFC-AES*' 12” Pipe), VtQrn = 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), Vtorn = 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 mphm 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 vtorn » 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

Tvk ^

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(Ty ) 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 tornadovk

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

.)P(TVk

) = p(T, Vtorn

Vk+1" Vk-1

torn = V,

For maximum tornado speeds less than 310 mph, the curve representing thepercent probability of exceeding the value of any given wind speed, includedin Ref. 2, was used as a guide.

The resulting missile speed hits Vm , and their calculated probabilities ofoccurrence, are given below:

Missile II ("EPRI" automobile)

k = 0.3

k = 0.5

k = 0.9

f

m= 47 m/

s

P(47) = 2.47 X 10 ^/yearr

in

= 48 m/

s

P(48) = 0.73 X 10 '/yearr

m= 49 m/

s

P(49) = 0

m= 58 m/

s

P(58) =s 1.44 X 10 ^/yearr1

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

r

m— 60 m/

s

P ( 6 0

)

= 0

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

m= 67 m/

s

P(67

)

= 0.68 X 10 /year

m— 70 m/

s

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 versus58 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 postulatedmissiles hit any given set of targets in a nuclear power plant or similarinstallation. H^t speeds corresponding to probabilities of occurrence of

the order of 10 were calculated for a given nuclear power plant, undervarious assumptions concerning the magnitude of the force opposing missiletake-off, direction of tornado axis of translation, number and initiallocation of missiles, and size of target area. One feature of the calcu-

lations that distinguishes them from those of Ref. 1 is that the missilemotion does not start from an initial position postulated a priori. Rather,

the initial position of the missile is determined by the condition that theaerodynamic force induced by the tornado wind field exceed a specifiedrestraining force specified via a nondimensional parameter k. As explainedin some detail in Section 4.2, the results no longer depend on the parameterCjjA/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 givenin 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/

s

= 45 m/s in lieu of 41 m/

s

t lieu of 59 m/sl lieu of 52 m/st lieu of 41 m/

s

l lieu of 83 m/

s

l lieu of 70 m/

s

i lieu of 58 m/

s

Missile IV ("NBS" 12" pipe)

Region I:

Region II:

Region III:

Vm

"

Vm"

Vm

"

65 m/s in lieu of 47 m/s60 m/s in lieu of 28 m/s50 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/sRegion II: = 52 m/s in lieu of 15 m/sRegion III: = 45 m/s in lieu of 6 m/s

The design values suggested above are tentative and subject to three majorqualifications. First, they are based upon climatological, meteorological andaerodynamic models that are uncertain. In the writers' opinion these uncer-tainties are extremely difficult, if not impossible, to quantify in the pre-

sent state of the art. Second, the suggested values are based upon a singlenuclear power plant basic set-up. Calculations carried out for a differentset-up might yield somewhat different results. Third, although calculationswere 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 limitedresources (approximately one half man year, including computer program devel-

opment) available for this project,

In spite of these limitations, the writers believe that useful new insightsinto 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 andof 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 NP-

748, 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 Probabilitiesof 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

107

x Probability

k 1.0 0.5 0.06

0.3 20 (20) 22 (23) 24 (24)0.5 27 37 430.9 43 45 47

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

2.0 62 64 65

aNumbers between parentheses correspond to tornado direction a = 1°

Numbers between brackets correspond to tornado direction a = 45°

Ia2. Influence of Location of Lot IV

107

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 64 652.0 60, - 200 - 40 65

160, - 200 63 64 65

ameters

16

Ia3. Influence of Number of Missiles

107x Probability

n/ntyp v> v a1.0 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

107

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 buildings1 through 9.

17

Ib * Vt 0m = 300 mph ^ VH

per NBSIR 76-1050: 52 m/s)

Ibl. Basic Case, and Influence of Target Area3

107x 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)

aNumbers not between parentheses represent speeds of hits on any of buildings1 through 9.

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

Ib2. Influence of Location of Lot IV

107 x Probability

xo"> V,a1,0 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

107 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


Numbers between bracktes correspond to tornado direction a = 45°

Ic2. Influence of Location of Lot IV

107

x Probability

k V’ va 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

107

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 * Vtorn

= 380 mph

Idl. Basic Case

107

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

107x 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 Per ^BSIR 76-1050: 46 m/s)

Hal. Basic Casea

107

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°


IIa2. Influence of Location of Lot IV

107

x Probability

k xo" » 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

107x Probability

l / ntyP V » V* 1.0 0.5 0.06

1 55 64 69

1/8 60 ,•- 100 54 63 66

1/50 - 55 66

160 ,

- 200•

i

-- 64 68

1/8 49 68

1160 ,

•- 200 64 66 68

1/8 63 66 66

1

1/860

,- 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 7x 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)


22

maxlib. ^torn

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

Ilbl. Basic Case, and Influence of Target Areaa

107

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—aNumber 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

107

x Probability

v- > v a1.0 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

107

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 - - -


Numbers between brackets correspond to tornado direction a ~ 45°

IIc2. Influence of Location of Lot IV

107

x Probability

xo "> 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

107

x Probability

k n/ntyp 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

107

x Probability

k 1.0 0.5 0.06

0.9 62 65 70

2.0 71 74 77

He.

k

vtorn= 200 ”Ph

Ilda. Basic Case

107

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 CR = 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

107x 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]


Numbers between bracket correspond to tornado direction a 45°

IIIa2. Influence of Location of Lot IV

107

x Probability

k xo" » y -

aJ 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 55 622.0 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/ntyp

1

V* v a

4

1/8

1/50

60, - 100

1

1/860, - 200

1

1/8

1

160, - 200

4

1/8

1/50

60, - 100

1

1/860, - 200

1

1/8

1

160, - 200

4

1/8

1/50

60, - 100

1

1/860, - 200

1

1/8160, - 200

10^ x Probability

1.0 0.5 0.06

40 55 62

40 55 6340 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

107

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)


maXnib. Vtorn = 300 mph (V

Rper NBSIR 76-1050: 70 m/s)

Illba. Basic Case, and Influences of Target Area3

107

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)

aNumbers not between parentheses represent speeds of hits on any of buildings1 through 9.

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

IIIb2. Influence of Location of Lot IV

107

x Probability

xo" 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

107

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]



IIIc2. Influence of Location of Lot IV

107

x Probability

k V’ y ..

a1.0 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

107

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

Hid

.

Vtorn 380 mph

Illdl. Basic Case

107 x Probability

k 1.0 0.5 0.06

0.9 43 53 62

2.0 37 54 635.0 30 54 63

Ille

.

Vtorn 380 mph

Illel. Basic Case

107

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

IVal. Basic Casea

107

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

aNumber between parentheses correspond to tornado direction a = 1°

Number between brackets correspond to tornado direction a = 45°

Influence of Location of Lot IV

107

x Probability

v> v a1.0 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

107

x Probability

l/ntyp xo"

»

y »a

J o1.0 0.5 0.06

1 55 64 68

460, - 100 58 66 68

1/4 61 67

1/16 — 52 67

160, - 200

' - 65 67

1/4 ~~ 41 66

1160, - 200

- 66 67

1/4 — 65 67

1 70 73 75

460, - 100 70 73 75

1/4 56 69 74

1/16 — 62 69

160, - 200

- 71 73

1/4 71 71

1160, - 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. Vtorn

= 300 mph ^ VII

per NBSIR 76-1050: 28 m/s)

IVbl. Basic Case, and Influence of Target Area3

107

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)

aNumbers 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

107

x Probability

xo"

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

107

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 xo" » y »

a•ô

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 52 532.0 60, - 200 - - -

160, - 200 - - -

ameters

IVc3. Influence of Number of Missiles

107 x Probability

k n ^ ntyp 1.0 0.5 0.06

1 45 47 52

0 94 46 50 52

1/8 39 47 51

1/50 26 40 47

2.0

1

4

-

1/8 - - -

1/50 - - -

IVdl. Vtorn = 380 mph

Idl. Basic Case

107

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

107 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 (VmaxH

per NBSIR 76-050: 38 m/s)

Val • Basic Case3

107

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 ( vh

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 correspondingt0 n/ntyp

= 1/50

Vc. Vtorn= 240 mph ( vh

3X per NBSIR 76-1050 = 6 m/s

Vcl

.

Basic Casea

107x Probability

k 1.0 0.5 0.06

0.3

0.92.0

34

20(-)

41

45(34)

44

46(46)

36

b/2 rr b/2

Figure 1

Schematic Representation ofa Tornado Path

37

iMBU.

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

1

0?l

MMo

do u•h dU dd rHMl CMd

<}• <D UCO 0)

OJ (1) 3M M Od a cmbo a)

•rl Qj HPm d

40

Schematic

APPENDIX A1

PROBABILITY DENSITY FUNCTIONS OFMAXIMUM TORNADO WIND SPEED

In this Appendix an approximate representation, consistent with the

assumptions implicit in Ref. 2, will be given for the probability densityfunction of the maximum tornado wind speed Vtorn at a location where the

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

occur is 10-7

/year. Let P(T) and p (Vtorn ) denote the probability that a

tornado will hit the location in question, and the probability that themaximum wind in a tornado is higher than Vtorn ,

respectively. Then

P <T > Vtorn>“ p ( T ) p< vtorn> (A1 >

From Figs. A1 and A2 if follows that, in the regions where, nominally,P(T, Vtorn ) = 10” 7 /year, the following approximate probabilities P(T) andP(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 geographicallocation, it follows from Eq. A1 that, at a location where P(T, 360) =10" 7

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

Q ). For various values of VQ ,

P(T, Vtorn )

will than have the values tabulated below

vtorn <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 - Pcu|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 thatthe tail of the probability density function p(T, Vtorn ) corresponding toP cum ( T >

Vtorn) be rePresented approximately as in Fig. A3.

Similar calculations can be made for regions where P(T, VtQrn ) = 10-^ for

vtorn = 300 m?h and Vtorn= 240 mPh *

Note that the calculations presented in this Appendix are merely illustra-tive. 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

434-1 •

•H 0) M-4

4d ai

4-J pdtx4-J d•H •d co

rH cu

•H CO 4-J

' 1 a) d<3 d !-< 4-J

43 d COCU O di-i cr -dd Ph CO 00

4J a) CO

CO n di o

O a) dT3 > 00d •H •Hd pH 4-J

d do oH o

43

125

120

115

110

105

100

mo mo m

r-»

CM<3

<U

V-t

dbO•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 x8. 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 NationalTechnical 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 orderfor that particular out-

put to occur.

<Module> is the name of the modulewhere the printing is done.

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

.

-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 basistrajectory.

4 (more than 3) Full output of each basistrajectory.

JPN, JSA, JHS

,

913 Problem definition indices.

JUT, HAM,,ITT, Note

:

These values do not affect the operationIAD, 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 theC^x^y^zj, coordinate system definedbelow. They are used internally to

locate efficiently regions wheremissile trajectories may intersecttargets.

)

XC,YC,LC = Coordinates of the point 0^ (inmeters ) respect to the origin 0 of

the reference Oxyz coordinate system.

0^ is the center of the rectangularregion that includes all the poten-tial missiles at their initial posi-tions. The system Oxyz is chosenarbitrarily for convenience.

LX,LY,LZ = Length of the sides parallel to the

°MX1> °Myl» °MZ 1axes meters )

respectively of the parallelepipedcontaining all the potentialmissiles at their initial posi-tions. 0MXj, 0^, C^Zj are paral-lel 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 hitregions numbered 1 through 9], For eachhit region:

NHRReal [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 thehit region. It is always assumed thatthis base is in a horizontal plane.

The 3 lines that form the corner aredenoted by 0^2 , 0_y2 > ®

cz2‘ °cz2

isparallel to the axis 0

zof the refer-

ence system Oxyz. The coordinatesystem 0

cX2y2 z 2 must be tight handed .

THETDX = Counterclockwise angle (in degrees ) by

which the vector 0X must be rotated inorder to be parallel to and have the samedirection as the vector 0„xo

.

c L

LX,LY,LZ = Lengths (in meters ) of the sides of

the hit region (hit regions are alwaysassumed 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 byk 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 unionInteger I, NC(I

)

13,16 of NC(I) component lattices. Each com-

ponent lattice has NX*NY*NZ missilesNC(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 are1

NTT

NC(I) = 4 component lattices, denotedby I, II, III, IV].

Real [ PTT ( I ) ] [5E12.5] PAM(I) “ The probability of occurrence of the1 I-th missile set-up [denoted by P(SM )

in the report].

Real, LUSER, RMXRTS, 2F8.0, 13 LUSER - Distance (in meters) between tornadoInteger 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 thatpotential missiles would be swept offthe ground even if tornado were at a verylarge distance from the site. (Recallthat the theoretical wind speed at thesite is equal to the tornado translation

velocity, even if the tornado is at aninfinite 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-thtornado type (in miles/hour ) [Denotedby Vtorni

in the re P°rt J-

“ means that this format is used repeatedly.


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-thtornado type, divided by 10~' [denotedin the report by P(T

V )/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 the1

NAD

I-th direction of the tornado axis oftranslation [this angle is denoted in the

report by a^]. AD(I) are the counter—[PAD(I )

]

1

[5E12.5] clockwise angles [denoted in report byou] by which the vector Oy must be

rotated in order to be parallel to andhave the same direction as the tornadotranslation velocity vector.

PAD(I) = Probability of occurrence of the I-thangle [denoted in the report by PL(ou)].

Real USXORG, USYORG 2F8.0 (USXORG, USYORG) = Coordinates x,y (in systemOxyz) of point 0 (in meters ) of segment

Real LPTTD, DELTD 2F8.0, 13 O'B. O'B is normal to and intersectsInteger NTD the tornado axes of translation. The

direction of O'B is such that the tor-nado translation velocity vector must be

rotated counterclockwise by 90° in orderto be parallel to and have the samedirection as O'B.

NTDReal [PTD(I ) ] [5E12.5]

1

Real HWUSER F8.0

Integer, TYPXBM, 13, F8.0Real DELXBM

Integer, TYPLBM, 13, F8.0Real 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 [denotedin the report by N^].

Note : NDT is same for all angles AD(I).

PTD(I) = Probability of occurrence of the I-thtornado translation axis [denoted inthe 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 orright width distances can be computedinternally (see comment for variableLUSER, Group 7).

Note : The left (right) widths is the

the maximum orthogonal distance (inmeters ) to the left (right) of the tor-nado translation axis such that a sta-tionary missile could still be moved(horizontally or vertically) by thetornado wind field.

TYPXBM = 1 (Variable used internally in the pro-gram, indicating a set of basis missilesequally spaced on a straight line normalto tornado direction).

DELXBM = Horizontal distance (in meters ) betweenbasis missiles.

TYPZBM = 1 (Variable used internally in the pro-

gram, indicating a set of basis missilesequally spaced on a vertical line).

DELLBM = Vertical distance (In meters ) betweenbasis missiles.

.] = means that this format Is used repeatedly.

49


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, DELZNX, NY, NZ]

1

I3 ,

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 withcomplete information about the lattices.There are NIAM sets of data. The I-thset of data has NC(I) descriptors. Eachdescriptor describes a component latticeof NX*NY*NZ missiles.

XCT, YCT, ZCT = Coordinates in Oxyz system (inmeters ) of one of the 4 corners of bottomhorizontal plane of the lattice

THETDX “ A system of coordinates°l

x3^3^3 isdefined for each lattice, analogous to the

system Ocx2Y2 z

2^ or each hit region

THETDX is the counterclockwise angle (in

degrees ) for which the vector Ox mustbe rotated in order to be parallel andhave the same direction as the vector

°LX3

*

DELX, DELY, DELZ = Missile separations in the

lattice (in the x3 , y3 , z

3directions,

respectively).

Description 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 theHeal

,

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 orderfor that particular outputto occur. If <Level> isnull the output will alwaysoccur

<Module> is the natae of the modulewhere the printing is done.

-1 Summary of all results0 = (more output than -l) Input proba-

bilities are listed.

1 j> (more output than 0) Hit velocitiesby distribution are listed.

VCUT = Smallest value (in meters sec ^ considerîn histograms of hit velocities.

MXNHVD = Maximum number of velocities of hittingmissiles being listed (starting fromlargest velocity).

DELHV = Interval (in meters/sec ) in the velocityhistogram.

NHVI = The number of intervals in the velocityhistograms starting from U.U.

i»ote : One extra interval is added at the higii

end to handle any velocities exceedingthe velocity interval of the last bar.

Ill

X

o 1 K aX < 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 ucr 1 1

ta- 1- »-4 z X z Q > Z X a < >-• u.

o H 1 z z X •— < X K h m »- *- H <• 3o Z 1 at « 44 j z 1- K i- X < - 3 in z CD

a UJ 1 < X Oa Z

1x 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 za i

M1

»-• Hi < 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 1mt 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 mlCD -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 UJo O a 1 i UJ o X o t-

a z a • 1 i X tmt 0) UJ X a I < ”> z3 in 1 i h- u. I V UJ UJ o > u X X X X UJ XU z < UJ 1 (A < UJ a IL h* 19 n L- (M X < a: 0. X 19 X X K N X os —

*

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 zin 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 XW I •-* z 1 U 1- o o o X Z <u k u f M u. K z n a #-/ 1 a o z Xo 1 o n <1 1 IL < u za.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^Biesirô - eg "i <t it u> r--

3 -.-----«-^^(MN(\i(M('jMNMWNrinnr)nr)n'nr^n<»4^«^^<f<f<t*jiiflifiiniflininin2

10 52

-J<

u<

>z<

a Z • • (/)

mm z z za 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 MM CD IL V) m- a < < IL u_ fc-t aO cr z 5! IL K- to or cr z < K M a i- or zZ < 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 zIL H IL Q i— Q u. Ho U z z O u z o U z

UJ MM UJ UJ *-M UJ UJ Ma: 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 XD mm MM DZ Z 2 z Z

h- U) wz -> X Xuioii/iiu. m t- _j a

UJ

at/> u.x

J *- -J

U. IL Z IL U. V)

M *- O t- - Xaaaaaarwwwi/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

< <r1

D • at- CO cc zUJ z < t-H X 3T< o < < <

MM to X z au. h- H-

o O U zCD 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 K1ii»lD ^ o o o o

•ONJJOO-'\l*)tfiO'CStOOO-N^<fifl'OSitlOvd'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£STCoooooooooo O - « n If

53

EFFECTS

APR

AYS

IN

MAIN

CAMLCBM

X

in

in

<CP

L-o

N

z

z in

D -Z X

Xa a -j

h I I *)

z x x aa z x kj x z y

•

in

UJ

uz<yV)Mo

zo

<_Jin

z<a

i

L

o

(X

UJoXDZ

>z<

UJI

ozoJ<

y • in

O cr in UJ

a o UJ -Jy 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

 a z a t- f y > o FH cr Ja 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 Uin z a u f in in z f in z a F F F F U W in zy IL in F U. F u. Fu z z Q u z o <J z Z o U ZUJ 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 XZ CD Z Z <

o o(\J

ooin

ooo

ii it il H il

yCD

-1

zXX

oyzXX

cr

KZXX

KKzXz

XCDXzXz

* * *

UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUIJUUUU

54

MXNYTN

=

100

NUMBER

OF

Y

TRANSLATION

INTERVALS

k kUJ 44 UJ Z to

k k tr X at a •

o -v 44 UJ < o UJ Ji

n

• < 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 UJ2 z — z M < k o u. k a k kUJ < tu o (0 X UJ (/) u o *4 < zk X N 44 10 33 a k u. X M< u 33 k « u. *-< o X CL kh* in < x V) a b. k u UJ Ul z© UJ X y- < u • X k oX 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 kk J j u. < k M I u u. k << © o 5 z Z u. u. o k 44 M U JQ UJ o i i— UJ • o U. a 44 * a UJ (0

D a k CM X o * w z to 3 zZ 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 kk D » < x UJ o k X 10 IL to oUJ 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 Xu X < cr a Ul a: tr UJ < cr t3 3T UJ UJ ua 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 UJu O

in kcr UJ

U.I X kk k in

UJ z>

2 IL ->

< «-• nX < —

.

< Q u a <4

a U Nl i15 • 4-4 z +

UJ Z z to UJ X Z© < o N z a X kUJ X Mf V) X X kx u k u. • z z zk < 3 <0 X X X

UJ 2 m w s 2 sk CO cr

< oX k lLk <0 Z •D CM * * —* *-*

(0 2 .j w * * *z z cr k w v?» w< o o UJ UJ z 3 zUj z *-3 u. u at X k2 <f in < u. u. t- >

z z 3 to u. J u.* UJ aj X k-J M

2• *3 » — A . A

UJ O z a 4- tr w

a kk to o to «

z UJ • Ul o 4—4 UJ o JN4 > J UJ J u. -J z UJ IL

o < «r to UJ in UJ • o kX < > o Za UJ > UJ J X D o I o k in UJ —

<

J tr to O -J ** u UJ k V- 4— h* (/) 0» X J z Ik UJ ta* k to < o (/) X I a *« 2 u o kto k k to to to UJ k N4 z tr V < 2 <c < UJ M •—

i

< < Z < o (0 M 44 UJ a UJ h» V UJ J KJ I *4 ID UJ (—1 X u. O X J i o J in J uk o X a UJ u k K CD < o X in u.» in

UJ Z UJ UJ J to M k UJ U 4-4 UJ D 2 k* in n UJ

I k o I UJ _1 < to to X < C3 UJ to T k < M *-« o -j

k a k z < 3 UJ < 3 X O (0 y- U X ji 2 cr •-4

o k 3 k k a k < o < a IT

IL k < U. to k U < f- UJ a a u. z o in in

a U -J o _J O < • Z a M z to o IL k-« UJ —

*

X •-4

Ul to UJ < Z 4-4 o X o k < O k- in 2to 3 z to > k o a k U u. in in < < 2UJ < <c UJ UJ _J z a U UJ •< UJ a cr UJ a UJ QJ Jo a. a u J J UJ k o UJ z z o U d k- u 2 <y- k k < cr 3 o > k* UJ z in IL kX Q < o O *-« DO Q UJ a (D u h* a o z Q a z in UJ z k-

z UJ k z J UJ 3 1-4 • X D o u o I Z 15 *-< in tr *-< OM X J U tr N -J cr a k M u kH Q < tern 2 <k X to o k UJ o a 10 k H tr X a D

UJ U UJ 10 z UJ to UJ > B CD < U < UJ u o 2 O U -J

X U. < I t-t < I i-i I UJ D o I LU UJ X < o < UJ X -J

k o UJ k * I k a k -J < in k k in to UJ u N a k* <

CM

+ +

z X X X 2k CD ID tr CD Dk J J X J -J

Z Z Z z Z ZX X X X X XT T X X X 2

# ** w A w

43* # in *Z * X W ah» 3# 2 in k- 25k 2 m J z X-J <Z < 7

rr

x<

UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUU

c D OD O' c 4-. «M c in £ N CO o r4 M n 10 vO s © O' e *3 CM ro in 0 s © O' C CM in vC k- f 0 O' O CM n in v£ N © O' oN N N N k r*- CO a. 00 © QO 00 QO CD © CD O' 0» O' a O' O’ O' O' 0* o o O O o o o o o o P3 w <3 — —* *3 CM CM CM (M CM CM CM CM CM CM n CO*-* 4-. *-• *-* -3 —

*

-4 -* -4 — 3* 3-* CM CM CVJ CM CM CM CM CM CM CM N CM CM CM CM CM CM CM CM CM cv fvJ CM O' CM CM 0. CM CVi Ck- CM CM

55

UJ u.

-J ct V) UJ UJ o-1 < UJ u u< j z z to to

> UJ • UJ < to UJ

QC UJ to a Z a I 0 co

O X to a o a toIL H to 3 to 3 19 Ul to

• X U to U UJ a: Z X ZJ K in • u U y J o to to UlUJ a z J z c UJ o to to a a> UJ o « o a 10 U UJ aUJ u to* 3 to* a to U. 10 UJ o J 3-1 • X w- a K o o o to > a • a >* z Ul U. Ul

< —

*

to* to < to J o a o XQ - * o a a to J to < • to toUJ K w a o k -J 3 J 3 z to UJ IM

< -> a 0) M 13 to to o < X Za a a to* ID Z 01 V to to 13 to

d u. X X UJ o « < < < K 3 zu o X C CD CD D X 1/) to (0

u z X X I O I O X CD (X to 10 UJo W X 3 3 u a u a u to* UJ U < J

UJ X Z < a < 0. < QC a UJ UJ MX J UJ to* UJ UJ Ul b -J a (0

u o * X UJ UJ UJ 0) UJ a o (0< z to* « I z X IL X IL to* X Ul z to

UJ < J X to ** to o to O o to a 1—< X

-J(3 * UJ • o (0

Z 3 X -j UJ < Zto to h- UJ CO X > ocx U > 3 CD MUJ < X UJ to

Q H -1 o CO a C3 U <a a UJ to* to to o Z UJ to

o o X B UJ H — (0 M ato UJ to J Q X U a I oU cx o to UJ Ul UJ UJ Ul uUl a UJ (0 crt to > a I i <> Ul o (0 CO I a to u i

• i < to « B z o < a uin z to X to* X a o UJ u. UJ to aUJ o u to to* a o <J to 10 <3 o co a M K to 13 UJ tto* to to z m to o I < UJ to a Z eo to

 to a co N* UJ o UJ

(X UJ a UJ to to UJ to (0 3 a UJ -1

J UJ QC u J Z X 3 a CJ < < id u CD

< a z to* UJ a O Ul Ul a UJ <D to to* in QC o a < J a to a u. (0

H UJ < in QC * CD u u a a CO

U i X > to* 3 3 in UJ z U. o 3 o< to to ffi X U < CO < QC O u CO a

ID UJ UJ

UJ • UJ I z a. uu UJ u to M < z UJ

z u z < J < CD

Ul z Ul a > UJ J •

a « a a UJ I in UJ z >a a o UJ i k- ** > < cr

3 in 3 a to k o O X Q ft o a Xto J to o to a < —s o < o u.«— in < o Z « UJ K z k < CD

J z J z IL a W I • aM < l—

1

a O to o X K a X o X u GCD cr CD u a to K z D to D cr

< k < to X a O o X X oCD CD to J X * K _J •* I to* LL OO X O I O U J z O z UJ UJ

a u a CJ •—

i

a < K in a to* < to* CD aa < a < B X lu X a X a X

Ul UJ to UJ K to UJ -J

UJ UJ Ul a O Z UJ a UJ X ui U. i u I O o ** to* a I o X to* UJ

to O to o to to a J B u h- a K b- c

CD < o < X X a a H to K K_J to* < to* < * w-> X z in *to X X Q Ka * # # < < X * # K b- K >X w w w < o X w w Q o iny X o X X T a a K B B z zX < < < a cr UJ to K J cr X X.

X z a CL a a a a a K K b- H

* cr a cr cr a a a a cc cr

UUUUUUUUUUUVJUUUUUUUUUUUUUUUUUUUOUUUUUUUUUUUUUUUUUUUUUUUUUU

•n «T. 4* N •r O' o r\J in N CO a o to- OJ <* in vO N CD O' O •* CM ro <* in N co O' o to* CM n in o N co O' O to* OJ ro <± in <0 K X O'n n n n ro n <* <r in rn in in in in in in in in vL> VO n 4) 4) 4) 'O to N s N N r^- N N N s CO CO <r CO 00 00 CTi ac ao QC'

nj nj r\i Csj rvj OJ 'VJ nj OJ OJ cu OJ OJ OJ OJ OJ OJ IM OJ OJ CM CM CM CM CM CM CM CM CM CM CM CM CM CM <M N <M CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM nj CM

56

9 a z 9 XQ CO Ul UJ A X or UJ z a o Z X a

> UJ UJ a z N z or UJ I < X o «« o cr T «J X 19 Ul UJ X X < »-4 UJ M I K a L u. C9 1-4 X cr U

PO UJ -J < Z a or < z J a CO Z J u. t- z • < o Ul CD z o < >I UJ G a < < < Z UJ >- < M *-• X b* U a z CO a X X cr X X

o b > o h- UJ or Hi & UJ UJ if) w X X 10 UJ o M o > UJ CO a o o a < iz -J b X or > > n a X X i < X h* LI 19 t-l X 1- UJ c- u o a? o h< X -J UJ CD V1 • X b o X 9 b lL X X > X o Z < a bb u. I u UJ CD z ao (0 O < a I o a X cj — UJ J a a B X Ul o X *-< (0 u. K c (J o X X z o X*-* K UJ > o K1 3 UJ X b CO X UJ UJ b J Q h- — t- a a a z b J X H X c — ub Z or b o > a x X to b > u if) (0 CO (0 or z V I M X o o — Z CD b X Hi C

9

X*-<

LIJ 1- UJ u X 6 a UJ UJ UJ Hi UJ X UJ UJ X X X X o b* a X u o H a X a b CD Ul XCO Z < »- UJ O UJ o -J u u O y X J UJ b J b u b J u o »- O X CJ UJ z O a UJ X cr

o o z -) a X a X • UJ b 9 < *-4 < < < t-4 0 a H z X e Q > o X o i X a •

Q a UJ Hi <r <0 G UJ cd UJ t

o

UJ (0 y J Hi Ul A CO Z (0 a X z CO J >< O — z CO N Z o a y X i- o H * to

T -J x UJ O X z Ul UJ a * B J * UJ >-4 CO [Li M CO X o; 1C or Ul A X < CJ y a bb K — W Xn O H4 UJ h b a H H4 A b A K o G Hi Hi b o M z b o NH > Ul UJ z * h> W o o (0 UJ X f-4 X X bu co 3fc < CD V) * < * < cr z X < a z X z a > o W < 2' -I o X X CJ I b <

UJ to h4 UJ z Q < Z Hi Z to U UJ (0 if) z o CD o J u. or o o a a Z u. O < CO b u. < a zi >- *-* >- X H4 U) Z UJ y Hi I t~» Z < b Hi X *-« a CO CO o CO o a U y X H4 a J- m X z < a X CD z i Hi

k b y K n UJ < a < o < o < < y < o u -1 o X u »-4 X u a c CJ O H o CJ < Z Z UJ u GHi Q a J u X a X a x UJ Hi X a (0 b J CO z 10 c J u X a (0 O j < a «-4 10 y H- z X a

io u (0 UJ O o Hi -J z o o X X u (0 o X < 1-4 X < X * <t t- < o X o X H o i- o cc o oo c i=t <J z o CO UJ i UJ o Ul a X o Hi UJ G X Q CO X o: CO X X o u a z b X a X cJ J to < o u <0 > * u * u UJ <0 (0 X u UJ U (0 X a Ul UJ o u u o UJ UJ G X o bb b > 2 * uo X' < CL J H4 UJ > *-« X X Lo < M X u. CO M X X G J X I J < Hi J I I z X o o o o O «—

r > CD <0 < X y _J CD -J > -J N X o < CP J >- h- o G y b o 0 CO t- o UJ X > CO 1- h- « K u 0 m u CJ V

A A A A A— «—4 Pi -* -*

+ •f 4- X +

CM CM z a cr cr Xa X X X X Xb 4* 4* z z z z zz X X X X XX y y y y y y yy y y y y y CD CD W w V w Hi

< < < < < X X* Z z z z z z z * * * * *

i X X X X X X X'O y y y y y y y <t CM

A A A * ** * A * A A A Hi W

—

*

A A A •w w « W * * X X* * * * X X — X W Hi Hi H-W 0-4 W W h- b y y a a X X X-> y T y T y * m r X X T ra < < < < N X >• X X X > N X >

Aa cr cr cr cr X

OVJlJOUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUVJUUVJOUUUUUUUUUUUUU

& O' if Q' O' O' O' O'f\j CM’ CM CM CM OJ OJ CM

®0'OHfMnînO'O'OOOOOO(MCMnrnpnnnro

>CNCCQ' 0 -(Mff)OOOO-* —

r'orrnronr. n

Î/1 ON 0) 0'Oh(\j

ponnnnn.'onr^nînoNaro'o^(MCMCMCMCjCMCMnnnnnromrnnr, n

n n n r. ro ro ri ro

n m ro r> ro ro n ro

o-*<Mfo<tin'CNronnwr^rr'o

57

Ul UJ IL cn o F CL UJ

a cr o F Ul < UJ u X U. b< < Z cn a X UJ 13 in M UJ UJ o z

>- UJ M a. M UJ F X Z m F a a »0 UJ

LU > < -J UJ >- J o UJ X F F b M in UJ M < c X u. u ob u X o > in b u i z a y UJ J U z X < T < > >- o < a

< b a in < b < J a < F u C3 a M UJ K J X z z Ul F UJ UJ UJ zu. LU H o «-< LL UJ in -I * z X Ul o < IM o i Z i X in oo • b FF b Z o • b z X < Z j + z < X in F i

n

z cr a M F UJ b b X cr uz J a z u z J a u J n *-< D > u n UJ < F a I 13 • u Ul z a z F in O UJ o a a cr a a J uJ in cr X • < in J in a X • * X II! F F UJ T <r < UJ < Nrf I u a z UJ UJ UJ ID CD in

 a < < k UJ UJ in a o F a UJ UJ o K > O X UJ I o u CD u ID a UJ> 2 b UJ a h- CD > z h UJ F o O 13 F F in z in o V a X U) X Z Z y y oa w UJ M a: Z z z > H F F a < cn O z o z o 4 F >0 cr < # Z Z o z in UJ

D > u L- -> in M D > o K UJ Q F O u V) Ul F O u F u F UJ Z o Ul w U w u u. UJ uZ cr *-« > X < in D Z CL FF > N J z < a. F UJ M F UJ < F«4 UJ b UJ u u in M in M in z u <•— u K z cr F O ff U K Z o o F I « Ul »- K < X < •— u. aU -J X 3 a • *-• u J N D < w O m X _J UJ *—

1

u ID J w J Ul FI z z Ul a u < UJ < UJ a h- dZ UJ (/) Z > in J z UJ in Z UJ < F X o o in > in z o o o UJ z UJ Ul < a U h* U in

z UJ *-* i tu -> z UJ I a z F z F a F z u z 3 z cr F u (C Ul u. UJ UJ UJ

LU < < X X UJ in u » UJ < < X X u a a W a < o UJ U> < F < U) o D C3 Ul o z u a X o X Q UJ cr UJ »-

r cr a < X < < UJ X a a •-« < < o o 3 o (X Z o i 3 a o a U) J o Ul F J 3 < D 1 F-l X X F**- b J z b cn UJ J b b b J z UJ <j F X u. F M V F Z b F < m Z u in -J >- _J N b n b I

a a cr Xi X i Iz z z z

z z z z z X X X XK H an *- h o a z z z z> > J > > < <z z z z z z z # « # *X X X X X X Xy y z y y y z <0 VO >0 vO

** a F>F

# # * # * * #w w w w w # w F» Wz z z z z w > # # # Uu

h- J »- - > u. W w W H>• >• > > IL h in in m in7 X cr z X K u. X T T Xz z k z z a o u. LL LL u.

X > N N • < < < CD U <z

—

*

FF ocr cr a z cr cr a cr

ZOu

<ÛVUUUUUUUUUUUUUUUUUUUUUUUUVUUUUUUUUUUUUUUUUUUUUUUUUUUUUUU

•t 'T o — (vj n <r &<t * \r. it m in it u,*) rn m m *o m n ro

*0 N a T c ^ CVJ n <t

ininini/i'CiO'U'n^'^nn^'om.-n'nn

n\nînao-«f\jfnnnrnr.nnro

n<ti0'i>sooa'0Nh-NNNKNCDnnrnnrrnrnr)

-Mnîr.'ONojO'QOCnoOOOGDCPQOOOGOmroronromrnmn

o -* cm ro < in v(71 O' O' O' O' O' O'ro rr) ro m ro ro rn

Ncncro-rvjn<tinU'U'O'OCOOOCronro^<t<t<j<t<*

58

f3FHSTF<*>

6

*

MXNHR

LIKE

AFHSTFI*)

EXCEPT

THEY

ARE

® ZUJ

O “

wx -t- i

LU UJ

X I

z- IW O

<

<J D(/)

z «<

a aUI UJW K

aou. iu

i/i <UJ UJ

H< U.

UJ t-

I “J- X

IL Ka

y -1 U *-4 < y cc z UJ y UJ H a z < o z a UJ H y <D UJ y CC• CD o M cc UJ a z UJ UJ a y CD X K y cc u M u X X z a o UI

cn X U UJ O > *-« a •-< < h- a V, < H L- u u o UJ IL

X O IL a u a a a >-• QC u o C O CD UJ a in u. a a o < a u z <UJ UJ 0 UJ u n J cc o C3 o • o IL X Q M 2 u o u a UJ UI J UJ T X *4 ycc CO y o (D D D y z J z < X UJ z o < 3 u u CD a UJ CD

2 D u LU cd O u UJ CD U il* o UJ Z < *- UJ o u. </> X X cc u yd y o UJ o I ** UJ < > cc - X 3 • h- y o > > UJ X <0 1- CD CD UJ IL i # CO o I

o X CVJ x <r y X CP o o UJ < K CD u <-* UJ UJ 2 u w UI y yz K o j < y o UJ z z z X Q -J o « UJ >0 UJ X * H * L- CC (D u u *4 > cd z < UJ cc X w < w < o UJ UJ K < UJ y»-« UJ z y y a < N4 a y z a UJ fr- u. t- >- CD Z CD z (D y (D z -> CDy > *— 'C o -j cc o u. y o UJ •4 UJ CD D < 2 CD < z 2 o o UJ X o o o 1- Q l/l < o Ui<-« o CC D < U. X “> 2 J *-« UJ z X UJ D z cc 2 K u X a UJ o UJ o CC UJ li- UJ o -i CCo 3* CD O U. a < K cc u X J cc u X CD o o o CD o u x X u X u UJ O u ce X u -J

D u JJ D UJ a •—

<

UJ UJ < *-• o < < CO -1 o X > J < o •~4 X O < D M < UJ

y < <D o or vT (0 CD y X Q o 2 2 h- UJ y < < u LL CD n UJ u J y -J N y u u. CD J V CD

cc a cc CC CC CD M IL UJ y* X X X X X Ul IL J X

z z z z z a y *•« <X X X X X y D U- z

y a 2 2 2 2 2 D a. »-4

* y y a y IL* CD

z Z * * # * * z D L3X X o < Z2 2 0 4) vO X —

o o o •

cc cc y Z 2< < CD UJ <

•-* o o y cc* —

»

* * z z CD y o* —

»

w < < CD « aCD * * * * LL u K y < a xX W > w w w y y CD CD 2 ^ au. > U ID (D CD CD CDUJ UJ y X X X T Io o a IL u. u_ LL ILu CD y X y N X y

OUUUiJUUU<JU)U<JUUU'-'UUU'->'-IUWUUUUJU(JUUiU>JOUUU(JUOUIJ'J>-J(J(J(JUU'JUUUJJ'-l(J<JU

COOO->rtrtHrt»rtH-rt(\|NW«ftJN<\INNI\inni'l <t in >c !-

r> n m "i9- <t » <T

eo'o«('!"i9inoNo'jc-n; ,)<»iJiflKooffo«Nn

59

k 1 1 1•

V M1 1

•1

44

CD X o 1 1 u 1 oUJ z • UJ 1 1 <

1 ©z Q < (0 Z • cr CO 1 1 k 1

44

G UJ k k 4 z o UJ 1 1 UJ 1• w

k o UI Z X < u. z 1 1 I 1—

*

z*4 < < z z te4 k o k- u. 1 1 • • CD 1 CVJ • >< < *4 o k V) z o z UJ 1 1

A • *41

W A o zz O k o G z X UJ Q 1 1 o o u. 1 X CVJ CVJ z

u O o V a z 1 1 'O VO k •1 X © W N

UJ IL < (0 a u J UJ I 1 1-w *•* y Q 1 CJ o T

X O k z UJ »- u 1 1 u. l

L

> k 1 N —

«

-J •b UJ z X UJ j < < 1 1 k k z M

1>4- “) 44

k CD UJ u X o k- z 1 1CO (0 • CD •

1• z X u. o

o LU z - CP X • < k » »

1 <* X T Wz O G < z z UI k- IL 1 1

««» > o UJ u. IL 1 w • CJ zcr UJ 1 k *4 z 1 VO k • k • U. u 1 y CVJ *4 co 44 5o UJ M k N4 k z M I k 1 1 IL *** w if) G LL y CD 1 w w -4 o Xu o X < k UJ o K b 1 1 k u. U- < k > 1

» X o w oG o < O g if) o 1 1 a k k • *< • y IL • • i

a k k z CO oo UJ < k k* CD 1 1 k CO if) O z > k IL IL 1 o X < ~4

k I z LL z X z < 1 1 I I if) • < * o k k 1 B N W ok *«* UJ k G < X •U t t • u. X k t-* u • k co CO 1 w X • z o

o a z < h- k I 1 1 a X < m k mm LL U. I I 1 X k < -4

IU • X G • g J z (/) k •1 1 O CO X k • LL IL 1 I © 44 < W

a z u O g < 44 z k (D 1 1 CVJ » • k » X > X < 1 u • CVJ o z zM G «r V o G CL o U* k 1 1W X • k • > U 1 X 0m. w o X k

G cr Z z o Z u o < k 1 1 > o o X Z Z if) k 91 o c CO X y

O o z < o a " if) 1 1 IL VO VO z < "> if) • u. u. if) CO 1• CVJ < — z

U o a k g u Z z k- o Z u 1 1 k W w X *-• < u k o X I 1W X w • z

or kIDj X < z u. N D M if) 1 1 U. CO (0 »-4 # z k o < IL iL 1 OJ X z 44 X

o o k UJ UJ r-l k a o o 1 1 O X I • (0 if) k N U 1w k • < o

co Z z k g G X o k W k < X k 00 1 1 < IL LL CJ • I •1 X o 4^ y o •

< < < < IU z u z O X Z) z < o o 1 1 N U IL k n < • • > m •1 z B o 10 44

-J M z if) UI < UJ z u a UJ G ^41 1 • X z LU o U. U. if) CO 1 CJ -J CVJ • •4 •4

co a X a o G CL z CL < k I Z 1 1—

*

• • *> • X CO k k I X 1 N k w 44 —

t

cUi u a a UI 44 UJ o z k < X 1 1 o 0m, • < < o X tL IL 1 k o IL oN G < o u. UJ u. *— a a •-* C < k n UJ 1 1 CVJ o o if) • CO » y < y OD 1

• • > o k o— C r a z UJ z </> rsj CD 1 1 w G vO if) U. CO • CO in 1 k CO z w1 X > •-* a g *4 a *» o z I 1 1 > w 

1 4 a X < CD a UL CNJ UJ u 1 1 IL (0 if) z O •> • < X IL > co if) u. 1 CVJ z w y X1 y z < UJ g UJ UJ o u X 1 1 k X X k z X X k UI X I UJ 1 X w k z k

< IU (0 X < Z fc-4 • UJ < 1 01 X IL IL • • a Q z O o LL U. o 1 z k < •

o X J UJ to k z J D u G z 1 </) 1 < >- CD < • < -> U X X if) X V \ \ V 1 o • o-J ac k UJ z G < UJ UJ < a vO 1 w

1a <•% CVJ < O X X X X 1

• • CVJ 44 10*4 k a 3 z *-» a z X) Q D • CVJ 1 *-

1 o o o w > • X a a X 1w CVJ —

•

Wa co O UJ > y Z X a X z 1 1 < 1 CVJ »0 o if) • z CD n CJ CO 1 <* o o CVJ 44 uz G aj cr k o X Ui O o «4 «4

1 a i W w w X i3 • X X CL UJ X 1w ••4 k w iL k

o n < z cr G z u u -J k <VJ i < 1 > (0 (0 X < IL X k > X 1 X w (0 z b Xcj o *-< z k UJ o o u < o z 1 J 1 UJ I I UJ X k \ N V \ 1 z z z X Z X

< <o *-• CO cr IL > a z X z z u UJ l <->1 o u u. o CJ O X 1 CJ < z CJ < CJ

IL *-• UJ o —

*

k 1 UJ 1 CO X ar a k k t-H I *4 CO < 1 O I o o a o G 1o —

<\J a Z k co o X o 1 1 J J UI z z z z 1 -J

LL < UJ < < ro UJ a 1 Z 1 < < k z z z z 1<

l; z u Z * w > 1 U I UJ UJ z a a o o 1• UI

r i y i X X •— u CJ CJ u 1 UJ X•

1 Z 1 * # # * # # * 1 o * * * * *> 1 O 1 1 ocn 1 U 1

i i

1

1

G

g o v u u cj g g G g u g u u U u u V u u u U CJ u u ui i

U U <J o u u1

(J CJ CJ CJ

* -0 h* X* e © ^4 X •0 <» 10 0 k CD c

^

© CVJ f0 Ifl yC k X o ^4 CVJ n <) X k X © © *4 CVJ ro <* X < k X © o P4 CVJ ro 4 o V0 k X © c 44

•u 4) o u 'O N k k k k k k k k k a) co X co X 9 CD X X X cr © © © © © U 1 © © © o o o o o o o o o o 44 f"4 44 44 *-> 4-

•

-4 —

<

44 —4 CVJ CVJ

<* 4 <* <* <r <* 0 * <* <* 10 ID X 10 X X X X X X X X U) X u> X X X X X X X

60

a S• o K cnA o X X •

•H IT) X z X*4 CM y <««r w) • • X*5 a X o Ga UJ “> N O K X My IL a • •m z <J LL y a • W -J O

-* D Z X X X • -> JCC z y < o <

• > y z < • X 9a • X • z J X«-« • X X • *-» K«-< o U. X —

*

•w o y e» o H X *> » Jo O a 9 o y z Q £a y X V) •H z y < •

y z z w * ”5 N na. y * h- •> z • y g cr•— y IL z u y x y • b~

X y X > < •) a 9 IS’ o c* J >*4 X XN < o 4 z • u <

CVJ U < 2 z a 9

c » * < o 9 s> < go a J IL M —

»

a J <f4 ro u h- o X z J e> *)

w w o f-* 9 o z G zJ V- y X X r-< X •>

X CL < * (0 > UJCD I •> • z J y X uu o > > y UJ X * s: <X » y X > > z J f-4 IL

««, 9 LL UJ "•>

9 o • • X *-4 -J • 9o 'G x < a K < z •

<N X_l

UJ .

Q Xx

X 7. J-

Z 3-

* Z• Q II « -X ->

- •- Xz 0u

9 Xa

cr X 9

s: u Xu N CD

N X• Z

9 aa «•* X •X u au > y X> y z

z o 9 y9 X y cr X

cr y a X Xx uu o 9 X •

X Q a a—

K

y y • X9 a X (/) z y z

CD r < z (0 ya u a X • a zo N y o o Xy • <z • X z y •

H a < y iX z 10 • * y

• u a o X ay » o a CD *

a X 3 o J a jo 9 < y y Z y UJ

X cr z X Oz X z 9 y X • »-H u y Q X

X • y < • • y •• X a Q. CD X' a oZ • < a CD ? yy a z • • o X J> i X y Q X z y •

-J z X y < z X XUJ z Z y X • 0

* *

IS (.9

U) UJ

z z

II II za

3 3 U--03in u) m

or

aH I

3 I

a i

z i

- i

j -j _i _j -i j _i

_i _i j j j j _J<<<<<< o z D z • • < 9 • • 9 UJ — a • • o u U. i

X a (

*

> o ® • y z V X X X X -J _j -1 J -J 9 • * * H J Z —

*

Q -4

X a a < J • X a (0 X o o o o o a UJ 9 UJ UJ UJ _l J _J -J Z 44 -4 0 1

G v » * o 9 X fXS y a X o o CVJ o o > J > > > UJ UJ UJ UJ •14 a

• • X -» X <0 • z> < X o o 0 0 0 o UJ UJ UJ UJ UJ > > > > • X I -4 *4

—

t

-X z UJ X o G IL 3t • (VI 9-1 e-o —

»

e c J > -1 J J Ul UJ UJ UJ o IT y • o3 o y Q X y o L0 CO y X UJ CVJ J o a UJ a a a _J J J -J < _J < UJ » Xf\l > z CVJ X 9 9 m u N X X X X X UJ w -J w w a 0. a a z z a V3 D -4

•w * « u V* U) » X X • a < co X X > •H o a — — w w • O(0 z © U- X J G 0 0 CK z z X U» UJ X n X u u UJ y— X u. w u. a IL o 0 w

a X y < y 10 < g -J y Q UJ G N X 0 a 0 < < o J • CVJ UJ UJ o: y UJ UL u IL IL o -J wX X y X X y -J -1 '0 z y z *-4 IS H 0 CO <r J y X X X G - -J o UJ m y C UJ UJ UJ UJ < ID yX a -j -J X IL Z z z z w6 II 1- *-« w 0 m y H J Q O o o Q z > UJ <z UJ 0 D a a a 3 a a D X X X X t- M z 0 o a *4 — 0 X H- o o X a UJ y XX a n Q n UJ UJ UJ < Ul UJ 0 X T X 3: y — w y a a 0 X X <c K < 1- 0 o -J *-* a

a a— 35

V u u u u u u u U U U <-J o

A] ro 0 C N 0 c- -4 CVJ 0 0 a y 0 a o -4 CM m 4- 0 0 y CO a O CM ro 0 0 y CO a o ^4 CM ro <* 0 0 y co a c -» CM ro 0 0 y oc aCM OJ CVJ CM CM (VI (M CM n m ro n 0 n m n m n * <* <t 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 y y y y y y y y y yT 0 0 0 0 0 0 IT 0 0 0 0 in 0 0 0 0 0 0 0 0 0 U) 0 0 0 U/ L0 0 u) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

61

z •cn -i

j a• 2 z I UJ -J <X < X X -V

o 44 » z b> w UJ

• 4* w cr z “) IX • 2 i a a KIT • X *- > • X -J• u 44 • I u z o Z -J

O z W eg © < • a u b- 2 <T < o ~4 u. o: j b-

b- 4 m H i o © • aX • X 44 u • t- w a a UJ

V M eg • I X 2 X 2 J >n X < Q f* Z 2 o

in >-4 2 • © • -J UJ o K © uUJ 2 UJ 2 o O 3 X Ui- D • -J < • cr • UJ J 2 X o< 2 CD X o 2 UJ H K2 *-• I O I vO > < A z 4 •44 Z *4 a © z J b • a -i oK 44 W a • H Z h 4% 2 2 2 UJ

(ft 2 • i • in “> N © Z © oUJ X V © X h* • • U K X Ll1

or O O' V O' 2 O 2 » z X Z z UJ

UJ z • Z • cr < 44 — 44 2 z> 44 » X X • I in o N z 44 • •

o b- X K © X Ul X < 4 2 •a >4 o © j z • < -J © 2 X

in < Q •-« • » b- Z 2 w UJ X K <> k 4- 3 •» X in < a O > Z K J z< in 3 X o X in • >- a 4 UJ -> © 44

 2 JUj • -J a z 44 H » X “1 a M z —

*

UJ X 44

X X z z H I in D 2 a > • in 2 -J <r X ©< in u UJ a 4- a © < © < • h K 4 J in • < a k 2 ©

> > -> < < o © 44 44 o v 4 UJ 44 J w 44 •

(/) • ** *+ #4» z • 2 a < O Z > 2 • “> 2 ©u o L- H #4 • 1 © X II IL < h • z • o UJ © II o z3 o © U -4 o 44 O' © O 44 © J © < • J © UJ 2 J © oJ < UJ IL in z 44 o 1 i a -4 Z 44 UJ • a z - a M J 2 < © 44 44

« z u. lL • 441 (VJ X l

• I • © H o > z 2 a © 44 < J 2 ©> or u. UL (VJ o *4 w i I z *4 UJ • UJ © X a II

•* © J © < «a UJ UJ < • o 2 • in 44 UJ J u X h a © © -) II X CL —

J

X >- X X UJ UJ UJ • I X Z • II 44 -J a -J 2 4 4 44 ©eg r o .4 a I D eg o X • 44 4 I II

44 44 X 4 4 X 2 o 2 J I z© N Cg CVI — • O •4 •4 © in 44 H u © u ~> O 4 u o a -J u

2 in w z II z UJ < 2 O in a « < -1 44 -i < < aUJ —J w o in u D Ul < o o 44 2 UJ O II J UJ < (VJ © u UJ H-1 UJ h* 44 -> ei LL Z 44 II 2 « O J DX > UJ < H <\J in 44 UJ a II II a «m r < a b- o a: Oa UJ H 2 < o •4 X - D o o in -1 J o w z u o U o o za -J 4 a M in z Z IL o I H H < -1 u. LL < IL <a X ct o 44 eg o o 44 © 2 2 2 < o

w 3 u. J *4 o u H • eg z Z Z V- U • o • •

i *- i < Z O u P4 (VJ ©1 D 1 U. 44 a o o <1 0. 1

44 >- o u a o a a a* * # * * 1 K | * * # 44 o h- # * o o * # o

1 D 1 o z in o Q UJ o o o1 O 1 o 44 0J in -j O j J -j

eg CSJ eg

u c c c u u u u c c c <J U U u V u u c C C u U V u U u

o -• (VJ © <* © o K X J o CJ © © X K © O' o ^4 ej © © © N X <* o p4 (VJ © <* © © N X O' o 44 (VJ © © © X O' o 44 (VJ © <* (ft © NX © X X X X X X X X o> o o O' O' O' O' o O' 01 o o c o o o o o o o 44 44 44 44 «-4 44 44 •4 (VJ (VJ (VJ eg (VJ (VJ (VJ (VJ (VJ (VJ © © © © © © © m© © © © © © © © © •n © © © © © © © © © © o © © c © © •© © © <0 © © © © o © © © © © © © © L © © © 'Ll © © © © © © © © © 0

62

j

o k o oz a z z *X o n < < It

k CO OH u. k• •—

<

IL 9 0> k « XX 3C Ul It k -J X cc X CO «UJ X k X G UJ X UJ UJ X ok 6 k x < X k It <J k k Z10 UJ < k < <0 k k (0 < UJ 9 <k k e X Z k a k Z I J •«**

(/> < a •> CO X » CO H4 k G X o •-* UJ • Ul » CJ u. o X <r V

UJ U o **> k X UJ k k «-* UJ a U < X • ak o a J X —

*

< k cc u. k o o z G o G< 10 o t G < It o < • X k < o UJ kz cr X X k X z Ii. CJ or z or u k • • CJ

< o o 09 »-4 X QL k X X M X z -J • • Ul

o z k J w * < a a CC u a z Lt X »* X X 10 X Ga CO U < s J > a X • k cc k o CD < < <o UJ o UJ J < G » o <J a o • O UJ a U X a X ao J z > G k X m k o X X • o Lt k > X -J a G ku -* UJ w « It X u u It <J k < CD a *-«

(0 u z k 9 z k X •> z k Q • X z 9 j W Ul

o (0 CO o z 09 G o cc an D < O *-< X • X<— UJ H < n -J * < O UJ X • l UJ k k k CD It it • o kU a X k -J G o X cr CJ CD CJ o: • G < a X k o Q ok UJ z < X a • UJ k CC X UJ CD X <r G Q Z Ul

Q k J •>-4 h 191 o • It k o k a: •> k k k o < k

< z < G W >• -J k z • k 9 Z o a co # z • <UJ g CO 5“ x z n X UJ cc z a UJ k < CO J • Ul G a:

* u k z (X t—

1

< k- X UJ UJ UJ Lt k UJ

O u c UJ X < k <* u u k Z o J I > k UJ o z<T z < OH a + z z X • z Z O K k UJ X X O UJ

G G k • o « o * CD o •> *H Z j 10 J < k • CD CD

J • Q UJ M < *•% J IL cc • It «—

«

• CC • *-* CD k UJ CO It 0. V oX z < 9 o I CO < X G k o It k o —

*

CC O IL CD CC CJ 9 > »— c w c UJ o 09 9

CD a Z -J UJ k o o -J < X x X k X UJ P>t X X k UJ Q UJ UJ X k • o X zX M 111 a a z G J < < z O < CC O CJ z Q a X a J UJ I CO CD oz k * > UL < w G z k k < X (0 + z k < z •-4

II a J k CJ X X - z **

• cj •-4 UJ UJ O X k w w •w w W UJ z w w w UJ k Q w < < a CJ < UJ k• HI 'U J J CO z k J o a -i w Q G Z < z X o CD <

in a II a »-* CO a z a Z k k k k —» 1-4 I k k k CH Z k o k Ul < -) k w XJ *-< w in z i-* o J a X X X CC co CD z X X X co (0 o k u o • to a N« a

II < o Q in a UJ M -J > z k O CO UJ w > z k CO X < cc > CD w O CL oit < o k-4 X k ii o cc O CO — cc o a o *-* It k o -1 a a: J w CD *-4 u.

X o cc G < x k k >—

1

ii X k a CO X II X k a X • k < o J It o o -j k zCD < 91 (0 J k CO -J CO < o CJ k < k UX II J O J IU in k G G J -J J j -J UJ ~ a: J -j J UJ !JJ J CO CJ u CJ a i—

G G o J X O a a X •> J J J -J X X X J J J X u -1 z k X U) X kX CD o < k a G < X < < < k u < < < k < < < G UJ G UJ q:

o CD z <-0 u (0 k Z H CJ u u u CD z u CJ o Lt CJ •X O (0 Ul < oo Z < o j o z o a k CD X a (0 ko UJ o k < » UJ k ~ k D G k k CJOJ o X a k X QC CO X CO UJ

u UJ k X k UJ UJ UJ LJ o to J Go < k t— UJ k > k k < UJ k — < <o UJ < Z z cd < o < •— Ul X to > cr

J ,-- z -J u J I k r <r a kd <n 0 o CO CO a CD Ul UJo z UJ X J z -J z -J o a G k UJ

U < X tn < < -J < -J u o O Q z Na k _j cc < a < it z UJ *-• Mk G c0 k k • UJ k J

<r UJ UJ UJ UJ 10 I k > a * > k > k o < o z * *0 o G UJ < G O o O o UJ -J IU U zJ X a J u T CC X a j (0 CJ CD *"<

CJ U' cj u u u CJ u CJ c c c u u u u u CJ CJ CJ CJ CJ CJ CJ VJ CJ CJ u u CJ u u

a ^ — Cv| r lO N CC O' o CM G m vO k 30 0> o ro 10 vO k CC O' o CJ n 10 vO k CD 0> o 1—4 CVJ n in vC k CO O' o (M n *• GG ^ it 10 CO 10 J) in in 10 in 10 to vO vO vO vO VO vO vO vO vC vO k k k k k k k k k k ao cc CO ac <D co CO co 30 co O' O' O' O' O'^ vC c t vC' 0 VJ VJ NO o vO o '0 o vO vO vO vO vt» w vO vO >0 VO V O VO o VO vO vO vO vC o o vO vO o vO vO o vO vO vO <0 vO vO o vO vO o vO o

63

-> ->

cr a

xtr

J•

Ul wD1 ny a• y

xCD JZ JID <O U

y O y ywzX

-> Xor x

XZ >

"> ->

a ay yZ XX xX >

X • xCD -* XX - Xn w >

->

• a • •X H —m n aJ • W H--> *) "J X

a a x• y y yy oy U- • •

• M Ct• -> W ».

x a -> z< y a x~ z y y

o-* in

n

xX -*

> z> «-

<XI

oy •X XCVJ vO

• XXCD

J •“> ")

I a<t yz

• IX *

x ->

o a:

h-

z• X0 yX X1 OCJ

X XCO -

X r*

X -X> •X X<t *)

X• oX -

n •

X Xm cc

X• *>

X I•H *

oN

-> Xa csj

KO •

Itsin -

J -a. a

i h i

I 3 i

i a i

I <r- I

I 3 I

I O I

u u o u u

N

• z

I • N- X —- in

s •

• CVJ

X *z w UJ

> a

x -- N

ZK

• >•

-> Za zi- • x —Z Z z*»-•>->- V z >z j- x

• x y x-) - Ja «

o j- •o z<»• • t- z (-— ->>•->-

a _i >- zo I- UJ ll rK z a - n

e> _j “)

uj o:->->-n uj x x

_i x x• a v -a *-

UJ• •“»

a3 Ka u.- z13 -u.

z z»- H-

>XXX

~ Ju. <« u

*«**«- *#*«-oin

PO

UJ 1- m • XX z LL z <*» UJ h- H N

z n • >- -I

tr o K a J • UJ

o a X -> oU- X 1 • u • ao —* N • z y •

1- u -I X z y UL X") m < e y • Z Z • •

u. o u. • h- y -> XX u. X i- » • y y a << X < X a U. a X X y XX u u a « X H k 2 X LP mJ

o a; a n X < ct z *-* X IL UJ** UJ w a X O

LL) N X m -> u • • • •in z < J w X z Z z Z •

X o o UJ LL h* H y y ->

< o z X > H • > y y y aX H a UJ X a J z z X yJ in a J N4 0 > z o hH X N M

a **

II o (/> XK t-c X

X U I Ll Ul

< UJ h- oa *> z-> < U. II M

• at MUJ o t- X JJ o o < JN4 N UJ z N <in X < n uin HM o zX o U. o

o MmJ o< J UJ

D < ay >U a: h-

< UJ 1-4

i- XI zu — o< zUJ UJ

X nr

a »- UJ •

o > zu. UJ o o

z u *-*

• M o£ X J UJ

a < aa UJ CO

o - o H * * # « * *o O UJ -J •—

<

_J o Q o I*

u u u U u u u

13 +

~ in

o \-

X• zoUJ II

in

X KI- X- z

> oX 13

J-l/CPO' OOOOQO>c o c o n c< s *>• n k

o v mao-Nr'^jiOOOO — — — — -I —p-ksn-ksnnnnCN 0CO'O-«(\jm<t— -i — —< fM f\J Pvj OJ C\JNP-NNNP*NP*N

in o Mr 3 e - n n <cvifutucvjfunnjnmx)

IfllCNCOffOHftJ"* <t <t <t <t <t \ti in in in

64

• u.

ao CVJ <n »

o UJ w • X co

IT X -> -> X-4 K a < X

K >- * X• o z H J > UJ

a a *-< UJ X az D o< D L* o •

• O UJ a » >a X X a a

—

*

z «f H- Ho o X Xo z • -J • *)

• < lL UJ ->

a • K Q aUJ o a o h- H• UJ D h* • Z a

• U Xu • N •

a o J •—* -s UJ “) « UJ

W co > a N u-> W u UJ h- -J <a -> o u J UJ Upb or o a. •-« nIL k w

J KW *— H 1-

w t-4

X lL X** X *-<

u. *— J*-* U. HI -Jw X-l z <

*-* u5 Za ow —

Q<Z

- *

+ Q

I Zz

II

II

zX oz *-

I

*a

a << ->

z *-

* *

Q Q OI- H I-

z z ->

z A • • >a X X Q X

z u. < < < < »

M 3 a a 4^ 0+ Xm *4 -> -> N CVJ N X

o w w W w •

IXi •> + IL IL H b 1- •

x > K k- a a b X UJ

u z a ‘S X X X X < u« UJ IL < <a » u. a > > * * » > u.

z u. co X n111 o 3 II X # # CO u < •

CO CD n i-t X •• <-» CO u 1 < LL

o UJ • » u. * • -> aH u J UJ a uj 1 •f k- X CO

UJ M (0 u X Ll IL X I> LL > V) x < < K h* z • *0 ->

h- UJ U. -> LL N X X O C X aM Q -J 3 -) -> < < - b « < • »-

^4 u Z a on » w a a •J n > Xo < w uj k X > •>

1 | UJ X+ J u z < w w > •

UJ UJ UJ o a IL UL o X IL ll " o K o X m* -J L- X XX < o “> CO vO a 1- I- X a X a < w w 0 H Nz b- u. b ^ X <•4 • a o a < o <T o NJ K o b C5 w

a l/) 1- a: w < < X X X > *) a a a aII z D z o + o z z w i c X o —

*

oCO J o K h* X 1 i * H * i- X w X w > ro u

X UJ -J IL K a M w w < z z w KX X >- < co O o X »-* Ll u :

i" (0 i N * J- * K “ zz K CD U I o • Z a CO z a a

o u o *-4II II II u 1 CO 1 i a

a </> II CO II u COz h- II UJ X X X ii II n -j< Z h- o X II II < < < -jD > X < -> -> i X i <

a: O I z 1- -> u (0 X > N X > N u

z z UJ oUJ H-l o X • LLJ *-* 1- h-

CD z h tp4 COH u 3 UJ X UJ

CO *-• • CD K i-<

CO CO K t-4 < <•-4 t-4 a a

a -J X b a b h»

-J CO d o Z(0 o < z <X u Q o DUJ CO z CO Ou n < UJ < <CO UJ M X 3t UJ

a I- a bUJ UJ UJ D

D a CO u. aX o ***•** UJ * * * (0 IL * * UJ 5

UJ X < D l o o o< a b a X b o o u

in

u c c c c c c u u u u <J u u u u u

inmir, if'inin'U't.<t<'u>0'O'0«tvcSNSNf'-f-.NNf-f'-Nf'-r^Nt--

-fcr-'Nf^NI'-NNf'-Nf-.®®®®®®N.^-Nfs.^-(^h-Nh-NNNNNSr~^S

IT) ®cn®(7'0-*(\j®<j-®cs ®0'o — tMrn<r®'CN®ao-<

®®®0'CT'cr<7'(7'Cr(7'aCT'(7'Oooooooooo^- —SNSNSSt^NSNSNN®®®®®®®®®®®. ®

65

u

• •c X• C X

Q z nUJ UJ <

-J X 4^ •

< z V «4

UJ X u. z UJ m • ACD K U. z X UJ X

D # z H • in VJ

UJ B CD i- < <0 a> K • • Q z u. • ** Q< a • K z K Z D I OI UJ UJ z u z < • O • H-

u. N M z u UJ X inin u. © * K a • u nz D U. D • o II

1- X < w i

o cd D o CD X K M in IL <0 iM CD < ++ z Q. ** I X I

K UJ z a z I • <0 •D I • K a • • m UJ X X® k H * © • V UJ (VJ VJ • (VJ O'

Z ** A (/) u < Xa X a o O z in UJ < • u. m • •K IL h- < • o u. • X a (VJ

© < D z UJ **<\j a m D • —

a CD w J w ^4 o UJ D w in ro 1-»

o w z UJ z u. Z - « I •z h* © < a ** u. < z N UJ X •

Q UJ Z < © z K z> u I U NUJ < X a o ** < (D UJ u. p* • < zD Z H < J z • • z u in X u. • UJZ z u. z (VJ *•« m < X \ n X -J*-* * >- -1 < p* z UJ u. w \0 X X- M J s < M M a N a • P-4 oz o X J o in UJ tn D • z o • »-P z cr

o UJ < P-* L- h u. in -> 1-4 X X 0 CLu 3 z UJ u X u o • D < PM n I

z z z < X UJ • CD >- z s ®*•* UJ L- u • z 1 CVJ i o OD 1 \ • M*

L- © o a *•» UJ rvj i- z • o -4 (VJ NO • A o •z z «r K o z • •> UJ in | UJ 13 Ml o Xo UJ J © • H L- o UJ • i X Z t- 1 m a u UJ UJ Z 1 •«t nVJ V- D < • UJ vj < D I (/) a z (VJ w < VJ u pt (VJ

z z UJ L- a z < o DC • O p-4 ** •-4 U- 3 • o u. < < O • •o *“• Uj X -J o • U- -J o w 9 z D o UJ • i u. Up z UJ • ou h* D H b~ IL u. J w M CD u D -4 X I X UJ V3 D I

z z H a I V- UJ >- a a. w • O p* in NO <0 • o m*

o »* cr < ** Z UJ M II © > UJ < UJ J- in w z in wVJ Q a ~ D I K UJ *- z u. UJ I M J UJ J W

z U. © vj z u J J or Up cr in T UJ L- J UJ HvJ < © U. ~ UJ < 3 a a: o UJ D o D > UJ < 'll > UJ <<J V) B UJ -< V— I u. © W 9 u. D lD U. -J UJ UJ H Z o UJ H z

K n z K - UJ Z UJ U. X J »— a a J —• az UJ u *-* a u. *-* UJ CD V- a a o a a a oUJ a o u UJ I *—

•

1- X J w B u. w V U.> UJ z H 1 K 1 Z h- a J 1 1- 1 i »- i

UJ X •-* 3 1 3 1 o UJ < 1 D 1 IL 1 3 1 Up

H x a i a i u y IL u i a i i a i

J cr z « U C 1 H 1 # * # # i *- i *o c o o o J U. < o o 1 D 1 o o < D 1 3 1 o 1 3 1 Oo o o o o < —• o u 1 O 1 in o a CD 1 O 1 in 1 (3 1 oK X O' o -4 (VJ (VJ m m <tp- p- -4 O] OJ (VJ (VJ (VJ (VJ

u vj u vj u u u vj VJ c c c u u v u u u VJ c c c u (J c c c VJ vj

ao oh- z© UJ

a:

aOl o N O’; O o ^4 (VJ n & >0 N r a o —4 (VJ m m © N rc O' o ^4 (VJ m <t in vO © O' O r-4 (VJ m <* in © N © o M* (VJ m in

(VJ (VJ (\J (VJ (VJ (VJ (VJ (VJ (VJ (VJ m n r> n n r> n n n m <1 <r <r <t <* in in in in in in in in in © © © © © © © GV. r ay cr cr GO T r, cr ® or>

r> © cr © <L 00 CL cr. cr © «L a; © CL <T © © © © © © © © cn © © © © © a © © Z(U

66

5PfiT,S

PTORUOF-OOC.

M

ARKE

DD

ATA1/CASE5

1

i

•“*

CM •H oCM

o o Otu UJ LU 04 in pH

sD '£> N ph ph

O O Oo • 0 9 O o o o0 o O o a 9 • •

O O o o o'

c

o o O © o o o o o• 0 tu UJ UJ 0 • • •o a O VO o 0J o m

<? o o o• 9 •

© o o

o o o © o o0 o • • • •

o O o m o e*J

o •tf m pH

in o o oLU UJ UJ

'O o sO © o

o o in • 9 • o © o o9 a o © o o • • • 9

© 0 0 o o o ©

i

i

!

o o 00 O o o o o o o0 e • UJ UJ UJ 9 9 • 9

a O © o VO VO o © o ©o •-* © o o

CD 0 « 9

-« vC © o oo

O O CC O O O O O O Oa 9 ® 9 9 9 9 © 9 9 9 ©

o O n S) o o © o © m Oo in <* o CM o CM o

o »H © O O «—1 © © O O PH pH 1 H1 UJ UJ UJ 1 UJ UJ LU UJ o O s 1 1

«— o o o vO o «D N 9 0

o •-* w "H © o 0 o o O O m O <*

O o in m r-H o O o o OP* o o a 9 0 9 O O o o o om e fi a 9 9 9 9 Q 9 9 O o O © 9 9 9 9 9 9

LU O O in <\J p-J —* CM —

»

O o o - CM in o o o o © o oin in n ro CM VO CM ro in o N CM N VO

< c— rn ~ •=4 vO pH 1

u o *-* »H CM in .p* <w 1 pH «-h1 I

\ -< «* «H

- 1

< A A A A A A A A A A A A A A A A AAA A A A A A A A A A A A A A A A A

<Q *H •9 CM ?M «H N n r0 vO <* ine -J -J J J -J -J -j -J -J -j jUJ O 9 9 9* ft a> 9 © o 9

a —1 pH< M oH pH CM <M amt «al «H pH pH «H

u o U U u <J u u u u9 V V V V V V V V V V Vz Uu u. a U.w UJ o: > UJ U- IL u. it

u Q UJ cn h o Ul UJ UJ UJo »-H EQ K H- J o o o o o ©o < cr *-« *-* in J h-* c. Q s:

1 a cn «• X * 5 < ft ft -ft -ft ft ft ft ft < ft ft - ft ft ft * * n * it- * < *u_

a pp. —

*

-pp o pH-* CM ro . in s> N CO a PH pH

h-

Cl

•ft

or — n,

3kC O' o

a(\i p <r in C’ ^ co a o - (vjnîn^Nfcoc - cm r«"* in^^^H^-H^jMpjtxiMfMtMMwcMwnnnrnfnfnc

zLU

in

LU

in

<uV

<H<O•

uo0

1

IL

O35

aaKa

in

a:a367

IV

IU-

3•

-’TOKVHOF

—

DCC

(I

)•0ATA1/C

ASE5

(0I

o

o©

o o oUJ UJ UJ

'O <C No o o• e •

O O O

— M — O

CJ ID -4 *

o o o o• • • •o o o o

o o• •

o o

o o oUJ UJ UJ'CONo o o

o o o o• • • •O <\J © m

o © o

o o• •o oo «in

o o in• • •

o o oinN

o o oUJ UJ UJO >0 No o o• • •

o o o

o o o o• • • •

© n © -^

m -

o o o o• • • •

o o o o

o oin

o o o o o o o o o• • UJ UJ UJ • • • •

o o © © © o o o ow* o o o

• • •

•4 •4 © o o o

o ro o o o - o o o o• • • • • • • • • •o n © o o o o o © oin <* o -4 <\J o r\j o

O o O «4 o o o o mt w-t 1 *4

UJ UJ UJ 1 UJ UJ UJ UJ o o 1 1 1

o o o <0 © © N • •

<t -• «4 • o • o o o o © oin in •4 o © o o -4 o o • • • • o <* o o o o o• • • • • • • • o © o o • • • • • •

rvj cvj — o o o rvj in o o o o o o om CM * © *\J n in o s CM h- ©

—

*

n «4 ** © ~4 —1

— - CM in - <t -• i •*4 -4 1 1

<t m © x O' © <\in<*©©N30>©— C m ir iMJ3H(\jr, If

c>j fMawwnnnnr)

cr

nmm o

zUJ

J

z»o01ft

68

*ING

VALUES

ARE

ALWAYS

OVERESTIMATES

II-

c*

K

§a

£

<v:

o+

vO

*sCVJ

ro

uUJU.

a-UJ

u *«

< olL I

k 00~ ro

i oX N •*

k O or> + •M IT

B N>C

k* >C in o oIL o kUJ • X UJ

rJ z u1 <

UJ IL

>»-»

0 in

UJ

u. UJ

U. k GO uU! X o <

z o U-

in

<* ^

ox(r

'.il

1

Z

< IL.

I

a

UJ

u<IL

UJ cvj X VO ou © X o *-«

z + z in • •

< m ro ok N in

(0 CO UJ ••

M u o in

a •0 < ao -4

• IL in

X •4 k UJ UJ oD a u a n CO

X < < o a N<-4 k ro u. CVJ N k o CVJ

z m X 0 U) u OJ*— < ro o UJ V \X i H z u 1 CVJ v0

iw < < 1 v o

o i X IL 1 kz < UJ in »-*

>H o z u O l

k < z kII IL cr k <*

< a cvj < kk 3 UJ ro X inuj X in u •

< U- Q ro

ffl a Ul

cni

U.».) — k O D

z 3S

*

1

X - D UJ —A X 01

Z z IL Z G u UJ o a— _J - U < -J k CO

c < cn < LL (D a CVJ

k X 3 X k CT o1 a 1

- D cr IT an - X in a • D

1 1 k Xa 0. a cr

d D(9 II

69

(VI I

19 •

K I

I/I I

I I

- I

a i

3t I

a i

a i

X 1 to

H UJ 1 -J

J 1(0 UJ <

ID < 19 >X to 1 < aa (0 1 UJ 1- UJo IN

j o in -U- * 1 a za 1 «r UJ

UJ O 1 -J r0l O 1 t- >-

< 1 • to h-

X Z 1 in a < z —

«

u a i a UJ uM O 1 J u. UJ • oI >- 1 o IL CD o in JJt

l z 3 UJ > UJIL 1 (0 K in < a >

X O| | (0 3 • a UJ

u. -Ja ~x

33 Xaz

aui <n a

in t/> o>- u. aI 3 or

h oi a

ui ui

N H- ain z

Z IL< « u.

< 3in x mr*o zUJ MU.

U.UJ

o <r (0 1 1 t- a o a UJ UJu z UJ 1 to < CVJ <\J * M a o\ u. UJ U > > a 1-4 a orj < a >- 1 z *-• H-t a z V) 3 inO X • -J a a 3 O <\j

K UJ U | UJ h* a XtO UJ o O 1 (0 3 a UJ II II

1 I < -J 1 3 O < Jz h H UJ 1 or n CD X ffl a KJ— co > 1 J to > a CD u. H u H o UJ to< (O 1 < J *4 X a Q 3 to < a a H IL

-N o >- 1 a < I - a m N- • X o a UJ CT• z U 1 UJ z H UJ UJ a z o (0 m4 to X X

'O £ < 1 z u o o X »-• a -J 1-4 to X < X-N u a i UJ ** a o 3 aW I UJ X 1 t5 o o X in z

. >I I

u zU “u.

u.UJ

uUJ

a

in i

>- i

 I

 to

a 13 o a »• (0 • UJ Z < UJ a z

to h- o m f UJ F o OUJ z UJ X F o UJ a IX Z X ou UJ o D M 0 > z H z • uz z z Z X IL o UJ z < J< UJ < UJ O CO u o >• < JH- H X IN z I K < in M K H > > <tO < o fp. o F D UJ !f < 0 a >*-» • K- w M M V in o < 0 U I >-• 0 ao <0 (0 UJ |- X IU X 0 o K V >- 0

UJ a: x in D UJ f z QC tD J o zz a < < UJ e> 0 in > F F o < 0 >- -J zo > - _! _J

*-* UJ c ~t u. or > H 0 «-<

k < in on o a j 0 U o z o »* > 0« • C) UJ a x w- < a UJ H 0 h J X V

< (/) i o to | D a to in _j F to M H4 < K K_J > o > 1 z a k-M in <o UJ a F X 0 F-*

CO < i< < 1 < o M 0 > o F to < 0 O u

z a z QC > X X in X 0 X 0 > z o< a: z a X z h* r> UJ K F 

<0 X a to a til X to < Q o 0 F z 0 00 K 0 h* UJ a < to J -J F a a o a 0 J U Ho U Z o u z a IX X FN u. 0 _J D a o a c X X •-«

0 w UJ te*4 < o z o > < V o in 0 0 5 0 Xa IL a 0 u oUJ LL UJ 0 to H0 UJ 0 UJ a UJ

UJ Xt- t-

U1

X u.

<a< O w 0a 0 N 0o • »—

i

0 z z to N M *-*

to < a > > (0 > >0 X X X 0 X II o H- z z CD X X!~ < X X X z z0 z z z z

»- 0 q:

< oI 0K- to z

D *-M # *(0 z —» w * wz z # * X w H< Q o 0 w w 0 0 Z0 z *-* z z > 0 Q. uT < to « o X 0 U »-<

z z z z D > >* 0 < < 0 X X

z• »—

4

• —

»

*-» «•*

0 Q z a a cc cc *-•

UUUUUUUUUOUUUUUUUUUUUOlJlJUUUIJOU'JUUUljUUUUUUUIJOlJUU'JlJUUUUUULiUU

u . O’ O - M "1 <t .1 i S (t ffinin-O'O'C'O'O'O'OOvO'O

OHninînoN®i>NNNNNNNNNN C-Wn<tlI'OKtC(3’O«Nn^K'>0St;ffoncroDCDccoorcDooooo'tT'C'O'CT'Cj'a'a'O'Cj'

e-nintiooMto c - oi w ÔOOOOOOCOO — — — — —

71

MXNIAM

THE

NUMBER

OF

ACTUAL

MISSILES

IN

EACH

DISTRIBUTION.

g •

UJ UJ • UJ D iMM

u u UJ u O • o2 z u z z o >- H i

oUJ UJ z UJ o • z z (/) i ea a < g g z z g UJ g UJ i oa: a K a IL g UJ > o o o z i CM

D o <n 3 o -J o IL a Z u. M i wU UJ u *— u z U. X in z 3 • UJ u. i Zu J u o u • < o h UJ l- o in a. K UJ i oo o o UJ g > K g Z g MM > 1- UJ z o i z

in z a o g D g Ul X z o UJ i <u. in IL o IL > o < a z V UJ o < z X i

o m c MM o K a z H UJ UJ X z UJ UJ u i •k- a MM N H H « in z • < V < y O CD *-* < c O z H z V- z i o zK -J H J K o ** in H UJ z UJ o I < in •M i o LL*— < • MM in MM < Z g in h- z u u g MM

i o H-J z -1 z -J z UJ mm D z < o M < o o UJ z o K u. i CJ •CD U MM CL

1 a CD o < o >- z K MM 3 X g < o iW M-

< < K < k < L- h* < M < K in o h- > a O i > >X X ob CD in UJ K X o u K a J z i I go X CD c X O I g UJ < < z o z UJ UJ o i za VJ •— or u a u UJ UJ Z IL UJ UJ z o J X K i

< •

a < g a < a < X in z o UJ z X MM o K K iMM

UJ K UJ UJ *- ** UJ X UJ K z UJ X o i• >

LU in UJ UJ o X • h» g I B K X iMM J

i u. X IL i u. z h- H s UJ K < Z UJ »- < i oK o c K O - o fp o < in in »- M UJ X UJ i <\J •

MM Q o a D in UJ U) X X i w Xz o K UJ H o o z z Q z H H • i a aa UJ < g o UJ < o M K CO i L- aM z i—

•

Z a g UJ K M o < z UJ K i CL g1- < g D g a •—

<

z < H- - K MM o < M i

a • UJ o O O in MM C < z g M in i• •

M • UJ a IL UJ IL UJ X h» J o in o M* Z L> i Xa UJ J u z g z o u IL Z < u H IL N 3 MM in i o ou -1 MM Q UJ « MM UJ D z MM K o ^ o i CJ mM gV) u. UJ in <J o UJ z z z I < h- W H < g S X i

w o aUJ IL J v < < X • 3 m H- K a H UJ u N a UJ u > z u M u o MM < 1- n UJ i

• u zZ z Z z 3 o UJ M z X < D UJ z z in CM X i > zX X X MM O < ">

1 m < K z o mJ I UJ A A O Z X i o X 37 z * g < 1 *- o \- g < X o IL (VJ ID u i

0* oo Q Q g 1 > in > •Ml u UJ hJ O U g i

MM •

g a h- < K o UJ UJ IL *M • UJ Q Q X z g UJ z z < o 3 g • a < • mM i a o IZ Z in u M < z 3 M MM g a in a UJ o rn i X J< < m M -J UJ a K g IL UJ UJ UJ UJ < g O i • CM UJ

—

*

< X *-« L- g g z z CO O D » CMi

MM Q* # * in 7 B a tn UJ G o u M MM z g g X z 1 i o gw w w z X £ g g I X UJ o o o mM MM mM

i-M UJ •

z n L- • o o a Ul u u z u l

L

J H CJ i NM u. h-

< h- K in u O UJ O z a X < < UJ < o O' z i z U- 3a a a UJ < g H •—

1

« H z z (X z g z z a uj i < D uh- 11 MM UJ u MM a - H i a m >

0m o g 0m A K H MM I MM in D i • UJ UJ

lL' 3 o CO i UJ g gJ < • i Q *

in V i Ou. d X i

i

u

u u u u U u u u u u u C C C c c u u u u u u u u u u u o V u u u u u Li u u u U U u U u U u u u u ui

u u u u

f* ryj r» <t or>j r\i cm rsj cm rvj

*• Xi & O mm CMcj cm cj cj m m n

n * it •£ n co c*

m n rj rn n n no — cj *n * in <o<t <t <t <t <t <t *

N ® 'T' O — rvj

<t <j 10 10 40n<rm»o^T*ain in in in m tn m

o — cj ro ^ in vO~

>IJ -UJ Q.

O 0>

v rX 0 t— 0 & in X z X a z

«*fr“ CM r- in Hi < c z o <

-4. X > z eg JC D a „Jj Z 04 • o a 04II

04 s X > -J o u <vi 0-3 K *> N oo z UJ X > 0 in 0 D > in *4 o f Xin «• »- z iX in X oc X H K 04

w -1 I- V c> 04 < 04 z a o in > >h- UJ 0 -J H -J 0 £ 04 a X X H 04 r X 4*

z > > » 0H UJ N z u- z S’ X z z 04

u UJ X an o > 0 u > -J *4 in O _j W >—i J z < H X \ \ Hi UJ 0*3 < 0 a 04 0 0 o > UJ > X> a —• m z o o a J 3 -1 04 r> -J l- >- o zX <r X o o in a » 5- LJ > UJ z <4 04 04 X

* -4 J y in o in U > 04 X c. I > a o o 0 < •

o D H a <\j o o —

*

9 < uu Z o • U HI U- + o 44 V-04 o • K- » CVJ 40 o CM -J X o < J D • J 13

o in 04 n » X N) 04 CM o V* H a 0 II UJ a m o X UJ II K •

0* Cl h* u in \ V W> W in 04 HI O 04 • 04 04 II 04 HI 7* > z* *— 0 X —

*

in • Q 04 04 xs D > O •XI £ CD N u u UJ • a CD z I II

04 —

*

in Q Z 44

< 04 X < Z —

J

X in > < <1 K in • CM UJ a o z W 04 c o UJ > > 04 o II 44

z in z a 04 T H X 7 IU ;~ O 04 CD n 04 04 >- W* o o u X I II X oX z -4 04 s -1 t4 V 7 h- K II z CD UJ o o II ii o K 2 X H

X tr a X X X 04 04 < -j in D UJ < o u a D o II II a UJ I UJ 04 04 44

liJ U! UJ HI s: X a in •w 2 13 N 04 o 04 u Z II II 0 UJ a U) Hi 5 X13 0 13 CD II II < UJ 04 a CVJ > > >4 II K z NJ r o V- oUJ HI UJ UU < a a Q 5 UJ 0 J -J 04 04 X X K > X X in a w • -J w z oK K h* h h- 3 < a X (/) -J < > z > X 3 HI < u. u. o -J dJz Z Z z < >- C i i- I H! o >» > < «»4 X o o X z o z -J 3 < H >-

0- 04 04 O in in 1 o i a H — 0J m0* 04 04

u u u u u u u u u u U/ u u u u u u u u u u u u

in N 00 a o 0.J CVJ n <• a o N CC a c H CVJ ro •u* a o s r- a o 04 'VJ r a NO (I a O 04 CM n <y 10 vO N SO a C 04 CVJ m a 30 a e 0.

N r^ N f*- N CO 00 CO CO CD CD CO QQ CD oo a a 0^ a a O' a a a a o o o o c o o c o o — 04 *4 —

i

04 04 04 0* 04 -4 CM CM CM CM CM CM CM CM CM CM n ro**4 — — 4- -4 — 44 ** .0* 44 **4 *4 *4 •4 — *4 04 -< 44 CVJ CVJ CM rvj rj cvj nj CM CJ CM CM CM CM CM C\J CM CM CM CM CM CM IM CM CM OJ CM CM CM CM CM W rj

73

UPDATE

THE

HIT

VELOCITY

CUMULATIVE

PROBABILITY

HISTOGRAM

• UJx X UJ K<r - X I WMM K u M

J D _l» -J mm 0 in A

CJ a •• k UJ a UJ X in •

c < 2 a 0 m UJ 0< J UJ < mm z D •

a cr u CM J mm

a u X z < W» 0 UJ ct 1 u -* >0 Ul 0 UJ a D z< 0 • UJ z Z e>

z b z 0 a > fe UJ O • MM

Z> UJ 0 0 X z U X cr inmm • O I ro z MM UJ < 0

b H mm u> 0 • •

4 K O z • O UJ UJ

a UJ O 0 MM > z z > -ia MM -J z H in X < UJ mm MM •

> • CD O —A «r < X z 1- ->

X b O z mm 0 UJ D cr * < w MM

J mm k a CD mm in 0 a O UJ > MM

UJ a Z a O in 4 UJ u a UJ I MM

MM X • M* UJ • cr UJ Z X> • • a UJ > i- 0 K 0 >• 0 < 1

V I MM x 0 © X -« UJ X 1- Iz MM < k 4 z V •- z X z 1- •

A rnm a -7 i- w 0 u. > MM • 0 3 MM 0 MM HI wmm 11 mm w z j in in ip O a M z z

4 • • mm D 0 UJ « > • in cr VO h- -J • 04 X X *m > X X > H I UJ UJ UJ mrn •> in UJ in X

MM > < < X I < < z 0 MM CD z MM > UJ MM <> I «-< -> a z > b © > J • H X 0 0 J MM > *M

X MM z Z X u J -1

mm z UJ MM D H X J a X •z MM w • > HI mm X in z 0 ** p4 u z < n < H z 1 0 IPw > z • h X a u II

MM J > 0 0 UJ D Z • CVJ

> X Q z K • 0 u. UJ • I 1 J Z 0 • K 0 UJ » -> «M OX z z 0 mm 11 4 J —A O IL 0 mrn z UJ u > cr UJ fU MM W mm

X < w UJ U. AW > > MM A X n UJ >< • w II > > a 0 II > I H mrn X in u. X II X z aw H CD mm 1 4 UJ b I z 0 1- D < 0 H X 0 HO X a •-4 z K a d > mm X 0 mm © • s»> Uj MM < MM

- • 1* a m UJ b mm > X u r <r II UJ © I MM UJ I a -J MM w in Oz LL a O a D I X 3 z O w D ^M a J K H D -J IP w wMM X MM X in u Z 11 z z > O > z IL' K • or a < CvJ II

mm <t > mm h- W K 11 IP LL I MM 0 X in 0 I a vO u.IIw II _) mm 1 b > in • z LLJ MM mrn MM z h- K MM > in e> X mm MM

-j Z 1 UJ b 0 I u > z O X in D -X u. z < 0 O z O z X 1- 0 X 0 0 0 J z O > MM 0mm MM 0 u 0 u K a UJ « J z 0 u 0 J UJ MM mJ tr z 9 0

< X UJ UJ < J J I <j I- > MM IL < K

< < h- in MM u M X* UJ UJ O H a in z < < * *

0 1 a X MM 0 0 MM O D X »- Op K >- r> 1 0 in X O a h in mrn

«* IP vD

mrn

U u u u u u u u u u u u u u u U 0 u

o

omm MM •M

“)

w MM O«M > -M z Hmm I mrn 0

X X O1 < 1 «

a aII X ->

II zMM Ul «M UJ CM

> H- z MM »-

I »M Q M4 •

X II X IImrn UJ

< 1 < 1

MM a1 •

II-> “>

II n “>

W W w w -> ->

a > > a z z wX X X X 0 0 II

UJ X X UJ X X ULb- < 

u u

f\i ri 4 \T 'O it- o*r< n n n n n n n 4'M r\j m <\j <\J rj 'Vi oj rj

r\i © <* iP k<* <t <* <* <* «rsj r\j r\j €\j <m cm cm

^CLOtninininininC\J <M CM <V CVJ CM <M eg CM

K cr j r - (\j rintPin'i.vj'u

^^NJaoHf\jn•LCM (Vi PJ (M <M <M *M <Ni CM

<tlP DN0nO*C —rMKNNr^râocr0 (\. cm cm cm r\j m cm

rvj r. <t it) N u'> <7

x cn co cri a ar cr 4,

rvj <\j cm pi c\. rj w cm

74

1625

CONTINUE

OUTPUT

THE

HIT

OHJER1NG

Vt

ITH

PROBABILITIES

u u o

• 01

k o Xk * « 0 k© X s oX >•0 o <r or 0ro X z *-< 0. k o

<M • < UJ u k•> X • b-4 *•»*

X » X in k o » u oro —4

i >- k 0 o •1—4

i< IL a O J o •

• W Vi a »-4 cr 0 0

T CD i a • a > 0 <o < O CO i < k o 4*. 0 k

HI a k i k k • vC k 8 0 oX X a e~> i UJ z 4»-* >- *-< © 0 kk ro X I i u J 0 4 X 0M i X 0 X z XX O z X ( a: < < a r -4 X z kro X X © i cr 0 a > s k u

z ro » G O + X < •> z X ot~4 • 4~* »

i U a • X 0* 0 u ka H Z * i u a Q m < • 0 k 0 *-l

HI X • O X X <* o < Q o • < o I XQ ~4 *-> w *0 UJ Z cr • k O 0 <cr •—» 0 u. > a UJ O CM a a ao » v-» a • \ • o *-> • • u z 0 D 0 o

X > 0 X k k • a m > 0 ok in X X X 1 >0 > < > k ii 0 —4 0 X I < k

i vO 4-41 k -J a < *•' Z G z > 0

I * in 1• KX d k a 0 CM < Z k k cr •-*

X X * V 1 -J ? < • 0 a z 0 X© ro * X 1 I 3 o k o c 1 • • © 0 > j k

X —41 1 r* CD U UJ k a a k 0 k X 0 Z V

* k 1 1 < z z a u k 0 z k z k *— k• o • o 1 1 \ 0 UJ W O CM 0 k z >—

4

X X • CM1

1 O X k 4-* * a > .—41 > X > k 0ro r-4 a N i 1 o a k 0 o o X • 0 0 k * 0 0 •—

k »-4 o X.'i 1 UJ a in 4-* < k z z D. *- z a ©

• \ 0 V- in i S t- UJ a o « < < o 1-4 0 3? t-4 44* k 4-4 n o X 1 </> UJ k z N-- k w i-4 t-4 UJ o %m0 o -> 0 ©

—

*

X if) ro X t-i k N 1 y* X < 0 z • # J Vi • Q X k oo —

<

0 1 X J k o 0 o 2 o • • 4- 4» a a cr < Z 0 a> H-4 * • o O o •

1 0. 0 X < < o H-4 o *-4 0 0 z X a kI \ k X HI k e> H X 1 Vi o D < H-4 "0 z Z 0 0 N * k kz •X ro O N vO

1—1 t- k in z < o z —

u

0 ZX -1 • o •X *—

i

1 o • — o • < 1-4 o 0 o • D 0 Q w 0 > <y z H-4 » o o •

1 ro X X > in k X X • k W in o X Z 0 < k < k O ** w •*M> 03 O > • o 1 N vO X UJ k M z k z a © ro 0 *-4 z Z z k z

• o < <r < • 0 X X O «d o z u cr IL o Q o •M J D z > u > <> o x X -> © o UJ O —4 N in o z M J 0 M w * * « 0 0 * *-4 k 0 r II

X s 1 o X O z in 0 o o X • Q 0 w < 0 ii • k U • z > —4 0 o —z -4 a a: n a • • -4 0 X o *-c Z z 0 k X O z 44ri k k X 0 X • ro

w W a a k k O in •4 < G in a o z o 1-4 k k N4 0 o II —

J

» o X • X O > 0 < o in w O' o II 0 Z 0 cr X • o in w II II Z II © uz 0 X © X CO 0 X k X k w 8 UJ O < a *-i 0 w 0 k o w < II

-4 O(-4 o O' H ro -4 Z HH IX k o IH X tr Z i 0 in k X < —1 k © >- 0 0JX if) *-* Q k a o o u < a II k a u M a 0 < UJ k I II z 0 II

— o k 4— Ow > w /S u. o k 3F k II o •—

!

II 0 w w C9 k Z 13 k o > D W X *-4 o CM

II k X H- CC z o UJ k k 0 *-* a Z 0 k o 0 z k k a u wLU <r Z 0 a O o CD o O' z z D z < 0 0 a o t-* Z J z o z >— Z z o a o O

a k SF w B U. e> O UJ M UJ co o u t-4 B 0 1- 1-4 < > CM k k > u 0 0 Cl CM O> >—

«

a a V) I > M Z X > 0 z 0 h-; i 0 uX a O 11. a a o a. UJ cr o cr cr z o o z > k > > 0z b IL t- — *4 -4 —4 —4 CM

u u u U U U u U u u u u U U u u

O -- (\] P'1 >t IT Na a a cp a cp

ri (\1 CVj M !V (\J (\) (V

a) j' o - c\n>*inoNa)a © -< cm r> <t in vc

O'O'OOOOOOOOOO*-*-*^.-.-*^-*N-oC'C'o^c«rn^'invON(r»0'0^-c\jr'<fino^cro'c^f'jn<j'in-CNro ro ro ro "O ro ro n rn ro r ro ro ro ro ro ro 10 10 ro r> o ro ro n © ro © ro n ro

75

• X I II

UJ o X © © CVJ

> X © • 04mm rnm CVJ • \ 04

• 04 o< V K UJ I CVJ •-J u a mrn m4

D x UJ mm 04II

< -J sD a I • • ©

* CJ o <* X zo © ** o II

mm

—

s

a V K • 04 © mm I ©CVJ <* K U) X —* • a • z-J j 04 mm © «-4 CVJ HM CVJ < X ow u X W o4 > mrn X w- 04

i- o o • X k-4 I UJ a M KH- H -1 > X a z a u Ji Da a UJ K © » u • w •4 LL X

> — X > X X z © 04

# * <J • © i N a • 04 z a- o u X o k

Ok 04 J X • • • > © > 04 ©o4 © I UJ mm v) «-» © X a. H MM

mi -l > K M • • < D Qw w UJ \ Z W cv • CVJ s XX o X h* UJ 44 mrn X 04 U< < 1- *-< mi > z UJ •* *-* d a O0. a X < UJ <J Q. a if) i»

o X > 1-4 04 mm » X © az CJ a IL > > X O' 04 UJ

< CVJ UJ a I • I N o —4 o X4— h- X z z if) X04 * • Z cl > • mm •> • f- U. D

< X 04 UJ o* X M4 H X • X 04 o Z3 x X © x mm J > • z © X m Xi- a o > x h- UJ a © U 04 o X a J

cj o • • i- 3 U. a > • mm a • U- UJ <o > f- M z UJ X • CVJ > • z z o X H< » X (/> < X u I J # mi mm I © • I X Oz o4 MO a mi a vC UJ > UJ • z * * 04 a o K

II X o j m* • o J a • CM > UJ z I• II o V UJ UJ mrn —4 04 mm a X V X CVJ

04 > f- > m CJ * > UJ f- < z X J *<J- mm i- t/> —> i X • mm

| o • J a < z K —• D <II -J w *-4 *-• z K © > —fc o X mm X z Z h- •

X u u i rnm > X ~ mm M © a a * Ok *-4 o X© o a o o < • w Z w w CVJ o • o o < mi fo m-J <* <j z -J > o x • h- © • o X LL V- o X < Io > M4» UJ UJ H mt 1 X I u • H K • r> z K © 1 h* CVJ •

*3 CVJ X f- D > 04 CVJ a © o X < < D I CVJ -4 Z CVJ a o© z Z -J w — a Q O O o4 • W K Ic o o — UJ f- 04 • © • CL X II mi -J if) W * > # • o I • 04

n o <J D 04 X O l X I N u a. D X CL D X CM XZ 7 T < o o © © o4 K mm a mrn < X o O' ro V

o c -m UJ X if) w II II UJ < UJ > © w X < ©o CJ h~ D UJ CJ W o z D a X w

z Z X a H o *-• *-4 •— CL z K D z KCj *—* H a UJ < n > > or O *-<

ii X < if) Hi cr o 1 D 1 o a ou i a i * u o U J 3c LL i a i z i u

1 K i * * * 1 H 1 * * *a o o o 1 X i o o O O 1 D 1 o<t © cvj mrn 1 o i © o o o 1 C 1 oo o o —4 CVJ © ©

w © © CVj © CVJ CVJ CVJ (VJ

u u u» cj u u <J u o c c c CJ CJ

*

V

aa aH Zl/) UJ

h-

aa

t 0* ^ rv. <t © ^ ^ rr, ?*c — cvjn<}©'0r^',r0'G-Mr\jr':<*©©N©0O — rgnînjSDO'O-W^^<yj}«'>ir(/)ir ,liirînifi»C^04;0'0'0'-U'0'UNNSNNNNNNNDflD»Cff'COflD10(r(C(^(7»0'0'0© * ©©ronton© ©©©©©©©10©©©© r n n n n ’'i ^ 'n ci ©©©©©©©©©©©©©©©©Z

UJ

76XlPP

Tc

S

PTOR*DF-OOC.

MARK

E

00

AT

A

2/C

ASE

5

o

o•

oo

o

UJ

to<r

u\oj

<l

A

<o iT>

o _J UJUJ » (0

y <q: u< Ny u Ai• V <

—

<

<c

7 e— Vj

n <1 ci

''l

LL 1

5 — r>

CX *C a

n.

Hr

i

sr

to

Q

(0

u.r_

77

XQT

PTOH

V*

OF

—

DOC

•

STG2

zoIDto

ao

>r

LU

>

CD

Oae

o <-* *4 ~1 —

<

»-5 —

«

—1 -4 —1 m* •H .-4 —

*

«-4 -4 *-4 -4 4-i •M *»4 -4 -4 ~4 -4 —4 —4 *-* — •-« -4

h- o o o o o o o o o o o o © o o o o o o o 9 o c o o © o o o o o o o © o o o o o oui + 1 1 1 1 1 t I 1 1 1 1 1 1 1 1 i 1 1 1 T 1 1 1 ! 1 J 1 1 1 1 1 1 1 1 1 1 1 1 1

(M ID © o o o o © o o o o o o c o o o o o o o o o o o o o © o o o o © o o o © o o o ©W -J o o o o o o o o o o o o c o Q o o o o o o o o o o o o o o o o o o o o © o c o cm o o o o o o o o o o o o o o o o o o © o o o o o o o o o o o o o o o o c o © o ca • o o o c o o o o o c o o o o o o o o © o o o o o o o o o o o o o o o o o o c © Qa LU

O•

o to VC nO >0 0 nO >0 to to to to v0 v0 nO VO NO v0 NO to vO NO NO NO to NO NO to « NO o> NO nO NO NO vO NO NO NO c

nO *0 to <c >0 tfi to VO to >0 to <0 nO O NO o to NO NO NO -0 'O NO to NO to to to to to •0 tO to <o NO to >0 o to

>

CD

Oor

CL

l/>f\JOOOOOOOOOOOOOOOOOOOOOOOO»-«CVJ(O rOOOt'O pr>K©sOlDint\JaC-’'Dr>koZ in

M LU^ >> UJ

xU,o

l/>

LU O-

a>oCD

XT)

Z

1-4 J o © o o o o o Q oCD c < T o o o © o o o o o o o o o o o o © o o o o © o o o o o o o o o c o o o o o © o o o< < > o 4- 4- + + 4* + + 4- 4- 4» 4- 4- + 4- 4- 4- 4- 4* 4- 4- 4- 4* 4- + 4- 4- 4- + 4- + 4- 4- 4* 4- 4- 4> 4- 4-

UJ -> 3F cr -* o o o o o o o o o o o o o o c o o o o o o o o o o o c o o o o o o o o o o o o © oo < UJ cr o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o e ocr a h* o o o o o o o o o o o o o o o o o o o o © o o o c o o o o o o © o © o © o o o o oa z o o o c o o o o o c o o o o © o o o o o © o o o c o © o o o o o o o o c o o o o o

h- a -4 o a o o o o o o o o w* C\] ro in NO r*» CO O' o .-4 CM m < in NO s OD O' o CM n <* in O a; O' o —

<

X »-1 Q 1 K

h- © 1 'U 1

1 t- 1

1 co I

1 -J 1

(0 >h*

•"* 04 n <* in o N CO a> ** ** *”* •* -* *"* ** 04 C\J CM CM CM CM CM CM CM CM n fp m rn n m n rj n m

y >uc h- o o o o o o © t ( -4 t —* t t

.

7 <1 1 h» -J u. o o o o o o o o c o o © o o o o o o o o o o o o o o o o o o o o o o o o o o o o

*-« *—

•

1 (0 I i-H LU ID f + 4- + 4- 4- 4- + 4» 4- 4- 4- 4> 4- + 4* 4- 4- 4* 4- 4- 4- 4- 4- 4- 4- -f 4- 4- 4- + 4- 4- + 4- 4- 4* +cr I H- 1 u > -J o © o o o o o o o o o o o o o o o o o o o o c o o o c o o o o © o o o c o © o c o•D o o o o o o o o © o o o o o o o o © o o o o o o o o o o o o o o o o o o o o © o © oo 1 X 1 -J o o o o o o o o o © o o o o c o o © o o o o o o o o o o o o o © o o o 3 o o o © ccr •—1

1 ! LU o 3 o o o o o © o o o o o o o o © a © o o o c o o o c o o o o c o 3 o o o © o c oa 1 C 1 ^ > o © o o © © o Q o © o -1 04 n in NO r- CP © © " CM m L0 t£t N CD © o ”* CM m in o on a o

o - CM m in vC N r> © - * - _ - - _ -4 _ CM CM CM CM CM CM CM CM CM rr n © © © n rr\ pr* rn rn

79

000-0

1

10000

+

o o o o © o © o o o O oCM

oCM

Oo c o o o o o o o o o o o o o o o o o o o o o c o o o o o o o c o c o o o o o o o o o o o o o o o o o o © o o o © oo o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o oo c o o o o o o o o c o c o o o o o o o o o o o o o o o o o o o o o o o o o o o c o o o o o o o o o c o o o o o o oo c o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o e o e © o o o c o o o c o n o o o o o c oo CO CO VO o o <t <fr o o o o o o o o o o o c o c o o o o o o o c o o o c o o o o o o c o o o o o o o e o o o o o

'O I/) rr fO m n m CVJ C\J CM vO o o o o o c o o o o o o o o o o o o c o c o c o o o © o o o o o o o o © o © o o o o o © o

COff)^'OC(D'Olf)^'OH^Hp- oooooooooooooooooooooooooooooooooooooooooooo

OOOCOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOCOOOOOOOOO4.4-4.4-4. + 4«4-4' + 4-4. + 4« + 4-4'4-4-4-4»4- + 4-4>4- + 4> + 4.4-4’4- + + 4’4«4-4-4-4- + 4.4-4'4. + 4.4-4.4-4.4*4. + 4’ +OOOOOOOOOOCOCOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOoooccooooooooooooooooooooooooooooooooooooooooooooooooooocoor>oooooooooooooooooo©ooooooooooooooooooooooo©oooooooooooooOCOCOOOOOOOOCOCOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOCO

w'n<rino^®(J'c-‘^nîr'ON'X)(7'o-^n<tifl>oNcD(roHfgn<tin^N'X)U'o--fyin<tifi^Niry'3HtNjn<tin'ONcca'

ococcooooocoeoooooooooooooo4'4-4. + 4’4- + 4-4-4’4-4-4' + 4-4-4-4'4-«f4-4-4-4-4< +OOOOOOOOOCOOOCOOOOOOOOCOOOCOOOOOOOOOOOOOOCOOOOOOOOOOCOGOOCOOOOOOOOOOOOOCOOOOOOCOCCOOOOOCOCOOUOOOOOOOOOOO

- (\i 'n <t <c k t a o — (vjnînoN^ <t 'f *<*<t«*tpint/>i/>ininiflinin»nvo a o %c >o vo vc

yONSSNNNNNSNCOflODOCO(CCC(IlCOCC(ta'00'C>0'0'0'3'7'0'

OOOOOOOOOOOOOOOOOOOO+ 4-4-4-4-4-4>4-4. + 4-4'4-4-4-4-4- + 4'4-OOOOOOCOCOOOOCOCOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOD 0'O-^n<ttriv0 N(r/ 0'o^M^<tin^N

o o o o o o o4* 4- 4- + 4- + 4-

o o o o o o oo o o c o o oo o o o o o oo o o o o o ocn O' o - w n

coco4- 4- 4. +o o c oo o o ococoo o o oin 'O mi

vO\OKNNNNNNNN^flOfRrr<nTOC'r<rX. OPO'O‘CO‘O'OO'O' 0'

80

(P-MAI

N)

S'JMÂPY

INFORMATION

o oo oo oo oo o• «

o ovO -o - —in

o o

oJ

o+ooo

II II II

10

H

I

X

9

(/> in

z 2a U

K KD DX n*-«

rt ac

in k HH in CO

*—

i

*—

«

X a a

LL LL ULO Q

cr a aw Hi UJ

X w nx 2. 2D D D2 2 2

.J J -1

< < <h- h- HD o nK H

81

NBS-114A IREV. 9-7B)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATASHEET

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 STANDARDSDEPARTMENT OF COMMERCEWASHINGTON, DC 20234

11. Contract/Grant No.

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

U.S. Nuclear Regulatory Commission1717 H Street, NWWashington, 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 hitany given set of targets in a nuclear power plant or similar installation. Hit speedscorresponding 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 nameseparated by semicolons)

Missiles; engineering; structural engineering; tornadoes; wind.

18. AVAILABILITY J^XÛnlimited

[ j For Official Distribution. Do Not Release to NTIS

Order From Sup. of Doc., U.S. Government Printing Office, Washington, DC20402, 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. OFPRINTED PAGES

85

22 . Price

$8.00

USCOMM-DC

Documents

Probabilistic assessment of tornado-borne missile speeds · 2019-04-10 · NBSIR80-2117 PROBABILISTICASSESSMENTOF TORNADO-BORNEMISSILESPEEDS NationalBureauofStandards Library.E-01Admin.Bldg